7,501 research outputs found
Non-crossing Brownian paths and Dyson Brownian motion under a moving boundary
We compute analytically the probability that a set of Brownian
paths do not cross each other and stay below a moving boundary up to time . We show that for large it decays as a power
law . The decay exponent is obtained
as the ground state energy of a quantum system of non-interacting fermions
in a harmonic well in the presence of an infinite hard wall at position .
Explicit expressions for are obtained in various limits of and
, in particular for large and large . We obtain the joint
distribution of the positions of the walkers in the presence of the moving
barrier at large time. We extend our results to the
case of Dyson Brownian motions (corresponding to the Gaussian Unitary
Ensemble) in the presence of the same moving boundary .
For we show that the system provides a realization of a Laguerre
biorthogonal ensemble in random matrix theory. We obtain explicitly the average
density near the barrier, as well as in the bulk far away from the barrier.
Finally we apply our results to non-crossing Brownian bridges on the
interval under a time-dependent barrier .Comment: 44 pages, 13 figure
Wigner function of noninteracting trapped fermions
We study analytically the Wigner function of
noninteracting fermions trapped in a smooth confining potential in
dimensions. At zero temperature, is constant over a
finite support in the phase space and vanishes outside.
Near the edge of this support, we find a universal scaling behavior of
for large . The associated scaling function is
independent of the precise shape of the potential as well as the spatial
dimension . We further generalize our results to finite temperature .
We show that there exists a low temperature regime where
is an energy scale that depends on and the confining potential , where the Wigner function at the edge again takes a universal scaling
form with a -dependent scaling function. This temperature dependent scaling
function is also independent of the potential as well as the dimension . Our
results generalize to any and the and results
obtained by Bettelheim and Wiegman [Phys. Rev. B , 085102 (2011)].Comment: 16 pages, 4 figure
How important is the credit channel? An empirical study of the US banking crisis
We examine whether by adding a credit channel to the standard New Keynesian model we can account better for the behaviour of US macroeconomic data up to and including the banking crisis. We use the method of indirect inference which evaluates statistically how far a model's simulated behaviour mimics the behaviour of the data. We find that the model with credit dominates the standard model by a substantial margin. Credit shocks are the main contributor to the variation in the output gap during the crisis
Equation of state of strongly coupled Hamiltonian lattice QCD at finite density
We calculate the equation of state of strongly coupled Hamiltonian lattice
QCD at finite density by constructing a solution to the equation of motion
corresponding to an effective Hamiltonian using Wilson fermions. We find that
up to and beyond the chiral symmetry restoration density the pressure of the
quark Fermi sea can be negative indicating its mechanical instability. This
result is in qualitative agreement with continuum models and should be
verifiable by future numerical simulations.Comment: 14 pages, 2 EPS figures. Revised version - added discussion on the
equation of stat
Statistics of fermions in a -dimensional box near a hard wall
We study noninteracting fermions in a domain bounded by a hard wall
potential in dimensions. We show that for large , the
correlations at the edge of the Fermi gas (near the wall) at zero temperature
are described by a universal kernel, different from the universal edge kernel
valid for smooth potentials. We compute this dimensional hard edge kernel
exactly for a spherical domain and argue, using a generalized method of images,
that it holds close to any sufficiently smooth boundary. As an application we
compute the quantum statistics of the position of the fermion closest to the
wall. Our results are then extended in several directions, including non-smooth
boundaries such as a wedge, and also to finite temperature.Comment: 5 pages + 14 pages (Supp. Mat.), 6 figure
Why Use a Hamilton Approach in QCD?
We discuss in the Hamiltonian frame work. We treat finite density
in the strong coupling regime. We present a parton-model inspired
regularisation scheme to treat the spectrum (-angles) and distribution
functions in . We suggest a Monte Carlo method to construct
low-dimensionasl effective Hamiltonians. Finally, we discuss improvement in
Hamiltonian .Comment: Proceedings of Hadrons and Strings, invited talk given by H.
Kr\"{o}ger; Text (LaTeX file), 3 Figures (ps file
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