8 research outputs found
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
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
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
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
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
Quantum Hall effect in a p-type heterojunction with a lateral surface quantum dot superlattice
The quantization of Hall conductance in a p-type heterojunction with lateral
surface quantum dot superlattice is investigated. The topological properties of
the four-component hole wavefunction are studied both in r- and k-spaces. New
method of calculation of the Hall conductance in a 2D hole gas described by the
Luttinger Hamiltonian and affected by lateral periodic potential is proposed,
based on the investigation of four-component wavefunction singularities in
k-space. The deviations from the quantization rules for Hofstadter "butterfly"
for electrons are found, and the explanation of this effect is proposed. For
the case of strong periodic potential the mixing of magnetic subbands is taken
into account, and the exchange of the Chern numbers between magnetic subands is
discussed.Comment: 12 pages, 5 figures; reported at the 15th Int. Conf. on High Magnetic
Fields in Semicond. Phys. (Oxford, UK, 2002