Prof. Alexander Abanov (Department of Physics, Stony Brook University, USA)
"Dispersive shock waves in interacting one-dimensional systems and edge states of FQHE"
The hydrodynamic description of many body systems in one spatial
dimension is discussed. For simplest integrable models in one dimension, such as Calogero-Sutherland model, it is
possible to find an exact quantum hydrodynamic
description of the system. [1] The exact form of hydrodynamic equations
is very specific to the integrable model under
consideration. However, the hydrodynamic description itself is based on
local conservation laws and is intrinsically
universal. The presence of nonlinear and dispersive terms in
hydrodynamic equations leads to the effects which are
missed in the linearized hydrodynamic description (bosonization). I plan
to describe one of such effects - the formation
of dispersive shock waves. The relevance of this phenomenon to the
dynamics of edge states in fractional Quantum
Hall Effect will be discussed. [2]
[1] A. G. Abanov and P. B. Wiegmann, Phys. Rev. Lett 95, 076402 (2005).
[2] E. Bettelheim, A. G. Abanov, and P. Wiegmann, Phys. Rev. Lett. 97,
246401 (2006).