Related papers: Fermi's "Golden Rule" and Non-Exponential Decay
Consider a system governed by the time-dependent Schr\"odinger equation in its ground state. When subjected to weak (size $\epsilon$) parametric forcing by an "ionizing field" (time-varying), the state decays with advancing time due to…
We study the quantum Zeno effect and the anti-Zeno effect in the case of `indirect' measurements, where a measuring apparatus does not act directly on an unstable system, for a realistic model with finite errors in the measurement. A…
We derive the expression for the energy uncertainty of the final state of a decay of an unstable quantum state prepared at the initial time $t=0$. This expression is function of the time $t$ at which a measurement is performed to determine…
This paper addresses the analysis of a boundary feedback system involving a non-homogeneous Euler-Bernoulli beam governed by the equation $m(x)u_{tt}+\mu(x)u_{t}$$+\left(r(x)u_{xx}\right)_{xx}=0$, subject to the initial $u(x,0)=u_0(x)$,…
The decay of an excited is shown to slow down in the presence of a photo detector. This is similar to the behavior of an atom in a mistuned cavity, and under the conditions of the quantum Zeno effect. No external perturbing field is applied…
The main goal in this work is to prove the exponential decay of the semigroup associated with a thermoelastic system composed of an Euler-Bernoulli type equation that models the transverse oscillation of a homogeneous microbeam with axial…
The decay rate of an interstitial two-level spin impurity, located in the center of a unit cell of an anisotropic ferromagnetic lattice subjected to an external magnetic field is derived. The impurity is coupled to nearest-neighbor spins…
We study the short-time and medium-time behavior of the survival probability of decaying states in the framework of the $N$-level Friedrichs model. The degenerated and nearly degenerated systems are discussed in detail. We show that in…
We study the dephasing of fermions interacting with a fluctuating transverse gauge field. The divergence of the imaginary part of the fermion self energy at finite temperatures is shown to result from a breakdown of Fermi's golden rule due…
Some dynamical properties of a bouncing ball model under the presence of an external force modeled by two nonlinear terms are studied. The description of the model is made by use of a two dimensional nonlinear measure preserving map on the…
We study the decay of a prepared state $E_0$ into a continuum {E_k} in the case of non-Ohmic models. This means that the coupling is $|V_{k,0}| \propto |E_k-E_0|^{s-1}$ with $s \ne 1$. We find that irrespective of model details there is a…
The destruction of Fermi liquid behavior when a gapless Fermi surface is coupled to a fluctuating gapless boson field is studied theoretically. This problem arises in a number of different contexts in quantum many body physics. Examples…
We study the non-equilibrium phase transition between survival and extinction of spatially extended biological populations using an agent-based model. We especially focus on the effects of global temporal fluctuations of the environmental…
We study the stationary states of a quantum mechanical system describing an atom coupled to black-body radiation at positive temperature. The stationary states of the non-interacting system are given by product states, where the particle is…
Equilibrium is a rather ideal situation, the exception rather than the rule in Nature. Whenever the external or internal parameters of a physical system are varied its subsequent relaxation to equilibrium may be either impossible or take…
In this work we study global well-posedness and large time behaviour for a typical reaction--diffusion system, which include degenerate diffusion, and whose non-linearities arise from chemical reactions. We show that there is an {\it…
Electron transfer reactions play an essential role in many chemical and biological processes. Fermi's Golden rule, which assumes that the coupling between electronic states is small, has formed the foundation of electron transfer rate…
Approximately forty years ago it was realized that the time development of decaying systems might not be precisely exponential. Rolf Winter (Phys. Rev. {\bf 123}, 1503 (1961)) analyzed the simplest nontrivial system - a particle tunneling…
We generalize an orthonormality relation between decay eigenmodes of equilibrium systems to nonequilibrium markovian generators which commute with their time-reversal. Viewing such modes as tangent vectors to the manifold of statistical…
We propose a new low-energy theory for itinerant fermions near a ferromagnetic quantum critical point. We show that the full low-energy model includes, in addition to conventional interaction via spin fluctuations, another type of…