arXiv subjects

H. T. Quan

Publications and source records attributed to H. T. Quan.

At least 55 records · Page 3Linked to original sources

arXiv2018

Work Distributions in 1-D Fermions and Bosons with Dual Contact Interactions

We extend the well-known static duality \cite{girardeau1960relationship, cheon1999fermion} between 1-D Bosons and 1-D Fermions to the dynamical version. By utilizing this dynamical duality we find the duality of non-equilibrium work distributions between interacting 1-D bosonic (Lieb-Liniger model) and 1-D fermionic (Cheon-Shigehara model) systems with dual contact interactions. As a special case, the work distribution of the Tonks-Girardeau (TG) gas is identical to that of 1-D free fermionic system even though their momentum distributions are significantly different. In the classical limit, the work distributions of Lieb-Liniger models (Cheon-Shigehara models) with arbitrary coupling strength converge to that of the 1-D noninteracting distinguishable particles, although their elemetary excitations (quasi-particles) obey different statistics, e.g. the Bose-Einstein, the Fermi-Dirac and the fractional statistics. We also present numerical results of the work distributions of Lieb-Liniger model with various coupling strengths, which demonstrate the convergence of work distributions in the classical limit.

quant-ph↗

arXiv2018

Experimental test of the differential fluctuation theorem and a generalized Jarzynski equality for arbitrary initial states

Nonequilibrium processes of small systems such as molecular machines are ubiquitous in biology, chemistry and physics, but are often challenging to comprehend. In the past two decades, several exact thermodynamic relations of nonequilibrium processes, collectively known as fluctuation theorems, have been discovered and provided critical insights. These fluctuation theorems are generalizations of the second law, and can be unified by a differential fluctuation theorem. Here we perform the first experimental test of the differential fluctuation theorem, using an optically levitated nanosphere in both underdamped and overdamped regimes, and in both spatial and velocity spaces. We also test several theorems that can be obtained from it directly, including a generalized Jarzynski equality that is valid for arbitrary initial states, and the Hummer-Szabo relation. Our study experimentally verifies these fundamental theorems, and initiates the experimental study of stochastic energetics with the instantaneous velocity measurement.

cond-mat.stat-mech↗

arXiv2017

Experimental realization of Feynman's ratchet

Feynman's ratchet is a microscopic machine in contact with two heat reservoirs, at temperatures $T_A$ and $T_B$, that was proposed by Richard Feynman to illustrate the second law of thermodynamics. In equilibrium ($T_A=T_B$), thermal fluctuations prevent the ratchet from generating directed motion. When the ratchet is maintained away from equilibrium by a temperature difference ($T_A \ne T_B$), it can operate as a heat engine, rectifying thermal fluctuations to perform work. While it has attracted much interest, the operation of Feynman's ratchet as a heat engine has not been realized experimentally, due to technical challenges. In this work, we realize Feynman's ratchet with a colloidal particle in a one dimensional optical trap in contact with two heat reservoirs: one is the surrounding water, while the effect of the other reservoir is generated by a novel feedback mechanism, using the Metropolis algorithm to impose detailed balance. We verify that the system does not produce work when $T_A=T_B$, and that it becomes a microscopic heat engine when $T_A \ne T_B$. We analyze work, heat and entropy production as functions of the temperature difference and external load. Our experimental realization of Feynman's ratchet and the Metropolis algorithm can also be used to study the thermodynamics of feedback control and information processing, the working mechanism of molecular motors, and controllable particle transportation.

cond-mat.stat-mech↗

arXiv2017

Probing the excited-state quantum phase transition through statistics of Loschmidt echo and quantum work

