Related papers: Visualizing quantum mechanics in phase space
In contrast to classical physics, the language of quantum mechanics involves operators and wave functions (or, more generally, density operators). However, in 1932, Wigner formulated quantum mechanics in terms of a distribution function…
The Wigner function plays a central role in QCD as a phase space object encoding correlations among quarks, antiquarks, and gluons, yet its interpretation remains subtle due to its quasiprobabilistic nature and possible negativity. Recent…
The dynamics of a quantum system following a sudden, highly non-adiabatic change of its control parameter (quantum quench) is studied with quasiclassical techniques. Recent works have shown, using exact quantum mechanical approach, that…
Conventional approach to quantum mechanics in phase space, (q,p), is to take the operator based quantum mechanics of Schrodinger, or and equivalent, and assign a c-number function in phase space to it. We propose to begin with a higher…
A quantum mechanical observer might be describable as having a reference system that is a superposition of classical inertial reference frames. The present paper suggests a possible weighting function in such superpositions, determined by…
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…
With approaching quantum/noncommutative models for the deep microscopic spacetime in mind, and inspired by our recent picture of the (projective) Hilbert space as the model of physical space behind basic quantum mechanics, we reformulate…
There are no phase-space trajectories for anharmonic quantum systems, but Wigner's phase-space representation of quantum mechanics features Wigner current~$\bf J$. This current reveals fine details of quantum dynamics -- finer than is…
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…
We consider the quantum mechanical equivalence of the Seiberg-Witten map in the context of the Weyl-Wigner-Groenewold-Moyal phase-space formalism in order to construct a quantum mechanics over noncommutative Heisenberg algebras. The…
A quantum state can be written in phase space, but the resulting object is not generally the probability density of a positive stochastic process on ordinary phase space. We spell this out for Wigner dynamics. If a positive phase-space…
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…
We present a reformulation of quantum mechanics in terms of probability measures and functions on a general classical sample space and in particular in terms of probability densities and functions on phase space. The basis of our proceeding…
We investigate the tomography of unknown unitary quantum processes within the framework of a finite-dimensional Wigner-type representation. This representation provides a rich visualization of quantum operators by depicting them as shapes…
Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…
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…
We perform a systematic study of the discrete time Quantum Walk on one dimension using Wigner functions, which are generalized to include the chirality (or coin) degree of freedom. In particular, we analyze the evolution of the negative…
We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime." We show that this covariant starting point makes…
The time dependence of one-dimensional quantum mechanical probability densities is presented when the potential in which a particle moves is suddenly changed, called a quench. Quantum quenches are mainly addressed but a comparison with…
Wigner function is a quasi-distribution that provides a representation of the state of a quantum mechanical system in the phase space of position and momentum. In this paper we find a relation between Wigner function and appropriate…