arXiv subjects

B. L. Hu

Publications and source records attributed to B. L. Hu.

At least 37 records · Page 2Linked to original sources

arXiv2014

Nonequilibrium Steady State in Open Quantum Systems: Influence Action, Stochastic Equation and Power Balance

The existence and uniqueness of a steady state for nonequilibrium systems (NESS) is a fundamental subject and a main theme of research in statistical mechanics for decades. For Gaussian systems, such as a chain of harmonic oscillators connected at each end to a heat bath, and for anharmonic oscillators under specified conditions, definitive answers exist in the form of proven theorems. Answering this question for quantum many-body systems poses a challenge for the present. In this work we address this issue by deriving the stochastic equations for the reduced system with self-consistent backaction from the two baths, calculating the energy flow from one bath to the chain to the other bath, and exhibiting a power balance relation in the total (chain + baths) system which testifies to the existence of a NESS in this system at late times. Its insensitivity to the initial conditions of the chain corroborates to its uniqueness. The functional method we adopt here entails the use of the influence functional, the coarse-grained and stochastic effective actions, from which one can derive the stochastic equations and calculate the average values of physical variables in open quantum systems. This involves both taking the expectation values of quantum operators of the system and the distributional averages of stochastic variables stemming from the coarse-grained environment. This method though formal in appearance is compact and complete. It can also easily accommodate perturbative techniques and diagrammatic methods from field theory. Taken all together it provides a solid platform for carrying out systematic investigations into the nonequilibrium dynamics of open quantum systems and quantum thermodynamics.

cond-mat.stat-mech↗

arXiv2014

Gravitational Decoherence, Alternative Quantum Theories and Semiclassical Gravity

In this report we discuss three aspects: 1) Semiclassical gravity theory (SCG): 4 levels of theories describing the interaction of quantum matter with classical gravity; 2) Alternative Quantum Theories: Discerning those which are derivable from general relativity (GR) plus quantum field theory (QFT) from those which are not; 3) Gravitational Decoherence: Derivation of a master equation and examination of the assumptions which led to the claims of observational possibilities. We list three sets of corresponding problems worthy of pursuit: a) Newton-Schrödinger Equations in relation to SCG; b) Master equation of gravity-induced effects serving as discriminator of 2); and c) Role of gravity in macroscopic quantum phenomena.

gr-qc↗

arXiv2014

Newton-Schrödinger Equations are not derivable from General Relativity + Quantum Field Theory

In this note we show that Newton-Schrödinger Equations (NSEs) [arXiv:1210.0457 and references therein] do not follow from general relativity (GR) and quantum field theory (QFT) by way of two considerations: 1) Taking the nonrelativistic limit of the semiclassical Einstein equation, the central equation of relativistic semiclassical gravity, a fully covariant theory based on GR+QFT with self-consistent backreaction of quantum matter on the spacetime dynamics; 2) Working out a model [see C. Anastopoulos and B. L. Hu, Class. Quant. Grav. 30, 165007 (2013), arXiv:1305.5231] with a matter scalar field interacting with weak gravity, in procedures analogous to the derivation of the nonrelativistic limit of quantum electrodynamics. We conclude that the coupling of classical gravity with quantum matter can only be via mean fields, there are no $N$-particle NSEs and theories based on Newton-Schrödinger equations assume unknown physics.

gr-qc↗

arXiv2013

Unruh Effect under Non-equilibrium conditions: Oscillatory motion of an Unruh-DeWitt detector

The Unruh effect refers to the thermal fluctuations a detector experiences while undergoing linear motion with uniform acceleration in a Minkowski vacuum. This thermality can be demonstrated by tracing the vacuum state of the field over the modes beyond the accelerated detector's event horizon. However, the event horizon is well-defined only if the detector moves with eternal uniform linear acceleration. This idealized condition cannot be fulfilled in realistic situations when the motion unavoidably involves periods of non-uniform acceleration. Many experimental proposals to test the Unruh effect are of this nature. Often circular or oscillatory motion, which lacks an obvious geometric description, is considered in such proposals. The proper perspective for theoretically going beyond, or experimentally testing, the Unruh-Hawking effect in these more general conditions has to be offered by concepts and techniques in non-equilibrium quantum field theory. In this paper we provide a detailed analysis of how an Unruh-DeWitt detector undergoing oscillatory motion responds to the fluctuations of a quantum field. Numerical results for the late-time temperatures of the oscillating detector are presented. We comment on the digressions of these results from what one would obtain from a naive application of Unruh's result.

