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Motivated by neutron scattering experiments, we investigate the decay of the fidelity with which a wave packet is reconstructed by a perfect time-reversal operation performed after a phase space displacement. In the semiclassical limit, we…
The goal of this paper is to study a nonlinear viscoelastic wave equation with strong damping, time-varying delay and dynamical boundary condition. By introducing suitable energy and Lyapunov functionals, under suitable assumptions, we then…
The first article in a two-part series (the second article being [arXiv:2205.13197]) assumes a weak local energy decay estimate holds and proves that solutions to the linear wave equation with variable coefficients in $\mathbb R^{1+3}$,…
We study a $1$-dimensional chain of $N$ weakly anharmonic classical oscillators coupled at its ends to heat baths at different temperatures. Each oscillator is subject to pinning potential and it also interacts with its nearest neighbors.…
The mechanism of decoherence for a quantum system with rotational degrees of freedom is studied. From a simple model of elastic scattering, we show that the non-diagonal density matrix elements of the system exponentially decay. The decay…
Supernova neutrinos could be well-suited for probing neutrino decay, since decay may be observed even for very small decay rates or coupling constants. We will introduce an effective operator framework for the combined description of…
We consider the construction of a polyhedral Delaunay partition as a limit of the sequence of power diagrams (radical partitions). The dual Voronoi diagram is obtained as a limit of the sequence of weighted Delaunay partitions. The problem…
The standard wave function approach for the treatment of neutrino oscillations fails in situations where quantum ensembles at a finite temperature with or without an interacting background plasma are encountered. As a first step to treat…
We prove a sufficient condition for the Jacobian problem in the setting of real, complex and mixed polynomial mappings. This follows from the study of the bifurcation locus of a mapping subject to a new Newton non-degeneracy condition.
We prove stochastic homogenization for integral functionals defined on Sobolev spaces, where the stationary, ergodic integrand satisfies a degenerate growth condition of the form \begin{equation*} c|\xi A(\omega,x)|^p\leq…
In the presence of non-standard neutrino interactions (NSI), a degeneracy exists in neutrino oscillation data, which involves the flipping of the octant of the mixing angle ${\theta_{12}}$ and the type of the neutrino mass ordering. In this…
We investigate a scenario in which neutrinos are coupled to a pseudoscalar degree of freedom $\ph$ and where decays $\nu_1 \to \nu_2+\ph$ and inverse decays are the responsible mechanism for obtaining equilibrium. In this context we discuss…
This paper concerns integral varifolds of arbitrary dimension in an open subset of Euclidean space with its first variation given by either a Radon measure or a function in some Lebesgue space. Pointwise decay results for the quadratic…
We study solutions to a one-phase singular perturbation problem that arises in combustion theory and that formally approximates the classical one-phase free boundary problem. We introduce a natural density condition on the transition layers…
Recent advances in levitated optomechanics provide new perspectives for the use of rotational degrees of freedom for the development of quantum technologies as well as for testing fundamental physics. As for the translational case, their…
In solving the differential equation for a non damped harmonic oscillator one meets, after subjecting the equation to a Fourier transformation, an integration in the complex $\omega$ plane. In most cases such an integral is evaluated by…
We derive an analytical expression of a Wigner function that approximately describes the time evolution of the one-dimensional motion of a particle in a nonharmonic potential. Our method involves two exact frame transformations, accounting…
We derive a decomposition for the gradient of the innovation loss with respect to the filter gain in a linear time-invariant system, decomposing as a product of an observability Gramian and a term quantifying the ``non-orthogonality"…
We theoretically investigate interactions between non-degenerate mechanical oscillators mediated by a time-dependent cavity field. We obtain a reduced master equation valid for all optomechanical systems operating in the weak coupling…
The Mishchenko-Fomenko theorem on noncommutative integrability of Hamiltonian systems on a symplectic manifold is extended to the case of noncompact invariant submanifolds.