Related papers: Phase Space Representation of the Density Operator…
As already known for nonrelativistic spinless particles, Bopp operators give an elegant and simple way to compute the dynamics of quasiprobability distributions in the phase space formulation of Quantum Mechanics. In this work, we present a…
The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…
Wigner's quasi-probability distribution function in phase-space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum transport in quantum optics; nuclear physics; decoherence (eg, quantum…
Relation between Bopp-Kubo formulation and Weyl-Wigner-Moyal symbol calculus, and non-commutative geometry interpretation of the phase space representation of quantum mechanics are studied. Harmonic oscillator in phase space via creation…
The Moyal quantization is described as a discretization of the classical phase space by using difference analogue of vector fields. Difference analogue of Lie brackets plays the role of Heisenberg commutators.
We present a quantum Monte-Carlo simulation for a pumped atom in a strong coupling cavity with dissipation, where two ordered spatial modes are formed for the atomic probability density, with the peaks distributed either only in the odd…
We present a phase space formulation of quantum mechanics in the Schr\"odinger representation and derive the associated Weyl pseudo-differential calculus. We prove that the resulting theory is unitarily equivalent to the standard…
Completely positive quantum operations are frequently discussed in the contexts of statistical mechanics and quantum information. They are customarily given by maps forming positive operator-values measures. To intuitively understand…
The primary motivation for Moyal's approach to quantum mechanics was to develop a phase space formalism for quantum phenomena by generalising the techniques of classical probability theory. To this end, Moyal introduced a quantum version of…
Motivated by some well-known results in the phase space description of quantum optics and quantum information theory, we aim to describe the formalism of quantum field theory by explicitly considering the holomorphic representation for a…
We review several procedures of quantization formulated in the framework of (classical) phase space M. These quantization methods consider Quantum Mechanics as a "deformation" of Classical Mechanics by means of the "transformation" of the…
We introduce the Gaussian quantum operator representation, using the most general multi-mode Gaussian operator basis. The representation unifies and substantially extends existing phase-space representations of density matrices for Bose…
Inspired by the fact that the Moyal quantization is related with nonlocal operation, I define a difference analogue of vector fields and rephrase quantum description on the phase space. Applying this prescription to the theory of the…
Deformation quantization (sometimes called phase-space quantization) is a formulation of quantum mechanics that is not usually taught to undergraduates. It is formally quite similar to classical mechanics: ordinary functions on phase space…
An operational time of arrival is introduced using a realistic position and momentum measurement scheme. The phase space measurement involves the dynamics of a quantum particle probed by a measuring device. For such a measurement an…
A formulation of quantum mechanics with additive and multiplicative (q-)difference operators instead of differential operators is studied from first principles. Borel-quantisation on smooth configuration spaces is used as guiding…
Phase spaces as given by the Wigner distribution function provide a natural description of infinite-dimensional quantum systems. They are an important tool in quantum optics and have been widely applied in the context of time-frequency…
We examine relationships between various quantization schemes for an electrically charged particle in the field of a magnetic monopole. Quantization maps are defined in invariant geometrical terms, appropriate to the case of nontrivial…
A Lie algebraic approach to the unitary transformations in Weyl quantization is discussed. This approach, being formally equivalent to the $\star$-quantization, is an extension of the classical Poisson-Lie formalism which can be used as an…
The paper provides an introduction into p-mechanics, which is a consistent physical theory suitable for a simultaneous description of classical and quantum mechanics. p-Mechanics naturally provides a common ground for several different…