416 research outputs found
Band Crossing and Novel Low-Energy Behaviour in a Mean Field Theory of a Three-Band Model on a Cu--O lattice
We study correlation effects in a three-band extended Hubbard model of Cu --
O planes within the 1/N mean field approach, in the infinite U limit. We
investigate the emerging phase diagram and discuss the low energy scales
associated with each region. With increasing direct overlap between oxygen
orbitals, , the solution displays a band crossing which, for an
extended range of parameters, lies close to the Fermi level. In turn this leads
to the nearly nested character of the Fermi surface and the resulting linear
temperature dependence of the quasi-particle relaxation rate for sufficiently
large T. We also discuss the effect of band crossing on the optical
conductivity and comment on the possible experimental relevance of our
findings.Comment: 12 pages, Latex-Revtex, 6 PostScript figures. Submitted to Phys. Rev.
Completeness and Decidability Results for First-order Clauses with Indices
Session: Inference systems (www.cl.cam.ac.uk/~gp351/cade24)International audienceWe define a proof procedure that allows for a limited form of inductive reasoning. The first argument of a function symbol is allowed to belong to an inductive type. We will call such an argument an index. We enhance the standard superposition calculus with a loop detection rule, in order to encode a particular form of mathematical induction. The satisfiability problem is not semi-decidable, but some classes of clause sets are identified for which the proposed procedure is complete and/or terminating
Bose-representation for a strongly coupled nonequilibrim fermionic superfluid in a time-dependent trap
Using the functional integral formulation of a nonequilibrium quantum
many-body theory we develop a regular description of a Fermi system with a
strong attractive interaction in the presence of an external time-dependent
potential. In the strong coupling limit this fermionic system is equivalent to
a noequilibrium dilute Bose gas of diatomic molecules. We also consider a
nonequilibrim strongly coupled Bardeen-Cooper-Schrieffer (BCS) theory and show
that it reduces to the full nonlinear time-dependent Gross-Pitaevski (GP)
equation, which determines an evolution of the condensate wave function.Comment: RevTeX 4, 6 pages, 2 eps figure
Water adsorption on amorphous silica surfaces: A Car-Parrinello simulation study
A combination of classical molecular dynamics (MD) and ab initio
Car-Parrinello molecular dynamics (CPMD) simulations is used to investigate the
adsorption of water on a free amorphous silica surface. From the classical MD
SiO_2 configurations with a free surface are generated which are then used as
starting configurations for the CPMD.We study the reaction of a water molecule
with a two-membered ring at the temperature T=300K. We show that the result of
this reaction is the formation of two silanol groups on the surface. The
activation energy of the reaction is estimated and it is shown that the
reaction is exothermic.Comment: 12 pages, 6 figures, to be published in J. Phys.: Condens. Matte
Capillary Waves in a Colloid-Polymer Interface
The structure and the statistical fluctuations of interfaces between
coexisting phases in the Asakura-Oosawa (AO) model for a colloid--polymer
mixture are analyzed by extensive Monte Carlo simulations. We make use of a
recently developed grand canonical cluster move with an additional constraint
stabilizing the existence of two interfaces in the (rectangular) box that is
simulated. Choosing very large systems, of size LxLxD with L=60 and D=120,
measured in units of the colloid radius, the spectrum of capillary wave-type
interfacial excitations is analyzed in detail. The local position of the
interface is defined in terms of a (local) Gibbs surface concept. For small
wavevectors capillary wave theory is verified quantitatively, while for larger
wavevectors pronounced deviations show up. For wavevectors that correspond to
the typical distance between colloids in the colloid-rich phase, the
interfacial fluctuations exhibit the same structure as observed in the bulk
structure factor. When one analyzes the data in terms of the concept of a
wavevector-dependent interfacial tension, a monotonous decrease of this
quantity with increasing wavevector is found. Limitations of our analysis are
critically discussed.Comment: 12 pages, 15 figure
Nonlinear effects in charge stabilized colloidal suspensions
Molecular Dynamics simulations are used to study the effective interactions
in charged stabilized colloidal suspensions. For not too high macroion charges
and sufficiently large screening, the concept of the potential of mean force is
known to work well. In the present work, we focus on highly charged macroions
in the limit of low salt concentrations. Within this regime, nonlinear
corrections to the celebrated DLVO theory [B. Derjaguin and L. Landau, Acta
Physicochem. USSR {\bf 14}, 633 (1941); E.J.W. Verwey and J.T.G. Overbeck, {\em
Theory of the Stability of Lyotropic Colloids} (Elsevier, Amsterdam, 1948)]
have to be considered. For non--bulklike systems, such as isolated pairs or
triples of macroions, we show, that nonlinear effects can become relevant,
which cannot be described by the charge renormalization concept [S. Alexander
et al., J. Chem. Phys. {\bf 80}, 5776 (1984)]. For an isolated pair of
macroions, we find an almost perfect qualitative agreement between our
simulation data and the primitive model. However, on a quantitative level,
neither Debye-H\"uckel theory nor the charge renormalization concept can be
confirmed in detail. This seems mainly to be related to the fact, that for
small ion concentrations, microionic layers can strongly overlap, whereas,
simultaneously, excluded volume effects are less important. In the case of
isolated triples, where we compare between coaxial and triangular geometries,
we find attractive corrections to pairwise additivity in the limit of small
macroion separations and salt concentrations. These triplet interactions arise
if all three microionic layers around the macroions exhibit a significant
overlap. In contrast to the case of two isolated colloids, the charge
distribution around a macroion in a triple is found to be anisotropic.Comment: 10 pages, 9 figure
Interaction effects on 2D fermions with random hopping
We study the effects of generic short-ranged interactions on a system of 2D
Dirac fermions subject to a special kind of static disorder, often referred to
as ``chiral.'' The non-interacting system is a member of the disorder class BDI
[M. R. Zirnbauer, J. Math. Phys. 37, 4986 (1996)]. It emerges, for example, as
a low-energy description of a time-reversal invariant tight-binding model of
spinless fermions on a honeycomb lattice, subject to random hopping, and
possessing particle-hole symmetry. It is known that, in the absence of
interactions, this disordered system is special in that it does not localize in
2D, but possesses extended states and a finite conductivity at zero energy, as
well as a strongly divergent low-energy density of states. In the context of
the hopping model, the short-range interactions that we consider are
particle-hole symmetric density-density interactions. Using a perturbative
one-loop renormalization group analysis, we show that the same mechanism
responsible for the divergence of the density of states in the non-interacting
system leads to an instability, in which the interactions are driven strongly
relevant by the disorder. This result should be contrasted with the limit of
clean Dirac fermions in 2D, which is stable against the inclusion of weak
short-ranged interactions. Our work suggests a novel mechanism wherein a clean
system, initially insensitive to interaction effects, can be made unstable to
interactions upon the inclusion of weak static disorder.Comment: 16 pages, 10 figures; References added, figures enlarged; to be
published in Phys. Rev.
