Related papers: Relating the Lorentzian and exponential: Fermi's a…
We present a theoretical analysis of quantum decay in which the survival probability is replaced by a decay rate that is equal to the absolute value squared of the wave function in the time representation. The wave function in the time…
In the production or annihilation of a pair of fermions, the initial-state or final-state interactions often lead to significant effects on the reaction cross sections. For Coulomb-type interactions, the Gamow factor has been traditionally…
A direct procedure for determining the propagator associated with a quantum mechanical problem was given by the Path Integration Procedure of Feynman. The Green function, which is the Fourier Transform with respect to the time variable of…
In the probability representation of quantum mechanics, quantum states are represented by a classical probability distribution, the marginal distribution function (MDF), whose time dependence is governed by a classical evolution equation.…
A finite quantum system evolving unitarily equilibrates in a probabilistic fashion. In the general many-body setting the time-fluctuations of an observable \mathcal{A} are typically exponentially small in the system size. We consider here…
Starting from the model of continuous time random walk, we focus our interest on random walks in which the probability distributions of the waiting times and jumps have fat tails characterized by power laws with exponent between 0 and 1 for…
Long-time asymptotic of field-field correlator for radiation propagated through a medium composed of random point-like scatterers is studied using Bete-Salpeter equation. It is shown that for plane source the fluctuation intensity (zero…
We study chaotic scattering outside the wide band limit, as the Fermi energy $E_F$ approaches the band edges $E_B$ of a one-dimensional lattice embedding a scattering region of M sites. We show that the delay-time and thermopower…
Decay law of a complicated unstable state formed in a high energy collision is described by the Fourier transform of the two-point correlation function of the scattering matrix. Although each constituent resonance state decays exponentially…
A quantum mechanical wave of a finite size moves like a classical particle and shows a unique decay probability. Because the wave function evolves according to the Schr\"{o}dinger equation, it preserves the total energy but not the kinetic…
We formulate the weak intramolecular coupling F\"orster resonance energy transfer theory in a form suitable for calculating ultrafast nonlinear response of molecular systems. We introduce a formally exact time-dependent factorization of the…
We establish a fluctuation-correlation theorem by relating the quantum fluctuations in the generator of the parameter change to the time integral of the quantum correlation function between the projection operator and force operator of the…
Standard derivations of ``time-independent perturbation theory'' of quantum mechanics cannot be applied to the general case where potentials are energy dependent or where the inverse free Green function is a non-linear function of energy.…
We inspect the initial and the long time evolution of excitations a Fermi liquids by analyzing the time behavior of the electron spectral function. Focusing on the short-time limit we study the electron-boson model for the homogenous…
The fluctuation-dissipation theorem (FDT) is a central result in statistical physics, both for classical and quantum systems. It establishes a relationship between the linear response of a system under a time-dependent perturbation and time…
We consider a slowly rotating rectangular billiard with moving boundaries and use the canonical perturbation theory to describe the dynamics of a billiard particle. In the process of slow evolution certain resonance conditions can be…
The lasso and elastic net linear regression models impose a double-exponential prior distribution on the model parameters to achieve regression shrinkage and variable selection, allowing the inference of robust models from large data sets.…
Time-dependent quantum mechanics provides an intuitive picture of particle propagation in external fields. Semiclassical methods link the classical trajectories of particles with their quantum mechanical propagation. Many analytical results…
We prove existence of propagators for a time dependent Schr\"odinger equation with a new class of softened Coulomb potentials, which we allow to be time dependent, in the context of time dependent density functional theory. We compute…
We study the crossover of the quantum Loschmidt echo (or fidelity) from the golden rule regime to the perturbation-independent exponential decay regime by using the kicked top model. It is shown that the deviation of the…