An International Research Journal


SSN : 0971 - 3093

Vol 25, No 6, June 2016

25th Anniversary Year of AJP-2016

Accepted papers: Vol 25, No 6, 2016

Special Section on

“Static and dynamic---cold atoms and molecules"


Asian Journal of Physics                                                                                                                    Vol. 25 No 6 (2016) 00-00

Dynamics of atomic and molecular solitary waves in atom-molecular hybrid Bose-Einstein condensates coupled byMagnetic Feshbach Resonance: Role of induced decays of Feshbach Molecules


Krishna Rai Dastidar, and Deb Shankar Ray

Indian Association for the Cultivation of Science, Kolkata-700 032, India


Dynamics of atomic and molecular bright solitons in a hybrid atom-molecular BEC (Bose Einstein Condensate) system of 85Rb coupled through Magnetic Feshbach Resonance (MFR) has been investigated. By solving the time  independent atom-molecular coupled equations, the initial atomic and molecular wavefunctions were obtained and the dynamics of the initial atomic and molecular waves in a spherical one-dimensional trap were studied by solving the time-dependent atom-molecular coupled equations. During evolution two types of induced or stimulated decays of the feshbach molecules were switched on. These two types of stimulated decays of the feshbach molecules (i) to the two-atom continuum and (ii) to the bound level of the lowest hyperfine state of the molecule were induced by laser/RF (Radio Frequency) fields. Hence the strength of these two induced decays can be controlled by varying the laser/RF field parameters e.g. intensity, detuning etc. It is found that depending on the relative strength of these two types of stimulated or induced decays initial atomic and molecular waves assume solitonic nature as bright solitons during evolution and the stability of these solitonic waves can be achieved by controlling the relative strength of induced decays in two different channels. It is shown that these two induced decays lead to the formation of stable atomic and molecular solitons by suppressing the initial oscillations and instability in the atom-molecular coupled system of 85Rb atoms. © Anita Publications. All rights reserved.

Total Refs: 52

  1.   K. M. Jones, E. Tiesinga, P. D. Lett and P. S. Juliene, Rev. Mod. Phys. 78, 483(2006)

  2.   C. Chin, R. Grimm, P. Julienne and Tiesinga, Rev. Mod. Phys. 82, 1225(2010)

  3.   Immanuel Bloch, Jean Dalibard and Wilhelm Zwerger, Rev. Mod. Phys. 80, 885(2008)

  4.   Elizabeth A. Donley, Neil R. Claussen, Sarah T. Thompson and Carl E. Wieman, Nature 417, 529(2002)

  5.   S. L. Cornish, N. R. Claussen, J. L. Roberts, E. A. Cornell,* and C. E. Wieman, Phys. Rev. Lett 85, 1795(2000)

  6.   Stephan Durr, Thomas Volz, Andreas Marte, and Gerhard Rempe, Phys. Rev. Lett. 92, 020406 (2004)

  7.   Fudong Wang, Dezhi Xiong, Xiaoke Li, and Dajun Wang, Phys. Rev. A 87, 050702(R) (2013)

  8.   Shinya Kato, Seiji Sugawa, Konske Shibata, Ryuta Yamamoto and Yoshiro Takahashi, Phys. Rev. Lett. 110, 173201 (2013)

  9.   J. M. Gerton, D. Strekalov, I. Prodan and R. G. Hulet, Nature (london) 408, 692(2000)

10.   R. Wynar, R. S. Freeland, D. J. Han, C. Ryu and D. J. Heinzen, Science 287, 1016(2000)

11.   K. Winkler et al., Phys. Rev. Lett. 98, 043201(2007)

12.   J. G. Danzl et al., Science 321, 1062(2008)

13.   E. Timmermans et al., Phys. Rev. Lett. 83, 2691 (1999)

14.   E. Timmermans et al., Phys. Rep. 315,199 (1999)

15.   D. J. Heinzen, R. Wynar, P. D. Drummond and K. V. Kheruntsyan, Phys. Rev. Lett. 84, 5029 (2000)

16.   J. J. Hope and M. K. Olsen, Phys. Rev. Lett. 86, 3220 (2001)

17.   F. D. de Oliveira and M. K. Olsen, Opt. Comm. 234, 235 (2004)

18.   S. V. Manakov, Sov.Phys. JETP, 38, 248(1874)

19.   J. Javanainen and M. Mackie, Phys. Rev. A 58, R789 (1998); Phys. Rev. A 59, R3186 (1999)

20.   M. Gupta and K. R. Dastidar, Phys. Rev. A 80, 043618 (2009)

21.   M. Gupta and K. R. Dastidar, Phys. Rev. A 81, 033610 (2010)

22.   M Gupta and K R Dastidar, Phys. Rev. A, 81, 063631 (2010)

23.   M. Gupta and K. Rai dastidar, Phys. Rev. A 88, 033619 (2013)

24.   S. L. Cornish, S. T. Thompson and C. E. Wieman, Phys. Rev. Lett. 96, 170401 (2006)

25.   C. P. Koch and M. Shapiro, Chem Rev 112, 4928 (2012)

26.   K. K. Ni, S. Ospelkaus, M. H. G. de Miranda, A. Peer, B. Neyenhuis, J. J. Zirbel, S. Ko-tochigova, P. S. Juliene, D. S. Jin and J. Ye, Science 322, 231 (2008)

27.   Z. Fu, P. Wang, L. Huang, Z. Meng, H. Hu and J. Zhang, Phys. Rev. A 88, 041601 (2013)

28.   S. K. Adhikari, Journal of Low Temperature Physics 143, 267 ( 2006)

29.   M. S. Bigelow, Q-Han Park and Robert W. Boyd, Phys. Rev. E 66, 046631 (2002)

30.   U. AI Khawaja, H. T. C. Stoof, R. G. Hulet, K. E. Strecker and G. B. Partridge, Phys. Rev. Lett. 89, 200404 (2002)

31.   K. E. Strecker, G. B. Partrdge, A. G. Truscott and R. G. Hulet, Nature 417, 150 (2002)

32.   L. Khaykovich et al., Science 296, 1200 (2002)

33.   J. Denschlag et al., Science 287, 97 (2000)

34.   G. Theocharis et al., Phys. Rev. A 67, 063610 (2003)

35.   S. Burger et al., Phys. Rev. Lett 83, 5198 (1999)

36.   Shunji Tsuchiya, Franco Dalfovo and Lev Pitaevskii, Phys. Rev. A 77, 045601 (2008)

37.   A. D. Jackson et al., Phys. Rev. A 58, 2417 (1998)

38.   L. D. Carr and J. Brand, Phys. Rev. Lett 92, 040401 (2004)

39.   U. Al. Khawaja and H. T. C. Stoof, New J. Phys. 13 085003 (2011)

40.   M I Qadir1, H Susanto and P C Matthews, J. Phys. B: At. Mol. Opt. Phys. 45 035004 (2012)

41.   Deng-Shan Wang, Yu-Ren Shi, KwokWing Chow, Zhao-Xian Yu, and Xiang-Gui Li, Eur. Phys. J. D 67, 242 (2013)

42.   Matthew S. Bigelow, Q-Han Park and Robert W. Boyd, Phys. Rev. E 66, 046631 (2002)

43.   Benedict J. Cusack, Tristram J. Alexander, Elena A. Ostrovskaya, and Yuri S. Kivshar, Phys. Rev. A, 65, 013609 (2001)

