Quantum State Diffusion Theory (QSD)

Walter T. Strunz, Ian Colin Percival

Quantum state diffusion (QSD) provides a natural unravelling of a mixed-state open quantum system into component pure states. We investigate the semiclassical limit of QSD in a phase-space approach using the Wigner function. As , QSD exhibits two very different dynamical regimes, depending on the volume of phase space covered by the quantum state. For large volumes there is a localization regime represented by classical nonlinear and nonlocal diffusion processes. For small volumes, comparable in size with a Planck cell, there is a wavepacket regime . Here, the centroid of the wavepacket follows a classical Langevin equation, obtained through the adiabatic elimination of the dynamics of the second-order moments of the wavepacket. The corresponding Fokker-Planck equation is identical to the one obtained from the classical limit of the original mixed-state dynamics. In the companion paper we present an axiomatic approach to a classical theory of quantum localization without using the underlying QSD theory.

Timothy P. Spiller

Nicolas Gisin, Todd A. Brun, M. Rigo

Ting Yu, Lajos Diósi, Nicolas Gisin +1 more

We present a perturbation theory for non-Markovian quantum-state diffusion (QSD), the theory of diffusive quantum trajectories for open systems in a bosonic environment [Phys. Rev. A 58, 1699 (1998)]. We establish a systematic expansion in the ratio between the environmental correlation time and the typical system time scale. The leading order recovers the Markov theory, so here we concentrate on the next-order correction corresponding to first-order non-Markovian master equations. These perturbative equations greatly simplify the general non-Markovian QSD approach, and allow for efficient numerical simulations beyond the Markov approximation. Furthermore, we show that each perturbative scheme for QSD naturally gives rise to a perturbative scheme for the master equation which we study in some detail. Analytical and numerical examples are presented, including the quantum Brownian motion model.

Nicolas Gisin

Timothy P. Spiller, J. R. Ralph, Terrence D. Clark +2 more

We apply quantum state diffusion theory to an open angular system, such as a quantum capacitor or rotor. We consider various physically interesting Hamiltonian and environment terms, such as those which give rise to tunnelling, and dissipation. Quantum state diffusion (QSD) models the irreversible behaviour of an individual open system, underpinned by the statistics corresponding to a Bloch type of master equation evolution. Our work therefore provides examples of individual quantum device behaviour for cases where the ensemble evolution is Markovian. Since the Markovian approximation is decent for many experiments and since quantum device experiments usually address just one device, QSD should prove to be a useful tool for future device research.