Incoherent hydrodynamics of density waves in magnetic fields

We use holography to derive effective theories of fluctuations in spontaneously broken phases of systems with finite temperature, chemical potential, magnetic field and momentum relaxation in which the order parameters break translations. We analytically construct the hydrodynamic modes corresponding to the coupled thermoelectric and density wave fluctuations and all of them turn out to be purely diffusive for our system. Upon introducing pinning for the density waves, some of these modes acquire not only a gap, but also a finite resonance due to the magnetic field. Finally, we study the optical properties and perform numerical checks of our analytical results. A crucial byproduct of our analysis is the identification of the correct current which describes the transport of heat in our system.

Global zero-relaxation limit of the non-isentropic Euler–Poisson system for ion dynamics

This paper is concerned with smooth solutions of the non-isentropic Euler–Poisson system for ion dynamics. The system arises in the modeling of semi-conductor, in which appear one small parameter, the momentum relaxation time. When the initial data are near constant equilibrium states, with the help of uniform energy estimates and compactness arguments, we rigorously prove the convergence of the system for all time, as the relaxation time goes to zero. The limit system is the drift-diffusion system.

Scattering-constrained dynamics

This chapter discusses the statics and dynamics of particle ensemble evolution under multiple stimuli—electrical, magnetic and thermal, particularly (thermoelectromagnetic interaction)—by developing the evolution of the distribution function in a generalized form from its thermal equilibrium form. In the presence of electrical and magnetic fields, this shows the Hall effect, magnetoresistance, et cetera. Add thermal gradients, and one can elaborate additional consequences that can be calculated in terms of momentum relaxation times and the nature of impulse interaction, since momentum and energies carried by the ensemble are accounted for. So, parameters such as thermal conductivity due to the carriers can be determined, thermoelectric, thermomagnetic and thermoelectromagnetic interactions can be quantified and the Ettinghausen effect, the Nernst effect, the Righi-Leduc effect, the Ettinghausen-Nernst effect, the Seebeck effect, the Peltier effect and the Thompson coefficient understood. The dynamics also makes it possible to determine the frequency dependence of the phenomena.