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Friday, January 27, 2012
Physics Building, Room 204
Note special time.
[Host: Dinko Pocanic]
University of Virginia
"N-polaron systems and mathematics"
The polaron is a mathematical model for a “dressed”
particle consisting of an electron together with its entourage of
local excitations of a quantized phonon field. We will give a brief
historical review of the polaron, including the analysis of its ground
state by a Brownian motion functional integral and by a related
For the case of two or more electrons,
the interaction of the electrons with the phonon field gives rise to
an effective attraction between electrons that causes the particles to
bind together. For N electrons, N → ∞, the
systems are unstable in the sense that the binding energy grows faster
than linearly in N. We will discuss recent work with Frank,
Lieb, and Seiringer which shows that sufficiently strong Coulomb
repulsion between electrons can compensate for this binding and
provide stability for polaron systems for large N.
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