We show how a relativistic Langevin equation can be derived from a Lorentz-covariant version of the Caldeira-Leggett particle-bath Lagrangian. In one of its limits, we identify the obtained equation with the Langevin equation used in contemporary extensions of statistical mechanics to the near-light-speed motion of a tagged particle in non-relativistic dissipative fluids. The proposed framework provides a more rigorous and first-principles form of the weakly-relativistic and partially-relativistic Langevin equations often quoted or postulated as ansatz in previous works. We then refine the aforementioned results to obtain a generalized Langevin equation valid for the case of both fully-relativistic particle and bath, using an analytical approximation obtained from numerics where the Fourier modes of the bath are systematically replaced with covariant plane-wave forms with a length-scale relativistic correction that depends on the space-time trajectory in a parabolic way. A new relativistic force term appears in this fully-relativistic limit, which has been derived here for the first time. We discuss the implications of the apparent breaking of space-time translation and parity invariance, showing that these effects are not necessarily in contradiction with the assumptions of statistical mechanics. The intrinsically non-Markovian character of the fully relativistic generalised Langevin equation derived here, and of the associated fluctuation-dissipation theorem, is also discussed.
Relativistic Langevin equation derived from a particle-bath Lagrangian / A. Petrosyan, A. Zaccone. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 55:1(2022 Jan 06), pp. 015001.1-015001.33. [10.1088/1751-8121/ac3a33]
Relativistic Langevin equation derived from a particle-bath Lagrangian
A. Zaccone
Ultimo
2022
Abstract
We show how a relativistic Langevin equation can be derived from a Lorentz-covariant version of the Caldeira-Leggett particle-bath Lagrangian. In one of its limits, we identify the obtained equation with the Langevin equation used in contemporary extensions of statistical mechanics to the near-light-speed motion of a tagged particle in non-relativistic dissipative fluids. The proposed framework provides a more rigorous and first-principles form of the weakly-relativistic and partially-relativistic Langevin equations often quoted or postulated as ansatz in previous works. We then refine the aforementioned results to obtain a generalized Langevin equation valid for the case of both fully-relativistic particle and bath, using an analytical approximation obtained from numerics where the Fourier modes of the bath are systematically replaced with covariant plane-wave forms with a length-scale relativistic correction that depends on the space-time trajectory in a parabolic way. A new relativistic force term appears in this fully-relativistic limit, which has been derived here for the first time. We discuss the implications of the apparent breaking of space-time translation and parity invariance, showing that these effects are not necessarily in contradiction with the assumptions of statistical mechanics. The intrinsically non-Markovian character of the fully relativistic generalised Langevin equation derived here, and of the associated fluctuation-dissipation theorem, is also discussed.File | Dimensione | Formato | |
---|---|---|---|
2107.07205_ArXiv.pdf
Open Access dal 07/01/2023
Tipologia:
Post-print, accepted manuscript ecc. (versione accettata dall'editore)
Dimensione
7.5 MB
Formato
Adobe PDF
|
7.5 MB | Adobe PDF | Visualizza/Apri |
Petrosyan_2022_J._Phys._A _Math._Theor._55_015001.pdf
accesso riservato
Tipologia:
Publisher's version/PDF
Dimensione
2.39 MB
Formato
Adobe PDF
|
2.39 MB | Adobe PDF | Visualizza/Apri Richiedi una copia |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.