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Conjugate measurements, equilibration and emergent classicality

S. Adarsh, P. N. Bala Subramanian, Sreeraj T. P

Abstract

Simultaneous decoherence of conjugate observables of an open quantum system leads to a classical statistical mechanical description with constant phase space probability density in terms of a uniform ensemble. We investigate a scenario where this may be realized by measurement of basic conjugate observables of a quantum system by the environment.

Conjugate measurements, equilibration and emergent classicality

Abstract

Simultaneous decoherence of conjugate observables of an open quantum system leads to a classical statistical mechanical description with constant phase space probability density in terms of a uniform ensemble. We investigate a scenario where this may be realized by measurement of basic conjugate observables of a quantum system by the environment.

Paper Structure

This paper contains 5 sections, 17 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Equilibration, open quantum systems and quantum decoherence
  3. Conjugate measurements, classicality and equal apriori probabilities.
  4. An illustrative example
  5. Conclusion

Figures (1)

  • Figure 1: Graphical depiction of the time evolution of reduced density matrix for a particle with environment interaction of the form (\ref{['hint']}). Initial wavefunctions of the system and both the environments are chosen to be Gaussians with standard deviation of $1$. Units are chosen such that $\hbar$ is set to 1. The contour plot (a) and (b) shows the time evolution of $|\rho_s(x,\bar{x})|$ and $|\rho_s(p,\bar{p})|$ respectively.