Quantum Arnol'd diffusion in a rippled waveguide

We study the quantum Arnol'd diffusion for a particle moving in a quasi-1D waveguide bounded by a periodically rippled surface, in the presence of the time-periodic electric field. It was found that in a deep semiclassical region the diffusion-like motion occurs for a particle in the region corresponding to a stochastic layer surrounding the coupling resonance. The rate of the quantum diffusion turns out to be less than the corresponding classical one, thus indicating the influence of quantum coherent effects. Another result is that even in the case when such a diffusion is possible, it terminates in time due to the mechanism similar to that of the dynamical localization. The quantum Arnol'd diffusion represents a new type of quantum dynamics, and may be experimentally observed in measurements of a conductivity of low-dimensional mesoscopic structures.Comment: 13 pages, 3 figure

Hall Conductance of a Two-Dimensional Electron Gas in Periodic Lattice with Triangular Antidots

The topic of this contribution is the investigation of quantum states and quantum Hall effect in electron gas subjected to a periodic potential of the lateral lattice. The potential is formed by triangular quantum antidos located on the sites of the square lattice. In a such system the inversion center and the four-fold rotation symmetry are absent. The topological invariants which characterize different magnetic subbands and their Hall conductances are calculated. It is shown that the details of the antidot geometry are crucial for the Hall conductance quantization rule. The critical values of lattice parameters defining the shape of triangular antidots at which the Hall conductance is changed drastically are determined. We demonstrate that the quantum states and Hall conductance quantization law for the triangular antidot lattice differ from the case of the square lattice with cylindrical antidots. As an example, the Hall conductances of magnetic subbands for different antidot geometries are calculated for the case when the number of magnetic flux quanta per unit cell is equal to three.Comment: 6 pages, 5 figure

Localization of Quantum States at the Cyclotron Resonance

A new type of localization - localization over the quantum resonance cells - in an intrinsically degenerate system is explored by using the quasienergy eigenstates.Comment: 6 pages of Latex, 6 figure

Harper-Hofstadter problem for 2D electron gas with k{\bf k}-linear Rashba spin-orbit coupling

The Harper-Hofstadter problem for two-dimensional electron gas with Rashba spin-orbit coupling subject to periodic potential and perpendicular magnetic field is studied analytically and numerically. The butterfly-like energy spectrum, spinor wave functions as well as the spin density and average spin polarization are calculated for actual parameters of semiconductor structure. Our calculations show that in two-dimensional electron gas subject to periodic potential and uniform magnetic field the effects of energy spectrum splitting caused by large spin-orbit Rashba coupling can be observed experimentally.Comment: 8 pages, 6 figures. submitted to Europhys. Letter

Hall Conductance of a Two-Dimensional Electron Gas with Spin-Orbit Coupling at the Presence of Lateral Periodic Potential

We evaluate the distribution of Hall conductances in magnetic subbands of two-dimensional electron gas with Rashba spin-orbit (SO) coupling placed in a periodic potential and perpendicular magnetic field. In this semiconductor structure the spin-orbit coupling mixes the states of different magnetic subbands and changes the distribution of their Hall conductances in comparison with the case of spinless particles. The calculations were made for semiconductor structures with a weak ($AlGaAs/GaAs$) and relatively strong ($GaAs/InGaAs$) SO and Zeeman interactions. The Hall conductances of fully occupied magnetic subbands depend on the system parameters and can be changed when neighboring subbands touch each other. It was shown that in the real semiconductor structures with relatively strong SO coupling the distribution of Hall conductance differs from the quantization law predicted by Thouless et al\cite{Thoul} for systems without spin-orbit coupling. In the case of weak SO interaction and relatively large lattice period the Hall conductance of magnetic subbands are the same as for spinless particles, but as the lattice period decreases and two neighboring subbands touch each other the distribution of Hall conductances is changed drastically.Comment: 8 pages, 4 figure

Quantum Arnol'd Diffusion in a Simple Nonlinear System

We study the fingerprint of the Arnol'd diffusion in a quantum system of two coupled nonlinear oscillators with a two-frequency external force. In the classical description, this peculiar diffusion is due to the onset of a weak chaos in a narrow stochastic layer near the separatrix of the coupling resonance. We have found that global dependence of the quantum diffusion coefficient on model parameters mimics, to some extent, the classical data. However, the quantum diffusion happens to be slower that the classical one. Another result is the dynamical localization that leads to a saturation of the diffusion after some characteristic time. We show that this effect has the same nature as for the studied earlier dynamical localization in the presence of global chaos. The quantum Arnol'd diffusion represents a new type of quantum dynamics and can be observed, for example, in 2D semiconductor structures (quantum billiards) perturbed by time-periodic external fields.Comment: RevTex, 11 pages including 12 ps-figure

Dynamical Stability of an Ion in a Linear Trap as a Solid-State Problem of Electron Localization

When an ion confined in a linear ion trap interacts with a coherent laser field, the internal degrees of freedom, related to the electron transitions, couple to the vibrational degree of freedom of the ion. As a result of this interaction, quantum dynamics of the vibrational degree of freedom becomes complicated, and in some ranges of parameters even chaotic. We analyze the vibrational ion dynamics using a formal analogy with the solid-state problem of electron localization. In particular, we show how the resonant approximation used in analysis of the ion dynamics, leads to a transition from a two-dimensional (2D) to a one-dimensional problem (1D) of electron localization. The localization length in the solid-state problem is estimated in cases of weak and strong interaction between the cites of the 2D cell by using the methods of resonance perturbation theory, common in analysis of 1D time-dependent dynamical systems.Comment: 18 pages RevTe