Microcanonical ensemble study of a gas column under gravity

The study of a classical ideal gas column of finite height H in a uniform gravitational field g is made by the microcanonical ensemble at energy E. The primary functions of this ensemble, the phase volume and the density of states, are derived. Related statistical quantities, such as the entropy, the temperature and the heat capacity, are also reported. The equivalence in the thermodynamic limit between the calculated microcanonical expressions and those obtained from the canonical ensemble is shown numerically. The expression for the temperature is used to analyze the temperature change when the gas is permitted to expand into an evacuated region increasing the height of the column from H ₁ to H ₂. The microcanonical single-particle momentum and height distributions are also reported.     

Collisionless self-consistent trapping of electrons into a nonstationary potential well: Dynamics of trapped electrons

The subject of investigation is the early stage of self-consistent trapping of electrons into a potential well that forms during the development of aperiodic Pierce instability. An analytical estimate for threshold gap δ_th = d _th/λ_D (λ_D is the Debye beam length) above which the trapping begins is derived. The nonlinear dynamics and distribution function of trapped electrons are studied in detail using a numerical method ((E, K) code). It is found that the trapped particles produce a localized steep-edge bunch, which “dangles” around between the electrodes, causing potential oscillations. Trapped electrons render the well shallower. Some of the particles in the bunch are shown to periodically escape to the electrodes. As a result, the potential oscillation amplitude fades away and the mean depth of the well increases.     

Generation of the ballistic particle transport in a periodic Hamiltonian system subjected to small time-dependent perturbation

The problem of the motion of an ensemble of classical particles in a periodic potential field has been considered. A method is proposed for generating directed ballistic transport by means of a perturbation oscillating in time and space. This method makes it possible to significantly reduce the perturbation intensity required to generate a particle flux. In particular, it has been shown that, even if the ensemble of particles is initially near the stable-equilibrium states, a directed flux appears at a perturbation amplitude of about 10^?2 of the potential barrier height. The flux generation mechanism is associated with the creation of global chaotic diffusion due to resonances between spatial and time oscillations of perturbation. A nonlinear pendulum is considered as an example.     

Structure, dsingle-particle and many-particle coefficients of Lennard—Jones liquid Al

We investigate the effects of temperature and density on the single-particle and many-particle coefficients as well as on the structures of homogenous systems in which the particles are assumed to interact via a continuous soft sphere potential in the microcanonical ensemble. The pair distribution function and therefore the structures of the systems studied are affected by temperature close to and above the melting point through migrations of atoms from the first shell in the pair distribution function. The dynamics of atomic pairs in the short-time regime in liquid aluminium may be said to be governed by the potential of mean force, which depends on the static structure of liquid Al at all investigated temperatures. A polynomial dependence ofD on density and temperature was observed in contradiction to Arrhenius law. The shear viscosities of the systems studied are largely nonlinear. It was observed that the soft sphere potential used in our calculations overestimates the Stoke-Einstein relation.     

Single particles in a reflection-asymmetric potential

Single particles moving in a reflection-asymmetric potential are investigated by solving the Schr ¨odinger equation of the reflectionasymmetric Nilsson Hamiltonian with the imaginary time method in 3 D lattice space and the harmonic oscillator basis expansion method. In the 3 D lattice calculation, the l2 divergence problem is avoided by introducing a damping function, and the(l~2) Nterm in the non-spherical case is calculated by introducing an equivalent N-independent operator. The efficiency of these numerical techniques is demonstrated by solving the spherical Nilsson Hamiltonian in 3 D lattice space. The evolution of the single-particle levels in a reflection-asymmetric potential is obtained and discussed by the above two numerical methods, and their consistency is shown in the obtained single-particle energies with the differences smaller than 10~(-4)[hω_0].     