By analyzing the probability distributions of the Loschmidt echo (LE) and quantum work, we examine the nonequilibrium effects of a quantum many-body system, which exhibits an excited-state quantum phase transition (ESQPT). We find that depending on the value of the controlling parameter the distribution of the LE displays different patterns. At the critical point of the ESQPT, both the averaged LE and the averaged work show a cusplike shape. Furthermore, by employing the finite-size scaling analysis of the averaged work, we obtain the critical exponent of the ESQPT. Finally, we show that at the critical point of ESQPT the eigenstate is a highly localized state, further highlighting the influence of the ESQPT on the properties of the many-body system.

quant-ph↗

arXiv2017

Verification of the Quantum Nonequilibrium Work Relation in the Presence of Decoherence

Although nonequilibrium work and fluctuation relations have been studied in detail within classical statistical physics, extending these results to open quantum systems has proven to be conceptually difficult. For systems that undergo decoherence but not dissipation, we argue that it is natural to define quantum work exactly as for isolated quantum systems, using the two-point measurement protocol. Complementing previous theoretical analysis using quantum channels, we show that the nonequilibrium work relation remains valid in this situation, and we test this assertion experimentally using a system engineered from an optically trapped ion. Our experimental results reveal the work relation's validity over a variety of driving speeds, decoherence rates, and effective temperatures and represent the first confirmation of the work relation for non-unitary dynamics.

cond-mat.stat-mech↗

arXiv2017

Shortcuts to isothermality and nonequilibrium work relations

In conventional thermodynamics, it is widely acknowledged that the realization of an isothermal process for a system requires a quasi-static controlling protocol. Here we propose and design a strategy to realize a finite-rate isothermal transition from an equilibrium state to another one with same temperature, which is named shortcut to isothermality~(STI). By using STI, we unexpectedly derive three nonequilibrium work relations, including an identity between the free energy difference and the mean work due to the potential of the original system, a generalized Jarzynski equality, and the inverse relationship between the irreversible work and the total driving time. We numerically confirm these three relations by considering the motion of a Brownian particle trapped in a harmonic potential and dragged by a time-dependent force.

cond-mat.stat-mech↗

arXiv2017

Fluctuation Theorems Containing Information for Autonomous Maxwell's Demon-assisted Machines

In this article, we introduce two kinds of Fluctuation Theorems (FT) containing information for autonomous Maxwell's demon-assisted machines. Using Jensen's Inequality, we obtain Landauer's principle formulation of the second law for the whole process of the machine. Finally we make use of our results to analyze a new information device. \pacs{05.70.Ln, 05.40.-a, 89.70.Cf}

cond-mat.stat-mech↗

arXiv2017

Understanding quantum work in a quantum many-body system

Based on previous studies in a single particle system in both the integrable [Jarzynski, Quan, and Rahav, Phys.~Rev.~X {\bf 5}, 031038 (2015)] and the chaotic systems [Zhu, Gong, Wu, and Quan, Phys.~Rev.~E {\bf 93}, 062108 (2016)], we study the the correspondence principle between quantum and classical work distributions in a quantum many-body system. Even though the interaction and the indistinguishability of identical particles increase the complexity of the system, we find that for a quantum many-body system the cumulative quantum work distribution still converges to its classical counterpart in the semiclassical limit. Our results imply that there exists a correspondence principle between quantum and classical work distributions in an interacting quantum many-body system, especially in the large particle number limit, and further justify the definition of quantum work via two point energy measurements in quantum many-body systems.

quant-ph↗

arXiv2016

Stochastic Thermodynamics of a Particle in a Box

The piston system (particles in a box) is the simplest and paradigmatic model in traditional thermodynamics. However, the recently established framework of stochastic thermodynamics (ST) fails to apply to this model system due to the embedded singularity in the potential. In this Letter we study the stochastic thermodynamics of a particle in a box by adopting a novel coordinate transformation technique. Through comparing with the exact solution of a breathing harmonic oscillator, we obtain analytical results of work distribution for an arbitrary protocol in the linear response regime, and verify various predictions of the Fluctuation-Dissipation Relation. When applying to the Brownian Szilard's engine model, we obtain the optimal protocol $λ_t = λ_0 2^{t/τ}$ for a given sufficiently long total time $τ$. Our study not only establishes a paradigm for studying ST of a particle in a box, but also bridges the long-standing gap in the development of ST.

