Time-dependent escape rate from a potential well

Time-dependent desorption from an interface is studied by obtaining the Green function for the Smoluchowski equation for a one-dimensional model potential barrier and calculating the time-dependence of the number density, particle current, and escape rate. The asymptotic behavior of the system for long times can be described by equations with independent rate constants. For high potential barriers (relative to k_BT) the Kramers expression for the escape rate is recovered, but for low barriers the escape rate can go through a maximum. The steady state Onsager model is related to the transient solution and numerical results are presented for different potential shapes and sizes.     

Noise-activated escape from a sloshing potential well

We treat the noise-activated escape from a one-dimensional potential well of an overdamped particle, to which a periodic force of fixed frequency is applied. Near the well top, the relevant length scales and the boundary layer structure are determined. We show how behavior near the well top generalizes the behavior determined by Kramers, in the case without forcing. Our analysis includes the case when the forcing does not die away in the weak-noise limit. We discuss the relevance of scaling regimes, defined by the relative strengths of the forcing and the noise, to recent optical trap experiments.     

Amplitude modulation control of escape from a potential well

We demonstrate the effectiveness of periodic amplitude modulations in controlling (suppressing and enhancing) escape from a potential well through the universal model of a damped Helmholtz oscillator subjected to an external periodic excitation (the escape-inducing excitation) whose amplitude is periodically modulated (the escape-controlling excitation). Analytical and numerical results show that this multiplicative control works reliably for different subharmonic resonances between the two periodic excitations involved, and that its effectiveness is comparable to those of different methods of additive control. Additionally, we demonstrate the robustness of the multiplicative control against the presence of low-intensity Gaussian noise.     

Diffusion and convection after escape from a potential well

The escape by diffusion of a particle from a potential well in one dimension is strongly influenced by the application of a field in the adjacent half-space. At long times the probability distribution becomes a uniformly moving and steadily broadening gaussian in this half-space. The mean time of escape from the well is given by a simple expression in terms of the mean first passage time and the coefficient of the long-time tail in the occupation probability of the well in the absence of the field. Transient effects in space and time are studied in explicit form for a parabolic potential well.     

Role of parametric resonance in the inhibition of chaotic escape from a potential well

This paper shows how a periodic parametric modulation can inhibit chaotic escape of a driven oscillator from the cubic potential well that typically models a metastable system close to a fold. Melnikov analysis shows that, depending on its amplitude, period, and initial phase, a periodic parametric modulation of the linear potential term suppresses chaotic escape when certain resonance conditions are met. In particular, it is shown that chaotic escape suppression is impossible under a period-1 parametric perturbation. The effect of nonlinear damping on the inhibition scenario is also studied.     

Fractal basins and chaotic bifurcations prior to escape from a potential well

The escape of a periodically driven damped oscillator from a potential well is intimately associated with homoclinic tangles, fractal basins, and a variety of chaotic bifurcations. A bifurcation diagram, including an analytical Melnikov solution is presented for a canonical asymmetric cubic potential, and comparisons are made with recent results for the Holmes two-well oscillator.     

Studies on tunneling escape time of electrons from a quantum well in multilayered heterostructures

By considering the time variation of band-edge profile arising from the decay of injected charge in quantum wells(QWs), we employ a wave packet method to verify that the actual escape time of certain amount of electrons from QWs could be much larger than that for a single electron. The theoretical result is also in agreement with our measurement of escape time, performed by using a newly developed method--transient current response.     

Incursive fractals: a robust mechanism of basin erosion preceding the optimal escape from a potential well

Comparative cell-to-cell mappings of the basins of driven oscillators with cubic and quartic potential wells show remarkable qualitative and quantitative correlations. We conclude that the recently identified erosion by incursive fractals is a robust phenomenon facilitating the optimal escape from a well.     

Hurst-Kolmogorov dynamics as a result of extremal entropy production

It is demonstrated that extremization of entropy production of stochastic representations of natural systems, performed at asymptotic times (zero or infinity) results in constant derivative of entropy in logarithmic time and, in turn, in Hurst-Kolmogorov processes. The constraints used include preservation of the mean, variance and lag-1 autocovariance at the observation time step, and an inequality relationship between conditional and unconditional entropy production, which is necessary to enable physical consistency. An example with real world data illustrates the plausibility of the findings.     

Calculation of quantum escape rates from a metastable well

The quantum-mechanical decay of a metastable state of a system coupled to a heat bath environment is studied. A functional integral method is presented allowing for the calculation of decay rates at finite temperatures and in the presence of dissipation. Analytical methods for high and intermediate temperatures are combined with an accurate numerical method for low temperatures where the system decays by quantum tunneling. Explicit results are given for a system with a cubic potential and frequency-independent damping.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

Efficient procedure to compute the microcanonical volume of initial conditions that lead to escape trajectories from a multidimensional potential well

A procedure is presented for computing the phase space volume of initial conditions for trajectories that escape or "react" from a multidimensional potential well. The procedure combines a phase space transition state theory, which allows one to construct dividing surfaces that are free of local recrossing and that minimize the directional flux, and a classical spectral theorem. The procedure gives the volume of reactive initial conditions in terms of a sum over each entrance channel of the well of the product of the phase space flux across the dividing surface associated with the channel and the mean residence time in the well of trajectories which enter through the channel. This approach is illustrated for HCN isomerization in three dimensions, for which the method is several orders of magnitude more efficient than standard Monte Carlo sampling.     

