Classical Representation of a Quantum System at Equilibrium

A quantum system at equilibrium is represented by a corresponding classical system, chosen to reproduce the thermodynamic and structural properties. The objective is to develop a means for exploiting strong coupling classical methods (e.g., MD, integral equations, DFT) to describe quantum systems. The classical system has an effective temperature, local chemical potential, and pair interaction that are defined by requiring equivalence of the grand potential and its functional derivatives with respect to the external and pair potentials for the classical and quantum systems. Practical inversion of this mapping for the classical properties is effected via the hypernetted chain approximation, leading to representations as functionals of the quantum pair correlation function. As an illustration, the parameters of the classical system are determined approximately such that ideal gas and weak coupling RPA limits are preserved (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Strong correlation effects in 2D Bose-Einstein condensed dipolar excitons

By doing quantum Monte Carlo ab initio simulations we show that dipolar excitons, which are now under experimental study, actually are strongly correlated systems. Strong correlations manifest in significant deviations of excitation spectra from the Bogoliubov one, large Bose condensate depletion, short-range order in the pair correlation function, and peak(s) in the structure factor.     

Random field effects in classical and quantum critical phenomena

The effect of quenched random fields on classical and quantum critical behaviour is studied by means of the ?-analysis for a number of systems. The investigation is performed in terms of a generalized random-field correlation function. The interplay of short-range correlations as well as of a parameter-dependent variety of long-range correlations with thermal and quantum fluctuations is revealed.     

高压下液态硝基甲烷的分子动力学模拟

 对高压下液态硝基甲烷的性质进行经典和基于第一性原理计算的Car-Parrinello分子动力学（CPMD）模拟。利用经典势的分子动力学（MD）模拟研究了高压压缩状态下液态硝基甲烷的结构和热力学性质,得到了高达14.2 GPa压力下的理论Hugoniot数据。对于一些热力学函数,如总能和粒子速度,经典势模拟给出了很好的总趋势,基本特征和实验观测一致。但是在给定的密度下,经典模拟预言的Hugoniot压力偏高。在几个选定的密度下,进行了CPMD模拟,得到了二体相关函数、速度自相关函数、振动光谱和其它的热力学性质,并与经典模拟结果进行了比较。对二体相关函数的分析表明经典势的短程部分的刚性可能太强,从而导致了比实验值高的理论压力值。对于某些二体相关函数,CPMD模拟和经典模拟结果差别很大,可以归结为量子效应。当压力增高时,量子模拟得到的振动光谱向高频部分移动的现象与实验观测相符合。     

Modeling hot, dense hydrogen with a classical spin dependent hamiltonian

Hot, dense hydrogen is studied with a classical model in which the interaction energy between atoms depends on their internal spins as well as their separation distance. The spins are treated as classical variables. This model is used in Monte Carlo simulations to calculate internal energies, pressures, and pair correlation functions, as well as the Hugoniot for shocked liquid deuterium. The results clearly show the transition of hot, dense hydrogen from a molecular to an atomic fluid. Our results are in reasonable agreement with far more elaborate quantum mechanical simulations.     

Quantum Correlation in Matrix Product States of One-Dimensional Spin Chains

For our proposed composite parity-conserved matrix product state (MPS), if only a spin block length is larger than 1, any two such spin blocks have correlation including classical correlation and quantum correlation. Both the total correlation and the classical correlation become larger than that in any subcomponent; while the quantum correlations of the two nearest-neighbor spin blocks and the two next-nearest-neighbor spin blocks become smaller and for other conditions the quantum correlation becomes larger, i.e., the increase or the production of the long-range quantum correlation is at the cost of reducing the short-range quantum correlation, which deserves to be investigated in the future; and the ration of the quantum correlation to the total correlation monotonically decreases to a steady value as the spacing spin length increasing.     

