@article {hsiang_nonequilibrium_2021,
title = {Nonequilibrium quantum free energy and effective temperature, generating functional, and influence action},
journal = {Phys. Rev. D},
volume = {103},
number = {6},
year = {2021},
note = {Place: ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA Publisher: AMER PHYSICAL SOC Type: Article},
month = {mar},
abstract = {A definition of nonequilibrium free energy F-s is proposed for dynamical Gaussian quantum open systems strongly coupled to a heat bath and the formal relation with the generating functional, the coarse-grained effective action and the influence action is indicated. For Gaussian open quantum systems exemplified by the quantum Brownian motion model studied here, a time-varying effective temperature can be introduced in a natural way, and, with it, the nonequilibrium free energy F-s, von Neumann entropy S-vN and internal energy U-s of the reduced system (S) can be defined accordingly. In contrast to the nonequilibrium free energy found in the literature which references the bath temperature, the nonequilibrium thermodynamic functions we find here obey the familiar relation F-s(t) = U-s(t)-T-EFF(t)S-vN(t) at any and all moments of time in the system{\textquoteright}s fully nonequilibrium evolution history. After the system equilibrates they coincide, in the weak coupling limit, with their counterparts in conventional equilibrium thermodynamics. Since the effective temperature captures both the state of the system and its interaction with the bath, upon the system{\textquoteright}s equilibration, it approaches a value slightly higher than the initial bath temperature. Notably, it remains nonzero for a zero-temperature bath, signaling the existence of system-bath entanglement. Reasonably, at high bath temperatures and under ultraweak couplings, it becomes indistinguishable from the bath temperature. The nonequilibrium thermodynamic functions and relations discovered here for dynamical Gaussian quantum systems should open up useful pathways toward establishing meaningful theories of nonequilibrium quantum thermodynamics.},
issn = {2470-0010},
doi = {10.1103/PhysRevD.103.065001},
author = {Hsiang, Jen-Tsung and Hu, Bei-Lok}
}
@article {hsiang_fluctuation-dissipation_2020,
title = {Fluctuation-dissipation relation for open quantum systems in a nonequilibrium steady state},
journal = {Phys. Rev. D},
volume = {102},
number = {10},
year = {2020},
note = {Place: ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA Publisher: AMER PHYSICAL SOC Type: Article},
month = {nov},
abstract = {Continuing our work on the nature and existence of fluctuation-dissipation relations (FDR) in linear and nonlinear open quantum systems [J.-T. Hsiang, B. L. Hu, and S.-Y. Lin, Phys. Rev. D 100, 025019 (2019); J.-T. Hsiang, B. L. Hu, S.-Y. Lin, and K. Yamamoto, Phys. Lett. B 795, 694 (2019); J.-T. Hsiang and B. L. Hu, Physics (Utrecht) 1, 430 (2019); J.-T. Hsiang and B. L. Hu, Phys. Rev. D 101, 125003 (2020)], here we consider such relations when a linear system is in a nonequilibrium steady state (NESS). With the model of two-oscillators (considered as a short harmonic chain with the two ends) each connected to a thermal bath of different temperatures we find that when the chain is fully relaxed due to interaction with the baths, the relation that connects the noise kernel and the imaginary part of the dissipation kernel of the chain in one bath does not assume the conventional form for the FDR in equilibrium cases. There exists an additional term we call the {\textquotedblleft}bias current{\textquotedblright} that depends on the difference of the bath{\textquoteright}s initial temperatures and the interoscillator coupling strength. We further show that this term is related to the steady heat flow between the two baths when the system is in an NESS. The ability to know the real-time development of the interheat exchange (between the baths and the end-oscillators) and the intraheat transfer (within the chain) and their dependence on the parameters in the system offers possibilities for quantifiable control, and in the design of quantum heat engines, or thermal devices.},
issn = {2470-0010},
doi = {10.1103/PhysRevD.102.105006},
author = {Hsiang, Jen-Tsung and Hu, Bei-Lok}
}
@article {hsiang_fluctuation-dissipation_2020-1,
title = {Fluctuation-dissipation relation from the nonequilibrium dynamics of a nonlinear open quantum system},
journal = {Phys. Rev. D},
volume = {101},
number = {12},
year = {2020},
note = {Place: ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA Publisher: AMER PHYSICAL SOC Type: Article},
month = {jun},