gr-qc↗

arXiv2013

A Master Equation for Gravitational Decoherence: Probing the Textures of Spacetime

We give a first principles derivation of a master equation for the evolution of a quantum matter field in a linearly perturbed Minkowski spacetime, based solely on quantum field theory and general relativity. We make no additional assumptions nor introduce extra ingredients, as is often done in alternative quantum theories. When the quantum matter field is projected to a one-particle state, the master equation for a non-relativistic quantum particle in a weak gravitational field predicts decoherence in the energy basis, in contrast to most existing theories of gravitational decoherence. We point out the gauge nature of time and space reparameterizations in matter-gravity couplings, and warn that `intrinsic' decoherence or alternative quantum theories invoking stochastic dynamics arising from temporal or spatial fluctuations violate this fundamental symmetry of classical general relativity. Interestingly we find that the decoherence rate depends on extra parameters other than the Planck scale, an important feature of gravitational decoherence. This is similar to the dependence of the decoherence rate of a quantum Brownian particle to the temperature and spectral density of the environment it interacts with. The corresponding features when gravity acts as an environment in decohering quantum objects are what we call the `textures' of spacetime. We point out the marked difference between the case when gravity is represented as a background spacetime versus the case when gravity acts like a thermodynamic bath to quantum particles. This points to the possibility of using gravitational decoherence measurements to discern whether gravity is intrinsically elemental or emergent.

gr-qc↗

arXiv2013

Entanglement Structure of an Open System of $N$ Quantum Oscillators: II. Strong Disparate Couplings N=3

In this paper we study a system of $N$ coupled quantum oscillators interacting with each other directly with varying coupling strengths and indirectly through linear couplings to a scalar massless quantum field as its environment. The influence of the quantum field on the system is calculated with the use of the influence functional formalism. We take the direct route of seeking solutions to the evolutionary operator of the reduced density matrix for the derivation of the correlation functions. They are then used to construct the covariance matrix which we use to perform an analysis of the structure of quantum entanglement in the open system at a stationary state. To see the physical features more explicitly we specialize to a system of three quantum coupled oscillators placed at the vertices of a equilateral triangle and allowed to have disparate pairwise couplings. We analyze the entanglement between one oscillator and the other two with equal (symmetric) and unequal (asymmetric) coupling strengths. As an illustration we use the results for these two different configurations to address two representative issues in macroscopic quantum phenomena. We also mention possible extensions of our work and applications of our analysis and results to issues in some current areas of research in quantum thermodynamics and mesoscopic quantum systems.

quant-ph↗

arXiv2013

Pathways toward understanding Macroscopic Quantum Phenomena

Macroscopic quantum phenomena refer to quantum features in objects of `large' sizes, systems with many components or degrees of freedom, organized in ways where they can be identified as macroscopic objects. This emerging field is ushered in by several categories of definitive experiments in superconductivity, electromechanical systems, Bose-Einstein condensates and others. Yet this new field which is rich in open issues at the foundation of quantum and statistical physics remains little explored theoretically [1]. This talk summarizes our thoughts on attempting a systematic investigation into its foundation, with the goal of ultimately revealing or building a viable theoretical framework. Three major themes discussed in three intended essays are the large N expansion [2], the correlation hierarchy [3] and quantum entanglement [4]. We give a sketch of the first two themes and then discuss several key issues in the consideration of macro and quantum, namely, a) recognition that in a composite body there exist many 'levels of structure' characterized by collective variables. The quantum features of a macroscopic object can be captured by understanding how these collective variables function; b) 'quantum entanglement', an exclusively quantum feature [5], is known to persist to high temperatures [6] and large scales [7] under certain conditions, and may actually decrease with increased connectivity in a quantum network [8]. Here we use entanglement as a measure of quantumness and pick out these somewhat counter-intuitive examples to show that there are blind spots worthy of our attention and issues which we need to analyze closer. Our purpose is to try to remove the stigma that quantum only pertains to micro, in order to make way for deeper probes into the conditions whereby quantum features of macroscopic systems manifest.

