# Many-body formalism for thermally excited wave-packets: A way to connect the quantum regime to the classical regime

## TL;DR

This paper introduces a many-body formalism using thermally excited wave-packets to bridge the gap between quantum delocalized states and classical localized particles at finite temperatures.

## Contribution

It develops a novel formalism based on wave-packet operators that connects quantum and classical regimes, incorporating thermal effects into many-body Hamiltonians.

## Key findings

- Formalism connects quantum and classical particle descriptions.
- States are diagonal in the Boltzmann operator at finite temperature.
- Effective scatterings are derived for thermally excited wave-packets.

## Abstract

Free classical particles have well-defined momentum and position, while free quantum particles have well-defined momentum but a position fully delocalized over the sample volume. We develop a many-body formalism based on wave-packet operators that connects these two limits, the thermal energy being distributed between the state spatial extension and its thermal excitation. The corresponding `mixed quantum-classical' states, which render the Boltzmann operator diagonal, are the physically relevant states when the temperature is finite. The formulation of many-body Hamiltonians in terms of these thermally excited wave-packets and the resulting effective scatterings is provided.