1,048 research outputs found
Linear Amplifier Breakdown and Concentration Properties of a Gaussian Field Given that its -Norm is Large
In the context of linear amplification for systems driven by the square of a
Gaussian noise, we investigate the realizations of a Gaussian field in the
limit where its -norm is large. Concentration onto the eigenspace
associated with the largest eigenvalue of the covariance of the field is
proved. When the covariance is trace class, the concentration is in probability
for the -norm. A stronger concentration, in mean for the sup-norm, is
proved for a smaller class of Gaussian fields, and an example of a field
belonging to that class is given. A possible connection with Bose-Einstein
condensation is briefly discussed.Comment: REVTeX file, 11 pages, 1 added paragraph in the introduction, 2 added
references, minor modifications in the text and abstract, submitted to J.
Stat. Phy
Numerical analysis of a spontaneous collapse model for a two-level system
We study a spontaneous collapse model for a two-level (spin) system, in which
the Hamiltonian and the stochastic terms do not commute. The numerical solution
of the equations of motions allows to give precise estimates on the regime at
which the collapse of the state vector occurs, the reduction and delocalization
times, and the reduction probabilities; it also allows to quantify the effect
that an Hamiltonian which does not commute with the reducing terms has on the
collapse mechanism. We also give a clear picture of the transition from the
"microscopic" regime (when the noise terms are weak and the Hamiltonian
prevents the state vector to collapse) to the "macroscopic" regime (when the
noise terms are dominant and the collapse becomes effective for very long
times). Finally, we clarify the distinction between decoherence and collapse.Comment: 7 pages, RevTeX. Significative improvements made. To appear on Phys.
Rev.
Mid-infrared frequency comb spanning an octave based on an Er fiber laser and difference-frequency generation
We describe a coherent mid-infrared continuum source with 700 cm-1 usable
bandwidth, readily tuned within 600 - 2500 cm-1 (4 - 17 \mum) and thus covering
much of the infrared "fingerprint" molecular vibration region. It is based on
nonlinear frequency conversion in GaSe using a compact commercial 100-fs-pulsed
Er fiber laser system providing two amplified near-infrared beams, one of them
broadened by a nonlinear optical fiber. The resulting collimated mid-infrared
continuum beam of 1 mW quasi-cw power represents a coherent infrared frequency
comb with zero carrier-envelope phase, containing about 500,000 modes that are
exact multiples of the pulse repetition rate of 40 MHz. The beam's
diffraction-limited performance enables long-distance spectroscopic probing as
well as maximal focusability for classical and ultraresolving near-field
microscopies. Applications are foreseen also in studies of transient chemical
phenomena even at ultrafast pump-probe scale, and in high-resolution gas
spectroscopy for e.g. breath analysis.Comment: 8 pages, 2 figures revised version, added reference
The long-wavelength behaviour of the exchange-correlation kernel in the Kohn-Sham theory of periodic systems
The polarization-dependence of the exchange-correlation (XC) energy functional of periodic insulators within Kohn-Sham (KS) density-functional theory requires a divergence in the XC kernel for small vectors q. This behaviour, exemplified for a one-dimensional model semiconductor, is also observed when an insulator happens to be described as a KS metal, or vice-versa. Although it can occur in the exchange-only kernel, it is not found in the usual local, semi-local or even non-local approximations to KS theory. We also show that the test-charge and electronic definitions of the macroscopic dielectric constant differ from one another in exact KS theory, but are equivalent in the above-mentioned approximations
Euclidean Black Hole Vortices
We argue the existence of solutions of the Euclidean Einstein equations that
correspond to a vortex sitting at the horizon of a black hole. We find the
asymptotic behaviours, at the horizon and at infinity, of vortex solutions for
the gauge and scalar fields in an abelian Higgs model on a Euclidean
Schwarzschild background and interpolate between them by integrating the
equations numerically. Calculating the backreaction shows that the effect of
the vortex is to cut a slice out of the Euclidean Schwarzschild geometry.
Consequences of these solutions for black hole thermodynamics are discussed.Comment: 24 page
Heavy Quark Potentials in Quenched QCD at High Temperature
Heavy quark potentials are investigated at high temperatures. The temperature
range covered by the analysis extends from values just below the
deconfinement temperature up to about in the deconfined phase. We
simulated the pure gauge sector of QCD on lattices with temporal extents of 4,
6 and 8 with spatial volumes of . On the smallest lattice a tree level
improved action was employed while in the other two cases the standard Wilson
action was used. Below we find a temperature dependent logarithmic term
contributing to the confinement potential and observe a string tension which
decreases with rising temperature but retains a finite value at the
deconfinement transition. Above the potential is Debye-screened, however
simple perturbative predictions do not apply.Comment: 20 pages, 9 figure
The distribution of extremal points of Gaussian scalar fields
We consider the signed density of the extremal points of (two-dimensional)
scalar fields with a Gaussian distribution. We assign a positive unit charge to
the maxima and minima of the function and a negative one to its saddles. At
first, we compute the average density for a field in half-space with Dirichlet
boundary conditions. Then we calculate the charge-charge correlation function
(without boundary). We apply the general results to random waves and random
surfaces. Furthermore, we find a generating functional for the two-point
function. Its Legendre transform is the integral over the scalar curvature of a
4-dimensional Riemannian manifold.Comment: 22 pages, 8 figures, corrected published versio
Single-Inclusive Jet Production in Polarized pp Collisions at O(alpha_s^3)
We present a next-to-leading order QCD calculation for single-inclusive
high-p_T jet production in longitudinally polarized pp collisions within the
``small-cone'' approximation. The fully analytical expressions obtained for the
underlying partonic hard-scattering cross sections greatly facilitate the
analysis of upcoming BNL-RHIC data on the double-spin asymmetry A_{LL}^{jet}
for this process in terms of the unknown polarization of gluons in the nucleon.
We simultaneously rederive the corresponding QCD corrections to unpolarized
scattering and confirm the results existing in the literature. We also
numerically compare to results obtained with Monte-Carlo methods and assess the
range of validity of the ``small-cone'' approximation for the kinematics
relevant at BNL-RHIC.Comment: 23 pages, 8 eps-figure
Exact Kohn-Sham exchange kernel for insulators and its long-wavelength behavior
We present an exact expression for the frequency-dependent Kohn-Sham
exact-exchange (EXX) kernel for periodic insulators, which can be employed for
the calculation of electronic response properties within time-dependent (TD)
density-functional theory. It is shown that the EXX kernel has a
long-wavelength divergence behavior of the exact full exchange-correlation
kernel and thus rectifies one serious shortcoming of the adiabatic
local-density approximation and generalized-gradient approximations kernels. A
comparison between the TDEXX and the GW-approximation-Bethe-Salpeter-equation
approach is also made.Comment: two column format 6 pages + 1 figure, to be publisehd in Physical
Review
- …