JournalsprimsVol. 31 , No. 4DOI 10.2977/prims/1195163914

The Quantum Weak Coupling Limit (II): Langevin Equation and Finite Temperature Case

  • Luigi Accardi

    Università di Roma Tor Vergata, Italy
  • Alberto Frigerio

    Università di Roma Tor Vergata, Italy
  • Yun G. Lu

    Beijing Normal University, China
The Quantum Weak Coupling Limit (II): Langevin Equation and Finite Temperature Case cover

Abstract

We complete the program started in [4] by proving that, in the weak coupling limit, the matrix elements, in the collective coherent vectors, of the Heisenberg evolved of an observable of a system coupled to a quasi-free reservoir through a laser type interaction, converge to the matrix elements of a quantum stochastic process satisfying a quantum Langevin equation driven by a quantum Brownian motion. Our results apply to an arbitrary quasi-free reservoir so, in particular, the finite temperature case is included.