Related papers: Phase-space gaussian ensemble quantum camouflage
The von Neumann trace form of quantum statistical mechanics is transformed to an integral over classical phase space. Formally exact expressions for the resultant position-momentum commutation function are given. A loop expansion for wave…
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…
In this tutorial, we introduce the basic concepts and mathematical tools needed for phase-space description of a very common class of states, whose phase properties are described by Gaussian Wigner functions: the Gaussian states. In…
Non-classical states are of practical interest in quantum computing and quantum metrology. These states can be detected through their Wigner function negativity in some regions. In this paper, we calculate the ground state of the…
The phase-space formulation of quantum mechanics has recently seen increased use in testing quantum technologies, including metho ds of tomography for state verification and device validation. Here, an overview of quantum mechanics in phase…
The Wigner-Weyl isomorphism for quantum mechanics on a compact simple Lie group $G$ is developed in detail. Several New features are shown to arise which have no counterparts in the familiar Cartesian case. Notable among these is the notion…
Just as a coherent state may be considered as a quantum point, its restriction to a factor space of the full Hilbert space can be interpreted as a quantum plane. The overlap of such a factor coherent state with a full pure state is akin to…
In this first of a series of four articles, it is shown how a hamiltonian quantum dynamics can be formulated based on a generalization of classical probability theory using the notion of quasi-invariant measures on the classical phase space…
A nonequilibrium statistical operator method is developed for ensembles of particles obeying non-Hamiltonian equations of motion in classical phase space. The main consequences of non-zero compressibility of phase space are examined in…
Exact results are derived on the averaged dynamics of a class of random quantum-dynamical systems in continuous space. Each member of the class is characterized by a Hamiltonian which is the sum of two parts. While one part is…
The quasilinear theory of the Wigner-Poisson system in one spatial dimension is examined. Conservation laws and properties of the stationary solutions are determined. Quantum effects are shown to manifest themselves in transient periodic…
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…
A quasi-Gaussian quantum superposition of Ho\v{r}ava-Lifshitz (HL) stationary states is built in order to describe the transition of the quantum cosmological problem to the related classical dynamics. The obtained HL phase-space superposed…
We apply the generalized Wigner function formalism to detect and characterize a range of quantum phase transitions in several cyclic, finite-length, spin-$\frac{1}{2}$ one-dimensional spin-chain models, viz., the Ising and anisotropic $XY$…
The quantum evolution of the Wigner function for Gaussian wave packets generated by a non-Hermitian Hamiltonian is investigated. In the semiclassical limit $\hbar\to 0$ this yields the non-Hermitian analog of the Ehrenfest theorem for the…
General statistical ensembles in the Hamiltonian formulation of hybrid quantum-classical systems are analyzed. It is argued that arbitrary probability densities on the hybrid phase space must be considered as the class of possible…
We formulate, with full generality, the asymptotic estimation theory for Gaussian states in terms of their first and second moments. By expressing the quantum Fisher information (QFI) and the elusive symmetric logarithmic derivative (SLD)…
Non-Gaussian correlations in a pure state are inextricably linked with non-classical features, such as a non positive-definite Wigner function. In a commonly used simulation technique in ultracold atoms and quantum optics, known as the…
In the second part of this paper in micro canonical ensemble the new numerical approach for consideration of quantum dynamics and calculations of the average values of quantum operators and time correlation functions in the Wigner…
The time evolution of the Wigner function for Gaussian states generated by Lindblad quantum dynamics is investigated in the semiclassical limit. A new type of phase-space dynamics is obtained for the centre of a Gaussian Wigner function,…