Winding Numbers of Paths of Analytic Functions Zeros in Finite Quantum Systems
The paper contains an investigation of winding numbers
of paths of zeros of analytic theta functions. We have considered
briefly an analytic representation of finite quantum systems ZN.
The analytic functions on a torus have exactly N zeros. The brief
introduction to the zeros of analytic functions and there time evolution
is given. We have discussed the periodic finite quantum systems. We
have introduced the winding numbers in general. We consider the
winding numbers of the zeros of analytic theta functions.
<p>[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. M´uller, 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)</p>
<p>[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. M´uller, 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)</p>
@article{"International Journal of Engineering, Mathematical and Physical Sciences:49867", author = "Muna Tabuni", title = "Winding Numbers of Paths of Analytic Functions Zeros in Finite Quantum Systems", abstract = "The paper contains an investigation of winding numbers
of paths of zeros of analytic theta functions. We have considered
briefly an analytic representation of finite quantum systems ZN.
The analytic functions on a torus have exactly N zeros. The brief
introduction to the zeros of analytic functions and there time evolution
is given. We have discussed the periodic finite quantum systems. We
have introduced the winding numbers in general. We consider the
winding numbers of the zeros of analytic theta functions.
", keywords = "Winding numbers, period, paths of zeros.", volume = "7", number = "8", pages = "1223-4", }