On the Fermi Function of Squeezed Coherent States

TL;DR

This paper explores Fermi's function for squeezed coherent states, relating it to the Wigner transform and analyzing the phase space geometry, revealing bounds on the symplectic capacity linked to quantum uncertainty.

Contribution

It generalizes the relation between Fermi's function and the Wigner transform for squeezed coherent states and establishes bounds on the symplectic capacity of associated phase space ellipsoids.

Findings

Bound on symplectic capacity by h/2 and nh/2

Relation between Fermi's function and Wigner transform for squeezed states

Generalization of previous results to more complex states

Abstract

Fermi observed in 1930 that the state of a quantum system may be defined in two different (but equivalent) ways, namely by its wavefunction $\Psi$ or by a certain function $g_F$ on phase space canonically associated with $\Psi$. In this Note we study we study Fermi's function when $\Psi$ is a squeezed coherent state. We relate it with the Wigner transform of $\Psi$, thus generalising a previous observation of Benenti and Strini. We show that the symplectic capacity of the phase space ellipsoid $g_{F}(x,p)\leq0$ is bounded by $h/2$ and $nh/2$ (n the number of degrees of freedom).