arXiv subjects

Xiao Zheng

Publications and source records attributed to Xiao Zheng.

At least 73 records · Page 4Linked to original sources

arXiv2019

Detecting Non-Markovianity via Linear Entropy of Choi State

Non-Markovian dynamics detection is one of the most popular subjects in the quantum information science. In this paper, a linear-entropy-based non-Markovianity witness scheme is constructed. The positive definiteness of the Choi state will be broken in the non-Markovian evolution, which can be witnessed by its linear entropy. Thus, the linear entropy of the Choi state can be used to witness the non-Markovian dynamics. The effectiveness of the proposed method is verified by an example of the pure dephasing channel. Also, it is shown that this method can be extended to the one based on Rényi entropy.

quant-ph↗

arXiv2019

Local Temperatures Out of Equilibrium

The temperature of a physical system is operationally defined in physics as "that quantity which is measured by a thermometer" weakly coupled to, and at equilibrium with the system. This definition is unique only at global equilibrium in view of the zeroth law of thermodynamics: when the system and the thermometer have reached equilibrium, the "thermometer degrees of freedom" can be traced out and the temperature read by the thermometer can be uniquely assigned to the system. Unfortunately, such a procedure cannot be straightforwardly extended to a system out of equilibrium, where local excitations may be spatially inhomogeneous and the zeroth law of thermodynamics does not hold. With the advent of several experimental techniques that attempt to extract a single parameter characterizing the degree of local excitations of a (mesoscopic or nanoscale) system out of equilibrium, this issue is making a strong comeback to the forefront of research. In this paper, we will review the difficulties to define a unique temperature out of equilibrium, the majority of definitions that have been proposed so far, and discuss both their advantages and limitations. We will then examine a variety of experimental techniques developed for measuring the non-equilibrium local temperatures under various conditions. Finally we will discuss the physical implications of the notion of local temperature, and present the practical applications of such a concept in a variety of nanosystems out of equilibrium.

cond-mat.stat-mech↗

arXiv2019

SYZ mirror symmetry for hypertoric varieties

We construct a Lagrangian torus fibration on a smooth hypertoric variety and a corresponding SYZ mirror variety using $T$-duality and generating functions of open Gromov-Witten invariants. The variety is singular in general. We construct a resolution using the wall and chamber structure of the SYZ base.

math.SG↗

arXiv2019

Multiparticle Entanglement Resolution Analyzer based on Quantum-Control-Assisted Uncertainty Relation

We construct a quantum-control-assisted multi-observable variance-based uncertainty relation, and the uncertainty relation obtained indicates that we can prepare a quantum state, in which the measurement results of any observables can be predicted precisely with the help of quantum control and entanglement resource. The new variance-based uncertainty relation provides a concept of "multiparticle entanglement resolution lines" for multiparticle entangled pure states, that can delineate different multiparticle entanglement classes, and thus it can be considered as an analyzer of multiparticle entanglement classes. The analyzer is used to identify different multiparticle entanglement classes with a suitable number of incompatible measurements, without a complete knowledge of the quantum state.

quant-ph↗

arXiv2018

A Unified and Strengthened Framework for the Uncertainty Relation

We provide a unified and strengthened framework for the product form and the sum form variance-based uncertainty relations by constructing a unified uncertainty relation. In the unified framework, we deduce that the uncertainties of the incompatible observables are bounded by not only the commutator of themselves, but also the quantities related with the other operator. This operator can provide information so that we can capture the uncertainty of the measurement result more accurately, and thus is named as the information operator. The introduction of the information operator can fix the deficiencies in both the product form and the sum form uncertainty relations, and provides a more accurate description of the quantum uncertainty relation. The unified framework also proposes a new interpretation of the uncertainty relation for non-Hermitian operators; i.e., the "observable" second-order origin moments of the non-Hermitian operators cannot be arbitrarily small at the same time when they are generalized-incompatible on the new definition of the generalized commutator.

quant-ph↗

arXiv2018

Stochastic Representation of Non-Markovian Fermionic Quantum Dissipation

Quantum Brownian motion plays a fundamental role in many areas of modern physics. In the path-integral formulation, the environmental quantum fluctuations driving the system dynamics can be characterized by auxiliary stochastic fields. For fermion bath environment the stochastic fields are Grassmann-valued, and cannot be represented by conventional classical numbers. In this Letter, we propose a strategy to map the nonclassical Grassmann fields onto Gaussian white noises along with a set of quantized pseudo-states. This results in a numerically feasible stochastic equation of motion (SEOM) method for fermionic open systems. The SEOM yields exact physical observables for noninteracting systems, and accurate approximate results for interacting systems. The practicality and accuracy of the proposed SEOM are exemplified by direct stochastic simulations conducted on a single-impurity Anderson model.

cond-mat.stat-mech↗

arXiv2017

Localized Orbital Scaling Correction for Systematic Elimination of Delocalization Error in Density Functional Approximations

