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.     

Quasi-2D and prewetting transitions of square-well fluids on a square-well substrate

Molecular simulation methodologies are employed to study the first-order transition of variable square-well (SW) fluids on a wide range of weak attractive surfaces. Surface phase diagram of SW fluids of attractive well diameter λ _ff = 1.5, 1.75, 2.0 on a smooth, structureless surface modelled by a SW potential is reported via grand-canonical transition-matrix Monte Carlo (GC-TMMC) and histogram reweighting techniques. Fluids with λ _ff = 1.5 and 1.75 show quasi-2D vapour–liquid phase transition; on the other hand, prewetting transition is visible for a SW fluid with larger well-extent λ _ff = 2.0. The prewetting line, its length, and closeness to the bulk saturation curve are found to depend strongly on the nature of the fluid–fluid and fluid–wall interaction potentials. Boundary tension of surface coexistence films is calculated by two methods. First, the finite size scaling approach of Binder is used to evaluate the boundary tension via GC-TMMC. Second, the results of the boundary tension are verified by virtue of its relation to the pressure tensor components, which are calculated using a NVT-Monte Carlo approach. The results from the two methods are in good agreement. Boundary tension is found to increase with the increase in the wall–fluid interaction range for the quasi-2D system; conversely, boundary tension for thin–thick film, at prewetting transition, decreases with the increase in the wall–fluid interaction range.     

Analysis of one-dimensional Fibonacci-class quasicrystals using perturbation theory

In this work, we present a new and semi-analytical method to investigate one-dimensional Fibonacci-class photonic quasicrystals from waveguiding properties point of view. Usually, the exact treatment for obtaining band diagram in these situations is very hard and the numerical methods are used. In this paper, we investigate the waveguiding properties of one-dimensional quasicrystals by using perturbation method. In this direction, the band diagram and field distribution of this structure are investigated.     

Molecular simulation study of triangle-well fluids confined in slit pores

Grand canonical Monte Carlo simulations are used to study the behaviour of triangle-well (TW) fluids with variable well widths confined inside slit pores. The effect of individual factors influencing the properties of confined fluids such as fluid–fluid interactions, pore size and pore wall–fluid interactions are obtained using simulations as it is difficult to experimentally determine the same. An interesting observation of this study is that inside the narrow pore of slit height h* = 5 at the high-pressure condition of P* = 0.8, for the TW fluid with long-range attraction or for the fluid at a low temperature for even a short-range attraction, the density profiles show layering such that there is a sticking tendency of the particles at centre, while there is a depletion of particles near the wall (as the layers at the centre have higher density peak heights than near the walls).     

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.     

Sum rules for zeros and intersections of Bessel functions from quantum mechanical perturbation theory

Bessel functions play an important role for quantum states in spherical and cylindrical geometries. In cases of perfect confinement, the energy of Schrödinger and massless Dirac fermions is determined by the zeros and intersections of Bessel functions, respectively. In an external electric field, standard perturbation theory therefore expresses the polarizability as a sum over these zeros or intersections. Both non-relativistic and relativistic polarizabilities can be calculated analytically, however. Hence, by equating analytical expressions to perturbation expansions, several sum rules for the zeros and intersections of Bessel functions emerge.     

Perturbation theory for thermodynamic properties of a ν-dimensional square-well fluid

The Barker-Henderson perturbation theory is used for a ν-dimensional fluid with square-well potential. Analytic expressions are given for the equation of state, excess free energy per particle and internal energy. The numerical results are discussed. A significant feature is the increase of the thermodynamic properties with increasing dimensionality.     

Confined Quantum Hard Spheres

We present computer simulation and theoretical results for a system of N Quantum Hard Spheres (QHS) particles of diameter σ and mass m at temperature T, confined between parallel hard walls separated by a distance Hσ, within the range 1≤H≤∞. Semiclassical Monte Carlo computer simulations were performed adapted to a confined space, considering effects in terms of the density of particles ρ*=N/V, where V is the accessible volume, the inverse length H−1 and the de Broglie’s thermal wavelength λB=h/2πmkT, where k and h are the Boltzmann’s and Planck’s constants, respectively. For the case of extreme and maximum confinement, 0.5<H−1<1 and H−1=1, respectively, analytical results can be given based on an extension for quantum systems of the Helmholtz free energies for the corresponding classical systems.     

量子相空间纠缠轨线力学

量子相空间理论已用来研究物理学、化学等有关问题, 并为人们研究经典物理和量子物理的对应关系提供了一种有力工具. 在量子相空间中, 基于Wigner表象下的量子刘维尔方程, 建立分子纠缠轨线力学. 与经典分子力学方法不同, 分子纠缠轨线力学中的轨线不再是独立的, 而是“纠缠”在一起的, 这正是体系量子效应的体现. 这种半经典 的理论方法能给出体系的量子效应及具有启示意义的物理图像. 分子纠缠轨线力学被用来研究量子隧穿效应、分子光解反应动力学、自关联函数等. 本文综述了分子纠缠轨线力学最近的发展. 关键词： 纠缠轨线 量子相空间 半经典理论     

量子力学定态不是驻波

作为一种经典或半经典的观点，可以认为定态是由波的干涉形成的驻波，但在量子力学中，定态本身是基本的，不是驻波。     

An equation of state contribution for dipolar and quadrupolar square-well fluids

A dipolar–quadrupolar contribution to the residual Helmholtz energy for a polar square well (a square well plus either a point dipole or a point quadrupole) fluid is developed based on the Padé approximation. Taking the square well system as reference, the contribution is formulated using an expansion for radial distribution function of the reference system. In addition to square well potential parameters the contribution depends only on dipole and quadrupole moments. This term is added as perturbation to a generalized equation of state for square well fluids. The results are then compared with the available simulation data in the literature. With the new equation obtained, it was possible to predict liquid–vapour equilibrium properties and critical properties of polar square well fluids more accurately than with available perturbation theories for multipolar square well systems. Application of the equation of state to a real dipolar (water) and a real quadrupolar (carbon dioxide) fluid indicated that the polar contribution greatly improved the predictions of saturation properties. Accurate prediction of critical properties for polar square well fluids remains as a challenge. This work can be useful in the development of better equations of state.     

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     

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.     

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.     

Determination of the vapor–liquid transition of square-well particles using a novel generalized-canonical-ensemble-based method

The square-well(SW) potential is one of the simplest pair potential models and its phase behavior has been clearly revealed, therefore it has become a benchmark for checking new theories or numerical methods. We introduce the generalized canonical ensemble(GCE) into the isobaric replica exchange Monte Carlo(REMC) algorithm to form a novel isobaric GCE-REMC method, and apply it to the study of vapor–liquid transition of SW particles. It is validated that this method can reproduce the vapor–liquid diagram of SW particles by comparing the estimated vapor–liquid binodals and the critical point with those from the literature. The notable advantage of this method is that the unstable vapor–liquid coexisting states,which cannot be detected using conventional sampling techniques, are accessed with a high sampling efficiency. Besides,the isobaric GCE-REMC method can visit all the possible states, including stable, metastable or unstable states during the phase transition over a wide pressure range, providing an effective pathway to understand complex phase transitions during the nucleation or crystallization process in physical or biological systems.