Fokker-Planck equations for a trapped particle in a quantum-thermal Ohmic bath: general theory and applications to Josephson junctions
Year: 2023
Authors: Furutani K., Salasnich L.
Autors Affiliation: Univ Padua, Dipartimento Fis & Astron Galileo Galilei, Via Marzolo 8, I-35131 Padua, Italy; Univ Padua, QTech Ctr, Via Marzolo 8, I-35131 Padua, Italy; INFN, Sez Padova, Via Marzolo 8, I-35131 Padua, Italy; CNR, Ist Nazl Ott, Via Nello Carrara 2, I-50019 Sesto Fiorentino, Italy.
Abstract: We consider a particle trapped by a generic external potential and under the influence of a quantum-thermal Ohmic bath. Starting from the Langevin equation, we derive the corresponding Schwinger-Keldysh action. Then, within the path-integral formalism, we obtain both the semiclassical Fokker-Planck equation and the quantum Fokker-Planck equation for this out-of-equilibrium system. In the case of an external harmonic potential and in the underdamped regime, we find that our Fokker-Planck equations contain an effective temperature Teffdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$T_{ ext {eff}}$$end{document}, which crucially depends on the interplay between quantum and thermal fluctuations in contrast to the classical Fokker-Planck equation. In the regime of high temperatures, one recovers the classical Fokker-Planck equation. As an application of our result, we also provide the stationary solution of the semiclassical Fokker-Planck equations for a superconducting Josephson circuit and for a Bose Josephson junction, which are experimentally accessible.
Journal/Review: AAPPS BULLETIN
Volume: 33 (1) Pages from: 19-1 to: 19-9
More Information: The authors acknowledge Pietro Faccioli, Amos Maritan, Fabio Sattin, and Sandro Azaele for useful suggestions.KeyWords: Zero-voltage State; Dynamics; Renormalization; Agitation; Diagram; Motion; NoiseDOI: 10.1007/s43673-023-00087-2Citations: 1data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2024-11-24References taken from IsiWeb of Knowledge: (subscribers only)
