393 research outputs found
Josephson Effect in a Coulomb-blockaded SINIS Junction
The problem of Josephson current through Coulomb-blocked nanoscale
superconductor-normal-superconductor structure with tunnel contacts is
reconsidered. Two different contributions to the phase-biased supercurrent are
identified, which are dominant in the limits of weak and strong Coulomb
interaction. Full expression for the free energy valid at arbitrary Coulomb
strength is found. The current derived from this free energy interpolates
between known results for weak and strong Coulomb interaction as phase bias
changes from 0 to pi. In the broad range of Coulomb strength the current-phase
relation is substantially non-sinusoidal and qualitatively different from the
case of semi-ballistic SNS junctions. Coulomb interaction leads to appearance
of a local minimum in the current at some intermediate value of phase
difference applied to the junction.Comment: 5 pages, 2 EPS figures, JETP Letters style file include
Electric Transport Theory of Dirac Fermions in Graphene
Using the self-consistent Born approximation to the Dirac fermions under
finite-range impurity scatterings, we show that the current-current correlation
function is determined by four-coupled integral equations. This is very
different from the case for impurities with short-range potentials. As a test
of the present approach, we calculate the electric conductivity in graphene for
charged impurities with screened Coulomb potentials. The obtained conductivity
at zero temperature varies linearly with the carrier concentration, and the
minimum conductivity at zero doping is larger than the existing theoretical
predictions, but still smaller than that of the experimental measurement. The
overall behavior of the conductivity obtained by the present calculation at
room temperature is similar to that at zero temperature except the minimum
conductivity is slightly larger.Comment: 6 pages, 3 figure
Subcritical multiplicative chaos for regularized counting statistics from random matrix theory
For an NĂN random unitary matrix U_N, we consider the random field defined by counting the number of eigenvalues of U_N in a mesoscopic arc of the unit circle, regularized at an N-dependent scale Æ_N>0. We prove that the renormalized exponential of this field converges as N â â to a Gaussian multiplicative chaos measure in the whole subcritical phase. In addition, we show that the moments of the total mass converge to a Selberg-like integral and by taking a further limit as the size of the arc diverges, we establish part of the conjectures in [55]. By an analogous construction, we prove that the multiplicative chaos measure coming from the sine process has the same distribution, which strongly suggests that this limiting object should be universal. The proofs are based on the asymptotic analysis of certain Toeplitz or Fredholm determinants using the Borodin-Okounkov formula or a Riemann-Hilbert problem for integrable operators. Our approach to the LÂč-phase is based on a generalization of the construction in Berestycki [5] to random fields which are only asymptotically Gaussian. In particular, our method could have applications to other random fields coming from either random matrix theory or a different context
Thermal diffusion of solitons on anharmonic chains with long-range coupling
We extend our studies of thermal diffusion of non-topological solitons to
anharmonic FPU-type chains with additional long-range couplings. The observed
superdiffusive behavior in the case of nearest neighbor interaction (NNI) turns
out to be the dominating mechanism for the soliton diffusion on chains with
long-range interactions (LRI). Using a collective variable technique in the
framework of a variational analysis for the continuum approximation of the
chain, we derive a set of stochastic integro-differential equations for the
collective variables (CV) soliton position and the inverse soliton width. This
set can be reduced to a statistically equivalent set of Langevin-type equations
for the CV, which shares the same Fokker-Planck equation. The solution of the
Langevin set and the Langevin dynamics simulations of the discrete system agree
well and demonstrate that the variance of the soliton increases stronger than
linearly with time (superdiffusion). This result for the soliton diffusion on
anharmonic chains with long-range interactions reinforces the conjecture that
superdiffusion is a generic feature of non-topological solitons.Comment: 11 figure
Online/Offline OR Composition of Sigma Protocols
Proofs of partial knowledge allow a prover to prove knowledge of witnesses for k out of n instances of NP languages. Cramer, Schoenmakers and DamgÄrd [10] provided an efficient construction of a 3-round public-coin witness-indistinguishable (k, n)-proof of partial knowledge for any NP language, by cleverly combining n executions of Σ-protocols for that language. This transform assumes that all n instances are fully specified before the proof starts, and thus directly rules out the possibility of choosing some of the instances after the first round. Very recently, Ciampi et al. [6] provided an improved transform where one of the instances can be specified in the last round. They focus on (1, 2)-proofs of partial knowledge with the additional feature that one instance is defined in the last round, and could be adaptively chosen by the verifier. They left