Three approaches to classical thermal field theory

Gozzi, E.; Penco, Riccardo

doi:10.1016/j.aop.2010.11.018

Cited by 12 publications

(9 citation statements)

References 42 publications

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“…Modern developments and applications of the Koopman-von Neumann classical mechanics can be found in, e.g., Refs. [38,39,48,[54][55][56][57][58][59][60][61][62][63][64][65][66][67].…”

Section: Open Systemsmentioning

confidence: 99%

Efficient method to generate time evolution of the Wigner function for open quantum systems

et al. 2015

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The Wigner function is a useful tool for exploring the transition between quantum and classical dynamics, as well as the behavior of quantum chaotic systems. Evolving the Wigner function for open systems has proved challenging however; a variety of methods have been devised but suffer from being cumbersome and resource intensive. Here we present an efficient fast-Fourier method for evolving the Wigner function, that has a complexity of O(N log N ) where N is the size of the array storing the Wigner function. The efficiency, stability, and simplicity of this method allows us to simulate open system dynamics previously thought to be prohibitively expensive. As a demonstration we simulate the dynamics of both one-particle and two-particle systems under various environmental interactions. For a single particle we also compare the resulting evolution with that of the classical Fokker-Planck and Koopman-von Neumann equations, and show that the environmental interactions induce the quantum-to-classical transition as expected. In the case of two interacting particles we show that an environment interacting with one of the particles leads to the loss of coherence of the other.

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“…Modern developments and applications of the Koopman-von Neumann classical mechanics can be found in, e.g., Refs. [38,39,48,[54][55][56][57][58][59][60][61][62][63][64][65][66][67].…”

Section: Open Systemsmentioning

confidence: 99%

Efficient method to generate time evolution of the Wigner function for open quantum systems

et al. 2015

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“…(The Koopman-von Neumann approach has been extended to classical field theories in Refs. [17,19,20]. )…”

Section: Classical Field Theorymentioning

confidence: 99%

“…Koopman and von Neumann [4,5] pioneered the recasting of classical mechanics in a form similar to quantum mechanics by introducing classical complex valued wave functions and representing associated physical observables by means of commuting self-adjoint operators (for modern developments and applications see Refs. [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]). Our operational formulation is closely related to the approach proposed in Ref.…”

mentioning

confidence: 99%

Operational Dynamic Modeling Transcending Quantum and Classical Mechanics

et al. 2012

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We introduce a general and systematic theoretical framework for operational dynamic modeling (ODM) by combining a kinematic description of a model with the evolution of the dynamical average values. The kinematics includes the algebra of the observables and their defined averages. The evolution of the average values is drawn in the form of Ehrenfest-like theorems. We show that ODM is capable of encompassing wide-ranging dynamics from classical non-relativistic mechanics to quantum field theory. The generality of ODM should provide a basis for formulating novel theories.

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“…We will show in this paper that the answer lies in the classic works of Koopman [9], von Neumann [10] and later others [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25]. Sudarshan [26] developed a complete theory of Classical Mechanics (CM) based on Hilbert spaces associated with commuting hermitian operators as observables (hereinafter referred to as the KvNS theory).…”

Section: Introductionmentioning

confidence: 99%

Hilbert space theory of classical electrodynamics

Rajagopal

Ghose

2016

Pramana - J Phys

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Classical electrodynamics is reformulated in terms of wave functions in the classical phase space of electrodynamics, following the Koopman-von Neumann-Sudarshan prescription for classical mechanics on Hilbert spaces sans the superselection rule which prohibits interference effects in classical mechanics. This is accomplished by transforming from a set of commuting observables in one Hilbert space to another set of commuting observables in a larger Hilbert space. This is necessary to clarify the theoretical basis of much recent work on quantum-like features exhibited by classical optics. Furthermore, following Bondar et al (Phys.Rev. A 88, 052108, (2013)), it is pointed out that quantum processes that preserve the positivity or nonpositivity of the Wigner function can be implemented by classical optics. This may be useful in interpreting quantum information processing in terms of classical optics.

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Three approaches to classical thermal field theory

Cited by 12 publications

References 42 publications

Efficient method to generate time evolution of the Wigner function for open quantum systems

Efficient method to generate time evolution of the Wigner function for open quantum systems

Operational Dynamic Modeling Transcending Quantum and Classical Mechanics

Hilbert space theory of classical electrodynamics

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