cond-mat.stat-mech↗

arXiv2016

Ergodicity and Mixing in Quantum Dynamics

After a brief historical review of ergodicity and mixing in dynamics, particularly in quantum dynamics, we introduce definitions of quantum ergodicity and mixing using the structure of the system's energy levels and spacings. Our definitions are consistent with usual understanding of ergodicity and mixing. Two parameters concerning the degeneracy in energy levels and spacings are introduced. They are computed for right triangular billiards and the results indicate a very close relation between quantum ergodicity (mixing) and quantum chaos. At the end, we argue that, besides ergodicity and mixing, there may exist a third class of quantum dynamics which is characterized by a maximized entropy.

cond-mat.stat-mech↗

arXiv2016

Quantum-Classical Correspondence Principle for Work Distributions in a Chaotic System

We numerically study the work distributions in a chaotic system and examine the relationship between quantum work and classical work. Our numerical results suggest that there exists a correspondence principle between quantum and classical work distributions in a chaotic system. This correspondence was proved for one-dimensional (1D) integrable systems in a recent work [Jarzynski, Quan, and Rahav, Phys. Rev. X 5, 031038 (2015)]. Our investigation further justifies the definition of quantum work via two point energy measurements.

cond-mat.stat-mech↗

arXiv2015

The quantum-classical correspondence principle for work distributions

For closed quantum systems driven away from equilibrium, work is often defined in terms of projective measurements of initial and final energies. This definition leads to statistical distributions of work that satisfy nonequilibrium work and fluctuation relations. While this two-point measurement definition of quantum work can be justified heuristically by appeal to the first law of thermodynamics, its relationship to the classical definition of work has not been carefully examined. In this paper we employ semiclassical methods, combined with numerical simulations of a driven quartic oscillator, to study the correspondence between classical and quantal definitions of work in systems with one degree of freedom. We find that a semiclassical work distribution, built from classical trajectories that connect the initial and final energies, provides an excellent approximation to the quantum work distribution when the trajectories are assigned suitable phases and are allowed to interfere. Neglecting the interferences between trajectories reduces the distribution to that of the corresponding classical process. Hence, in the semiclassical limit, the quantum work distribution converges to the classical distribution, decorated by a quantum interference pattern. We also derive the form of the quantum work distribution at the boundary between classically allowed and forbidden regions, where this distribution tunnels into the forbidden region. Our results clarify how the correspondence principle applies in the context of quantum and classical work distributions, and contribute to the understanding of work and nonequilibrium work relations in the quantum regime.

cond-mat.stat-mech↗

arXiv2015

Jarzynski Equality, Crooks Fluctuation Theorem and the Fluctuation Theorems of Heat for Arbitrary Initial States

By taking full advantage of the dynamic property imposed by the detailed balance condition, we derive a new refined unified fluctuation theorem (FT) for general stochastic thermodynamic systems. This FT involves the joint probability distribution functions of the final phase space point and a thermodynamic variable. Jarzynski equality, Crooks fluctuation theorem, and the FTs of heat as well as the trajectory entropy production can be regarded as special cases of this refined unified FT, and all of them are generalized to arbitrary initial distributions. We also find that the refined unified FT can easily reproduce the FTs for processes with the feedback control, due to its unconventional structure that separates the thermodynamic variable from the choices of initial distributions. Our result is heuristic for further understanding of the relations and distinctions between all kinds of FTs, and might be valuable for studying thermodynamic processes with information exchange.

cond-mat.stat-mech↗

arXiv2015

Thermodynamics of Information Processing Based on Enzyme Kinetics: an Exactly Solvable Model of Information Pump

