Dilute Fermi gas in quasi-one-dimensional traps: from weakly interacting fermions via hard core bosons to a weakly interacting Bose gas

We study equilibrium properties of a cold two-component Fermi gas confined in a quasi-one-dimensional trap of the transverse size l(perpendicular). In the dilute limit (nl(perpendicular)<1, where n is the 1D density) the problem is exactly solvable for an arbitrary 3D fermionic scattering length aF. When l(perpendicular)/aF goes from -infinity to +infinity, the system successively passes three regimes: weakly interacting Fermi gas, hard core Bose gas, and weakly coupled Bose gas. The regimes are separated by two crossovers at aF approximately +/-nl2(perpendicular). In conclusion, we discuss experimental implications of these results.     

Effect of short- and long-range forces on the properties of fluids. III. Dipolar and quadrupolar fluids

Using realistic pair potential models for acetone and carbon dioxide, both the spatial and orientational structure of these two typical multipolar (i.e. dipolar and quadrupolar, respectively) fluids is investigated in detail by computing the complete set of the site-site correlation functions, multipole-multipole correlation functions, and selected 2D correlation functions. The effect of the range of interactions on both the structural and thermodynamic properties of these fluids is studied by decomposing the potential into short- and long-range parts in the same manner as for water [Kolafa, J. and Nezbeda, I., 2000, Molec. Phys., 98, 1505; Nezbeda, I. and Lísal, M., 2001, Molec. Phys., 99, 291]. It is found that the spatial arrangement of the molecules is only marginally affected by the long-range forces. The effect of the electrostatic interactions is significant at short separations and cannot be neglected but nevertheless the overall structure of the short-range and full systems is similar as well as their dielectric constants. These findings are also reflected in the dependence of the thermodynamic properties on the potential range with the short-range models providing a very good approximation to those of the full system.     

Kinetic crystallisation instability in liquids with short-ranged attractions

ABSTRACT

Liquids in systems with spherically symmetric interactions are not thermodynamically stable when the range of the attraction is reduced sufficiently. However, these metastable liquids have lifetimes long enough that they are readily observable prior to crystallisation. Here we investigate the fate of liquids when the interaction range is reduced dramatically. Under these conditions, we propose that the liquid becomes kinetically unstable, i.e. its properties are non-stationary on the timescale of structural relaxation. Using molecular dynamics simulations, we find that in the square well model with range 6% of the diameter, the liquid crystallises within the timescale of structural relaxation for state points except those so close to criticality that the lengthscale of density fluctuations couples to the length of the simulation box size for typical system sizes. Even very close to criticality, the liquid exhibits significant structural change on the timescale of relaxation.     

Evaluation of bridge function for hard sphere fluid confined in a narrow slit-pore via TMMC Mayer-sampling

The bridge function required to yield a singlet integral equation (IE) up to the second order in density expansion for the hard sphere fluid confined in a slit-pore is evaluated. The slit-fluid bridge function can be divided into wall-particle bridge diagrams with h _b-bond, which were evaluated by recently proposed Transition Matrix Monte Carlo (TMMC) Mayer-sampling method. The bulk-fluid total correlation function h _b(r) used in cluster integrals is determined by solution of the bulk-fluid Ornstein–Zernike (OZ) equation with a hypernetted chain closure (HNC). The calculation is performed for the reduced density of bulk fluid in equilibrium with the fluid in slit-pores from 0.3 to 0.7 with narrow slit width of 3.0σ and 4.0σ. The quantity of the slit-fluid bridge function is assessed by comparison of the density profile obtained from the singlet IE theory and the grand canonical Monte Carlo (GCMC) simulation. Good agreement between the proposed approach and the GCMC data is observed. The reduced normal pressure is also calculated, and agrees well with the simulation data at low to medium densities but becomes a little larger at high density. It is expected that the result can be improved by adding higher order bridge coefficients. The direct evaluation of the slit-fluid bridge function seems to be practical since a great improvement of the quality of the singlet IE theory has been achieved for predicting the structural and thermodynamic properties of fluids confined in narrow slit pores.     