quant-ph↗

arXiv2013

Relativistic Quantum Information in Detectors-Field Interactions

We review Unruh-DeWitt detectors and other models of detector-field interaction in a relativistic quantum field theory setting as a tool for extracting detector-detector, field-field and detector-field correlation functions of interest in quantum information science, from entanglement dynamics to quantum teleportation. We in particular highlight the contrast between the results obtained from linear perturbation theory which can be justified provided switching effects are properly accounted for, and the nonperturbative effects from available analytic expressions which incorporate the backreaction effects of the quantum field on the detector behaviour.

quant-ph↗

arXiv2013

Exact noise kernel for quantum fields in static de Sitter and conformally-flat spacetimes

We compute exact expressions of the noise kernel, defined as the expectation value of the symmetrized connected stress energy bitensor, for conformally-invariant scalar fields with respect to the conformal vacuum, valid for an arbitrary separation (timelike, spacelike and null) of points in a class of conformally-flat spacetimes. We derive explicit expressions for the noise kernel evaluated in the static de Sitter coordinates with respect to the Gibbons-Hawking vacuum and analyze the behavior of the noise kernel in the region near the cosmological horizon. We develop a quasi-local expansion near the cosmological horizon and compare it with the exact results. This gives insight into the likely range of validity of the quasi-local approximation expressions for the noise kernel for the conformally invariant scalar field in Schwarzschild spacetime which are given in PHYSICAL REVIEW D{\bf 85}, 044037 (2012).

gr-qc↗

arXiv2013

Boundary Effects on Quantum Entanglement and its Dynamics in a Detector-Field System

In this paper we analyze an exactly solvable model consisting of an inertial Unruh-DeWitt detector which interacts linearly with a massless quantum field in Minkowski spacetime with a perfectly reflecting flat plane boundary. Firstly a set of coupled equations for the detector's and the field's Heisenberg operators are derived. Then we introduce the linear entropy as a measure of entanglement between the detector and the quantum field under mirror reflection, and solve the early-time detector-field entanglement dynamics. After coarse-graining the field, the dynamics of the detector's internal degree of freedom is described by a quantum Langevin equation, where the dissipation and noise kernels respectively correspond to the retarded Green's functions and Hadamard elementary functions of the free quantum field in a half space. At late times when the combined system is in a stationary state, we obtain exact expressions for the detector's covariance matrix and show that the detector-field entanglement decreases for smaller separation between the detector and the mirror. We explain the behavior of detector-field entanglement qualitatively with the help of a detector's mirror image, compare them with the case of two real detectors and explain the differences.

quant-ph↗

arXiv2012

Entanglement Dynamics between Inertial and Non-uniformly Accelerated Detectors

We study the time-dependence of quantum entanglement between two Unruh-DeWitt detectors, one at rest in a Minkowski frame, the other non-uniformly accelerated in some specified way. The two detectors each couple to a scalar quantum field but do not interact directly. The primary challenge in problems involving non-uniformly accelerated detectors arises from the fact that an event horizon is absent and the Unruh temperature is ill-defined. By numerical calculation we demonstrate that the correlators of the accelerated detector in the weak coupling limit behaves like those of an oscillator in a bath of time-varying "temperature" proportional to the instantaneous proper acceleration of the detector, with oscillatory modifications due to non-adiabatic effects. We find that in this setup the acceleration of the detector in effect slows down the disentanglement process in Minkowski time due to the time dilation in that moving detector