Frequency dependent specific heat of viscous silica
We apply the Mori-Zwanzig projection operator formalism to obtain an
expression for the frequency dependent specific heat c(z) of a liquid. By using
an exact transformation formula due to Lebowitz et al., we derive a relation
between c(z) and K(t), the autocorrelation function of temperature fluctuations
in the microcanonical ensemble. This connection thus allows to determine c(z)
from computer simulations in equilibrium, i.e. without an external
perturbation. By considering the generalization of K(t) to finite wave-vectors,
we derive an expression to determine the thermal conductivity \lambda from such
simulations. We present the results of extensive computer simulations in which
we use the derived relations to determine c(z) over eight decades in frequency,
as well as \lambda. The system investigated is a simple but realistic model for
amorphous silica. We find that at high frequencies the real part of c(z) has
the value of an ideal gas. c'(\omega) increases quickly at those frequencies
which correspond to the vibrational excitations of the system. At low
temperatures c'(\omega) shows a second step. The frequency at which this step
is observed is comparable to the one at which the \alpha-relaxation peak is
observed in the intermediate scattering function. Also the temperature
dependence of the location of this second step is the same as the one of the
peak, thus showing that these quantities are intimately connected to
each other. From c'(\omega) we estimate the temperature dependence of the
vibrational and configurational part of the specific heat. We find that the
static value of c(z) as well as \lambda are in good agreement with experimental
data.Comment: 27 pages of Latex, 8 figure
Metal-insulator transition from combined disorder and interaction effects in Hubbard-like electronic lattice models with random hopping
We uncover a disorder-driven instability in the diffusive Fermi liquid phase
of a class of many-fermion systems, indicative of a metal-insulator transition
of first order type, which arises solely from the competition between quenched
disorder and interparticle interactions. Our result is expected to be relevant
for sufficiently strong disorder in d = 3 spatial dimensions. Specifically, we
study a class of half-filled, Hubbard-like models for spinless fermions with
(complex) random hopping and short-ranged interactions on bipartite lattices,
in d > 1. In a given realization, the hopping disorder breaks time reversal
invariance, but preserves the special ``nesting'' symmetry responsible for the
charge density wave instability of the ballistic Fermi liquid. This disorder
may arise, e.g., from the application of a random magnetic field to the
otherwise clean model. We derive a low energy effective field theory
description for this class of disordered, interacting fermion systems, which
takes the form of a Finkel'stein non-linear sigma model [A. M. Finkel'stein,
Zh. Eksp. Teor. Fiz. 84, 168 (1983), Sov. Phys. JETP 57, 97 (1983)]. We analyze
the Finkel'stein sigma model using a perturbative, one-loop renormalization
group analysis controlled via an epsilon-expansion in d = 2 + epsilon
dimensions. We find that, in d = 2 dimensions, the interactions destabilize the
conducting phase known to exist in the disordered, non-interacting system. The
metal-insulator transition that we identify in d > 2 dimensions occurs for
disorder strengths of order epsilon, and is therefore perturbatively accessible
for epsilon << 1. We emphasize that the disordered system has no localized
phase in the absence of interactions, so that a localized phase, and the
transition into it, can only appear due to the presence of the interactions.Comment: 47 pages, 25 figures; submitted to Phys. Rev. B. Long version of
arXiv:cond-mat/060757
Critical phenomena in colloid-polymer mixtures: interfacial tension, order parameter, susceptibility and coexistence diameter
The critical behavior of a model colloid-polymer mixture, the so-called AO
model, is studied using computer simulations and finite size scaling
techniques. Investigated are the interfacial tension, the order parameter, the
susceptibility and the coexistence diameter. Our results clearly show that the
interfacial tension vanishes at the critical point with exponent 2\nu ~ 1.26.
This is in good agreement with the 3D Ising exponent. Also calculated are
critical amplitude ratios, which are shown to be compatible with the
corresponding 3D Ising values. We additionally identify a number of subtleties
that are encountered when finite size scaling is applied to the AO model. In
particular, we find that the finite size extrapolation of the interfacial
tension is most consistent when logarithmic size dependences are ignored. This
finding is in agreement with the work of Berg et al.[Phys. Rev. B, V47 P497
(1993)]Comment: 13 pages, 16 figure
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