6,101 research outputs found

### Infinite compressibility states in the Hierarchical Reference Theory of fluids. II. Numerical evidence

Continuing our investigation into the Hierarchical Reference Theory of fluids
for thermodynamic states of infinite isothermal compressibility kappa[T] we now
turn to the available numerical evidence to elucidate the character of the
partial differential equation: Of the three scenarios identified previously,
only the assumption of the equations turning stiff when building up the
divergence of kappa[T] allows for a satisfactory interpretation of the data. In
addition to the asymptotic regime where the arguments of part I
(cond-mat/0308467) directly apply, a similar mechanism is identified that gives
rise to transient stiffness at intermediate cutoff for low enough temperature.
Heuristic arguments point to a connection between the form of the Fourier
transform of the perturbational part of the interaction potential and the
cutoff where finite difference approximations of the differential equation
cease to be applicable, and they highlight the rather special standing of the
hard-core Yukawa potential as regards the severity of the computational
difficulties.Comment: J. Stat. Phys., in press. Minor changes to match published versio

### Solvent mediated forces in critical fluids

The effective interaction between two planar walls immersed in a fluid is
investigated by use of Density Functional Theory in the super-critical region
of the phase diagram. A hard core Yukawa model of fluid is studied with special
attention to the critical region. To achieve this goal a new formulation of the
Weighted Density Approximation coupled with the Hierarchical Reference Theory,
able to deal with critical long wavelength fluctuations, is put forward and
compared with other approaches. The effective interaction between the walls is
seen to change character on lowering the temperature: The strong oscillations
induced by layering of the molecules, typical of the depletion mechanism in
hard core systems, are gradually smoothed and, close to the critical point, a
long range attractive tail emerges leading to a scaling form which agrees with
the expectations based on the critical Casimir effect. Strong corrections to
scaling are seen to affect the results up to very small reduced temperatures.
By use of Derjaguin approximation, this investigation has natural implications
for the aggregation of colloidal particles in critical solvents.Comment: 15 pages, 16 figure

### Depletion interaction between spheres of unequal size and demixing in binary mixtures of colloids

The possibility to induce demixing in a colloidal mixture by adding small
polymers, or other equivalent depletant agents, is theoretically investigated.
By use of Mean Field Theory, suitably generalized to deal with short range
effective interactions, the phase diagram of a binary mixture ofcolloidal
particles (modelled as hard spheres) in a solvent is determined as a function
of the polymer concentration on the basis of the Asakura-Oosawa model.The
topology of the phase diagram changes when the relative size of the colloidal
particles is reduced: the critical line connecting the liquid-vapour critical
points of the two pure fluids breaks and the branch starting from the critical
point of the bigger particles bends to higher volume fractions, where
concentration fluctuations drive the transition. The effects of a softer
colloid-polymer interaction is also investigated: Even the presence of a small
repulsive tail in the potential gives rise to a significant lowering of the
stability threshold. In this case, phase transitions may take place by adding
just a few percent of depletant in volume fraction. These results may be
relevant for the interpretation of recent experiments of solidification
kinetics in colloidal mixtures.Comment: To be published in Molecular Physic

### On the theory of phase transitions in binary fluid mixtures

The microscopic approach to the description of the phase behaviour and
critical phenomena in binary fluid mixtures is proposed. It is based on the
method of collective variables with a reference system. The physical nature of
the order parameter in a binary mixture is discussed. The basic density measure
(Ginsburg-Landau-Wilson Hamiltonian) is obtained in the collective variable
phase space which contains the variable connected with the order parameter of
the system. It is shown that the problem can be reduced to the 3D Ising model
in an external field.Comment: 22 pages, latex, 6 eps-figures included, uses cmp209.st

### Shell Effects and Phase Separation in a Trapped Multi-Component Fermi System

Shell effects in the coordinate space can be seen with degenerate Fermi
vapors in non-uniform trapping potentials. In particular, below the Fermi
temperature, the density profile of a Fermi gas in a confining harmonic
potential is characterized by several local maxima. This effect is enhanced for
"magic numbers" of particles and in quasi-1D (cigar-shaped) configurations. In
the case of a multi-component Fermi vapor, the separation of Fermi components
in different spatial shells (phase-separation) depends on temperature, number
of particles and scattering length. We derive analytical formulas, based on
bifurcation theory, for the critical density of Fermions and the critical
chemical potential, which give rise to the phase-separation.Comment: to be published in the Proceedings of the VIII Meeting on Problems in
Theoretical Nuclear Physics, Cortona, October 18-20, 2000, Ed. G. Pisent, A.
Fabrocini and L. Canton (World Scientific

