Quantum mechanical analogs of classical non-equilibrium systems

The growth of an interface under some form of random deposition appears in many areas of physics, biology, and society. The dynamics of these growth problems is often mathematically similar and insensitive to details of the setup.

The challenge is to link stochastic differential equations for the growth to statistical properties of the interface, which has been an open problem in non-equilibrium physics for the past 50-years.Significant progress has been made recently by mapping the interface dynamics to a seemingly unrelated problem, the quantum mechanics of an interacting Bose gas.

In this way, it has been possible to determine the non-equilibrium dynamics of a line, i.e., to solve the one-dimensional case.

However, the solution does not carry over to higher dimensions, and the statistical mechanics of interfaces in 2D and 3D is a frontier of current research.Here I propose an entirely new approach to non-equlibrium physics in 2D and 3D, based on my own research in quantum many-body theory.

I have spent the past years studying quantum gases using few-body solutions and developed novel quantum-field theory techniques for strong interactions.

I have shown that these methods are highly successful to describe interacting quantum gases, and now I intend to apply them to solve the statistical mechanics of interfaces in 2D and 3D.