@article { WOS:000704987700003,
title = {Fluctuation-dissipation relation for a quantum Brownian oscillator in a parametrically squeezed thermal field},
journal = {Ann. Phys.},
volume = {433},
year = {2021},
month = {OCT},
publisher = {ACADEMIC PRESS INC ELSEVIER SCIENCE},
type = {Article},
abstract = {In this paper we study the nonequilibrium evolution of a quantum Brownian oscillator, modeling the internal degree of freedom of a harmonic atom or an Unruh-DeWitt detector, coupled to a nonequilibrium and nonstationary quantum field bath and inquire whether a fluctuation-dissipation relation (FDR) can exist after/if it approaches equilibration. This is a nontrivial issue because a squeezed field bath cannot reach equilibration and yet, as this work shows, the system oscillator indeed can, which is a necessary condition for FDRs. We discuss three different settings: (A) The bath field essentially remains in a squeezed thermal state throughout, whose squeeze parameter is a mode- and time-independent constant. This situation is often encountered in quantum optics and quantum thermodynamics. (B) The bath field is initially in a thermal state, but is subjected to a parametric process leading to mode- and time-dependent squeezing. This scenario is encountered in cosmology and dynamical Casimir effects. The squeezing in the bath in both types of processes will affect the oscillator{\textquoteright}s nonequilibrium evolution. We show that at late times it approaches equilibration and this stationarity condition warrants the existence of a FDR. The trait of squeezing is marked by the oscillator{\textquoteright}s effective equilibrium temperature, and the proportionality factor in the FDR is only related to the stationary component of the noise kernel of the bath field. Setting (C) is more subtle: A finite system-bath coupling strength can set the oscillator in a squeezed state even though the bath field is stationary and does not engage in any parametric process. The squeezing of the system in this case is in general time-dependent but becomes constant when the internal dynamics is fully relaxed. We begin with comments on the broad range of physical processes involving squeezed thermal baths and end with some remarks on the significance of FDRs in capturing the essence of quantum backreaction in nonequilibrium and stochastic systems. (C) 2021 Elsevier Inc. All rights reserved.},
keywords = {Fluctuation-dissipation relation, nonequilibrium field theory, Parametric oscillator, Squeezed thermal field, Strongly interacting Gaussian system, Time-dependent background},
issn = {0003-4916},
doi = {10.1016/j.aop.2021.168594},
author = {Hsiang, Jen-Tsung and Hu, Bei-Lok}
}
@article { WOS:000723344800001,
title = {Intrinsic Entropy of Squeezed Quantum Fields and Nonequilibrium Quantum Dynamics of Cosmological Perturbations},
journal = {Entropy},
volume = {23},
number = {11},
year = {2021},
month = {NOV},
publisher = {MDPI},
type = {Article},
abstract = {Density contrasts in the universe are governed by scalar cosmological perturbations which, when expressed in terms of gauge-invariant variables, contain a classical component from scalar metric perturbations and a quantum component from inflaton field fluctuations. It has long been known that the effect of cosmological expansion on a quantum field amounts to squeezing. Thus, the entropy of cosmological perturbations can be studied by treating them in the framework of squeezed quantum systems. Entropy of a free quantum field is a seemingly simple yet subtle issue. In this paper, different from previous treatments, we tackle this issue with a fully developed nonequilibrium quantum field theory formalism for such systems. We compute the covariance matrix elements of the parametric quantum field and solve for the evolution of the density matrix elements and the Wigner functions, and, from them, derive the von Neumann entropy. We then show explicitly why the entropy for the squeezed yet closed system is zero, but is proportional to the particle number produced upon coarse-graining out the correlation between the particle pairs. We also construct the bridge between our quantum field-theoretic results and those using the probability distribution of classical stochastic fields by earlier authors, preserving some important quantum properties, such as entanglement and coherence, of the quantum field.},
keywords = {cosmological particle creation, cosmological perturbations, entropy generation, nonequilibrium field theory},
doi = {10.3390/e23111544},
author = {Hsiang, Jen-Tsung and Hu, Bei-Lok}
}
@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 { WOS:000723992400001,
title = {NonMarkovianity in cosmology: Memories kept in a quantum field},
journal = {Ann. Phys.},
volume = {434},
year = {2021},
month = {NOV},
publisher = {ACADEMIC PRESS INC ELSEVIER SCIENCE},
type = {Article},
