Decay Of Metastable State Research Articles

Resonant decay of parity odd bubbles in hot hadronic matter

We investigate the decay of metastable states with broken CP-symmetry which have recently been proposed by Kharzeev, Pisarski and Tytgat to form in hot hadronic matter. We consider the efficiency of the amplification of the η′-field via parametric resonance, taking the backreaction into account. For times of the order t≈10 fm, we find a particle density of about 0.7/fm 3 and a correlation length of ξ max≈2.4 fm. The corresponding momentum spectra show a non-thermal behaviour.

Crossovers in the thermal decay of metastable states in discrete systems

The thermal decay of linear chains from a metastable state is investigated. A crossover from rigid to elastic decay occurs when the number of particles, the single-particle energy barrier, or the coupling strength between the particles is varied. In the rigid regime, the single-particle energy barrier is small compared to the coupling strength, and the decay occurs via a uniform saddle-point solution, with all degrees of freedom decaying instantly. Increasing the barrier one enters the elastic regime, where the decay is due to bent saddle-point configurations using the elasticity of the chain to lower their activation energy. Close to the rigid-to-elastic crossover, nucleation occurs at the boundaries of the system. However, in large systems, a second crossover from boundary to bulk nucleation can be found within the elastic regime, when the single-particle energy barrier is further increased. We compute the decay rate in the rigid and elastic regimes within the Gaussian approximation. Around the rigid-to-elastic crossover, the calculations are performed beyond the steepest-descent approximation. In this region, the prefactor exhibits a scaling property. The theoretical results are discussed in the context of discrete Josephson transmission lines and pancake vortex stacks that are pinned by columnar defects.

False vacuum decay in the de sitter space-time

We suggest a technique that explicitly accounts for the structure of an initial state of quantum field in the semiclassical calculations of path integral in curved space-time, and consider decay of metastable state (conformal vacuum of scalar particles above false classical vacuum) in background de Sitter space-time as an example. Making use of this technique, we justify the Coleman-De Luccia approach to the calculation of the decay probability. We propose an interpretation of the Hawking-Moss instanton as a limiting case of constrained instantons. We find that an inverse process of the transition from true vacuum to false one is allowed in de Sitter space-time, and calculate the corresponding probability.

Decay of metastable states: Mean relaxation time formulation

The mean relaxation time formalism introduced by Nadler and Schulten [J. Chem. Phys. 82, 151 (1985)] in their generalized moment expansion method is extended to a general diffusion process in arbitrary dimensions. The utility of the approach is demonstrated by calculating analytically the rate of noise-induced transitions in a bistable system with an isolated transition point. The rate formula obtained summarizes in a uniform manner much of what had been done before in this field. Limitations of its validity are discussed and a perturbation procedure to systematically improve it is proposed. The validity of our theoretical predictions for the rate is confirmed by comparing with exact numerical results.

Theory of nucleation and growth during phase separation

We present a new model for the entire process of phase-separation that combines steady-state homogeneous nucleation theory with the classical Lifshitz-Slyozov mechanism of ripening, modified to account for the substantial correlations among the droplets. A set of self-consistent interface equations describes the decay of metastable states, incorporating naturally the crossover from early-stage nucleation to the late-stage scaling regime without ad hoc assumptions. We present simulation results for both two and three dimensions. We also present a mean-field, Thomas-Fermi approximation that provides an approximate solution to the many-body problem. @S1063-651X~99!05503-8# PACS number~s!: 64.60.My

Size-dependent light emission from mass-selected clusters

The emission of photons in the visible wavelength range from mass-selected Ag+ n, Cu+ n, Pt+ n and Pd+ n ( ) clusters is observed. Photons are detected 10-4 s after the cluster generation in a sputter source. The emission intensities display distinct variations with cluster size and material. The observations are interpreted in terms of the decay of metastable states which are excited during the high-energy sputtering process used for the generation of these clusters.

