Nonrelativistic conformal field theories

We study representations of the Schr\"odinger algebra in terms of operators in nonrelativistic conformal field theories. We prove a correspondence between primary operators and eigenstates of few-body systems in a harmonic potential. Using the correspondence we compute analytically the energy of fermions at unitarity in a harmonic potential near two and four spatial dimensions. We also compute the energy of anyons in a harmonic potential near the bosonic and fermionic limits.Comment: 26 pages, 9 figures; added a comment on the convergence of epsilon expansion

Ab initio derivation of electronic low-energy models for C60 and aromatic compounds

We present a systematic study for understanding the relation between electronic correlation and superconductivity in C60 and aromatic compounds. We derived, from first principles, extended Hubbard models for twelve compounds; fcc K3C60, Rb3C60, Cs3C60 (with three different lattice constants), A15 Cs3C60 (with four different lattice constants), doped solid picene, coronene, and phenanthrene. We show that these compounds are strongly correlated and have a similar energy scale of the bandwidth and interaction parameters. However, they have a different trend in the relation between the strength of electronic correlation and superconducting transition temperature; while the C60 compounds have a positive correlation, the aromatic compounds exhibit negative correlation.Comment: 13 pages, 7 figures, 7 table

Formation of Protoplanets from Massive Planetesimals in Binary Systems

More than half of stars reside in binary or multiple star systems and many planets have been found in binary systems. From theoretical point of view, however, whether or not the planetary formation proceeds in a binary system is a very complex problem, because secular perturbation from the companion star can easily stir up the eccentricity of the planetesimals and cause high-velocity, destructive collisions between planetesimals. Early stage of planetary formation process in binary systems has been studied by restricted three-body approach with gas drag and it is commonly accepted that accretion of planetesimals can proceed due to orbital phasing by gas drag. However, the gas drag becomes less effective as the planetesimals become massive. Therefore it is still uncertain whether the collision velocity remains small and planetary accretion can proceed, once the planetesimals become massive. We performed {\it N}-body simulations of planetary formation in binary systems starting from massive planetesimals whose size is about 100-500 km. We found that the eccentricity vectors of planetesimals quickly converge to the forced eccentricity due to the coupling of the perturbation of the companion and the mutual interaction of planetesimals if the initial disk model is sufficiently wide in radial distribution. This convergence decreases the collision velocity and as a result accretion can proceed much in the same way as in isolated systems. The basic processes of the planetary formation, such as runaway growth and oligarchic growth and final configuration of the protoplanets are essentially the same in binary systems and single star systems, at least in the late stage where the effect of gas drag is small.Comment: 26pages, 11 figures. ApJ accepte

Pairing instabilities in quasi-two-dimensional Fermi gases

We study non-equilibrium dynamics of ultracold two-component Fermi gases in low-dimensional geometries after the interactions are quenched from weakly interacting to strongly interacting regime. We develop a T-matrix formalism that takes into account the interplay between Pauli blocking and tight confinement in low-dimensional geometries. We employ our formalism to study the formation of molecules in quasi-two-dimensional Fermi gases near Feshbach resonance and show that the rate at which molecules form depends strongly on the transverse confinement. Furthermore, Pauli blocking gives rise to a sizable correction to the binding energy of molecules.Comment: 6 pages, 3 figure

Universal four-component Fermi gas in one dimension

A four-component Fermi gas in one dimension with a short-range four-body interaction is shown to exhibit a one-dimensional analog of the BCS-BEC crossover. Its low-energy physics is governed by a Tomonaga-Luttinger liquid with three spin gaps. The spin gaps are exponentially small in the weak coupling (BCS) limit where they arise from the charge-density-wave instability, and become large in the strong coupling (BEC) limit because of the formation of tightly-bound tetramers. We investigate the ground-state energy, the sound velocity, and the gap spectrum in the BCS-BEC crossover and discuss exact relationships valid in our system. We also show that a one-dimensional analog of the Efimov effect occurs for five bosons while it is absent for fermions. Our work opens up a very rich new field of universal few-body and many-body physics in one dimension.Comment: 9 pages, 3 figures; (v2) Efimov effect for 5 bosons in 1D is discussed; (v3) expanded versio

A fundamental test for stellar feedback recipes in galaxy simulations

Direct comparisons between galaxy simulations and observations that both reach scales < 100 pc are strong tools to investigate the cloud-scale physics of star formation and feedback in nearby galaxies. Here we carry out such a comparison for hydrodynamical simulations of a Milky Way-like galaxy, including stochastic star formation, HII region and supernova feedback, and chemical post-processing at 8 pc resolution. Our simulation shows excellent agreement with almost all kpc-scale and larger observables, including total star formation rates, radial profiles of CO, HI, and star formation through the galactic disc, mass ratios of the ISM components, both whole-galaxy and resolved Kennicutt-Schmidt relations, and giant molecular cloud properties. However, we find that our simulation does not reproduce the observed de-correlation between tracers of gas and star formation on < 100 pc scales, known as the star formation 'uncertainty principle', which indicates that observed clouds undergo rapid evolutionary lifecycles. We conclude that the discrepancy is driven by insufficiently-strong pre-supernova feedback in our simulation, which does not disperse the surrounding gas completely, leaving star formation tracer emission too strongly associated with molecular gas tracer emission, inconsistent with observations. This result implies that the cloud-scale de-correlation of gas and star formation is a fundamental test for feedback prescriptions in galaxy simulations, one that can fail even in simulations that reproduce all other macroscopic properties of star-forming galaxies.Comment: 13 pages, 10 figures, accepted for publication in MNRA

One loop renormalization for the axial Ward-Takahashi identity in Domain-wall QCD

We calculate one-loop correction to the axial Ward-Takahashi identity given by Furman and Shamir in domain-wall QCD. It is shown perturbatively that the renormalized axial Ward-Takahashi identity is satisfied without fine tuning and the ``conserved'' axial current receives no renormalization, giving $Z_A=1$. This fact will simplify the calculation of the pion decay constant in numerical simulations since the decay constant defined by this current needs no lattice renormalization factor.Comment: 16 pages, 3 axodraw.sty figure