gr-qc↗

arXiv2012

The equilibrium states of open quantum systems in the strong coupling regime

In this work we investigate the late-time stationary states of open quantum systems coupled to a thermal reservoir in the strong coupling regime. In general such systems do not necessarily relax to a Boltzmann distribution if the coupling to the thermal reservoir is non-vanishing or equivalently if the relaxation timescales are finite. Using a variety of non-equilibrium formalisms valid for non-Markovian processes, we show that starting from a product state of the closed system = system + environment, with the environment in its thermal state, the open system which results from coarse graining the environment will evolve towards an equilibrium state at late-times. This state can be expressed as the reduced state of the closed system thermal state at the temperature of the environment. For a linear (harmonic) system and environment, which is exactly solvable, we are able to show in a rigorous way that all multi-time correlations of the open system evolve towards those of the closed system thermal state. Multi-time correlations are especially relevant in the non-Markovian regime, since they cannot be generated by the dynamics of the single-time correlations. For more general systems, which cannot be exactly solved, we are able to provide a general proof that all single-time correlations of the open system evolve to those of the closed system thermal state, to first order in the relaxation rates. For the special case of a zero-temperature reservoir, we are able to explicitly construct the reduced closed system thermal state in terms of the environmental correlations.

cond-mat.stat-mech↗

arXiv2012

Theory of optomechanics: Oscillator-field model of moving mirrors

In this paper we present a model for the kinematics and dynamics of optomechanics which describe the coupling between an optical field, here modeled by a massless scalar field, and the internal (e.g., determining its reflectivity) and mechanical (e.g., displacement) degrees of freedom of a moveable mirror. As opposed to implementing boundary conditions on the field we highlight the internal dynamics of the mirror which provides added flexibility to describe a variety of setups relevant to current experiments. The inclusion of the internal degrees of freedom in this model allows for a variety of optical activities of mirrors from those exhibiting broadband reflective properties to the cases where reflection is suppressed except for a narrow band centered around the characteristic frequency associated with the mirror's internal dynamics. After establishing the model and the reflective properties of the mirror we show how appropriate parameter choices lead to useful optomechanical models such as the well known Barton-Calogeracos model [G. Barton and A. Calogeracos, Ann. Phys. 238, 227 (1995)] and the important yet lesser explored nonlinear models (e.g., $Nx$ coupling) for small photon numbers $N$, which present models based on side-band approximations [H. Kimble et al., Phys. Rev. D 65, 022002 (2001)] cannot cope with. As a simple illustrative application we consider classical radiation pressure cooling with this model. To expound its theoretical structure and physical meanings we connect our model to field-theoretical models using auxiliary fields and the ubiquitous Brownian motion model of quantum open systems. Finally we describe the range of applications of this model, from a full quantum mechanical treatment of radiation pressure cooling, quantum entanglement between macroscopic mirrors, to the backreaction of Hawking radiation on black hole evaporation in a moving mirror analog.

quant-ph↗

arXiv2012

Quantum teleportation between moving detectors in a quantum field

We consider the quantum teleportation of continuous variables modeled by Unruh-DeWitt detectors coupled to a common quantum field initially in the Minkowski vacuum. An unknown coherent state of an Unruh-DeWitt detector is teleported from one inertial agent (Alice) to an almost uniformly accelerated agent (Rob, for relativistic motion), using a detector pair initially entangled and shared by these two agents. The averaged physical fidelity of quantum teleportation, which is independent of the observer's frame, always drops below the best fidelity value from classical teleportation before the detector pair becomes disentangled with the measure of entanglement evaluated around the future lightcone of the joint measurement event by Alice. The distortion of the quantum state of the entangled detector pair from the initial state can suppress the fidelity significantly even when the detectors are still strongly entangled around the lightcone. We point out that the dynamics of entanglement of the detector pair observed in Minkowski frame or in quasi-Rindler frame are not directly related to the physical fidelity of quantum teleportation in our setup. These results are useful as a guide to making judicious choices of states and parameter ranges and estimation of the efficiency of quantum teleportation in relativistic quantum systems under environmental influences.

gr-qc↗

arXiv2012

Stress-energy Tensor Correlators in N-dim Hot Flat Spaces via the Generalized Zeta-Function Method

