On the Quantum Kinetic Equation in Weak Turbulence

TL;DR

This paper revisits the quantum kinetic equation for weak turbulence with quartic interactions, providing a perturbative approach that simplifies calculations by focusing on mode number operators, offering insights into quantum turbulence dynamics.

Contribution

It introduces a perturbation expansion framework for the quantum kinetic equation with quartic interactions, emphasizing a Hamiltonian formulation based on mode number operators.

Findings

Perturbative calculation of the time derivative of mode number operators.

Simplification of quantum turbulence analysis through mode number operator Hamiltonian.

Framework applicable to generic quartic interaction models.

Abstract

The quantum kinetic equation used in the study of weak turbulence is reconsidered in the context of a theory with a generic quartic interaction. The expectation value of the time derivative of the mode number operators is computed in a perturbation expansion which places the large diagonal component of the quartic term in the unperturbed Hamiltonian. Although one is not perturbing around a free field theory, the calculation is easily tractable owing to the fact that the unperturbed Hamiltonian can be written solely in terms of the mode number operators.