200 research outputs found
Invariant measures for Burgers equation with stochastic forcing
In this paper we study the following Burgers equation
du/dt + d/dx (u^2/2) = epsilon d^2u/dx^2 + f(x,t)
where f(x,t)=dF/dx(x,t) is a random forcing function, which is periodic in x
and white noise in t. We prove the existence and uniqueness of an invariant
measure by establishing a ``one force, one solution'' principle, namely that
for almost every realization of the force, there is a unique distinguished
solution that exists for the time interval (-infty, +infty) and this solution
attracts all other solutions with the same forcing. This is done by studying
the so-called one-sided minimizers. We also give a detailed description of the
structure and regularity properties for the stationary solutions. In
particular, we prove, under some non-degeneracy conditions on the forcing, that
almost surely there is a unique main shock and a unique global minimizer for
the stationary solutions. Furthermore the global minimizer is a hyperbolic
trajectory of the underlying system of characteristics.Comment: 84 pages, published version, abstract added in migratio
Herman's Theory Revisited
We prove that a -smooth orientation-preserving circle
diffeomorphism with rotation number in Diophantine class ,
, is -smoothly conjugate to a rigid
rotation. We also derive the most precise version of Denjoy's inequality for
such diffeomorphisms.Comment: 10 page
Ballistic deposition patterns beneath a growing KPZ interface
We consider a (1+1)-dimensional ballistic deposition process with
next-nearest neighbor interaction, which belongs to the KPZ universality class,
and introduce for this discrete model a variational formulation similar to that
for the randomly forced continuous Burgers equation. This allows to identify
the characteristic structures in the bulk of a growing aggregate ("clusters"
and "crevices") with minimizers and shocks in the Burgers turbulence, and to
introduce a new kind of equipped Airy process for ballistic growth. We dub it
the "hairy Airy process" and investigate its statistics numerically. We also
identify scaling laws that characterize the ballistic deposition patterns in
the bulk: the law of "thinning" of the forest of clusters with increasing
height, the law of transversal fluctuations of cluster boundaries, and the size
distribution of clusters. The corresponding critical exponents are determined
exactly based on the analogy with the Burgers turbulence and simple scaling
considerations.Comment: 10 pages, 5 figures. Minor edits: typo corrected, added explanation
of two acronyms. The text is essentially equivalent to version
Low-frequency dynamics of disordered XY spin chains and pinned density waves: from localized spin waves to soliton tunneling
A long-standing problem of the low-energy dynamics of a disordered XY spin
chain is re-examined. The case of a rigid chain is studied where the quantum
effects can be treated quasiclassically. It is shown that as the frequency
decreases, the relevant excitations change from localized spin waves to
two-level systems to soliton-antisoliton pairs. The linear-response correlation
functions are calculated. The results apply to other periodic glassy systems
such as pinned density waves, planar vortex lattices, stripes, and disordered
Luttinger liquids.Comment: (v2) Major improvements in presentation style. One figure added (v3)
Another minor chang
Novel Scintillation Material - ZnO Transparent Ceramics
ZnO-based scintillation ceramics for application in HENPA LENPA analyzers
have been investigated. The following ceramic samples have been prepared:
undoped ones (ZnO), an excess of zinc in stoichiometry (ZnO:Zn), doped with
gallium (ZnO:Ga) and lithium (ZnO:Li). Optical transmission, x-ray excited
emission, scintillation decay and pulse height spectra were measured and
analyzed. Ceramics have reasonable transparency in visible range (up to 60% for
0.4 mm thickness) and energy resolution (14.9% at 662 keV Cs137 gamma
excitation). Undoped ZnO shows slow (1.6 {\mu}s) luminescence with maximum at
2.37 eV and light yield about 57% of CsI:Tl. ZnO:Ga ceramics show relatively
low light yield with ultra fast decay time (1 ns). Lithium doped ceramics
ZnO:Li have better decay time than undoped ZnO with fair light yield. ZnO:Li
ceramics show good characteristics under alpha-particle excitation and can be
applied for the neutral particle analyzers.Comment: 4 pages, 8 figures, research covered in this paper was presented at
SCINT2011 conference as a poster, submitted for publication at IEEE Trans.
Nucl. Sc
Nonlinear electron transport in normally pinched-off quantum wire
Nonlinear electron transport in normally pinched-off quantum wires was
studied. The wires were fabricated from AlGaAs/GaAs heterostructures with
high-mobility two-dimensional electron gas by electron beam lithography and
following wet etching. At certain critical source-drain voltage the samples
exhibited a step rise of the conductance. The differential conductance of the
open wires was noticeably lower than e^2/h as far as only part of the
source-drain voltage dropped between source contact and saddle-point of the
potential relief along the wire. The latter limited the electron flow injected
to the wire. At high enough source-drain voltages the decrease of the
differential conductance due to the real space transfer of electrons from the
wire in GaAs to the doped AlGaAs layer was found. In this regime the sign of
differential magnetoconductance was changed with reversing the direction of the
current in the wire or the magnetic field, whet the magnetic field lies in the
heterostructure plane and is directed perpendicular to the current. The
dependence of the differential conductance on the magnetic field and its
direction indicated that the real space transfer events were mainly mediated by
the interface scattering.Comment: LaTeX 2e (epl.cls) 6 pages, 3 figure
Acoustic Phonon-Assisted Resonant Tunneling via Single Impurities
We perform the investigations of the resonant tunneling via impurities
embedded in the AlAs barrier of a single GaAs/AlGaAs heterostructure. In the
characteristics measured at 30mK, the contribution of individual donors
is resolved and the fingerprints of phonon assistance in the tunneling process
are seen. The latter is confirmed by detailed analysis of the tunneling rates
and the modeling of the resonant tunneling contribution to the current.
Moreover, fluctuations of the local structure of the DOS (LDOS) and Fermi edge
singularities are observed.Comment: accepted in Phys. Rev.
A magnetically-induced Coulomb gap in graphene due to electron-electron interactions
Insights into the fundamental properties of graphene's Dirac-Weyl fermions
have emerged from studies of electron tunnelling transistors in which an
atomically thin layer of hexagonal boron nitride (hBN) is sandwiched between
two layers of high purity graphene. Here, we show that when a single defect is
present within the hBN tunnel barrier, it can inject electrons into the
graphene layers and its sharply defined energy level acts as a high resolution
spectroscopic probe of electron-electron interactions in graphene. We report a
magnetic field dependent suppression of the tunnel current flowing through a
single defect below temperatures of 2 K. This is attributed to the
formation of a magnetically-induced Coulomb gap in the spectral density of
electrons tunnelling into graphene due to electron-electron interactions
Statistical Theory for the Kardar-Parisi-Zhang Equation in 1+1 Dimension
The Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimension dynamically develops
sharply connected valley structures within which the height derivative {\it is
not} continuous. There are two different regimes before and after creation of
the sharp valleys. We develop a statistical theory for the KPZ equation in 1+1
dimension driven with a random forcing which is white in time and Gaussian
correlated in space. A master equation is derived for the joint probability
density function of height difference and height gradient when the forcing correlation length is much smaller than
the system size and much bigger than the typical sharp valley width. In the
time scales before the creation of the sharp valleys we find the exact
generating function of and . Then we express the time
scale when the sharp valleys develop, in terms of the forcing characteristics.
In the stationary state, when the sharp valleys are fully developed, finite
size corrections to the scaling laws of the structure functions are also obtained.Comment: 50 Pages, 5 figure
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