arXiv subjects

Jen-Tsung Hsiang

Publications and source records attributed to Jen-Tsung Hsiang.

At least 37 records · Page 2Linked to original sources

arXiv2022

No intrinsic decoherence of inflationary cosmological perturbations

After a brief summary of decoherence and quantum to classical transition in cosmology we focus on the study of quantum decoherence of cosmological perturbations in inflationary universe, that does not rely on any environment. This is what `intrinsic' in the title refers to -- a closed quantum system. The question is, does its quantum perturbations decohere with an inflationary expansion of the universe. A dominant view which had propagated for a quarter of a century asserts yes, based on the belief that the large squeezing of a quantum state after a duration of inflation renders the system effectively classical. This paper debunks this view by identifying the technical fault-lines in its derivations and revealing the pitfalls in its arguments which drew earlier authors to this wrong conclusion. We use a few simple quantum mechanical models to expound where the fallacy originated: The highly squeezed ellipse quadrature in phase space cannot be simplified to a line, and the Wigner function cannot be replaced by a delta function. These amount to taking only the leading order contributions in seeking the semiclassical limit and ignoring the subdominant contributions where quantum features reside. Doing so violates the bounds of the Wigner function, and its wave functions possess negative eigenvalues. Moreover, the Robertson-Schrodinger uncertainty relation for a pure state is violated. For inflationary cosmological perturbations, in addition to these features, entanglement exists between the created pairs. This uniquely quantum feature cannot be easily argued away. Indeed it could be our best hope to retroduce the quantum nature of cosmological perturbations and the trace of an inflaton field. All this point to the fact that a closed quantum system, even when highly squeezed, evolves unitarily without loss of coherence; quantum cosmological perturbations do not by itself decohere.

gr-qc↗

arXiv2021

Intrinsic Entropy of Squeezed Quantum Fields and Nonequilibrium Quantum Dynamics of Cosmological Perturbations

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, as 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 probability distribution of classical stochastic fields by earlier authors. From this we can see the clear advantages of the quantum field-theoretical approach over the stochastic classical field treatment since the latter misses out in some important quantum properties, such as entanglement and coherence, of the quantum field.

gr-qc↗

arXiv2021

Quantum Parametric Oscillator Heat Engines in Squeezed Thermal Baths: Foundational Theoretical Issues

In this paper we examine some foundational issues of a class of quantum engines where the system consists of a single quantum parametric oscillator, operating in an Otto cycle consisting of 4 stages of two alternating phases: the isentropic phase is detached from any bath (thus a closed system) where the natural frequency of the oscillator is changed from one value to another, and the isothermal phase where the system (now rendered open) is put in contact with one or two squeezed baths of different temperatures, whose nonequilibrium dynamics follows the Hu-Paz-Zhang (HPZ) master equation for quantum Brownian motion. The HPZ equation is an exact nonMarkovian equation which preserves the positivity of the density operator and is valid for a) all temperatures, b) arbitrary spectral density of the bath, and c) arbitrary coupling strength between the system and the bath. Taking advantage of these properties we examine some key foundational issues of theories of quantum open and squeezed systems for these two phases of the quantum Otto engines. This include, i) the nonMarkovian regimes for non-Ohmic, low temperature baths, ii) what to expect in nonadiabatic frequency modulations, iii) strong system-bath coupling, as well as iv) the proper junction conditions between these two phases. Our aim here is not to present ways for attaining higher efficiency but to build a more solid theoretical foundation for quantum engines of continuous variables covering a broader range of parameter spaces hopefully of use for exploring such possibilities.

quant-ph↗

arXiv2020

Zeroth Law in Quantum Thermodynamics at Strong Coupling: `in Equilibrium', not `Equal Temperature'

