Related papers: Localization in Strongly Chaotic Systems
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…
Quantum systems that violate the eigenstate thermalisation hypothesis thereby falling outside the paradigm of conventional statistical mechanics are of both intellectual and practical interest. We show that such a breaking of ergodicity may…
Following a recent work (briefly reviewed below) we consider temporal fluctuations in the reduced density matrix elements for a coupled system involving a pair of kicked rotors as also one made up of a pair of Harper Hamiltonians. These…
The reduced density matrix of many-body systems possessing an additive conserved quantity can be decomposed in orthogonal sectors which can be independently analyzed. Recently, these have been proven to equally contribute to entanglement…
We study the response of the quasi-energy levels in the context of quantized chaotic systems through the level velocity variance and relate them to classical diffusion coefficients using detailed semiclassical analysis. The systematic…
We elaborate on the principle that for gapped quantum spin systems with local interaction "local perturbations [in the Hamiltonian] perturb locally [the ground state]". This principle was established in [Bachmann et al. 2012], relying on…
The Eigenstate Thermalization Hypothesis explains thermalization in isolated quantum systems through the statistical properties of observables in the energy eigenbasis. We investigate the crossover from integrability to chaos in the…
Certain disorder-free Hamiltonians can be non-ergodic due to a \emph{strong fragmentation} of the Hilbert space into disconnected sectors. Here, we characterize such systems by introducing the notion of `statistically localized integrals of…
There is a newly emerging understanding that in the chaotic domain of isolated finite interacting many particle systems smoothed densities define the statistical description of these systems and these densities follow from embedded…
Chaotic Hamiltonians are known to follow Random Matrix Theory (RMT) ensembles in the apparent randomness of their spectra and wavefunction statistics. Deviations form RMT also do occur, however, due to system-specific properties, or as…
We study the statistical properties of the off-diagonal matrix elements of observables in the energy eigenstates of integrable quantum systems. They have been found to be dense in the spin-1/2 XXZ chain, while they are sparse in…
The energy level spacing distribution of a tight-binding hamiltonian is monitored across the mobility edge for a fixed disorder strength. Any mixing of extended and localized levels is avoided in the configurational averages, thus…
We argue that in a large class of disordered quantum many-body systems, the late time dynamics of time-dependent correlation functions is captured by random matrix theory, specifically the energy eigenvalue statistics of the corresponding…
Manifestation of dynamical instability and Hamiltonian chaos in the fundamental near-resonant matter-radiation interaction has been found analitically and in a Monte Carlo simulation in the behavior of atoms moving in a rigid optical…
We consider some random band matrices with band-width $N^\mu$ whose entries are independent random variables with distribution tail in $x^{-\alpha}$. We consider the largest eigenvalues and the associated eigenvectors and prove the…
Scattering is a ubiquitous phenomenon which is observed in a variety of physical systems which span a wide range of length scales. The scattering matrix is the key quantity which provides a complete description of the scattering process.…
It is commonly expected that for quantum chaotic many body systems, the statistical properties approach those of random matrices when increasing the system size. We demonstrate for various kicked spin-1/2 chain models that the average…
We consider Hermitian and symmetric random band matrices $H$ in $d \geq 1$ dimensions. The matrix elements $H_{xy}$, indexed by $x,y \in \Lambda \subset \Z^d$, are independent, uniformly distributed random variables if $\abs{x-y}$ is less…
We study quantum localization phenomena in chaotic systems with a parameter. The parametric motion of energy levels proceeds without crossing any other and the defined avoided crossings quantify the interaction between states. We propose…
In order to analyze the effect of chaos or order on the rate of decoherence in a subsystem we aim to distinguish effects of the two types of dynamics from those depending on the choice of the wave packet. To isolate the former we introduce…