arXiv subjects

Sergio Andrés Yuhjtman

Publications and source records attributed to Sergio Andrés Yuhjtman.

2 recordsLinked to original sources

arXiv2015

A sensible estimate for the stability constant of the Lennard-Jones potential

We show that the stability constant of the Lennard-Jones potential in $\mathbb R^3$, $Φ(x)=\lVert x \rVert^{-12}-2 \lVert x \rVert^{-6}$, is smaller than $14.316$. This is remarkably smaller than the best previously known bound. Our method is probably applicable to other similar potentials such as the Morse potentials. We also improve slightly, in the Lennard-Jones case, the lower bound for the minimum interparticle distance of an optimal $n$-particle configuration to $0.684$.

math-ph↗

arXiv2015

The quasi-state space of a C*-algebra is a topological quotient of the representation space

We show that for any C*-algebra $A$, a sufficiently large Hilbert space $H$ and a unit vector $ξ\in H$, the natural application $rep(A:H) \to Q(A)$, $π\mapsto \langle π(-)ξ,ξ\rangle$ is a topological quotient, where $rep(A:H)$ is the space of representations on $H$ and $Q(A)$ the set of quasi-states, i.e. positive linear functionals with norm at most $1$. This quotient might be a useful tool in the representation theory of C*-algebras. We apply it to give an interesting proof of Takesaki-Bichteler duality for C*-algebras which allows to drop a hypothesis.

math.OA↗