Related papers: Time Dependent Quantum Perturbations Uniform in th…
An important class of resonance problems involves the study of perturbations of systems having embedded eigenvalues in their continuous spectrum. Problems with this mathematical structure arise in the study of many physical systems, e.g.…
Gaussian quantum systems exhibit many explicitly quantum effects but can be simulated classically. Using both the Hilbert space (Koopman) and the phase-space (Moyal) formalisms we investigate how robust this classicality is. We find…
We general-quantize the dynamics of the quantum harmonic oscillator to obtain a covariant finite quantum dynamics in a finite quantum time. The usual central (``superselected'') time results from a self-organization. Unitarity necessarily…
Standard derivations of ``time-independent perturbation theory'' of quantum mechanics cannot be applied to the general case where potentials are energy dependent or where the inverse free Green function is a non-linear function of energy.…
Time evolution of a perturbed thermal state is studied in a quantum-mechanical system with O(N) symmetry. In the limit of large N, time dependence of O(N)-singlet expectation values can be described by classical equations of motion in a…
Corresponding to two ways of realizing the q-deformed Heisenberg algebra by the undeformed variables there are two q-perturbative Hamiltonians with the additional momentum-dependent interactions, one originates from the perturbative…
We investigate the quantum dynamics of many-body systems subject to local, i.e. restricted to a limited space region, time-dependent perturbations. If the perturbation drives the system across a quantum transition, an off-equilibrium…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
Branching flow -- a phenomenon known for steady wave propagation in two-dimensional weak correlated random potential is also present in the time-dependent Schr\"odinger equation for a single particle in one dimension, moving in a…
We establish Lieb-Thirring type inequalities for non self-adjoint relatively compact perturbations of certain operators of mathematical physics. We apply our results to quantum Hamiltonians of Schr{\"o}dinger and Pauli with constant…
We consider nonlinear Schrodinger equations with either local or nonlocal nonlinearities. In addition, we include periodic potentials as used, for example, in matter wave experiments in optical lattices. By considering the corresponding…
We consider the semiclassical Schr\"odinger equation on a compact negatively curved surface. For any sequence of initial data microlocalized on the unit cotangent bundle, we look at the quantum evolution (below the Ehrenfest time) under…
We consider time-dependent perturbations which are relatively bounded with respect to the square root of an unperturbed Hamiltonian operator, and whose commutator with the latter is controlled by the full perturbed Hamiltonian. The…
We study the classical and quantum perturbation theory for two non--resonant oscillators coupled by a nonlinear quartic interaction. In particular we analyze the question of quantum corrections to the torus quantization of the classical…
We investigate quench dynamics in a one-dimensional spin model, comparing both quantum and classical descriptions. Our primary focus is on the different timescales involved in the evolution of the observables as they approach statistical…
We study the universal fluctuations of the Wigner-Smith time delay for systems which exhibit chaotic dynamics in their classical limit. We present a new derivation of the semiclassical relation of the quantum time delay to properties of the…
In the process of work it has been found that space-time quantum fluctuations are naturally described in terms of the deformation parameter introduced on going from the well-known quantum mechanics to that at Planck scales and put forward…
We consider the classical obstacle problem on bounded, connected Lipschitz domains $D \subset \mathbb{R}^n$. We derive quantitative bounds on the changes to contact sets under general perturbations to both the right hand side and the…
This paper examines the variance of quantum and classical predictions in the quantum realm, as well as unexpected presence and absence of variances. Some features are found that share an indirect commonality with the Aharonov-Bohm and…
A formalism is developed for describing approximate classical behaviour in finite (but possibly large) quantum systems. This is done in terms of a structure common to classical and quantum mechanics, viz. a Poisson space with a transition…