Quantum-classical transition in the Caldeira-Leggett model

TL;DR

This paper investigates the quantum-classical transition in the Caldeira-Leggett model using the functional renormalization group, revealing critical behavior and universal critical exponents unaffected by cutoff schemes.

Contribution

It introduces a renormalization approach to analyze the quantum-classical transition in the Caldeira-Leggett model, identifying universal critical exponents.

Findings

Divergent quadratic term due to heat bath identified

Critical exponents for susceptibility and correlation length determined

Critical exponents are independent of cutoff and scheme

Abstract

The quantum-classical transition in the Caldeira-Leggett model is investigated in the framework of the functional renormalization group method. It is shown that a divergent quadratic term arises in the action due to the heat bath in the model. By removing the divergence with a frequency cutoff we considered the critical behavior of the model. The critical exponents belonging to the susceptibility and the correlation length are determined and their independence of the frequency cutoff and the renormalization scheme is shown.