Special Properties of the Zeros of the Analytic Representations of Finite Quantum Systems
Keywords:
Construction, analytic, representation, zeros.
Abstract
The paper contains an investigation on the special properties of the zeros of the analytic Representations of Finite Quantum Systems.
These zeros and its paths define the completely the finite quantum system.
The present paper study Construction of the analytic representation from its zeros.
A brief introduction to analytic representation of nite quantum systems is given. The zeros of this function and there evolution time are considered.
The analytic function f(z) have exactly d zeros.
The analytic function have been constructed from its zeros.
Downloads
Download data is not yet available.
References
[1] A.M. Perelomov, `Generalized coherent states and their applications' (Springer, Berlin, 1986)
[2] A. Vourdas, J. Phys. A39, R65 (2006)
[3] A. Vourdas, R.F. Bishop, Phys. Rev. A50, 3331 (1994)
[4] V. Bargmann, Commun. Pure Appl. Math. 14, 187 (1961)
V. Bargmann, Commun. Pure Appl. Math. 20, 1 (1967)
[5] S. Schweber, J. Math. Phys. 3, 861 (1962)
S. Schweber, Ann. Phys.(NY) 41, 205 (1967)
[6] J. Kurchan, P. Leboeuf, M. Saraceno, Phys. Rev. A40, 6800 (1989)
A. Voros, Phys. Rev. A40, 6814 (1989)
[7] J.H. Hannay, J. Phys. A29, L101 (1996)
J.H. Hannay, J. Phys. A31, L755 (1998)
[8] N.L. Balazs, A. Voros, Phys. Rep. C143, 109 (1986)
[9] P. Leboeuf, A. Voros, J. Phys. A23, 1765 (1990)
P. Leboeuf, J. Phys. A24, 4575 (1991)
M.B. Cibils, Y. Cuche, P. Leboeuf, W.F. Wreszinski, Phys. Rev A46, 4560 (1992)
J.M. Tualle, A. Voros, Chaos, Solitons and Fractals, 5, 1085 (1995)
S. Nonnenmacher, A. Voros, J. Phys. A30, L677 (1997)
[10] H.J. Korsch, C. Muller, H. Wiescher, J. Phys. A30, L677 (1997)
F. Toscano, A.M.O. de Almeida, J. Phys. A32, 6321 (1999)
D. Biswas, S. Sinha, Phys. Rev. E60, 408 (1999)
[11] A. Vourdas, Rep. Prog. Phys. 67, 267 (2004)
[12] S. Zhang, A. Vourdas, J. Phys. A37, 8349 (2004)
S. Zhang, A. Vourdas, J. Phys. A38, 1197 (2005) (corrigendum)
[13] M. Tabuni, A. Vourdas and S. Zhang, 'Zer os in analytic representations of fnite quantum systems on
a torus'(Physica Scripta, 2010)
[14] S. Zhang. Quantum Phase Space Methods and Their Applications. PhD thesis, University of Bradford,
UK, August 2005.
[15] S. Zhang and A. Vourdas. Analytic representation of nite quantum systems. J. Phys. A: Math. Gen.,
37:8349, 2004.
[16] G. G. Athanasiu and E. G. Floratos. Coherent states in nite quantum mechanics. Nuclear Physics B,
425:343, 1994.
[17] J. Tolar and G. Chadzitaskos. Quantization on ZM and coherent states over ZM ZM: J. Phys. A,
30:2509, 1997.
[18] P. Leboeuf and A. Voros. Chaos-revealing multiplicative representation of quantum eigenstates. J. Phys.
A, 23:1765, 1990.
[2] A. Vourdas, J. Phys. A39, R65 (2006)
[3] A. Vourdas, R.F. Bishop, Phys. Rev. A50, 3331 (1994)
[4] V. Bargmann, Commun. Pure Appl. Math. 14, 187 (1961)
V. Bargmann, Commun. Pure Appl. Math. 20, 1 (1967)
[5] S. Schweber, J. Math. Phys. 3, 861 (1962)
S. Schweber, Ann. Phys.(NY) 41, 205 (1967)
[6] J. Kurchan, P. Leboeuf, M. Saraceno, Phys. Rev. A40, 6800 (1989)
A. Voros, Phys. Rev. A40, 6814 (1989)
[7] J.H. Hannay, J. Phys. A29, L101 (1996)
J.H. Hannay, J. Phys. A31, L755 (1998)
[8] N.L. Balazs, A. Voros, Phys. Rep. C143, 109 (1986)
[9] P. Leboeuf, A. Voros, J. Phys. A23, 1765 (1990)
P. Leboeuf, J. Phys. A24, 4575 (1991)
M.B. Cibils, Y. Cuche, P. Leboeuf, W.F. Wreszinski, Phys. Rev A46, 4560 (1992)
J.M. Tualle, A. Voros, Chaos, Solitons and Fractals, 5, 1085 (1995)
S. Nonnenmacher, A. Voros, J. Phys. A30, L677 (1997)
[10] H.J. Korsch, C. Muller, H. Wiescher, J. Phys. A30, L677 (1997)
F. Toscano, A.M.O. de Almeida, J. Phys. A32, 6321 (1999)
D. Biswas, S. Sinha, Phys. Rev. E60, 408 (1999)
[11] A. Vourdas, Rep. Prog. Phys. 67, 267 (2004)
[12] S. Zhang, A. Vourdas, J. Phys. A37, 8349 (2004)
S. Zhang, A. Vourdas, J. Phys. A38, 1197 (2005) (corrigendum)
[13] M. Tabuni, A. Vourdas and S. Zhang, 'Zer os in analytic representations of fnite quantum systems on
a torus'(Physica Scripta, 2010)
[14] S. Zhang. Quantum Phase Space Methods and Their Applications. PhD thesis, University of Bradford,
UK, August 2005.
[15] S. Zhang and A. Vourdas. Analytic representation of nite quantum systems. J. Phys. A: Math. Gen.,
37:8349, 2004.
[16] G. G. Athanasiu and E. G. Floratos. Coherent states in nite quantum mechanics. Nuclear Physics B,
425:343, 1994.
[17] J. Tolar and G. Chadzitaskos. Quantization on ZM and coherent states over ZM ZM: J. Phys. A,
30:2509, 1997.
[18] P. Leboeuf and A. Voros. Chaos-revealing multiplicative representation of quantum eigenstates. J. Phys.
A, 23:1765, 1990.
Published
2021-07-20
How to Cite
Tabuni, M. (2021). Special Properties of the Zeros of the Analytic Representations of Finite Quantum Systems. Journal of Progressive Research in Mathematics, 18(2), 69-83. Retrieved from http://www.scitecresearch.com/journals/index.php/jprm/article/view/2063
Issue
Section
Articles
Copyright (c) 2021 Journal of Progressive Research in Mathematics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
