Markov processes in Hilbert space and continuous spontaneous localization of systems of identical particles

Gian Carlo Ghirardi, Philip Pearle, and Alberto Rimini
Phys. Rev. A 42, 78 – Published 1 July 1990
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Abstract

Stochastic differential equations describing the Markovian evolution of state vectors in the quantum Hilbert space are studied as possible expressions of a universal dynamical principle. The general features of the considered class of equations as well as their dynamical consequences are investigated in detail. The stochastic evolution is proved to induce continuous dynamical reduction of the state vector onto mutually orthogonal subspaces. A specific choice, expressed in terms of creation and annihilation operators, of the operators defining the Markov process is then proved to be appropriate to describe continuous spontaneous localization of systems of identical particles. The dynamics obtained in such a way leaves practically unaffected the standard quantum evolution of microscopic systems and induces a very rapid suppression of coherence among macroscopically distinguishable states. The classical behavior of macroscopic objects as well as the reduction of the wave packet in a quantum measurement process can be consistently derived from the postulated universal dynamical principle.

  • Received 15 June 1989

DOI:https://doi.org/10.1103/PhysRevA.42.78

©1990 American Physical Society

Authors & Affiliations

Gian Carlo Ghirardi

  • Dipartimento di Fisica Teorica, Università degli Studi di Trieste, Trieste, Italy
  • International Center for Theoretical Physics, Trieste, Italy

Philip Pearle

  • Hamilton College, Clinton, New York 13323

Alberto Rimini

  • Dipartimento di Fisica Nucleare e Teorica, Università degli Studi di Pavia, Pavia, Italy

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Vol. 42, Iss. 1 — July 1990

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