Quantum Correlation in Matrix Product States of One-Dimensional Spin Chains

For our proposed composite parity-conserved matrix product state(MPS), if only a spin block length is larger than 1, any two such spin blocks have correlation including classical correlation and quantum correlation. Both the total correlation and the classical correlation become larger than that in any subcomponent; while the quantum correlations of the two nearest-neighbor spin blocks and the two next-nearest-neighbor spin blocks become smaller and for other conditions the quantum correlation becomes larger, i.e., the increase or the production of the long-range quantum correlation is at the cost of reducing the short-range quantum correlation, which deserves to be investigated in the future; and the ration of the quantum correlation to the total correlation monotonically decreases to a steady value as the spacing spin length increasing.     

温稠密参数下的双流不稳定性分析

温稠密物质状态是惯性约束聚变过程及天体演化过程中的重要物质发展阶段。随着密度的增加,量子效应逐渐显现并导致包括温稠密参数下集体激发行为与经典等离子体模型之间出现差异。密度泛函动理学方法是基于含时密度泛函理论建立的统计模型,并依据Wigner分布函数(相空间量子力学)发展的动理学输运方法,可以有效弥补经典等离子体理论对量子效应的忽略。基于密度泛函动理学方法,发现温稠密特征参数内费米狄拉克分布、交换关联效应、量子衍射效应等性质都对双流不稳定性起到抑制作用。密度泛函动理学方法有望为等离子体视角研究温稠密系统输运性质提供第一性的理论平台。     

Equilibrium properties of two-component classical plasmas

Two-component overall neutral classical Coulomb Gas is considered in the canonical ensemble for any value of the space dimensionality ν. The equilibrium properties, i.e. pair correlations and thermodynamic functions are investigated in two complementary ways. The first one is adequate in considering the low temperature range and uses the “molecular” interaction within a pair of unlike charges as a zero order starting point. On the other hand, the high-temperature fully ionized and translation-invariant plasma is considered within the nodal expression with respect to the classical plasma parameter. These two ways are possible through the use of effective temperature-dependent classical interaction for ν > 2. As a by-product, we obtain a unified treatment of the Coulomb Gas thermal properties with respect to dimensionality (integer or real). We also obtain a contrasting comparison with corresponding properties of the one component plasma model which are already known. In this analysis the ν = 2 two-component Coulomb Gas seems to be a landmark for the other TCP'₈. I do not consider degeneracy effects. I consider diffraction corrections in a first order expansion with respect to the Coulomb interaction, in the high-temperature range. The “Hydrogen atom” spectrum is explained for all ν. The long-range hypernetted chain resummation of the pair correlation functions asymptotic behavior does not hold for symmetrical (Z₁ = ?Z₂) plasmas; the corresponding onset of short-range order disappears when the plasma parameter increases. The modified long- and short-range behaviors of the pair correlation functions are then displayed with the canonical thermodynamics.     

LMG model: Markovian evolution of classical and quantum correlations under decoherence

We have investigated the quantum phase transition in the ground state of collective Lipkin-Meshkov-Glick model (LMG model) subjected to decoherence due to its interaction, represented by a quantum channel, with an environment. We discuss the behavior of quantum and classical pair wise correlations in the system, with the quantumness of correlations measured by quantum discord (QD), entanglement of formation (EOF), measurement-induced disturbance (MID) and the Clauser-Horne-Shimony-Holt-Bell function (CHSH-Bell function). The time evolution established by system-environment interactions is assumed to be Markovian in nature and the quantum channels studied include the amplitude damping (AD), phase damping (PD), bit-flip (BF), phase-flip (PF), and bit-phase-flip (BPF) channels. One can identify appropriate quantities associated with the dynamics of quantum correlations signifying quantum phase transition in the model. Surprisingly, the CHSH-Bell function is found to detect all the phase transitions, even when quantum and classical correlations are zero for the relevant ground state.     

Universal low-temperature properties of frustrated classical spin chain near the ferromagnet-helimagnet transition point

The thermodynamics of the classical frustrated spin chain near the transition point between the ferromagnetic and the helical phases is studied. The calculation of the partition and spin correlation functions at low temperature limit is reduced to the quantum mechanical problem of a particle in potential well. It is shown that the thermodynamic quantities are universal functions of the temperature normalized by the chiral domain wall energy. The obtained behavior of the static structure factor indicates that the short-range helical-type correlations existing at low temperatures on the helical side of the transition point disappear at some critical temperature, defining the Lifshitz point. It is also shown that the low-temperature susceptibility in the helical phase near the transition point has a maximum at some temperature. Such behavior is in agreement with that observed in several materials described by the quantum s = 1/2 version of this model.     

