Related papers: Upper bounds on wavepacket spreading for random Ja…
We study quantum transport for the discrete one-dimensional random Jacobi operator of divergence-gradient type. For strictly positive and bounded random variables, we analyze the q-moments of the position operator and establish both upper…
We develop a general method to bound the spreading of an entire wavepacket under Schr\"odinger dynamics from above. This method derives upper bounds on time-averaged moments of the position operator from lower bounds on norms of transfer…
We prove upper bounds on outside probabilities for generic non-autonomous Schr\"odinger operators on lattices of arbitrary dimension. Our approach is based on a combination of commutator method originated in scattering theory and novel…
We develop further the approach to upper and lower bounds in quantum dynamics via complex analysis methods which was introduced by us in a sequence of earlier papers. Here we derive upper bounds for non-time averaged outside probabilities…
We derive a general upper bound on the spreading rate of wavepackets in the framework of Schr\"odinger time evolution. Our result consists of showing that a portion of the wavepacket cannot escape outside a ball whose size grows dynamically…
We consider transport exponents associated with the dynamics of a wavepacket in a discrete one-dimensional quantum system and develop a general method for proving upper bounds for these exponents in terms of the norms of transfer matrices…
Lyapunov exponents describe the asymptotic behavior of the singular values of large products of random matrices. A direct computation of these exponents is however often infeasible. By establishing a link between Lyapunov exponents and an…
We consider periodic Jacobi operators and obtain upper and lower estimates on the sizes of the spectral bands. Our proofs are based on estimates on the logarithmic capacities and connections between the Chebyshev polynomials and logarithmic…
The Lieb-Robinson bound sets a theoretical upper limit on the speed at which information can propagate in non-relativistic quantum spin networks. In its original version, it results in an exponentially exploding function of the evolution…
The dynamics of a particle propagating in free space is described by its position and momentum, where quantum mechanics prohibits the simultaneous identification of two non-commutative physical quantities. Recently, a lower bound on the…
In this paper, we study the expectation of the operator norm of the random matrix (a_{ij} X_{ij}) for i,j <= n, under the assumption that the random variables (X_{ij}) are independent, symmetric and satisfy the moment growth condition…
We study Jacobi matrices that are uniformly approximated by periodic operators. We show that if the rate of approximation is sufficiently rapid, then the associated quantum dynamics are ballistic in a rather strong sense; namely, the…
Motivated by recent results in random matrix theory we will study the distributions arising from products of complex Gaussian random matrices and truncations of Haar distributed unitary matrices. We introduce an appropriately general class…
Controlling the spectral norm of the Jacobian matrix, which is related to the convolution operation, has been shown to improve generalization, training stability and robustness in CNNs. Existing methods for computing the norm either tend to…
We prove pointwise bounds for two-parameter families of Jacobi polynomials. Our bounds imply estimates for a class of functions arising from the spectral analysis of distinguished Laplacians and sub-Laplacians on the unit sphere in…
This paper is concerned with quadratic-exponential moments (QEMs) for dynamic variables of quantum stochastic systems with position-momentum type canonical commutation relations. The QEMs play an important role for statistical…
Quantum mechanics predicts that massive particles exhibit wave-like behavior. Matterwave interferometry has been able to validate such predictions through ground-breaking experiments involving microscopic systems like atoms and molecules.…
We consider multitype Markovian branching processes evolving in a Markovian random environment. To determine whether or not the branching process becomes extinct almost surely is akin to computing the maximal Lyapunov exponent of a sequence…
In the stochastic formulation of chemical kinetics, the stationary moments of the population count of species can be described via a set of linear equations. However, except for some specific cases such as systems with linear reaction…
The class of three-diagonal Jacobi matrix with exponentially increasing elements is considered. Under some assumptions the matrix corresponds to unbounded self-adjoint operator in the weighted space. The weight depends on elements of the…