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A Iomin

Publications and source records attributed to A Iomin.

11 recordsLinked to original sources
PubMed2004

Superdiffusion 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 the Lévy-like process enriches this transport phenomenon. It is shown that an inhomogeneous convection flow is a mechanism for the realization of the Lévy-like process. It leads to superdiffusion of particles on the comb structure. This superdiffusion is an enhanced one with an arbitrary large transport exponent, but all moments are finite. A frontier case of superdiffusion, where the transport exponent approaches infinity, is studied. The log-normal distribution with the exponentially fast superdiffusion is obtained for this case.

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PubMed2004

Loschmidt echo for a chaotic oscillator.

Chaotic dynamics of a nonlinear oscillator is considered in the semiclassical approximation. The Loschmidt echo as a measure of quantum stability to a time dependent variation is calculated. It is shown that an exponential decay of the Loschmidt echo is due to a Lyapunov exponent and it has a pure classical nature. The Lyapunov regime is observed for a time scale which is of the power law in semiclassical parameter.

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PubMed2003

Semiclassical quantization of separatrix maps.

Quantization of energy balance equations, which describe a separatrixlike 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)-->(I,theta). 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.

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PubMed2003

Breaking time for the quantum chaotic attractor.

A model of a quantum dissipative system is considered in the regime when the classical limit corresponds to a chaotic attractor, and the breaking time tau(Planck) of the classical-quantum correspondence is obtained. The model describes a periodically kicked harmonic oscillator (or a particle in a constant magnetic field) with a dissipation. Another analog of this problem is the dissipative kicked Harper model. It is shown that in the limit of the so-called dying attractor, the breaking time tau(Planck) can be arbitrarily large.

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PubMed2002

Quantum localization for a kicked rotor with accelerator mode islands.

Dynamical localization of classical superdiffusion for the quantum kicked rotor is studied in the semiclassical limit. Both classical and quantum dynamics of the system become more complicated under the conditions of mixed phase space with accelerator mode islands. Recently, long time quantum flights due to the accelerator mode islands have been found. By exploration of their dynamics, it is shown here that the classical-quantum duality of the flights leads to their localization. The classical mechanism of superdiffusion is due to accelerator mode dynamics, while quantum tunneling suppresses the superdiffusion and leads to localization of the wave function. Coupling of the regular type dynamics inside the accelerator mode island structures to dynamics in the chaotic sea proves increasing the localization length. A numerical procedure and an analytical method are developed to obtain an estimate of the localization length which, as it is shown, has exponentially large scaling with the dimensionless Planck's constant (tilde)h<<1 in the semiclassical limit. Conditions for the validity of the developed method are specified.

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PubMed2001

Quantum breaking time scaling in 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 tau(Planck's over 2pi) approximately (1/Planck's over 2pi)(1/mu) with the transport exponent mu>1 that corresponds to superdiffusive dynamics [B. Sundaram and G. M. Zaslavsky, Phys. Rev. E 59, 7231 (1999)]. We discuss also other possibilities for the breaking time scaling and transition to the logarithmic one tau(Planck's over 2pi) approximately ln(1/Planck's over 2pi) with respect to Planck's over 2pi.

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PubMed2000

Quantum response for chaotic resonances

Chaotic dynamics of conducting electrons in the presence of a high-frequency electromagnetic field and a constant homogeneous magnetic field is considered. It is shown that quantum fluctuations become important in this case on a time scale shorter than mean free time. Nonperturbative approach for calculation of a kinetic coefficient (conductivity) is developed. An analytical expression for the kinetic coefficient as a function of the magnetic field and a localization length is obtained. Dependence of the conductivity on the quantum localization length is studied.

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PubMed1999

Immense delocalization from fractional kinetics.

We observe immense delocalization of the order of 10(9) for a kicked Harper model when a control parameter K is taken to be K*=6.349 972. This "magic" value corresponds to special phase space topology in the classical limit, when a hierarchical self-similar set of sticky islands emerges. The origin of the effect is of the general nature and similar immense delocalization can be found in other systems.

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