Quantum stochastic processes III

A Frigerio

J. Martin Lindsay, Adam Skalski

Every Markov-regular quantum Levy process on a multiplier C*-bialgebra is shown to be equivalent to one governed by a quantum stochastic differential equation, and the generating functionals of norm-continuous convolution semigroups on a multiplier C*-bialgebra are then completely characterised. These results are achieved by extending the theory of quantum Levy processes on a compact quantum group, and more generally quantum stochastic convolution cocycles on a C*-bialgebra, to locally compact quantum groups and multiplier C*-bialgebras. Strict extension results obtained by Kustermans, together with automatic strictness properties developed here, are exploited to obtain existence and uniqueness for coalgebraic quantum stochastic differential equations in this setting. Then, working in the universal enveloping von Neumann bialgebra, we characterise the stochastic generators of Markov-regular, *-homomorphic (respectively completely positive and contractive), quantum stochastic convolution cocycles.

M. Dugić

Many Time Interpretation (MTI) proposes that each stochastic "quantum jump" ("reduction") concerning each single object (of an ensemble) represents a consequence of a (stochastic) choice (change) of Time. Therefore, each single object experiences its own (local), stochastically chosen Time, which is as real for it, as the macroscopic Time is real in classical physics. Therefore, instead of the "indeterminism" with regard to the macroscopic Time, MTI proposes "determinism", but with regard to the set(s) of (stochastically chosen) local Times. Within an axiomatization, which includes the composite system "single object+apparatus+environment, MTI leads to : (i) Recognizing the amplification process as the fundamental "part" of the measurement process, (ii) Nonvalidity of the Schrodinger equation concerning the "whole", O+A+E, which makes the "state reduction process" unnecessary and unphysical, (iii) Natural deducibility of the macroscopic irreversibility, and (iv) Nonequivalence of MTI with any existing measurement theory, or interpretation. Thus, within MTI, the measurement problem reduces basically onto the search for quantum effect, which would allow forthe local, stochastic change of Time.

E. B. Davies

Dustin Keys, Jan Wehr

This paper studies a class of quantum stochastic differential equations, modeling an interaction of a system with its environment in the quantum noise approximation. The space representing quantum noise is the symmetric Fock space over L2R+. Using the isomorphism of this space with the space of square-integrable functionals of the Poisson process, the equations can be represented as classical stochastic differential equations, driven by Poisson processes. This leads to a discontinuous dynamical state reduction which we compare to the Ghirardi-–Rimini–Weber model. A purely quantum object, the norm process, is found, which plays the role of an observer {in the sense of Everett [H. Everett III, Rev. Mod. Phys. 29(3), 454 (1957)]}, encoding all events occurring in the system space. An algorithm introduced by Dalibard et al. [Phys. Rev. Lett. 68(5), 580 (1992)] to numerically solve quantum master equations is interpreted in the context of unraveling, and the trajectories of expected values of system observables are calculated.

John T. Lewis