Related papers: Static and dynamic variational principles for stro…
The rich and diverse dynamics of particle-based systems ultimately originates from the coupling of their degrees of freedom via internal interactions. To arrive at a tractable approximation of such many-body problems, coarse-graining is…
We briefly review some equilibrium and nonequilibrium properties of systems with long-range interactions. Such systems, which are characterized by a potential that weakly decays at large distances, have striking properties at equilibrium,…
The existence of more than one steady-state in a many-body quantum system driven out-of-equilibrium has been a matter of debate, both in the context of simple impurity models and in the case of inelastic tunneling channels. In this Letter,…
These are introductory lectures to some aspects of the physics of strongly correlated electron systems. I first explain the main reasons for strong correlations in several classes of materials. The basic principles of dynamical mean-field…
The homogenization of periodic elastic composites is addressed through the reformulation of the local equations of the mechanical problem in a geometric functional setting. This relies on the definition of Hilbert spaces of kinematically…
Solid state physics deals with systems composed of atoms with strongly bound electrons. The tunneling probability of each electron is determined by interactions that typically extend to neighboring sites, as their corresponding wave…
We study gapless quantum spin chains with spin 1/2 and 1: the Fredkin and Motzkin models. Their entangled groundstates are known exactly but not their excitation spectra. We first express the groundstates in the continuum which allows for…
We study three different experiments that involve dry friction and periodic driving, and which employ both single and many-particle systems. These experimental set-ups, besides providing a playground for investigation of frictional effects,…
A field theory approach for the nonequilibrium relaxation dynamics in open systems at late times is developed. In the absence of conservation laws, all excitations are subject to dissipation. Nevertheless, ordered stationary states satisfy…
We study transport through an interacting model system consisting of a central correlated site coupled to finite bandwidth tight-binding leads, which are considered as effectively noninteracting. Its nonequilibrium properties are determined…
The concept of electronic correlations plays an important role in modern condensed matter physics. It refers to interaction effects which cannot be explained within a static mean-field picture as provided by Hartree-Fock theory. Electronic…
Deterministic diffusive systems such as the periodic Lorentz gas, multi-baker map, as well as spatially periodic systems of interacting particles, have non-equilibrium stationary states with fractal properties when put in contact with…
For most stochastic dynamical systems, variables which are tightly regulated tend to respond slowly to external changes. This idea is often discussed for applicable systems, within a linear response regime, through the Fluctuation…
The global steady state of a system in thermal equilibrium exponentially favors configurations with lesser energy. This principle is a powerful explanation of self-organization because energy is a local property of a configuration. For…
The formalism of Kohn and Sham uses a specific (model) hamiltonian which highly simplifies the many-electron problem to that of noninteracting fermions. The theorem of Hohenberg and Kohn tells us that, for a given ground state density, this…
The variational method is very important in mathematical and theoretical physics because it allows us to describe the natural systems by physical quantities independently from the frame of reference used. A global and statistical approach…
A new perturbational approach to spectral and thermal properties of strongly correlated electron systems is presented: The Anderson model is reexamined for $U\to\infty$\,, and it is shown that an expansion of Green's functions with respect…
This article describes the various experimental bounds on the variation of the fundamental constants of nature. After a discussion on the role of fundamental constants, of their definition and link with metrology, the various constraints on…
This paper considers discontinuous dynamical systems, i.e., systems whose associated vector field is a discontinuous function of the state. Discontinuous dynamical systems arise in a large number of applications, including optimal control,…
The relationship between the densities of ground-state wave functions (i.e., the minimizers of the Rayleigh--Ritz (RR) variation principle) and the ground-state densities in density-functional theory (i.e., the minimizers of the…