Quantum non-equilibrium and relaxation to equilibrium for a class of de Broglie-Bohm-type theories

Abstract

The de Broglie-Bohm theory is about non-relativistic point-particles that move deterministically along trajectories. The theory reproduces the predictions of standard quantum theory, given that the distribution of particles over an ensemble of systems, all described by the same wavefunction $\psi$, equals the quantum equilibrium distribution $|\psi {|}^2$. Numerical simulations by Valentini and Westman have illustrated that non-equilibrium particle distributions may relax to quantum equilibrium after some time. Here we consider non-equilibrium distributions and their relaxation properties for a particular class of trajectory theories, first studied in detail by Deotto and Ghirardi, that are empirically equivalent to the de Broglie-Bohm theory in quantum equilibrium. For the examples of such theories that we consider, we find a speed-up of the relaxation compared to the ordinary de Broglie-Bohm theory. Hence non-equilibrium predictions that depend strongly on relaxation properties, such as those studied recently by Valentini, may vary for different trajectory theories. As such these theories might be experimentally distinguishable.

25 pages, 8 figures, PDFLaTeX; v2 minor corrections

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• The zig-zag road to reality
• Anomalous spectral lines and relic quantum nonequilibrium
• Extreme quantum nonequilibrium, nodes, vorticity, drift, and relaxation retarding states
• Bouncing oil droplets, de Broglie's quantum thermostat and convergence to equilibrium
• de Broglie's double solution program: 90 years later
• Wavepacket approach to particle diffraction by thin targets: Quantum trajectories and arrival times
• Evolution of Quantum Nonequilibrium for Coupled Harmonic Oscillators
• Pilot-wave quantum theory with a single Bohm's trajectory
• Testing de Broglie's double solution in the mesoscopic regime
• Sub-Compton quantum non-equilibrium and Majorana systems
• Signatures of relic quantum nonequilibrium
• Quantum Equilibrium in Stochastic de Broglie-Bohm-Bell Quantum Mechanics
• A Proposed Experimental Test of Quantum Theory using the Techniques of Atom Optics
• On the Quantum-to-Classical Transition of Primordial Perturbations