Related papers: Golden ratio autocorrelation function and the expo…
The autocorrelation function of the force acting on a slow classical system, resulting from interaction with a fast quantum system is calculated following Berry-Robbins and Jarzynski within the leading order correction to the adiabatic…
Fermi's golden rule describes the leading-order behaviour of the reaction rate as a function of the diabatic coupling. Its asymptotic $(\hbar \rightarrow 0)$ limit is the semiclassical golden-rule instanton rate theory, which rigorously…
We introduce a formalism for time-dependent correlation functions for systems whose evolutions are governed by non-Hermitian Hamiltonians of general type. It turns out that one can define two different types of time correlation functions.…
We revisit the external source method for Kubo-transformed quantum correlation functions recently proposed by Krishna and Voth. We derive an exact formula and show that the Krishna-Voth formula can be derived as an approximation of our…
Time-dependent response and correlation functions are studied in random quantum systems composed of infinitely many parts without mutual interaction and defined with statistically independent random matrices. The latter are taken within the…
We study the multi-periodic oscillations in the spontaneous emission rate of an atom in a medium with refractive index n sandwiched between two parallel mirrors. The oscillations are not obvious in the analytical formula for the rate…
The Kubo formula for the electrical conductivity is rewritten in terms of a sum of Drude-like contributions associated to the exact eigenstates of the interacting system, each characterized by its own frequency-dependent relaxation time.…
We derive a simple and general relation between the fidelity of quantum motion, characterizing the stability of quantum dynamics with respect to arbitrary static perturbation of the unitary evolution propagator, and the integrated time…
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…
We present a short proof of the fact that the exponential decay rate of partial autocorrelation coefficients of a short-memory process, in particular an ARMA process, is equal to the exponential decay rate of the coefficients of its…
It is demonstrated that iterative repeating of some simple geometric construction leads unavoidably in the limit to the golden ratio. The procedure appears to be quickly convergent regardless of a ratio of initial elements sizes. This could…
The focus of this paper is on formal power series analogs of the golden ratio. We are interested in both their continued fractions expansions as well as their Laurent series expansions. Our approach studies the Hankel matrices that are…
Reversible reaction-diffusion systems display anomalous dynamics characterized by a power-law relaxation toward stationarity. In this paper we study in the aging regime the nonequilibrium dynamical properties of some model systems with…
In the first part of these short lecture notes, we will present an introduction on (auto-)correlation functions and linear-response functions in the language of a physicist. In particular, the fluctuation-dissipation theorem in classical…
By considering correlations between classical orbits we derive semiclassical expressions for the decay of the quantum fidelity amplitude for classically chaotic quantum systems, as well as for its squared modulus, the fidelity or Loschmidt…
We calculate Euclidean correlation functions through next-to-leading order in the low energy effective theory of gravity. We focus on correlation functions of curvature and volume operators, calculating these functions through one-loop…
Generic self-gravitating quantum solutions that are not critically dependent on the specifics of microscopic interactions are presented. The solutions incorporate curvature effects, are consistent with the universality of gravity, and have…
Reversible work extraction from identical quantum systems via collective operations was shown to be possible even without producing entanglement among the sub-parts. Here, we show that implementing such global operations necessarily imply…
The method proposed by Pratt to derive recursion relations for systems of degenerate fermions [Phys. Rev. Lett. 84, 4255 (2000), arXiv:nucl-th/9905055] relies on diagrammatic techniques. This efficient formalism assumes no explicit two-body…
We examine numerically the full spatio-temporal correlation functions for all hydrodynamic quantities for the random collision model introduced recently. The autocorrelation function of the heat current, through the Kubo formula, gives a…