We calculate the expectation values of the stress-energy bitensor defined at two different spacetime points $x, x'$ of a massless, minimally coupled scalar field with respect to a quantum state at finite temperature $T$ in a flat $N$-dimensional spacetime by means of the generalized zeta-function method. These correlators, also known as the noise kernels, give the fluctuations of energy and momentum density of a quantum field which are essential for the investigation of the physical effects of negative energy density in certain spacetimes or quantum states. They also act as the sources of the Einstein-Langevin equations in stochastic gravity which one can solve for the dynamics of metric fluctuations as in spacetime foams. In terms of constitutions these correlators are one rung above (in the sense of the correlation -- BBGKY or Schwinger-Dyson -- hierarchies) the mean (vacuum and thermal expectation) values of the stress-energy tensor which drive the semiclassical Einstein equation in semiclassical gravity. The low and the high temperature expansions of these correlators are also given here: At low temperatures, the leading order temperature dependence goes like $T^{N}$ while at high temperatures they have a $T^{2}$ dependence with the subleading terms exponentially suppressed by $e^{-T}$. We also discuss the singular behaviors of the correlators in the $x'\rightarrow x$ coincident limit as was done before for massless conformal quantum fields.

hep-th↗

arXiv2012

Quantum and classical fluctuation theorems from a decoherent histories, open-system analysis

In this paper we present a first-principles analysis of the nonequilibrium work distribution and the free energy difference of a quantum system interacting with a general environment (with arbitrary spectral density and for all temperatures) based on a well-understood micro-physics (quantum Brownian motion) model under the conditions stipulated by the Jarzynski equality [C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997)] and Crooks' fluctuation theorem [G. E. Crooks, Phys. Rev. E 60, 2721 (1999)] (in short FTs). We use the decoherent history conceptual framework to explain how the notion of trajectories in a quantum system can be made viable and use the environment-induced decoherence scheme to assess the strength of noise which could provide sufficient decoherence to warrant the use of trajectories to define work in open quantum systems. From the solutions to the Langevin equation governing the stochastic dynamics of such systems we were able to produce formal expressions for these quantities entering in the FTs, and from them prove explicitly the validity of the FTs at the high temperature limit. At low temperatures our general results would enable one to identify the range of parameters where FTs may not hold or need be expressed differently. We explain the relation between classical and quantum FTs and the advantage of this micro-physics open-system approach over the phenomenological modeling and energy-level calculations for substitute closed quantum systems.

quant-ph↗

arXiv2011

Non-Markovian Dynamics of Open Quantum Systems: Stochastic Equations and their Perturbative Solutions

We treat several key stochastic equations for non-Markovian open quantum system dynamics and present a formalism for finding solutions to them via canonical perturbation theory, without making the Born-Markov or rotating wave approximations (RWA). This includes master equations of the (asymptotically) stationary, periodic, and time-nonlocal type. We provide proofs on the validity and meaningfulness of the late-time perturbative master equation and on the preservation of complete positivity despite a general lack of Lindblad form. More specifically, we show how the algebraic generators satisfy the theorem of Lindblad and Gorini, Kossakowski and Sudarshan, even though the dynamical generators do not. These proofs ensure the mathematical viability and physical soundness of solutions to non-Markovian processes. Within the same formalism we also expand upon known results for non-Markovian corrections to the quantum regression theorem. Several directions where these results can be usefully applied to are also described, including the analysis of near-resonant systems where the RWA is inapplicable and the calculation of the reduced equilibrium state of open systems.

quant-ph↗

arXiv2011

Effect of Interatomic Separation on Entanglement Dynamics in a Two-Atom Two-Mode Model

We analyze the time evolution of quantum entanglement in a model consisting of two two-level atoms interacting with a two-mode electromagnetic field for a variety of initial states and interatomic separations. We study two specific atomic separations which give rise to symmetric atom-field couplings. For general atomic distances we consider a subset of initial states analytically, and then treat the more general situation numerically. We examine a variety of qualitative features such as entanglement sudden death, dynamical generation, protection, and transfer between subsystems. Our analysis shows a stark contrast in features of entanglement between the two special coupling schemes often considered; further, these features are uncharacteristic of those arising for general distances, due to the high degree of symmetry present in the special cases. The variety of behaviors in these two-mode cases suggest the importance of considering atomic separation carefully for any model where two atoms interact with a common field.

quant-ph↗