abstract = {Continuing our inquiry into the conditions when fluctuation-dissipation relations (FDR) may appear in the context of nonequilibrium dynamics of open quantum systems (over and beyond the conventional FDR from linear response theory) we turn to non-Gaussian systems and consider this issue for an anharmonic quantum oscillator interacting with a scalar quantum field bath. We present the general nonperturbative expressions for the rate of energy (power) exchange between the anharmonic oscillator and its thermal bath. For the cases that a stable final equilibrium state exists, and the nonstationary components of the two-point functions of the anharmonic oscillator have negligible contributions to the power balance, we can show nonperturbatively that equilibration implies an FDR for the anharmonic oscillator. We then use a weakly anharmonic oscillator as an example to illustrate the validity of those two assumptions and show that in the weak anhamonicity limit, they are satisfied according to our first-order perturbative results..},
issn = {1550-7998},
doi = {10.1103/PhysRevD.101.125003},
author = {Hsiang, Jen-Tsung and Hu, Bei-Lok}
}
@article {hsiang_nonequilibrium_2020,
title = {Nonequilibrium nonlinear open quantum systems: {Functional} perturbative analysis of a weakly anharmonic oscillator},
journal = {Phys. Rev. D},
volume = {101},
number = {12},
year = {2020},
note = {Place: ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA Publisher: AMER PHYSICAL SOC Type: Article},
month = {jun},
abstract = {We introduce a functional perturbative method for treating weakly nonlinear systems coupled with a quantum field bath. We demonstrate using this method to obtain the covariance matrix elements and the correlation functions of a quantum anharmonic oscillator interacting with a heat bath. We identify a fluctuation-dissipation relation based on the nonequilibrium dynamics of this nonlinear open quantum system. To establish its connection with dynamical equilibration, we further examine the energy flows between the anharmonic oscillator and the bath field. The vanishing of the net flow is an indication of the existence of an equilibrium state for such an open-system configuration. The results presented here are useful for studying the nonequilibrium physical processes of nonlinear quantum systems such as heat transfer or electron transport.},
issn = {1550-7998},
doi = {10.1103/PhysRevD.101.125002},
author = {Hsiang, Jen-Tsung and Hu, Bei-Lok}
}
@article { ISI:000504638400005,
title = {Ground state excitation of an atom strongly coupled to a free quantum field},
journal = {Phys. Rev. D},
volume = {100},
number = {12},
year = {2019},
month = {DEC 26},
pages = {125019},
publisher = {AMER PHYSICAL SOC},
type = {Article},
abstract = {This paper presents a nonperturbative treatment of strong-coupling induced effects in atom-field systems which cannot be seen in traditional perturbative treatments invoking compromising assumptions such as the Born-Markov, rotating wave, or Fermi Golden rule. We consider an atom whose internal degrees of freedom are modeled by a harmonic oscillator which is bilinearly coupled to a scalar quantum field, representing one of the two polarizations of an electromagnetic field. Because the whole system is Gaussian we can solve this problem exactly. Using the open quantum system conceptual framework and the influence functional formalism we derive the dynamics of the reduced density matrix for the atom which enables the calculation of atomic transition probability and other relevant physical quantities. Finding an exact solution to this problem has the distinct advantage of enabling one to capture fully the strong coupling regime and discover interesting effects such as spontaneous ground state excitation {[}R. Passante, T. Petrosky, and I. Prigogine, Long-time behaviour of self-dressing and indirect spectroscopy, Physica (Amsterdam) 218A, 437 (1995).] which is unfathomable in perturbative treatments. The conventional description of atomic-optical activities is predicated on the assumption that the state of the total atom-field system is a product state of the atomic excitations and the photon number states, an assumption which is valid only for vanishingly weak coupling. The correct energy eigenfunctions to use should be that of the Hamiltonian of the combined atom-field system. Other features associated with finite to strong coupling effects such as resonance peak broadening and transition from a gapped to a gapless spectrum can all be understood from this perspective. Finally, to put the issues in a proper perspective we take the perturbative limit of the exact results and compare them with those from conventional time-dependent perturbation theory (TDPT). This enables one to pin-point where the deficiencies of TDPT lie as one removes the ultraweak coupling assumption.},
issn = {2470-0010},
doi = {10.1103/PhysRevD.100.125019},
author = {Hsiang, Jen-Tsung and Hu, Bei-Lok}
}
@article { ISI:000436275400032,
title = {Quantum Thermodynamics at Strong Coupling: Operator Thermodynamic Functions and Relations},
journal = {ENTROPY},
volume = {20},
number = {6},
year = {2018},
month = {JUN},
pages = {423},
keywords = {operator thermodynamic functions, quantum thermodynamics, strong coupling},
issn = {1099-4300},
doi = {10.3390/e20060423},
author = {Hsiang, Jen-Tsung and Hu, Bei-Lok}
}