The anharmonic small matrix path integral (anh-SMatPI) algorithm is adapted to composite environments, where each anharmonic bath unit couples to the system and to its own harmonic bath. The propagation matrices are obtained from numerical evaluation of the composite influence functional, which is based on separate iterative path integral calculations for each bath module. The numerically exact nature of the algorithm is demonstrated on a two-level system (TLS) coupled to dissipative TLS baths of one, two, and 50 units.The anharmonic small matrix path integral (anh-SMatPI) algorithm is adapted to composite environments, where each anharmonic bath unit couples to the system and to its own harmonic bath. The propagation matrices are obtained from numerical evaluation of the composite influence functional, which is based on separate iterative path integral calculations for each bath module. The numerically exact nature of the algorithm is demonstrated on a two-level system (TLS) coupled to dissipative TLS baths of one, two, and 50 units.

Journal of Chemical Theory and ComputationSep 20, 20246 citations

The Second-Order Correlation Function for Two-Level Systems

WORLD SCIENTIFIC eBooksNov 1, 20180 citations

Dynamics of simple dissipative systems

F. Guinea

The dynamics of a two-level system (TLS) coupled to an external heat bath has been studied. Correlation functions are obtained by combining analytical and numerical renormalization-group methods. It is shown that perturbation theory can be applied to obtain the low-energy, long-time behavior of the system. Analytical expressions are given for 〈${\ensuremath{\sigma}}_{z}$(t)${\ensuremath{\sigma}}_{z}$(0) ${〉}_{T=0}$ valid in the long- and short-time limits (as compared with the renormalized frequency of the TLS). It is shown that other correlation functions, like 〈${\ensuremath{\sigma}}_{x}$(t)${\ensuremath{\sigma}}_{x}$(0)〉, depend sensitively on the nature of the high-energy cutoff of the environment. Thermodynamic functions, like the susceptibility to a bias potential and the correction to the specific heat of the environment, are also calculated. Finally, it is discussed how, in these systems, the experimental setup may influence the quantity being measured.The dynamics of a two-level system (TLS) coupled to an external heat bath has been studied. Correlation functions are obtained by combining analytical and numerical renormalization-group methods. It is shown that perturbation theory can be applied to obtain the low-energy, long-time behavior of the system. Analytical expressions are given for 〈${\ensuremath{\sigma}}_{z}$(t)${\ensuremath{\sigma}}_{z}$(0)${〉}_{T=0}$ valid in the long- and short-time limits (as compared with the renormalized frequency of the TLS). It is shown that other correlation functions, like 〈${\ensuremath{\sigma}}_{x}$(t)${\ensuremath{\sigma}}_{x}$(0)〉, depend sensitively on the nature of the high-energy cutoff of the environment. Thermodynamic functions, like the susceptibility to a bias potential and the correction to the specific heat of the environment, are also calculated. Finally, it is discussed how, in these systems, the experimental setup may influence the quantity being measured.

Physical review. B, Condensed matterOct 1, 198543 citations

Two-Level Systems with a Time-Dependent Interaction

WORLD SCIENTIFIC eBooksNov 1, 20180 citations

{〉}_{T=0}

valid in the long- and short-time limits (as compared with the renormalized frequency of the TLS). It is shown that other correlation functions, like 〈${\ensuremath{\sigma}}_{x}$(t)${\ensuremath{\sigma}}_{x}$(0)〉, depend sensitively on the nature of the high-energy cutoff of the environment. Thermodynamic functions, like the susceptibility to a bias potential and the correction to the specific heat of the environment, are also calculated. Finally, it is discussed how, in these systems, the experimental setup may influence the quantity being measured.