Statistical geometry of particle packings. II. “Weak spots” in liquids

We investigate the statistical geometry of inherent structures ~mechanically stable arrangements of particles generated by a steepest-descent mapping of equilibrium configurations to local potential minima! of liquid configurations of the shifted-force Lennard-Jones system, as an approach to elucidating mechanisms for the decay of metastable states. For a wide range of densities, including some higher than the triple point density, inherent structures are found to display remarkably heterogeneous geometry, with an apparently bicontinuous structure consisting of a compact phase and a void region. The void region is found to consist of a single system-spanning cavity. The volume fraction of this cavity vanishes above the density r*50.89. This density coincides with the minimum in the pressure vs density curve for inherent structures, at negative pressure, indicating that the observed heterogeneity of the inherent structures is triggered by the crossing of a threshold of mechanical instability, much like the familiar spinodal concept. Analysis of spontaneous density fluctuations in the equilibrium and superheated liquid reveals that atoms present in regions of low density ~weak spots! map predominantly to the cavity interface in the inherent structures. We discuss the relevance of these observations to limits of stability of the metastable liquid, nucleation, and, possibly, the glass transition. @S1063-651X~97!09811-5#

Decay of metastable states: Sharp transition from quantum to classical behavior

The decay rate of metastable states is determined at high temperatures by thermal activation, whereas at temperatures close to zero quantum tunneling is relevant. At some temperature $T_{c}$ the transition from classical to quantum-dominated decay occurs. The transition can be first-order like, with a discontinuous first derivative of the Euclidean action, or smooth with only a second derivative developing a jump. In the former case the crossover temperature $T_{c}$ cannot be calculated perturbatively and must be found as the intersection point of the Euclidean actions calculated at low and high temperatures. In this paper we present a sufficient criterion for a first-order transition in tunneling problems and apply it to the problem of the tunneling of strings. It is shown that the problem of the depinning of a massive string from a linear defect in the presence of an arbitrarily strong dissipation exhibits a first-order transition.

Role of fermions in bubble nucleation

We present a study of the role of fermions in the decay of metastable states of a scalar field via bubble nucleation. We analyze both one- and three-dimensional systems by using a gradient expansion for the calculation of the fermionic determinant. The results of the one-dimensional case are compared to the exact results of previous work.

Eliminating metastability in first-order phase transitions.

We propose a Monte Carlo cluster algorithm which eliminates metastability in first-order phase transitions of spin-1 models. As an example, we apply it to the Blume-Emery-Griffiths model. Our prescription for growing clusters accelerates the decay of metastable states eliminating hysteresis effects completely. In this way, a precise location of first-order lines of this model is obtained. The high quality of the data allows us to perform an accurate finite size analysis which shows that on first-order lines physical quantities scale with the volume of the system. \textcopyright{} 1996 The American Physical Society.

Quantum decay of metastable states in small magnetic particles.

We present an imaginary-time path-integral study of the problem of quantum decay of a metastable state of a uniaxial magnetic particle placed in the magnetic field at an arbitrary angle. Our findings agree with earlier results of Zaslavskii obtained by mapping the spin Hamiltonian onto a particle Hamiltonian. In the limit of low barrier, weak dependence of the decay rate on the angle is found, except for the field which is almost normal to the anisotropy axis, where the rate is sharply peaked, and for the field approaching the parallel orientation, where the rate rapidly goes to zero. This distinct angular dependence, together with the dependence of the rate on the field strength, provides an independent test for macroscopic spin tunneling. \textcopyright{} 1996 The American Physical Society.

Exact solution of Kramers' problem for piecewise parabolic potential profiles

This paper presents a general procedure for deducing exact time characteristics of Brownian diffusion in the high damping limit in piecewise parabolic pontential profiles. Our approach to solve this problem is based on the Laplace transform method for obtaining the desired time characteristics. For some concrete examples of piecewise parabolic profiles' exact values of metastable state decay times and bistable system relaxation times are found. These results are valid for any height of the potential barrier and coincide with Kramer's results for a high potential barrier. Conditions for the validity of Kramer's formula are also derived.

DECAY OF METASTABLE STATES IN SPATIALLY EXTENDED REACTION-DIFFUSION SYSTEMS: ITS DEPENDENCE ON PARTIALLY REFLECTING BOUNDARY CONDITIONS

We study a piecewise linear version of a one-component, two-dimensional reaction-diffusion bistable model with partially reflecting boundary conditions, with the aim of analyzing the decay of metastable states in spatially extended systems. We have studied the dependence of systems’ Lyapunov functional in terms of a control parameter: the reflectivity at the boundary. Through the knowledge of this functional, we have computed the mean first-passage time for the decay of metastable nonhomogeneous stationary states, providing in this way dynamical information on the changes of the relative stability between attractors.