44.   F.Kh. Abdullaev, R.A. Kraenke, and B.A. Umarov1, Eur. Phys. J. D 30, 369377 (2004)

45.   P. D. Drummond et al., Phys. Rev. A 65, 063619 (2002)

46.   P. D. Drummond et al., Phys. Rev. Lett. 81, 3055 (1998)

47.   T. G. Vaughan, K. V. Kheruntsyan, and P. D. Drummond, Phys. Rev. A 70, 063611 (2004)

48.   B. Oles and K. Sacha, J. Phys. B 40, 1103(2007)

49.   Xiao-Fei Zhang a,b,., Deng-Shan Wang a, Lin Wen a, Xing-Hua Hu a, Qin Yang c, W.M. Liu, Opt. Commu. 285 487 (2012)

50.   K. Rai Dastidar and D. S. Ray, Euro. Phys. Jour. D 67, 249(2013)

51.   N. Bogoliubov, J. Phys. (Moscow) 11, 23 (1947)

52.   W. B. Cardoso, A. T. Avelar and D. Bazeia, Phys. Rev. E 86, 027601 (2012)



Asian Journal of Physics                                                                                                                    Vol. 25 No 6 (2016) 00-00


Dispersion coefficients for the interaction of inert gas atoms with alkali and alkaline earth ions and 

alkali atoms with their singly ionized ions


Sukhjit Singha, KiranpreetKaura, B K Sahoob* and Bindiya Aroraa

aDepartment of Physics, Guru Nanak Dev University, Amritsar, Punjab-143 005, India

bTheoretical Physics Division, Physical Research Laboratory, Navrangpura, Ahemadabad-380 009, India


We report the dispersion coefficients for the interacting inert gas atoms with the alkali ions, alkaline earth ions and alkali atoms with their singly charged ions. We use our relativistic coupled-cluster method to determine dynamic dipole and quadrupole polarizabilities of the alkali atoms and singly ionized alkaline earth atoms, whereas a relativistic random phase approximation approach has been adopted to evaluate these quantities for the closed-shell configured inert gas atoms and the singly and doubly ionized alkali and alkaline earth atoms, respectively. Accuracies of these results are adjudged from the comparison of their static polarizability values with their respective experimental results. These polarizabilities are further compared with the other theoretical results. Reason for the improvement in the accuracies of our estimated dispersion coefficients than the data listed in [At. Data and Nucl.Data Tables 101, 158 (2015)] are discussed. Results for some of the atom-ion interacting systems were not available earlier, these results and the other reported improved results will be very useful for the comprehensive understanding of the collisional physics involving these atom-atom and atom-ion interactions in the cold atom and atom-ion hybrid trapping experiments at the low-temperature regime.© Anita Publications. All rights reserved.

