Santa Monica College

output

20092021

most citedElectron coherent and incoherent pairing instabilities in inhomogeneous bipartite and nonbipartite nanoclusters

24 citations

researchers with a paper here

collaborating institutions

7 papers

math.NT2021★ 1 cited

On the reciprocal sum of lcm of k-tuples

Sungjin Kim

We prove that the reciprocal sum $S_{k} (x)$ of the least common multiple of $k \geq 3$ positive integers in $N \cap [1, x]$ satisfies $S_{k} (x) = P_{2^{k} - 1} (lo g x) + O (x^{- θ_{k} + ε})$ where…

cond-mat.stat-mech2020

A real-space renormalization-group calculation for the quantum Z_2 gauge theory on a square lattice

Steve T. Paik

We revisit Fradkin and Raby's real-space renormalization-group method to study the quantum Z_2 gauge theory defined on links forming a two-dimensional square lattice. Following an…

quant-ph2017★ 5 cited

Teaching renormalization, scaling, and universality with an example from quantum mechanics

Steve T. Paik

We discuss the quantum mechanics of a particle restricted to the half-line $x > 0$ with potential energy $V = α / x^{2}$ for $- 1/4 < α < 0$ . It is known that two scale-invariant theorie…

math.NT2016

The average number of divisors of the Euler function

Sungjin Kim

The upper bound and the lower bound of average numbers of divisors of Euler Phi function and Carmichael Lambda function are obtained by Luca and Pomerance (see \cite{LP}). We impro…

math.NT2015

Explicit constants in averages involving the multiplicative order

Sungjin Kim

Let $a > 1$ . Denote by $l_{a} (p)$ the multiplicative order of $a$ modulo $p$ . We look for an estimate of sum of $\frac{l _{a} ( p )}{p - 1}$ over primes $p \leq x$ on average. When we average o…

physics.class-ph2013★ 10 cited

Is the mean free path the mean of a distribution?

Steve T. Paik

We bring attention to the fact that Maxwell's mean free path for a dilute hard-sphere gas in thermal equilibrium, $(2 σ n)^{- 1}$ , which is ordinarily obtained by multiplying t…