Dissipative Linear Response in a Fermion System .II.

C. Toepffer, P.‐G. Reinhard

Arnold J. Glick

C. Di Castro, Roberto Raimondi

Rhys Matt Andrew Anderson

In this thesis, we observe and characterize the current response of neutral fermions to a periodic applied force, thereby obtaining their conductivity. The experiment takes place in a 3D optical lattice subject to weak harmonic confinement, where a quantum gas microscope enables high-resolution fluorescence imaging of atoms pinned to lattice sites. Using micron-scale periodic displacements of an underlying harmonic potential to provide the oscillating uniform force, we measure the global current response of the atoms up to frequencies sufficient to characterize intraband transport, but well below the bandgap. We observe that the current response scales linearly with the forcing, providing experimental verification that data is taken in the linear response regime. The resulting conductivity spectra are analyzed and fit using five different models, from which a broadening parameter and the spectral weight of the response may be obtained. Broadening of the current response spectrum provides a measure of the rate of dissipation, and increases with lattice depth, interaction strength, and density. This dissipation occurs purely due to fermion-fermion collisions, given the absence of phonons or impurities in our potentials. It is observed to require a finite lattice depth in order to break Galilean invariance, as well as to enable Umklapp scattering events, which play a significant role in the dynamics. Measured dissipation rates collapse onto the predictions of a kinetic theory under the wide range of conditions studied. The spectral weight of the conductivity spectrum predicts the impulse response of the global current. It satisfies a sum rule in the limit of small lattice depth, but diminishes as the depth increases, reflecting an increase in the band-averaged effective mass. Measured under varying temperatures, densities, interaction strengths, and lattice depths, the spectral weight is shown to collapse onto the predictions of a thermodynamic description of the system. Furthermore, it is shown to be unaffected by varying the strength of interactions between the fermions, illustrating a fundamental prediction for conductivity spectra. As our measurements approach a high-temperature regime, the inverse of the spectral weight is shown to approach T-linear behaviour.

A.S. Reiner

Using the Green's-function technique of Martin, Schwinger, and Puff, a calculation is made of the total linear response of nuclear matter, as measurable, for instance, in an inelastic electron or muon scattering experiment. In the independent-pair approximation used, two contributions stand out: the quasielastic response of properly dressed particles with well-defined lifetimes, and the contribution due to the scattering between those particles. An extensive analysis is made of the importance of the transverse component of the electromagnetic interaction as well as of the two mentioned contributions. The properly defined quasielastic scattering is predicted to dominate the scattering. A comparison is made with previous calculations by Czy\ifmmode \dot{z}\else \.{z}\fi{} and Gottfried.