Total Refs: 60

    1.    Marinescu M, Sadeghpour H R, Dalgarno A, Phys Rev A,  49(1994)982.
    2.     Roberts J L, Claussen N R, J. P. B. Jr, C. H. Greene, E. A. Cornell, C. E. Wieman, Phys Rev Lett, 81, 5109 (1998).pl check authors names
    3.    Harber D M, McGuirk J M, Obrecht J M, Cornell E A, J Low Temp Phys, 133(2003)229.
    4.    Lin Y, Teper I, Chin C, Vuletic V, Phys Rev Lett, 92(2004)050404.
    5.    Leanhardt A E, Shin Y, Chikkatur A P, Kielpinski D, Ketterle W, Pritchard D E, Phys Rev Lett, 90 (2003)100404.
    6.    Leo P J, Williams C J, Julienne P S, Phys Rev Lett, 85(2000)2721.
    7.    Saffman M, Walker T G, Molmer K, Rev Mod Phys, 82(2010) 2313.
    8.    Joachim C, Gimzewski J K, Aviram A, Nature, 4089(2000)541.
    9.    Ravi K, Lee S, Sharma A, Werth G, Rangwala S, Nature Communications, 3(2012)1126.A bberiviation
    10.    Hall F H J, Willitsch S, Phys Rev Lett, 109(2012)233202.
    11.    Cote R, Dalgarno A, Phys Rev A,  62(2000)012709.
    12.    Cote R, Kharchenko V, Lukin M D, Phys Rev Lett, 89(2002)093001.
    13.    Rakshit A and B. Deb, Phys Rev A,  83(2011)022703.
    14.    Ratschbacher L, Zipkes C, Sias C, Kohl M, Nat Phys, 8(2012 649.
    15.    Willitsch S, Proc Int Sch Phys, Enrico Fermi, 189(2015)255.
    16.    Harter A, Denschlag J H, Contemporary Physics, 55(2014)33. A bberiviation
    17.    Zhu C, Dalgarno A, Porsev S G, Derevianko A, Phys Rev A, 70(2004)032722.
    18.    Chen M K, Chung K T, Phys Rev A, 53(1996)1439.
    19.    Peach G, Adv Phys, 30(1981)367.
    20.    Allard N, Kielkopf J, Rev Mod Phys, 54(1982)1103.
    21.    Viehland L A, Hampt D S, J Chem Phys, 97(1992)4964.
    22.    McGuirk M F, Viehland L A, Lee E P F, Breckenridge W H, Withers C D, Gardner A M, Plowright R J, Wright T G, J Chem Phys, 130(2009)194305.
    23.    Gardner A M, Withers C D, Wright T G, Kaplan K I, Chapman C Y N, Viehland L A, Lee E P F Breckenridge W H, J Chem Phys, 132(2010)054302.
    24.    Senff U E, Burton P G, Mol  Phys, 58(1986)637.
    25.    Champenois C, Eudouard E, Duplaa P, Vigue J, J Phys, II 7(1997)523. Pl check
    26.    Blanchard S, Civello D, Forrey R C, Phys Rev A,  67(2003)013604.
    27.    Roberts T D, Cronin A D, Kokorowski D A, Pritchard D E, Phys Rev Lett, 89(2002)200406.
    28.    Mitroy J, Zhang J.-Y, Phys Rev A,  76(2007)032706.
    29.    Mitroy J,  Zhang J. Y, Bromley M W, Phys Rev A, 77(2008)032512.
    30.    Harima H, Tachibana K, Urano Y, Phys Rev A,  35(1987)109.
    31.    Xantheas S S, Fanourgakis G S, Farantos S C, Velegrakis M, J Chem Phys, 108(1998)46.
    32.    Prekas D, Feng B.-H, Velegrakis M, J Chem Phys, 108(1998)2712.
    33.    Zhang J -Y, Mitroy J, Phys Rev A,  76(2007)022705.
    34.    Mitroy J, Zhang J Y, Eur  Phys J D, 46(2008)415.
    35.    Derevianko A, Johnson W R, Safronova M, Babb J, Phys Rev Lett, 82(1999)3589.
    36.    Porsev S G, Derevianko A, J Chem Phys, 119(2003)844.
    37.    Dalgarno A, Davison W D, Adv At Mol Phys, 2(1966)1.
    38.    Dalgarno A, Adv Chem Phys, 12(1967)143.
    39.    Miller T M, Bederson B, Adv At  Mol Phys, 13(1977)1.
    40.    Tang L Y, Zhang J Y, Yan Z C, Shi T Y, Mitroy J, J Chem Phys, 133(2010)104306.
    41.    Jiang J, Mitroy J, Cheng Y, Bromley M W J, At Data Nucl Data Tables, 101(2015)158.
    42.    Kaur J, Nandy D K, Arora B, Sahoo B K, Phys Rev A,  91(2015)012705.
    43.    Itano W M, J Res NIST, 105(2000)829.
    44.    Standard J M, Certain P R, J Chem Phys, 83(1985)3002.
    45.    Marinescu M, Babb J F, Dalgarno A, Phys Rev A,  50(1994)3096.
    46.    Sahoo B K, Chem Phys Lett, 448(2007)144.
    47.    Kharchenko P, Babb J F, Dalgarno A, Phys Rev A,  55(1997)3566.
    48.    Mitroy J, Safronova M S, Clark C W, J  Phys B, 43(2010)202001.
    49.    Arora B, Sahoo B K, Phys Rev A,  89(2014)022511.
    50.    Johnson W R, Kolb D, Huang K, At Data Nucl Data Tables, 28(1983)333).
    51.    Soldan P, Lee E P F, Wright T G, Phys Chem Chem Phys, 3(2001)4661.
    52.    Nakajima T, Hirao K, Chem  Lett, 30(2001)706.
    53.    Langhoff P W, Karplus M, J Opt Soc Am, 59(1969)863.
    54.     Thakkar A J, Hettema H, Wormer P E S, J Chem  Phys, 97(1992)3252.
    55    Bhatia A K, Drachman R J, Can  J Phys, 75(1997)11.
    56.    Lim I S, Laerdahl J K, Schwerdtfeger P, J Chem Phys, 116(2002)172.
    57.    Cooke W E, Gallagher T F, Hill R M, Edelstein S A, Phys Rev A,  16 (1977)1141end page/or doi.
    58.    Eissa H, Opik U, Phys Soc, 92(1967)566.
    59.    Johansson I, Ark  Fys, 20(1961)135.
    60.    Lee S, Ravi K, Rangwala S A, Phys Rev A,  87(2013), 052701.

Dispersion coeffcients for the interaction of inert gas atoms with....pdf
Sukhjit Singh, Kiranpreet Kaur, B K Sahoo and Bindiya Arora


Asian Journal of Physics                                                                                                                      Vol. 25 No 6 (2016) 00-00


A method to solve nonlinear Schrodinger equation using Riccati equation


Vivek M Vyas1, Rama Gupta2, C N Kumar3 and Prasanta K Panigrahi4

1Chennai Mathematical Institute, SIPCOT IT Park, Siruseri- 603 103, India

2Department of Physics, DAV University, Jalandhar- 144 008, India

3Department of Physics, Panjab University, Chandigarh- 160 014, India

4Indian Institute of Science Education and Research Kolkata, Mohanpur, Nadia- 741 246, India


A method to find exact solutions to nonlinear Schrodinger equation, defined on a line and on a plane, is found by connecting it with second order linear ordinary differential equation. The connection is essentially made using Riccati equation. Generalisation of several known solutions is found using this method, in case of nonlinear Schrodinger equation defined  on a line. This method also yields non-singular and singular vortex solutions, when applied to nonlinear Schrodinger equation on a plane.© Anita Publications. All rights reserved.

Total Refs: 23

  1.   Agrawal Govind P, Nonlinear fiber optics, (Academic Press), 2007.

  2.   Fetter Alexander L, Walecka John Dirk, Quantum theory of many-particle systems, (Dover Publications),2003.

  3.   Huang Kerson, Quantum field theory: From operators to path integrals, (John Wiley & Sons), 2008.

  4.   Peregrine D H, Water waves, nonlinear Schrödinger equations and their solutions, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics,25(1983)16-43.

  5.   Das Ashok. Integrable Models, Vol 30, (World Scientific), 1989.

  6.   Zakharov V E, Shabat A B, Exact theory of two-dimensional self-focussing and one-dimensional self-modulating waves in nonlinear media, Sov Phys, JETP, 34, 1972.

  7.   Hirota Ryogo. The direct method in soliton theory, Vol 155, (Cambridge University Press), 2004.

  8.   Nakamura Akira, Hirota Ryogo, A new example of explode-decay solitary waves in one-dimension, J Physical Soc Japan, 54(1985)491-499.

  9.   Lakshmanan Muthusamy, Rajasekar Shanmuganathan, Nonlinear dynamics: integrability, chaos and patterns, (Springer), 2003.

10.   Clarkson Peter A, Painleve equations-nonlinear special functions. In Orthogonal polynomials and special functions, (Springer), 2006.

11.   Toikka L A, Hietarinta J, Suominen K-A, Exact soliton-like solutions of the radial Gross-Pitaevskii equation, J Phys A: Mathematical and Theoretical,45(2012)485203-.

