Posted in | Quantum Physics

Researchers Use Quantum Mechanical Rules to Derive an Infinite Number of Quasi-Distributions

In quantum mechanics, the Heisenberg uncertainty principle proves to be an obstacle for an external observer intending to measure the position and speed, or momentum, of a particle at the same instance. The observer can measure only one of them with a high certainty—in contrast to the occurrence at large scales where both are known.

In order to determine the characteristics of a given particle, physicists came up with the concept of quasi-distribution of momentum and position. This strategy was an endeavor toward reconciling quantum-scale interpretation of what happens particles with the standard technique applied to gain insights into motion at normal scale, a field known as classical mechanics.

In a new research reported in EPJ ST, Dr J.S. Ben-Benjamin and his team from Texas A&M University, United States, reverse this technique; they started with quantum mechanical rules to explore ways to derive an infinite number of quasi-distributions, to simulate the classical mechanics technique. This technique can also be applied to various other variables found in quantum-scale particles, such as the particle spin.

For instance, it is possible to use such quasi-distributions of momentum and position to calculate the quantum version of the properties of a gas, called the second virial coefficient, and extend it to obtain an infinite number of such quasi-distributions, to verify whether it matches the conventional expression of this physical entity as a joint distribution of momentum and position in classical mechanics.

This strategy is so powerful that it can be applied to substitute the quasi-distributions of momentum and position with time and frequency distributions. According to the authors, this holds good not just for well-determined scenarios in which time and frequency quasi-distributions are known but also for random cases in which the average of time and the average of frequency are used alternatively.


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