wigner function harmonic oscillator
Società Italiana Di Fisica, IOS Press, Amsterdam (2005), Sellier, J.M., Nedjalkov, M., Dimov, I., Selberherr, S.: A benchmark study of the Wigner Monte-Carlo method. Learn more about Institutional subscriptions, Wigner, E.: On the quantum correction for thermodynamic equilibrium. This process is experimental and the keywords may be updated as the learning algorithm improves. Article 212.52.142.20. The most general form of the generators of such semigroups was given by Lindblad1. The Moyal equation for the harmonic oscillator has been presented as the wave equation of a 2D membrane in the phase plane.
http://www.nano-archimedes.com. This formalism has been studied for the case of damped harmonic oscillators2,3 and applied to various physical phenomena, for instance, to the damping of collective modes in deep inelastic collisions in nuclear physics4. 25A, 1113, Sofia, Bulgaria, You can also search for this author in Rev. Sellier, J.M., Dimov, I. Wigner functions, signed particles, and the harmonic oscillator. Its motion can be completely described by a point in the phase space – the two-dimensional space with the particle’s coordinate X and momentum P as dimensions (quadratures) [Fig.
On the one hand, one may see it as a short review effort to demonstrate the convenience of utilizing a phase-space approach in this particular context, suggesting that it could be the case again for different interesting problems. This work is, thus, twofold. © 2020 Springer Nature Switzerland AG. Phys. , it follows that (69) D ς (C) D τ = − ∫ 0 2 π d τ Δ J Ω α (x C (τ), k C (τ); β) k C (τ) = 0, since the integrand is an odd function on τ. 0
S`V"ã~Ôâ�B�°Ì=) 6OLÏs›ÉÈ^Œ=Ùc'hÔRt¶÷¾C#H9I«õ§xµAşœ `Z˜‹[Fí This service is more advanced with JavaScript available, Frontier Topics in Nuclear Physics By using the Wang-Uhlenbeck method, the Fokker-Planck equation, obtained from the master equation for the density operator, is solved for the Wigner distribution function, subject to either the Gaussian type or the $\delta$-function type of initial conditions. In this paper, we introduce the simple harmonic oscillator and we address it in the Wigner formulation of quantum mechanics, therefore describing the whole problem in terms of quasi-distribution functions defined over the phase-space. Part of Springer Nature. Immediate online access to all issues from 2019. 55–103. Wigner function representation for n=8 e xcited state of the harmonic oscillator in phase space with negatives values. Exercise 1: Choose different excited states of the harmonic oscillator and calculate the Wigner function. Not logged in J. Comput. Consider a classical harmonic oscillator. Phys. volume 14, pages907–915(2015)Cite this article. These discrete Wigner functions possess a number of properties similar to the Wigner function for a continuous quantum system such as the quantum harmonic oscillator. 40, 749–760 (1932), Article 45. - 213.108.198.204. Cite as. : The Wigner representation of quantum mechanics. Not affiliated The values of the Wigner function are equal to the deviation values of the points on the surface of the membrane from the equilibrium state. the dynamics out of equilibrium, although this topic is not addressed 273, 589–597 (2014), MathSciNet From Eq. Today 51, 22–28 (1998), Nedjalkov, M.: Wigner Transport in Presence of Phonons: Particle Models of the Electron Kinetics, From Nanostructures to Nanosensing Applications, vol. In this paper, we introduce the simple harmonic oscillator and we address it in the Wigner formulation of quantum mechanics, therefore describing the whole problem in terms of quasi-distribution functions defined over the phase-space.
pp 481-482 | https://doi.org/10.1007/s10825-015-0722-0, DOI: https://doi.org/10.1007/s10825-015-0722-0, Over 10 million scientific documents at your fingertips, Not logged in Phys. rotationally invariant functions in the phase-space, showing no evolution in time of the distribution function as expected. This is a preview of subscription content, © Springer Science+Business Media New York 1994, https://doi.org/10.1007/978-1-4615-2568-4_64.
one notices that the thermalized Wigner function does not depend explicitly on time, and thus W Ω α (x C (τ), k C (τ); β), the Wigner function whose arguments follow Eqs. 26, 311–327 (1983), Sellier, J.M. As an example, we consider the so-called su(2) oscillator model in dimension 2j+ 1, which is known to tend to the canonical oscillator when jtends to infinity. 313, 110–146 (2004), Tatarskii, V.I. Phys. These keywords were added by machine and not by the authors. According to the axiomatic theory of Lindblad1, the usual von Neumann-Liouville equation ruling the time evolution of closed quantum systems is replaced in the case of open systems by the following time-homogeneous quantum mechanical Markovian master equation for the density operator ρ: Over 10 million scientific documents at your fingertips. G. Bonchev Str. The harmonic oscillator with dissipation is studied within the framework of the Lindblad theory for open quantum systems. Rev. : Quantum mechanics as a statistical theory, vol. 160, pp. Journal of Computational Electronics New time dependent Wigner functions for the quantum harmonic oscillator have been obtained in this work. Subsequently, we outline the time-dependent signed particle Wigner Monte Carlo method and simulate the oscillator problem starting from stationary initial conditions, i.e. : Admissible states in quantum phase space.
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