TY - JOUR

T1 - Quantum Brownian motion

T2 - Drude and Ohmic baths as continuum limits of the Rubin model

AU - Das, Avijit

AU - Dhar, Abhishek

AU - Santra, Ion

AU - Satpathi, Urbashi

AU - Sinha, Supurna

N1 - Publisher Copyright:
© 2020 American Physical Society.

PY - 2020/12/14

Y1 - 2020/12/14

N2 - The motion of a free quantum particle in a thermal environment is usually described by the quantum Langevin equation, where the effect of the bath is encoded through a dissipative and a noise term, related to each other via the fluctuation dissipation theorem. The quantum Langevin equation can be derived starting from a microscopic model of the thermal bath as an infinite collection of harmonic oscillators prepared in an initial equilibrium state. The spectral properties of the bath oscillators and their coupling to the particle determine the specific form of the dissipation and noise. Here we investigate in detail the well-known Rubin bath model, which consists of a one-dimensional harmonic chain with the boundary bath particle coupled to the Brownian particle. We show how in the limit of infinite bath bandwidth, we get the Drude model, and a second limit of infinite system-bath coupling gives the Ohmic model. A detailed analysis of relevant equilibrium correlation functions, such as the mean squared displacement, velocity autocorrelation functions, and response function are presented, with the aim of understanding the various temporal regimes. In particular, we discuss the quantum-to-classical crossover time scales where the mean square displacement changes from a ~lnt to a ~t dependence. We relate our study to recent work using linear response theory to understand quantum Brownian motion.

AB - The motion of a free quantum particle in a thermal environment is usually described by the quantum Langevin equation, where the effect of the bath is encoded through a dissipative and a noise term, related to each other via the fluctuation dissipation theorem. The quantum Langevin equation can be derived starting from a microscopic model of the thermal bath as an infinite collection of harmonic oscillators prepared in an initial equilibrium state. The spectral properties of the bath oscillators and their coupling to the particle determine the specific form of the dissipation and noise. Here we investigate in detail the well-known Rubin bath model, which consists of a one-dimensional harmonic chain with the boundary bath particle coupled to the Brownian particle. We show how in the limit of infinite bath bandwidth, we get the Drude model, and a second limit of infinite system-bath coupling gives the Ohmic model. A detailed analysis of relevant equilibrium correlation functions, such as the mean squared displacement, velocity autocorrelation functions, and response function are presented, with the aim of understanding the various temporal regimes. In particular, we discuss the quantum-to-classical crossover time scales where the mean square displacement changes from a ~lnt to a ~t dependence. We relate our study to recent work using linear response theory to understand quantum Brownian motion.

UR - http://www.scopus.com/inward/record.url?scp=85098140190&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.102.062130

DO - 10.1103/PhysRevE.102.062130

M3 - Article

C2 - 33466102

AN - SCOPUS:85098140190

SN - 2470-0045

VL - 102

JO - Physical Review E

JF - Physical Review E

IS - 6

M1 - 062130

ER -