Microcanonical-ensemble computer simulation of the high-temperature expansion coefficients of the Helmholtz free energy of a square-well fluid

The microcanonical-ensemble computer simulation method (MCE) is used to evaluate the perturbation terms A_i of the Helmholtz free energy of a square-well (SW) fluid. The MCE method offers a very efficient and accurate procedure for the determination of perturbation terms of discrete-potential systems such as the SW fluid and surpass the standard NVT canonical ensemble Monte Carlo method, allowing the calculation of the first six expansion terms. Results are presented for the case of a SW potential with attractive ranges 1.1 ≤ λ ≤ 1.8. Using semi-empirical representation of the MCE values for A_i, we also discuss the accuracy in the determination of the phase diagram of this system.     

Nuclear quantum effects in liquid water from path-integral simulations using an ab initio force-matching approach

We have applied path integral simulations, in combination with new ab initio based water potentials, to investigate nuclear quantum effects in liquid water. Because direct ab initio path integral simulations are computationally expensive, a flexible water model is parameterised by force-matching to density functional theory-based molecular dynamics simulations. Static and dynamic properties of liquid water at ambient conditions are presented and the role of nuclear quantum effects, exchange-correlation functionals and dispersion corrections are discussed in regards to reproducing the experimental properties of liquid water.     

Lennard-Jones binary fluids: A comparative study between the molecular dynamics and Monte Carlo descriptions of their structural properties

Molecular dynamics and Monte Carlo techniques are employed for the study of binary Lennard-Jones fluids. Systematic comparisons between the predictions of both techniques are discussed, with particular emphasis on the dependency of the structural properties with respect to temperature and Lennard-Jones potential parameters.     

Thermodynamic properties of a hard-core Lennard-Jones fluid from computer simulation and the coupling parameter series expansion

ABSTRACT

The thermodynamic properties of a fluid with an interaction potential consisting in a hard-sphere core plus a Lennard-Jones tail have been obtained by Monte Carlo (MC) NVT simulation as a function of the density along several isotherms. In addition, the liquid–vapour coexistence has been determined by means of histogram-reweighting MC. These data have been used to analyse the performance of perturbation theory. To this end, the first three perturbation terms of the inverse temperature expansion of the Helmholtz free energy have been obtained by means of MC NVT simulations to test the convergence of the perturbation series and to compare with the predictions of the coupling parameter series expansion. Then, the predictions of the latter theory for the thermodynamic properties have been compared with the simulations, revealing the overall excellent performance of this perturbation theory for this model fluid, except in the vicinity of the critical point.     

Adsorption and interfacial phenomena of a Lennard-Jones fluid adsorbed in slit pores: DFT and GCMC simulations

ABSTRACT

Confinement of fluids in porous media leads to the presence of solid–fluid (SF) interfaces that play a key role in many different fields. The experimental characterisation of SF interfacial properties, in particular the surface tension, is challenging or not accessible. In this work, we apply mean-field density functional theory (DFT) to determine the surface tension and also density profile of a Lennard-Jones fluid in slit-shaped pores for realistic amounts of adsorbed molecules. We consider the pore walls to interact with fluid molecules through the well-known 10-4-3 Steele potential. The results are compared with those obtained from Monte Carlo simulations in the Grand Canonical Ensemble (GCMC) using the test-area method. We analyse the effect on the adsorption and interfacial phenomena of volume and energy factors, in particular, the pore diameter and the ratio between SF and fluid–fluid dispersive energy parameters, respectively. Results from DFT and GCMC simulations were found to be comparable, which points to their reliability.     

量子Harper模型的量子计算鲁棒性与耗散退相干

运用量子轨迹和量子Monte Carlo仿真的方法，研究耗散退相干对周期驱动的量子Harper (quantum kicked Harper, QKH)模型量子计算的影响.数值仿真结果表明，一定强度的耗散干扰将破坏QKH特征状态的动态局域化以及相空间的随机网结构.以相位阻尼信道噪声模型为例分析了保真度的衰减规律以及可信计算时间尺度.与静态干扰相比，在干扰强度小于某一阈值时，耗散干扰下的可信计算时间尺度随量子比特的增加而快速下降；而在干扰强度大于该阈值时，静态干扰下的可信计算时间尺度下降更快.     

