Les Houches-École d’Été de Physique Theorique
Volume 69 / 1999 to Volume 78 / 2003
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Article
Non-compact Quantum Spin Chains as Integrable Stochastic Particle Processes
In this paper we discuss a family of models of particle and energy diffusion on a one-dimensional lattice, related to those studied previously in Sasamoto and Wadati (Phys Rev E 58:4181–4190, 1998), Barraquand...
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Article
Quantum Bound to Chaos and the Semiclassical Limit
We discuss the quantum bound on chaos in the context of the free propagation of a particle in an arbitrarily curved surface at low temperatures. The semiclassical calculation of the Lyapunov exponent can be pe...
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Article
A Model with Darwinian Dynamics on a Rugged Landscape
We discuss the population dynamics with selection and random diffusion, kee** the total population constant, in a fitness landscape associated with Constraint Satisfaction, a paradigm for difficult optimizat...
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Article
Stochastic Perturbation of Integrable Systems: A Window to Weakly Chaotic Systems
Integrable non-linear Hamiltonian systems perturbed by additive noise develop a Lyapunov instability, and are hence chaotic, for any amplitude of the perturbation. This phenomenon is related, but distinct, fro...
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Article
Fractal free energy landscapes in structural glasses
Glasses are amorphous solids whose constituent particles are caged by their neighbours and thus cannot flow. This sluggishness is often ascribed to the free energy landscape containing multiple minima (basins)...
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Article
Non-equilibrium glass transitions in driven and active matter
The glass transition, extensively studied in dense fluids, polymers or colloids, corresponds to a marked evolution of equilibrium transport coefficients on a modest change of control parameter, such as tempera...
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Article
Simulating Rare Events in Dynamical Processes
Atypical, rare trajectories of dynamical systems are important: they are often the paths for chemical reactions, the haven of (relative) stability of planetary systems, the rogue waves that are detected in oil...
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Chapter
Glasses
It is customary to present glasses as an outstanding unsolved question in condensed matter. The problem is the following: supercooled liquids in equilibrium appear to have typical relaxation timescales that di...
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Article
Order in Extremal Trajectories
Given a chaotic dynamical system and a time interval in which some quantity takes an unusually large average value, what can we say of the trajectory that yields this deviation? As an example, we study the tra...
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Article
Thinking Transport as a Twist
The determination of the conductivity of a deterministic or stochastic classical system coupled to reservoirs at its ends can in general be mapped onto the problem of computing the stiffness (the ‘energy’ cost...
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Article
Open AccessDuality and Hidden Symmetries in Interacting Particle Systems
In the context of Markov processes, both in discrete and continuous setting, we show a general relation between duality functions and symmetries of the generator. If the generator can be written in the form of...
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Article
Gallavotti–Cohen Theorem, Chaotic Hypothesis and the Zero-Noise Limit
The Fluctuation Relation for a stationary state, kept at constant energy by a deterministic thermostat—the Gallavotti–Cohen Theorem— relies on the ergodic properties of the system considered. We show that when p...
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Article
Probing rare physical trajectories with Lyapunov weighted dynamics
In nonlinear dynamical systems, atypical trajectories often play an important role. For instance, resonances and separatrices determine the fate of planetary systems, and localized objects such as solitons and...
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Article
Kramers Equation and Supersymmetry
Hamilton’s equations with noise and friction possess a hidden supersymmetry, valid for time-independent as well as periodically time-dependent systems. It is used to derive topological properties of critical p...
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Article
Metastable States, Transitions, Basins and Borders at Finite Temperatures
Langevin/Fokker-Planck processes can be immersed in a larger frame by adding fictitious fermion variables. The (super) symmetry of this larger structure has been used to derive Morse theory in an elegant way. ...
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Book Series
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Book and Conference Proceedings
Slow Relaxations and nonequilibrium dynamics in condensed matter
Les Houches Session LXXVII, 1-26 July, 2002
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Article
Testing the thermodynamic approach to granular matter with a numerical model of a decisive experiment
Edwards has proposed1,2,3 a thermodynamic description of dense, slowly flowing granular matter, in which the grains (the ‘atoms’ of the system) interact with inelastic forces and enduring contacts. In Edwards' en...