Reflection from a composite potential well

Hitherto, the variation of reflectivity as a function of energy for a 1-D potential well has been observed to be either monotonically decreasing or entailing multiple minima. We report that a composite (two-piece) potential well may exhibit an unusual feature, viz., a pronounced single minimum in the reflectivity.     

Chaotic diffusion for particles moving in a time dependent potential well

The chaotic diffusion for particles moving in a time dependent potential well is described by using two different procedures: (i) via direct evolution of the mapping describing the dynamics and; (ii) by the solution of the diffusion equation. The dynamic of the diffusing particles is made by the use of a two dimensional, nonlinear area preserving map for the variables energy and time. The phase space of the system is mixed containing both chaos, periodic regions and invariant spanning curves limiting the diffusion of the chaotic particles. The chaotic evolution for an ensemble of particles is treated as random particles motion and hence described by the diffusion equation. The boundary conditions impose that the particles can not cross the invariant spanning curves, serving as upper boundary for the diffusion, nor the lowest energy domain that is the energy the particles escape from the time moving potential well. The diffusion coefficient is determined via the equation of the mapping while the analytical solution of the diffusion equation gives the probability to find a given particle with a certain energy at a specific time. The momenta of the probability describe qualitatively the behavior of the average energy obtained by numerical simulation, which is investigated either as a function of the time as well as some of the control parameters of the problem.     

Escape rate of Brownian particles from a metastable potential well under time derivative Ornstein-Uhlenbeck noise

We investigate the escape rate of Brownian particles that move in a cubic metastablepotential subjected to an internal time derivative Ornstein-Uhlenbeck noise (DOUN). Thisnoise can induce the ballistic diffusion of force-free Brownian particles. Some newfeatures are found. The escape rate for DOUN shows qualitative different dependence onpotential well width compared with OUN which induces normal diffusion. As the potentialbarrier height decreases, the escape rate of DOUN deviates from Arrhenius law considerablyearlier than that of Ornstein-Uhlenbeck noise (OUN). The Brownian particles escape fasterunder DOUN than that under OUN. A quasi-periodic oscillation occurs in transient state. Asolvable case is presented to demonstrate the significant cancellation behavior in thebarrier region that governs most of these phenomena. The physical mechanism of thefindings can be clarified by the noise features. These characteristics should be commonfor internal noises that induce superdiffusion, especially the ballistic diffusion.     

Quantum tunneling and information entropy in a double square well potential: The ammonia molecule

We study the implications of quantum tunneling on information entropy measures (Shannon and Fisher), disequilibrium and LMC complexity in a Double Square Well Potential (DSWP), using the ammonia molecule as a test bed. We also apply a similar analysis to the Infinite Square Well Potential (ISWP) in order to compare the corresponding results with a system where tunneling is absent. In particular, we show that contrary to the Heisenberg uncertainty product, information-theoretic tools provide a more sensitive analysis and manage to differentiate DSWP from ISWP case, formulating an empirical criterion whether the tunneling effect is present or not.     

FeO double-well potential as a result of spin density redistribution

According to the calculation of the electron structure of the FeO molecule performed by the ZINDO1 semi-empirical technique, the ground-state adiabatic potential has two close minima, each containing one vibration level. The states of the system in this minima differ in the spatial distribution of the spin density: the spin density is centered in the iron atom in the lowest well at 1.95 Å and a fraction of the spin with the opposite sign is transferred to oxygen in the other well at 1.8 Å. The temperature dependence of the fractions of molecules with the different bond lengths in the FeO gas has been found. The probability of switching the spin states has been shown to increase with pressure and temperature.     

The case of escape probability as linear in short time

We derive rigorously the short-time escape probability of a quantum particle from its compactly supported initial state, which has a discontinuous derivative at the boundary of the support. We show that this probability is linear in time, which seems to be a new result. The novelty of our calculation is the inclusion of the boundary layer of the propagated wave function formed outside the initial support. This result has applications to the decay law of the particle, to the Zeno behaviour, quantum absorption, time of arrival, quantum measurements, and more.     

Carrier escape dynamics in a single quantum well waveguide modulator

Picosecond excite-probe studies are performed on a single quantum well waveguide modulator giving a direct measure of the escape of photogenerated carriers from a quantum well. Both the effects of exciton saturation and external field screening are observed in the transient transmission change. The results are consistent with the escape of carriers by thermionic emission.