Related papers: Long time deviations from the exponential decay la…
Non-equilibrium states of a thermodynamic statistical system are investigated using the thermodynamic parameter of the system lifetime, first-passage time, the time before degeneration of the system under influence of fluctuations.…
A study is made of the behavior of unstable states in simple models which nevertheless are realistic representations of situations occurring in nature. It is demonstrated that a non-exponential decay pattern will ultimately dominate decay…
The most important law of radioactivity is that of the exponential decay. In the realm of quantum mechanics, however, this decay law is neither rigorous nor fundamental. The deviations from the exponential decay have been observed…
We derive the expression for the energy uncertainty of the final state of a decay of an unstable quantum state prepared at the initial time $t=0$. This expression is function of the time $t$ at which a measurement is performed to determine…
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 show that the electromagnetic moments of unstable particles (resonances) have an absorptive contribution which quantifies the change of the particle's lifetime in an external electromagnetic field. To give an example we compute here the…
Relativistic quantum theory shows that the known Einstein time dilation (ED) approximately holds for the decay law of the unstable particle having definite momentum p (DP). I use a different definition of the moving particle as the state…
We discuss the possibility of non-exponential Auger decay of atoms irradiated by X-ray photons. This effect can occur at times, which are greater than the lifetime of a system under consideration. The mechanism for non-exponential depletion…
It is demonstrated that, if one remains in the framework of quantum mechanics taken alone, stationary states (energy eigenstates) are in no way singled out with respect to nonstationary ones, and moreover the stationary states would be…
The decay of a moving system is studied in case the system is initially prepared in a two-mass unstable quantum state. The survival probability $\mathcal{P}_p(t)$ is evaluated over short and long times in the reference frame where the…
This paper explores the exponential stability of two nonlinear wave equations coupled through their velocities. The analysis is divided into two main cases. First, we consider a system where one equation is damped, while the other…
After reviewing the description of an unstable state in the framework of nonrelativistic Quantum Mechanics (QM) and relativistic Quantum Field Theory (QFT), we consider the effect of pulsed, ideal measurements repeated at equal time…
We study properties of moving relativistic quantum unstable systems. We show that in contrast to the properties of classical particles and quantum stable objects the velocity of moving freely relativistic quantum unstable systems can not be…
It is shown that a periodic emergence and destruction of an additional quantum number leads to an exponential growth of energy of a quantum mechanical system subjected to a slow periodic variation of parameters. The main example is given by…
We discuss the emergence of non-stationarity in open quantum many-body systems. This leads us to the definition of dissipative time crystals which display experimentally observable, persistent, time-periodic oscillations induced by noisy…
Weak measurements offer new insights into the behavior of quantum systems. Combined with post-selection, quantum mechanics predicts a range of new experimentally testable phenomena. In this paper I consider weak measurements performed on…
Quantal systems are predicted to show a change-over from exponential decay to power law decay at very long times. Although most theoretical studies predict integer power-law exponents, recent measurements by Rothe et al. of decay…
By using an exact analytical non-Hermitian approach in terms of resonance (quasinormal) states we express the decaying wave function as the sum of exponential and nonexponential decaying solutions to the time-dependent Schr\"odinger…
In equilibrium systems with short-ranged interactions, the relative stability of different thermodynamic states generally does not depend on system size (as long as this size is larger than the interaction range). Here, we use a large…
Quantum gravitational effects may induce stochastic fluctuations in the structure of space-time, to produce a characteristic foamy structure. It has been known for some time now that these fluctuations may have observable consequencies for…