SAIP2025

Adiabatic elimination approach to the completely positive master equation for open quantum Brownian motion

Not scheduled

1h

Solomon Mahlangu House (University of the Witwatersrand, Johannesburg)

Oral Presentation Track G - Theoretical and Computational Physics Theoretical and Computational Physics

Speaker

Mr Ayanda Zungu (Centre for Space Research, North-West University, Mahikeng 2745, South Africa)

Description

Recently, Bauer et al. [1,2] introduced open quantum Brownian motion (OQBM) as a scaling limit of discrete-time open quantum walks [3,4], providing a new mathematical framework for quantum Brownian motion. In this setting, the dynamics of the Brownian particle are governed by dissipative interactions with a thermal bath and depend on the state of internal degrees of freedom. A microscopic derivation of OQBM for a free Brownian particle subject to decoherent interaction with a thermal environment was subsequently proposed [5,6]. In our recent work [7], we extended this framework by deriving OQBM in a generic dissipative scenario using the method of adiabatic elimination of fast variables. However, this approach led to a master equation that is not completely positive, consistent with the limitations of the standard Caldeira-Leggett model [8,9]. To resolve the issue of positivity, we now apply the rotating wave approximation (RWA) to the system-bath interaction Hamiltonian. This leads to a completely positive master equation for OQBM in the case of a weakly driven open Brownian particle confined within a quadratic potential and dissipatively coupled to a thermal bath. From the resulting dynamics, we derive equations for the first, second, and third cumulants of the position distribution of the OQBM walker.

[1] M. Bauer, D. Bernard, and A. Tilloy, 2013 Phys. Rev. A 88, 062340.
[2] M. Bauer, D. Bernard, and A. Tilloy, 2014 J. Stat. Mech. P09001.
[3] S. Attal, F. Petruccione, C. Sabot, and I. Sinayskiy, 2012 J. Stat. Phys. 147, 832.
[4] S. Attal, F. Petruccione, and I. Sinayskiy, 2012 Phys. Rev. A 376, 1545.
[5] I. Sinayskiy, and F. Petruccione, 2015 Phys. Scr. T 165, 014017.
[6] I. Sinayskiy, and F. Petruccione, 2017 Fortschr. Phys. 65, 1600063.
[7] A. Zungu, I. Sinaykiy, and F. Petruccione, 2025 arXiv:2503.10379.
[8] A. Caldeira and A. Leggett, 1983 Phys. A 121, 587.
[9] A. Caldeira and A. Leggett, 1983 Ann. Phys. (NY) 149, 374.