Related papers: Level statistics for nearly integrable systems
We study the spectrum of a random matrix, whose elements depend on the Euclidean distance between points randomly distributed in space. This problem is widely studied in the context of the Instantaneous Normal Modes of fluids and is…
This chapter discusses the conditions and timescales under which isolated many-body quantum systems, initially far from equilibrium, ultimately reach thermal equilibrium. We also examine quantities that, during the relaxation process,…
The phenomenon of quantum localization in classically chaotic eigenstates is one of the main issues in quantum chaos (or wave chaos), and thus plays an important role in general quantum mechanics or even in general wave mechanics. In this…
The impression gained from the literature published to date is that the spectrum of the stadium billiard can be adequately described, semiclassically, by the Gutzwiller periodic orbit trace formula together with a modified treatment of the…
Random matrix spectral correlations is a defining feature of quantum chaos. Here, we study such correlations in a minimal model of chaotic many-body quantum dynamics where interactions are confined to the system's boundary, dubbed…
Classical counterparts of a great variety of quantum systems, from atomic physics to quantum wells and quantum dots, to optical, microwave, and acoustic resonators exhibit partially chaotic dynamics. Since it is often impossible to measure…
The boundary integral method for calculating the stationary states of a quantum particle in nano-devices and quantum billiards is presented in detail at an elementary level. According to the method, wave functions inside the domain of the…
Numerical calculation and analysis of extremely high-lying energy spectra, containing thousands of levels with sequential quantum number up to 62,000 per symmetry class, of a generic chaotic 3D quantum billiard is reported. The shape of the…
Some of the subtleties of the integrability of the elliptic quantum billiard are discussed. A well known classical constant of the motion has in the quantum case an ill-defined commutator with the Hamiltonian. It is shown how this problem…
We propose a measure of quantum state complexity defined by minimizing the spread of the wave-function over all choices of basis. Our measure is controlled by the "survival amplitude" for a state to remain unchanged, and can be efficiently…
We consider a nonlinear autonomous system of $N\gg 1$ degrees of freedom randomly coupled by both relaxational ('gradient') and non-relaxational ('solenoidal') random interactions. We show that with increased interaction strength such…
We study level statistics of a critical random matrix ensemble of a power-law banded complex Hermitean matrices. We compute numerically the level compressibility via the level number variance and compare it with the analytical formula for…
In a recent letter [Phys. Rev. Lett. {\bf 100}, 164101 (2008)] and within the context of quantized chaotic billiards, random plane wave and semiclassical theoretical approaches were applied to an example of a relatively new class of…
The transition from arbitrary to chaotic fluctuation properties in quantum systems is studied in a random matrix model. It is assumed that the Hamiltonian can be written as the sum of an arbitrary and a chaos producing part. The Gaussian…
Spectral statistics of systems that undergo many--body localization transition are studied. An analysis of the gap ratio statistics from the perspective of inter- and intra-sample randomness allows us to pin point differences between…
It has been proposed to investigate the equilibration properties of a small isolated quantum system by means of the matrix of asymptotic transition probabilities in some preferential basis. The trace $T$ of this matrix measures the degree…
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…
Resonance states in quantum chaotic scattering systems have a multifractal structure that depends on their decay rate. We show how classical dynamics describes this structure for all decay rates in the semiclassical limit. This result for…
We study the complex-valued resonance spectrum of a dc-SQUID coupled to a flux qubit, where the former is treated in the cubic and the latter in the two-level approximation. It is shown that this spectrum is well-defined and contains most…
We report on the experimental investigation of the fluctuation properties in the resonance frequency spectra of a flat resonator simulating a dissipative quantum billiard subject to partial time-reversal invariance violation (TIV) which is…