Abstract
We initiate the study of relaxation to quantum equilibrium over long timescales in pilotwave theory. We simulate the time evolution of the coarsegrained Hfunction for a twodimensional harmonic oscillator. For a (periodic) wave function that is a superposition of the first 25 energy states we confirm an approximately exponential decay of over five periods. For a superposition of only the first four energy states we are able to calculate over 50 periods. We find that, depending on the set of phases in the initial wave function, can decay to a large nonequilibrium residue exceeding 10% of its initial value or it can become indistinguishable from zero (the equilibrium value). We show that a large residue in is caused by a tendency for the trajectories to be confined to subregions of configuration space for some wave functions, and that this is less likely to occur for larger numbers of energy states (if the initial phases are chosen randomly). Possible cosmological implications are briefly discussed.
Original language  English 

Article number  395306 
Journal  Journal of Physics A: Mathematical and Theoretical 
Volume  47 
Issue number  39 
DOIs  
Publication status  Published  3 Oct 2014 
Keywords
 de BroglieBohm theory
 pilotwave theory
 quantum equilibrium
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Profiles

Eitan Abraham
 School of Engineering & Physical Sciences  Honorary Associate Professor
Person: Honorary