Statistics of quantum recurrences in the Hilbert space
This paper has been withdrawn by the authors due to a crucial error.
nlin.CD↗
arXiv subjects
A. Iomin
Publications and source records attributed to A. Iomin.
Sensitivity of ray paths to initial condition
Using a parabolic equation, we consider ray propagation in a waveguide with the sound speed profile that corresponds to the dynamics of a nonlinear oscillator. An analytical consideration of the dependence of the travel time on the initial conditions is presented. Using an exactly solvable model and the path integral representation of the travel time, we explain the step-like behavior of the travel time (T) as a function of the starting momentum (p_0) (related to the starting ray grazing angle (χ_0) by (p_0=\tanχ_0)). A periodic perturbation of the waveguide along the range leads to wave and ray chaos. We explain an inhomogeneity of distribution of the chaotic ray travel times, which has obvious maxima. These maxima lead to the clustering of rays and each maximum relates to a ray identifier, {\em i.e.} to the number of ray semi--cycles along the ray path.
nlin.CD↗
Wave localization as a manifestation of ray chaos in underwater acoustics
Wave chaos is demonstrated by studying a wave propagation in a periodically corrugated wave-guide. In the limit of a short wave approximation (SWA) the underlying description is related to the chaotic ray dynamics. In this case the control parameter of the problem is characterized by the corrugation amplitude and the SWA parameter. The considered model is fairly suitable and tractable for the analytical analysis of a wave localization length. The number of eigenmodes characterized the width of the localized wave packet is estimated analytically.
nlin.CD↗
Accelerator dynamics of a fractional kicked rotor
It is shown that the Weyl fractional derivative can quantize an open system. A fractional kicked rotor is studied in the framework of the fractional Schrodinger equation. The system is described by the non-Hermitian Hamiltonian by virtue of the Weyl fractional derivative. Violation of space symmetry leads to acceleration of the orbital momentum. Quantum localization saturates this acceleration, such that the average value of the orbital momentum can be a direct current and the system behaves like a ratchet. The classical counterpart is a nonlinear kicked rotor with absorbing boundary conditions.
nlin.CD↗
On tumor development: fractional transport approach
A growth of malignant neoplasm is considered as a fractional transport approach. We suggested that the main process of the tumor development through a lymphatic net is fractional transport of cells. In the framework of this fractional kinetics we were able to show that the mean size of main growth is due to subdiffusion, while the appearance of metaphases is determined by superdiffusion.
q-bio.TO↗
On log--normal distribution on a comb structure
We study specific properties of particles transport by exploring an exact solvable model, a so-called comb structure, where diffusive transport of particles leads to subdiffusion. A performance of Lévy -- like process enriches this transport phenomenon. It is shown that an inhomogeneous convection flow, as a realization of the Lévy--like process, leads to superdiffusion of particles on the comb structure. A frontier case of superdiffusion that corresponds to the exponentially fast transport is studied and the log--normal distribution is obtained for this case.
cond-mat.dis-nn↗
Negative superdiffusion due to the inhomogeneous convection
Fractional transport of particles on a comb structure in the presence of an inhomogeneous convection flow is studied. The large scale asymptotics is considered. It is shown that a contaminant spreads superdiffusively in the direction opposite to the convection flow. Conditions for the realization of this new effect is discussed in detail.
cond-mat.dis-nn↗
Loschmidt echo for a chaotic oscillator
Chaotic dynamics of a nonlinear oscillator is considered in the semiclassical approximation. The Loschmidt echo is calculated for a time scale which is of the power law in semiclassical parameter. It is shown that an exponential decay of the Loschmidt echo is due to a Lyapunov exponent and it has a pure classical nature.
nlin.CD↗
Semiclassical approximation for a nonlinear oscillator with dissipation
An $S$--matrix approach is developed for the chaotic dynamics of a nonlinear oscillator with dissipation. The quantum--classical crossover is studied in the framework of the semiclassical expansion for the $S$--matrix. Analytical expressions for the braking time and the $S$--matrix are obtained.
nlin.CD↗
Semiclassical quantization of maps with a variable time scale
Quantization of energy balance equations, which describe a separatrix -- like motion is presented. The method is based on an exact canonical transformation of the energy--time pair to the action-angle canonical pair, $ (E,t)\to (I,θ) $. Quantum mechanical dynamics can be studied in the framework of the new Hamiltonian. This transformation also establishes a relation between a wide class of the energy balance equations and dynamical localization of classical diffusion by quantum interference, that was studied in the field of quantum chaos. An exact solution for a simple system is presented as well.
nlin.CD↗
Quantum manifestation of Levy-type flights in a chaotic system
Semi--classical dynamics of quantum wave packets spreading is studied for a kicked rotor. Quantum flights are established for a specific, "magic" value of a chaos control parameter when the classical stickiness of trajectories is most effective. By studying of survival probability and distribution of the accelerations we identify the presence of quantum Levy-type flights.
nlin.CD↗
Quantum Breaking Time Scaling in the Superdiffusive Dynamics
We show that the breaking time of quantum-classical correspondence depends on the type of kinetics and the dominant origin of stickiness. For sticky dynamics of quantum kicked rotor, when the hierarchical set of islands corresponds to the accelerator mode, we demonstrate by simulation that the breaking time scales as $τ_{\hbar} \sim (1/\hbar)^{1/μ}$ with the transport exponent $μ> 1$ that corresponds to superdiffusive dynamics. We discuss also other possibilities for the breaking time scaling and transition to the logarithmic one $τ_{\hbar} \sim \ln(1/\hbar)$ with respect to $\hbar$.
nlin.CD↗
Metal-insulator transitions in cyclotron resonance of periodic nanostructures due to avoided band crossings
A recently found metal-insulator transition in a model for cyclotron resonance in a two-dimensional periodic potential is investigated by means of spectral properties of the time evolution operator. The previously found dynamical signatures of the transition are explained in terms of avoided band crossings due to the change of the external electric field. The occurrence of a cross-like transport is predicted and numerically confirmed.
cond-mat.mes-hall↗
The possibility of a metal insulator transition in antidot arrays induced by an external driving
It is shown that a family of models associated with the kicked Harper model is relevant for cyclotron resonance experiments in an antidot array. For this purpose a simplified model for electronic motion in a related model system in presence of a magnetic field and an AC electric field is developed. In the limit of strong magnetic field it reduces to a model similar to the kicked Harper model. This model is studied numerically and is found to be extremely sensitive to the strength of the electric field. In particular, as the strength of the electric field is varied a metal -- insulator transition may be found. The experimental conditions required for this transition are discussed.
cond-mat↗