The delocalization error of popular density functional approximations (DFAs) leads to diversified problems in present-day density functional theory calculations. For achieving a universal elimination of delocalization error, we develop a localized orbital scaling correction (LOSC) framework, which unifies our previously proposed global and local scaling approaches. The LOSC framework accurately characterizes the distributions of global and local fractional electrons, and is thus capable of correcting system energy, energy derivative and electron density in a self-consistent and size-consistent manner. The LOSC-DFAs lead to systematically improved results, including the dissociation of cationic species, the band gaps of molecules and polymer chains, the energy and density changes upon electron addition and removal, and photoemission spectra.

physics.chem-ph↗

arXiv2017

Variance-based uncertainty relation for incompatible observers

Based on mixedness definition as M=1-tr(\r{ho}^2), we obtain a new variance-based uncertainty equality along with an inequality for Hermitian operators of a single-qubit system. The obtained uncertainty equality can be used as a measure of the system mixedness. A qubit system with feedback control is also exploited to demonstrate the new uncertainty.

quant-ph↗

arXiv2017

The effects of mixedness and entanglement on the properties of the entropic uncertainty in Heisenberg model with Dzyaloshinski-Moriya interaction

The effects of mixedness and entanglement on the lower bound and tightness of the entropic uncertainty in the Heisenberg model with Dzyaloshinski-Moriya (DM) interaction have been investigated. It is found that the mixedness can reflect the essence of the entropic uncertainty better than the entanglement. Meanwhile, the uncertainty of measurement results will be reduced by the entanglement and improved by the mixedness.The entanglement can destroy the tightness of the uncertainty, while the tightness will be improved with the increasing of the mixedness. In addition, the tightness of the uncertainty in Heisenberg model can be expressed as a function of the magnetic properties, the strength of the DM interaction as well as the mixedness of the state and the functional form has no relationship with temperature. What's more, the entropic uncertain inequality becomes uncertain equality when the mixedness of the system reach the minimum value.For a given mixedness, the tightness will be reduced with the increasing of the strength of DM interaction at the antiferromagnetic case while the situation is just the opposite for the ferromagnetic case.

quant-ph↗

arXiv2017

The effects of different quantum feedback types on the tightness of the variance-based uncertainty

The effect of the quantum feedback on the tightness of the variance-based uncertainty, the possibility of using quantum feedback to prepare the state with a better tightness, and the relationship between the tightness of the uncertainty and the mixedness of the system are studied. It is found that the tightness of Schrodinger-Robertson uncertainty (SUR) relation has a strict liner relationship with the mixedness of the system. As for the Robertson uncertainty relation (RUR), we find that the tightness can be enhanced by tuning the feedback at the beginning of the evolution. In addition, we deduce that the tightness of RUR has an inverse relationship with the mixedness and the relationship turns into a strict linear one when the system reach the steady state.

quant-ph↗

arXiv2016

The thermodynamic meaning of local temperature of nonequilibrium open quantum systems

Measuring the local temperature of nanoscale systems out of equilibrium has emerged as a new tool to study local heating effects and other local thermal properties of systems driven by external fields. Although various experimental protocols and theoretical definitions have been proposed to determine the local temperature, the thermodynamic meaning of the measured or defined quantities remains unclear. By performing analytical and numerical analysis of bias-driven quantum dot systems both in the noninteracting and strongly-correlated regimes, we elucidate the underlying physical meaning of local temperature as determined by two definitions: the zero-current condition that is widely used but not measurable, and the minimal-perturbation condition that is experimentally realizable. We show that, unlike the zero-current one, the local temperature determined by the minimalperturbation protocol establishes a quantitative correspondence between the nonequilibrium system of interest and a reference equilibrium system, provided the probed system observable and the related electronic excitations are fully local. The quantitative correspondence thus allows the well-established thermodynamic concept to be extended to nonequilibrium situations.

cond-mat.mes-hall↗

arXiv2015

Generating Giant and Tunable Nonlinearity in a Macroscopic Mechanical Resonator from Chemical Bonding Force

Nonlinearity in macroscopic mechanical system plays a crucial role in a wide variety of applications, including signal transduction and processing, synchronization, and building logical devices. However, it is difficult to generate nonlinearity due to the fact that macroscopic mechanical systems follow the Hooke's law and response linearly to external force, unless strong drive is used. Here we propose and experimentally realize a record-high nonlinear response in macroscopic mechanical system by exploring the anharmonicity in deforming a single chemical bond. We then demonstrate the tunability of nonlinear response by precisely controlling the chemical bonding interaction, and realize a cubic elastic constant of \mathversion{bold}$2 \times 10^{18}~{\rm N}/{\rm m^3}$, many orders of magnitude larger in strength than reported previously. This enables us to observe vibrational bistate transitions of the resonator driven by the weak Brownian thermal noise at 6~K. This method can be flexibly applied to a variety of mechanical systems to improve nonlinear responses, and can be used, with further improvements, to explore macroscopic quantum mechanics.

