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 $c$-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