1 / 15

Classical evolution of quantum fluctuations in spin-like systems

This article explores the classical evolution of quantum fluctuations in spin-like systems using the phase space formulation. It discusses the invertible map, density matrix, Wigner function, spin operators, semiclassical limit, evolution equations, initial states, observables, and generation of squeezed and entangled states.

chollenbeck
Download Presentation

Classical evolution of quantum fluctuations in spin-like systems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Classical evolution of quantum fluctuations in spin-like systems Andrei B. Klimov

  2. Phase space formulation for spin-like sistems Invertible map: - Weyl simbol, is the kernel operator so that Density matrix Wigner function Stratonovich 1956, Agarwal 1971

  3. Spin operators - generators of 2S+1 dim irrep of su(2) algebra Semiclassical limit: Evolution equation quantum corrections - Weyl symbol of the Hamiltonian - Poisson brackets on

  4. Correspondence rules in limit

  5. Semiclassical dynamics of quantum systems Evolution equation: Solution: Each point of the initial distribution evolves along classical trajectories Initial states: localized states for which the norm of quantum corrections is small Evolution of observables:

  6. Ehrenfest equations in limit integration by parts averaged Heisenberg equations Second order spin Hamiltonians semiclassical evolution time:

  7. Quasiclassical description of squeezed states on the sphere Generation of squeezed states - non-linear evolution

  8. Evolution equation for Loiuville equation, Classical evolution of the Wigner function - classical trajectories Initial coherent state on the equator:

  9. Wigner evolution and semiclassical evolution: Evolution of the angle of minimal fluctations and from semiclassical approximation, S=50

  10. Quasiclassical evolution of entangled satates on the sphere Consider two quantum systems H1y H2 Factorized states: Entangled states: Phase space represenatation: Maximally entangled states pure states and - plane distribution

  11. Example: and Entangled state: Factorized state: (pure states) Systems of dimension N: - factorized state - maximilly entangled state

  12. Generation of entangled states Factorized state nonlocal interactions Entangled state Hamiltonian: H1 • classical evolution • Entanglement classical evolution H2

  13. Semiclassical orrespondence rules,

  14. Example: Semiclassical initial state: where are coherent states on equator Evolution equation in semiclassical limit: Solution where

More Related