The zeroth law of thermodynamics involves a transitivity relation (pairwise between three objects) expressed either in terms of `equal temperature' (ET), or `in equilibrium' (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 be in equilibrium and yet have different effective temperatures. A recent result \cite{NEqFE} for Gaussian quantum systems shows that an effective temperature $T^{*}$ can be defined at all times during a system's nonequilibrium evolution, but because of the inclusion of interaction energy, after equilibration the system's $T^*$ is slightly higher than the bath temperature $T_{\textsc{b}}$, with the deviation depending on the coupling. A second object coupled with a different strength with an identical bath at temperature $T_{\textsc{b}}$ will not have the same equilibrated temperature as the first object. Thus $ET \neq 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 `temperature' appearing in thermodynamic relations becomes universally defined and makes better physical sense.

cond-mat.stat-mech↗

arXiv2020

Nonequilibrium Quantum Free Energy and Effective Temperature, Generating Functional and Influence Action

A definition of nonequilibrium free energy $\mathcal{F}_{\textsc{s}}$ is proposed for dynamical Gaussian quantum open systems strongly coupled to a heat bath and a formal derivation is provided by way of the generating functional in terms of the coarse-grained effective action and the influence action. 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 $\mathcal{F}_{\textsc{s}}$, von Neumann entropy $\mathcal{S}_{vN}$ and internal energy $\mathcal{U}_{\textsc{s}}$ 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 $\mathcal{F}_{\textsc{s}}(t)=\mathcal{U}_{\textsc{s}}(t)- T_{\textsc{eff}} (t)\,\mathcal{S}_{vN}(t)$ {\it at any and all moments of time} in the system'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'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 ultra-weak 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.

cond-mat.stat-mech↗

arXiv2020

Nonequilibrium Thermodynamics of Quantum Friction

Thermodynamic principles are often deceptively simple and yet surprisingly powerful. We show how a simple rule, such as the net flow of energy in and out of a moving atom under nonequilibrium steady state condition, can expose the shortcomings of many popular theories of quantum friction. Our thermodynamic approach provides a conceptual framework in guiding atom-optical experiments, thereby highlighting the importance of fluctuation-dissipation relations and long-time correlations between subsystems. Our results introduce consistency conditions for (numerical) models of nonequilibrium dynamics of open quantum systems.

quant-ph↗

arXiv2020

Nonequilibrium Steady State and Heat Transport in Nonlinear Open Quantum Systems: Stochastic Influence Action and Functional Perturbative Analysis

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. Here we consider an oscillator chain containing three-types of anharmonicity in the Fermi-Pasta-Ulam-Tsingou (FPUT) model: cubic $α$- and quartic $β$-type 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 flow in different junctures of 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 flow 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.

quant-ph↗

arXiv2020

Fluctuation-Dissipation Relation for Open Quantum Systems in Nonequilibrium Steady State

Continuing our work on the nature and existence of fluctuation-dissipation relations (FDR) in linear and nonlinear open quantum systems [1-3], 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 `bias current' that depends on the difference of the bath's initial temperatures and the inter-oscillator coupling strength. We further show that this term is related to the steady heat flow between the two baths when the system is in NESS. The ability to know the real-time development of the inter-heat exchange (between the baths and the end-oscillators) and the intra-heat 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.

quant-ph↗

arXiv2020

Nonequilibrium Nonlinear Open Quantum Systems I. Functional Perturbative Analysis of a Weakly Anharmonic Oscillator

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.

hep-th↗

arXiv2020

Fluctuation-Dissipation Relation from the Nonequilibrium Dynamics of a Nonlinear Open Quantum System

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 nonGaussian systems and consider this issue for an anharmonic 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 the 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 evaluation of 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 that those two assumptions indeed are satisfied according to our first-order perturbative results: that the net energy exchange vanishes after relaxation in the open system dynamics and an equilibrium state exists at late times.

hep-th↗

arXiv2019

Atom-Field Interaction: From Vacuum Fluctuations to Quantum Radiation and Quantum Dissipation / Radiation Reaction

