Related papers: Upper bounds on wavepacket spreading for random Ja…

We revisit key notions related to the evolution of quantum information in few-body quantum mechanics (fbQM) and, for a wide class of dispersion relations, prove uniform bounds on the maximal speed of propagation of quantum information for…

Consideration is given to the three different analytical methods for the computation of upper bounds for the rate of convergence to the limiting regime of one specific class of (in)homogeneous continuous-time Markov chains. This class is…

In this paper, we study the numerical range of Jacobi operators and it is shown that under certain conditions, the boundary of the numerical range of these operators can be non-round only at the points where it touches the essential…

For the spatially homogeneous Boltzmann equation with cutoff hard potentials it is shown that solutions remain bounded from above, uniformly in time, by a Maxwellian distribution, provided the initial data have a Maxwellian upper bound. The…

We prove upper bounds on the rate, called "mixing rate", at which the von Neumann entropy of the expected density operator of a given ensemble of states changes under non-local unitary evolution. For an ensemble consisting of two states,…

We consider Jacobi matrices with eventually increasing sequences of diagonal and off-diagonal Jacobi parameters. We describe the asymptotic behavior of the subordinate solution at the top of the essential spectrum, and the asymptotic…

While over the last century or more considerable effort has been put into the problem of finding approximate solutions for wave equations in general, and quantum mechanical problems in particular, it appears that as yet relatively little…

We study the spectral properties of bounded and unbounded Jacobi matrices whose entries are bounded operators on a complex Hilbert space. In particular, we formulate conditions assuring that the spectrum of the studied operators is…

Lyapunov exponents, a purely classical quantity, play an important role in the evolution of quantum chaotic systems in the semiclassical limit. We conjecture the existence of an upper bound on the Lyapunov exponents that contribute to the…

We consider upper exponential bounds for the probability of the event that an absolute deviation of sample mean from mathematical expectation p is bigger comparing with some ordered level epsilon. These bounds include 2 coefficients {alpha,…

We present a new technique to obtain polynomial decay estimates for the matrix coefficients of unitary operators. Our approach, based on commutator methods, applies to nets of unitary operators, unitary representations of topological…

By extending methods of arXiv:1503.01409, we investigate the bound on the growth of higher point OTOCs by studying their complex analytical properties. We explore some subtleties in our mathematical investigation, and carefully examine the…

We consider the iteration of a unitary operator on a separable Hilbert space and study the spreading rates of the associated discrete-time dynamical system relative to a given orthonormal basis. We prove lower bounds for the transport…

Using a dynamical model relevant to cold-atom experiments, we show that long-lasting exponential spreading of wave packets in momentum space is possible. Numerical results are explained via a pseudo-classical map, both qualitatively and…

The Koopman Operator (KO) provides an analytical solution of dynamical systems in terms of orthogonal polynomials. This work exploits this representation to include the propagation of uncertainties, where the polynomials are modified to…

We consider an ensemble of nxn real symmetric random matrices A whose entries are determined by independent identically distributed random variables that have symmetric probability distribution. Assuming that the moment 12+2delta of these…

We present a simple method, not based on the transfer matrices, to prove vanishing of dynamical transport exponents. The method is applied to long range quasiperiodic operators.

We propose new Lieb-Robinson bounds (bounds on the speed of propagation of information in quantum systems) with an explicit dependence on the interaction strengths of the Hamiltonian. For systems with more than two interactions it is found…

In the Majorana equation for particles with arbitrary spin, wave packets occur due to not only the uncertainty that affects position and momentum but also due to infinite components with decreasing mass that form the Majorana spinor. In…

We consider the statistics of the results of a measurement of the spreading operator in the Krylov basis generated by the Hamiltonian of a quantum system starting from a specified initial pure state. We first obtain the probability…