Resonant tunneling in a system with correlated pure point spectrum

Resonant multilead point-contact tunneling

We analyze a model of resonant point-contact tunneling between multiple Luttinger-liquid leads. The model is a variant of the multichannel Kondo model and can be related to the quantum Brownian motion of a particle on lattices with p flux through each plaquette ~in the three-lead case, it is a honeycomb lattice with p flux!. By comparing the perturbative and instanton gas expansions, we find a ...

A Floquet Operator with Pure Point Spectrum and Energy Instability

It is not immediate whether a self-adjoint operator H with purely point spectrum implies absence of transport under the time evolution U(t) = e−iHt; in fact, it is currently known examples of Schrödinger operators with such kind of spectrum and transport. In case of tight-binding models on l2(IN) the transport is usually probed by the moments of order m > 0 of the position operator Xek = kek, t...

On quantum integrability and Hamiltonians with pure point spectrum

We prove that any n-dimensional Hamiltonian operator with pure point spectrum is completely integrable via self-adjoint first integrals. Furthermore, we establish that given any closed set Σ ⊂ R there exists an integrable n-dimensional Hamiltonian which realizes it as its spectrum. We develop several applications of these results and discuss their implications in the general framework of quantu...

Weakly Regular Floquet Hamiltonians with Pure Point Spectrum

We study the Floquet Hamiltonian −i∂t + H + V (ωt), acting in L([ 0, T ],H, dt), as depending on the parameter ω = 2π/T . We assume that the spectrum of H in H is discrete, Spec(H) = {hm}m=1, but possibly degenerate, and that t 7→ V (t) ∈ B(H) is a 2π-periodic function with values in the space of Hermitian operators on H. Let J > 0 and set Ω0 = [ 89J, 98J ]. Suppose that for some σ > 0 it holds...

Resonant tunneling in a pulsed phonon field