Related papers: Boundaries and profiles in the Wigner formalism
The Wigner function of quantum systems is an effective instrument to construct the approximate classical description of the systems for which the classical approximation is possible. During the last time, the Wigner function formalism is…
In this dissertation the Weyl-Wigner approach is presented as a map between functions on a real cartesian symplectic vector space and a set of operators on a Hilbert space, to analyse some aspects of the relations between quantum and…
We analyze the quantum dynamics of a non-relativistic particle moving in a bounded domain of physical space, when the boundary conditions are rapidly changed. In general, this yields new boundary conditions, via a dynamical composition law…
In designing and optimizing new-generation nanomaterials and related quantum devices, dissipation versus decoherence phenomena are often accounted for via local scattering models, such as relaxation-time and Boltzmann-like schemes. Here we…
The problem of boundary behaviour at the origin of coordinates is discussed for D-dimensional Schrodinger equation in the framework of hyper spherical formalism, which have been often considered last time. We show that the Dirichlet…
The relativistic semi-classical approximation for a free massive particle is studied using the Wigner-Weyl formalism. A non-covariant Wigner function is proposed using the Newton-Wigner position operator. The perturbative solution for the…
We study the boundary behavior of solutions to the Dirichlet problems for integro-differential operators with order of differentiability $s \in (0, 1)$ and summability $p>1$. We establish a nonlocal counterpart of the Wiener criterion,…
In this paper, we propose two approaches to apply boundary conditions for bond-based peridynamic models. There has been in recent years a renewed interest in the class of so-called non-local models, which include peridynamic models, for the…
We analyze vacuum tunneling in quantum field theory in a general formalism by using the Wigner representation. In the standard instanton formalism, one usually approximates the initial false vacuum state by an eigenstate of the field…
The use of the Wigner function for the study of quantum transport in open systems present severe criticisms. Some of the problems arise from the assumption of infinite coherence length of the electron dynamics outside the system of…
In the present work the conditions appearing in the WKB approximation formalism of quantum mechanics are analyzed. It is shown that, in general, a careful definition of an approximation method requires the introduction of two length…
Robin (or mixed) boundary conditions in quantum mechanics have received considerable attention in the last two decades, in particular, for applications to nanoscale systems. However, their utility has remained obscure to the larger physics…
We investigate the role of external constraints in quantum field theory using the path integral formalism. We begin by reviewing the quantization of constrained systems and extend the analysis to cases where constraints are added to the…
In a configuration space whose boundary can be identified with a subset of its interior, a boundary condition can relate the behaviour of a function on the boundary and in the interior. Additionally, boundary values can appear as additive…
We discuss the role of boundary conditions in determining the physical content of the solutions of the Schrodinger equation. We study the standing-wave, the ``in,'' the ``out,'' and the purely outgoing boundary conditions. As well, we…
Contextuality is a necessary resource for universal quantum computation and non-contextual quantum mechanics can be simulated efficiently by classical computers in many cases. Orders of Planck's constant, $\hbar$, can also be used to…
Based on empirical evidence, quantum systems appear to be strictly linear and gauge invariant. This work uses concise mathematics to show that quantum eigenvalue equations on a one dimensional ring can either be gauge invariant or have a…
A phase space formulation of the filtering process upon an incident quantum state is developed. This formulation can explain the results of both quantum interference and delayed-choice experiments without making use of the controversial…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
We present a unified approach to quantum teleportation in arbitrary dimensions based on the Wigner-function formalism. This approach provides us with a clear picture of all manipulations performed in the teleportation protocol. In addition…