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Several aspects of classical and quantum mechanics applied to a class of strongly chaotic systems are studied. These consist of single particles moving without external forces on surfaces of constant negative Gaussian curvature whose…
The climate system is a forced, dissipative, nonlinear, complex and heterogeneous system that is out of thermodynamic equilibrium. The system exhibits natural variability on many scales of motion, in time as well as space, and it is subject…
Temperature chaos is a striking phenomenon in spin glasses, where even slight changes in temperature lead to a complete reconfiguration of the spin state. Another intriguing effect is the reentrant transition, in which lowering the…
In this talk I review some recent developments which shed light on the main connections between structural glasses and mean-field spin glass models with a discontinuous transition. I also discuss the role of quantum fluctuations on the…
We characterize the disorder induced localization in momentum space for ultracold atoms in one-dimensional incommensurate lattices, according to the dual Aubry-Andr\'e model. For low disorder the system is localized in momentum space, and…
This paper continues our study of quasicrystals initiated in Part I. We propose a general mechanism for constructing quasicrystals, existing globally in time, in spatially-extended systems (partial differential equations with Euclidean…
We consider a physical model where the total energy is governed by surface tension and attractive screened Coulomb potential on the 3-dimensional space. We obtain different periodic equilibrium patterns i.e. stationary sets for this energy,…
We address the problem of chaotic temperature dependence in disordered glassy systems at equilibrium by following states of a random-energy random-entropy model in temperature; of particular interest are the crossings of the free-energies…
We uncover and characterize different chaotic transport scenarios on perfect periodic surfaces by controlling the chaotic dynamics of particles subjected to periodic external forces in the absence of a ratchet effect. After identifying…
The article presents results of preliminary study of solutions to recently offered basic thermodynamic equation for equilibrium in chemical systems with focus on chaotic behavior. Classical part of that equation was investigated earlier in…
We introduce a family of two-dimensional lattice models of quasicrystals, using a range of square hard cores together with a soft interaction based on an aperiodic tiling set. Along a low temperature isotherm we find, by Monte Carlo…
In a one dimensional lattice thermal fluctuations destroy the long-range order making particles of the lattice move on a scale much larger than the lattice spacing. We discuss the assumption that this motion may be responsible for the…
The relation between the notion of crystalline symmetry and characteristic time intervals when this symmetry could be observed is analyzed. Several time scales are shown to exist for a system of interacting particles. It is only when the…
Quasiperiodic modulation can prevent isolated quantum systems from equilibrating by localizing their degrees of freedom. In this article, we show that such systems can exhibit dynamically stable long-range orders forbidden in equilibrium.…
We show that in small and low density systems described by a lattice gas model with fixed number of particles the location of a thermodynamic phase transition can be detected by means of the distribution of the fluctuations related to an…
A quantum dynamical model of two interacting spins, with chaotic and regular components, is investigated using a finite two-particles symmetrized basis. Chaotic eigenstates give rise to an equilibrium occupation number distribution in close…
Spin glasses occupy a unique place in condensed matter: they freeze collectively while remaining struc-turally disordered, and they exhibit slow, history-dependent dynamics that reflect an exceptionally rug-ged free-energy landscape. This…
It is well-known that spontaneous symmetry breaking in one spatial dimension is thermodynamically forbidden at finite energy density. Here we show that mirror-symmetric disorder in an interacting quantum system can invert this paradigm,…
Understanding the interplay between topology and ordering in systems on curved manifolds, governed by anisotropic interactions, takes a central role in many fields of physics. In this paper, we investigate the effects of lattice symmetry…
Contributions of quantum interference effects occuring in quasicrystals are emphasized. First conversely to metallic systems, quasiperiodic ones are shown to enclose original alterations of their conductive properties while downgrading long…