Quantum Correlation Properties in Composite Parity-Conserved Matrix Product States

We give a new thought for constructing long-range quantum correlation in quantum many-body systems. Our proposed composite parity-conserved matrix product state has long-range quantum correlation only for two spin blocks where their spin-block length larger than 1 compared to any subsystem only having short-range quantum correlation, and we investigate quantum correlation properties of two spin blocks varying with environment parameter and spacing spin number. We also find that the geometry quantum discords of two nearest-neighbor spin blocks and two next-nearest-neighbor spin blocks become smaller and for other conditions the geometry quantum discord becomes larger than that in any subcomponent, i.e., the increase or the production of the long-range quantum correlation is at the cost of reducing the short-range quantum correlation compared to the corresponding classical correlation and total correlation having no any characteristic of regulation. For nearest-neighbor and next-nearest-neighbor all the correlations take their maximal values at the same points, while for other conditions no whether for spacing same spin number or for different spacing spin numbers all the correlations taking their maximal values are respectively at different points which are very close. We believe that our work is helpful to comprehensively and deeply understand the organization and structure of quantum correlation especially for long-range quantum correlation of quantum many-body systems; and further helpful for the classification, the depiction and the measure of quantum correlation of quantum many-body systems.     

Photon statistics of pulse-pumped four-wave mixing in fiber with weak signal injection

We study the photon statistics of pulse-pumped four-wave mixing in fibers with weak coherent signal injection by measuring the intensity correlation functions of individual signal and idler fields. The experimental results show that the intensity correlation function of individual signal(idler) field g_(s(i))~(2) decreases with the intensity of signal injection. After applying narrow band filter in signal(idler) band, the value of g_(s(i))~(2) decreases from 1.9 ± 0.02(1.9 ± 0.02) to 1.03 ± 0.02(1.05 ± 0.02) when the intensity of signal injection varies from 0 to 120 photons/pulse. The results indicate that the photon statistics changes from Bose–Einstein distribution to Poisson distribution. We calculate the intensity correlation functions by using the multi-mode theory of four-wave mixing in fibers. The theoretical curves well fit the experimental results.Our investigation will be useful for mitigating the crosstalk between quantum and classical channels in a dense wavelength division multiplexing network.     

Influence of a random telegraph process on the transport through a point contact

We describe the transport properties of a point contact under the influence of a classical two-level fluctuator. We employ a transfer matrix formalism allowing us to calculate arbitrary correlation functions of the stochastic process by mapping them on matrix products. The result is used to obtain the generating function of the full counting statistics of a classical point contact subject to a classical fluctuator, including extensions to a pair of two-level fluctuators as well as to a quantum point contact. We show that the noise in the quantum point contact is a sum of the (quantum) partitioning noise and the (classical) noise due to the two-level fluctuator. As a side result, we obtain the full counting statistics of a quantum point contact with time-dependent transmission probabilities.     

On the measurability of quantum correlation functions

The concept of correlation function is widely used in classical statistical mechanics to characterize how two or more variables depend on each other. In quantum mechanics, on the other hand, there are observables that cannot be measured at the same time; the so-called incompatible observables. This prospect imposes a limitation on the definition of a quantum analog for the correlation function in terms of a sequence of measurements. Here, based on the notion of sequential weak measurements, we circumvent this limitation by introducing a framework to measure general quantum correlation functions, in principle, independently of the state of the system and the operators involved. To illustrate, we propose an experimental configuration to obtain explicitly the quantum correlation function between two Pauli operators, in which the input state is an arbitrary mixed qubit state encoded on the polarization of photons.     

Bifurcation in kinetic equation for interacting Fermi systems

The recently derived nonlocal quantum kinetic equation for dense interacting Fermi systems combines time derivatives with finite time stepping known from the logistic mapping. This continuous delay differential equation is a consequence of the microscopic delay time representing the dynamics of the deterministic chaotic system. The responsible delay time is explicitly calculated and discussed for short-range correlations. As a novel feature oscillations in the time evolution of the distribution function itself appear and bifurcations up to chaotic behavior occur. The temperature and density conditions are presented where such oscillations and bifurcations arise indicating an onset of phase transition.     

