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NATO science for peace and security series. B, Physics and biophysics

Inducing Current in One Dimensional Systems of Interacting Fermions

Marcin Mierzejewski, J. Bonča, Peter Prelovšek

Published Aug 21, 2012• 0 citations
Publisher
DOI
10.1007/978-94-007-4984-9_14

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It has been shown that a quantum quench of interactions in a one-dimensional fermion system at zero temperature induces a universal power law proportional to t^{-2} t − 2 in its long-time dynamics. In this paper we demonstrate that this behaviour is robust even in the presence of thermal effects. The system is initially prepared in a thermal state, then at a given time the bath is disconnected and the interaction strength is suddenly quenched. The corresponding effects on the long times dynamics of the non-equilibrium fermionic spectral function are considered. We show that the non-universal power laws, present at zero temperature, acquire an exponential decay due to thermal effects and are washed out at long times, while the universal behaviour proportional to t^{-2} t − 2 is always present. To verify our findings, we argue that these features are also visible in transport properties at finite temperature. The long-time dynamics of the current injected from a biased probe exhibits the same universal power law relaxation, in sharp contrast with the non-quenched case which features a fast exponential decay of the current towards its steady value, and thus represents a fingerprint of quench-induced dynamics. Finally, we show that a proper tuning of the probe temperature, compared to that of the one-dimensional channel, can enhance the visibility of the universal power-law behaviour.
In the present thesis, we discuss the dynamical response to a static forcing of collisionally interacting, neutral fermionic atoms loaded into a one-dimensional optical lattice. It is well known that for a single particle, as well as for many non-interacting particles, there are two fundamental results: the Bloch oscillations of the total momentum and the absence of a net current, which are accompanied by the localization of the particles in configuration space. In our work, we recall (and, in the presence of an additional parabolic confinement, generalize) the single particle results and, then, solve the associated transport problem for two many-particle systems with non-vanishing atom-atom interactions. In the first case, we analyze the behavior of a two-component (i.e., non-pola-rized) fermionic gas under static forcing. We show that, while the atom-atom interactions do not induce a net current of fermions in this system, a variety of new phenomena emerge. These range from the amplitude modulation of Bloch oscillations with a new frequency, which is proportional to the interaction constant, over doubling of the Bloch frequency, to a rescaling of the characteristic time scales at strong interactions. In the second case, we discuss the requirements to witness directed atomic transport, and propose a microscopic model to describe the normal transport behavior of a dilute gas of polarized (hence non-interacting) fermions, where the net current emerges due to the collision-induced coupling with the finite bath, which is made of bosonic atoms loaded in to the same optical lattice. The outcome is a current-voltage'' characteristics which displays both Ohmic and negative differential conductivity, and a maximum current right at the transition between both regimes. This transition point is completely determined by the microscopic model parameters, and weakly depends on the bath temperature, while the current amplitude asymptotically vanishes with increasing temperature.