Israel Michael Sigal
Information for Students
Presently I am working in the following areas:

Quantum Field Theory
Consider a quantum system, such as a hydrogen atom, which is originally
in an excited state. We expect such a system to emit photons
and descend into its ground state. This is the process of radiation
which in particular produces the light we see. We would like to develop
mathematical understanding of the dynamics of this and similar
processes.

Nonlinear Partial Differential Equations of Quantum Physics
Consider (nonintegrable) evolution equations which have
soliton solutions. Examples of such equations are nonlinear
Schrödinger, GinzburgLandau, LandauLifshitz
and Heisenberg ferromagnet equations to name just a few. One would like
to understand solutions of such equations in a presence of inhomogeneities and/or describing
several (interacting) solitons.

Mathematical Biology
Here we are interested in aggregation phenomena for living organisms, such as cells and
bacteria (e.g. chemotaxis), and for proteins.

Nonequilibrium Statistical Mechanics
Quantum systems are never isolated but they interact with their
environments. The latter can be assumed to be near their states of
(local) equilibrium. The problem here is to describe the dynamics of
such a coupled system. One would like to see in mathematically rigorous
way how dynamics of isolated quantum systems is affected by
interaction with its environment.
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