In this seminar, I will discuss exact results obtained for some non-equilibrium many-body systems, with special emphasis on dynamics in low dimensions where fluctuations are crucial. I will first review the so-called "stochastic Hamiltonian formalism" and mention some solution methods. As an illustration of the fermion field-theoretical approach, I will then discuss in some details the one-dimensional A+A ↔ 0 + 0 diffusion-limited reaction, which is completely solvable. Alternative solution techniques will also be commented on. Then, I will illustrate an approach allowing to deal with some stochastic many-body systems in arbitrary dimensions and in the presence of inhomogeneities: I will describe the solution of a paradigmatic kinetic spin system, namely an inhomogeneous version of the "voter model". Finally, some possible future lines of research will be outlined.

We study how lipid raft-induced clustering of receptor proteins on the cell surface leads to longer association of ligands, thereby boosting the chemical signal. We show analytically that, even with a homogeneous distribution of receptors, rebinding considerably slows down the release of ligands over long times (power-law replacing exponential). This effect is enhanced in the presence of lipid rafts, where numerical simulations show that the surface diffusion of bound ligands inside a raft plays a crucial role. We compare our results to current and past experimental studies.

At the atomic and molecular level, very little is understood about basic electrochemical adsorption processes. The subject, in general, can be classified as a surface science problem with chemical or electrochemical potential control, but unlike vacuum systems, the electrochemical environment is quite complex, containing water molecules, ions, and possibly surface charges. Many problems of industrial or applied interest depend on a fundamental understanding of electrochemical adsorption processes, although very little is actually known about such systems. Examples of applied problems include fuel cells, catalysis of environmental pollutants, electroplating, and neurochemistry, particularly synaptic function. We begin to understand the fundamental issues of the field by studying chemically simple adsorption problems, like halide adsorption on single crystal surfaces. Because of the complexity of even the simplest electrochemical systems, a wide variety of simulation methods must be used, ranging from simple lattice-gas models to DFT calculations and more complex off-lattice models, and we vigorously encourage quantitative comparison with experiments.

The complete solution of the kinetic one-dimensional nonequilibrium Ising model, as first introduced by Racz and Zia, and whose exact stationary properties have been recently studied by Schmittmann and Schmüser, is presented. The genuine far-from-equilibrium many-body problem under consideration (detailed balance is violated) is an Ising-like model evolving according to a generalization of Glauber spin flip rates, where spins at even and odd lattice sites are coupled to heat baths with different effective temperatures. In this seminar, we show how it has been possible to compute the dynamical magnetization and all correlation functions of this model. We then explain how these quantities provide the full time-dependent probability distribution function of the system through a Wick theorem involving three different kinds of spin-spin correlation functions. Finally, we also mention the duality of this spin system with a pair-annihilation and pair-creation reaction-diffusion model through a domain-wall mapping.

We consider nonlinear dynamic systems under the influence of noise. Time delayed feedback control that was earlier introduced for the purpose of control of deterministic chaotic oscillations in nonlinear dynamic systems, is exploited for controlling noise-induced motion modelled by stochastic differential equations. Such noise-induced oscillations are widespread in systems near bifurcations, and in excitable systems like neurons, semiconductor nanostructures, or chemical reaction systems. Under appropriate choice of time delay, one can either increase or decrease the regularity of motion. In an excitable system, delayed feedback stabilizes the frequency of oscillations against variation of noise strength. Also, for fixed noise intensity, the phenomenon of entrainment of basic periods of oscillations by the delayed feedback is found. This allows one to steer the timescales of noise-induced motion by changing the time delay.

Molecular interactions are the basis of life, understanding their intricate details is critical to progress in many areas of the life sciences. However, current experimental methods alone do not provide us with complete picture of what is going on at this microscopic level (mainly because the objects involved are too complex and their parts move too fast), and this is where computer modeling can make a difference. My research focuses on development of novel physics-based computational methodologies and applying them to biomolecular systems; in this talk I will give a brief overview of some of the recent projects I have been working on. I will introduce the ``virtual water" methodology and show how it can be successfully applied to the protein folding problem; I will them describe my work on understanding the molecular mechanism behind the proton-pumping function of the protein bacteriorhodopsin - the smallest natural solar panel. Finally, I will show how simple physics can be used to understand the molecular basis of stability of proteins from organisms that survive under extreme conditions, e.g. halo-bacteria from the Dead Sea.