1,046 research outputs found
Thermodynamics of the glassy state: effective temperature as an additional system parameter
A system is glassy when the observation time is much smaller than the
equilibration time. A unifying thermodynamic picture of the glassy state is
presented. Slow configurational modes are in quasi-equilibrium at an effective
temperature. It enters thermodynamic relations with the configurational entropy
as conjugate variable. Slow fluctuations contribute to susceptibilities via
quasi-equilibrium relations, while there is also a configurational term.
Fluctuation-dissipation relations also involve the effective temperature.
Fluctuations in the energy are non-universal, however. The picture is supported
by analytically solving the dynamics of a toy model.Comment: 5 pages, REVTEX. Phys. Rev. Lett, to appea
Even-visiting random walks: exact and asymptotic results in one dimension
We reconsider the problem of even-visiting random walks in one dimension.
This problem is mapped onto a non-Hermitian Anderson model with binary
disorder. We develop very efficient numerical tools to enumerate and
characterize even-visiting walks. The number of closed walks is obtained as an
exact integer up to 1828 steps, i.e., some walks. On the analytical
side, the concepts and techniques of one-dimensional disordered systems allow
to obtain explicit asymptotic estimates for the number of closed walks of
steps up to an absolute prefactor of order unity, which is determined
numerically. All the cumulants of the maximum height reached by such walks are
shown to grow as , with exactly known prefactors. These results
illustrate the tight relationship between even-visiting walks, trapping models,
and the Lifshitz tails of disordered electron or phonon spectra.Comment: 24 pages, 4 figures. To appear in J. Phys.
Minimal Work Principle and its Limits for Classical Systems
The minimal work principle asserts that work done on a thermally isolated
equilibrium system, is minimal for the slowest (adiabatic) realization of a
given process. This principle, one of the formulations of the second law, is
operationally well-defined for any finite (few particle) Hamiltonian system.
Within classical Hamiltonian mechanics, we show that the principle is valid for
a system of which the observable of work is an ergodic function. For
non-ergodic systems the principle may or may not hold, depending on additional
conditions. Examples displaying the limits of the principle are presented and
their direct experimental realizations are discussed.Comment: 4 + epsilon pages, 1 figure, revte
Critical Indices as Limits of Control Functions
A variant of self-similar approximation theory is suggested, permitting an
easy and accurate summation of divergent series consisting of only a few terms.
The method is based on a power-law algebraic transformation, whose powers play
the role of control functions governing the fastest convergence of the
renormalized series. A striking relation between the theory of critical
phenomena and optimal control theory is discovered: The critical indices are
found to be directly related to limits of control functions at critical points.
The method is applied to calculating the critical indices for several difficult
problems. The results are in very good agreement with accurate numerical data.Comment: 1 file, 5 pages, RevTe
Black Holes in Magnetic Monopoles
We study magnetically charged classical solutions of a spontaneously broken
gauge theory interacting with gravity. We show that nonsingular monopole
solutions exist only if the Higgs vacuum expectation value is less than or
equal to a critical value , which is of the order of the Planck mass.
In the limiting case the monopole becomes a black hole, with the region outside
the horizon described by the critical Reissner-Nordstrom solution. For
, we find additional solutions which are singular at , but which
have this singularity hidden within a horizon. These have nontrivial matter
fields outside the horizon, and may be interpreted as small black holes lying
within a magnetic monopole. The nature of these solutions as a function of
and of the total mass and their relation to the Reissner-Nordstrom
solutions is discussed.Comment: (28 pages
To maximize or not to maximize the free energy of glassy systems, !=?
