Related papers: Localized States in the Chaotic Ce Atom
Dynamics of a periodically time dependent quantum system is reflected in the features of the eigenstates of the Floquet operator. Of the special importance are their localization properties quantitatively characterized by the eigenvector…
The properties of the entanglement entropy (EE) in one-dimensional disordered interacting systems are studied. Anderson localization leaves a clear signature on the average EE, as it saturates on length scale exceeding the localization…
We show that a newly proposed Shannon-like entropic measure of shape complexity applicable to spatially-localized or periodic mathematical functions known as configurational entropy (CE) can be used as a predictor of spontaneous decay rates…
In quantum statistical mechanics, it is of fundamental interest to understand how close the bipartite entanglement entropy of eigenstates of quantum chaotic Hamiltonians is to maximal. For random pure states in the Hilbert space, the…
We consider $N\times N$ Hermitian random matrices with i.i.d. entries. The matrix is normalized so that the average spacing between consecutive eigenvalues is of order $1/N$. We study the connection between eigenvalue statistics on…
We study the relative entropy of highly excited quantum states. First, we sample states from the Wishart ensemble and develop a large-N diagrammatic technique for the relative entropy. The solution is exactly expressed in terms of…
A statistical analysis of the ionization yield of one-dimensional, periodically driven hydrogen Rydberg states is provided. We find excellent agreement with predictions for the conductance across an Anderson-localized, quasi…
We used the von Neumann entropy to study the single and many-particle on-site localizations of stationary states for an anisotropic Heisenberg spin-1/2 chain. With a constructed bounded sequence of on-site energies for single and…
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…
Employing the chiral Unitary Ensemble of random matrices we calculate the probability distribution of the local density of states for zero-dimensional ("quantum chaotic") two-sublattice systems at the point of chiral symmetry E=0 and in the…
For systems whose classical dynamics is chaotic, it is generally believed that the local statistical properties of the quantum energy levels are well described by Random Matrix Theory. We present here two counterexamples - the hydrogen atom…
We consider $N\times N$ Hermitian random matrices with independent identically distributed entries (Wigner matrices). The matrices are normalized so that the average spacing between consecutive eigenvalues is of order $1/N$. Under suitable…
We consider ensembles of $N \times N$ Hermitian Wigner matrices, whose entries are (up to the symmetry constraints) independent and identically distributed random variables. Assuming sufficient regularity for the probability density…
We prove that any deterministic matrix is approximately the identity in the eigenbasis of a large random Wigner matrix with very high probability and with an optimal error inversely proportional to the square root of the dimension. Our…
First theoretical and numerical results on the global structure of the energy shell, the Green function spectra and the eigenfunctions, both localized and ergodic, in a generic conservative quantum system are presented. In case of quantum…
The Wigner localization is an electron phase at low densities when the electrons are sharply localized around equilibrium positions. The simulation of the Wigner localization phenomenon requires careful treatment of the many-body…
We study whether a generic isolated quantum system initially set out of equilibrium can be considered as localized close to its initial state. Our approach considers the time evolution in the Krylov basis, which maps the dynamics onto that…
We present exact analytical results revealing the existence of a countable infinity of unusual single particle states, which are localized with a multitude of localization lengths in a Vicsek fractal network with diamond shaped loops as the…
We introduce and prove local Wegner estimates for continuous generalized Anderson Hamiltonians, where the single-site random variables are independent but not necessarily identically distributed. In particular, we get Wegner estimates with…
We show that a discrete tight-binding model representing either a random or a quasiperiodic array of bonds, can have the entire energy spectrum or a substantial part of it absolutely continuous, populated by extended eigenfunctions only,…