相关论文: Energy transfer, weak resonance, and Fermi's golde…

In this paper, we consider Klein-Gordon equations with cubic nonlinearity in three spatial dimensions, which are Hamiltonian perturbations of the linear one with potential. It is assumed that the corresponding Klein-Gordon operator $B =…

We consider a class of nonlinear Klein-Gordon equations which are Hamiltonian and are perturbations of linear dispersive equations. The unperturbed dynamical system has a bound state, a spatially localized and time periodic solution. We…

In this paper, we explore the metastable states of nonlinear Klein-Gordon equations with potentials. These states come from the instability of a bound state under a nonlinear Fermi's golden rule. In [16], Soffer and Weinstein studied the…

We study long-time dynamics of small even perturbations of the soliton in 1D quadratic Klein-Gordon equation. The soliton possesses both an internal mode and the unstable mode. On a codimension-one manifold of fine-tuned initial data the…

The energy evolution of a quantum chaotic system under the perturbation that harmonically depends on time is studied for the case of large perturbation, in which the rate of transition calculated from the Fermi golden rule exceeds the…

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…

The energy evolution of a quantum chaotic system under the perturbation that harmonically depends on time is studied for the case of large perturbation, in which the rate of transition calculated from the Fermi golden rule (FGR) is about or…

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.…

We establish the conditional asymptotic stability in a local energy norm of the unstable soliton for the one-dimensional quadratic Klein-Gordon equation under even perturbations. A key feature of the problem is the positive gap eigenvalue…

We establish the long time soliton asymptotics for the translation invariant nonlinear system consisting of the Klein-Gordon equation coupled to a charged relativistic particle. The coupled system has a six dimensional invariant manifold of…

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…

Consider a linear autonomous Hamiltonian system with a time periodic bound state solution. In this paper we study the structural instability of this bound state ^M relative to time almost periodic perturbations which are small, localized…

Fermi's golden rule describes the decay dynamics of unstable quantum systems coupled to a reservoir, and predicts a linear decay in time. Although it arises at relatively short times, the Fermi regime does not take hold in the earliest…

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…

A simple quantum mechanical model consisting of a discrete level resonantly coupled to a continuum of finite width, where the coupling can be varied from perturbative to strong (Fano-Anderson model), is considered. The particle is initially…

A Fermi's Golden Rule for population transfer between instantaneous eigenstates of elliptical quantum billiards with oscillating boundaries is derived. Thereby, both the occurrence of the recently observed resonant population transfer…

Resonances appearing by perturbation of embedded non-degenerate eigenvalues are studied in the case when the Fermi Golden Rule constant vanishes. Under appropriate smoothness properties for the resolvent of the unperturbed Hamiltonian, it…

A novel and readily understandable derivation of the Golden Rule of time dependent perturbation theory is presented. The derivation is based on adiabatic turning on of the perturbation as used, for instance, in some formal developments of…

We consider the Hamiltonian $H$ of a 3D spinless non-relativistic quantum particle subject to parallel constant magnetic and non-constant electric field. The operator $H$ has infinitely many eigenvalues of infinite multiplicity embedded in…

We study the solutions of linear Schroedinger equations in which the potential energy is a periodic function of time and is sufficiently localized in space. We consider the potential to be close to one that is time periodic and yet…