3,733 research outputs found
Escaping free-energy minima
We introduce a novel and powerful method for exploring the properties of the
multidimensional free energy surfaces of complex many-body systems by means of
a coarse-grained non-Markovian dynamics in the space defined by a few
collective coordinates.A characteristic feature of this dynamics is the
presence of a history-dependent potential term that, in time, fills the minima
in the free energy surface, allowing the efficient exploration and accurate
determination of the free energy surface as a function of the collective
coordinates. We demonstrate the usefulness of this approach in the case of the
dissociation of a NaCl molecule in water and in the study of the conformational
changes of a dialanine in solution.Comment: 3 figure
Theories of Low-Energy Quasi-Particle States in Disordered d-Wave Superconductors
The physics of low-energy quasi-particle excitations in disordered d-wave
superconductors is a subject of ongoing intensive research. Over the last
decade, a variety of conceptually and methodologically different approaches to
the problem have been developed. Unfortunately, many of these theories
contradict each other, and the current literature displays a lack of consensus
on even the most basic physical observables. Adopting a symmetry-oriented
approach, the present paper attempts to identify the origin of the disagreement
between various previous approaches, and to develop a coherent theoretical
description of the different low-energy regimes realized in weakly disordered
d-wave superconductors. We show that, depending on the presence or absence of
time-reversal invariance and the microscopic nature of the impurities, the
system falls into one of four different symmetry classes. By employing a
field-theoretical formalism, we derive effective descriptions of these
universal regimes as descendants of a common parent field theory of
Wess-Zumino-Novikov-Witten type. As well as describing the properties of each
universal regime, we analyse a number of physically relevant crossover
scenarios, and discuss reasons for the disagreement between previous results.
We also touch upon other aspects of the phenomenology of the d-wave
superconductor such as quasi-particle localization properties, the spin quantum
Hall effect, and the quasi-particle physics of the disordered vortex lattice.Comment: 42 Pages, 8 postscript figures, published version with updated
reference
Monte Carlo study of the scaling of universal correlation lengths in three-dimensional O(n) spin models
Using an elaborate set of simulational tools and statistically optimized
methods of data analysis we investigate the scaling behavior of the correlation
lengths of three-dimensional classical O() spin models. Considering
three-dimensional slabs , the results over a
wide range of indicate the validity of special scaling relations involving
universal amplitude ratios that are analogous to results of conformal field
theory for two-dimensional systems. A striking mismatch of the
extrapolation of these simulations against analytical calculations is traced
back to a breakdown of the identification of this limit with the spherical
model.Comment: 18 pages, 9 figures, REVTeX4, slightly shortened, updated critical
exponent estimate
An Improved Calculation of the Non-Gaussian Halo Mass Function
The abundance of collapsed objects in the universe, or halo mass function, is
an important theoretical tool in studying the effects of primordially generated
non-Gaussianities on the large scale structure. The non-Gaussian mass function
has been calculated by several authors in different ways, typically by
exploiting the smallness of certain parameters which naturally appear in the
calculation, to set up a perturbative expansion. We improve upon the existing
results for the mass function by combining path integral methods and saddle
point techniques (which have been separately applied in previous approaches).
Additionally, we carefully account for the various scale dependent combinations
of small parameters which appear. Some of these combinations in fact become of
order unity for large mass scales and at high redshifts, and must therefore be
treated non-perturbatively. Our approach allows us to do this, and to also
account for multi-scale density correlations which appear in the calculation.
We thus derive an accurate expression for the mass function which is based on
approximations that are valid over a larger range of mass scales and redshifts
than those of other authors. By tracking the terms ignored in the analysis, we
estimate theoretical errors for our result and also for the results of others.
We also discuss the complications introduced by the choice of smoothing filter
function, which we take to be a top-hat in real space, and which leads to the
dominant errors in our expression. Finally, we present a detailed comparison
between the various expressions for the mass functions, exploring the accuracy
and range of validity of each.Comment: 28 pages, 13 figures; v2: text reorganized and some figured modified
for clarity, results unchanged, references added. Matches version published
in JCA
Dominant Reaction Pathways in High Dimensional Systems
This paper is devoted to the development of a theoretical and computational
framework to efficiently sample the statistically significant thermally
activated reaction pathways, in multi-dimensional systems obeying Langevin
dynamics. We show how to obtain the set of most probable reaction pathways and
compute the corrections due to quadratic thermal fluctuations around such
trajectories. We discuss how to obtain predictions for the evolution of
arbitrary observables and how to generate conformations which are
representative of the transition state ensemble. We present an illustrative
implementation of our method by studying the diffusion of a point particle in a
2-dimensional funneled external potential.Comment: 18 pages, 7 figures. Improvement in the text and in the figures.
Version submitted for publicatio
Aspects of stochastic resonance in reaction-diffusion systems: The nonequilibrium-potential approach
We analyze several aspects of the phenomenon of stochastic resonance in
reaction-diffusion systems, exploiting the nonequilibrium potential's
framework. The generalization of this formalism (sketched in the appendix) to
extended systems is first carried out in the context of a simplified scalar
model, for which stationary patterns can be found analytically. We first show
how system-size stochastic resonance arises naturally in this framework, and
then how the phenomenon of array-enhanced stochastic resonance can be further
enhanced by letting the diffusion coefficient depend on the field. A yet less
trivial generalization is exemplified by a stylized version of the
FitzHugh-Nagumo system, a paradigm of the activator-inhibitor class. After
discussing for this system the second aspect enumerated above, we derive from
it -through an adiabatic-like elimination of the inhibitor field- an effective
scalar model that includes a nonlocal contribution. Studying the role played by
the range of the nonlocal kernel and its effect on stochastic resonance, we
find an optimal range that maximizes the system's response.Comment: 16 pages, 15 figures, uses svjour.cls and svepj-spec.clo. Minireview
to appear in The European Physical Journal Special Topics (issue in memory of
Carlos P\'erez-Garc\'{\i}a, edited by H. Mancini
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