61 research outputs found
The Optical Approach to Casimir Effects
We propose a new approach to the Casimir effect based on classical ray
optics. We define and compute the contribution of classical optical paths to
the Casimir force between rigid bodies. Our approach improves upon the
proximity force approximation. It can be generalized easily to arbitrary
geometries, different boundary conditions, to the computation of Casimir energy
densities and to many other situations. This is a brief introduction to the
method. Joint work with R.L.Jaffe.Comment: Talk given at the conference `Continuous Advances in QCD 2004',
University of Minnesot
The forward approximation as a mean field approximation for the Anderson and Many Body Localization transitions
In this paper we analyze the predictions of the forward approximation in some
models which exhibit an Anderson (single-) or many-body localized phase. This
approximation, which consists in summing over the amplitudes of only the
shortest paths in the locator expansion, is known to over-estimate the critical
value of the disorder which determines the onset of the localized phase.
Nevertheless, the results provided by the approximation become more and more
accurate as the local coordination (dimensionality) of the graph, defined by
the hopping matrix, is made larger. In this sense, the forward approximation
can be regarded as a mean field theory for the Anderson transition in infinite
dimensions. The sum can be efficiently computed using transfer matrix
techniques, and the results are compared with the most precise exact
diagonalization results available.
For the Anderson problem, we find a critical value of the disorder which is
off the most precise available numerical value already in 5 spatial
dimensions, while for the many-body localized phase of the Heisenberg model
with random fields the critical disorder is strikingly close
to the most recent results obtained by exact diagonalization. In both cases we
obtain a critical exponent . In the Anderson case, the latter does not
show dependence on the dimensionality, as it is common within mean field
approximations.
We discuss the relevance of the correlations between the shortest paths for
both the single- and many-body problems, and comment on the connections of our
results with the problem of directed polymers in random medium
Soap films with gravity and almost-minimal surfaces
Motivated by the study of the equilibrium equations for a soap film hanging
from a wire frame, we prove a compactness theorem for surfaces with
asymptotically vanishing mean curvature and fixed or converging boundaries. In
particular, we obtain sufficient geometric conditions for the minimal surfaces
spanned by a given boundary to represent all the possible limits of sequences
of almost-minimal surfaces. Finally, we provide some sharp quantitative
estimates on the distance of an almost-minimal surface from its limit minimal
surface.Comment: 34 pages, 6 figures. Version 2: more detailed description of the
proof of the estimates in Section 5 adde
Impact of jamming criticality on low-temperature anomalies in structural glasses
We present a novel mechanism for the anomalous behaviour of the specific heat
in low-temperature amorphous solids. The analytic solution of a mean-field
model belonging to the same universality class as high-dimensional glasses, the
spherical perceptron, suggests that there exists a crossover temperature above
which the specific heat scales linearly with temperature while below it a cubic
scaling is displayed. This relies on two crucial features of the phase diagram:
(i) The marginal stability of the free-energy landscape, which induces a
gapless phase responsible for the emergence of a power-law scaling (ii) The
vicinity of the classical jamming critical point, as the crossover temperature
gets lowered when approaching it. This scenario arises from a direct study of
the thermodynamics of the system in the quantum regime, where we show that,
contrary to crystals, the Debye approximation does not hold.Comment: 7 pages + 38 pages SI, 5 figure
Many-body localization dynamics from gauge invariance
We show how lattice gauge theories can display many-body localization
dynamics in the absence of disorder. Our starting point is the observation
that, for some generic translationally invariant states, Gauss law effectively
induces a dynamics which can be described as a disorder average over gauge
super-selection sectors. We carry out extensive exact simulations on the
real-time dynamics of a lattice Schwinger model, describing the coupling
between U(1) gauge fields and staggered fermions. Our results show how memory
effects and slow entanglement growth are present in a broad regime of
parameters - in particular, for sufficiently large interactions. These findings
are immediately relevant to cold atoms and trapped ions experiments realizing
dynamical gauge fields, and suggest a new and universal link between
confinement and entanglement dynamics in the many-body localized phase of
lattice models.Comment: 5Pages + appendices; V2: updated discussion in page 2, more numerical
results, added reference
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