Physics (Internal)

Propagation of an impurity through a quantum medium

This event is part of the Biophysics/Condensed Matter Seminar Series.

I will discuss the equilibrium momentum distribution function of a single distinguishable impurity particle immersed in a gas of either free fermions or Tonks-Girardeau bosons in one spatial dimension. I will construct a Fredholm determinant representation for exactly solvable model of a repulsive and attractive impurity-gas $\delta$-function interaction potential, at zero temperature. The resulting distribution is characterized by fourth power decay at a large momentum, and a weakly divergent (quasi-condensate) peak at a finite momentum. I will also discuss the steady state of the impurity past the injection into the gas. I will show that the value of the impurity's velocity at infinite time lies between zero and the speed of sound in the gas, and is determined by the injection protocol. This way, the impurity's frictionless motion is a dynamically emergent phenomenon whose description goes beyond accounting for the kinematic constraints of Landau's approach to superfluidity.