Related papers: Nonperturbative Analysis of a Quantum Mechanical M…
Evolution of a particle in an inverse square potential is studied. We derive an equation of motion for $\left<r^2\right>$ and solve it exactly. It gives us a possibility to identify the conditions under which a falling of a quantum particle…
We discuss decay of unstable particles and pair annihilation of stable heavy particles that occur in the cosmic medium, from the point of the fundamental microscopic theory. A fully quantum mechanical treatment shows that the effect of…
Quantum particles interacting with potential barriers are ubiquitous in physics, and the question of how much time they spend inside classically forbidden regions has attracted interest for many decades. Recent developments of new…
Time crystals are a nonequilibrium phase of matter that extend fundamental spontaneous symmetry breaking into the temporal dimension, typically requiring external driving for their realization. Here, we explore the nonequilibrium phase…
We describe the dynamics of a bound state of an attractive $\delta$-well under displacement of the potential. Exact analytical results are presented for the suddenly moved potential. Since this is a quantum system, only a fraction of the…
We describe the bound state and scattering properties of a quantum mechanical particle in a scalar $N$-prong potential. Such a study is of special interest since these situations are intermediate between one and two dimensions. The energy…
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…
Quantum decay rates for barrier potentials driven by external stochastic and periodic forces in the strong damping regime are studied. Based on the recently derived quantum Smoluchowski equation [Phys. Rev. Lett. {\bf 87}, 086802 (2001)]…
We analyse a one-dimensional model of hard particles, within ensembles of trajectories that are conditioned (or biased) to atypical values of the time-averaged dynamical activity. We analyse two phenomena that are associated with these…
Unstable particles are notorious in perturbative quantum field theory for producing singular propagators in scattering amplitudes that require regularization by the finite width. In this review I discuss the construction of an effective…
Consider a discrete-time quantum walk on the $N$-cycle subject to decoherence both on the coin and the position degrees of freedom. By examining the evolution of the density matrix of the system, we derive some new conclusions about the…
Active matter denotes a system of particles immersed in an external environment, from which the particles extract energy continuously in order to perform directed motion. Extending the paradigm of active matter to a quantum framework…
We observe that quantum indistinguishability is a dynamical effect dependent on measurement duration. We propose a quantitative criterion for observing indistinguishability in quantum fluids and its implications including quantum statistics…
Unstable particles cannot be treated as asymptotic external states in $S$-matrix theory and when they occur as resonant states cannot be described by finite-order perturbation theory. The known facts concerning unstable particles are…
It is often stated that quantum mechanics only makes statistical predictions and that a quantum state is described by the various probability distributions associated with it. Can we describe a quantum state completely in terms of…
We present models in which the indeterministic feature of Quantum Mechanics is represented in the form of definite physical mechanisms. Our way is completely different from so-called hidden parameter models, namely, we start from a certain…
We experimentally and theoretically investigate the non-equilibrium phase structure of a well-controlled driven-disspative quantum spin system governed by the interplay of coherent driving, spontaneous decay and long-range spin-spin…
Time evolution of unstable particles that occur in the expanding universe is investigated. The off-shell effect not included in the Boltzmann-like equation is important for the decay process when the temperature becomes much below the mass…
The nonadiabatic geometric phase in a time dependent quantum evolution is shown to provide an intrinsic concept of time having dual properties relative to the external time. A nontrivial extension of the ordinary quantum mechanics is thus…
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…