arXiv subjects
Publications and source records attributed to Pierre Levy-Bruhl.
For a class of infinite lattices of interacting anharmonic oscillators, we study the existence of the dynamics, together with Lieb-Robinson bounds, in a suitable algebra of observables
We prove some estimations of the correlation of two local observables in quantum spin systems (with Schrödinger equations) at large temperature. For that, we describe the heat kernel of the Hamiltonian for a finite subset of the lattice, allowing the dimension to tend to infinity. This is an improved version of an earlier unpublished manuscript.
We give an estimate of the number $N(λ)$ of eigenvalues $<λ$ for the image under an irreducible representation of the ``sublaplacian'' on a stratified nilpotent Lie algebra. We also give an estimate for the trace of the heat-kernel associated with this operator. The estimates are formulated in term of geometrical objects related to the representation under consideration. An important particular case is the Schrödinger equation with polynomial electrical and magnetical fields.