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After reviewing the description of an unstable state in the framework of Lee Hamiltonians (valid both for Quantum Mechanics (QM) and Quantum Field Theory (QFT)), we consider some theoretical aspects of non-exponential decays: the case of…
Our exact theory for continuous harmonic perturbation of a one dimensional model atom by parametric variations of its potential is generalized for the cases when a) the atom is exposed to short pulses of an external harmonic electric field…
We discuss quantum evolution of a decaying state in relation to a recent experiment of Katz et al. Based on exact analytical and numerical solutions of a simple model, we identify a regime where qubit retains coherence over a finite time…
The irreversible evolution of a microscopic system under measurement is a central feature of quantum theory. From an initial state generally exhibiting quantum uncertainty in the measured observable, the system is projected into a state in…
The master equation of quantum optical density operator is transformed to the equation of characteristic function. The parametric amplification and amplitude damping as well as the phase damping are considered. The solution for the most…
Using a combination of semiclassical and recently developed wave packet propagation techniques we find the quantum self-ionization process of highly excited ions moving in magnetic fields which has its origin in the energy transfer from the…
We discuss dissipative systems in Quantum Field Theory by studying the canonical quantization of the damped harmonic oscillator (dho). We show that the set of states of the system splits into unitarily inequivalent representations of the…
According to the Schr\"odinger equation, a closed quantum system evolves continuously in time. If it is subject to a measurement however, its state changes randomly and discontinuously, which is mathematically described by the projection…
We study the localization properties of bipartite channels, whose action on a subsystem yields a unitary channel. In particular we show that, under such channel, the subsystem must evolve independent of its environment. This point of view…
The time evolution of the correlation functions of an ensemble of anharmonic N-component oscillators with O(N) symmetry is described by a flow equation, exact up to corrections of order $1/N^2$. We find effective irreversibility.…
We investigate temporal evolution of von Neumann's entropy in exemplary quantum mechanical systems and show that it grows in systems evolving with incrementally increasing decoherence during scattering processes. We demonstrate that the…
Modulating macroscopic parameters of materials in time offers innovative avenues for manipulating electromagnetic waves. Due to such enticing prospects, the general research subject of time-varying systems is expanding today in different…
In quantum mechanics, time is introduced as a non-measurable quantity, as there is no possibility to build a hermitian operator canonically conjugated to the Hamiltonian. We cannot have, therefore, the time operator, which means that the…
We consider a two-body quantum system in dimension one composed by a test particle interacting with an harmonic oscillator placed at the position $a>0$. At time zero the test particle is concentrated around the position $R_0$ with average…
We consider a quantum system dynamics caused by successive selective and non-selective measurements of the probe coupled to the system. For the finite measurement rate $\tau^{-1}$ and the system-probe interaction strength $\gamma$ we derive…
In the covariant canonical approach to classical physics, each point in phase space represents an entire classical trajectory. Initial data at a fixed time serve as coordinates for this ``timeless'' phase space, and time evolution can be…
The wave function transformation of the quantum particle considered as a continuous medium was described by the evolution operator with the kernel in the form of path integral. It is shown that this approach allows considering not only…
We study the effects of the environment on tunneling in an open system described by a static double-well potential. We describe the evolution of a quantum state localized in one of the minima of the potential at $t=0$, both in the limits of…
Starting from our idea of combining the Feynman path integral spirit and the Dyson series kernel, we find an explicit and general form of time evolution operator that is a $c$-number function and a power series of perturbation including all…
The temporal evolution of an unstable quantum mechanical system undergoing repeated measurements is investigated. In general, by changing the time interval between successive measurements, the decay can be accelerated (inverse quantum Zeno…