2015/03/02 by Francesco Avanzini, Barbara Fresch, Giorgio J. Moro · 5 citations
Physics and Astronomy · #Probability distribution #Quantum #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #Quantum algorithm #Quantum chaos and dynamical systems #Quantum probability #Quantum process #Realization (probability) #Representation (politics) #Trajectory #Wave function #quant-ph
paper · pdf · doi:10.1007/s10701-015-9979-1
published in Foundations of Physics 46(5), 575-605 (Springer Science+Business Media)
arxiv created 2015/03/02 · arxiv updated 2015/11/26 · openalex publication_date 2015/12/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.