arXiv subjects

Jinyeop Lee

Publications and source records attributed to Jinyeop Lee.

26 records · Page 2Linked to original sources

arXiv2021

Rate of convergence towards mean-field evolution for weakly interacting bosons with singular three-body interactions

In this paper, we investigate the dynamics of a system of $N$ weakly interacting bosons with singular three-body interactions in three dimensions. By assuming factorized initial data $Ψ_{N,0}=φ_{0}^{\otimes N}$ and triple collisions, we prove that in the many-particle limit, its mean-field approximation converges to quintic Hartree dynamics. Moreover, we prove that the rate of convergence towards the mean-field quintic Hartree evolution is of $O(N^{-(1+4a)/(3+2a)})$ for $φ_{0}\in H^{(3/2)+a}(\mathbb{R}^{3})$ where $0\leq a<1/2$ and $O(N^{-1})$ for $a>1$. Our proof is based on and extends the Fock space approach.

math-ph↗

arXiv2021

Real eigenvalues of elliptic random matrices

We consider the real eigenvalues of an $(N \times N)$ real elliptic Ginibre matrix whose entries are correlated through a non-Hermiticity parameter $τ_N\in [0,1]$. In the almost-Hermitian regime where $1-τ_N=Θ(N^{-1})$, we obtain the large-$N$ expansion of the mean and the variance of the number of the real eigenvalues. Furthermore, we derive the limiting empirical distributions of the real eigenvalues, which interpolate the Wigner semicircle law and the uniform distribution, the restriction of the elliptic law on the real axis. Our proofs are based on the skew-orthogonal polynomial representation of the correlation kernel due to Forrester and Nagao.

math.PR↗

arXiv2019

Rate of convergence towards equations of Hartree type for mixture condensates with factorized initial data

We consider a system of $p$ components of bosons, each of which consists of $N_{1},N_{2},\dots,N_{p}$ particles, respectively. The bosons are in three dimensions with interactions via a generalized interaction potential which includes the Coulomb interaction. We set the initial condition to describe a mixture condensate, i.e., a tensor product of factorized states. We show that the difference between the many-body Schrödinger evolution in the mean-field regime and the corresponding $p$-particle dynamics due to a system of Hartree equation is $O(N^{-1})$ where $N=\sum_{q=1}^{p}N_{q}$.

math-ph↗

arXiv2019

On the time dependence of the rate of convergence towards Hartree dynamics for interacting Bosons

We consider interacting $N$-Bosons in three dimensions. It is known that the difference between the many-body Schrödinger evolution in the mean-field regime and the corresponding Hartree dynamics is of order $1/N$. We investigate the time dependence of the difference. To have sub-exponential bound, we use the results of time decay estimate for small initial data. We also refine time dependent bound for singular potential using Strichartz estimate. We consider the interaction potential $V(x)$ of type $λ\exp(-μ|x|)|x|^{-γ}$ for $λ\in\mathbb{R}$, $μ\geq0$, and $0<γ<3/2$, which covers the Coulomb and Yukawa interaction.

math-ph↗

arXiv2018

Applicability of the interface spring model for micromechanical analyses with interfacial imperfections to predict the modified exterior Eshelby tensor and effective modulus

Closed-form solutions for the modified exterior Eshelby tensor, strain concentration tensor, and effective moduli of particle-reinforced composites are presented when the interfacial damage is modeled as a linear spring layer of vanishing thickness; the solutions are validated against finite element analyses. Based on the closed-form solutions, the applicability of the interface spring model is tested by calculating those quantities using finite element analysis (FEA) augmented with a matrix-inhomogeneity non-overlapping condition. The results indicate that the interface spring model reasonably captures the characteristics of the stress distribution and effective moduli of composites, despite its well-known problem of unphysical overlapping between the matrix and inhomogeneity.

cond-mat.other↗

arXiv2018

Modified Eshelby tensor for an anisotropic matrix with interfacial damage

We derive a simple tensor algebraic expression of the modified Eshelby tensor for a spherical inclusion embedded in an arbitrarily anisotropic matrix in terms of three tensor quantities (the 4th order identity tensor, the elastic stiffness tensor, and the Eshelby tensor) and two scalar quantities (the inclusion radius and interfacial spring constant), when the interfacial damage is modelled as a linear-spring layer of vanishing thickness. We validate the expression for a triclinic crystal involving 21 independent elastic constants against finite element analysis (FEA).

cond-mat.other↗

arXiv2018

A micromechanics-based analytical solution for the effective thermal conductivity of composites with orthotropic matrices and interfacial thermal resistance

We obtained an analytical solution for the effective thermal conductivity of composites composed of orthotropic matrices and spherical inhomogeneities with interfacial thermal resistance using a micromechanics-based homogenization. We derived the closed form of a modified Eshelby tensor as a function of the interfacial thermal resistance. We then predicted the heat flux of a single inhomogeneity in the infinite media based on the modified Eshelby tensor, which was validated against the numerical results obtained from the finite element analysis. Based on the modified Eshelby tensor and the localization tensor accounting for the interfacial resistance, we derived an analytical expression for the effective thermal conductivity tensor for the composites by a mean-field approach called the Mori-Tanaka method. Our analytical prediction matched very well with the effective thermal conductivity obtained from finite element analysis with up to 10% inhomogeneity volume fraction.

cond-mat.mtrl-sci↗

arXiv2018

Rate of Convergence towards Hartree Dynamics with Singular Interaction Potential

We consider a system of $N$-Bosons with a two-body interaction potential $V \in L^2(\mathbb{R}^3)+L^\infty(\mathbb{R}^3)$, possibly singular than the Coulomb interaction. We show that, with $H^1(\mathbb{R}^3)$ initial data, the difference between the many-body Schrödinger evolution in the mean-field regime and the corresponding Hartree dynamics is of order $1/N$, for any fixed time. The $N$-dependence of the bound is optimal.

math-ph↗