1,800,502 research outputs found
Ageing in the contact process: Scaling behavior and universal features
We investigate some aspects of the ageing behavior observed in the contact
process after a quench from its active phase to the critical point. In
particular we discuss the scaling properties of the two-time response function
and we calculate it and its universal ratio to the two-time correlation
function up to first order in the field-theoretical epsilon-expansion. The
scaling form of the response function does not fit the prediction of the theory
of local scale invariance. Our findings are in good qualitative agreement with
recent numerical results.Comment: 20 pages, 3 figure
Emergence of superconductivity in the cuprates via a universal percolation process
A pivotal step toward understanding unconventional superconductors would be
to decipher how superconductivity emerges from the unusual normal state upon
cooling. In the cuprates, traces of superconducting pairing appear above the
macroscopic transition temperature , yet extensive investigation has led
to disparate conclusions. The main difficulty has been the separation of
superconducting contributions from complex normal state behaviour. Here we
avoid this problem by measuring the nonlinear conductivity, an observable that
is zero in the normal state. We uncover for several representative cuprates
that the nonlinear conductivity vanishes exponentially above , both with
temperature and magnetic field, and exhibits temperature-scaling characterized
by a nearly universal scale . Attempts to model the response with the
frequently evoked Ginzburg-Landau theory are unsuccessful. Instead, our
findings are captured by a simple percolation model that can also explain other
properties of the cuprates. We thus resolve a long-standing conundrum by
showing that the emergence of superconductivity in the cuprates is dominated by
their inherent inhomogeneity
Realization of the Optimal Universal Quantum Entangler
We present the first experimental demonstration of the ''optimal'' and
''universal'' quantum entangling process involving qubits encoded in the
polarization of single photons. The structure of the ''quantum entangling
machine'' consists of the quantum injected optical parametric amplifier by
which the contextual realization of the 1->2 universal quantum cloning and of
the universal NOT (U-NOT) gate has also been achieved.Comment: 10 pages, 3 figures, to appear in Physical Review
The largest root of random Kac polynomials is heavy tailed
We prove that the largest and smallest root in modulus of random Kac
polynomials have a non-universal behavior. They do not converge towards the
edge of the support of the limiting distribution of the zeros. This
non-universality is surprising as the large deviation principle for the
empirical measure is universal. This is in sharp contrast with random matrix
theory where the large deviation principle is non-universal but the
fluctuations of the largest eigenvalue are universal. We show that the modulus
of the largest zero is heavy tailed, with a number of finite moments bounded
from above by the behavior at the origin of the distribution of the
coefficients. We also prove that the random process of the roots of modulus
smaller than one converges towards a limit point process. Finally, in the case
of complex Gaussian coefficients, we use the work of Peres and Vir{\'a}g [PV05]
to obtain explicit formulas for the limiting objects
Universal representations of braid and braid-permutation groups
Drinfel'd used associators to construct families of universal representations
of braid groups. We consider semi-associators (i.e., we drop the pentagonal
axiom and impose a normalization in degree one). We show that the process may
be reversed, to obtain semi-associators from universal representations of
3-braids. We view braid groups as subgroups of braid-permutation groups. We
construct a family of universal representations of braid-permutation groups,
without using associators. All representations in the family are faithful,
defined over \bbQ by simple explicit formulae. We show that they give
universal Vassiliev-type invariants for braid-permutation groups.Comment: 19 pages, references adde
Bubble break-off in Hele-Shaw flows : Singularities and integrable structures
Bubbles of inviscid fluid surrounded by a viscous fluid in a Hele-Shaw cell
can merge and break-off. During the process of break-off, a thinning neck
pinches off to a universal self-similar singularity. We describe this process
and reveal its integrable structure: it is a solution of the dispersionless
limit of the AKNS hierarchy. The singular break-off patterns are universal, not
sensitive to details of the process and can be seen experimentally. We briefly
discuss the dispersive regularization of the Hele-Shaw problem and the
emergence of the Painlev\'e II equation at the break-off.Comment: 27 pages, 9 figures; typo correcte
The universal Airy_1 and Airy_2 processes in the Totally Asymmetric Simple Exclusion Process
In the totally asymmetric simple exclusion process (TASEP) two processes
arise in the large time limit: the Airy_1 and Airy_2 processes. The Airy_2
process is an universal limit process occurring also in other models: in a
stochastic growth model on 1+1-dimensions, 2d last passage percolation,
equilibrium crystals, and in random matrix diffusion. The Airy_1 and Airy_2
processes are defined and discussed in the context of the TASEP. We also
explain a geometric representation of the TASEP from which the connection to
growth models and directed last passage percolation is immediate.Comment: 13 pages, 4 figures, proceeding for the conference in honor of Percy
Deift's 60th birthda
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