Quantum mechanics in phase space: First order comparison between the Wigner and the Fermi function

TL;DR

This paper compares the Fermi function and Wigner function in phase space, showing that for peaked wave packets, the Fermi function's zero contour approximates the Wigner function's level, aiding in quantum fluctuation analysis.

Contribution

It provides the first order comparison between the Fermi and Wigner functions, highlighting the Fermi function's utility in semiclassical quantum fluctuation studies.

Findings

Fermi g_F(x,p)=0 curve approximates Wigner function contours for peaked wave packets.

Fermi function effectively describes wave packet size and shape.

Useful for investigating quantum fluctuations semiclassically.

Abstract

The Fermi g_F(x,p) function provides a phase space description of quantum mechanics conceptually different from that based on the the Wigner function W(x,p). In this paper, we show that for a peaked wave packet the g_F(x,p)=0 curve approximately corresponds to a phase space contour level of the Wigner function and provides a satisfactory description of the wave packet's size and shape. Our results show that the Fermi function is an interesting tool to investigate quantum fluctuations in the semiclassical regime.