Related papers: Fermi's "Golden Rule" and Non-Exponential Decay
We modify the theory of the Quantum Zeno Effect to make it consistent with the postulates of quantum mechanics. This modification allows one, throughout a sequence of observations of an excited system, to address the nature of the…
Results of theoretical studies of the quantum unstable systems caused that there are rather widespread belief that a universal feature od the quantum decay process is the presence of three time regimes of the decay process: the early time…
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…
The decay of a local spin excitation in an inhomogeneous spin chain is evaluated exactly: I) It starts quadratically up to a spreading time t_{S}. II) It follows an exponential behavior governed by a self-consistent Fermi Golden Rule. III)…
We present a Fermi golden rule giving rates of decay of states obtained by perturbing embedded eigenvalues of a quantum graph. To illustrate the procedure in a notationally simpler setting we also present a Fermi Golden Rule for boundary…
The decay dynamics of a local excitation interacting with a non-Markovian environment, modeled by a semi-infinite tight-binding chain, is exactly evaluated. We identify distinctive regimes for the dynamics. Sequentially: (i) early quadratic…
Fermi's Golden Rule (FGR) applies in the limit where an initial quantum state is weakly coupled to a {\it continuum} of other final states overlapping its energy. Here we investigate what happens away from this limit, where the set of final…
The quantum-mechanical theory of the decay of unstable states is revisited. We show that the decay is non-exponential both in the short-time and long-time limits using a more physical definition of the decay rate than the one usually used.…
An unstable quantum state generally decays following an exponential law, as environmental decoherence is expected to prevent the decay products from recombining to reconstruct the initial state. Here we show the existence of deviations from…
An effect generated by the nonexponential behavior of the survival amplitude of an unstable state in the long time region is considered. We find that the instantaneous energy of the unstable state for a large class of models of unstable…
We study the short-time and medium-time behavior of the survival probability in the frame of the $N$-level Friedrichs model. The time evolution of an arbitrary unstable initial state is determined. We show that the survival probability may…
While exponential decay is ubiquitous in Nature, deviations at both short and long times are dictated by quantum mechanics. Non-exponential decay is known to arise due to the possibility of reconstructing the initial state from the decaying…
The initial stages of the quasiparticle decay in a Fermi liquid are governed by a time-scale distinct from the scattering rates as derived from the Fermi golden rule approach. We show that the initial decay is nonexponential and that it is…
The evolution of a surface excitation in a two dimentional model is analyzed. I) It starts quadratically up to a spreading time t_{S}. II) It follows an exponential behavior governed by a self-consistent Fermi Golden Rule. III) At longer…
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…
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…
Deviations of the decay law from exponents are discussing for a long time, however, experimental proofs of such deviations are absent. Here in the general form is shown that the conclusions about non-exponential contributions are due to the…
We use (nonconservative) dynamical semigroups to investigate the decay law of a quantum unstable system weakly coupled with a large environment. We find that the deviations from the classical exponential law are small and can be safely…
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…
The transformation of canonical decay laws of moving unstable quantum systems is studied by approximating, over intermediate times, the decay laws at rest with superpositions of exponential modes via the Prony analysis. The survival…