Coherent-state path-integral calculation of the Wigner function

Samson, J. H.

doi:10.1088/0305-4470/33/29/306

Cited by 2 publications

(3 citation statements)

References 37 publications

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“…For completeness, we note that Samson [12,13], and Scully and Wódkiewicz [14], made use of a similar characteristic function argument to generate Wigner functions with a phase space parametrized by three degrees of freedom. Their Wigner functions were generated by a kernel that was the Fourier transform of a characteristic function kernel.…”

Section: B Su(2) and Orbital Angular Momentum Statesmentioning

confidence: 99%

“…These two classical distributions, being two-dimensional Fourier transforms of each other are, are naturally complementary and extremely powerful. There have been numerous attempts to bring to general quantum systems a similar framework -each of which have suffered from issues such as being informationally incomplete or being singular in nature (see, for example, [11][12][13][14][15]). In this work we describe how, by taking account of the underlying group structure, we can use a single general approach to quantum mechanics as a statistical theory that resolves these * m.j.everitt@physics.org issues.…”

Section: Introductionmentioning

confidence: 99%

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General approach to quantum mechanics as a statistical theory

et al. 2019

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Since the very early days of quantum theory there have been numerous attempts to interpret quantum mechanics as a statistical theory. This is equivalent to describing quantum states and ensembles together with their dynamics entirely in terms of phase-space distributions. Finite dimensional systems have historically been an issue. In recent works [Phys. Rev. Lett. 117, 180401 and Phys. Rev. A 96, 022117] we presented a framework for representing any quantum state as a complete continuous Wigner function. Here we extend this work to its partner function -the Weyl function. In doing so we complete the phase-space formulation of quantum mechanics -extending work by Wigner, Weyl, Moyal, and others to any quantum system. This work is structured in three parts. Firstly we provide a brief modernized discussion of the general framework of phasespace quantum mechanics. We extend previous work and show how this leads to a framework that can describe any system in phase space -putting it for the first time on a truly equal footing to Schrödinger's and Heisenberg's formulation of quantum mechanics. Importantly, we do this in a way that respects the unifying principles of "parity" and "displacement" in a natural broadening of previously developed phase space concepts and methods. Secondly we consider how this framework is realized for different quantum systems; in particular we consider the proper construction of Weyl functions for some example finite dimensional systems. Finally we relate the Wigner and Weyl distributions to statistical properties of any quantum system or set of systems.

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Section: B Su(2) and Orbital Angular Momentum Statesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

General approach to quantum mechanics as a statistical theory

et al. 2019

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“…The present author has previously shown a correspondence between the pathcentroid distribution and the Wigner function W (S) for components of a free spin s [16,17]. This is a singular distribution, with derivatives of delta functions supported on spheres of quantized radius.…”

Section: Introductionmentioning

confidence: 58%

Phase-space path-integral calculation of the Wigner function

Samson¹

2003

J. Phys. A: Math. Gen.

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The Wigner function W (q, p) is formulated as a phase-space path integral, whereby its sign oscillations can be seen to follow from interference between the geometrical phases of the paths. The approach has similarities to the path-centroid method in the configuration-space path integral. Paths can be classified by the midpoint of their ends; short paths where the mid-point is close to (q, p) and which lie in regions of low energy (low P function of the Hamiltonian) will dominate, and the enclosed area will determine the sign of the Wigner function. As a demonstration, the method is applied to a sequence of density matrices interpolating between a Poissonian number distribution and a number state, each member of which can be represented exactly by a discretized path integral with a finite number of vertices. Saddle point evaluation of these integrals recovers (up to a constant factor) the WKB approximation to the Wigner function of a number state.

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Coherent-state path-integral calculation of the Wigner function

Cited by 2 publications

References 37 publications

General approach to quantum mechanics as a statistical theory

General approach to quantum mechanics as a statistical theory

Phase-space path-integral calculation of the Wigner function

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