Systems of oblate molecules. Monte Carlo study

Monte Carlo (MC) simulations were performed for systems of hard oblate spherocylinders with breadth-to-height ratios φ = 0.5–3.5 and packing fractions y = 0.25–0.45 and for Kihara oblate molecule systems of φ = 1 at reduced temperatures T* = 0.75 and 1.0 and y = 0.05–0.45. The compression factors and the dependence of the average correlation functions on the shortest surface-to-surface distance were determined for the case of hard oblate spherocylinders and the compression factors, residual internal energies and average correlation functions for the case of the generalized Kihara molecule systems. In addition, values of the third virial coefficient of the hard oblate spherocylinders were evaluated in the range of φ = 1–3. Results of the MC simulations for the hard oblate spherocylinders compare well with the available data in the literature and theoretical values; thermodynamic functions of the Kihara molecule systems were determined from the second-order perturbation theory. They agree well with our MC values at lower densities and higher reduced temperatures.     

Assessment of long-range correlation in animal behavior time series: The temporal pattern of locomotor activity of Japanese quail (Coturnix coturnix) and mosquito larva (Culex quinquefasciatus)

Detrended Fluctuation Analysis (DFA) is a method that has been frequently used to determine the presence of long-range correlations in human and animal behaviors. However, according to previous authors using statistical model systems, in order to correctly use DFA different aspects should be taken into account such as: (1) the establishment by hypothesis testing of the absence of short term correlation, (2) an accurate estimation of a straight line in the log–log plot of the fluctuation function, (3) the elimination of artificial crossovers in the fluctuation function, and (4) the length of the time series. Taking into consideration these factors, herein we evaluated the presence of long-range correlation in the temporal pattern of locomotor activity of Japanese quail (Coturnix coturnix) and mosquito larva (Culex quinquefasciatus  ). In our study, modeling the data with the general autoregressive integrated moving average (ARFIMA) model, we rejected the hypothesis of short-range correlations (d=0)$(d=0)$ in all cases. We also observed that DFA was able to distinguish between the artificial crossover observed in the temporal pattern of locomotion of Japanese quail and the crossovers in the correlation behavior observed in mosquito larvae locomotion. Although the test duration can slightly influence the parameter estimation, no qualitative differences were observed between different test durations.     

Two Hard Spheres in a Spherical Pore: Exact Analytic Results in Two and Three Dimensions

The partition function and the one- and two-body distribution functions are evaluated for two hard spheres with different sizes constrained into a spherical pore. The equivalent problem for hard disks is addressed too. We establish a relation valid for any dimension between these partition functions, second virial coefficient for inhomogeneous systems in a spherical pore, and third virial coefficients for polydisperse hard spheres mixtures. Using the established relation we were able to evaluate the cluster integral b ₂(V) related with the second virial coefficient for the Hard Disc system into a circular pore. Finally, we analyse the behaviour of the obtained expressions near the maximum density.     

Structure and dynamics of water confined in a nanoporous sol-gel silica glass: a neutron scattering study

During recent years, the understanding of the modification of the structure and dynamics of water confined in different environments has been the focus of much interest in scientific research. This topic is in fact of great relevance in a lot of technological areas and, in living systems, essential water-related phenomena occur in restricted geometries in cells, and active sites of proteins and membranes, or at their surface. In this paper we report on the most recent up to date account of structural and dynamical properties of confined water in comparison with the bulk state. In particular, as far as structure is concerned, we present new neutron diffraction results on heavy water confined in a fully hydrated sol-gel silica glass (GelSil) as a function of the temperature. At low T, the nucleation of cubic ice superimposed to liquid water, already observed for water within Vycor glasses, is discussed. As far as the dynamics is concerned, we report results of a detailed spectroscopic analysis of diffusive relaxation and vibrational properties of water confined in nanopores of Gelsil glass, at different temperatures and hydration percentages, performed by our research group during recent years by means of incoherent quasi-elastic (IQENS) and inelastic (IINS) neutron scattering. IQENS spectra are analysed in the framework of the relaxing cage model (RCM). IINS spectra show the evolution of the one-phonon-amplitude weighted proton vibrational density of states (VDOS), Z(ω), when water loses its peculiar bulk properties and originates new structural environments due to its surface interactions.     

