Infinite number of quantum particles gives clues to big-picture behavior at large scale

In a new study published in EPJ ST, Dr J.S. Ben-Benjamin and colleagues from Texas A&M University, USA, reverse this approach; starting with quantum mechanical rules, they explore how to derive an infinite number of quasi-distributions, to emulate the classical mechanics approach. This approach is also applicable to a number of other variables found in quantum-scale particles, including particle spin.

For example, such quasi-distributions of position and momentum can be used to calculate the quantum version of the characteristics of a gas, referred to as the second virial coefficient, and extend it to derive an infinite number of these quasi-distributions, so as to check whether it matches the traditional expression of this physical entity as a joint distribution of position and momentum in classical mechanics.

This approach is so robust that it can be used to replace quasi-distributions of position and momentum with time and frequency distributions. This, the authors note, works for both well-determined scenarios where time and frequency quasi-distributions are known, and for random cases where the average of time and average of frequency are used instead.

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Journal Reference:

1. J. S. Ben-Benjamin, L. Cohen, M. O. Scully. From von Neumann to Wigner and beyond. The European Physical Journal Special Topics, 2019; 227 (15-16): 2171 DOI: 10.1140/epjst/e2018-800063-2