Related papers: Time as a dynamical variable in quantum decay
Gamow's explanation of the exponential decay law uses complex "eigenvalues" and exponentially growing "eigenfunctions". This raises the question, how Gamow's description fits into the quantum mechanical description of nature, which is based…
Gamow's approach to exponential decay of meta-stable particles via complex 'eigenvalues' (resonances) of a Hamiltonian is scrutinized. We explain the sense in which the non-square-integrable 'eigenfunctions' that belong to these resonances…
In the present paper we show that the Temporal Wave Function approach of the decay process, which is a multicomponent version of the Time Operator approach leads to new, non-standard, predictions concerning the statistical properties of…
The decay of an unstable system is usually described by an exponential law. Quantum mechanics predicts strong deviations of the survival probability from the exponential: indeed, the decay is initially quadratic, while at very large times…
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…
Results of theoretical studies of the quantum unstable systems caused that there are rather widespread belief that a universal feature od the quantum decay process is the presence of three time regimes of the decay process: the early time…
The transformation of canonical decay laws of moving unstable quantum systems is studied by approximating, over intermediate times, the decay laws at rest with superpositions of exponential modes via the Prony analysis. The survival…
We express the probabilistic character associated to the wave function by treating it as a stochastic variable. This is accomplished by means of a stochastic equation for the wave function whose noise changes the phase of the wave function…
Gamow vectors have been developed in order to give a mathematical description for quantum decay phenomena. Mainly, they have been applied to radioactive phenomena, scattering and to some decoherence models. They play a crucial role in the…
We analyze, both analytically and numerically, the time-dependence of the return probability in closed systems of interacting particles. Main attention is paid to the interplay between two regimes, one of which is characterized by the…
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…
Decay law of a complicated unstable state formed in a high energy collision is described by the Fourier transform of the two-point correlation function of the scattering matrix. Although each constituent resonance state decays exponentially…
Decaying states can be represented by Gamow vectors with an exponential, asymmetric time evolution. This asymmetric evolution is a manifestation of irreversibility on the microphysical level. The Rigged Hilbert Space provides a mathematical…
The dynamics of a quantum mechanical particle in a time-independent potential are found to contain many interesting phenomena. These are direct consequences of the (typical) existence of more than one time scale governing the problem. This…
A simple quantum model explains the Levy-unstable distributions for individual stock returns observed by ref.[1]. The probability density function of the returns is written as the squared modulus of an amplitude. For short time intervals…
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 put forward a model that describes a decaying and evanescent point source of non-interacting quantum waves in 1D. This point-source assumption allows for a simple description that captures the essential aspects of the dynamics of a wave…
Each scheme of state reconstruction comes down to parametrize the state of a quantum system by expectation values or probabilities directly measurable in an experiment. It is argued that the time evolution of these quantities provides an…
The decay of quasi-stable quantum system involves primarily an outgoing probability current density. However, during the transition from exponential to inverse-power-law decay there are time intervals during which this current, although…
We analyze a simple example of wave equation with a time-dependent damping term, whose coefficient decays at infinity at the scale-invariant rate and includes an oscillatory component that is integrable but not absolutely integrable. We…