For citation:
Demikhovskii V. I., Malyshev A. I. Quantum Arnold diffusion in rippled channel at the presence of alternating electric field. Izvestiya VUZ. Applied Nonlinear Dynamics, 2004, vol. 12, iss. 5, pp. 3-15. DOI: 10.18500/0869-6632-2004-12-5-3-15
Quantum Arnold diffusion in rippled channel at the presence of alternating electric field
We study quantum Arnold diffusion for the particle. moving in the rippled channel at the presence of periodic external electric field. The evolution operator for arbitrary number of field periods and diffusion rate was calculated for different ripple amplitude and electric field intensity. Two new effects which limit quantum Arnold diffusion have been observed - the diffusion suppression due to dynamical localization and diffusion stop in the case when the number of quantum states corresponding to the classical near separatrix chaotic region has the order of unity. For any model parameters the quantum diffusion coefficient prove to be smaller then classical one.
- Luna-Acosta GA, Krokhin AA, Rodriguez MA, Hernandez-Tejeda PH. Classical chaos and ballistic transport in а mesoscopic channel. Phys. Rev. В. 1996;54(16):11410–11416. DOI: 10.1103/PhysRevB.54.11410.
- Luna-Acosta GA, Na K, Reichl LE, Krokhin AA. Band structure and quantum Poincare sections of a classically chaotic quantum rippled channel. Phys. Rev. Е. 1996;53(4):3271–3283. DOI: 10.1103/PhysRevE.53.3271; Luna-Acosta G.A., Rodriguez MA, Krokhin AA, Na K, Mendez RA. Quantum and classical ballistic transport in а chaotic 2D electron channel. Rev. Мех. Fis. 1998;44:7–13.
- Luna-Acosta GA, Mendez-Bermudez JA, Izrailev FM. Periodic chaotic billiards: Quantum-classical correspondence in energy space. Phys. Rev. Е. 2001;64(3):036206. DOI: 10.1103/PhysRevE.64.036206.
- Kouwenhoven LP, Hekking FWJ, van Wees BJ, Harmans CJPM, Timmering CE, Foxon CT. Transport through a finite one-dimensional crystal. Phys. Rev. Lett. 1990;65(3):361–364.
- Lent CS, Leng M. Magnetic edge states in а corrugated quantum channel. J. Appl. Phys. 1991;70:3157.
- Arnold VI. Instability of dynamical systems with several degrees of freedom. Proceedings of the Academy of Sciences. 1964;156(1):9–12.
- Lichtenberg AJ, Lieberman MA. Regular and Stochastic Motion. Moscow: Mir; 1984. 528 p.
- Ferraz-Mello S, Sessin W. Resonances in the Motion of Planets, Satellites and Asteroids. Sao Paulo: Brazil; 1985. 197 p.
- Reichl LE. The Transition to Chaos. New-York: Springer-Verlag; 1992. xvi, 551 p.
- Binney J, Tremaine S. Galactic Dynamics. Princeton: Princeton University Press; 1987. 733 p.
- Nonlinear dynamics aspects of particle accelerators. Lecture Notes in Physics. Berlin: Springer-Verlag; 1986. Vol. 247. VIII, 583 p. DOI: 10.1007/BFb0107342.
- Milczewski J von, Diercksen GHF, Uzer T. Computation of the Arnold web for the hydrogen atom in crossed electric and magnetic fields. Phys. Rev. Lett. 1996;76(16):2890. DOI: 10.1103/PhysRevLett.76.2890.
- Leitner DM, Wolynes PG. Quantization of the stochastic pump model of Arnold diffusion. Phys. Rev. Lett. 1997;79(1):55. DOI: 10.1103/PhysRevLett.79.55.
- Demikhovskii VYa, Izrailev FM, Malyshev А. Manifestation оf Arnold diffusion in quantum systems. Phys. Rev. Lett. 2002;88(15):154101. DOI: 10.1103/PhysRevLett.88.154101; Demikhovskii VYa, Izrailev FM, Malyshev AI. Quantum Armold diffusion in а simple nonlinear system. Phys. Rev. E. 2002;66(3):036211. DOI: 10.1103/PhysRevE.66.036211.
- Chirikov BV. A universal instability оf many dimensional oscillator systems. Phys. Rep. 1979;52(5):263–379. DOI: 10.1016/0370-1573(79)90023-1.
- Demikhovskii VYa, Potapenko SYu, Satanin AM. Electron spectrum of systems with a periodically modulated surface. Soviet Physics Semiconductors. 1983;17(2):213–216.
- Casati G, Chirikov BV, Izrailev FM, Ford J. Stochastic behavior оf а quantum pendulum under а periodic perturbation. Lecture Notes in Physics. 1979;93:334–352. DOI: 10.1007/BFb0021757.
- Chirikov BV, Izrailev FM, Shepelyansky DL. Dynamical stochasticity in classical and quantum mechanics. Sov. Sci. Rev. 1981;2:209–267.
- Fishman S, Grempel DR, Prange RE. Chaos, quantum recurrence and Anderson localization. Phys. Rev. Lett. 1989;49(8):509–512.
- 324 reads