Related papers: Probabilistic Interpretation of Resonant States
The paper examines stochastic diffusion within an expanding space-time framework. It starts with providing a rationale for the considered model and its motivation from cosmology where the expansion of space-time is used in modelling various…
We study the mobility of an overdamped particle in a periodic potential tilted by a constant force. The mobility exhibits a stochastic resonance in inhomogeneous systems with space dependent friction coefficient. The result indicates that…
Explainability plays an increasingly important role in machine learning. Furthermore, humans view the world through a causal lens and thus prefer causal explanations over associational ones. Therefore, in this paper, we develop a causal…
The standard interpretation of the observed redshifted spectra and luminosities towards distant astrophysical objects is that the universe is expanding, an inference which is found to be consistent with other cosmological probes as well.…
Resonance, defined as the oscillation of a system when the temporal frequency of an external stimulus matches a natural frequency of the system, is important in both fundamental physics and applied disciplines. However, the spatial…
A canonical structure compatible with the action of the Lorentz group can be obtained considering the energy and time as conjugate variables of an extended phase space. Scalar probability waves, describing free relativistic particles, are…
It is shown, that the exponential decrease of the energy spectra of the fragments with growing its energy, which does not depend from the fragment type, targets, projectiles and projectile energies, and which sometimes accompanied slight…
In this paper we construct coherent states for the two-dimensional Morse potential. We find the dependence of the spectrum on the physical parameters and use this to understand the emergence of accidental degeneracies. It is observed that,…
A continuous-state polynomial branching process is constructed as the pathwise unique solution of a stochastic integral equation with absorbing boundary condition. The extinction and explosion probabilities and the mean extinction and…
The effect of multiplicative white noise on the resonance capture in non-isochronous systems with time-decaying pumping is investigated. It is assumed that the intensity of perturbations decays with time, and its frequency is asymptotically…
Resonances, or scattering poles, are complex numbers which mathematically describe meta-stable states: the real part of a resonance gives the rest energy, and its imaginary part, the rate of decay of a meta-stable state. This description…
We present a theory of topological edge states in one-dimensional resonant photonic crystals with a compound unit cell. Contrary to the traditional electronic topological states the states under consideration are radiative, i.e., they decay…
We present a classical approximation for the peaks of survival resonances occurring when diffracting matter waves from absorption potentials. Generally our simplified model describes the absorption-diffraction process around the Talbot time…
An effect generated by the nonexponential behavior of the survival amplitude of an unstable state in the long time region is considered. We find that the instantaneous energy of the unstable state for a large class of models of unstable…
We celebrate this year hundred years of quantum mechanics but there is still no consensus regarding its interpretation and limitations. In this article we advocate the statistical contextual interpretation which is free of paradoxes. State…
A two-dimensional model of an electron moving under the influence of an attractive zero-range potential as well as external magnetic and electric fields is analyzed. We prove by numerical investigations that there are formed such resonances…
Linear systems with many degrees of freedom containing multiplicative and additive noise are considered. The steady state probability distribution for equations of this kind is examined. With multiplicative white noise it is shown that…
Quantum states evolving at equidistant steps into a set of mutually orthogonal states of finite or infinite cardinality p exhibit an interesting physical effect. The analysis of the amplitudes of the state at half the step time with the…
Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding…
It is well known, both theoretically and experimentally, that the survival probability for an unstable quantum state, formed at $t=0,$ is not a simple exponential function, even if the latter is a good approximation for intermediate times.…