Decay of metastable states in wetting and dewetting transitions

In a first-order wetting transition metastable surface states can be produced by overheating a nonwet wall or by undercooling a wetting layer covering the wall. These metastable states decay via the formation and subsequent growth of supercritical nuclei. The size and excess free energy of the critical nuclei diverge when some internal point on the line of phase transitions between wet and nonwet states is approached. For the case of overheating the critical nuclei are droplets on the wall, whereas for undercooling they are dents in the wetting layer. The critical droplets show a very different behaviour in the partial-wetting, complete-wetting and prewetting regimes. It is shown that the critical dents also differ significantly from each other in three regimes of the phase diagram which we denote by the partial-dewetting, dewetting and pre-dewetting regimes.

Thermal decays in a hot Fermi gas.

We present a study of the decay of metastable states of a scalar field via thermal activation, in the presence of a finite density of fermions. The process we consider is the nucleation of ``droplets'' of true vacuum inside the false one. We analyze a one-dimensional system of interacting bosons and fermions, considering the latter at finite temperature and with a given chemical potential. As a consequence of a nonequilibrium formalism previously developed, we obtain time-dependent decay rates.

First-order phase transition and metastability in the critical two-dimensional Ising model

The fermionic version of the two-dimensional Ising model in a uniform magnetic field is studied. Its approximate but rather accurate solution was obtained recently in a variational procedure based on the BCS ansatz for the ground state. Here, this solution is continued analytically into the complex H-plane in the vicinity of the origin. In the ferromagnetic phase an essential singularity in the free-energy is observed at the point H=0 of the type predicted by the droplet condensation theory. Simple phenomenological estimates for the radius of the critical droplet and for the rate of decay of metastable states are confirmed by microscopic calculations.

Quantum Nucleation : Decay of Metastable States in Many Particle Systems at Ultralow Temperatures

Quantum Nucleation : Decay of Metastable States in Many Particle Systems at Ultralow Temperatures

Decay of metastable states of high Tc and conventional “low Tc” superconductors

The time decay of the zero field cooled and remanent magnetization has been measured in several high-temperature superconductors, Ti 50V 50 and V 3Si single crystals. It is shown that the dynamics of vortices in both types of superconductors can be described on a very coherent way by using the mean relaxation time τ defined at a constant level of mixed state. The mean energy barrier E which is associated with this relaxation time is found to be proportional to the reciprocal magnetic field. The temperature variation of the penetration and exclusion rate of vortices obeys an Arrhenius type equation with an effective temperature T ∗=( θ 2) coth( θ 2T ) . Here, θ is a characteristic temperature closely related to the crossover from thermal process and to quantum tunneling of vortices. At still lower temperatures, large flux jumps appear in the magnetization curves. Temperature changes have been observed corresponding to these jumps in V 3Si crystals.

Decay of metastable states with discrete dynamics.

We consider the escape from invariant sets of one-dimensional piecewise linear maps which are additively disturbed by weak Gaussian white noise. The escape rates from point attractors and from strange invariant sets in the vicinity of the crisis at fully developed chaos are analytically determined and compared with results from numerical simulations. Both situations are combined resulting in a model with a point attractor which has a strange invariant set as basin boundary. Numerically a nonexponential decay of the attractor is found that can be described by a Markovian three-state model with transition rates known from the previous analysis.

Nucleation in supersaturated 3He— 4He liquid mixtures: decay of metastable states at ultralow temperatures

In order to investigate the possibility of observing the crossover of the nucleation process from the classical to the quantum regime, the decomposition of supersaturated 3He– 4He mixtures in the dilute phase has been studied in the temperature range from 160 mK down to 400 μK. The observed amount of critical supersaturation becomes almost independent of temperature below about 10 mK, while it increases with temperature above about 10 mK. The data are analyzed with the recent theory of Burmistrov, Dubovskii and Tsymbalenko. The results indicate a crossover temperature around 70 mK and the existence of the effect of dissipation.