arXiv subjects

O. V. Zhirov

Publications and source records attributed to O. V. Zhirov.

24 records · Page 2Linked to original sources

arXiv2001

Fractal Spin Glass Properties of Low Energy Configurations in the Frenkel-Kontorova chain

We study numerically and analytically the classical one-dimensional Frenkel-Kontorova chain in the regime of pinned phase characterized by phonon gap. Our results show the existence of exponentially many static equilibrium configurations which are exponentially close to the energy of the ground state. The energies of these configurations form a fractal quasi-degenerate band structure which is described on the basis of elementary excitations. Contrary to the ground state, the configurations inside these bands are disordered.

cond-mat↗

arXiv2000

Big Entropy Fluctuations in Statistical Equilibrium: The Macroscopic Kinetics

Large entropy fluctuations in an equilibrium steady state of classical mechanics were studied in extensive numerical experiments on a simple 2--freedom strongly chaotic Hamiltonian model described by the modified Arnold cat map. The rise and fall of a large separated fluctuation was shown to be described by the (regular and stable) "macroscopic" kinetics both fast (ballistic) and slow (diffusive). We abandoned a vague problem of "appropriate" initial conditions by observing (in a long run)spontaneous birth and death of arbitrarily big fluctuations for any initial state of our dynamical model. Statistics of the infinite chain of fluctuations, reminiscent to the Poincaré recurrences, was shown to be Poissonian. A simple empirical relation for the mean period between the fluctuations (Poincaré "cycle") has been found and confirmed in numerical experiments. A new representation of the entropy via the variance of only a few trajectories ("particles") is proposed which greatly facilitates the computation, being at the same time fairly accurate for big fluctuations. The relation of our results to a long standing debates over statistical "irreversibility" and the "time arrow" is briefly discussed too.

nlin.CD↗

arXiv1999

Quantum Resonances and Regularity Islands in Quantum Maps

We study analytically as well as numerically the dynamics of a quantum map near a quantum resonance of an order q. The map is embedded into a continuous unitary transformation generated by a time-independent quasi-Hamiltonian. Such a Hamiltonian generates at the very point of the resonance a local gauge transformation described the unitary unimodular group SU(q). The resonant energy growth of is attributed to the zero Liouville eigenmodes of the generator in the adjoint representation of the group while the non-zero modes yield saturating with time contribution. In a vicinity of a given resonance, the quasi-Hamiltonian is then found in the form of power expansion with respect to the detuning from the resonance. The problem is related in this way to the motion along a circle in a (q^2-1)-component inhomogeneous "magnetic" field of a quantum particle with $q$ intrinsic degrees of freedom described by the SU(q) group. This motion is in parallel with the classical phase oscillations near a non-linear resonance. The most important role is played by the resonances with the orders much smaller than the typical localization length, q << l. Such resonances master for exponentially long though finite times the motion in some domains around them. Explicit analytical solution is possible for a few lowest and strongest resonances.

chao-dyn↗

arXiv1999

Quantum Resonances of Kicked Rotor and SU(q) group

The quantum kicked rotor (QKR) map is embedded into a continuous unitary transformation generated by a time-independent quasi-Hamiltonian. In some vicinity of a quantum resonance of order $q$, we relate the problem to the {\it regular} motion along a circle in a $(q^2-1)$-component inhomogeneous "magnetic" field of a quantum particle with $q$ intrinsic degrees of freedom described by the $SU(q)$ group. This motion is in parallel with the classical phase oscillations near a non-linear resonance.

chao-dyn↗

arXiv1997

Density-Density Correlators in Infinite Random Matrices

Using the BRM theory developed recently by Fyodorov and Mirlin we calculate the density-density correlators for Banded Random Matrix of infinite size. Within the accuracy of $1/b^2$ ($b$ is the matrix bandwidth) it appears to be the same in both cases of orthogonal and unitary symmetry. Moreover, its form coincides exactly with the formula obtained long ago by Gogolin for electron density-density correlator in strictly 1D disordered metals. In addition to the ``fixed energy'' density-density correlator considered in the solid state physics we calculate also the ``time averaged'' one, which has different properties at small separations. Our predictions are compared with the existing numerical data.

chao-dyn↗

arXiv1997

How long does the quantum chaos last?

The main purpose of this Comment is to point out that besides the short time scale of quantum chaos, confirmed once more in recent paper by Alicki et al, there is generally another time scale t_R, which is much longer and on which a partial quantum-classical correspondence persists. Namely, the quantum diffusion closely follows the classical one even though the former is dynamically stable. The absence of the long scale t_R in model studied by Alicki et al. is a result of a special choice for one model's parameters value.

chao-dyn↗