The static free energy of glassy systems can be expressed in terms of the
Parisi order parameter function. When this function has a discontinuity, the
location of the step is determined by maximizing the free energy. In dynamics a
transition is found at larger temperature, while the location of the step
satisfies a marginality criterion. It is shown here that in a replica
calculation this criterion minimizes the free energy. This leads to first order
phase transitions at the dynamic transition point. Though the order parameter
function is the same as in the long-time limit of a dynamical analysis,
thermodynamics is different.Comment: 4 pages PostScript, one figur
Traffic of Molecular Motors
Molecular motors perform active movements along cytoskeletal filaments and
drive the traffic of organelles and other cargo particles in cells. In contrast
to the macroscopic traffic of cars, however, the traffic of molecular motors is
characterized by a finite walking distance (or run length) after which a motor
unbinds from the filament along which it moves. Unbound motors perform Brownian
motion in the surrounding aqueous solution until they rebind to a filament. We
use variants of driven lattice gas models to describe the interplay of their
active movements, the unbound diffusion, and the binding/unbinding dynamics. If
the motor concentration is large, motor-motor interactions become important and
lead to a variety of cooperative traffic phenomena such as traffic jams on the
filaments, boundary-induced phase transitions, and spontaneous symmetry
breaking in systems with two species of motors. If the filament is surrounded
by a large reservoir of motors, the jam length, i.e., the extension of the
traffic jams is of the order of the walking distance. Much longer jams can be
found in confined geometries such as tube-like compartments.Comment: 10 pages, latex, uses Springer styles (included), to appear in the
Proceedings of "Traffic and Granular Flow 2005
Mode regularization of the susy sphaleron and kink: zero modes and discrete gauge symmetry
To obtain the one-loop corrections to the mass of a kink by mode
regularization, one may take one-half the result for the mass of a widely
separated kink-antikink (or sphaleron) system, where the two bosonic zero modes
count as two degrees of freedom, but the two fermionic zero modes as only one
degree of freedom in the sums over modes. For a single kink, there is one
bosonic zero mode degree of freedom, but it is necessary to average over four
sets of fermionic boundary conditions in order (i) to preserve the fermionic
Z gauge invariance , (ii) to satisfy the basic principle of
mode regularization that the boundary conditions in the trivial and the kink
sector should be the same, (iii) in order that the energy stored at the
boundaries cancels and (iv) to avoid obtaining a finite, uniformly distributed
energy which would violate cluster decomposition. The average number of
fermionic zero-energy degrees of freedom in the presence of the kink is then
indeed 1/2. For boundary conditions leading to only one fermionic zero-energy
solution, the Z gauge invariance identifies two seemingly distinct `vacua'
as the same physical ground state, and the single fermionic zero-energy
solution does not correspond to a degree of freedom. Other boundary conditions
lead to two spatially separated solutions, corresponding to
one (spatially delocalized) degree of freedom. This nonlocality is consistent
with the principle of cluster decomposition for correlators of observables.Comment: 32 pages, 5 figure
Maximal atmospheric neutrino mixing and the small ratio of muon to tau mass
We discuss the problem of the small ratio of muon mass to tau mass in a class
of seesaw models where maximal atmospheric neutrino mixing is enforced through
a -- interchange symmetry. We introduce into those models an
additional symmetry such that in the case of exact
invariance. The symmetry may be softly broken in the Higgs potential, and
one thus achieves in a technically natural way. We speculate
on a wider applicability of this mechanism.Comment: 10 pages, plain LaTeX, no figures, minor changes, final version for
J. Phys.
The many faces of OSp(1|32)
We show that the complete superalgebra of symmetries, including central
charges, that underlies F-theories, M-theories and type II string theories in
dimensions 12, 11 and 10 of various signatures correspond to rewriting of the
same OSp(1|32) algebra in different covariant ways. One only has to distinguish
the complex and the unique real algebra. We develop a common framework to
discuss all signatures theories by starting from the complex form of OSp(1|32).
Theories are distinguished by the choice of basis for this algebra. We
formulate dimensional reductions and dualities as changes of basis of the
algebra. A second ingredient is the choice of a real form corresponding to a
specific signature. The existence of the real form of the algebra selects
preferred spacetime signatures. In particular, we show how the real d=10 IIA
and IIB superalgebras for various signatures are related by generalized
T-duality transformations that not only involve spacelike but also timelike
directions. A third essential ingredient is that the translation generator in
one theory plays the role of a central charge operator in the other theory. The
identification of the translation generator in these algebras leads to the star
algebras of Hull, which are characterized by the fact that the positive
definite energy operator is not part of the translation generators. We apply
our results to discuss different T-dual pictures of the D-instanton solution of
Euclidean IIB supergravity.Comment: 30 pages, Latex, using lscape.st
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