12.   Piaggio H T H, An elementary treatise on differential equations and their applications, (Bell), 1952.

13.   Cooper Fred, Khare Avinash, Sukhatme Uday, Supersymmetry in quantum mechanics, (World Scientific), 2001.

14.   Gautam Sandeep, Adhikari S K, Fractional-charge vortex in a spinor Bose-Einstein condensate, Phys Rev A, 93(2016)013630; doi

15.   Hadzibabic Zoran, Kruger Peter, Cheneau Marc, Rath Steffen Patrick, Dalibard Jean, The trapped two-dimensional Bose gas: from Bose-Einstein condensation to Berezinskii-Kosterlitz-Thouless physics, New Journal of Physics, 10(4):045006, 2008.

16.   Faddeev Ludwig D, Takhtajan Leon A, Hamiltonian methods in the theory of solitons, (Springer), 2007.

17.   Umezawa Hiroomi, Advanced field theory, AIP, 1993.

18.   Wu L, Li , Zhang J F, Mihalache D, Malomed B A, Liu W M, Exact solutions of the Gross-Pitaevskii equation for stable vortex modes in two-dimensional Bose-Einstein condensates, Phys Rev A, 81(2010)061805; doi

19.   Toikka L A, Hietarinta J, Suominen K A, Exact soliton like solutions of the radial Gross-Pitaevskii equation, J. Phys. A: Math. Theor. 45(2012)485203;

20.   Atre Rajneesh, Panigrahi P K, Agarwal G S, Class of solitary wave solutions of the one-dimensional Gross-Pitaevskii equation, Phys Rev E, 73(2006)056611;

21.   Goyal Amit, Gupta Rama, Loomba Shally, Kumar C N, Riccati parameterized self similar waves in tapered graded-index waveguides, Phys Lett A, 376(2012)3454-3457.

22.   Raju T S, Kumar C N, Panigrahi P K, On exact solitary wave solutions of the nonlinear Schrödinger equation with a source, JPhys A: Math Gen, 38(2005)L271;

23.   Vyas V M, Raju T S, Kumar C N, Panigrahi P K, Soliton solutions of driven nonlinear Schrödinger equation, J Phys A: Math Gen, 39(2006)9151;


Asian Journal of Physics                                                                                                               Vol 25, No 6, (2016) 00-00

 Experimental and DFT vibrational spectra and structure of 3-Iodopyridine

Nandini V. Aralikatti ,  J. Tonannavar , Jayashree Yenagi †*

Vibrational Spectroscopy Group, Department. of Physics

 Karnatak University, Dharwad-580003, India

     ‡Department. of Physics, Kittel  Science College, Dharwad-580001, India

                                        *;  Tel:+9108362215316


A complete review and reassignment of the vibrational spectra of 3-Iodopyridine have been proposed. The measured vibrational spectra include IR (3500 – 400 cm-1) and Raman (3500–100 cm-1) spectra. Geometry and harmonic vibrational frequencies of 3-Iodopyridine have been computed by employing a batch of four density functional theoretical methods(DFTs) - ab initio RHF, hybrid - B3LYP, B3PW91 and MP2 methods using the LANL2DZ basis set. Analysis has shown that some vibrational modes of 3-Iodopyridine change both in intensity and frequency with respect to Pyridine, mono-substituted halo-pyridines including 2-Iodopyridine. Absence of two characteristic C-H stretching modes near 3069 and 3051cm-1 as IR and Raman bands is attributed to the weakening of the sp2 hybridization in the pyridine ring. The C-H bending modes near 1450 -1400 cm-1 are IR strong. The characteristically strong Raman ring breathing mode near 1100 – 900 cm-1 is IR strong at 1007 cm-1 but Raman weak, suggesting ring strain. However, a trigonal mode near 1038 cm-1 and C-I stretching at 267 cm-1 are Raman strong.  Of the four DFT methods, the B3LYP/LANL2DZ level has produced spectral results in very good agreement with the experiment. Further, the LANL2DZ basis set with effective core potential representation for the heavy Iodine is proved satisfactory for 3-Iodopyridine.©Anita Publications. All rights reserved.

Keywords: 3-Iodopyridine, IR, Raman, B3LYP, B3PW91, MP2, LANL2DZ

Total Refs: 29


Asian Journal of Physics                                                                                                               Vol 25, No 6, (2016) 00-00

Gravitation and Radiation

Francis T S Yu

Emeritus Evan Pugh Professor of Electrical Engineering

Penn State University, University Park, PA 16802, USA


Gravitation is one of the most intriguing forces in space that govern all the interstellar spectacles motion in this universe. In this article we have shown there is a profound relationship between gravitational fields with respect to its converted energy. Since time is an inevitable element in every aspect of science; we have developed a partial differential equation from Einstein’s energy equation in which we show that gravitational field can be coupling with its diverging energy radiation.  We have also shown that energy to mass conversion in principle is conceivable by means of energy convergent operation (i.e., in-flow) into a unit space. In fact this could have been happen by the eventuality of a black hole explosion, as remains to be observed. .©Anita Publications. All rights reserved.

Keywords: Gravitation, Interstellar spectacles, Einstein’s energy equation, Black hole

Total Refs: 11

    1.    Einstein A, Relativity, The Special and General Theory, Crown Publishers, New York, 1961.
    2.    Yu FTS, Time, Space, Information and Life, Asian J Phys, 24(2015)217-223.
    3.    R. Zimmerman, “The Universe in a Mirror: The saga of the Hubble Space Telescope” Princeton Press, N.J. 2018.
    4.    B. P. Abbott et. Al. Observation of Gravitational Waves from a Binary Black Hole Merger, Phys. Rev. Lett. 116, 061102 (2016)
    5.    J. D. Kraus, “Electro-Magnetics,” McGraw-Hill Book Company, Inc. New York, p370, 1953.
    6.    G. O. Abell, D. Morrison and S. C. Wolff, “Exploration of the Universe” 5th ed. Saunders College Publishing, New York, p587, 1987.
    7.    H. L. Shipman, “Black Holes, Quasard, and the Universe”, 2nd ed. Boston: Houghton Mifflin. 1980
    8.    Newton, Isaac. “The Principia: Mathematical Principles of Natural Philosophy”, University of California Press, Berkeley, 1999
    9.    Abell G O, Morrison D, Wolff S C, “Exploration of the Universe” 5th edn, (Saunders College Publishing, New  York), 1987. p47-88
    10.  Feldman S, "Gersonides' Proofs for the Creation of the Universe". Proceedings of the American Academy for Jewish Research (Proceedings of

the American Academy for Jewish Research, Vol. 35) 35: 113–137. 1967.
    11.  Craig W L, "Whitrow and Popper on the Impossibility of an Infinite Past". The British Journal for the Philosophy of Science, 30 (1979)165-170


