Related papers: Quantum Distributions for the Plane Rotator
A gauge-invariant Wigner quasi-distribution function for charged particles in classical electromagnetic fields is derived in a rigorous way. Its relation to the axial gauge is discussed, as well as the relation between the kinetic and…
We study decoherence, diffusion, friction, and how they thermalize a planar rotor in the presence of an external potential. Representing the quantum master equation in terms of auxiliary Wigner functions in periodic phase space not only…
Interactions between charged particles and light occur in real space and time, yet quantum field theory usually describes them in momentum space. Whereas this approach is well suited for calculating emission probabilities and cross…
Quantum mechanics is often developed in the position representation, but this is not necessary, and one can perform calculations in a representation-independent fashion, even for wavefunctions. In this work, we illustrate how one can…
Focusing particularly on one-qubit and two-qubit systems, I explain how the quantum state of a system of n qubits can be expressed as a real function--a generalized Wigner function--on a discrete 2^n x 2^n phase space. The phase space is…
We calculate the Wigner quasiprobability distribution function of quantum elliptical vortex in elliptical beam (EEV), produced by coupling squeezed coherent states of two modes. The coupling between the two modes is performed by using beam…
We shall revisit the conventional treatment of open quantum devices based on the Wigner-Function formalism. Our analysis will show that the artificial spatial separation between device active region and external reservoirs -properly defined…
A quantum version of transition state theory based on a quantum normal form (QNF) expansion about a saddle-centre-...-centre equilibrium point is presented. A general algorithm is provided which allows one to explictly compute QNF to any…
Thermal fluctuations in time-dependent quantum processes are treated by a constant-temperature generalization of Wigner's formulation of quantum mechanics in phase space. To this end, quantum Nos\`e-Hoover dynamics is defined by…
We prove a formula expressing the gradient of the phase function of a function $f: \mathbb R^d \mapsto \mathbb C$ as a normalized first frequency moment of the Wigner distribution for fixed time. The formula holds when $f$ is the Fourier…
Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert…
Quantum statistical mechanics is formulated as an integral over classical phase space. Some details of the commutation function for averages are discussed, as is the factorization of the symmetrization function used for the grand potential…
Drawing inspiration from Dirac's work on functions of non commuting observables, we develop a fresh approach to phase space descriptions of operators and the Wigner distribution in quantum mechanics. The construction presented here is…
We study a class of phase-space distribution functions that is generated from a Gaussian convolution of the Wigner distribution function. This class of functions represents the joint count probability in simultaneous measurements of…
We formulate and argue in favor of the following conjecture: There exists an intimate connection between Wigner's quantum mechanical phase space distribution function and classical Fresnel optics.
We derive a quantum version of the classical-optics Wiener-Khintchine theorem within the framework of detection of phase-space displacements with a suitably designed quantum ruler. A phase-pace based quantum mutual coherence function is…
Systems built out of N-body interactions, beyond 2-body interactions, are formulated on the plane, and investigated classically and quantum mechanically (in phase space). Their Wigner Functions--the density matrices in phase-space…
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 develop a dynamical theory, based on a system of ordinary differential equations describing the motion of particles which reproduces the results of quantum mechanics. The system generalizes the Hamilton equations of classical mechanics…
Special stochastic representation of the wave function in Quantum Mechanics (QM), based on soliton realization of extended particles, is suggested with the aim to model quantum states via classical computer. Entangled solitons construction…