Related papers: Egorov's theorem in the Weyl--H\"ormander calculus
The notion of a continuous $G$-action on a topological space readily generalizes to that of a continuous $D$-action, where $D$ is any small category. Dror Farjoun and Zabrodsky introduced a generalized notion of orbit, which is key to…
We consider the quantum mechanical propagator for a particle moving in a $d$-dimensional Lorentz gas, with fixed, hard sphere scatterers. To evaluate this propagator in the semi-classical region, and for times less than the Ehrenfest time,…
We develop a phase-space framework for fractional generalised anharmonic oscillators and their heat semigroups on weighted modulation spaces. We consider operators of the form \[ \mathcal{H}_{k,l}=(-\Delta)^{l}+V(x), \] where $V$ is a…
The classical unified theory of Weyl is revisited. The possibility of stable extended electron model in the Einstein-Weyl space is suggested.
The formalism of generalized Wigner transformations developped in a previous paper, is applied to kinetic equations of the Lindblad type for quantum harmonic oscillator models. It is first applied to an oscillator coupled to an equilibrium…
We show uniform-in-time propagation of algebraic and stretched exponential moments for the Becker-D\"oring equations. Our proof is based upon a suitable use of the maximum principle together with known rates of convergence to equilibrium.
We discuss the r\^ole of quantum deformation of Weyl-Heisenberg algebra in dissipative systems and finite temperature systems. We express the time evolution generator of the damped harmonic oscillator and the generator of thermal Bogolubov…
We show a result on propagation of the anisotropic Gelfand--Shilov wave front set for linear operators with Schwartz kernel which is a Gelfand--Shilov ultradistribution of Beurling type. This anisotropic wave front set is parametrized by…
We study generalized solutions of an evolutionary equation related to some densely defined skew-symmetric operator in a real Hilbert space. We establish existence of a contractive semigroup, which provides generalized solutions, and suggest…
We consider an open quantum system which contains unstable states. The time evolution of the system can be described by an effective non-hermitian Hamiltonian H_{eff}, in accord with the Wigner--Weisskopf approximation, and an additional…
The propagation of electrons in static and uniform electromagnetic fields is a standard topic of classical electrodynamics. The Hamilton function is given by a quadratic polynomial in the positions and momenta. The corresponding…
We study propagation of the Gabor wave front set for a Schr\"odinger equation with a Hamiltonian that is the Weyl quantization of a quadratic form with non-negative real part. We point out that the singular space associated to the quadratic…
We show that the phase-space formulation of general probabilistic theories can be extended to include a generalized time-evolution and that it can describe a nonquantum hydrogen-like system which is stable, has discrete energy levels, and…
Optimal realizations of quantum technology tasks lead to the necessity of a detailed analytical study of the behavior of a $d$-level quantum system (qudit) under a time-dependent Hamiltonian. In the present article, we introduce a new…
In this paper, we find the quantum propagator for a general time-dependent quadratic Hamiltonian. The method is based on the properties of the propagator and the fact that the quantum propagator fulfills two independent partial differential…
The extension of the phase-space Weyl-Wigner quantum mechanics to the subset of Hamiltonians in the form of $H(q,\,p) = {K}(p) + {V}(q)$ (with $K(p)$ replacing single $p^2$ contributions) is revisited. Deviations from classical and…
Generalized Weyl quantization formalism for the cylindrical phase space $S^1 \times \mathbb{R}^1$ is developed. It is shown that the quantum observables relevant to the phase of linear harmonic oscillator or electromagnetic field can be…
A propagation method for time-dependent Schr\"odinger equations with an explicitly time-dependent Hamiltonian is developed where time ordering is achieved iteratively. The explicit time-dependence of the time-dependent Schr\"odinger…
The paper describes a new approach to global smoothing problems for dispersive and non-dispersive evolution equations based on the global canonical transforms and the underlying global microlocal analysis. For this purpose, the Egorov-type…
The Weyl-Heisenberg symmetries originate from translation invariances of various manifolds viewed as phase spaces, e.g. Euclidean plane, semi-discrete cylinder, torus, in the two-dimensional case, and higher-dimensional generalisations. In…