Mixtures of hard spherocylinders and hard spheres

Monte Carlo simulations have been performed for equimolar mixtures of hard prolate spherocylinders of length: breadth ratio 2:1 and hard spheres, in the fluid region. Two systems have been studied. In the first the breadth of the spherocylinder was equal to the hard sphere diameter, and in the second system both components were of equal molecular volume.

The compressibility factor, PV/NkT, has been obtained for both mixtures at four reduced densities (packing fractions) from 0·20 to 0·45. The results have been compared with the predictions of several analytical equations appropriate to mixtures of hard convex molecules, and an equation due to Pavlicek et al. was found to be very accurate. The results have been used to calculate the excess volumes of mixing at constant pressure, in an attempt to establish the relative importance of the effects of differences in molecular volume and shape on the thermodynamic properties.

The structural properties of the mixtures have also been investigated by calculating pair distribution functions for the three types of pair interactions present in these mixtures.     

A Confined <Emphasis Type="Italic">N</Emphasis>-Dimensional Harmonic Oscillator

We compute the energy eigenvalues for the N-dimensional harmonic oscillator confined in an impenetrable spherical cavity. The results show their dependence on the size of the cavity and the space dimension N. The obtained results are compared with those for the free N-dimensional harmonic oscillator, and as a result, the notion of fractional dimensions is pointed out. Finally, we examine the correlation between eigenenergies for confined oscillators in different dimensions.     

Confinement effects on the spin potential of first row transition metal cations

Abstract

By using a spherical confinement method, the behaviour of spin potential and pairing energy is studied and compared to the free ion limit for a representative sample of first row transition metal cations. The study was carried out using three approximations within the Kohn–Sham model; exchange-only, exchange plus correlation contribution and correcting the self-interaction error. For the three approaches, the spin potential shows a close connection with the capability of a system to perform a spin-flip process. Namely, in accordance with Hund’s rule, the spin potential increases from low d occupation up to maximum for the half filled configurations; and it decreases from that point on, as d occupation grows. Such a conclusion is reached for confined and non-confined cations, even under extreme confinement conditions. In addition, two important observations are obtained: (a) In contrast to the neutral atoms situation, in the case of cations no eigenvalue crossings are observed under confinement conditions for the whole sample of ions tested. (b) The self-interaction error found in many exchange–correlation functionals does not affect the pairing energy over confined atoms, even when this error has an important contribution on a single eigenvalue. Therefore, pairing energy predicted by exchange–correlation functionals non-corrected by the self-interaction error can be made safely on transition metal cations under high pressures.     

Clay‐induced Preferred Orientation in Polyethylene/Compatibilized Clay Nanocomposites

Nanocomposites of the organically modified clay Cloisite^® 15A (CL15A) dispersed in HDPE‐g‐MA were prepared by melt‐compounding. Microcomposites of the same clay with HDPE were also obtained with similar procedures. The spherulitic morphology of the polymer matrix was evidenced by optical microscopy in thin films, whereas the structure of the up to 2‐mm–thick, compression‐molded samples was investigated by WAXD and SAXS. Preferred orientation of both the clay and the HDPE crystallites were evidenced in the microcomposites and, to a greater extent, in nanocomposites, whereas in HDPE and HDPE‐g‐MA control specimens hardly any anisotropy was detected. The degree of orientation of PE crystals increases with CL15A concentration, but also with clay exfoliation, with lower cooling rates and decreasing sample thickness. The orientation of the clay platelets parallel to the compression‐molded surface appears to be determined by the platelets anisotropy and by shear in the mixing and the compression‐molding procedures. In turn, it determines the preferred uniaxial orientation of HDPE crystals, which have their crystallographic a axis orthogonal, while b and c are coplanar, to the sample surface, as already reported in the literature for melt‐crystallized HDPE films with thickness below 0.3 μm. It is proposed that the HDPE orientation results from confined crystallization between parallel clay platelets which are on average less than 0.1 μm apart. Simple models, qualitatively accounting for the observed orientation of HDPE, are discussed. Organized architectures resulting from confined crystallization of the polymer matrix in nanocomposites with appropriate anisotropic fillers may be a general feature, important in determining key properties of these systems.     

