Fernando Galve — Page 3

arXiv2008

Optimal nonequilibrium entanglement of nanomechanical oscillators

We investigate nonequilibrium entanglement generation in a chain of harmonic oscillators with time-dependent linear coupling. We use optimal control theory to determine the coupling modulation that leads to maximum logarithmic negativity for a pair of opposite oscillators and show that it corresponds to a synchronization of the eigenmodes of the chain. We further analytically relate the maximum attainable entanglement to the irreversible work done to produce it, thus bridging nonequilibrium entanglement production and nonequilibrium thermodynamics.

quant-ph↗

arXiv2000

Inequalities for the Gamma Function and estimates for the volume of sections of $B_p^n$

We consider $k$-dimensional central sections of the unit ball of $\ell_p^n$ (denoted $B_p^n$) and we prove that their volume are bounded by the volume of $B_p^n$ whenever $1<p<2$ and $1\le k\le (n-1)/2$ or $k=n-1$. We also consider $0<p<1$ and other cases. We obtain sharp inequalities involving Gamma Function in order to get these results.

math.FA↗