量子Harper模型的量子计算鲁棒性与耗散退相干

运用量子轨迹和量子Monte Carlo仿真的方法,研究耗散退相干对周期驱动的量子Harper (quantum kicked Harper, QKH)模型量子计算的影响.数值仿真结果表明,一定强度的耗散干扰将破坏QKH特征状态的动态局域化以及相空间的随机网结构.以相位阻尼信道噪声模型为例分析了保真度的衰减规律以及可信计算时间尺度.与静态干扰相比,在干扰强度小于某一阈值时,耗散干扰下的可信计算时间尺度随量子比特的增加而快速下降;而在干扰强度大于该阈值时,静态干扰下的可信计算时间尺度下降更快. 关键词： 量子计算 量子Harper模型 主方程 量子Monte Carlo方法     

Heisenberg picture operators in the stochastic wave function approach to open quantum systems

A fast simulation algorithm for the calculation of multitime correlation functions of open quantum systems is presented. It is demonstrated that any stochastic process which “unravels” the quantum Master equation can be used for the calculation of matrix elements of reduced Heisenberg picture operators, and thus for the calculation of multitime correlation functions, by extending the stochastic process to a doubled Hilbert space. The numerical performance of the stochastic simulation algorithm is investigated by means of a standard example. Received: 30 May 1997 / Revised: 4 November 1997 / Accepted: 7 November 1997     

Perturbation theory of the Fermi surface in a quantum liquid. A general quasiparticle formalism and one-dimensional systems

We develop a perturbation theory formalism for the theory of the Fermi surface in a Fermi liquid of particles interacting via a bounded short-range repulsive pair potential. The formalism is based on the renormalization group and provides a formal expansion of the large-distance Schwinger functions in terms of a family of running couplings consisting of one- and two-body quasiparticle potentials. The flow of the running couplings is described in terms of a beta function, which is studied to all orders of perturbation theory and shown to obey, in thenth order,n! bounds. The flow equations are written in general dimensiond1 for the spinless case (for simplicity). The picture that emerges is that on a large scale the system looks like a system of fermions interacting via a-like interaction potential (i.e., a potential approaching 0 everywhere except at the origin, where it diverges, although keeping the integral bounded); the theory is not asymptotically free in the usual sense and the freedom mechanism is thus more delicate than usual: the technical problem of dealing with unbounded effective potentials is solved by introducing a mathematically precise notion ofquasiparticles, which turn out to be natural objects with finite interaction even when the physical potential diverges as a deltalike function. A remarkable kind of gauge symmetry is associated with the quasiparticles. To substantiate the analogy with the quasiparticle theory we discuss the mean field theory using our notion of quasiparticles: the resulting self-consistency relations are closely reminiscent of those of the BCS model. The formalism seems suited for a joint theory of normal states of Fermi liquids and of BCS states: the first are associated with the trivial fixed point of our flow or with nearby nontrivial fixed points (or invariant sets) and the second may naturally correspond to really nontrivial fixed points (which may nevertheless turn out to be accessible to analysis because the BCS state is a quasi free state, hence quite simple, unlike the nontrivial fixed points of field theory). Thed=1 case is deeply different from thed> 1 case, for our spinless fermions: we can treat it essentially completely for small coupling. The system is not asymptotically free and presents anomalous renormalization group flow with a vanishing beta function, and the discontinuity of the occupation number at the Fermi surface is smoothed by the interaction (remaining singular with a coupling-dependent singularity of power type with exponent identified with the anomalous dimension). Finally, we present a heuristic discussion of the theory for the flow of the running coupling constants in spinlessd> 1 systems: their structure is simplified further and the relevant part of the running interaction is precisely the interaction between pairs of quasiparticles which we identify with the Cooper pairs of superconductivity. The formal perturbation theory seems to have a chance to work only if the interaction between the Cooper pairs is repulsive: and to second order we show that in the spin-0 case this happens if the physical potential is repulsive. Our results indicate the possibility of the existence of a normal Fermi surface only if the interaction is repulsive.     

Thermodynamic properties for the triangular-well fluid

The thermodynamic properties of the triangular-well fluid with a well range of up to twice the hard sphere diameter were studied by means of a new developed equation of state and molecular simulation. This EoS is based on the perturbation theory of Barker and Henderson with the first and second-order perturbation terms evaluated by molecular simulation and then a fit with a simple function based on the radial distribution function of the reference fluid. The thermodynamic properties for the triangular-well fluid were also obtained directly by Gibbs ensemble and NPT Monte Carlo simulations. Good agreement is observed between the proposed EoS and the molecular simulation results. A model for the triangular-well solid is also presented; this has been used to calculate the solid–liquid transition line. Very good agreement is obtained with previously report values for this line and for the triple point temperature and pressure.     

低维量子磁性和量子海森伯反铁磁体之有效场论

文章对低维量子磁性的基本问题和相关研究进展作了简单评述，强调了量子非线性Sigma模型在研究量子海森伯反铁磁体的低能物理方面所起的作用以及理论本身存在的疑难问题，并简单介绍了作者最近提出的克服这些疑难问题的一个新建议．     

State sum invariants of three-manifolds: A combinatorial approach to topological quantum field theories

The construction of Turaev and Viro involving quantum 6j-symbols and giving rise to invariants of closed, compact three-manifolds is extended. It leads to invariants of coloured graphs on the boundary of compact three-manifolds. This allows one to derive surgery formulas when cutting along an arbitrary two-manifold. In particular all axioms of a topological quantum field theory may be verified and the dimensions of the associated Hilbert spaces are given by the square of the Verlinde formula.     

