Kicked particle dynamics in quantum graphs
https://doi.org/10.17586/2220-8054-2015-6-6-773-778
Abstract
The quantum dynamics of a delta-kicked driven particle in a star-shaped network is studied by obtaining an exact solution for the time-dependent Schr¨odinger equation within a single kicking period. The timedependence of the average kinetic energy and the Gaussian wave packet evolution are analyzed.
About the Authors
J. YusupovUzbekistan
17. Niyazov Str., 100095, Tashkent
V. Eshniyozov
Uzbekistan
100174, Tashkent
O. Karpova
Uzbekistan
17. Niyazov Str., 100095, Tashkent
100174, Tashkent
D. Sh. Saidov
Uzbekistan
Urganch
References
1. T. Kottos, U. Smilansky. Periodic Orbit Theory and Spectral Statistics for Quantum Graphs. Ann.Phys., 1999, 274(1), P. 76{124.
2. S. Gnutzmann, U. Smilansky. Quantum graphs: Applications to quantum chaos and universal spectral statistics. Adv.Phys., 2006, 55(5-6) P. 527{625.
3. S. Gnutzmann, J.P. Keating, F. Piotet. Eigenfunction statistics on quantum graphs. Ann.Phys., 2010, 325(12) P. 2595{2640.
4. R. Kostrykin, R. Schrader. Kirchhoff’s rule for quantum wires. J. Phys. A: Math. Gen., 1999, 32, P. 595.
5. B. Gutkin, U. Smilansky. Can one hear the shape of a graph? J. Phys A., 2001, 31, P. 6061.
6. J. Boman, P. Kurasov. Symmetries of quantum graphs and the inverse scattering problem. Adv. Appl. Math., 2005, 35(1), P. 58{70.
7. T. Cheon, P. Exner, O. Turek. Approximation of a general singular vertex coupling in quantum graphs. Ann.Phys., 2010, 325 P. 548{578.
8. O. Hul, S. Bauch, P. Pakonski, N. Savytskyy, K. Zyczkowski, L. Sirko. Experimental simulation of quantum graphs by microwave networks. Phys. Rev. E, 2004, 69, P. 056205.
9. Z. Sobirov, D. Matrasulov, K. Sabirov, S. Sawada, K. Nakamura. Integrable nonlinear Schrodinger equation on simple networks: Connection formula at vertices. Phys.Rev.E, 2010, 81, P. 066602.
10. R. Adami, C. Cacciapuoti, D. Finco, D. Noja. Fast solitons on star graphs. Rev. Math. Phys., 2011, 23(04), P. 409{451.
11. R. Adami, C. Cacciapuoti, D. Finco, D. Noja. Stationary states of NLS on star graphs. Europhys. Lett., 2012, 100, P. 10003.
12. R. Adami, C. Cacciapuoti, D. Finco, D. Noja. On the structure of critical energy levels for the cubic focusing NLS on star graphs. J. Phys. A: Math. Theor., 2012, 45, P. 192001.
13. R. Adami, D. Noja, and C. Ortoleva. Orbital and asymptotic stability for standing waves of a nonlinear Schr¨odinger equation with concentrated nonlinearity in dimension three. J. Math. Phys., 2013, 54, P. 013501.
14. K. Sabirov, Z. Sobirov, D. Babajanov, D. Matrasulov. Stationary Nonlinear Schr¨odinger Equation on Simplest Graphs. Phys.Lett. A, 2013, 377, P. 860.
15. D. Noja. Nonlinear Schr¨odinger equation on graphs: recent results and open problems. Philos. Trans. R. Soc. A, 2013, 372, P. 20130002.
16. C. Cacciapuoti, D. Finco, D. Noja. Topology-induced bifurcations for the nonlinear Schrdinger equation on the tadpole graph. Phys. Rev. E, 2015, 91, P. 013206.
17. G. Casati, B.V. Chirikov, J. Ford, F.M. Izrailev. Lecture Notes in Physics, Vol. 93, P. 334 (Springer, Berlin, 1979).
18. G.M. Izrailev. Simple models of quantum chaos: spectrum and eigenfunctions. Phys. Rep., 1990, 196, P. 299{392.
19. A. Buchleitner, D. Delande, J. Zakrzewski. Non-dispersive wave packets in periodically driven quantum systems. Phys. Rep., 2002, 368(5), P. 409{547.
20. R. Sankaranarayanan, V. Sheorey. Accelerator modes of square well system. Phys. Lett. A, 2005, 338, P. 288{296.
21. F. Haug, M. Bienert, W.P. Schleich, T.H. Seligman, M.G. Raizen. Motional stability of the quantum kicked rotor: A fidelity approach. Phys. Rev. A, 2005, 71, P. 043803.
22. J.P. Keating. Fluctuation statistics for quantum star graphs. Quantum graphs and their applications. Contemp. Math., 2006, 415, P. 191{200.
Review
For citations:
Yusupov J., Eshniyozov V., Karpova O., Saidov D.Sh. Kicked particle dynamics in quantum graphs. Nanosystems: Physics, Chemistry, Mathematics. 2015;6(6):773-778. https://doi.org/10.17586/2220-8054-2015-6-6-773-778