abstract = {In this work we ask how an Unruh-DeWitt (UD) detector with harmonic oscillator internal degrees of freedom Q measuring an evolving quantum matter field Phi(x, t) in an expanding universe with scale factor a(t) responds. We investigate the detector{\textquoteright}s response which contains non-Markovian information about the quantum field squeezed by the dynamical spacetime. The challenge is in the memory effects accumulated over the evolutionary history. We first consider a detector W, the {\textquoteleft}Witness{\textquoteright}, which co-existed and evolved with the quantum field from the beginning. We derive a nonMarkovian quantum Langevin equation for the detector{\textquoteright}s Q by integrating over the squeezed quantum field. The solution of this integro-differential equation would answer our question, in principle, but very challenging, in practice. Striking a compromise, we then ask, to what extent can a detector D introduced at late times, called the {\textquoteleft}Detective{\textquoteright}, decipher past memories. This situation corresponds to many cosmological experiments today probing specific stages in the past, such as COBE targeting activities at the surface of last scattering. Somewhat surprisingly we show that it is possible to retrieve to some degree certain global physical quantities, such as the resultant squeezing, particles created, quantum coherence and correlations. The reason is because the quantum field has all the fine-grained information from the beginning in how it was driven by the cosmic dynamics a(t). How long the details of past history can persist in the quantum field depends on the memory time. The fact that a squeezed field cannot come to complete equilibrium under continuous driving, as in an evolving space-time, actually helps to retain the memory. We discuss interesting features and potentials of this {\textquoteleft}archeological{\textquoteright} perspective toward cosmological issues. (C) 2021 Elsevier Inc. All rights reserved.},
keywords = {Nonequilibrium quantum dynamics, NonMarkovianity, Parametric process, Quantum field in a time-dependent background, Quantum memory in cosmological evolution},
issn = {0003-4916},
doi = {10.1016/j.aop.2021.168656},
author = {Hsiang, Jen-Tsung and Hu, Bei-Lok}
}
@article { WOS:000649079900009,
title = {Zeroth law in quantum thermodynamics at strong coupling: In equilibrium, not at equal temperature},
journal = {Phys. Rev. D},
volume = {103},
number = {8},
year = {2021},
month = {APR 13},
publisher = {AMER PHYSICAL SOC},
type = {Article},
abstract = {The zeroth law of thermodynamics involves a transitivity relation (pairwise between three objects) expressed either in terms of {\textquoteleft}{\textquoteleft}equal temperature{{\textquoteright}{\textquoteright}} (ET), or {\textquoteleft}{\textquoteleft}in equilibrium{{\textquoteright}{\textquoteright}} (EQ) conditions. In conventional thermodynamics conditional on vanishingly weak system-bath coupling these two conditions are commonly regarded as equivalent. In this work we show that for thermodynamics at strong coupling they are inequivalent: namely, two systems can he in equilibrium and yet have different effective temperatures. A recent result {[}J.-T. Hsiang and B. L. Hu, Phys. Rev. D 103, 065001 (2021) for Gaussian quantum systems shows that an effective temperature r can be defined at all times during a system{\textquoteright}s nonequilibrium evolution, but because of the inclusion of interaction energy, after equilibration the system{\textquoteright}s T{*} is slightly higher than the bath temperature T-B, with the deviation depending on the coupling. A second object coupled with a different strength with an identical bath at temperature T-B will not have the same equilibrated temperature as the first object. Thus ET not equal EQ for strong coupling thermodynamics. We then investigate the conditions for dynamical equilibration for two objects 1 and 2 strongly coupled with a common bath B, each with a different equilibrated effective temperature. We show this is possible, and prove the existence of a generalized fluctuation-dissipation relation under this configuration. This affirms that in equilibrium is a valid and perhaps more fundamental notion which the zeroth law for quantum thermodynamics at strong coupling should be based on. Only when the system-bath coupling becomes vanishingly weak that {\textquoteleft}{\textquoteleft}temperature{{\textquoteright}{\textquoteright}} appearing in thermodynamic relations becomes universally defined and makes better physical sense.},
issn = {2470-0010},
doi = {10.1103/PhysRevD.103.085004},
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 {yang_nonequilibrium_2020,
title = {Nonequilibrium steady state and heat transport in nonlinear open quantum systems: {Stochastic} influence action and functional perturbative analysis},
journal = {Ann. Phys.},
volume = {421},
year = {2020},
note = {Place: 525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA Publisher: ACADEMIC PRESS INC ELSEVIER SCIENCE Type: Article},
