Nonequilibrium steady state and heat transport in nonlinear open quantum systems: Stochastic influence action and functional perturbative analysis
Abstract
In this paper, we show that a nonequilibrium steady state (NESS) exists at late times in open quantum systems with weak nonlinearity by following its nonequilibrium dynamics with a perturbative analysis. We consider an oscillator chain containing three-types of anharmonicity: cubic α- and quartic β-type Fermi–Pasta–Ulam–Tsingou (FPUT) nearest-oscillator interactions and the on-site (pinned) Klein–Gordon (KG) quartic self-interaction. Assuming weak nonlinearity, we introduce a stochastic influence action approach to the problem and obtain the energy flows in different junctures across the chain. The formal results obtained here can be used for quantum transport problems in weakly nonlinear quantum systems. For α-type anharmonicity, we observe that the first-order corrections do not play any role in the thermal transport in the NESS of the configuration we considered. For KG and β-types anharmonicity, we work out explicitly the case of two weakly nonlinearly coupled oscillators, with results scalable to any number of oscillators. We examine the late-time energy flows from one thermal bath to the other via the coupled oscillators, and show that both the zeroth- and the first-order contributions of the energy flows become constant in time at late times, signaling the existence of a late-time NESS to first order in nonlinearity. Ourmore »
- Authors:
-
[1];
- Univ. of Rochester, NY (United States)
- National Central Univ., Changli (Taiwan); Fudan Univ., Shanghai (China)
- Univ. of Rochester, NY (United States); Fudan Univ., Shanghai (China)
- Univ. of Maryland, College Park, MD (United States)
- Publication Date:
- Research Org.:
- Univ. of Rochester, NY (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1852435
- Alternate Identifier(s):
- OSTI ID: 1809384; OSTI ID: 2222821
- Grant/Contract Number:
- SC0017890
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Annals of Physics
- Additional Journal Information:
- Journal Volume: 421; Journal Issue: C; Journal ID: ISSN 0003-4916
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; nonequilibrium steady state; anharmonic chain; feynman-vernon influence functional; functional perturbation; quantum transport; open quantum systems
Citation Formats
Yang, Jing, Hsiang, Jen-Tsung, Jordan, Andrew N., and Hu, B. L. Nonequilibrium steady state and heat transport in nonlinear open quantum systems: Stochastic influence action and functional perturbative analysis. United States: N. p., 2020.
Web. doi:10.1016/j.aop.2020.168289.
Yang, Jing, Hsiang, Jen-Tsung, Jordan, Andrew N., & Hu, B. L. Nonequilibrium steady state and heat transport in nonlinear open quantum systems: Stochastic influence action and functional perturbative analysis. United States. https://doi.org/10.1016/j.aop.2020.168289
Yang, Jing, Hsiang, Jen-Tsung, Jordan, Andrew N., and Hu, B. L. Tue .
"Nonequilibrium steady state and heat transport in nonlinear open quantum systems: Stochastic influence action and functional perturbative analysis". United States. https://doi.org/10.1016/j.aop.2020.168289. https://www.osti.gov/servlets/purl/1852435.
@article{osti_1852435,
title = {Nonequilibrium steady state and heat transport in nonlinear open quantum systems: Stochastic influence action and functional perturbative analysis},
author = {Yang, Jing and Hsiang, Jen-Tsung and Jordan, Andrew N. and Hu, B. L.},
abstractNote = {In this paper, we show that a nonequilibrium steady state (NESS) exists at late times in open quantum systems with weak nonlinearity by following its nonequilibrium dynamics with a perturbative analysis. We consider an oscillator chain containing three-types of anharmonicity: cubic α- and quartic β-type Fermi–Pasta–Ulam–Tsingou (FPUT) nearest-oscillator interactions and the on-site (pinned) Klein–Gordon (KG) quartic self-interaction. Assuming weak nonlinearity, we introduce a stochastic influence action approach to the problem and obtain the energy flows in different junctures across the chain. The formal results obtained here can be used for quantum transport problems in weakly nonlinear quantum systems. For α-type anharmonicity, we observe that the first-order corrections do not play any role in the thermal transport in the NESS of the configuration we considered. For KG and β-types anharmonicity, we work out explicitly the case of two weakly nonlinearly coupled oscillators, with results scalable to any number of oscillators. We examine the late-time energy flows from one thermal bath to the other via the coupled oscillators, and show that both the zeroth- and the first-order contributions of the energy flows become constant in time at late times, signaling the existence of a late-time NESS to first order in nonlinearity. Our perturbative calculations provide a measure of the strength of nonlinearity for nonlinear open quantum systems, which may help control the mesoscopic heat transport distinct from or close to linear transport. Furthermore, our results also give a benchmark for the numerical challenge of simulating heat transport. Our setup and predictions can be implemented and verified by investigating heat flow in an array of Josephson junctions in the limit of large Josephson energy with the platform of circuit QED.},
doi = {10.1016/j.aop.2020.168289},
journal = {Annals of Physics},
number = C,
volume = 421,
place = {United States},
year = {Tue Aug 18 00:00:00 EDT 2020},
month = {Tue Aug 18 00:00:00 EDT 2020}
}
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