Motivated by the recent proposed models of the information engine [D. Mandal and C. Jarzynski, Proc. Natl. Acad. Sci. 109, 11641 (2012)] and the information refrigerator [D. Mandal, H. T. Quan, and C. Jarzynski, Phys. Rev. Lett. 111, 030602 (2013)], we propose a minimal model of the information pump and the information eraser based on enzyme kinetics. This device can either pump molecules against the chemical potential gradient by consuming the information encoded in the bit stream or (partially) erase the information encoded in the bit stream by consuming the Gibbs free energy. The dynamics of this model is solved exactly, and the "phase diagram" of the operation regimes is determined. The efficiency and the power of the information machine is analyzed. The validity of the second law of thermodynamics within our model is clarified. Our model offers a simple paradigm for the investigating of the thermodynamics of information processing involving the chemical potential in small systems.

cond-mat.stat-mech↗

arXiv2014

Interference of Identical Particles and the Quantum Work Distribution

Quantum mechanical particles in a confining potential interfere with each other while undergoing thermodynamic processes far from thermal equilibrium. By evaluating the corresponding transition probabilities between many-particle eigenstates we obtain the quantum work distribution function, for identical Bosons and Fermions, which we compare with the case of distinguishable particles. We find that the quantum work distributions for Bosons and Fermions significantly differ at low temperatures, while, as expected, at high temperatures the work distributions converge to the classical expression. These findings are illustrated with two analytically solvable examples, namely the time-dependent infinite square well and the parametric harmonic oscillator.

cond-mat.stat-mech↗

arXiv2014

Experimental Test of Quantum Jarzynski Equality with a Trapped Ion System

The past two decades witnessed important developments in the field of non-equilibrium statistical mechanics. Among these developments, the Jarzynski equality, being a milestone following the landmark work of Clausius and Kelvin, stands out. The Jarzynski equality relates the free energy difference between two equilibrium states and the work done on the system through far from equilibrium processes. While experimental tests of the equality have been performed in classical regime, the verification of the quantum Jarzynski equality has not yet been fully demonstrated due to experimental challenges. Here, we report an experimental test of the quantum Jarzynski equality with a single \Yb ion trapped in a harmonic potential. We perform projective measurements to obtain phonon distributions of the initial thermal state. Following that we apply the laser induced force on the projected energy eigenstate, and find transition probabilities to final energy eigenstates after the work is done. By varying the speed of applying the force from equilibrium to far-from equilibrium regime, we verified the quantum Jarzynski equality in an isolated system.

quant-ph↗

arXiv2014

Maximum Efficiency of Heat Engines Based on a Small System: Carnot Cycle at the Nanoscale

We study the maximum efficiency of a Carnot cycle heat engine based on a small system. It is revealed that due to the finiteness of the system, irreversibility may arise when the working substance contacts with a heat bath. As a result, there is a working-substance-dependent correction to the usual Carnot efficiency, which is valid only when the working substance is in the thermodynamic limit. We derives a general and simple expression for the maximum efficiency of a Carnot cycle heat engine in terms of the relative entropy. This maximum efficiency approaches the usual Carnot efficiency asymptotically when the size of the working substance increases to the thermodynamic limit. Our study extends the Carnot's result to cases with arbitrary size working substance and demonstrates the subtlety of thermodynamics in small systems.

cond-mat.stat-mech↗

arXiv2013

Maxwell's Refrigerator: An Exactly Solvable Model

We describe a simple and solvable model of a device that -- like the "neat-fingered being" in Maxwell's famous thought experiment -- transfers energy from a cold system to a hot system by rectifying thermal fluctuations. In order to accomplish this task, our device requires a memory register to which it can write information: the increase in the Shannon entropy of the memory compensates the decrease in the thermodynamic entropy arising from the flow of heat against a thermal gradient. We construct the nonequilibrium phase diagram for this device, and find that it can alternatively act as an eraser of information. We discuss our model in the context of the second law of thermodynamics.

cond-mat.stat-mech↗