arXiv subjects

Jun Yin

Publications and source records attributed to Jun Yin.

169 records · Page 10Linked to original sources

arXiv2010

The local relaxation flow approach to universality of the local statistics for random matrices

We present a generalization of the method of the local relaxation flow to establish the universality of local spectral statistics of a broad class of large random matrices. We show that the local distribution of the eigenvalues coincides with the local statistics of the corresponding Gaussian ensemble provided the distribution of the individual matrix element is smooth and the eigenvalues ${x_j}_{j=1}^N$ are close to their classical location ${γ_j}_{j=1}^N$ determined by the limiting density of eigenvalues. Under the scaling where the typical distance between neighboring eigenvalues is of order 1/N, the necessary apriori estimate on the location of eigenvalues requires only to know that $\E |x_j - γ_j |^2 \le N^{-1-\e}$ on average. This information can be obtained by well established methods for various matrix ensembles. We demonstrate the method by proving local spectral universality for Wishart matrices.

math-ph↗

arXiv2010

The chemical evolution of IC10

Dwarf irregular galaxies are relatively simple unevolved objects where it is easy to test models of galactic chemical evolution. We attempt to determine the star formation and gas accretion history of IC10, a local dwarf irregular for which abundance, gas, and mass determinations are available. We apply detailed chemical evolution models to predict the evolution of several chemical elements (He, O, N, S) and compared our predictions with the observational data. We consider additional constraints such as the present-time gas fraction, the star formation rate (SFR), and the total estimated mass of IC10. We assume a dark matter halo for this galaxy and study the development of a galactic wind. We consider different star formation regimes: bursting and continuous. We explore different wind situations: i) normal wind, where all the gas is lost at the same rate and ii) metal-enhanced wind, where metals produced by supernovae are preferentially lost. We study a case without wind. We vary the star formation efficiency (SFE), the wind efficiency, and the time scale of the gas infall, which are the most important parameters in our models. We find that only models with metal-enhanced galactic winds can reproduce the properties of IC10. The star formation must have proceeded in bursts rather than continuously and the bursts must have been less numerous than ~10 over the whole galactic lifetime. Finally, IC10 must have formed by a slow process of gas accretion with a timescale of the order of 8 Gyr.

astro-ph.CO↗

arXiv2010

A Lower Bound on the Ground State Energy of Dilute Bose Gas

Consider an N-Boson system interacting via a two-body repulsive short-range potential $V$ in a three dimensional box $Λ$ of side length $L$. We take the limit $N, L \to \infty$ while keeping the density $ρ= N / L^3$ fixed and small. We prove a new lower bound for its ground state energy per particle $$\frac{E(N, Λ)}{N} \geq 4 πa ρ[ 1 - O(ρ^{1/3} |\log ρ|^3) ],$$ as $ρ\to 0$, where $a$ is the scattering length of $V$.

math-ph↗

arXiv2009

The Second Order Upper Bound for the Ground Energy of a Bose Gas

Consider $N$ bosons in a finite box $Λ= [0,L]^3\subset \mathbf R^3$ interacting via a two-body smooth repulsive short range potential. We construct a variational state which gives the following upper bound on the ground state energy per particle \[\bar\lim_{ρ\to0} \bar \lim_{L \to \infty, N/L^3 \to ρ} (\frac{e_0(ρ)- 4 πa ρ}{(4 πa)^{5/2}(ρ)^{3/2}})\leq \frac{16}{15π^2}, \] where $a$ is the scattering length of the potential. Previously, an upper bound of the form $C 16/15π^2$ for some constant $C > 1$ was obtained in \cite{ESY}. Our result proves the upper bound of the the prediction by Lee-Yang \cite{LYang} and Lee-Huang-Yang \cite{LHY}.

math-ph↗

arXiv2008

The Ground State Energy of Dilute Bose Gas in Potentials with Positive Scattering Length

The leading term of the ground state energy/particle of a dilute gas of bosons with mass $m$ in the thermodynamic limit is $2π\hbar^2 a ρ/m$ when the density of the gas is $ρ$, the interaction potential is non-negative and the scattering length $a$ is positive. In this paper, we generalize the upper bound part of this result to any interaction potential with positive scattering length, i.e, $a>0$ and the lower bound part to some interaction potentials with shallow and/or narrow negative parts.

math-ph↗

arXiv2007

Ground state energy of the low density Hubbard model

We derive a lower bound on the ground state energy of the Hubbard model for given value of the total spin. In combination with the upper bound derived previously by Giuliani, our result proves that in the low density limit, the leading order correction compared to the ground state energy of a non-interacting lattice Fermi gas is given by $8πa ρ_u ρ_d$, where $ρ_{u(d)}$ denotes the density of the spin-up (down) particles, and $a$ is the scattering length of the contact interaction potential. This result extends previous work on the corresponding continuum model to the lattice case.

math-ph↗

arXiv2007

The Lieb-Liniger Model as a Limit of Dilute Bosons in Three Dimensions

We show that the Lieb-Liniger model for one-dimensional bosons with repulsive $δ$-function interaction can be rigorously derived via a scaling limit from a dilute three-dimensional Bose gas with arbitrary repulsive interaction potential of finite scattering length. For this purpose, we prove bounds on both the eigenvalues and corresponding eigenfunctions of three-dimensional bosons in strongly elongated traps and relate them to the corresponding quantities in the Lieb-Liniger model. In particular, if both the scattering length $a$ and the radius $r$ of the cylindrical trap go to zero, the Lieb-Liniger model with coupling constant $g \sim a/r^2$ is derived. Our bounds are uniform in $g$ in the whole parameter range $0\leq g\leq \infty$, and apply to the Hamiltonian for three-dimensional bosons in a spectral window of size $\sim r^{-2}$ above the ground state energy.

math-ph↗