Related papers: Energy decay for evolution equations with glassy t…
Von Neumann entropy rate for open quantum systems is, in general, written in terms of entropy production and entropy flow rates, encompassing the second law of thermodynamics. When the open-quantum-system evolution corresponds to a quantum…
Background: Decay constants of unstable nuclei and particles are quantum constants. Recent controversy on the existence (versus non-existence) of variability in the observation of decay rate can be settled by considering mixing in decay…
In this paper we consider a class of $p$-evolution equations of arbitrary order with variable coefficients depending on time and space variables $(t,x)$. We prove necessary conditions on the decay rates of the coefficients for the…
The dynamical behavior of a kind of models with hierarchically constrained dynamics is investigated. The models exhibit many properties resembling real structural glasses. In particular, we focus on the study of time-dependent temperature…
Soil creeps imperceptibly downhill, but also fails catastrophically to create landslides. Despite the importance of these processes as hazards and in sculpting landscapes, there is no agreed upon model that captures the full range of…
This note is to conclude $L^1-L^1$ estimates for solutions to the following Cauchy problem for visco-elastic damped $\sigma$-evolution models: \begin{equation} \begin{cases} u_{tt}+ (-\Delta)^\sigma u+ (-\Delta)^\sigma u_t = 0, &\quad x\in…
We offer an alternative real-space description, based purely on activated processes, for the understanding of relaxation dynamics in hierarchical landscapes. To this end, we use the cluster model, a coarse-grained lattice model of a jammed…
Glassy systems are ubiquitous in nature, and are characterized by slow relaxations to equilibrium without a typical timescale, aging and memory effects. Understanding these is a long-standing problem in physics. We study the aging of the…
We consider N identical oscillators coupled to a single environment and show that the conditions for the existence of decoherence free subspaces are degeneracy of the oscillator frequencies and separability of the coupling with the…
In this article, we establish Gaussian decay for the Box_b-heat kernel on polynomial models in C^2. Our technique attains the exponential decay via a partial Fourier transform. On the transform side, the problem becomes finding quantitative…
For the time-fractional phase field models, the corresponding energy dissipation law has not been settled on both the continuous level and the discrete level. In this work, we shall address this open issue. More precisely, we prove for the…
We present a novel method to predict the fracture surface energy, {\gamma}, of isochemically crystallizing silicate glasses using readily available crystallographic structure data of their crystalline counterpart and tabled diatomic…
This paper addresses the question of change of decay rate from exponential to algebraic for diffusive evolution equations. We show how the behaviour of the spectrum of the Dirichlet Laplacian in the two cases yields the passage from…
The long- and short-time behavior of solutions to dissipative evolution equations is studied by applying the concept of hypocoercivity. Aiming at partial differential equations that allow for a modal decomposition, we compute estimates that…
The time evolution of the thermally activated decay rates is considered. This evolution is of particular importance for the recent nanoscale experiments discussed in the literature, where the potential barrier is relatively low (or the…
The present status of theoretical and experimental investigations of the decay rate of a positronium is considered. The increasing interest to this problem has been caused by the disagreement of the calculated value of $\Gamma_3 (o-Ps)$ and…
We present here results of stellar evolution calculations that include the latest advances in radiative opacities and neutrino cooling, and discuss on the basis of these models how the internal stellar structure responds to mass-loss from…
Quantum mechanical theory disallows the model that has been used to infer the neutrino mass difference from the reported "GSI oscillations" in the rates of decay of hydrogen-like ions by electron capture. It has not been proved that the…
We consider a rather general class of evolutionary PDEs involving dissipation (of possibly fractional order), which competes with quadratic nonlinearities on the regularity of the overall equation. This includes as prototype models,…
The dramatic slowdown of dynamics in supercooled liquids approaching the glass transition remains one of the central unresolved problems in condensed matter physics. We review approaches that attribute this slowdown to growing thermodynamic…