Asian Journal of Physics                                                                                                               Vol 25, No 6, (2016) 00-00

Cold ion based geometric phase generation: a tool or non-optical quantum computation

Debashis De Munshi

Centre for Quantum Technologies, National University of Singapore, Singapore - 117543

 Manas Mukherjee

Centre for Quantum Technologies, National University of Singapore, Singapore - 117543 and

 Department of Physics, National University of Singapore, Singapore - 117551


Abelian and Non-Abelian evolution of a quantum system manifests differently in the geometric phase acquired by the system under such evolutions. In this work, we develop the theory and study the properties of a experimentally realizable spin system which can be driven continuously from Abelian to non-Abelian geometry and vice versa. This unified framework allows us to characterize the parameter dependence of the geometric phase originating from different geometry of the Hilbert space. As geometric phase is key to robust quantum computation, we quantify the noise related to geometric phase and its dependence on external parameters. As a consequence we find the noise to be entirely dependent on the geometry of the system. © Anita Publications. All rights reserved.

Total Refs: 18

1. Bloch I, Dalibard J, Zwerger W, Rev Mod Phys, 80(2008) 885.

2. Buluta I, Nori F, Science, 326 (2009)108.

3. Ray M W, Ruokokoski E, Kandel S, Möttönen M, Hall D S, Nature, 505 (2014)657.

4. Barry Simon, Phys Rev Lett, 51(1984)2167;

5. Zanardi P,  Rasetti M, Phys Lett A, 264(1999) 94.

6. Ekert A,, J Mod Opt, 47,  (2000) 14

7. Duan L M, Cirac J I, Zoller P, Science, 292, , (2001) 1695.

8. Zhu Shi-Liang, Wang Z D, Phys Rev Lett, 91,  (2003) 18

9.  Lupo Cosmo, Aniello Paolo, Phys Scr, 79,  (2009) 065012

10. Knill E, Nature, 463(2010)441-443.

11.C. Zu,, Nature, 514, 72, (2014)

12. Sørensen A, Mølmer K, Phys Rev Lett, 82,  (1999) 1971.

13. Benhelm J, Kirchmair G, Roos C F, Blatt R, Nature Physics, 4(2008)463-466.

14. Munshi D De, Mukherjee M, Dutta-Roy B, Phys Lett A, 377(2013)228-231.

15. Wilczek F, Zee A, Phys Rev Lett, 52(1984)2111

16. Berry M V, Proc R Soc London A, 392(1984) 45

17. Meyer E R, Leanhardt A E, Cornell E A, Bohn J L, Phys Rev A, 80(2009) 062110

18. Berry M V, J Phys A, 42(2009)365303


Asian Journal of Physics                                                                                                               Vol 25, No 6, (2016) 00-00

Bosons in a trap: phases and dynamics

K Sengupta

Theoretical Physics Department, Indian Association for the Cultivation of Science, Jadavpur, Kolkata


We review a hopping expansion technique for studying phases and phase transition of strongly interacting bosons in an optical lattice in the presence of a harmonic trap. The advantage of this technique is that it allows one to study both the equilibrium phase diagram and non-equilibrium dynamics of the bosons at same footing. The technique also enables one to treat quantum fluctuations of the bosons systematically and leads to a the boson phase diagram which is almost as accurate as that found by quantum Monte Carlo. In addition, it predicts several novel non-equilibrium effects which are missed by mean-field theory. © Anita Publications. All rights reserved.

Keywords: Bosons; Phase transition; Monte Carlo

Total Refs: 29

  1.  Bloch I, Dalibard J, Zwerger W, Rev Mod Phys, 80(2008)885;

  2.   Kinoshita T, Wenger T, Weiss D S, Nature (London), 440(2006)900.

  3.   Bakr W S, Peng A, Tai M E, Ma R, Simon J, Gillen J I, Foelling S, Pollet L, Greiner M, Science, 329(2010)547-550.

  4.   Strohmaier N, Strohmaier N, Greif D, Jordens R, Tarruell L, Moritz H, Esslinger T, Sensarma R, Pekker D, Altman E, Demler E, Phys Rev Lett, 104(2010)080401.

  5.   L. E. Sadler, J. M. Higbie, S. R. Leslie, M. Vengalattore, D. M. Stamper-Kurn, Nature. 443(2006)312.

  6.   M. Greiner, O. Mandel, T. Esslinger, T. W. Hansch, I. Bloch, Nature (London) 415, 39 (2002); C. Orzel, A. K. Tuchman, M. L. Fenselau, M. Yasuda, and M. A. Kasevich, Science, 291, 2386 (2001).

  7.   See for example, S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, England), 1999.

  8.   S. Sachdev, K. Sengupta, and S.M. Girvin, Phys Rev B, 66, 075128 (2002).

  9.   A. Polkovnikov, K. Sengupta, A. Silva, and M. Vengalla-tore, Rev. Mod. Phys. 83, 863 (2011).

10.   (a) Fisher M P A, Weichman P B, Grinstein G, Fisher D S, Phys Rev B, 40, 546 (1989);

        (b) Sheshadri K, Krishnamurthy H R, Pandit R, Ramakrishnan T V, Europhys Lett, 22, (1993)257.

11.   (a) Freericks J K, H. Monien, Europhys Lett, 26, (1994) 545;

        (b) K. Sengupta and N. Dupuis, Phys Rev A, 71, 033629 (2005);

        (c) A. Rancon and N. Dupuis, Phys Rev B, 83(2011)172501;

        (d) J. K. Freericks, H. R. Krishnamurthy, Y. Kato, N. Kawashima, and N. Trivedi, Phys Rev A, 79, 053631 (2009).

12.   C. Trefzger and K. Sengupta, Phys. Rev. Lett. 106, 095702(2011);

        (b) A. Dutta, C. Trefzger, and K. Sengupta, Phys Rev B, 86, 085140 (2012).

13.   W. Krauth, N. Trivedi, Europhys Lett. 14, 627 (1991); B. Capogrosso-Sansone, N. V. Prokofev, B. V. Svistunov, Phys Rev B, 75, 134302 (2007).

