Power-law tails and non-Markovian dynamics in open quantum systems: An exact solution from Keldysh field theory

Ahana Chakraborty and Rajdeep Sensarma
Phys. Rev. B 97, 104306 – Published 16 March 2018

Abstract

The Born-Markov approximation is widely used to study the dynamics of open quantum systems coupled to external baths. Using Keldysh formalism, we show that the dynamics of a system of bosons (fermions) linearly coupled to a noninteracting bosonic (fermionic) bath falls outside this paradigm if the bath spectral function has nonanalyticities as a function of frequency. In this case, we show that the dissipative and noise kernels governing the dynamics have distinct power-law tails. The Green's functions show a short-time “quasi”-Markovian exponential decay before crossing over to a power-law tail governed by the nonanalyticity of the spectral function. We study a system of bosons (fermions) hopping on a one-dimensional lattice, where each site is coupled linearly to an independent bath of noninteracting bosons (fermions). We obtain exact expressions for the Green's functions of this system, which show power-law decay |tt|3/2. We use these to calculate the density and current profile, as well as unequal-time current-current correlators. While the density and current profiles show interesting quantitative deviations from Markovian results, the current-current correlators show qualitatively distinct long-time power-law tails |tt|3 characteristic of non-Markovian dynamics. We show that the power-law decays survive in the presence of interparticle interaction in the system, but the crossover time scale is shifted to larger values with increasing interaction strength.

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  • Received 16 September 2017
  • Revised 1 January 2018

DOI:https://doi.org/10.1103/PhysRevB.97.104306

©2018 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Ahana Chakraborty* and Rajdeep Sensarma

  • Department of Theoretical Physics, Tata Institute of Fundamental Research, Mumbai 400005, India

  • *ahana@theory.tifr.res.in
  • sensarma@theory.tifr.res.in

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Issue

Vol. 97, Iss. 10 — 1 March 2018

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