arXiv subjects
Publications and source records attributed to Juan Pablo Lopez.
In this work sufficient conditions on the order of the symbol are developed to ensure boundedness, compactness and r-nuclearity of pseudo-differential operators in $\hbar\mathbb{Z}^n$. In addition, these conditions allow us to obtain growth estimates for the eigenvalues of some elliptic operators, in particular perturbed discrete Schrödinger operator.
In the present paper we prove a family of tight upper and lower bounds for the Shannon entropy and von Neumann entropy based on the p-norms. This allows us to have an entropy estimate, a criterion for the finiteness of it and a bound on the difference of entropy, additionally, we did some numerical tests that show the efficiency of our approximations.
We give response to the question: in infinite dimension states,given a state with energy bounded by E, we can write the state as a countable convex combination of pure states with energy bounded by E. We review the Alicki-Fannes-Winter technique to obtain a uniform continuity bound for the von Neumann entropy in states that are a mix of pure states with bounded energy, using this bound we conclude that for a Hamiltonian satisfying the Gibb's hypothesis such states cannot exist.