quant-ph↗

arXiv2015

Local temperatures of strongly-correlated quantum dots out of equilibrium

Probes that measure the local thermal properties of systems out of equilibrium are emerging as new tools in the study of nanoscale systems. One can then measure the temperature of a probe that is weakly coupled to a bias-driven system. By tuning the probe temperature so that the expectation value of some observable of the system is minimally perturbed, one obtains a parameter that measures its degree of local statistical excitation, and hence its local heating. However, one anticipates that different observables may lead to different temperatures and thus different local heating expectations. We propose an experimentally realizable protocol to measure such local temperatures and apply it to bias-driven quantum dots. By means of a highly accurate open quantum system approach, we show theoretically that the measured temperature is quite insensitive both to the choice of observable and to the probe-system coupling. In particular, even with observables that are distinct both physically and in their degree of locality, such as the local magnetic susceptibility of the quantum dot and the global spin-polarized current measured at the leads, the resulting local temperatures are quantitatively similar for quantum dots ranging from noninteracting to Kondo-correlated regimes, and are close to those obtained with the traditional "local equilibrium" definition.

cond-mat.str-el↗

arXiv2014

Complex absorbing potential based Lorentzian fitting scheme and time dependent quantum transport

Based on the complex absorbing potential (CAP) method, a Lorentzian expansion scheme is developed to express the self-energy. The CAP-based Lorentzian expansion of self-energy is employed to solve efficiently the Liouville-von Neumann equation of one-electron density matrix. The resulting method is applicable for both tight-binding and first-principles models, and is used to simulate the transient currents through graphene nanoribbons and a benzene molecule sandwiched between two carbon-atom-chains.

cond-mat.mes-hall↗

arXiv2014

Hierarchical equations of motion for impurity solver in dynamical mean-field theory

A nonperturbative quantum impurity solver is proposed based on a formally exact hierarchical equations of motion (HEOM) formalism for open quantum systems. It leads to quantitatively accurate evaluation of physical properties of strongly correlated electronic systems, in the framework of dynamical mean-field theory (DMFT). The HEOM method is also numerically convenient to achieve the same level of accuracy as that using the state-of-the-art numerical renormalization group impurity solver at finite temperatures. The practicality of the novel HEOM+DMFT method is demonstrated by its applications to the Hubbard models with Bethe and hypercubic lattice structures. We investigate the metal-insulator transition phenomena, and address the effects of temperature on the properties of strongly correlated lattice systems.

cond-mat.str-el↗

arXiv2013

Time-dependent density-functional theory for real-time electronic dynamics on material surfaces

The real-time electronic dynamics on material surfaces is critically important to a variety of applications. However, their simulations have remained challenging for conventional methods such as the time-dependent density-functional theory (TDDFT) for isolated and periodic systems. By extending the applicability of TDDFT to systems with open boundaries, we achieve accurate atomistic simulations of real-time electronic response to local perturbations on material surfaces. Two prototypical scenarios are exemplified: the relaxation of an excess electron on graphene surface, and the electron transfer across the molecule-graphene interface. Both the transient and long-time asymptotic dynamics are validated, which accentuates the fundamental importance and unique usefulness of an open-system TDDFT approach. The simulations also provide insights into the characteristic features of temporal electron evolution and dissipation on surfaces of bulk materials.

physics.chem-ph↗

arXiv2013

Hierarchical Liouville-space approach to nonequilibrium dynamical properties of quantum impurity systems

We propose a hierarchical dynamics approach for evaluation of nonequilibrium dynamic response properties of quantum impurity systems. It is based on a hierarchical equations of motion formalism, in conjunction with a linear response theory established in the hierarchical Liouville space. This provides an accurate and universal tool for characterization of arbitrary response and correlation functions of local impurities, as well as transport related response properties. The practicality of our proposed approach is demonstrated via the evaluation of various dynamical properties of a single-impurity Anderson model. These include the impurity spectral density, local charge fluctuation, local magnetic susceptibility, and current-voltage admittance, in both equilibrium and nonequilibrium situations. The numerical results are considered to achieve the quantitative accuracy, as long as they converge with respect to the truncation of the hierarchy.

cond-mat.str-el↗

arXiv2013

Thermopower of few-electron quantum dots with Kondo correlations

The thermopower of few-electron quantum dots with Kondo correlations is investigated via a hierarchial equations of motion approach. The thermopower is determined by the line shape of spectral function within a narrow energy window defined by temperature. Based on calculations and analyses on single-level and two-level Anderson impurity models, the underlying relations between thermopower and various types of electron correlations are elaborated. In particular, an unconventional sign reversal behavior is predicted for quantum dots with a suitable inter-level spacing. The new feature highlights the significance of multi-level effects and their interplay with Kondo correlations. Our finding and understanding may lead to novel thermoelectric applications of quantum dots.

cond-mat.str-el↗