14.   T. Grass, T. F. E. A. dos Santos, and A. Pelster., Phys Rev. A 84, 013613 (2011).

15.   Kennett M P, Dalidovich D, Phys Rev A, 84(2011)033620.

16.   H. U. R. Strand, M. Eckstein, P. Werner, arXiv:1405.6941 (unpublished).

17.   A. Dutta, R. Sensarma, and K. Sengupta, J Phys Condens Matter, 28 (2016) 30LT01.

18.   G. G. Batrouni, V. Rousseau, R. T. Scalettar, M. Rigol, A. Muramatsu, P. J. H. Denteneer, M. Troyer, Phys Rev. Lett. 89, 117203 (2002).

19.   J-S. Bernier, D. Poletti, P. Barmettler, G.Roux, and C Kollath, Phys Rev A 85, 033641 (2012)

20.   S. S. Natu, K. R. A. Hazzard, and E. J. Mueller, Phys Rev. Lett. 106, 125301 (2010).

21.   We use a value of = 2; we have checked that our results are insensitive to the exact choice of

22.   See supplementary materials for a detailed derivation.

23.   O. Gygi, H. G. Katzgraber, M. Troyer, S. Wessel, and G. Batrouni, Phys Rev A 73μμ, 063606 (2006).

24.   This procedure is justfiied as long as zJ(t)=U 1 for all t and thus can be used to study the dynamics of the bosons in the SF region near the critical point.

25.   The emergence and decay of the coherent oscillations repeat themselves several times at a longer time scale. See supplementary materials for a more detailed discussion of this phenomenon.

26.   After the quench, bosons have small residual energy Q ~ |Ji – Jf |. This shifts the reflection boundary to (μr + Q) = 0, leading to r = Int {√ [( 2μ0+ |Ji – Jf |)/K]} » 22.The corresponding T0 = 2r/Jf » 220U1 is quite close to the numerical value obtained in Fig 2.

27.   (a) Kibble T W B, J Phys A, 9, 1387 (1976);

        (b) Zurek W H, Nature (London) 317, (1985)505;

        (c) Polkovnikov A, Phys Rev B, 72(2005)161201(R).

28.   Mondal S, D. Pekker, K. Sengupta, Europhys Lett, 100(2012)60007.

29.   Patil Y S, Aycock L M, Chakram S, Vengalattore M, arXiv:1404.5583 (unpublished).


Asian Journal of Physics                                                                                                               Vol 25, No 6, (2016) 00-00

Two-photon photoassociation of a pair of interacting atoms in a trap


Partha Goswami1, Arpita Pal1, Subrata Saha1 and Bimalendu Deb1;2

1Department of Materials Science,

Indian Association for the Cultivation of Science (IACS), Jadavpur, Kolkata-700 032, India,

2Raman Centre for Atomic, Molecular and Optical Sciences,

IACS, Jadavpur, Kolkata-700 032, India.


We show that it is possible to generate coherent coupling between the discreet eigenstates of a pair of interacting atoms in a trap by two-photon photoassociation, via adiabatic elimination of the excited molecular state involved in the PA transitions. We develop a fully quantum mechanical treatment of the problem and present a dressed state description for the eigenstates. This coherent coupling is important for manipulating the relative motional states of the two atoms. © Anita Publications. All rights reserved.

Keywords: Photoassociation (PA);Ultracold atoms; Coherent coupling

Total Refs: 48

    1.    Masnou-Seeuws F, Pillet P, Adv At Mol Phys, 47(2001)53.
    2.    Weiner J, Bagnato V S, Zilio S, Julienne P S, Rev Mod Phys, 71(1999)1.
    3.    Jones K M, Tiesinga E, Lett P D, Julienne P S, Rev Mod Phys, 78(2006)483.
    4.    Thorsheim H R, Weiner J, Julienne P S, Phys Rev Lett, 58(1987) 2420.
    5.    Fioretti A, Comparat D, Crubellier A, Dulieu O, Masnou-Seeuws F, Pillet P, Phys Rev Lett, 80 (1998)20.
    6.    Bagnato V, Marcassa L, Tsao C, Wang Y, Weiner J, Phys Rev Lett, 70(1993)3225.
    7.    Leonhardtand D, Weiner J, Phys Rev A, 52(1995)R4332.
    8.    Molenaar P A, Straten P V D, Heideman H G M, Phys Rev Lett, 77(1996)1460.
    9.    Jones K M, Maleki S, Ratliff L P, Lett P D, J Phys B: At Mol Opt Phys, 30 (1997)289.
    10.    Deiglmayr J, Grochola A, Repp M, Mörtlbauer K, Gluck C, Lange J, Dulieu O, Wester R, Weidemuller M, Phys Rev Lett, 101(2008)133004.
    11.    Lang F, Winkler K, Strauss C, Grimm R, Denschlag J H, Phys Rev Lett, 101(2008)133005.
    12.    K.-K. Ni et al., Science, 322, 231 (2008).
    13.    Reinaudi G, Osborn C B, McDonald M, Kotochigova S, Zelevinsky T, Phys Rev Lett, 109(2012)115303.
    14.    Skomorowski W, Moszynski R, Koch C P, Phys Rev A, 85(2012)043414.
    15.    Zwierlein M W, Stan C A, Schunck C H, Raupach S M F, Gupta S, Hadzibabic Z, Ketterle W, Phys Rev Lett, 91(2003)250401.
    16.    Wynar R, Freeland R S, Han D J, Ryu C, Heinzen D J, Science, 287(2000)1016.
    17.    Donley E A, Claussen N R, Thompson S T, Wieman C E, Nature, 417(2002)529.
    18.    Greiner M, Regal C A, Jin D S, Nature, 426(2003)537.
    19.    Herbig J, Kraemer T, Mark M, Weber T, Chin C, Nagerl H C, Grimm R, Science, 301(2003) 1510.
    20.    Jochim S, Bartenstein M, Altmeyer A, Hendl G, Riedl S, Chin C, Hecker Denschlag J, Grimm R, Science, 302(2003)2101.
    21.    Regal C A, Ticknor C, Bohn J L, Jin D S, Nature, 424(2003)47.
    22.    Yan M, DeSalvo B J, Huang Y, Naidon P, Killian T C, Phys Rev Lett, 111(2013)150402
    23.    Deb B, You L, Phys Rev A, 68(2003)033408;
    24.    Grishkevich S, Saenz A, Phys Rev A, 68(2007)033408.
    25.    Naidon P, Julienne P S, Phys Rev A, 74(2006)062713 .
    26.    Zelevinsky T et al., Phys Rev Lett, 96, 203201 (2006).
    27.    Paredes B et al., Nature, 429, 277 (2004).
    28.    Rom T et al., Phys Rev Lett, 93(2004)7.
    29.    K. Xu et al., Phys Rev A, 72, (2005) 043604.
    30.    Zhang R, Garner S R, Hau L V, Phys Rev Lett, 103(2009)233602
    31.    Tiesinga E, Verhaar B J, Stoof H T C, Phys Rev A, 47(1993)4114.
    32.    Inouye S, Andrews M R, Stenger J, Miesner H. -J, Stamper-Kurn D M, Ketterle W, Nature, 392(1998)151.
    33.    Roberts J L, Claussen N R, Burke James P (Jr), Greene Chris H, Cornell E A, Wieman C E, Phys Rev Lett, 81 (1998)5109.
    34.    Fedichev P O, Kagan Yu, Shlyapnikov G V, Walraven J T M, Phys Rev Lett, 77(1996)2913.
    35.    Fatemi F K, Jones K M, Lett P D, Phys Rev Lett, 85(2000)4462.
    36.    Theis M, Thalhammer G, Winkler K, Hellwig M, Ruff G, Grimm R, Denschlag J H, Phys Rev Lett, 93(2004) 123001.
    37.    G. Thalhammer, M. Theis, K. Winkler, R. Grimm and J. H. Denschlag, Phys Rev A, 71, 033403 (2005).
    38.    Deb B, J. Hazra, Phys Rev Lett, 103, 023201 (2009).
    39.    Deb B, J. Phys. B: At. Mol. Phys. 43, 085208 (2010)
    40.    Goswami P, Rakshit A, Deb B, Indian J Phys, 89(2015)8.
    41.    Deb B, Int J Mod Phys B, 30(2016)1650036
    42.     Busch T, Englert B G, Rzazewski K,Wilkens M, Foundation of Physics, 28(1998)549.
    43.    Goswami, Deb B, Physica Scripta
    44.    B.W. Shore andP.L. Knight,J. Mod. optics, 40, 1195 (1993)
    45.    M. Kitagawa et al., Phys Rev A, 76 (2008) 022704.
    46.    K. Enomoto,M. Kitagawa,S.Tojo andY.Takahashi, Phys Rev Lett, 100, 123001 (2008).
    47.    Shea P, van Zyl B P, Bhaduri R K, Am J Phys, 77(2009)511.
    48.    C.G. Gerry and J.H. Eberly, Phys Rev A, 42, 6805 (1990).


