6,868 research outputs found
Constrained Dynamics for Quantum Mechanics I. Restricting a Particle to a Surface
We analyze constrained quantum systems where the dynamics do not preserve the
constraints. This is done in particular for the restriction of a quantum
particle in Euclidean n-space to a curved submanifold, and we propose a method
of constraining and dynamics adjustment which produces the right Hamiltonian on
the submanifold when tested on known examples. This method we hope will become
the germ of a full Dirac algorithm for quantum constraints. We take a first
step in generalising it to the situation where the constraint is a general
selfadjoint operator with some additional structures.Comment: 49 pages, TEX, input files amssym.def, amssym.te
From Bloch model to the rate equations II: the case of almost degenerate energy levels
Bloch equations give a quantum description of the coupling between an atom
and a driving electric force. In this article, we address the asymptotics of
these equations for high frequency electric fields, in a weakly coupled regime.
We prove the convergence towards rate equations (i.e. linear Boltzmann
equations, describing the transitions between energy levels of the atom). We
give an explicit form for the transition rates. This has already been performed
in [BFCD03] in the case when the energy levels are fixed, and for different
classes of electric fields: quasi or almost periodic, KBM, or with continuous
spectrum. Here, we extend the study to the case when energy levels are possibly
almost degenerate. However, we need to restrict to quasiperiodic forcings. The
techniques used stem from manipulations on the density matrix and the averaging
theory for ordinary differential equations. Possibly perturbed small divisor
estimates play a key role in the analysis. In the case of a finite number of
energy levels, we also precisely analyze the initial time-layer in the rate
aquation, as well as the long-time convergence towards equilibrium. We give
hints and counterexamples in the infinite dimensional case
Decoherence time in self-induced decoherence
A general method for obtaining the decoherence time in self-induced
decoherence is presented. In particular, it is shown that such a time can be
computed from the poles of the resolvent or of the initial conditions in the
complex extension of the Hamiltonian's spectrum. Several decoherence times are
estimated: for microscopic systems, and
for macroscopic bodies. For the particular case of a
thermal bath, our results agree with those obtained by the einselection
(environment-induced decoherence) approach.Comment: 11 page
Fermi's golden rule and exponential decay as a RG fixed point
We discuss the decay of unstable states into a quasicontinuum using models of
the effective Hamiltonian type. The goal is to show that exponential decay and
the golden rule are exact in a suitable scaling limit, and that there is an
associated renormalization group (RG) with these properties as a fixed point.
The method is inspired by a limit theorem for infinitely divisible
distributions in probability theory, where there is a RG with a Cauchy
distribution, i.e. a Lorentz line shape, as a fixed point. Our method of
solving for the spectrum is well known; it does not involve a perturbation
expansion in the interaction, and needs no assumption of a weak interaction. We
use random matrices for the interaction, and show that the ensemble
fluctuations vanish in the scaling limit. Thus the limit is the same for every
model in the ensemble with probability one.Comment: 20 pages, 1 figur
Multiplicity Distributions and Rapidity Gaps
I examine the phenomenology of particle multiplicity distributions, with
special emphasis on the low multiplicities that are a background in the study
of rapidity gaps. In particular, I analyze the multiplicity distribution in a
rapidity interval between two jets, using the HERWIG QCD simulation with some
necessary modifications. The distribution is not of the negative binomial form,
and displays an anomalous enhancement at zero multiplicity. Some useful
mathematical tools for working with multiplicity distributions are presented.
It is demonstrated that ignoring particles with pt<0.2 has theoretical
advantages, in addition to being convenient experimentally.Comment: 24 pages, LaTeX, MSUHEP/94071
Bifurcation Phenomenon in a Spin Relaxation
Spin relaxation in a strong-coupling regime (with respect to the spin system)
is investigated in detail based on the spin-boson model in a stochastic limit.
We find a bifurcation phenomenon in temperature dependence of relaxation
constants, which is never observed in the weak-coupling regime. We also discuss
inequalities among the relaxation constants in our model and show the
well-known relation 2\Gamma_T >= \Gamma_L, for example, for a wider parameter
region than before.Comment: REVTeX4, 5 pages, 5 EPS figure
Clan structure analysis and new physics signals in pp collisions at LHC
The study of possible new physics signals in global event properties in pp
collisions in full phase space and in rapidity intervals accessible at LHC is
presented. The main characteristic is the presence of an elbow structure in
final charged particle MD's in addition to the shoulder observed at lower c.m.
energies.Comment: 9 pages, talk given at Focus on Multiplicity (Bari, Italy, June 2004
Manifestation of quantum chaos on scattering techniques: application to low-energy and photo-electron diffraction intensities
Intensities of LEED and PED are analyzed from a statistical point of view.
The probability distribution is compared with a Porter-Thomas law,
characteristic of a chaotic quantum system. The agreement obtained is
understood in terms of analogies between simple models and Berry's conjecture
for a typical wavefunction of a chaotic system. The consequences of this
behaviour on surface structural analysis are qualitatively discussed by looking
at the behaviour of standard correlation factors.Comment: 5 pages, 4 postscript figures, Latex, APS,
http://www.icmm.csic.es/Pandres/pedro.ht
Scalar density fluctuation at critical end point in NJL model
Soft mode near the critical end point in the phase diagram of two-flavor
Nambu--Jona-Lasinio (NJL) model is investigated within the leading 1/N_c
approximation with N_c being the number of the colors. It is explicitly shown
by studying the spectral function of the scalar channel that the relevant soft
mode is the scalar density fluctuation, which is coupled with the quark number
density, while the sigma meson mode stays massive.Comment: 9 pages, 4 figure
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