46,004 research outputs found
A microscopic mechanism for rejuvenation and memory effects in spin glasses
Aging in spin glasses (and in some other systems) reveals astonishing effects
of `rejuvenation and memory' upon temperature changes. In this paper, we
propose microscopic mechanisms (at the scale of spin-spin interactions) which
can be at the origin of such phenomena. Firstly, we recall that, in a
frustrated system, the effective average interaction between two spins may take
different values (possibly with opposite signs) at different temperatures. We
give simple examples of such situations, which we compute exactly. Such
mechanisms can explain why new ordering processes (rejuvenation) seem to take
place in spin glasses when the temperature is lowered. Secondly, we emphasize
the fact that inhomogeneous interactions do naturally lead to a wide
distribution of relaxation times for thermally activated flips. `Memory spots'
spontaneously appear, in the sense that the flipping time of some spin clusters
becomes extremely long when the temperature is decreased. Such memory spots are
capable of keeping the memory of previous ordering at a higher temperature
while new ordering processes occur at a lower temperature. After a qualitative
discussion of these mechanisms, we show in the numerical simulation of a
simplified example that this may indeed work. Our conclusion is that certain
chaos-like phenomena may show up spontaneously in any frustrated and
inhomogeneous magnetic system, without impeding the occurrence of memory
effects.Comment: 9 pages (11 figures) - revised version, to appear in Eur. Phys. J. B
(2001
The Cauchy Operator for Basic Hypergeometric Series
We introduce the Cauchy augmentation operator for basic hypergeometric
series. Heine's transformation formula and Sears'
transformation formula can be easily obtained by the symmetric property of some
parameters in operator identities. The Cauchy operator involves two parameters,
and it can be considered as a generalization of the operator . Using
this operator, we obtain extensions of the Askey-Wilson integral, the Askey-Roy
integral, Sears' two-term summation formula, as well as the -analogues of
Barnes' lemmas. Finally, we find that the Cauchy operator is also suitable for
the study of the bivariate Rogers-Szeg\"o polynomials, or the continuous big
-Hermite polynomials.Comment: 21 pages, to appear in Advances in Applied Mathematic
Universal Voting Protocol Tweaks to Make Manipulation Hard
Voting is a general method for preference aggregation in multiagent settings,
but seminal results have shown that all (nondictatorial) voting protocols are
manipulable. One could try to avoid manipulation by using voting protocols
where determining a beneficial manipulation is hard computationally. A number
of recent papers study the complexity of manipulating existing protocols. This
paper is the first work to take the next step of designing new protocols that
are especially hard to manipulate. Rather than designing these new protocols
from scratch, we instead show how to tweak existing protocols to make
manipulation hard, while leaving much of the original nature of the protocol
intact. The tweak studied consists of adding one elimination preround to the
election. Surprisingly, this extremely simple and universal tweak makes typical
protocols hard to manipulate! The protocols become NP-hard, #P-hard, or
PSPACE-hard to manipulate, depending on whether the schedule of the preround is
determined before the votes are collected, after the votes are collected, or
the scheduling and the vote collecting are interleaved, respectively. We prove
general sufficient conditions on the protocols for this tweak to introduce the
hardness, and show that the most common voting protocols satisfy those
conditions. These are the first results in voting settings where manipulation
is in a higher complexity class than NP (presuming PSPACE NP)
Effective theory of excitations in a Feshbach resonant superfluid
A strongly interacting Fermi gas, such as that of cold atoms operative near a
Feshbach resonance, is difficult to study by perturbative many-body theory to
go beyond mean field approximation. Here I develop an effective field theory
for the resonant superfluid based on broken symmetry. The theory retains both
fermionic quasiparticles and superfluid phonons, the interaction between them
being derived non-perturbatively. The theory converges and can be improved
order by order, in a manner governed by a low energy expansion rather than by
coupling constant. I apply the effective theory to calculate the specific heat
and propose a mechanism of understanding the empirical power law of energy
versus temperature recently measured in a heat capacity experiment.Comment: 4+ pages, 1 figure; Added references, corrected and clarified minor
statements (v.2
A data assimilation algorithm for the subcritical surface quasi-geostrophic equation
In this article, we prove that data assimilation by feedback nudging can be
achieved for the three-dimensional quasi-geostrophic equation in a simplified
scenario using only large spatial scale observables on the dynamical boundary.
On this boundary, a scalar unknown (buoyancy or surface temperature of the
fluid) satisfies the surface quasi-geostrophic equation. The feedback nudging
is done on this two-dimensional model, yet ultimately synchronizes the
streamfunction of the three-dimensional flow. The main analytical difficulties
are due to the presence of a nonlocal dissipative operator in the surface
quasi-geostrophic equation. This is overcome by exploiting a suitable partition
of unity, the modulus of continuity characterization of Sobolev space norms,
and the Littlewood-Paley decomposition to ultimately establish various
boundedness and approximation-of-identity properties for the observation
operators.Comment: 28 pages, referee comments incorporated, references added, abstract
and introduction modified, main theorems cover full subcritical range of
dissipation, certain boundedness properties of observation operators extende
Non-equilibrium Green's function theory for non-adiabatic effects in quantum transport: inclusion of electron-electron interactions
Non-equilibrium Green's function theory for non-adiabatic effects in quantum
transport [Kershaw and Kosov, J.Chem. Phys. 2017, 147, 224109 and J. Chem.
Phys. 2018, 149, 044121] is extended to the case of interacting electrons. We
consider a general problem of quantum transport of interacting electrons
through a central region with dynamically changing geometry. The approach is
based on the separation of time scales in the non-equilibrium Green's functions
and the use of Wigner transformation to solve the Kadanoff-Baym equations. The
Green's functions and correlation self-energy are non-adiabatically expanded up
to the second order central time derivatives. We produced expressions for
Green's functions with non-adiabatic corrections and modified formula for
electric current; both depend not only on instantaneous molecular junction
geometry but also on nuclear velocities and accelerations. The theory is
illustrated by the study of electron transport through a model single-resonant
level molecular junction with local electron-electron repulsion and a
dynamically changing geometry
Nonadiabatic corrections to electric current in molecular junction due to nuclear motion at the molecule-electrode interfaces
We present quantum electron transport theory that incorporates dynamical
effects of motion of atoms on electrode-molecule interfaces in the calculations
of the electric current. The theory is based on non-equilibrium Green's
functions. We separate time scales in the Green's functions on fast relative
time and slow central time. The derivative with respect to the central time
serves as a small parameter in the theory. We solve the real-time Kadanoff-Baym
equations for molecular Green's functions using Wigner representation and keep
terms up to the second order with respect to the central time derivatives.
Molecular Green's functions and consequently the electric current are expressed
as functions of molecular junction coordinates as well as velocities and
accelerations of molecule-electrode interface nuclei. We apply the theory to
model a molecular system and study the effects of non-adiabatic nuclear motion
on molecular junction conductivity
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