Asian Journal of Physics                                                                                                               Vol 25, No 6, (2016) 00-00

Vibrational study of Azobenzene: Comparative study with ab-initio calculation


Th.Gomti Devi

Department of Physics, North-Eastern RegionalInstitute of Science and Technology,

Arunachal  Pradesh-791 109, India


Azobenzene is a photochromic molecule which exhibits a reversible isomerisation process between its trans and cis isomers of different stability. An investigation has been conducted of the effects of temperature on intensity and position of Raman bands of N=N and C-N stretching mode of Azobenzene (AZBN). It was found that both the N=N stretching and the C-N stretching mode of Raman band shape shifts to lower frequency region with the increase in temperature. Ab initio calculation for geometry optimization and vibrational wavenumber calculation have been performed to support the experimental findings.  © Anita Publications. All rights reserved.                                                         

Key words : Azobenzene, isomerisation, IR and Raman spectra ab-initio

Total Refs: 23

    1.    Perelygin I S, J Struct Chem, 38(1997)218.
    2.    Morresi A, Mariani L, Distefano M R, Giorgini M G, J Raman Spectrosc, 26(1995)179.
    3.    Beamson G, Yarwood J, Mol Phys, 52(1984)907.
    4.    Devi T G, J Raman Spectrosc, 41 (2010) 1261.
    5.    Devi T G, Upadhayay G, Spectrochim Acta, A 91(2012)106.
    6.    Upadhyay G, Devi T G, Singh R K, Singh A, Alapati P R, Spectrochim Acta, A109(2013)239.
    7.    Upadhyay G, Devi T G, Spectrochim Acta A, 133(2014)250.
    8.    Upadhyay G, Devi T G, J Mol Liqs, 97(2014)263.
    9.    Devi T G, Vib Spectrosc, 75(2014)65.
    10.    Sultan K, Habib Z, Jan A, Ahmad Mir S, Ikram M, Asokan K, Adv Mat Lett, 5 (2014) 9.
    11.    Courtecuisse S, Cansell F, Fabre D, Petitet J P, J De physique iv, 5(1995) 359.
    12.    Li L, Chen F, Lu J Q, Luo M F, J Phys Chem A, 115(2011)7972.
    13.    Rau H, Azo compounds, In Photochromism: Molecules and Systems, (Eds) Durr H, Bouas-Laurent H, (Elsevier: New York), 1990.
    14.    Ikeda T, Tsutsumi O, Science, (Washington, DC, U.S.) 268(1995) 1873. ???????????
    15.    Volgraf M, Gorostiza P, Numano R, Kramer R H, Isacoff E Y, Trauner D, Nat Chem Biol, 2(2006)47-.
    16.    Renner C, Kusebauch, Loweneck U, Milbradt M, Moroder A G, Peptide Res, 65(2005)4-'.
    17.    Kojima M, Nebashi S, Ogawa K, Kurita N, J Phys Org Chem, 18(2005)994-.;doi
    18.    Kurita N, Nebashi S, Kojima M, Chem Phys Lett, 408(2005)197-. ;doi
    19.    Kurita N, Ikegami T, Ishikawa Y, Chem Phys Lett, 360(2002)349-.;doi
    20.    Frisch M J, Trucks G W, Schlegel H B, Scuseria G E, Robb M A, Cheeseman J R, Scalmani G, Barone V, Mennucci B, Petersson G A, Nakatsuji H, Caricato M, Li X, Hratchian H P, Izmaylov A F, Bloino J, Zheng G, Sonnenberg J, Hada L, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Montgomery J A (Jr), Peralta J E, Ogliaro F, Bearpark M, Heyd J J, Brothers E, Kudin K N, Staroverov V N, Keith T, Kobayashi R, Normand J, Raghavachari K, Rendell A, Burant J C, Iyengar S S, Tomasi J, Cossi M, Rega N, Millam J M, Klene M, Knox J E, Cross J B, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann R E, Yazyev O, Austin A J, Cammi R, Pomelli C, Ochterski J W, Martin R L, Morokuma K, Zakrzewski V G, Voth G A, Salvador P, Dannenberg J J, Dapprich S, Daniels A D, Farkas O, Foresman J B, Ortiz J V, Cioslowski J, Fox D J, Gaussian, Inc., Wallingford CT, 2010.
    21.    Merrick J P, Moran D, Radom L, J Phys Chem A, 111 (2007) 11683.
    22.    Gangopadhyay D, Sharma P, Singh Ranjan K, Spectrochim. Acta, 150A(2015)9.
    23.    Terpstra P A, Otto C, Greve J, Biophysical Chem, 48(1993)113.


