Stefano Iubini, Università di Firenze #
The nonequilibrium discrete nonlinear Schroedinger equation #
I will present the main features of
nonequilibrium steady states of the one-dimensional discrete nonlinear
Schroedinger (DNLS) equation.

Such equation has important applications in many domains of
physics. A classical example is electronic transport in biomolecules.
In the context of optics or
acoustics it describes the propagation of nonlinear waves
in a layered photonic or phononic system.  On the other hand, in
the realm of the physics of cold atomic gases, the model
is an approximate semiclassical description of bosons
trapped in periodic optical lattices.

While a vast literature has been devoted to the dynamical
behavior of the DNLS equation, much less is known about finite-temperature
properties and almost nothing about nonequilibrium properties.
Due to the presence of two conserved quantities,
energy and norm (or number of particles), the model displays coupled 
transport
in the sense of linear irreversible thermodynamics.
Suitable models of thermostat
are implemented to impose a given temperature and chemical potential at 
the
chain ends. As a result, we find that the system exhibits normal 
transport,
ruled by the Fourier law.
However, for large differences between the thermostat parameters, density 
and
temperature profiles may display an unusual nonmonotonic shape. This is 
due to
the strong dependence of the transport coefficients on the thermodynamic 
variables.