Quantum statistical mechanics for superstable interactions: Bose-Einstein statistics

We study quantum systems of interacting Bose particles confined to a bounded region ofR ^v . For any superstable and (strong) lower regular interaction, we obtain uniform bounds on the expectations of exponentials of local number operators for any activity and for any temperature. The method we use here is an improvement over our previous method on the same subject. As a consequence of the bounds, any infinite volume limit states are entire analytic and locally normal. Furthermore under an integrability condition on the interaction, the limit states are modular states. In this case, we use the Green's function method to construct an infinite volume limit Hilbert spece, a strongly continuous time evolution group of unitary operators and an invariant vector. Moreover we prove the existence of the pressure and its independence of boundary conditions.     

Charge density at the nucleus and radial behavior of ground state for lithium-like ions with Z = 21 to 30

By using the full-core plus correlation (FCPC) type wave functions, the accurate charge densities ρ(0) at the nucleus and the radial expectation values of the ground states for the lithium-like systems with Z = 21 to 30 are obtained. The determinantal conditions and the electron-nucleus cusp condition are used to calculate the inequalities of the upper and the lower bounds to ρ(0) with two or more expectation values. These inequalities, derived by Angulo and Dehesa [Phys. Rev. A 44 1516 (1991)], are verified to be also valid for these ions with higher nuclear charge. The present results show that the wave functions used in this paper are satisfactory in the whole configuration space for these ions with higher nuclear charge.     

Direct correlation functions and bridge functions in additive hard-sphere mixtures

A method to obtain (approximate) analytical expressions for the radial distribution functions in a multicomponent mixture of additive hard spheres that was recently introduced is used to obtain the direct correlation functions and bridge functions in these systems. This method, which yields results practically equivalent to the generalized mean spherical approximation and includes thermodynamic consistency, is an alternative to the usual integral equation approaches and requires as input only the contact values of the radial distribution functions and the isothermal compressibility. Calculations of the bridge functions for a binary mixture using the Boublik-Mansoori-Carnahan-Starling-Leland equation of state are compared to parallel results obtained from the solution of the Percus-Yevick equation. We find that the conjecture recently proposed by Guzman and del Rio (1998, 98, Molec. Phys., 95, 645), stating that the zeros of the bridge functions occur approximately at the same value of the shifted distance for all pairs of interactions, is at odds with our results. Moreover, in the case of disparate sizes, even the Percus-Yevick bridge functions do not have this property. It is also found that the bridge functions are not necessarily non-positive.     

Monte Carlo simulation of a confined hard ellipse fluid

The structural and thermodynamic properties of a confined hard ellipse fluid are studied using Monte Carlo simulation. The angular, average number densities and order parameters of hard ellipses confined between hard parallel walls are obtained for various bulk densities, aspect ratios and wall separations. The results show that the effect of the existence of the wall on the molecular fluid structure, either on their directions or their locations, with respect to the bulk, especially close to the walls, is significant. For this system the pressure is also obtained and it is shown that the average density at the wall is proportional to the pressure, βP=〈ρ_w〉. Our simulation results show that the order parameters depend on the number of the particles in the box unless it exceeds thousand.     

Equation of state for systems of soft diatomic molecules

A new potential that is a modification of the BBL (Bratko, D.,Blum, L., and Luzar, A.,1985, J. chem. Phys., 83, 6367; Blum, L., Vericat, F., and Bratko, D., 1995, J. chem. Phys., 102, 1461) potential and of the one recently solved analytically by Blum and Vericat (BV) (1995, Molec. Phys., 86, 809; 1996, J. phys. Chem., 100, 1197) is studied by Monte Carlo simulation. The main feature of this potential is that it can be solved using only a small number of parameters (3 in the case treated by BV), and therefore produces a substantial simplification of earlier work. The new potential has an orientational octupole–octupole interaction term which is found necessary to reproduce the broad peak of the oxygen–oxygen structure function due to the tetrahedral position of the second nearest neighbour water molecule. This important feature was absent in the original BBL potential. This model agrees also with the experimental pair correlation functions for oxygen–hydrogen and hydrogen–hydrogen, and yields 42·6 kJ mol^-1 for the internal energy of water, also in agreement with experiment. The hard core central repulsion causes the sharpness of the first peaks in all three correlation functions. This is not necessary but convenient for an analytical solution.