Optimization of Nanofluidic Devices for Geometry-Induced Electrostatic Trapping

Nanoparticle trapping in a nanofluidic device utilizing geometry-induced electrostatic (GIE) potential trap is an efficient and robust way to perform nano‑object confinement and single particle studies. The GIE‑trapping is a passive method that solely depends on the device geometry and device-particle surface interaction. Therefore, optimization of a nanofluidic device based on experimental requirements, helps to achieve stiffer single-particle trapping. The efficiency of a GIE‑trapping device is defined in terms of residence time and trapping stiffness of the nanoparticle inside a potential trap. The present study reveals all crucial parameters that affect the device efficiency, particle trapping stiffness, and particle residence time. Furthermore, the trends of particle trapping stiffness are presented as a function of crucial parameters and demonstrate two variants of simulations to estimate the particle trapping efficiency: (a) using charged particle, and (b) using point charge approximation. Simulations with charged particle give more realistic values related to particle trapping whereas simulations with point charge approximation is a faster approach which gives approximate values and a guideline for more rigorous simulations. The results demonstrate a good agreement with experimental observations and hold the key for future developments in this field, wherein a device geometry can be very precisely optimized.     

An optimised molecular model for ammonia

Based on molecular dynamics (MD) computer simulations we investigate the dynamic behaviour of a model complex fluid suspension consisting of large (A) particles (the ‘solute’) immersed in a bath of smaller ‘solvent’ (B) particles. The goal is to identify the effect of systematic simplifications (coarse-graining) of the solvent on typical microscopic time correlation functions characterizing the single-particle and collective dynamics of the solute. As a reference system we employ a binary Lennard–Jones mixture of spherical particles with significant differences in particle sizes (σ_A>σ_B) and masses (m _A>m _B). We then replace the original B particles step by step by a reduced number of larger and heavier particles such that the mass and volume fraction of B particles is kept constant. At each step of coarse-graining, the intermolecular interactions between A particles are chosen such that the static A–A structure of the reference system is preserved. Our MD results indicate that coarse-graining has a profound influence on both the single-particle dynamics as reflected by the self-diffusion constant and the collective dynamics represented by the distinct part of the van Hove time correlation function. The latter holds only at intermediate packing fractions, whereas the collective dynamics turns out to be essentially insensitive to coarse-graining at high packing fractions.     

Calculated ground-state properties of heavy nuclei

Ground-state distortions and single-particle corrections are calculated fornuclei with $\text{Z ≧ 68}\text{and}\text{N ≧ 106}$ by use of the macroscopic-microscopic method as developed by Strutinsky. The microscopic part is calculated primarily by use of the folded Yukawa single-particle potential. Its parameters are redetermined to fit a actinide data. The modified oscillator potential is also used in some of the studies. Two methods for calculating the macroscopic energy are investigated. One is the droplet model of Myers and Swiatecki, and other is a modified liquid-drop model in which the surface-energy term is modified to take into account the finite range of the nuclear force. Single-particle level diagrams for the folded Yukawa potential are also presented. They are plotted as functions of the distortion parameters ?, ?₄ and ?₆. Theoretical and experimental single-particle levels at the ground state for actinide nuclei are also compared.     

Novel electrodynamic trapping mechanism for neutral,polar particles

A conceptually new trapping mechanism for neutral, polar particles is introduced and discussed. Unlike existing mechanisms that are based on oscillating saddle-point potentials or rotating electric dipole fields, the new mechanism is based on a superposition of ac and dc electric monopolefields that dynamically generate a minimum of the effective ponderomotive potential in which the particles are trapped. Extensive numerical simulations of the dynamics and the stability properties of trapped HC₁₇N molecules and ferroelectric rods (made of barium titanate or croconic acid crystals) prove the validity of the new mechanism. The examples show that the same mechanism is applicable to the trapping of macroscopic as well as microscopic particles. The numerical results are backed by a physical pseudo-potential picture and an analytical stability analysis that provide physical insight into why and how the new mechanism works. A semi-quantum, Born-Oppenheimer-type calculation that treats the intrinsic rotational degree of freedom of HC₁₇N quantum mechanically is also presented. A detailed discussion of engineering aspects shows that laboratory implementation of the new mechanism is within current technological reach.     

