25 research outputs found
Generalized quantum Fokker-Planck, diffusion and Smoluchowski equations with true probability distribution functions
Traditionally, the quantum Brownian motion is described by Fokker-Planck or
diffusion equations in terms of quasi-probability distribution functions, e.g.,
Wigner functions. These often become singular or negative in the full quantum
regime. In this paper a simple approach to non-Markovian theory of quantum
Brownian motion using {\it true probability distribution functions} is
presented. Based on an initial coherent state representation of the bath
oscillators and an equilibrium canonical distribution of the quantum mechanical
mean values of their co-ordinates and momenta we derive a generalized quantum
Langevin equation in -numbers and show that the latter is amenable to a
theoretical analysis in terms of the classical theory of non-Markovian
dynamics. The corresponding Fokker-Planck, diffusion and the Smoluchowski
equations are the {\it exact} quantum analogues of their classical
counterparts. The present work is {\it independent} of path integral
techniques. The theory as developed here is a natural extension of its
classical version and is valid for arbitrary temperature and friction
(Smoluchowski equation being considered in the overdamped limit).Comment: RevTex, 16 pages, 7 figures, To appear in Physical Review E (minor
revision
Production of Lambda and Sigma^0 hyperons in proton-proton collisions
This paper reports results on simultaneous measurements of the reaction
channels pp -> pK+\Lambda and pp -> pK+\Sigma^0 at excess energies of 204, 239,
and 284 MeV (\Lambda) and 127, 162, and 207 MeV (\Sigma^0). Total and
differential cross sections are given for both reactions. It is concluded from
the measured total cross sections that the high energy limit of the cross
section ratio is almost reached at an excess energy of only about 200 MeV. From
the differential distributions observed in the overall CMS as well as in the
Jackson and helicity frames, a significant contribution of interfering nucleon
resonances to the \Lambda production mechanism is concluded while resonant
\Sigma^0-production seems to be of lesser importance and takes place only
through specific partial waves of the entrance channel. The data also indicate
that kaon exchange plays a minor role in the case of \Lambda- but an important
role for \Sigma^0-production. Thus the peculiar energy dependence of the
\Lambda-to-\Sigma^0 cross section ratio appears in a new light as its
explanation requires more than mere differences between the p\Lambda and the
p\Sigma^0 final state interaction. The data provide a benchmark for theoretical
models already available or yet to come.Comment: 18 pages, 10 figures; accepted by The European Physical Journal A
(EPJ A
The pK0\Sigma+ final state in proton-proton collisions
This paper reports results from a study of the reaction pp->pK0\Sigma+ at
beam momenta of p_{beam} = 2950, 3059, and 3200 MeV/c (excess energies of
\epsilon= 126, 161, and 206 MeV). Total cross sections were determined for all
energies; a set of differential cross sections (Dalitz plots; invariant mass
spectra of all two-body subsystems; angular distributions of all final state
particles; distributions in helicity and Jackson frames) are presented for
\epsilon= 161 MeV. The total cross sections are proportional to the volume of
available three-body phase-space indicating that the transition matrix element
does not change significantly in this range of excess energies. It is concluded
from the differential data that the reaction proceeds dominantly via the
N(1710)P_{11} and/or N(1720)P_{13} resonance(s); N(1650)S_{11} and
\Delta(1600)P_{33} could also contribute.Comment: 15 pages, 10 figure
Lifetime of the incoherent state of coupled phase oscillators
In this paper we have studied the relaxation of the incoherent state to the coherent
state of coupled phase oscillators with time delay in terms of lifetime of the incoherent
state both in the presence and absence of noise. To make the present study general we have
considered both Gaussian and non Gaussian noises. Our investigation shows that the mean
lifetime (MLT) decreases exponentially as the coupling strength among the oscillators
grows. It also shows that MLT changes non monotonically with an increase in time delay.
Another observation is that the mean lifetime increases exponentially as a function of
noise strength for white noise. However, for colour noise, it grows linearly with an
increase in noise strength. Enhancement of the correlation time of the coloured noise
suppresses MLT. The rate of suppression is faster for non-Gaussian noise compared to the
Gaussian case. Finally, we have observed that the mean lifetime increases exponentially as
the noise behaviour deviates more from the Gaussian characteristics