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Article overview
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Pilot-wave quantum theory with a single Bohm's trajectory | | Francesco Avanzini
; Barbara Fresch
; Giorgio J. Moro
; | | Date: |
2 Mar 2015 | | Abstract: | The representation of a quantum system as the spatial configuration of its
constituents evolving in time as a trajectory under the action of the
wave-function, is the main objective of the Bohm theory. However, its standard
formulation is referred to the statistical ensemble of its possible
trajectories. The statistical ensemble is introduced in order to establish the
exact correspondence (the Born’s rule) between the probability density on the
spatial configurations and the quantum distribution, that is the squared
modulus of the wave-function. In this work we explore the possibility of using
the pilot wave theory at the level of a single Bohm’s trajectory. The pilot
wave theory allows a formally self-consistent representation of quantum systems
as a single Bohm’s trajectory, but in this case there is no room for the Born’s
rule at least in its standard form. We will show that a correspondence exists
between the statistical distribution of configurations along the single Bohm’s
trajectory and the quantum distribution for a subsystem interacting with the
environment in a multicomponent system. To this aim, we present the numerical
results of the single Bohm’s trajectory description of the model system of six
confined rotors with random interactions. We find a rather close correspondence
between the coordinate distribution of one rotor along its trajectory and the
time averaged marginal quantum distribution for the same rotor. This might be
considered as the counterpart of the standard Born’s rule. Furthermore a
strongly fluctuating behavior with a fast loss of correlation is found for the
evolution of each rotor coordinate. This suggests that a Markov process might
well approximate the evolution of the Bohm’s coordinate of a single rotor and
it is shown that the correspondence between coordinate distribution and quantum
distribution of the rotor is exactly verified. | | Source: | arXiv, 1503.0581 | | Services: | Forum | Review | PDF | Favorites | |
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