大粒子数二维硬核玻色子系统的量子蒙特卡罗模拟

采用随机级数展开的量子蒙特卡罗方法研究二维硬核的玻色-赫伯德模型的热力学性质. 首先通过算符变换将模型映射成为二维反铁磁准海森伯模型. 变换后的模型比通常的海森伯模型多一项, 该项正比于系统的格点总数 N, 对于大粒子数的系统, 该项使模拟耗时指数增加, 所以难以计算大粒子数系统.采用非局域操作循环更新后, 这个困难可以得到很好的解决, 可使粒子数总数增大到几千个.研究结果表明, 粒子数密度在0-0.5范围内增大时, 能量呈递减趋势, 并趋于某一定值, 随着正方晶格系统尺度增大, 能量也随之增大;正方晶格系统尺度一定时, 能量和磁化强度随着温度的升高而增大, 化学势的变化对能量和磁化强度没有影响, 能量随着正方晶格系统尺度增大而增大, 磁化强度却随之减小;正方晶格系统尺度一定时, 化学势的增大对比热没有影响, 随着温度的升高比热出现先增大后减小的趋势, 最后趋于某个值, 达到平衡, 而正方晶格系统尺度越大, 比热曲线增大部分的趋势越大, 减小部分的趋势也更明显, 参照朗道超流理论, 本文模拟的能量和比热曲线趋势与朗道二流体模型下He II的理论研究一致; 不同正方晶格系统尺度的影响不大, 均匀磁化率倒数在0-0.5(J/k_B)的低温范围内有很小的波动, J为耦合能, k_B为玻尔兹曼常数, 温度在0.5-2 (J/k_B)的范围内, 均匀磁化率的倒数随着温度的升高而增大, 且曲线的趋势显示了一种类似近藤行为.     

A sport and a pastime: Model design and computation in quantum many-body systems

We summarize the recent developments in the model design and computation for a few representative quantum many-body systems, encompassing quantum critical metals beyond the Hertz-Millis-Moriya framework with pseudogap and superconductivity, SYK non-Fermi-liquid with self-tuned quantum criticality and fluctuation induced superconductivity, and the flat-band quantum Moiré lattice models in continuum where the interplay of quantum geometry of flat-band wave function and the long-range Coulomb interactions gives rise to novel insulating phases at integer fillings and superconductivity away from them. Although the narrative choreography seems simple, we show how important the appropriate model design and their tailor-made algorithmic developments - in other words, the scientific imagination inspired by the corresponding fast experimental developments in the aforementioned systems - compel us to invent and discover new knowledge and insights in the sport and pastime of quantum many-body research.     

压力和温度对固氘掺锂体系的影响

 利用路径积分蒙特卡罗方法，研究了压力和温度变化对固氘掺锂体系的影响。结果表明，在高压条件下（0.9~2.4 GPa），锂原子掺入固体氘后，要占据五个氘分子空位形成稳定结构。温度变化不能改变这一五空位占据。固氘掺锂体系锂原子吸收谱随压力和温度的变化趋势类似于固氢掺锂体系锂原子吸收谱随压力和温度变化的趋势。但在某一固定压力和温度点，这两种吸收谱却由于氘分子和氢分子零点振动的不同有着明显的差异。随着温度或压力的增加，这两种吸收谱间的差异越来越小。     

含时量子蒙特卡罗方法研究两电子原子在强激光作用下电子的动力学行为

通过改进含时量子蒙特卡罗方法研究了一维模型双电子原 子在强激光作用下的电子动力学过程. 与准确的数值积分求解含时薛定谔方程相比, 计算得到的波包对应的量子系综中粒子的动力学变化和含时波包演化结果定性一致, 且大幅度地提高了计算效率. 根据计算得到的经典粒子系综的动力学演化行为, 分析了原子在强激光作用下的激发、电离、重散射等非线性过程.     

G. N. Lewis' atom and quantum Monte Carlo studies of liquids

Liquids that involve changes in electronic structure are difficult to simulate using pairwise additive forces. In this paper we use a semiempirical model of the internal structure of atoms in order to simulate simultaneously electronic and nuclear dynamics of fluids. The proposed excitonic phase of mercury is critically examined with these models.     

D2/H2 quantum sieving in microporous carbons: a theoretical study on the effects of pore size and pressure

The adsorption of hydrogen and deuterium in slit-shaped carbon pores is studied by grand canonical Monte Carlo simulations. All interactions are assumed to be of Lennard–Jones type, while the Feynman–Hibbs expression is used to account for quantum effects. The interaction energy of both isotopes inside the slit pore space is discussed thoroughly. Furthermore, pure component adsorption isotherms of both isotopes were simulated at 77?K for pressures up to 20?bar in slit pores having widths of up to 2.0?nm. According to our simulations, in equilibrium, slit pores reveal slight deuterium selectivity over hydrogen, and this quantum-based selectivity depends both on pressure and pore size.