Understanding of physical properties for quantum many-body systems with strong interparticle interactions is one of key issues common to various subfields of physics. Such systems range from high-Tc superconductors in solid-state physics to neutron star interiors in nuclear physics. Among these systems, ultracold atoms are very pure atomic gases whose interactions can be tuned by optical and/or magnetic fields. The ultracold atoms thus provide an ideal platform to simulate the strongly interacting systems.

Recently, quantum transport of ultracold atoms have been actively investigated in order to clarify how strong interactions affect their nonequilibrium properties. Motivated by this experimental situation, we theoretically study spin transport for strongly interacting Fermi gases in two-terminal setup where the gases in left and right reservoirs are connected via a narrow construction (see Figure). In particular, the spin current for normal Fermi gases in two situations are focused on. The first situation is the pseudogap region, where both gases have small spin polarizations and are above the superfluid transition temperature. In this case, spin-up and spin-down fermions in each reservoir prefer to form pairs (so-called preformed Cooper pairs) due to the strong attractive interaction. Because of this pairing effect, the spin degrees of freedom tend to be frozen and thus the spin current is largely suppressed. The other situation is a region where the gases in the left and right reservoirs have large spin polarizations with opposite sign. In this case, minority-spin particles behave as the “Fermi polarons,” which are quasiparticles consisting of minority-spin particles dressed by majority-spin ones. The appearance of the Fermi polarons results in the increase of the minority densities of states, leading to the enhancement of the spin current. Our results suggest that the spin transport measurement becomes a sensitive probe to experimentally examine pseudogap and polaron phenomena, which have attracted much attention not only in atomic physics but also in solid-state physics.

The first iTHEMS Math seminar of this academic year was held on May 1st on Zoom, inviting our colleague Keita Mikami. The title of the talk was “From Eigenvalues to Resonances”. The main topic was Resonance, which is one of the most studied objects in mathematical study of Schrödinger operators.

In the first part, the speaker briefly reviewed spectral theory and how we use it in the study of Schrödinger operators, introducing some basic notions used in the study of Schrödinger operators. Especially, he explained that spectra can be classified into eigenvalues and continuous spectra. Then he introduced scattering theory, which can be used to analyze absolutely continuous spectra. One novelty is that generalized eigenfunction has a representation formula in terms of scattering matrices.

In the second part, the speaker gave a brief introduction of resonances and its application to both mathematicians and researchers in other fields. After introducing mathematical definition of resonances, he explained its applications in the other fields. One example was the following experimental result; when one makes a wave with certain frequency in aquarium, there appears special pattern in the distribution of speed. This phenomena can be explained mathematically by considering resonance of pseudodifferential operator on torus.

Title: Test of Eigenstate Thermalization Hypothesis Based on Local Random Matrix Theory
Author: Shoki Sugimoto, Ryusuke Hamazaki, Masahito Ueda
arXiv: http://arxiv.org/abs/2005.06379v1

Title: Black Hole as a Quantum Field Configuration
Author: Hikaru Kawai, Yuki Yokokura
arXiv: http://arxiv.org/abs/2002.10331v3

Title: F_K / F_π from Möbius Domain-Wall fermions solved on gradient-flowed HISQ ensembles
Author: Nolan Miller, Henry Monge-Camacho, Chia Cheng Chang, Ben Hörz, Enrico Rinaldi, Dean Howarth, Evan Berkowitz, David A. Brantley, Arjun Singh Gambhir, Christopher Körber, Christopher J. Monahan, M. A. Clark, Bálint Joó, Thorsten Kurth, Amy Nicholson, Kostas Orginos, Pavlos Vranas, André Walker-Loud
arXiv: http://arxiv.org/abs/2005.04795v2