Related papers: Propagation of Quantum Expectations with Husimi Fu…
We consider the Schr\"odinger equation with a Hamiltonian given by a second order difference operator with nonconstant growing coefficients, on the half one dimensional lattice. This operator appeared first naturally in the construction and…
We investigate quantum effects in the evolution of general systems. For studying such temporal quantum phenomena, it is paramount to have a rigorous concept and profound understanding of the classical dynamics in such a system in the first…
Projection operators arise naturally as one-particle density operators associated to Slater determinants in fields such as quantum mechanics and the study of determinantal processes. In the context of the semiclassical approximation of…
Consistent quantum formalism based on the localized basis of the Wannirer functions in Heisenberg and Schrodinger pictures to describe propagation of electromagnetic field in a three dimensional media including diffraction is presented. In…
The quantum mechanical time-evolution is studied for a particle under the influence of an explicitly time-dependent rotating potential. We discuss the existence of the propagator and we show that in the limit of rapid rotation it converges…
We extend our earlier "virtual detector" method [X. Wang, J. Tian, and J. H. Eberly, Phys. Rev. Lett. 110, 243001 (2013)], a hybrid quantum mechanical and classical trajectory method, to include phases in the classical trajectories. Effects…
We study the properties of quasi-distributions or Wigner measures in the context of noncommutative quantum mechanics. In particular, we obtain necessary and sufficient conditions for a phase-space function to be a noncommutative Wigner…
We consider elliptic second order partial differential operators with Lipschitz continuous leading order coefficients on finite cubes and the whole Euclidean space. We prove quantitative sampling and equidistribution theorems for…
We present a method for calculating expectation values of operators in terms of a corresponding c-function formalism which is not the Wigner--Weyl position-momentum phase-space, but another space. Here, the quantity representing the quantum…
Derivation of two-time second-order correlation function by following approaches such as stochastic differential equation, coherent-state propagator, and quasi-statistical distribution function is presented. In the process, the time…
Time-dependent quantum mechanics provides an intuitive picture of particle propagation in external fields. Semiclassical methods link the classical trajectories of particles with their quantum mechanical propagation. Many analytical results…
In this paper we consider Schr\"odinger equations with sublinear dispersion relation on the one-dimensional torus $\T := \R /(2 \pi \Z)$. More precisely, we deal with equations of the form $\partial_t u = \ii {\cal V}(\omega t)[u]$ where…
In this second in a series of four articles we create a mathematical formalism sufficient to represent nontrivial hamiltonian quantum dynamics, including resonances. Some parts of this construction are also mathematically necessary. The…
Using a simple geometrical construction based upon the linear action of the Heisenberg--Weyl group we deduce a new nonlinear Schr\"{o}dinger equation that provides an exact dynamic and energetic model of any classical system whatsoever, be…
We investigate the formulation of work distributions for quantum scalar fields in static curved spacetimes by extending the Ramsey interferometric protocol originally developed in previous works for flat spacetimes. The use of Unruh-DeWitt…
Quantum-statistical effects occur during the propagation of electromagnetic (EM) waves inside the dielectric media or metamaterials, which include a large class of nanophotonic and plasmonic waveguides with dissipation and noise. Exploiting…
The quantum mechanical version of the four kinds of classical canonical transformations is investigated by using non-hermitian operator techniques. To help understand the usefulness of this appoach the eigenvalue problem of a harmonic…
We construct, analytically and numerically, the Wigner distribution functions for the exact solutions of position-dependent effective mass Schr\"odinger equation for two cases belonging to the generalized Laguerre polynomials. Using a…
We study the semiclassical time evolution of observables given by matrix valued pseudodifferential operators and construct a decomposition of the Hilbert space $L^2(\rz^d)\otimes\kz^n$ into a finite number of almost invariant subspaces. For…
Building on work on Miura's transformation by Kappeler, Perry, Shubin, and Topalov, we develop a detailed spectral theoretic treatment of Schr\"odinger operators with matrix-valued potentials, with special emphasis on distributional…