Abstract
We derive a continuity equation for the evolution of the SU(2) Wigner function under nonlinear Kerr evolution. We give explicit expressions for the resulting quantum Wigner current, and discuss the appearance of the classical limit. We show that the global structure of the quantum current significantly differs from the classical one, which is clearly reflected in the form of the corresponding stagnation lines.
Highlights
An ensemble of particles is described by a distribution function f (x, p|t) that depends on the phase-space variables x and p and evolves in time
Wρ (Ω|t) Wρ (Ω(−t)|0), where Ω(t) are classical trajectories generated by WH (Ω). It has been pointed out [16,17,18], that one can construct a Wigner current ‡ in such a way that the evolution can be mapped as a continuity equation very much analogous to (1.1)
The form of the current, and especially the behavior in the vicinity of its stagnation points, can be used for the characterization of the quantumness of the evolution. We extend these ideas to spinlike systems, where the classical phase space is the unit sphere
Summary
An ensemble of particles is described by a distribution function f (x, p|t) that depends on the phase-space variables x and p and evolves in time. Wρ (Ω|t) Wρ (Ω(−t)|0), where Ω(t) are classical trajectories generated by WH (Ω) It has been pointed out [16,17,18], that one can construct a Wigner current ‡ in such a way that the evolution can be mapped as a continuity equation very much analogous to (1.1). We will show, using the simplest example of nonlinear Kerr dynamics, that the global structure of the quantum Wigner current significantly differs from the classical one Such a difference is clearly observable even during the short-time evolution of semiclassical states (specified by localized distributions in phase space), when the Wigner distribution can still be well described in terms of the semiclassical approximation. An extra benefit of bringing the Wigner current into play is that it can give a compelling visual representation of how nonclassical features arise during the evolution
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
