Quantum expectations via spectrograms

TL;DR

This paper introduces a novel phase space method using a Hermite spectrogram correction to the Husimi function, enabling accurate quantum expectation calculations and positive density sampling in high dimensions.

Contribution

The authors propose a new phase space density combining Hermite spectrograms with the Husimi function for improved quantum expectation computation.

Findings

Accurately approximates quantum expectation values in high dimensions.

Enables numerical sampling from non-negative phase space densities.

Demonstrates effectiveness through numerical experiments up to 128 dimensions.

Abstract

We discuss a new phase space method for the computation of quantum expectation values in the high frequency regime. Instead of representing a wavefunction by its Wigner function, which typically attains negative values, we define a new phase space density by adding a first-order Hermite spectrogram term as a correction to the Husimi function. The new phase space density yields accurate approximations of the quantum expectation values as well as allows numerical sampling from non-negative densities. We illustrate the new method by numerical experiments in up to $128$ dimensions.