### Approximating the ground state of fermion system by multiple determinant states: matching pursuit approach

We present a simple and stable numerical method to approximate the ground
state of a quantum many-body system by multiple determinant states. This method
searches these determinant states one by one according to the matching pursuit
algorithm. The first determinant state is identical to that of the Hartree-Fock
theory. Calculations for two-dimensional Hubbard model serve as a
demonstration.Comment: 5 Pages, 1 figur

### Implementation of the Hierarchical Reference Theory for simple one-component fluids

Combining renormalization group theoretical ideas with the integral equation
approach to fluid structure and thermodynamics, the Hierarchical Reference
Theory is known to be successful even in the vicinity of the critical point and
for sub-critical temperatures. We here present a software package independent
of earlier programs for the application of this theory to simple fluids
composed of particles interacting via spherically symmetrical pair potentials,
restricting ourselves to hard sphere reference systems. Using the hard-core
Yukawa potential with z=1.8/sigma for illustration, we discuss our
implementation and the results it yields, paying special attention to the core
condition and emphasizing the decoupling assumption's role.Comment: RevTeX, 16 pages, 2 figures. Minor changes, published versio

### Bosonic clouds with attractive interaction beyond the local interaction approximation

We study the properties of a Bose-Einstein condensed cloud of atoms with
negative scattering length confined in a harmonic trap. When a realistic non
local (finite range) effective interaction is taken into account, we find that,
besides the known low density metastable solution, a new branch of Bose
condensate appears at higher density. This state is self-bound but its density
can be quite low if the number $N$ of atoms is not too big. The transition
between the two classes of solutions as a function of $N$ can be either sharp
or smooth according to the ratio between the range of the attractive
interaction and the length of the trap. A tight trap leads to a smooth
transition. In addition to the energy and the shape of the cloud we study also
the dynamics of the system. In particular, we study the frequencies of
collective oscillation of the Bose condensate as a function of the number of
atoms both in the local and in the non local case. Moreover, we consider the
dynamics of the cloud when the external trap is switched off.Comment: Latex, 6 pages, 2 figure, 1 table, presented to the International
Symposium of Quantum Fluids and Solids 98, Amherst (USA), 9-14 June 199

### Effective wave-equations for the dynamics of cigar-shaped and disc-shaped Bose condensates

Starting from the 3D Gross-Pitaevskii equation and using a variational
approach, we derive an effective 1D wave-equation that describes the axial
dynamics of a Bose condensate confined in an external potential with
cylindrical symmetry. The trapping potential is harmonic in the transverse
direction and generic in the axial one. Our equation, that is a time-dependent
non-polynomial nonlinear Schr\"odinger equation (1D NPSE), can be used to model
cigar-shaped condensates, whose dynamics is essentially 1D. We show that 1D
NPSE gives much more accurate results than all other effective equations
recently proposed. By using 1D NPSE we find analytical solutions for bright and
dark solitons, which generalize the ones known in the literature. We deduce
also an effective 2D non-polynomial Schr\"odinger equation (2D NPSE) that
models disc-shaped Bose condensates confined in an external trap that is
harmonic along the axial direction and generic in the transverse direction. In
the limiting cases of weak and strong interaction, our approach gives rise to
Schr\"odinger-like equations with different polynomial nonlinearities.Comment: 7 pages, 5 figures, to be published in Phys. Rev.

### Spontaneous Symmetry Breaking and Proper-Time Flow Equations

We discuss the phenomenon of spontaneous symmetry breaking by means of a
class of non-perturbative renormalization group flow equations which employ a
regulating smearing function in the proper-time integration. We show, both
analytically and numerically, that the convexity property of the renormalized
local potential is obtained by means of the integration of arbitrarily low
momenta in the flow equation. Hybrid Monte Carlo simulations are performed to
compare the lattice Effective Potential with the numerical solution of the
renormalization group flow equation. We find very good agreement both in the
strong and in the weak coupling regime.Comment: 20 pages, 8 figure

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