Asian Journal of Physics                                                                                                               Vol 25, No 6, (2016) 00-00

Molecular structure, spectroscopic (FT-IR, FT-RAMAN), HOMO-LUMO, NMR,

and MEP analysis of methyl-m-toluate


I Sehar a, V Krishnakumarb and S Sivakumarc

aDepartment of Physics, Aditanar College of Arts and Science, Tiruchendur – 628 215, India

bDepartment of Physics, Periyar University, Salem - 636 011, India

cDepartment of Physics, Govt. Arts College, Salem - 636 007, India


The FT-IR and FT-Raman spectra of methyl-m-toluate (MMT) molecule were recorded in the range 4000–400 cm-1 and 4000–100 cm-1, respectively at room temperature. The molecular structure, fundamental vibrational frequencies and intensity of the vibrational bands were interpreted with the aid of structure optimizations and normal coordinate force field calculations based on density functional theory (DFT) method. The complete vibrational assignments of frequencies were made on the basis of potential energy distribution (PED). The scaled B3LYP/6-311+G** calculated results agreed well with the experimental values. The calculated HOMO and LUMO energies revealed that the charge transfer occurred within the molecule. Moreover, HOMO-LUMO energy gap related properties such as ionization potential, electron affinity, global hardness, global softness, chemical potential and electrophilicity index were calculated. The effects due to the substitution of methyl groups were also investigated. The calculated results from B3LYP/6-311+G** were applied to simulate the spectra of the title compound, which showed excellent agreement with the experimental spectra. Furthermore, Natural Bonding Orbital (NBO) analysis was done and stabilization energies E(2) were calculated. The change in electron density (ED) in the orbital and molecular electrostatic potential (MEP) were analyzed. © Anita Publications. All rights reserved.

Key words: FT-IR and FT-Raman spectra, MEP, HOMO-LUMO, DFT.


Asian Journal of Physics                                                                                                               Vol 25, No 6, (2016) 00-00

Integration of phoneme pattern recognition with hidden Markov models to enhance

performance of low level speech recognition

Mohammed Al-Darkazali, Rupert Young, and Chris Chatwin, Phil Birch

School of Engineering and Informatics, 2B09, Shawcross building, Brighton BN1 9QT 43, U K


The hidden Markov model (HMM) is commonly employed in automatic speech recognition (ASR). The HMM has been shown to have a good performance in many applications, although it has some well-known limitations in modelling speech. Therefore, the standard HMM topology has been modified in a variety of ways to reduce errors, including factorization of the HMM into multiple-streams. However, the gap between the theoretical representation of speech and its acoustic representation can be further reduced. This paper describes a new method of correcting the HMM based on matching two dimensional templates of word time-frequency patterns to assist in low level speech recognition (Pl correct sentence construction). This is shown to be a promising method to enhance speech recognition performance. © Anita Publications. All rights reserved.

Keywords: Pattern matching, image matching, hidden Markov models, automatic speech recognition.

Total Refs: 17

1.  Rabiner L, A tutorial on hidden Markov models and selected applications in speech recognition, Procd  IEEE, 
2. Rasipuram R, Razavi M, Magimai-Doss M, Integrated pronunciation learning for automatic speech recognition 
     using probabilistic lexical modeling, in Acoustics, Speech and Signal Processing (ICASSP), 2015 IEEE International 
     Conference on, 2015, pp. 5176-5180.
 3. Aggarwal R, Dave M, Acoustic modeling problem for automatic speech recognition system: advances and 
      refinements  (Part II), Int J Speech Technol, 14(2011)309-320.
 4. O'Shaughnessy D, Interacting with computers by voice: automatic speech recognition and synthesis,Procd  IEEE,
5.  Deller J R J, Hansen J H L, Proakis J G, Discrete-Time Processing of Speech Signals, (Wiley), 2000.
6. Renals S, Morgan N, Bourlard H, Cohen M, Franco H, Connectionist probability estimators in HMM speech
     recognition,IEEE Transactions on Speech and Audio Processing, 2(1994)161-174.
7. Aji S M, McEliece R J, The generalized distributive law,  IEEE Transactions on Information Theory, 46(2000)325-
 8. Ghahramani Z, An introduction to hidden Markov models and Bayesian networks, in Hidden Markov models, (ed)
     (World Scientific Publishing C., Inc.), 2002, pp. 9-42.
 9. Taemin C, KiBeom K, Bello J P, A Minimum Frame Error Criterion for Hidden Markov Model Training, in Machine
      Learning and Applications (ICMLA), 2012, 11th International Conference on, 2012, pp. 363-368.
10.  Young S J, Evermann G, Gales M J F, Hain T, Kershaw D, Moore G, Odell J, Ollason D, Povey D, Valtchev V,   Woodland P  C, The HTK Book. Cambridge , UK: Cambridge University Engineering Department, 2006.
11. Gales M J F,  The HMM error model, in Acoustics, Speech, and Signal Processing (ICASSP), 2002 IEEE   
      International  Conference on, 2002, pp. I-937-I-940.
12. Xiong X, Jinyu L, Siong C Eng, Haizhou L, Chin-Hui L, A study on hidden Markov model's
     generalization capability for speech recognition, in Automatic Speech Recognition & Understanding, 2009. ASRU 
     2009. IEEE Workshop on, 2009, pp. 255-260.
13. Biing-Hwang J, Wu H, Chin-Hui L, Minimum classification error rate methods for speech recognition," Speech and
      Audio Processing, IEEE Transactions on, 5(1997)257-265.
14. Gonzalez R C, Woods R E, Digital Image Processing, (Pearson/Prentice Hall), 2008.
15. Al-Darkazali M, Young R, Chatwin C, Birch P, Defining properties of speech spectrogram images to allow effective
      pre-processing prior to pattern recognition, 2013, pp. 87480G-87480G-11.
16. Owsinski B, The Recording Engineers Handbook, Thomson Course Technology PTR, 1989.
17. Schwartz D A, Howe C Q, Purves D, The Statistical Structure of Human Speech Sounds Predicts Musical
      Universals, The Journal of Neuroscience, 23(2003)7160-7168



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