In this paper we dwell on three issues: 1) revisit the relation between vacuum fluctuations and radiation reaction in atom-field interactions, which began in the 70s and settled in the 90s with its resolution recorded in monographs; 2) the fluctuation-dissipation relation (FDR) of the system, pointing out the differences between that in linear response theory (LRT) assuming ultra-weak coupling between the system and the bath, and the FDR in an equilibrated final state, relaxed from the nonequilibrium evolution of an open quantum system; 3) quantum radiation from an atom interacting with a quantum field: Begin with vacuum fluctuations in the field acting on the internal degrees of freedom (idf) of an atom, adding to its dynamics a stochastic component which engenders quantum radiation whose backreaction causes quantum dissipation in the idf of the atom. For a stationary atom, we show how the absence of radiation results from complex cancellations, at a faraway observation point, of the interference between emitted radiation from the atom and the local fluctuations in the free field. We point out that the entity which enters into the duality relation with vacuum fluctuations is not classical radiation reaction, but quantum dissipation. Finally, regarding Issue 2, for systems with many atoms, the existence of a set of correlation-propagation relations shows how the correlations between the atoms are related to the propagation of their mutual influence manifesting in the quantum field. The CPR is absolutely crucial in keeping the balance of energy flows between the constituents of the system, and between the system and its environment. Without the consideration of this additional relation in tether with the FDR, dynamical self-consistency cannot be sustained. Combination of these two sets of relations capture the physical essence of the interaction between an atom and a quantum field.

quant-ph↗

arXiv2019

Ground State Excitation of an Atom Strongly Coupled to a Free Quantum Field

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, 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 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 TDPT. This enables one to pin-point where the deficiencies of TDPT lie as one removes the ultra-weak coupling assumption.

quant-ph↗

arXiv2019

Fluctuation-Dissipation and Correlation-Propagation Relations in $(1+3)$D Moving Detector-Quantum Field Systems

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 {\it 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.

hep-th↗

arXiv2018

Quantum thermodynamics from the nonequilibrium dynamics of open systems: energy, heat capacity and the third law

We take the perspective of open quantum systems and examine from their nonequilibrium dynamics the conditions when the physical quantities, their relations and the laws of thermodynamics become well defined and viable for quantum many body systems. We first describe how an open system nonequilibrium dynamics (ONEq) approach is different from the closed combined system + environment in a global thermal state (CGTs) setup. Only after the open system equilibrates will it be amenable to conventional thermodynamics descriptions, thus quantum thermodynamics (QTD) comes at the end rather than assumed in the beginning. We see the open system approach having the advantage of dealing with nonequilibrium processes as many experiments in the near future will call for. Because it spells out the conditions of QTD's existence it can also aid us in addressing the basic issues in quantum thermodynamics from first principles in a systematic way. We then study one broad class of open quantum systems where the full nonequilibrium dynamics can be solved exactly, that of the quantum Brownian motion of $N$ strongly coupled harmonic oscillators, interacting strongly with a scalar field environment. Here we focus on the internal energy, heat capacity and the Third Law. We show for this class of physical models, amongst other findings, the extensive property of the internal energy, the positivity of the heat capacity and the validity of the Third Law from the perspective of the behavior of the heat capacity toward zero temperature. These conclusions obtained from exact solutions and quantitative analysis clearly disprove claims of negative specific heat in such systems and dispel allegations that in such systems the validity of the Third Law of thermodynamics relies on quantum entanglement.

quant-ph↗

arXiv2017

Thermodynamics of quantum systems strongly coupled to a heat bath I. Operator thermodynamic functions and relations

