Systems far from thermal equilibrium

Systems driven out of equilibrium by an external field such as temperature gradient or electric field, often reach a steady state which supports currents. These steady states are very different from thermal equilibrium states. In particular they tend to exhibit long-range correlations which may sometime result in phase transitions and long-range order in one dimension.

Our group is engaged in theoretical studies of the nature of non-equilibrium steady states and their dynamics by analyzing prototypical models introduced for this purpose.

Systems with long-range interactions

Long-range interactions are those where the two-body potential decays algebraically at large distances with a power smaller than the spatial dimension. Examples include self gravitating systems, dipolar magnets and others. These systems are non-additive, and as a result they exhibit some unusual properties such as negative specific heat, inequivalence of statistical ensembles and slow relaxation processes where the relaxation time diverges with the system size.

Such slow relaxation leads in some cases to non-Boltzmann states (termed quasistationary states) which are stationary in the thermodynamic limit.

Dynamical and thermodynamical properties resulting from long-range interactions are being explored in our group.

Statistical properties of biomolecules

Biomolecules such as DNA or RNA display some unique statistical properties resulting from their linear nature. For example a double stranded DNA exhibits a denaturation transition upon heating, whereby the two strands detach from each other. Similarly, RNA molecules lose their secondary structure through a melting process.

Our studies involve the analysis of phase transitions in such molecules, and the role played by loops formed in the melting process.