as an open question the existence of an efficient (1, 2)-proof of partial knowledge where no instance is known in the first round. More in general, they left open the question of constructing an efficient (k, n)-proof of partial knowledge where knowledge of all n instances can be postponed. Indeed, this property is achieved only by inefficient constructions requiring NP reductions [19]. In this paper we focus on the question of achieving adaptive-input proofs of partial knowledge. We provide through a transform the first efficient construction of a 3-round public-coin witness-indistinguishable (k, n)-proof of partial knowledge where all instances can be decided in the third round. Our construction enjoys adaptive-input witness indistinguishability. Additionally, the proof of knowledge property remains also if the adversarial prover selects instances adaptively at last round as long as our transform is applied to a proof of knowledge belonging to the widely used class of proofs of knowledge described in [9,21]. Since knowledge of instances and witnesses is not needed before the last round, we have that the first round can be precomputed and in the online/offline setting our performance is similar to the one of [10]. Our new transform relies on the DDH assumption (in contrast to the transforms of [6,10] that are unconditional)
Impurity-assisted tunneling in graphene
The electric conductance of a strip of undoped graphene increases in the
presence of a disorder potential, which is smooth on atomic scales. The
phenomenon is attributed to impurity-assisted resonant tunneling of massless
Dirac fermions. Employing the transfer matrix approach we demonstrate the
resonant character of the conductivity enhancement in the presence of a single
impurity. We also calculate the two-terminal conductivity for the model with
one-dimensional fluctuations of disorder potential by a mapping onto a problem
of Anderson localization.Comment: 6 pages, 3 figures, final version, typos corrected, references adde
Threshold detachment of negative ions by electron impact
The description of threshold fragmentation under long range repulsive forces
is presented. The dominant energy dependence near threshold is isolated by
decomposing the cross section into a product of a back ground part and a
barrier penetration probability resulting from the repulsive Coulomb
interaction. This tunneling probability contains the dominant energy variation
and it can be calculated analytically based on the same principles as Wannier's
description for threshold ionization under attractive forces. Good agreement is
found with the available experimental cross sections on detachment by electron
impact from , and .Comment: 4 pages, 4 figures (EPS), to appear in Phys.Rev.Lett, Feb. 22nd, 199
Counting function fluctuations and extreme value threshold in multifractal patterns: the case study of an ideal noise
To understand the sample-to-sample fluctuations in disorder-generated
multifractal patterns we investigate analytically as well as numerically the
statistics of high values of the simplest model - the ideal periodic
Gaussian noise. By employing the thermodynamic formalism we predict the
characteristic scale and the precise scaling form of the distribution of number
of points above a given level. We demonstrate that the powerlaw forward tail of
the probability density, with exponent controlled by the level, results in an
important difference between the mean and the typical values of the counting
function. This can be further used to determine the typical threshold of
extreme values in the pattern which turns out to be given by
with . Such observation provides a
rather compelling explanation of the mechanism behind universality of .
Revealed mechanisms are conjectured to retain their qualitative validity for a
broad class of disorder-generated multifractal fields. In particular, we
predict that the typical value of the maximum of intensity is to be
given by , where is the
corresponding singularity spectrum vanishing at . For the
noise we also derive exact as well as well-controlled approximate
formulas for the mean and the variance of the counting function without
recourse to the thermodynamic formalism.Comment: 28 pages; 7 figures, published version with a few misprints
corrected, editing done and references adde
Collective and independent-particle motion in two-electron artificial atoms
Investigations of the exactly solvable excitation spectra of two-electron
quantum dots with a parabolic confinement, for different values of the
parameter R_W expressing the relative magnitudes of the interelectron repulsion
and the zero-point kinetic energy of the confined electrons, reveal for large
R_W a remarkably well-developed ro-vibrational spectrum associated with
formation of a linear trimeric rigid molecule composed of the two electrons and
the infinitely heavy confining dot. This spectrum transforms to one
characteristic of a "floppy" molecule for smaller values of R_W. The
conditional probability distribution calculated for the exact two-electron wave
functions allows for the identification of the ro-vibrational excitations as
rotations and stretching/bending vibrations, and provides direct evidence
pertaining to the formation of such molecules.Comment: Published version. Latex/Revtex, 5 pages with 2 postscript figures
embedded in the text. For related papers, see
http://www.prism.gatech.edu/~ph274c
- âŠ