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Dividing line between quantum and classical trajectories in a measurement problem: Bohmian time constant
Antonio B Nassar1, Salvador Miret-Artés
1Science Department, Harvard-Westlake School, 3700 Coldwater Canyon, Studio City, California 91604, USA and Department of Sciences, University of California, Los Angeles, Extension Program, 10995 Le Conte Avenue, Los Angeles, California 90024, USA.
Physical Review Letters
|October 29, 2013
Summary
This study proposes a new method to define the quantum-classical boundary using a nonlinear Schrödinger equation. It reveals that continuous measurements and damping drive quantum systems towards classical Newtonian behavior over time.
Area of Science:
- Quantum mechanics
- Statistical physics
- Mathematical physics
Background:
- The quantum measurement problem highlights the unclear boundary between quantum and classical physics.
- Bell's challenge calls for a clearer definition of this quantum-classical dividing line.
Purpose of the Study:
- To propose a method for defining the boundary between quantum and classical regimes in quantum measurements.
- To investigate the role of continuous measurement and damping on quantum system evolution.
Main Methods:
- A generalized logarithmic nonlinear Schrödinger equation was formulated.
- Bohmian mechanics was employed to solve the proposed equation.
- Analysis of the time evolution of quantum trajectories under continuous measurement and damping.
Main Results:
- A novel time constant was identified, representing the quantum-classical trajectory dividing line.
- Continuous measurements and damping were shown to drive quantum systems towards a Newtonian regime.
- Quantum trajectories were found to converge exponentially to classical trajectories, with damping suppressing quantum effects.
Conclusions:
- The proposed nonlinear Schrödinger equation and Bohmian mechanics provide a framework for understanding the quantum-classical transition.
- Damping plays a crucial role in accelerating the convergence of quantum to classical behavior.
- An upper limit for the Bohmian time constant was determined to be 10(-26) s for an electron-sized wave packet.
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