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D. L. Shepelyansky

Publications and source records attributed to D. L. Shepelyansky.

107 records · Page 6Linked to original sources
arXiv1999

Two electron view on metal-insulator transition in two dimensions

The model of two electrons with Coulomb interaction on a two-dimensional (2D) disordered lattice is considered. It is shown that the interaction can give a sharp transition to delocalized states in a way similar to the Anderson transition in 3D. The localized phase appears when the ratio of the Coulomb energy to the Fermi energy becomes larger than some critical value dependent on the disorder. The relation to the experiments on metal-insulator transition in 2D is also discussed.

cond-mat↗
arXiv1999

Classical Chaos and its Quantum Manifestations

We present here the special issue of Physica D in honor of Boris Chirikov. It is based on the proceedings of the Conference "Classical Chaos and its Quantum Manifestations" held in Toulouse in July 1998. This electronic version contains the list of contributions, the introduction and the unformal conclusion. The introduction represents "X Chirikov Chaos Commandments" and reviews Chirikov's pioneering results in the field of classical and quantum chaos. The conclusion, written by P.M.Koch, gives an outlook on the development of the field of chaos associated with Chirikov, including the personal reminiscences of Professor Andy Sessler. This electronic version of the special issue has certain differences and extentions comparing to the journal.

cond-mat↗
arXiv1999

3D Anderson transition for two electrons in 2D

It is shown that the Coulomb interaction can lead to delocalization of two electron states in two-dimensional (2D) disordered potential in a way similar to the Anderson transition in three dimensions (3D). At fixed disorder strength the localized phase corresponds to low electron density and large value of parameter r_s.

cond-mat↗
arXiv1998

Asymptotic Statistics of Poincaré Recurrences in Hamiltonian Systems with Divided Phase Space

By different methods we show that for dynamical chaos in the standard map with critical golden curve the Poincaré recurrences P(τ) and correlations C(τ) asymptotically decay in time as P ~ C/τ~ 1/τ^3. It is also explained why this asymptotic behavior starts only at very large times. We argue that the same exponent p=3 should be also valid for a general chaos border.

cond-mat↗
arXiv1998

Integrability and Quantum Chaos in Spin Glass Shards

We study spin glass clusters ("shards") in a random transverse magnetic field, and determine the regime where quantum chaos and random matrix level statistics emerge from the integrable limits of weak and strong field. Relations with quantum phase transition are also discussed.

cond-mat↗
arXiv1997

Emergence of quantum chaos in finite interacting Fermi systems

We study the level spacing statistics P(s) in many-body Fermi systems and determine a critical two-body interaction strength Uc at which a crossover from Poisson to Wigner-Dyson statistics takes place. Near the Fermi level the results allow to find a critical temperature Tch above which quantum chaos and thermalization set in.

cond-mat↗
arXiv1996

Chaotic enhancement of hydrogen atoms excitation in magnetic and microwave fields

We numerically investigate multiphoton ionization of excited hydrogen atoms in magnetic and microwave fields when up to 600 photons are required for ionization. The analytical estimates for the quantum localization length in the classically chaotic regime are in agreement with numerical data. The excitation is much stronger as compared to the case with microwave field only due to the chaotic structure of eigenstates in magnetic field.

cond-mat↗
arXiv1996

Two interacting quasiparticles above the Fermi sea

We study numerically the interaction and disorder effects for two quasiparticles in two and three dimensions. The dependence of the interaction-induced Breit-Wigner width on the excitation energy above the Fermi level, the disorder strength and the system size is determined. A regime is found where the width is practically independent of the excitation energy. The results allow to estimate the two quasiparticle mobility edge.

cond-mat↗
arXiv1996

Low energy chaos in the Fermi-Pasta-Ulam problem

A possibility that in the FPU problem the critical energy for chaos goes to zero with the increase of the number of particles in the chain is discussed. The distribution for long linear waves in this regime is found and an estimate for new border of transition to energy equipartition is given.

chao-dyn↗
arXiv1996

Particle propagation in a random and quasiperiodic potential

We numerically investigate the Anderson transition in an effective dimension $d$ ($3 \leq d \leq 11$) for one particle propagation in a model random and quasiperiodic potential. The found critical exponents are different from the standard scaling picture. We discuss possible reasons for this difference.

cond-mat↗
arXiv1996

Two interacting particles in the Harper model

Dynamics of two particles with short range repulsive or attractive interaction is studied numerically in the Harper model. It is shown that interaction leads to appearance of localized states and pure-point spectrum component in the case when noninteractive system is quasi-diffusive or ballistic. In the localized phase interaction gives only stronger localization contrary to the case of two interacting particles in a random potential.

cond-mat↗
arXiv1996

Interactions and localization: two interacting particles approach

It is shown that two repulsing / attracting particles in a random potential can propagate coherently on a distance much larger than one-particle localization length without interaction. In dimension $d$ this leads to delocalization of pairs formed by two repulsing / attracting particles. The results of numerical simulations allow to understand some specific features of this effect.

cond-mat↗
arXiv1996

Few interacting particles in a random potential

We study the localization length of few interacting particles in a random potential. Concentrating on the case of three particles we show that their localization length is strongly enhanced comparing to the enhancement for two interacting particles.

cond-mat↗
arXiv1995

Hidden Breit-Wigner distribution and other properties of random matrices with preferential basis

We study statistical properties of a class of band random matrices which naturally appears in systems of interacting particles. The local spectral density is shown to follow the Breit-Wigner distribution in both localized and delocalized regimes with width independent on the band/system size. We analyse the implications of this distribution to the inverse participation ratio, level spacing statistics and the problem of two interacting particles in a random potential.

cond-mat↗
arXiv1995

Universal diffusion near the golden chaos border

We study local diffusion rate $D$ in Chirikov standard map near the critical golden curve. Numerical simulations confirm the predicted exponent $α=5$ for the power law decay of $D$ as approaching the golden curve via principal resonances with period $q_n$ ($D \sim 1/q^α_n$). The universal self-similar structure of diffusion between principal resonances is demonstrated and it is shown that resonances of other type play also an important role.

chao-dyn↗
arXiv1993

Kramers map approach for stabilization of hydrogen atom in a magnetic field

The phenomenon of stabilization of highly excited states of hydrogen atom in a strong monochromatic field is discussed. Approximate description of dynamics by the introduced Kramers map allows to understand the main properties of this phenomenon on the basis of analogy with the Kepler map. Analogy between the stabilization and the channeling of particles in a crystal is also discussed.

chao-dyn↗