Dividing Line between Quantum and Classical Trajectories in a Measurement Problem: Bohmian Time Constant

Antonio B. Nassar and Salvador Miret-Artés
Phys. Rev. Lett. 111, 150401 – Published 9 October 2013


This Letter proposes an answer to a challenge posed by Bell on the lack of clarity in regards to the dividing line between the quantum and classical regimes in a measurement problem. To this end, a generalized logarithmic nonlinear Schrödinger equation is proposed to describe the time evolution of a quantum dissipative system under continuous measurement. Within the Bohmian mechanics framework, a solution to this equation reveals a novel result: it displays a time constant that should represent the dividing line between the quantum and classical trajectories. It is shown that continuous measurements and damping not only disturb the particle but compel the system to converge in time to a Newtonian regime. While the width of the wave packet may reach a stationary regime, its quantum trajectories converge exponentially in time to classical trajectories. In particular, it is shown that damping tends to suppress further quantum effects on a time scale shorter than the relaxation time of the system. If the initial wave packet width is taken to be equal to 2.8×1015m (the approximate size of an electron), the Bohmian time constant is found to have an upper limit, i.e., τBmax=1026s.

  • Received 9 May 2013


© 2013 American Physical Society

Authors & Affiliations

Antonio B. Nassar1,2,* and Salvador Miret-Artés3

  • 1Science Department, Harvard-Westlake School, 3700 Coldwater Canyon, Studio City, California 91604, USA
  • 2Department of Sciences, University of California, Los Angeles, Extension Program, 10995 Le Conte Avenue, Los Angeles, California 90024, USA
  • 3Instituto de Física Fundamental, Consejo Superior de Investigaciones Científicas, Serrano 123, 28006 Madrid, Spain

  • *nassar@ucla.edu

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Vol. 111, Iss. 15 — 11 October 2013

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