month = {oct},
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 alpha- and quartic beta-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 alpha-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 beta-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. (C) 2020 Elsevier Inc. All rights reserved.},
keywords = {Anharmonic chain, Feynman-Vernon influence functional, Functional perturbation, Nonequilibrium steady state, Open quantum systems, quantum transport},
issn = {0003-4916},
doi = {10.1016/j.aop.2020.168289},
author = {Yang, Jing and Hsiang, Jen-Tsung and Jordan, Andrew N. and Hu, B. L.}
}
@article {ISI:000477908400014,
title = {Fluctuation-dissipation and correlation-propagation relations from the nonequilibrium dynamics of detector-quantum field systems},
journal = {Phys. Rev. D},
volume = {100},
number = {2},
year = {2019},
month = {JUL 29},
pages = {025019},
publisher = {AMER PHYSICAL SOC},
type = {Article},
abstract = {We consider N uniformly accelerating Unruh-DeWitt detectors whose internal degrees of freedom are coupled to a massless scalar field in (1 + 1)D Minkowski space. We use the influence functional formalism to derive the Langevin equations governing the nonequilibrium dynamics of the internal degrees of freedom and show explicitly that the system relaxes in time and equilibrates. We also show that once the equilibrium condition is established a set of fluctuation-dissipation relations (FDRs) and correlation-propagation relations emerges for the detectors, extending earlier results of Raval, Hu, and Anglin {[}Stochastic theory of accelerated detectors in quantum fields, Phys. Rev. D 53, 7003 (1996)] which discovered these relations for the quantum field. Although similar in form to the FDRs commonly known from linear response theory, which assumes an equilibrium condition a priori, their physical connotations are dissimilar from that of a nonequilibrium origin. We show explicitly that both sets of relations are needed to guarantee the balance of energy flow in and out of the system in dynamical equilibrium with the field. These results are helpful to investigations of quantum information and communications of detectors in space experiments and inquiries of theoretical issues in black holes and cosmology.},
issn = {2470-0010},
doi = {10.1103/PhysRevD.100.025019},
author = {Hsiang, Jen-Tsung and Hu, B. L. and Lin, Shih-Yuin}
}
@article {ISI:000477924000099,
title = {Fluctuation-dissipation and correlation-propagation relations in (1+3)D moving detector-quantum field systems},
journal = {Phys. Lett. B},
volume = {795},
year = {2019},
month = {AUG 10},
pages = {694-699},
publisher = {ELSEVIER},
type = {Article},
abstract = {The fluctuation-dissipation relations (FDR) are powerful relations which can capture the essence of the interplay between a system and its environment. Challenging problems of this nature which FDRs aid in our understanding include the backreaction of quantum field processes like particle creation on the spacetime dynamics in early universe cosmology or quantum black holes. The less familiar, yet equally important correlation-propagation relations (CPR) relate the correlations of stochastic forces on different detectors to the retarded and advanced parts of the radiation propagated in the field. Here, we analyze a system of N uniformly-accelerated Unruh-DeWitt detectors whose internal degrees of freedom (idf) are minimally coupled to a real, massless, scalar field in 4D Minkowski space, extending prior work in 2D with derivative coupling. Using the influence functional formalism, we derive the stochastic equations describing the nonequilibrium dynamics of the idfs. We show after the detector-field dynamics has reached equilibration the existence of the FDR and the CPR for the detectors, which combine to form a generalized fluctuation-dissipation matrix relation. We show explicitly the energy flows between the constituents of the system of detectors and between the system and the quantum field environment. This power balance anchors the generalized FDR. We anticipate this matrix relation to provide a useful guardrail in expounding some basic issues in relativistic quantum information, such as ensuring the self-consistency of the energy balance and tracking the quantum information transfer in the detector-field system. (C) 2019 The Authors. Published by Elsevier B.V.},
issn = {0370-2693},
doi = {10.1016/j.physletb.2019.06.062},
author = {Hsiang, Jen-Tsung and Hu, B. L. and Lin, Shih-Yuin and Yamamoto, Kazuhiro}
}
@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}
}
@article { ISI:000368079400004,
title = {Quantum entanglement at high temperatures? Bosonic systems in nonequilibrium steady state},
journal = {JOURNAL OF HIGH ENERGY PHYSICS},
number = {11},
year = {2015},
month = {NOV 13},
issn = {1029-8479},
doi = {10.1007/JHEP11(2015)090},
author = {Hsiang, Jen-Tsung and Hu, B. L.}
}