Related papers: Fermi's "Golden Rule" and Non-Exponential Decay
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…
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…
We study an exactly-solvable model which shows a zero-temperature transition from a non-Fermi liquid to a Fermi liquid as a function of particle density. The quantum critical point separating these two states is not associated with the…
This paper is a pedagogical yet critical introduction to the quantum description of unstable systems, mostly at the level of a graduate quantum mechanics course. Quantum decays appear in many different fields of physics, and their…
The nonexponential relaxation and aging inherent to complex dynamics manifested in a wide variety of dissipative systems is analyzed through a model of diffusion in phase space in the presence of a nonconservative force. The action of this…
The decay of a bound state weakly-coupled to a non-Hermitian tight-binding unstable continuum, i.e. a continuum of states comprising energies with positive imaginary part, is theoretically investigated. As compared to quantum decay in an…
A perturbative treatment of reduced density operators of quantum subsystems is implemented in the same spirit as Fermi Golden Rule for scattering. Analytic expressions for linear entropy (a measure of purity loss, and in some cases of…
We study the decay process in an open system, emphasizing on the relevance of the environment's spectral structure. Non-Markovian effects are included to quantitatively analyze the degradation rate of the coherent evolution. The way in…
In this paper we show an infinite measure set of exponentially escaping orbits for a resonant Fermi accelerator, which is realised as a square billiard with a periodically oscillating platform. We use normal forms to describe how the energy…
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…
Fluctuations of observables as functions of time, or "fluctuation patterns", are studied in a chaotic microscopically reversible system that has irreversibly reached a nonequilibrium stationary state. Supposing that during a certain, long…
Particle-gamma coincidences from the 46Ti(p,p' gamma)46Ti inelastic scattering reaction with 15-MeV protons are utilized to obtain gamma-ray spectra as a function of excitation energy. The rich data set allows analyzing the coincidence data…
Despite the importance of the Second Law of Thermodynamics, it is not absolute. Statistical mechanics implies that, given sufficient time, systems near equilibrium will spontaneously fluctuate into lower-entropy states, locally reversing…
Interpretation of empirical results based on a taxa's lifetime distribution shows apparently conflicting results. Species' lifetime is reported to be exponentially distributed, whereas higher order taxa, such as families or genera, follow a…
According to the competitive exclusion principle, in a finite ecosystem, extinction occurs naturally when two or more species compete for the same resources. An important question that arises is: when coexistence is not possible, which…
Atom-number states are a valuable resource for ultracold chemistry, atom interferometry and quantum information processing. Recent experiments have achieved their deterministic preparation in trapped few-fermion systems. We analyze the…
The problem of unstable particle decay is discussed to show how elementarity of a subsystem immersed in an infinitely larger environment is lost. The decay law, when the same kind of particles as decay product make up a thermal medium, is…
Deterministic population growth models with power-law rates can exhibit a large variety of growth behaviors, ranging from algebraic, exponential to hyperexponential (finite time explosion). In this setup, selfsimilarity considerations play…
Many-body states described by a Schr\"{o}dinger equation include states of overlapping waves of non-vanishing interaction energies. These peculiar states formed in many-body transitions remain in asymptotic regions, and lead a new component…
The survival probability of a quantum system with a finite ground energy is known to decay subexponentially at large times. Here we show that, under the same assumption, the average value of any quantum observable, whenever well-defined,…