Decay of an unstable state in the presence of multiplicative noise

The phenomenon of anomalous fluctuations associated with the decay of an unstable state is analyzed in the presence of multiplicative noise. A theory is presented and compared with a numerical simulation. Our results allow us to distinguish the roles of additive and multiplicative noise in the nonlinear relaxation process. We suggest the use of experiments on transient dynamics to understand the effect of these two sources of noise in problems in which parametric noise is thought to be important, such as dye lasers.

Decay of unstable states in the presence of colored noise and random initial conditions. I. Theory of nonlinear relaxation times

The general theory of nonlinear relaxation times is developed for the case of Gaussian colored noise. General expressions are obtained and applied to the study of the characteristic decay time of unstable states in different situations, including white and colored noise, with emphasis on the distributed initial conditions. Universal effects of the coupling between colored noise and random initial conditions are predicted.

Decay of unstable states in the presence of colored noise and random initial conditions. II. Analog experiments and digital simulations

The decay of an unstable state under the influence of external colored noise has been studied by means of analog experiments and digital simulations. For both fixed and random initial conditions, the time evolution of the second moment ¿x2(t)¿ of the system variable was determined and then used to evaluate the nonlinear relaxation time. The results obtained are found to be in excellent agreement with the theoretical predictions of the immediately preceding paper [Casademunt, Jiménez-Aquino, and Sancho, Phys. Rev. A 40, 5905 (1989)].

Generating vortex rings in Bose-Einstein condensates in the line-source approximation

We present a numerical method for generating vortex rings in Bose-Einstein condensates confined in axially symmetric traps. The vortex ring is generated using the line-source approximation for the vorticity, i.e., the curl of the superfluid velocity field is different from zero only on a circumference of a given radius located on a plane perpendicular to the symmetry axis and coaxial with it. The particle density is obtained by solving a modified Gross-Pitaevskii equation that incorporates the effect of the velocity field. We discuss the appearance of density profiles, the vortex core structure, and the vortex nucleation energy, i.e., the energy difference between vortical and ground-state configurations. This is used to present a qualitative description of the vortex dynamics.

Greece and Platonic Love in E. M. Forster's Maurice, or the greatness and limits of Antiquity as a source of inspiration.

The aim of this article is to show how, although the evident idealization of Greece and Platonic love throughout the Victorian-Edwardian England, both also show their limits. In order to make it clear the author refers constantly to the implicit Greek texts such as Plato's Symposium and Phaedrus and perhaps even to Plutarch¿s Eroticus in search of a Classical Tradition which is highly significant in order to understand that England at the beginning of the twentieth century.

Vacuum decay in quantum field theory

We study the contribution to vacuum decay in field theory due to the interaction between the long- and short-wavelength modes of the field. The field model considered consists of a scalar field of mass M with a cubic term in the potential. The dynamics of the long-wavelength modes becomes diffusive in this interaction. The diffusive behavior is described by the reduced Wigner function that characterizes the state of the long-wavelength modes. This function is obtained from the whole Wigner function by integration of the degrees of freedom of the short-wavelength modes. The dynamical equation for the reduced Wigner function becomes a kind of Fokker-Planck equation which is solved with suitable boundary conditions enforcing an initial metastable vacuum state trapped in the potential well. As a result a finite activation rate is found, even at zero temperature, for the formation of true vacuum bubbles of size M-1. This effect makes a substantial contribution to the total decay rate.

Evidence of the anomalous charge state 57Fe4+ in the nuclear decay of 57Co3+

The first observation of the elusive Fe4+ charge state coming from the nuclear decay of 57Co3+ has been found in the Mössbauer emission spectra of 57Co:La2Li0.5Co0.5O4. A Ti-doped sample was prepared in order to show that the Fe4+ fraction can be conveniently monitored. Both results were predicted on the basis of the electronic energy-band scheme of these oxides.

Dissipation, noise and vacuum decay in quantum field theory

We study the process of vacuum decay in quantum field theory focusing on the stochastic aspects of the interaction between long- and short-wavelength modes. This interaction results in a diffusive behavior of the reduced Wigner function describing the state of long-wavelength modes, and thereby to a finite activation rate even at zero temperature. This effect can make a substantial contribution to the total decay rate.