992 research outputs found

### The role of P-wave inelasticity in J/psi to pi+pi-pi0

We discuss the importance of inelasticity in the P-wave pi pi amplitude on
the Dalitz distribution of 3pi events in J/psi decay. The inelasticity, which
becomes sizable for pi pi masses above 1.4 GeV, is attributed to
KK to pi pi rescattering. We construct an analytical model for the
two-channel scattering amplitude and use it to solve the dispersion relation
for the isobar amplitudes that parametrize the J/psi decay. We present
comparisons between theoretical predictions for the Dalitz distribution of 3pi
events with available experimental data.Comment: 10 pages, 10 figure

### Universal Markovian reduction of Brownian particle dynamics

Non-Markovian processes can often be turned Markovian by enlarging the set of
variables. Here we show, by an explicit construction, how this can be done for
the dynamics of a Brownian particle obeying the generalized Langevin equation.
Given an arbitrary bath spectral density $J_{0}$, we introduce an orthogonal
transformation of the bath variables into effective modes, leading stepwise to
a semi-infinite chain with nearest-neighbor interactions. The transformation is
uniquely determined by $J_{0}$ and defines a sequence
$\{J_{n}\}_{n\in\mathbb{N}}$ of residual spectral densities describing the
interaction of the terminal chain mode, at each step, with the remaining bath.
We derive a simple, one-term recurrence relation for this sequence, and show
that its limit is the quasi-Ohmic expression provided by the Rubin model of
dissipation. Numerical calculations show that, irrespective of the details of
$J_{0}$, convergence is fast enough to be useful in practice for an effective
Markovian reduction of quantum dissipative dynamics

### Limiting Laws of Linear Eigenvalue Statistics for Unitary Invariant Matrix Models

We study the variance and the Laplace transform of the probability law of
linear eigenvalue statistics of unitary invariant Matrix Models of
n-dimentional Hermitian matrices as n tends to infinity. Assuming that the test
function of statistics is smooth enough and using the asymptotic formulas by
Deift et al for orthogonal polynomials with varying weights, we show first that
if the support of the Density of States of the model consists of two or more
intervals, then in the global regime the variance of statistics is a
quasiperiodic function of n generically in the potential, determining the
model. We show next that the exponent of the Laplace transform of the
probability law is not in general 1/2variance, as it should be if the Central
Limit Theorem would be valid, and we find the asymptotic form of the Laplace
transform of the probability law in certain cases

### The X-ray edge singularity in Quantum Dots

In this work we investigate the X-ray edge singularity problem realized in
noninteracting quantum dots. We analytically calculate the exponent of the
singularity in the absorption spectrum near the threshold and extend known
analytical results to the whole parameter regime of local level detunings.
Additionally, we highlight the connections to work distributions and to the
Loschmidt echo.Comment: 7 pages, 2 figures; version as publishe

### P-wave pi pi amplitude from dispersion relations

We solve the dispersion relation for the P-wave pi pi amplitude.We discuss
the role of the left hand cut vs Castillejo-Dalitz-Dyson (CDD), pole
contribution and compare the solution with a generic quark model description.
We review the the generic properties of analytical partial wave scattering and
production amplitudes and discuses their applicability and fits of experimental
data.Comment: 10 pages, 7 figures, typos corrected, reference adde

### The explicit expression of the fugacity for weakly interacting Bose and Fermi gases

In this paper, we calculate the explicit expression for the fugacity for two-
and three-dimensional weakly interacting Bose and Fermi gases from their
equations of state in isochoric and isobaric processes, respectively, based on
the mathematical result of the boundary problem of analytic functions --- the
homogeneous Riemann-Hilbert problem. We also discuss the Bose-Einstein
condensation phase transition of three-dimensional hard-sphere Bose gases.Comment: 24 pages, 9 figure

### Response of a Fermi gas to time-dependent perturbations: Riemann-Hilbert approach at non-zero temperatures

We provide an exact finite temperature extension to the recently developed
Riemann-Hilbert approach for the calculation of response functions in
nonadiabatically perturbed (multi-channel) Fermi gases. We give a precise
definition of the finite temperature Riemann-Hilbert problem and show that it
is equivalent to a zero temperature problem. Using this equivalence, we discuss
the solution of the nonequilibrium Fermi-edge singularity problem at finite
temperatures.Comment: 10 pages, 2 figures; 2 appendices added, a few modifications in the
text, typos corrected; published in Phys. Rev.

### On the applicability of the equations-of-motion technique for quantum dots

The equations-of-motion (EOM) hierarchy satisfied by the Green functions of a
quantum dot embedded in an external mesoscopic network is considered within a
high-order decoupling approximation scheme. Exact analytic solutions of the
resulting coupled integral equations are presented in several limits. In
particular, it is found that at the particle-hole symmetric point the EOM Green
function is temperature-independent due to a discontinuous change in the
imaginary part of the interacting self-energy. However, this imaginary part
obeys the Fermi liquid unitarity requirement away from this special point, at
zero temperature. Results for the occupation numbers, the density of states and
the local spin susceptibility are compared with exact Fermi liquid relations
and the Bethe ansatz solution. The approximation is found to be very accurate
far from the Kondo regime. In contrast, the description of the Kondo effect is
valid on a qualitative level only. In particular, we find that the Friedel sum
rule is considerably violated, up to 30%, and the spin susceptibility is
underestimated. We show that the widely-used simplified version of the EOM
method, which does not account fully for the correlations on the network, fails
to produce the Kondo correlations even qualitatively.Comment: 16 pages, 5 figure

### The spectrum of large powers of the Laplacian in bounded domains

We present exact results for the spectrum of the Nth power of the Laplacian
in a bounded domain. We begin with the one dimensional case and show that the
whole spectrum can be obtained in the limit of large N. We also show that it is
a useful numerical approach valid for any N. Finally, we discuss implications
of this work and present its possible extensions for non integer N and for 3D
Laplacian problems.Comment: 13 pages, 2 figure

### Conformal Dynamics of Precursors to Fracture

An exact integro-differential equation for the conformal map from the unit
circle to the boundary of an evolving cavity in a stressed 2-dimensional solid
is derived. This equation provides an accurate description of the dynamics of
precursors to fracture when surface diffusion is important. The solution
predicts the creation of sharp grooves that eventually lead to material failure
via rapid fracture. Solutions of the new equation are demonstrated for the
dynamics of an elliptical cavity and the stability of a circular cavity under
biaxial stress, including the effects of surface stress.Comment: 4 pages, 3 figure

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