Related papers: Analysis of resonant population transfer in time-d…
We analyze the quantum dynamics of the time-dependent elliptical billiard using the example of a certain breathing mode. A numerical method for the time-propagation of an arbitrary initial state is developed, based on a series of…
We consider a slowly rotating rectangular billiard with moving boundaries and use the canonical perturbation theory to describe the dynamics of a billiard particle. In the process of slow evolution certain resonance conditions can be…
This paper focuses on a class of nonlinear Klein-Gordon equations in three dimensions, which are Hamiltonian perturbations of the linear Klein-Gordon equation with potential. The unperturbed dynamical system has a bound state with frequency…
In this paper we show an infinite measure set of exponentially escaping orbits for a resonant Fermi accelerator, which is realised as a square billiard with a periodically oscillating platform. We use normal forms to describe how the energy…
We present a Fermi golden rule giving rates of decay of states obtained by perturbing embedded eigenvalues of a quantum graph. To illustrate the procedure in a notationally simpler setting we also present a Fermi Golden Rule for boundary…
Fermi's Golden Rule (FGR) is one of the most impactful formulas in quantum mechanics, providing a link between easy-to-measure observables - such as transition rates - and fundamental microscopic properties - such as density of states or…
We study the population transfer between resonance states for a time-dependent loop around exceptional points in spectra of the hydrogen atom in parallel electric and magnetic fields. Exceptional points are well-suited for population…
A well-known method of transferring the population of a quantum system from an eigenspace of the free Hamiltonian to another is to use a periodic control law with an angular frequency equal to the difference of the eigenvalues. For finite…
We explore the dynamical evolution of an ensemble of non-interacting particles propagating freely in an elliptical billiard with harmonically driven boundaries. The existence of Fermi acceleration is shown thereby refuting the established…
It is shown, that under very general conditions, a generic time-dependent billiard, for which a phase-space of corresponding static (frozen) billiards is of the mixed type, exhibits the exponential Fermi acceleration in the adiabatic limit.…
We explore Fermi acceleration in a driven oval billiard which shows unlimited to limited diffusion in energy when passing from the free to the dissipative case. We provide evidence for a second-order phase transition taking place while…
An important class of resonance problems involves the study of perturbations of systems having embedded eigenvalues in their continuous spectrum. Problems with this mathematical structure arise in the study of many physical systems, e.g.…
One manifestation of quantum resonances is a large sojourn time, or autocorrelation, for states which are initially localized. We elaborate on Lavine's time-energy uncertainty principle and give an estimate on the sojourn time. For the case…
We present a Gedankenexperiment that leads to a violation of detailed balance if quantum mechanical transition probabilities are treated in the usual way by applying Fermi's "golden rule". This Gedankenexperiment introduces a collection of…
Fermi's golden rule is of great importance in quantum dynamics. However, in many textbooks on quantum mechanics, its contents and limitations are obscured by the approximations and arguments in the derivation, which are inevitable because…
The Loschmidt echo (LE) measures the ability of a system to return to the initial state after a forward quantum evolution followed by a backward perturbed one. It has been conjectured that the echo of a classically chaotic system decays…
We propose a new quantum transition-state theory for calculating Fermi's golden-rule rates in complex multidimensional systems. This method is able to account for the nuclear quantum effects of delocalization, zero-point energy and…
We introduce and study a model of time-dependent billiard systems with billiard boundaries undergoing infinitesimal wiggling motions. The so-called quivering billiard is simple to simulate, straightforward to analyze, and is a faithful…
We formulate a method for incorporating quantum fluctuations into molecular- dynamics simulations of many-body systems, such as those employed for energetic nuclear collision processes. Based on Fermi's Golden Rule, we allow spontaneous…
Classical and quantum phase transitions involve observables which are non-analytic as functions of a controlled thermodynamical variable. As occurs with the self-consistent Fermi Golden Rule, one condition to obtain the discontinuous…