Electron correlation in two-dimensional systems: CHNC approach to finite-temperature and spin-polarization effects

Applying the classical-map hypernetted-chain method (CHNC) developed recently by Dharma-wardana and Perrot, we have studied the temperature and spin-polarization effects on electron correlation in the uniform quantum two-dimensional gas (2DEG) over a wide range of temperature T and spin-polarization ζ. The quantum fluid at the temperature T is mapped to a classical fluid at the temperature T_cf given by T_cf²=T²+T_q², where the quantum temperature T_q is determined by comparing the calculated correlation energy to that of Monte Carlo results for the fully spin-polarized quantum system at zero temperature. By the iterative solution of the modified HNC equation and the Ornstein-Zernike equation, we have obtained the pair distribution function (PDF) and correlation energy for the two-component classical 2DEG with a classical fluid temperature T_cf. The anti-parallel bridge function B₁₂(r) appearing in the modified HNC equation is determined by using the Monte Carlo correlation energy at T=0 or STLS (Singwi-Tosi-Land-Sjölander) result at T>0 and the numerical solution to the Percus-Yevick (PY) equation for the system of hard disks. By calculating the Pauli potential, the bridge function, PDFs, structure factors and correlation energy, we have shown that in some cases, the properties of the uniform quantum 2DEG depend remarkably on the temperature and spin-polarization.     

Quantum corrections for Boltzmann equation

We present the lowest order quantum correction to the semiclassical Boltzmann distribution function, and the equation satisfied by this correction is given. Our equation for the quantum correction is obtained from the conventional quantum Boltzmann equation by explicitly expressing the Planck constant in the gradient approximation, and the quantum Wigner distribution function is expanded in powers of Planck constant, too. The negative quantum correlation in the Wigner distribution function which is just the quantum correction terms is naturally singled out, thus obviating the need for the Husimi’s coarse grain averaging that is usually done to remove the negative quantum part of the Wigner distribution function. We also discuss the classical limit of quantum thermodynamic entropy in the above framework. Supported by the National Natural Science Foundation of China (Grant No. 10404037) and the Scientific Research Fund of GUCAS (Grant No. 055101BM03)     

Spatial correlation of two particles in semiconductor quantum ring

We analyze the effect of the spatial correlation on the ground state energy of two particles (two electrons and exciton–hole pair) confined in quantum ring (QR) with a soft-edge-barrier confinement potential. Starting from the Schrödinger variational principle we derive a one-dimensional differential equation for the spatial pair correlation function (SPCF), which we solve numerically by using the shooting method. The effect of the repulsive core in a self-assembled GaAs/InAs QR on the two-electron and exciton SPCF is analyzed. A comparative analysis of the dependencies of the two-particle ground state energies on the inner and outer radii of GaAs/InAs QRs with different confinement potential shapes is presented.     

An Orbital‐Free Quantum Hypernetted Chain Model Based Perturbation Theory for Equation of State of Hydrogen and Helium in Warm Dense Regime

We present in this work, a thermodynamic perturbation theory for equation of state of hydrogen and helium in the warm dense regime. The system is modeled as a mixture of classical point ions and quantum electrons. A perturbation series for Helmholtz free energy and correlation functions of the ions and electrons as a function of density and temperature is proposed. Combining the classical thermodynamic perturbation theory and the orbitial‐free quantum hyper‐netted chain theory, a systematic procedure to obtain the terms of the perturbation series is developed. The ion‐ion correlations are treated within the hyper‐netted chain approximation and the ion‐electron correlations are treated within the Thomas‐Fermi‐Dirac‐Weizsäcker approximation. The method has been applied to obtain isotherms of hydrogen and helium in the warm dense regime. The isotherms are compared with available ab‐initio data and the results are analyzed. A good agreement with ab‐initio data has been observed for pressures greater than one Mbar. Advantages and limitations of the present method are discussed along with possible future improvements. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)