Related papers: Generalized random matrix conjecture for chaotic s…
Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…
The probability distribution of the proper delay times during scattering on a chaotic system is derived in the framework of the random matrix approach and the supersymmetry method. The result obtained is valid for an arbitrary number of…
Wave scattering in chaotic systems can be characterized by its spectrum of resonances, $z_n=E_n-i\frac{\Gamma_n}{2}$, where $E_n$ is related to the energy and $\Gamma_n$ is the decay rate or width of the resonance. If the corresponding ray…
We study time evolution of a subsystem's density matrix under unitary evolution, generated by a sufficiently complex, say quantum chaotic, Hamiltonian, modeled by a random matrix. We exactly calculate all coherences, purity and…
We derive a set of spectral statistics whose power spectrum is characterized, in the case of chaotic quantum systems, by colored noise $1/f^{\gamma}$, where the integer parameter $\gamma$ critically depends on the specific energy-level…
We describe Generalized Hermitian matrices ensemble sometimes called Chiral ensemble. We give global asymptotic of the density of eigenvalues or the statistical density. We will calculate a Laplace transform of such a density for finite…
We study nonequilibrium properties of small and chaotic quantum systems, i.e., non-integrable systems whose size is small in the sense that the separations of energy levels are non-negligible as compared with other relevant energy scales.…
We present experimental and numerical results for the long-range fluctuation properties in the spectra of quantum graphs with chaotic classical dynamics and preserved time-reversal invariance. Such systems are generally believed to provide…
The random matrix ensembles (RMT) of quantum statistical Hamiltonian operators, e.g.Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied to following quantum statistical systems: nuclear…
We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted…
Recently, Bauke and Mertens conjectured that the local statistics of energies in random spin systems with discrete spin space should in most circumstances be the same as in the random energy model. This was proven in a large class of models…
This arXiv repository is a bundle of two closely related papers. Abstract of the first paper: In systems governed by "chaotic" local Hamiltonians, we conjecture the universality of eigenstate entanglement (defined as the average…
We investigate the probability distribution of Chern numbers (quantum Hall effect integers) for a parametric version of the GUE random matrix ensemble, which is a model for a chaotic or disordered system. The numerically-calculated…
In a frequency range where a microwave resonator simulates a chaotic quantum billiard, we have measured moduli and phases of reflection and transmission amplitudes in the regimes of both isolated and of weakly overlapping resonances and for…
Quantum many-body systems are commonly considered as quantum chaotic if their spectral statistics, such as the level spacing distribution, agree with those of random matrix theory. Using the example of the kicked Ising chain we demonstrate…
The time-dependent variational principle using generalized Gaussian trial functions yields a finite dimensional approximation to the full quantum dynamics and is used in many disciplines. It is shown how these 'semi-quantum' dynamics may be…
This paper establishes the universality of parametric correlations of eigenfunctions in chaotic and weakly disordered systems. We demonstrate this universality in the framework of the gaussian random matrix process and obtain predictions…
Understanding equilibration times in closed quantum systems is essential for characterising their approach to equilibrium. Chaotic many-body systems are paradigmatic in this context: they are expected to thermalise according to the…
We study the Eigenstate Thermalization Hypothesis (ETH) in chaotic conformal field theories (CFTs) of arbitrary dimensions. Assuming local ETH, we compute the reduced density matrix of a ball-shaped subsystem of finite size in the infinite…
We derive universal entanglement entropy and Schmidt eigenvalue behaviors for the eigenstates of two quantum chaotic systems coupled with a weak interaction. The progression from a lack of entanglement in the noninteracting limit to the…