Optical bottles: A quantitative analysis of optically confined nanoparticle ensembles in suspension

We present a novel method, an optical bottle, that uses a focused laser beam to trap and a second laser to analyze optically confined multiple nanoparticles. A theoretical framework based on the mechanical equilibrium of the optical radiation pressure produced by the focused laser beam and the osmotic pressure produced by the enriched particle concentration in the optical trap is developed for analyzing the ensemble behavior of the optically confined nanoparticles. Experiments were conducted for fluorescently labeled polystyrene nanospheres and unilamellar phospholipid vesicles to determine the optical trapping energy of individual particles as well as the osmotic compressibility of the colloids. The new method is not limited by the particle concentration and is relatively easy to implement.     

Linked cluster expansions in the equations of motion method II: Kinetic equations for the single-particle density matrix

The general method of paper I of this series is applied to derive kinetic equations (KE's), i.e. closed exact equations governing the time evolution of the single-particle density matrix. The short-memory approximation of these non-Markowian equations is formulated in such a way that it is valid even in strongly inhomogeneous systems. The c-number diagram expansion of the integral kernels of the KE's is obtained from the general rules of paper I. It is shown that certain secular divergent terms cancel each other. The diagrams decay into dynamic and correlational parts, the latter being given by cluster functions describing the correlations of the particles in the local equilibrium ensemble σ(t) which is formulated in terms of the single-particle density matrix and of the Hamiltonian. The appearance of the cluster functions is the most pronounced difference of our KE's in comparison with other KE's which are formulated in terms of the dynamics of isolated clusters of particles. It is argued that our KE's may be viewed as a highly summed version of these latter KE's and that the ultimate reason for this difference lies in the fact that in our theory the conservation of the average macroscopic energy is taken into account explicitly.     

Measurement of chemical potentials of systems with strong excluded volume interactions by computing the density of states

At high densities and low temperatures, the conventional Widom test particle method to compute the chemical potential of a system of particles with excluded volume interactions fails owing to bad statistics. A way to circumvent this problem is the use of expanded ensemble simulation techniques or thermodynamic integration. In this article, we will describe an alternative method to compute the chemical potential which is conceptually much easier, by computing the density of states of systems of N and N + 1 particles directly; and by performing a test particle simulation at very high temperature. The advantage of our technique is that the densities of states of the N and N + 1 particle system are computed in an ensemble in which particles can pass each other, resulting in a more efficient sampling. We will demonstrate our method not only for single particles but also for chain molecules with intramolecular interactions. By using an infinite temperature expansion and an extension of the density of states to very high energies, we will show that it is also possible to compute the chemical potential without having to compute the density of states for the N + 1 particle system.     

Slowly rocking symmetric, spatially periodic Hamiltonians: The role of escape and the emergence of giant transient directed transport

The nonintegrable Hamiltonian dynamics of particles placed in a symmetric, spatially periodic potential and subjected to a periodically varying field is explored. Such systems can exhibit a rich diversity of unusual transport features. In particular, depending on the setting of the initial phase of the drive, the possibility of a giant transient directed transport in a symmetric, space-periodic potential when driven with an adiabatically varying field arises. Here, we study the escape scenario and corresponding mean escape times of particles from a trapping region with the subsequent generation of a transient directed flow of an ensemble of particles. It is shown that for adiabatically slow inclination modulations the unidirectional flow proceeds over giant distances. The direction of escape and, hence, of the flow is entirely governed whether the periodic force, modulating the inclination of the potential, starts out initially positive or negative. In the phase space, this transient directed flow is associated with a long-lasting motion taking place within ballistic channels contained in the non-uniform chaotic layer. We demonstrate that for adiabatic modulations all escaping particles move ballistically into the same direction, leading to a giant directed current.     

