相关论文: Classical singularities and Semi-Poisson statistic…
PT-symmetric Hamiltonians and transfer matrices arise naturally in statistical mechanics. These classical and quantum models often require the use of complex or negative weights and thus fall outside of the conventional equilibrium…
The energy level statistics of 2D electrons with spin-orbit scattering are considered near the disorder induced metal-insulator transition. Using the Ando model, the nearest-level-spacing distribution is calculated numerically at the…
It is well known that for ordinary one-dimensional (1D) disordered systems, the Anderson localization length $\xi$ diverges as $\lambda^m$ in the long wavelength limit ($\lambda\rightarrow \infty$ ) with a universal exponent $m=2$,…
Given a quantum Hamiltonian, we explain how the dynamical properties of the underlying classical system affect the behaviour of quantum eigenstates in the semi-classical limit. We study this problem via the notion of semiclassical measures.…
Energy spectra of a particle with mass $m$ and charge $e$ in the cubic Aharonov-Bohm billiard containing around $10^4$ consecutive levels starting from the ground state have been analysed. The cubic Aharonov-Bohm billiard is a plane…
We assume that the level spectra of quantum systems in the initial phase of transition from integrability to chaos are approximated by superpositions of independent sequences. Each individual sequence is modeled by a random matrix ensemble.…
Triggered by a controversy surrounding a universal behaviour of the power spectrum in quantum systems exhibiting regular classical dynamics, we focus on a model of random diagonal matrices (RDM), often associated with the Poisson spectral…
The semiclassical theory for billiards with mixed boundary conditions is developed and explicit expressions for the smooth and the oscillatory parts of the spectral density are derived. The parametric dependence of the spectrum on the…
The paper is devoted to the derivation of random unitary matrices whose spectral statistics is the same as statistics of quantum eigenvalues of certain deterministic two-dimensional barrier billiards. These random matrices are extracted…
Quantum chaotic dynamics is obtained for a tight-binding model in which the energies of the atomic levels at the boundary sites are chosen at random. Results for the square lattice indicate that the energy spectrum shows a complex behavior…
We investigate the two-point correlations in the band spectra of spatially periodic systems that exhibit chaotic diffusion in the classical limit. By including level pairs pertaining to non-identical quasimomenta, we define form factors…
Dynamics of a randomly-perturbed quantum system with 3/2-degrees of freedom is considered. We introduce a transfer operator being the quantum analogue of the specific Poincar\'e map. This map was proposed in (Makarov, Uleysky, J. Phys. A:…
This paper reports the results of an ongoing in-depth analysis of the classical trajectories of the class of non-Hermitian $PT$-symmetric Hamiltonians $H=p^2+ x^2(ix)^\varepsilon$ ($\varepsilon\geq0$). A variety of phenomena, heretofore…
The effect of Coulomb and short-range interactions on the spectral properties of two-dimensional disordered systems with two spinless fermions is investigated by numerical scaling techniques. The size independent universality of the…
We study quantum chaos in a non-KAM system, i.e. a kicked particle in a one-dimensional infinite square potential well. Within the perturbative regime the classical phase space displays stochastic web structures, and the diffusion…
We seek the possibility of a disorder driven transition in a tight-binding lattice with a flat band using complexity parameter approach. Our results indicate the existence of a localized to extended states transition with increasing…
For classical billiards we suggest that a matrix of action or length of trajectories in conjunction with statistical measures, level spacing distribution and spectral rigidity, can be used to distinguish chaotic from integrable systems. As…
In mixed systems, besides regular and chaotic states, there are states supported by the chaotic region mainly living in the vicinity of the hierarchy of regular islands. We show that the fraction of these hierarchical states scales as…
While plenty of results have been obtained for single-particle quantum systems with chaotic dynamics through a semiclassical theory, much less is known about quantum chaos in the many-body setting. We contribute to recent efforts to make a…
What we are going to call in this paper "diffractive phenomena" in billiards is far from being deeply understood. These are sorts of singularities that, for example, some kind of corners introduce in the energy eigenfunctions. In this paper…