Decay Rate Of Metastable State Research Articles

FindBounce: Package for multi-field bounce actions

We are launching FindBounce, a Mathematica package for the evaluation of the Euclidean bounce action that enters the decay rate of metastable states in quantum and thermal field theories. It is based on the idea of polygonal bounces, which is a semi-analytical approach to solving the bounce equation by discretizing the potential into piecewise linear segments. This allows for a fast and robust evaluation of arbitrary potentials with specified precision and any number of scalar fields. Time cost grows linearly with the number of fields and/or the number of segments. Computation with 20 fields takes ∼2 s with 0.5% accuracy of the action. The FindBounce function is simple to use with the native Mathematica look and feel, it is easy to install, and comes with detailed documentation and physical examples, such as the calculation of the nucleation temperature. We also provide timing benchmarks with comparisons to existing tools, where applicable. Program summaryProgram title:FindBounceCPC Library link to program files:http://dx.doi.org/10.17632/tysw84skx3.1Developer’s repository link:https://github.com/vguada/FindBounceLicensing provisions: GNU General Public License 3Programming language:MathematicaNature of problem: Evaluation of the Euclidean bounce action that controls the decay rate of metastable local minima in thermal and quantum field theories.Solution method: Semi-analytical solution of a system of coupled differential equations, based on the polygonal bounce idea (Guada et al., 2019).Restrictions:Mathematica version 10 or above, works in D=3,4.

BBR-induced Stark shifts and level broadening in a helium atom

The precise calculations of blackbody radiation (BBR)-induced Stark shifts and depopulation rates for low-lying states of a helium atom with the use of the variational approach are presented. An effect of the BBR-induced Stark-mixing of energy levels is considered. It is shown that this effect leads to a significant reduction in the lifetimes of helium-excited states. As a consequence, the influence of the Stark-mixing effect on the decay rates of metastable states in helium is discussed in the context of formation processes of the cosmic microwave background.

Rare Events, Escape Rates and Quasistationarity: Some Exact Formulae

We present a common framework to study decay and exchanges rates in a wide class of dynamical systems. Several applications, ranging form the metric theory of continuons fractions and the Shannon capacity of contrained systems to the decay rate of metastable states, are given.

Emergence of complex spatio-temporal order in nonlinear field theories

We investigate the emergence of time-dependent nonperturbative configurations during the evolution of nonlinear scalar field models with symmetric and asymmetric double-well potentials. Complex spatio-temporal behavior emerges as the system seeks to establish equipartition after a fast quench. We show that fast quenches may dramatically modify the decay rate of metastable states in first order phase transitions. We discuss possible applications in condensed matter systems and in inflationary cosmology.

On the induced release of the energy of isomeric nucleiin a Bose—Einstein condensate

It is shown that the asymptotic temporal behaviour of the current value of the stimulated emission cross section leads to a complex dynamics of the radiative release of the nuclear energy of long-lived metastable states induced by the external flux of resonance gamma quanta. The stimulated emission cross section of isomeric nuclei in atoms of a Bose—Einstein condensate becomes sufficient to achieve a comparatively high efficiency of this process, which is manifested in a considerable increase in the decay rate of metastable states.

Calculation of the level splitting of energy and the decay rate of some one-dimensional potentials by instantons method

Using the popular Langer–Polyakov–Coleman instanton method, the decay rate of metastable states and the level splitting of energy, due to tunneling of some one-dimensional potentials have been calculated. The operators appearing in the prefactor of the decay rate or the level splitting of energy of these kinds of potentials possess the shape invariance symmetry, hence using this property, the determinant of these operators have been calculated analytically via heat kernel method.

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.

DECAY RATES OF METASTABLE STATES IN CUBIC POTENTIAL BY VARIATIONAL PERTURBATION THEORY

Variational perturbation theory is used to determine the decay rates of metastable states across a cubic barrier of arbitrary height. For high barriers, a variational resummation procedure is applied to the complex energy eigenvalues obtained from a WKB expansion. For low barriers, the variational resummation procedure converts the non-Borel-summable Rayleigh-Schrödinger expansion into an exponentially fast convergent approximation. The results in the two regimes match each other well and yield very accurate imaginary parts for the energy eigenvalues. This is demonstrated by comparison with the complex eigenvalues obtained from solutions of the Schrödinger equation via the complex-coordinate rotation method.

Semiclassical treatment of the path-integral approach to special effects in superconductivity

Distinctive features of the flux mode regime in the Anderson-Josephson potential are analyzed using both semiclassical path-integral and instanton techniques. This potential governs the behavior of a superconducting ring interrupted by a weak Josephson junction. After establishing the relation between WKB and functional-integral approximations, semiclassical expansions are derived from a discretized version of the Feynman propagator. The physical meaning of instantons is extended to the condensed matter problem of “energy spectrum” for weak-link ring states localized near the minimum energy regions. Under certain circumstances, an improved WKB approximation enables us to find expression for the decay rates of metastable states, performing the reduction of the original Anderson-Josephson shape to a double-hump structure. Although we have not discussed here the temperature dependence of the Josephson plasma frequency, our calculations are consistent with recent theories for systems at finite temperatures with two metastable states separated by a potential energy barrier.

Effect of the Subgap Conductance on the Metastable States in a Josephson Tunnel Junction

An investigation of the decay rate of metastable states in Josephson tunnel junctions in presence of thermal noise is presented. We have observed that, in the extremely underdamped regime, there is an exponential temperature dependence of the best fit value for the shunt conductance. Such a dependence shows a close relation with the temperature dependence of the subgap conductance, suggesting that the effective conductance for the escape from the metastable states obeys to a quasiparticle thermal activation mechanism. The introduction of this effective conductance into the lifetime expression for the zero-voltage states leads to significant changes in the width of the switching current distributions. A comparisons of the experimental data with the proposed model is reported.

Quasiclassical wave function in multidimensional quantum decay problems

The quantum decay rate of metastable state is calculated in quasiclassical accuracy. Specifically, the calculation is based entirely on the standard quasiclassical ansatz, where the wave function is put equal to exp-(action)/ħ, and where the action is expanded in powers of ħ. Such a calculation is well known in the case of one-dimensional systems, and not so well known for multidimensional systems. Therefore, this paper intends to give a comprehensive presentation of the quasiclassical method. A straightforward procedure leads to a decay rate which agrees with the one obtained by the instanton technique. However, a calculation of the entire wave function shows that the procedure is consistent only if the metastable state is dominated by an internal degree of freedom which is slow in comparison with the remaining degrees of freedom.

Quantum-thermal crossover in the dissipative dynamics of the Sine-Gordon model

The quantum-thermal crossover in the decay rate of metastable states of the quantum sine-Gordon model in dc field is discussed at low temperatures including dissipation in arbitrary dimension. In the low field limit, the thermal effect is always dominant, whereas in the higher field the quantum effect becomes important. The crossover field becomes larger by the dissipative effect. The crossover is sharp except the one dimensional underdamped case at low temperatures.

Metastable lifetimes, level crossings and vertical cuts in quantum mechanics

We illustrate the relationship between square-root branch points of energy eigenvalues and the decay rates of metastable states in a simple model in quantum mechanics involving decay through a delta-function potential barrier. The 'infinite volume' limit of the cut-structure is found to have an interesting pathology.

Decay Rate of Metastable State of Neon

Decay Rate of Metastable State of Neon