Related papers: Survival and Nonescape Probabilities for Resonant …
In our paper [Phys. Rev. Lett. 74, 337 (1995)], we derived an exact expression for the survival and nonescape probabilities as an expansion in terms of resonant states. It was shown that these quantities exhibit at long times a different…
An analytical solution for the time evolution of decay of two identical non interacting quantum particles seated initially within a potential of finite range is derived using the formalism of resonant states. It is shown that the wave…
Quantum escape of a particle via a time-dependent confining potential in a semi-infinite one-dimensional space is discussed. We describe the time-evolution of escape states in terms of scattering states of the quantum open system, and…
In [G. Garcia-Calderon, J. L. Mateos, and M. Moshinsky, Phys. Rev. Lett. 74, 337 (1995)], the time evolution of the quantum decay of a state initially located within an interaction region of finite range was investigated. In particular, it…
The short-time behavior of quantum decay of an unstable state initially located within an interaction region of finite range is investigated using a resonant expansion of the survival amplitude. It is shown that in general the short-time…
We examine an analytical expression for the survival probability for the time evolution of quantum decay to discuss a regime where quantum decay is nonexponential at all times. We find that the interference between the exponential and…
We investigate the persistence probability of a Brownian particle in a harmonic potential, which decays to zero at long times -- leading to an unbounded motion of the Brownian particle. We consider two functional forms for the decay of the…
An analytical solution to the time evolution of decay of one and two identical noninteracting particles is presented using the formalism of resonant states. It is shown that the time-dependent wave function and hence the survival and…
The long time behaviour of the survival probability of initial state and its dependence on the initial states are considered, for the one dimensional free quantum particle. We derive the asymptotic expansion of the time evolution operator…
We study the decay of a prepared state into non-flat continuum. We find that the survival probability $P(t)$ might exhibit either stretched-exponential or power-law decay, depending on non-universal features of the model. Still there is a…
Time evolution of the decay process of unstable particles is investigated in field theory models. We first formulate how to renormalize the non-decay amplitude beyond perturbation theory and then discuss short-time behavior of very…
Quantum escapes of a particle from an end of a one-dimensional finite region to $N$ number of semi-infinite leads are discussed by a scattering theoretical approach. Depending on a potential barrier amplitude at the junction, the…
The behavior of both the survival S(t) and nonescape P(t) probabilities at long times for the one-dimensional free particle system is shown to be closely connected to that of the initial wave packet at small momentum. We prove that both…
We study the survival probability of moving relativistic unstable particles with definite momentum $\vec{p} \neq 0$. The amplitude of the survival probability of these particles is calculated using its integral representation. We found…
We study the late time exponential decay of the survival probability $S_\pm(t,a|x_0)\sim e^{-\theta(a)t}$, of a one-dimensional run and tumble particle starting from $x_0<a$ with an initial orientation $\sigma(0)=\pm 1$, under a confining…
We study the the survival probability P(t) upto time t, of a test particle moving in a fluctuating external field. The particle moves according to some prescribed deterministic or stochastic rules and survives as long as the external field…
For many stochastic processes, the probability $S(t)$ of not-having reached a target in unbounded space up to time $t$ follows a slow algebraic decay at long times, $S(t)\sim S_0/t^\theta$. This is typically the case of symmetric compact…
Late time properties of moving relativistic particles are studied. Within the proper relativistic treatment of the problem we find decay curves of such particles and we show that late time deviations of the survival probability of these…
We investigate the survival probability of a localized 1-d quantum particle subjected to a time dependent potential of the form $rU(x)\sin{\omega t}$ with $U(x)=2\delta (x-a)$ or $U(x)= 2\delta(x-a)-2\delta (x+a)$. The particle is initially…
$N$-body simulations of non-resonant tightly-packed planetary systems have found that their survival time (i.e. time to first close encounter) grows exponentially with their interplanetary spacing and planetary masses. Although this result…