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Phase-space path-integral representation of the quantum density of states: Monte Carlo simulation of strongly correlated soft-sphere fermions.
Phys Rev E
February 2024
Joint Institute for High Temperatures RAS, Izhorskaya 13 Building 2, Moscow 125412, Russia.
The Wigner formulation of quantum mechanics is used to derive a path-integral representation of the quantum density of states (DOS) of strongly correlated fermions in the canonical ensemble. A path-integral Monte Carlo approach for the simulation of DOS and other thermodynamic functions is suggested. The derived Wigner function in the phase space resembles the Maxwell-Boltzmann distribution but allows for quantum effects.
View Article and Find Full Text PDFMatrix formulation of the Gaussian expansion of coherent multiple beams in arbitrary dimensions.
J Opt Soc Am A Opt Image Sci Vis
March 2024
Modeling the propagation of beams along laser beamlines is very challenging due to the multidimensional and multiscale configuration of the problem. Spatio-temporal couplings are particularly difficult to address with conventional numerical methods. Here we derive the Wigner function of a sum of Gaussian beams by calculating the multidimensional Fourier transform of the intercorrelation function of the fields.
View Article and Find Full Text PDFOperational Theories in Phase Space: Toy Model for the Harmonic Oscillator.
Phys Rev Lett
January 2022
Naturwissenschaftlich-Technische Fakultät, Universität Siegen, 57068 Siegen, Germany.
We show how to construct general probabilistic theories that contain an energy observable dependent on position and momentum. The construction is in accordance with classical and quantum theory and allows for physical predictions, such as the probability distribution for position, momentum, and energy. We demonstrate the construction by formulating a toy model for the harmonic oscillator that is neither classical nor quantum.
View Article and Find Full Text PDFA Classical Formulation of Quantum Theory?
Entropy (Basel)
January 2022
Department of Physics, Williams College, Williamstown, MA 01267, USA.
We explore a particular way of reformulating quantum theory in classical terms, starting with phase space rather than Hilbert space, and with actual probability distributions rather than quasiprobabilities. The classical picture we start with is epistemically restricted, in the spirit of a model introduced by Spekkens. We obtain quantum theory only by combining a of restricted classical pictures.
View Article and Find Full Text PDFA Divergence-Free Wigner Transform of the Boltzmann Operator Based on an Effective Frequency Theory.
J Phys Chem A
October 2021
Department of Chemistry and Molecular Biology, University of Gothenburg, SE 405 30 Gothenburg, Sweden.
The centroid effective frequency representation of path integrals as developed by Feynman and Kleinert was originally aimed at calculating partition functions and related quantities in the canonical ensemble. In its path integral formulation, only paths were relevant. This formulation has been used by the present authors in order to calculate the many-body Wigner function of the Boltzmann operator, which includes also open paths.
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