Modified spectral method in phase space: Calculation of the Wigner function. II. Generalizations

Hug, M.; Menke, Christoph; Schleich, Wolfgang P.

doi:10.1103/physreva.57.3206

Cited by 13 publications

(4 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[56], is more efficient and easier to maintain than the one in Refs. [58,59]. Figures 2(a) and 2(b) show the Wigner functions of ground and first exited states, respectively, for the Mexican hat potential.…”

Section: Wigner Functions Of Pure Stationary Statesmentioning

confidence: 99%

Efficient computations of quantum canonical Gibbs state in phase space

et al. 2016

View full text Add to dashboard Cite

The Gibbs canonical state, as a maximum entropy density matrix, represents a quantum system in equilibrium with a thermostat. This state plays an essential role in thermodynamics and serves as the initial condition for nonequilibrium dynamical simulations. We solve a long standing problem for computing the Gibbs state Wigner function with nearly machine accuracy by solving the Bloch equation directly in the phase space. Furthermore, the algorithms are provided yielding high quality Wigner distributions for pure stationary states as well as for Thomas-Fermi and Bose-Einstein distributions. The developed numerical methods furnish a long-sought efficient computation framework for nonequilibrium quantum simulations directly in the Wigner representation.

show abstract

Section: Wigner Functions Of Pure Stationary Statesmentioning

confidence: 99%

Efficient computations of quantum canonical Gibbs state in phase space

et al. 2016

View full text Add to dashboard Cite

show abstract

“…Among the several phase-space representations discussed in the literature, the Weyl-Wigner representation has come to play the role of a canonical phase-space representation, because of its simplicity [1,2]. As has been justified in previous work [3][4][5], it may be considered a representation in its own right. This fact makes it interesting to apply physical intuition to the form and behavior of the Wigner functions, just as physical intuition may be applied to the form and behavior of wavefunctions.…”

Section: The Weyl-wigner Representationmentioning

confidence: 99%

An elementary aspect of the Weyl‐Wigner representation

Dahl¹,

Schleich²

2003

Fortschritte der Physik

View full text Add to dashboard Cite

show abstract

“…First of all, the classical propagation in time requires a solution of a partial differential equation for a continuous distribution function in classical phase space. [20][21][22] Hence, the vast majority of existing quasiclassical numerical studies of ͑photoin-duced͒ reaction dynamics has been limited to the case of initial states of Gaussian shape thus excluding interesting quantum effects connected with delocalized initial molecular states, e.g., of vibrationally or rotationally excited states. Instead, the ubiquituous trajectory approach employs Monte Carlo sampling of the phase-space distribution by deltalike points and propagation of the corresponding trajectories.…”

Section: Introductionmentioning

confidence: 99%

Multidimensional classical Liouville dynamics with quantum initial conditions

Horenko

Schmidt

Schütte

2002

The Journal of Chemical Physics

View full text Add to dashboard Cite

A simple and numerically efficient approach to Wigner transforms and classical Liouville dynamics in phase space is presented. ͑1͒ The Wigner transform can be obtained with a given accuracy by optimal decomposition of an initial quantum-mechanical wave function in terms of a minimal set of Gaussian wave packets. ͑2͒ The solution of the classical Liouville equation within the locally quadratic approximation of the potential energy function requires a representation of the density in terms of an ensemble of narrow Gaussian phase-space packets. The corresponding equations of motion can be efficiently solved by a modified leap-frog integrator. For both problems the use of Monte Carlo based techniques allows numerical calculation in multidimensional cases where grid-based methods such as fast Fourier transforms are prohibitive. In total, the proposed strategy provides a practical and efficient tool for classical Liouville dynamics with quantum-mechanical initial states.

show abstract

Modified spectral method in phase space: Calculation of the Wigner function. II. Generalizations

Cited by 13 publications

References 4 publications

Efficient computations of quantum canonical Gibbs state in phase space

Efficient computations of quantum canonical Gibbs state in phase space

An elementary aspect of the Weyl‐Wigner representation

Multidimensional classical Liouville dynamics with quantum initial conditions

Contact Info

Product

Resources

About