Initial growth of Boltzmann entropy and chaos in a large assembly of weakly interacting systems

We introduce a high-dimensional symplectic map, modeling a large system, to analyze the interplay between single-particle chaotic dynamics and particles interactions in thermodynamic systems. We study the initial growth of the Boltzmann entropy, S_B, as a function of the coarse-graining resolution (the late stage of the evolution is trivial, as the system is subjected to no external drivings). We show that a characteristic scale emerges, and that the behavior of S_B vs t, at variance with the Gibbs entropy, does not depend on the resolution, as far as it is finer than this scale. The interaction among particles is crucial to achieve this result, while the rate of entropy growth, in its early stage, depends essentially on the single-particle chaotic dynamics. It is possible to interpret the basic features of the dynamics in terms of a suitable Markov approximation.     

Fringe visibility for two qubits interacting with a macroscopic medium

We study both the two-particle and single-particle fringe visibility in the generalized version of the Nakazato–Pascazio model where two qubits interact with a finite length one-dimensional array.Both the two-particle and single-particle fringe visibilities are investigated with different initial states of the particles spin.For different initial states of the particles spin,the two-particle fringe visibility either decreases or increases over time,and may even decrease first and increase later.Due to the interaction between the particles and the one-dimensional array,the single-particle fringe visibility increases over time when the initial state of the two particles spin is independent.The single-particle fringe visibility is equal to 0 as the two-particle spin is initially in the completely entangled state or in the singlet state.     

Scattering of a scalar wave from a two-dimensional randomly rough Neumann surface

Abstract

We present a reciprocity and unitarity preserving formulation of the scattering of a scalar plane wave from a two-dimensional, randomly rough surface on which the Neumann boundary condition is satisfied. The theory is formulated on the basis of the Rayleigh hypothesis in terms of a single-particle Green's function G(q_‖|k_‖) for the surface electromagnetic waves that exist at the surface due to its roughness, where k_‖ and q_‖ are the projections on the mean scattering plane of the wave vectors of the incident and scattered waves, respectively. The specular scattering is expressed in terms of the average of this Green's function over the ensemble of realizations of the surface profile function (G(q_‖|k_‖)). The Dyson equation satisfied by (G(q_‖|k_‖)) is presented, and the properties of the solution are discussed, with particular attention to the proper self-energy in terms of which the averaged Green's function is expressed. The diffuse scattering is expressed in terms of the ensemble average of a two-particle Green's function, which is the product of two single-particle Green's functions. The Bethe-Salpeter equation satisfied by the averaged two-particle Green's function is presented, and properties of its solution are discussed. In the small roughness limit, and with the irreducible vertex function approximated by the sum of the contribution from the maximally-crossed diagrams, which represent the coherent interference between all time-reversed scattering sequences, the solution of the Bethe-Salpeter equation predicts the presence of enhanced backscattering in the angular dependence of the intensity of the waves scattered diffusely.     

Gamow shell model description of neutron-rich nuclei

This work presents the first continuum shell-model study of weakly bound neutron-rich nuclei involving multiconfiguration mixing. For the single-particle basis, the complex-energy Berggren ensemble representing the bound single-particle states, narrow resonances, and the nonresonant continuum background is taken. Our shell-model Hamiltonian consists of a one-body finite potential and a zero-range residual two-body interaction. It is demonstrated that the residual interaction coupling to the particle continuum is important; in some cases, it can give rise to the binding of a nucleus.     

Definition of chemical potential for non-interacting particles in one dimension

Because of current interest in the chemical potential of N-electron systems, a definition is proposed for independent particles in one dimension. The method relies on analytic continuation of single-particle bound-state eigenvalues, infinite-simally close to integer N.     

Condensation for a Fixed Number of Independent Random Variables

A family of m independent identically distributed random variables indexed by a chemical potential φ∈[0,γ] represents piles of particles. As φ increases to γ, the mean number of particles per site converges to a maximal density ρ _c <∞. The distribution of particles conditioned on the total number of particles equal to n does not depend on φ (canonical ensemble). For fixed m, as n goes to infinity the canonical ensemble measure behave as follows: removing the site with the maximal number of particles, the distribution of particles in the remaining sites converges to the grand canonical measure with density ρ _c ; the remaining particles concentrate (condensate) on a single site.