13,209 research outputs found
Energy dynamics in the Sinai model
We study the time dependent potential energy of a
particle diffusing in a one dimensional random force field (the Sinai model).
Using the real space renormalization group method (RSRG), we obtain the exact
large time limit of the probability distribution of the scaling variable
. This distribution exhibits a {\it nonanalytic} behaviour at
. These results are extended to a small non-zero applied field. Using the
constrained path integral method, we moreover compute the joint distribution of
energy and position at time . In presence of a reflecting
boundary at the starting point, with possibly some drift in the + direction,
the RSRG very simply yields the one time and aging two-time behavior of this
joint probability. It exhibits differences in behaviour compared to the
unbounded motion, such as analyticity. Relations with some magnetization
distributions in the 1D spin glass are discussed.Comment: 21 pages, 4 eps figure
Extended Hubbard model for mesoscopic transport in donor arrays in silicon
Arrays of dopants in silicon are promising platforms for the quantum
simulation of the Fermi-Hubbard model. We show that the simplest model with
only on-site interaction is insufficient to describe the physics of an array of
phosphorous donors in silicon due to the strong intersite interaction in the
system. We also study the resonant tunneling transport in the array at low
temperature as a mean of probing the features of the Hubbard physics, such as
the Hubbard bands and the Mott gap. Two mechanisms of localization which
suppresses transport in the array are investigated: The first arises from the
electron-ion core attraction and is significant at low filling; the second is
due to the sharp oscillation in the tunnel coupling caused by the intervalley
interference of the donor electron's wavefunction. This disorder in the tunnel
coupling leads to a steep exponential decay of conductance with channel length
in one-dimensional arrays, but its effect is less prominent in two-dimensional
ones. Hence, it is possible to observe resonant tunneling transport in a
relatively large array in two dimensions
Derivation of the Functional Renormalization Group Beta-Function at order 1/N for Manifolds Pinned by Disorder
In an earlier publication, we have introduced a method to obtain, at large N,
the effective action for d-dimensional manifolds in a N-dimensional disordered
environment. This allowed to obtain the Functional Renormalization Group (FRG)
equation for N=infinity and was shown to reproduce, with no need for
ultrametric replica symmetry breaking, the predictions of the Mezard-Parisi
solution. Here we compute the corrections at order 1/N. We introduce two novel
complementary methods, a diagrammatic and an algebraic one, to perform the
complicated resummation of an infinite number of loops, and derive the
beta-function of the theory to order 1/N. We present both the effective action
and the corresponding functional renormalization group equations. The aim is to
explain the conceptual basis and give a detailed account of the novel aspects
of such calculations. The analysis of the FRG flow, comparison with other
studies, and applications, e.g. to the strong-coupling phase of the
Kardar-Parisi-Zhang equation are examined in a subsequent publication.Comment: 62 pages, 97 figure
Thermal fluctuations in pinned elastic systems: field theory of rare events and droplets
Using the functional renormalization group (FRG) we study the thermal
fluctuations of elastic objects, described by a displacement field u and
internal dimension d, pinned by a random potential at low temperature T, as
prototypes for glasses. A challenge is how the field theory can describe both
typical (minimum energy T=0) configurations, as well as thermal averages which,
at any non-zero T as in the phenomenological droplet picture, are dominated by
rare degeneracies between low lying minima. We show that this occurs through an
essentially non-perturbative *thermal boundary layer* (TBL) in the (running)
effective action Gamma[u] at T>0 for which we find a consistent scaling ansatz
to all orders. The TBL resolves the singularities of the T=0 theory and
contains rare droplet physics. The formal structure of this TBL is explored
around d=4 using a one loop Wilson RG. A more systematic Exact RG (ERG) method
is employed and tested on d=0 models. There we obtain precise relations between
TBL quantities and droplet probabilities which are checked against exact
results. We illustrate how the TBL scaling remains consistent to all orders in
higher d using the ERG and how droplet picture results can be retrieved.
Finally, we solve for d=0,N=1 the formidable "matching problem" of how this T>0
TBL recovers a critical T=0 field theory. We thereby obtain the beta-function
at T=0, *all ambiguities removed*, displayed here up to four loops. A
discussion of d>4 case and an exact solution at large d are also provided
Higher correlations, universal distributions and finite size scaling in the field theory of depinning
Recently we constructed a renormalizable field theory up to two loops for the
quasi-static depinning of elastic manifolds in a disordered environment. Here
we explore further properties of the theory. We show how higher correlation
functions of the displacement field can be computed. Drastic simplifications
occur, unveiling much simpler diagrammatic rules than anticipated. This is
applied to the universal scaled width-distribution. The expansion in
d=4-epsilon predicts that the scaled distribution coincides to the lowest
orders with the one for a Gaussian theory with propagator G(q)=1/q^(d+2 \zeta),
zeta being the roughness exponent. The deviations from this Gaussian result are
small and involve higher correlation functions, which are computed here for
different boundary conditions. Other universal quantities are defined and
evaluated: We perform a general analysis of the stability of the fixed point.
