The fluctuation-dissipation theorem and the linear Glauber model

We obtain exact expressions for the two-time autocorrelation and response functions of the $d$-dimensional linear Glauber model. Although this linear model does not obey detailed balance in dimensions $d\geq 2$, we show that the usual form of the fluctuation-dissipation ratio still holds in the stationary regime. In the transient regime, we show the occurence of aging, with a special limit of the fluctuation-dissipation ratio, $X_{\infty}=1/2$, for a quench at the critical point.Comment: Accepted for publication (Physical Review E

Irreversibility and the arrow of time in a quenched quantum system

Irreversibility is one of the most intriguing concepts in physics. While microscopic physical laws are perfectly reversible, macroscopic average behavior has a preferred direction of time. According to the second law of thermodynamics, this arrow of time is associated with a positive mean entropy production. Using a nuclear magnetic resonance setup, we measure the nonequilibrium entropy produced in an isolated spin-1/2 system following fast quenches of an external magnetic field and experimentally demonstrate that it is equal to the entropic distance, expressed by the Kullback-Leibler divergence, between a microscopic process and its time-reverse. Our result addresses the concept of irreversibility from a microscopic quantum standpoint.Comment: 8 pages, 7 figures, RevTeX4-1; Accepted for publication Phys. Rev. Let

On X-ray-singularities in the f-electron spectral function of the Falicov-Kimball model

The f-electron spectral function of the Falicov-Kimball model is calculated within the dynamical mean-field theory using the numerical renormalization group method as the impurity solver. Both the Bethe lattice and the hypercubic lattice are considered at half filling. For small U we obtain a single-peaked f-electron spectral function, which --for zero temperature-- exhibits an algebraic (X-ray) singularity ($|\omega|^{-\alpha}$) for $\omega \to 0$. The characteristic exponent $\alpha$ depends on the Coulomb (Hubbard) correlation U. This X-ray singularity cannot be observed when using alternative (Keldysh-based) many-body approaches. With increasing U, $\alpha$ decreases and vanishes for sufficiently large U when the f-electron spectral function develops a gap and a two-peak structure (metal-insulator transition).Comment: 8 pages, 8 figures, revte