The project will study the behavior of physical and biological systems in the presence of noise and/or disorder. These factors are ubiquitous in applied and fundamental science and models of real phenomena have to take them into account. Mathematical models of noise are based on stochastic differential equations (SDE), studied using techniques of probability theory, dynamical systems and partial differential equations. In particular, we willinvestigate the effective behavior of SDE systems as the noise correlation, response delay and other relevant time scales become small. Noisy systems of many interacting particles (microrobots or bacteria) will require additional statistical physics methods to describe their collective behavior. In the quantum case, other mathematical techniques will be brought in: coherent state transform and methods from quantum field theory. All of the above systems will be studied in the light of the new results about entropy production. In addition, systems with quenched disorder will be investigated, including interacting bosons in a random potential. Two types of randomness---noise and disorder occur jointly in models of diffusion in a random environment.
In nontechnical language, noise refers to random time-dependent factors, relevant for systems behavior (random forcing or thermal fluctuations, for example), while disorder means random parameters which do not change significantly in time (e.g. random environment or random structural defects). We will study several effects coming from both kinds of randomness, using methods of probability theory and theoretical physics. Interaction with experiment will go both ways: the developed theory will explain existing or planned experimental results and, conversely, will lead to a design of new experiments. The scope of the work includes diffusion in classical and quantum physics, quantum disordered systems and many-particle systems relevant for applications in biology.
