Related papers: Equivalence principle and critical behaviour for n…
Noether invariance in statistical mechanics provides fundamental connections between the symmetries of a physical system and its conservation laws and sum rules. The latter are exact identities that involve statistically averaged forces and…
The evolution of observable quantities of finite quantum systems is analyzed when the latter are subject to nondestructive measurements. The type and number of measurements characterize the level of decoherence produced in the system. A…
Kramers' degeneracy theorem underpins many interesting effects in quantum systems with time-reversal symmetry. We show that the generator of dynamics for Markovian open fermionic systems can exhibit an analogous degeneracy, protected by a…
We review results concerning the critical behavior of spin systems at equilibrium. We consider the Ising and the general O($N$)-symmetric universality classes, including the $N\to 0$ limit that describes the critical behavior of…
At a critical point of a second order phase transition the intrinsic energy surface is flat and there is no stable minimum value of the deformation. However, for a finite system, we show that there is an effective deformation which can…
We prove spatial decay estimates on disorder-averaged position-momentum correlations in a gapless class of random oscillator models. First, we prove a decay estimate on dynamic correlations for general eigenstates with a bound that depends…
We use simple models (the Ising model in one and two dimensions, and the spherical model in arbitrary dimension) to put to the test some recent ideas on the slow dynamics of nonequilibrium systems. In this review the focus is on the…
The complex eigenvalues of Markov generators govern oscillatory properties of relaxation, autocorrelation, and linear response. Here we show that these eigenvalues are localized by nonequilibrium cycles of the generator, thus revealing a…
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…
Recent work has connected the type of fidelity decay in perturbed quantum models to the presence of chaos in the associated classical models. We demonstrate that a system's rate of fidelity decay under repeated perturbations may be measured…
A critically enhanced decay of the Loschmidt echo is characteristic of sudden quench dynamics near a quantum phase transition. Here, we demonstrate that the decay and revival of the Loschmidt echo follows power-law scaling in the system…
Studying the structure of systems in nonequilibrium steady states necessitates tools that quantify population shifts and associated deformations of equilibrium free energy landscapes under persistent currents. Within the framework of…
Resonance states in quantum chaotic scattering systems have a multifractal structure that depends on their decay rate. We show how classical dynamics describes this structure for all decay rates in the semiclassical limit. This result for…
Nonequilibrium phase transitions can be typified in a similar way to equilibrium systems, for instance, by the use of the order parameter. However, this characterization hides the irreversible character of the dynamics as well as its…
We consider a nonequilibrium process on a timeline with discrete sites which evolves by a non-Markovian update rule in such a way that an active site at time t activates one or several sites in the future at time t+dt. The time intervals dt…
An ultracold gas of interacting fermionic atoms in a three-dimensional optical lattice is considered, where the lattice potential strength is periodically modulated. This non-equilibrium system is non-perturbatively described by means of a…
We derive a family of inequalities involving different phase-space distributions of a quantum state which have to be fulfilled by any classical state. The violation of these inequalities is a clear signature of nonclassicality. Our approach…
We consider the "membrane in the middle" optomechanical model consisting of a laser pumped cavity which is divided in two by a flexible membrane that is partially transmissive to light and subject to radiation pressure. Steady state…
Relevant and fundamental concepts of the statistical mechanical theory of classical liquids are ordinarily introduced in the context of the description of thermodynamic equilibrium states. This makes explicit reference to probability…
The earlier times of evolution of a magnetic system contain more information than we can imagine. Capturing correlation matrices G of different time evolutions of a simple testbed spin system, as the Ising model, we analyzed the density of…