krishna@thphys.ox.ac.uk
The December colloquium will be held the 13/12/2000
Non-Equilibrium Models of Aggregation, Evaporation and Deposition
Three simple lattice models of aggregation of masses will be introduced, in which we incorporate the elementary processes of diffusion, aggregation on contact, adsorption and desorption. These processes are ubiquitous in nature and arise in a variety of physical settings. The first two models exhibit non-equilibrium phase transitions in all dimensions with some highly unusual features in the steady state. In the third model, while the steady state is trivial, the approach to this state is highly non-trivial and is characterised by two dynamic exponents instead of one.
The November colloquium will be held the 15/11/2000
Statistical Approach to the Mechanical Behavior of Granular Media
We discuss the quasistatic rheology of ideal granular media consisting of rigid spheres or discs interacting via Coulomb law of friction and perfectly inelastic collisions. The macroscopic description of the rheology of quasistatic deformation of such media is rigid-plastic with hardening laws. A phenomenological approach is proposed along these lines. Development of microscopic/macroscopic inter-relations in this phenomenology raises fundamental questions on the relevance of temporal or spatial fluctuations in such a picture.
The October colloquium will be held the 18/10/2000
La Transizione Vetrosa: Problemi Aperti e Prospettive Future
Presentero' in modo introduttivo un resoconto dei problemi piu caratteristici ed universali che riguardano la transizione vetrosa. In particolare discutero' la fenomenologia assai generale dei vetri: cito ad esempio la presenza di fragilita', lo "stretching" delle correlazioni temporali, i fenomeni di invecchiamento e le eterogeneita' spaziali. Discutero' le teorie piu importanti utili a comprendere questa fenomenologia: in particolare le teorie termodinamiche entropiche e le teorie dinamiche di accoppiamenti di modi. Confrontero' queste teorie con quelle che descrivono i modelli di vetri di spin ed i sistemi disordinati.
The June colloquium will be held the 24/05/2000
The dynamics of supercooled liquids
Glass formers are liquids that do not easily crystallize even if they are cooled below their melting temperature. Experimentally it is found that with decreasing temperature the transport coefficients increase dramatically. Therefore there exists a glass transition temperature at which the relaxation time of the system exceeds the typical time scale of the experiments and hence the system falls out of equilibrium. In the talk we will present one theoretical framework, the so-called mode-coupling theory, to describe this slowing down and the results of computer simulations that were done to test this theory.
The May colloquium will be held the 12/05/2000
Meron-cluster Solution of Fermion and Other Sign Problems
The numerical simulation of fermions is a notorious problem that hinders progress in understanding a variety of problems ranging from high-temperature superconductivity to QCD at non-zero chemical potential. In particular, the minus signs that arise due to the antisymmetric nature of the fermion wave function prevent us from using standard importance sampling Monte Carlo techniques. The meron-cluster algorithm is a numerical method that identifies cancelling pairs of fermion paths. This method has been successfully applied to relativistic and non-relativistic lattice fermions, to quantum spin systems, as well as to field theories with non-zero chemical potential or non-zero vacuum angle. It leads to a complete solution of the sign problem in all these cases.
The April colloquium was held the 22/03/2000
Dynamics of recurrent networks of spiking neurons.
After a short presentation of basic models of simplified spiking neurons and of simplified cortical `modules', I will consider the dynamics of populations of uncoupled spiking cells. I will emphasize the fundamental differences between `spiking' and `firing rate' neuronal models. Then, random structureless recurrent connections will be introduced. For simplified synaptic models, the phase diagrams of the resulting networks can be obtained analytically and will be discussed in detail. Last, structure will be added to the synaptic architecture in two situations. The short-term memory properties of the resulting networks will be discussed.
Seminar given the 08/03/2000
Smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics.
We review various applications of the theory of smooth dynamical systems to conceptual problems of nonequilibrium statistical mecanics, adopting a point of view which has emerged progressively in recent years, and which takes seriously into account the chaotic character of the microscopic time evolution. The emphasis is on nonequilibrium steady states rather than the traditional "approach to equilibrium" point of view of Boltzmann. The nonequilibrium steady states, in presence of a Gaussian thermostat, are described by SRB measures. In terms of these one can prove the Gallavotti-Cohen fluctuation theorem. One can also prove a general linear response formula and study its consequences, which are not restricted to near equilibrium situations. At equilibrium one recovers in particular the Onsager reciprocity relations. Under suitable conditions the nonequilibrium steady states satisfy the pairing theorem of Dettmann and Morriss. The results just mentioned hold so far only for classical systems; they do not involve large size, i.e., they hold without a thermodynamic limit.
The February colloquium was paradoxically held the 02/03/2000
Dynamical Mean Field Theory of Strongly Correlated Electron Systems
A Dynamical Mean Field Theory (DMFT) has been developed for the quantitative study of strongly correlated electron systems. I will review this approach, as well as the resulting progress on several physics problems, such as the Mott metal-insulator transition. I will also describe the prospects for applying this method in the context of electronic structure calculations of correlated materials. The possibility of including the physics of short-range correlations within various extensions of DMFT will finally be discussed.
Seminar given the 19/01/2000
Campi e Particelle nella Turbolenza di Scalari Passivi
Si discuteranno i recenti progressi per il problema della turbolenza di campi scalari passivi (temperatura o densita` di contaminanti). L'origine dei fenomeni di intermittenza e delle conseguenti leggi di scala anomale e` stata identificata nella dinamica Lagrangiana, ovvero delle particelle del fluido. La distanza tra le particelle cresce con il tempo in accordo con semplici argomenti dimensionali. La geometria delle figure da esse identificate ha invece una dinamica piu complicata e le geometrie statisticamente preservate dalla dinamica (modi zero) sono in particolare responsabili delle leggi di scala anomale osservate per il campo scalare.
Seminar given the 9/12/1999
Statistical Physics of Glassy Phases
Glassy phases are ubiquitous, and have been for several decades a major challenge for statistical physics. The basic obstacles are clear: glassy systems do not reach equilibrium on accessible time scales, they are not translation invariant, there is a multiplicity of metastable states... Some systems, like spin glasses, are described by a 'disordered' Hamiltonian. Other ones, like structural glasses, have no quenched randomness in their microscopic description, but freeze nevertheless into amorphous states. Focusing on these two types of systems, I shall review some of the generic properties of glass phases and the basic ideas which are used to cope with the above obstacles in their first principle description.
Seminar given the 11/11/1999