The thermodynamics of small quantum many-body systems strongly coupled to a heat bath at low temperatures with non-Markovian behavior are new challenges for quantum thermodynamics, as traditional thermodynamics is built on large systems vanishingly weakly coupled to a non-dynamical reservoir. Important also are the quantum attributes, as in quantum coherence, correlations, entanglement and fluctuations. All told, one needs to reexamine the meaning of the thermodynamic functions, the viability of the thermodynamic relations and the validity of the thermodynamic laws anew. In one popular approach to quantum thermodynamics the closed system, comprising the system of interest and the bath it is strongly coupled to, is assumed to be in a global thermal state throughout. In this set-up three theories of thermodynamics at strong coupling have been proposed, those of Gelin & Thoss [1], Seifert [2] and Jarzynski [3]. This paper provides a quantum formulation of them, with Jarzynski's two different representations encompassing the former two. Operator thermodynamic potentials and thermodynamic relations are presented. We mention issues related to energy and entropy in the two representations, a possible way to define quantum work in our functional formulation, and how to connect with the open system nonequilibrium dynamics approach to quantum thermodynamics, as proposed in [4].

quant-ph↗

arXiv2017

Quantum Stress Tensor Fluctuations and Primordial Gravity Waves

We examine the effect of the stress tensor of a quantum matter field, such as the electromagnetic field, on the spectrum of primordial gravity waves expected in inflationary cosmology. We find that the net effect is a small reduction in the power spectrum, especially at higher frequencies, but which has a different form from that described by the usual spectral index. Thus this effect has a characteristic signature, and is in principle observable. The net effect is a sum of two contributions, one of which is due to quantum fluctuations of the matter field stress tensor. The other is a quantum correction to the graviton field due to coupling to the expectation value of this stress tensor. Both contributions are sensitive to initial conditions in the very early universe, so this effect has the potential to act as a probe of these initial conditions.

gr-qc↗

arXiv2015

"Hot Entanglement"? -- A Nonequilibrium Quantum Field Theory Scrutiny

The possibility of maintaining entanglement in a quantum system at finite, even high, temperatures -- the so-called `hot entanglement' -- has obvious practical interest, but also requires closer theoretical scrutiny. Since quantum entanglement in a system evolves in time and is continuously subjected to environmental degradation, a nonequilibrium description by way of open quantum systems is called for. To identify the key issues and the contributing factors that may permit `hot entanglement' to exist, or the lack thereof, we carry out a model study of two spatially-separated, coupled oscillators in a shared bath depicted by a finite-temperature scalar field. From the Langevin equations we derived for the normal modes and the entanglement measure constructed from the covariance matrix we examine the interplay between direct coupling, field-induced interaction and finite separation on the structure of late-time entanglement. We show that the coupling between oscillators plays a crucial role in sustaining entanglement at intermediate temperatures and over finite separations. In contrast, the field-induced interaction between the oscillators which is a non-Markovian effect, becomes very ineffective at high temperature. We determine the critical temperature above which entanglement disappears to be bounded in the leading order by the inverse frequency of the center-of-mass mode of the reduced oscillator system, a result not unexpected, which rules out hot entanglement in such settings.

hep-th↗

arXiv2015

Distance and Coupling Dependence of Entanglement in the Presence of a Quantum Field

We study the entanglement between two coupled detectors, whose internal degrees of freedom are modeled by harmonic oscillators, interacting with a common quantum field, paying special attention to two less studied yet important features: finite separation and direct coupling. Distance dependence is essential in quantum teleportation and relativistic quantum information considerations. The presence of a quantum field as the environment accords an indirect interaction between the two oscillators at finite separation of a non-Markovian nature which competes with the direct coupling between them. The interplay between these two factors results in a rich variety of interesting entanglement behaviors at late times. We show that the entanglement behavior reported in prior work assuming no separation between the detectors can at best be a transient effect at very short times, and claims that such behaviors represent late time entanglement are misplaced. Entanglement between the detectors with direct coupling enters in the consideration of macroscopic quantum phenomena and other frontline issues. We find that with direct coupling entanglement between the two detectors can sustain over a finite distance, in contrast to the no-direct coupling case reported before, where entanglement can not survive at separation more than a few inverse high frequency cutoff scales. This work provides a solid platform necessary for further systematic investigations into the entanglement behavior of continuous variable quantum systems.

quant-ph↗