Related papers: Loschmidt echo decay from local boundary perturbat…
We consider chaotic billiards in d dimensions, and study the matrix elements M_{nm} corresponding to general deformations of the boundary. We analyze the dependence of |M_{nm}|^2 on \omega = (E_n-E_m)/\hbar using semiclassical…
We prove decay estimates in the interior for solutions to elliptic equations in divergence form with Lipschitz continuous coefficients. The estimates explicitly depend on the distance from the boundary and on suitable notions of frequency…
The Loschmidt echo (LE) is a magnitude that measures the sensitivity of quantum dynamics to perturbations in the Hamiltonian. For a certain regime of the parameters, the LE decays exponentially with a rate given by the Lyapunov exponent of…
Quantum states extended over a large volume in phase space have oscillations from quantum interferences in their Wigner distribution on scales smaller than $\hbar$ [W.H. Zurek, Nature {\bf 412}, 712 (2001)]. We investigate the influence of…
In this work we study the nonlinear dynamics of the static and the driven ellipse. In the static case, we find numerically an asymptotical algebraic decay for the escape of an ensemble of non-interacting particles through a small hole due…
We investigate the classical scattering dynamics of the driven elliptical billiard. Two fundamental scattering mechanisms are identified and employed to understand the rich behavior of the escape rate. A long-time algebraic decay which can…
General theoretic approach to classical Loschmidt echoes in chaotic systems with many degrees of freedom is developed. For perturbations which affect essentially all degrees of freedom we find a doubly exponential decay with the rate…
We consider the degradation of the dynamics of a Gaussian wave packet in a harmonic oscillator under the presence of an environment. This last is given by a single non-degenerate two level system. We analyze how the binary degree of freedom…
We study the Loschmidt echo (LE) in a central spin model in which a central spin is globally coupled to an environment (E) which is subjected to a small and sudden quench at $t=0$ so that its state at $t=0^+$, remains the same as the ground…
We study the non-equilibrium evolution of concurrence of a Bell pair constituted of two qubits, through the measurement of Loschmidt echo (LE) under the scope of generalized central spin model. Having detected the Griffiths phase via…
We consider the initial-value problem for the one-dimensional, time-dependent wave equation with positive, Lipschitz continuous coefficients, which are constant outside a bounded region. Under the assumption of compact support of the…
The Loschmidt echo -- also known as fidelity -- is a very useful tool to study irreversibility in quantum mechanics due to perturbations or imperfections. Many different regimes, as a function of time and strength of the perturbation, have…
Dynamical properties are studied for escaping particles, injected through a hole in an oval billiard. The dynamics is considered for both static and periodically moving boundaries. For the static boundary, two different decays for the…
In this article we study the pointwise decay properties of solutions to the wave equation on a class of stationary asymptotically flat backgrounds in three space dimensions. Under the assumption that uniform energy bounds and a weak form of…
In this paper, we analyze a semilinear damped second order evolution equation with time-dependent time delay and time-dependent delay feedback coefficient. The nonlinear term satisfies a local Lipschitz continuity assumption. Under…
From a reflection measurement in a rectangular microwave billiard with randomly distributed scatterers the scattering and the ordinary fidelity was studied. The position of one of the scatterers is the perturbation parameter. Such…
We investigate the effect of white-noise perturbations on chaotic trajectories in open billiards. We focus on the temporal decay of the survival probability for generic mixed-phase-space billiards. The survival probability has a total of…
We study some dynamical properties of a classical time-dependent elliptical billiard. We consider periodically moving boundary and collisions between the particle and the boundary are assumed to be elastic. Our results confirm that although…
The Loschmidt echo, defined as the overlap between quantum wave function evolved with different Hamiltonians, quantifies the sensitivity of quantum dynamics to perturbations and is often used as a probe of quantum chaos. In this work we…
In the long quest to identify and compensate the sources of decoherence in many-body systems far from the ground state, the varied family of Loschmidt echoes (LEs) became an invaluable tool in several experimental techniques. A LE involves…