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An exponential behavior at all times is derived for a solvable dynamical model in the weak-coupling, macroscopic limit. Some implications for the quantum measurement problem are discussed, in particular in connection with dissipation.
A small momentum transfer to a particle interacting with a steep potential barrier gives rise to a quantum evaporation effect which increases the transmission appreciably. This effect results from the unexpectedly large population of…
Fermi acceleration is the process of energy transfer from massive objects in slow motion to light objects that move fast. The model for such process is a time-dependent Hamiltonian system. As the parameters of the system change with time,…
An oscillating universe cycles through a series of expansions and contractions. We propose a model in which ``phantom'' energy with $p < -\rho$ grows rapidly and dominates the late-time expanding phase. The universe's energy density is so…
Particle motion in a smoothly oscillating non-integrable billiard is known to result in unbounded energy growth. Though the asymptotic energy growth rate of an ensemble of particles in an oscillating chaotic billiard is known to be…
An unstable quantum state generally decays following an exponential law, as environmental decoherence is expected to prevent the decay products from recombining to reconstruct the initial state. Here we show the existence of deviations from…
Fast moving classical variables can generate quantum mechanical behavior. We demonstrate how this can happen in a model. The key point is that in classically (ontologically) evolving systems one can still define a conserved quantum energy.…
A process model of quantum mechanics utilizes a combinatorial game to generate a discrete and finite causal space upon which can be defined a self-consistent quantum mechanics. An emergent space-time M and continuous wave function arise…
Energy dissipation is of fundamental interest and crucial importance in quantum systems. However, whether energy dissipation can emerge inside topological systems remains a question, especially when charge transport is topologically…
Quantum mechanics is an inherently linear theory. However, collective effects in many body quantum systems can give rise to effectively nonlinear dynamics. In the present work, we analyze whether and to what extent such nonlinear effects…
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 demonstrate analytically and numerically that in isolated quantum systems of many interacting particles, the number of many-body states participating in the evolution after a quench increases exponentially in time, provided the…
We show for the one-dimensional quantum $XY$ model with $s=1/2$ that the energy gap between the ground and first excited states behaves anomalously as a function of the system size at the first-order quantum phase transition. Although it is…
Quantum dynamics of a particle in the vicinity of a hyperbolic point is considered. Expectation values of dynamical variables are calculated, and the singular behavior is analyzed. Exponentially fast extension of quantum dynamics is…
This work is concerned with the excited state quantum phase transitions (ESQPTs) defined in Ann.Phys. 323, 1106 (2008). In many-body models that exhibit such transitions, the ground state quantum phase transition (QPT) occurs in parallel…
In classical mechanics the local exponential instability effaces the memory of initial conditions and leads to practical irreversibility. In striking contrast, quantum mechanics appears to exhibit strong memory of the initial state. We…
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…
The phenomenon of resonant energization of a relativistic quantum particle, moving in unison with an intense ElectroMagnetic Wave, is demonstrated in a semiclassical calculation. The wave nature of the quantum particle is of essence because…
I consider a quantum system that possesses key features of quantum shape dynamics and show that the evolution of wave-packets will become increasingly classical at late times and tend to evolve more and more like an expanding classical…
The temporal behavior of quantum mechanical systems is reviewed. We study the so-called quantum Zeno effect, that arises from the quadratic short-time behavior, and the analytic properties of the ``survival" amplitude. It is shown that the…