We find that the correction-to-scaling exponent is omega=-epsilon and not
-epsilon/3 as used in the analysis of some simulations. A more detailed study
of the upper critical dimension is given, where the roughness of interfaces
grows as a power of a logarithm instead of a pure power.Comment: 15 pages revtex4. See also preceding article cond-mat/030146
Nonequilibrium dynamics of random field Ising spin chains: exact results via real space RG
Non-equilibrium dynamics of classical random Ising spin chains are studied
using asymptotically exact real space renormalization group. Specifically the
random field Ising model with and without an applied field (and the Ising spin
glass (SG) in a field), in the universal regime of a large Imry Ma length so
that coarsening of domains after a quench occurs over large scales. Two types
of domain walls diffuse in opposite Sinai random potentials and mutually
annihilate. The domain walls converge rapidly to a set of system-specific
time-dependent positions {\it independent of the initial conditions}. We obtain
the time dependent energy, magnetization and domain size distribution
(statistically independent). The equilibrium limits agree with known exact
results. We obtain exact scaling forms for two-point equal time correlation and
two-time autocorrelations. We also compute the persistence properties of a
single spin, of local magnetization, and of domains. The analogous quantities
for the spin glass are obtained. We compute the two-point two-time correlation
which can be measured by experiments on spin-glass like systems. Thermal
fluctuations are found to be dominated by rare events; all moments of truncated
correlations are computed. The response to a small field applied after waiting
time , as measured in aging experiments, and the fluctuation-dissipation
ratio are computed. For ,
, it equals its equilibrium value X=1, though time
translational invariance fails. It exhibits for aging regime
with non-trivial , different from mean field.Comment: 55 pages, 9 figures, revte
The Two-Dimensional Disordered Boson Hubbard Model: Evidence for a Direct Mott Insulator-to-Superfluid Transition and Localization in the Bose Glass Phase
We investigate the Bose glass phase and the insulator-to-superfluid
transition in the two-dimensional disordered boson Hubbard model in the Villain
representation via Monte Carlo simulations. In the Bose glass phase the
probability distribution of the local susceptibility is found to have a tail and the imaginary time Green's function decays algebraically
, giving rise to a divergent global susceptibility. By
considering the participation ratio it is shown that the excitations in the
Bose glass phase are fully localized and a scaling law is established. For
commensurate boson densities we find a direct Mott insulator to superfluid
transition without an intervening Bose glass phase for weak disorder. For this
transition we obtain the critical exponents and , which agree with those for the classical three-dimensional XY
model without disorder. This indicates that disorder is irrelevant at the tip
of the Mott-lobes and that here the inequality is violated.Comment: 15 pages RevTeX, 18 postscript-figures include
Localization of thermal packets and metastable states in Sinai model
We consider the Sinai model describing a particle diffusing in a 1D random
force field. As shown by Golosov, this model exhibits a strong localization
phenomenon for the thermal packet: the disorder average of the thermal
distribution of the relative distance y=x-m(t), with respect to the
(disorder-dependent) most probable position m(t), converges in the limit of
infinite time towards a distribution P(y). In this paper, we revisit this
question of the localization of the thermal packet. We first generalize the
result of Golosov by computing explicitly the joint asymptotic distribution of
relative position y=x(t)-m(t) and relative energy u=U(x(t))-U(m(t)) for the
thermal packet. Next, we compute in the infinite-time limit the localization
parameters Y_k, representing the disorder-averaged probabilities that k
particles of the thermal packet are at the same place, and the correlation
function C(l) representing the disorder-averaged probability that two particles
of the thermal packet are at a distance l from each other. We moreover prove
that our results for Y_k and C(l) exactly coincide with the thermodynamic limit
of the analog quantities computed for independent particles at equilibrium in a
finite sample of length L. Finally, we discuss the properties of the
finite-time metastable states that are responsible for the localization
phenomenon and compare with the general theory of metastable states in glassy
systems, in particular as a test of the Edwards conjecture.Comment: 17 page
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