相关论文: Upper bounds on wavepacket spreading for random Ja…
Many monostable reaction-diffusion equations admit one-dimensional travelling waves if and only if the wave speed is sufficiently high. The values of these minimum wave speeds are not known exactly, except in a few simple cases. We present…
We demonstrate for various systems that the variance of a wave packet $M(t)\propto t^\nu$, can show a {\it superballistic} increase with $2<\nu\le3$, for parametrically large time intervals. A model is constructed which explains this…
A central computational problem for analyzing and model checking various classes of infinite-state recursive probabilistic systems (including quasi-birth-death processes, multi-type branching processes, stochastic context-free grammars,…
A new method for the study of resonant behavior - using wave-packet dynamics - is presented, based on the powerful window operator technique. The method is illustrated and quantified by application to the astrophysically-important example…
In this paper we define distributions on moment spaces corresponding to measures on the real line with an unbounded support. We identify these distributions as limiting distributions of random moment vectors defined on compact moment spaces…
The properties of quantum mechanics with a discrete phase space are studied. The minimum uncertainty states are found, and these states become the Gaussian wave packets in the continuum limit. With a suitably chosen Hamiltonian that gives…
In the simple quantum hypothesis testing problem, upper bounds on the error probabilities are shown based on a key operator inequality between a density operator and its pinching. Concerning the error exponents, the upper bounds lead to a…
For the filtering of peaks in periodic signals, we specify polynomial filters that are optimally localized in space. The space localization of functions having an expansion in terms of orthogonal polynomials is thereby measured by a…
The Wegner orbital model is a class of random operators introduced by Wegner to model the motion of a quantum particle with many internal degrees of freedom (orbitals) in a disordered medium. We consider the case when the matrix potential…
Long-lasting quantum exponential spreading was recently found in a simple but very rich dynamical model, namely, an on-resonance double-kicked rotor model [J. Wang, I. Guarneri, G. Casati, and J. B. Gong, Phys. Rev. Lett. 107, 234104…
The stationary phase method is applied to diffusion by a potential barrier for an incoming wave packet with energies greater then the barrier height. It is observed that a direct application leads to paradoxical results. The correct…
For "static memory materials" the bulk properties depend on boundary conditions. Such materials can be realized by classical statistical systems which admit no unique equilibrium state. We describe the propagation of information from the…
We study the dynamics of an Airy wavepacket moving in a one-dimensional lattice potential. In contrast to the usual case of propagation in a continuum, for which such a wavepacket experiences a uniform acceleration, the lattice bounds its…
In Euclidean space there is a trivial upper bound on the maximum length of a compound "walk" built up of variable-length jumps, and a considerably less trivial lower bound on its minimum length. The existence of this non-trivial lower bound…
This work is devoted to almost sure and moment exponential stability of regime-switching jump diffusions. The Lyapunov function method is used to derive sufficient conditions for stabilities for general nonlinear systems; which further…
We consider solutions in frequency bands of dispersive equations on the line defined by Fourier multipliers, these solutions being considered as wave packets. In this paper, a refinement of an existing method permitting to expand…
We study a (1+1)-dimensional directed polymer in a random environment on the integer lattice with log-gamma distributed weights. Among directed polymers, this model is special in the same way as the last-passage percolation model with…
A randomized subspace action algorithm is investigated for fusion frame signal recovery problems. It is noted that Kaczmarz bounds provide upper bounds on the algorithm's error moments. The main question of which probability distributions…
This work analyzes accelerating and decelerating wall-driven flows by quantifying the upper bound of transient energy growth using a Lyapunov-type approach. By formulating the linearized Navier-Stokes equations as a linear time-varying…
Recent results in quantitative homogenisation of the wave equation with rapidly oscillating coefficients are discussed from the operator-theoretic perspective, which views the solution as the result of applying the operator of hyperbolic…