The emergence of classical behavior in magnetic adatoms

A wide class of nanomagnets shows striking quantum behavior, known as quantum spin tunneling (QST): instead of two degenerate ground states with opposite magnetizations, a bonding-antibonding pair forms, resulting in a splitting of the ground state doublet with wave functions linear combination of two classically opposite magnetic states, leading to the quenching of their magnetic moment. Here we study how QST is destroyed and classical behavior emerges in the case of magnetic adatoms, as the strength of their coupling, either to the substrate or to each other, is increased. Both spin-substrate and spin-spin coupling renormalize the QST splitting to zero allowing the environmental decoherence to eliminate superpositions between classical states, leading to the emergence of spontaneous magnetization.Comment: 5 pages, 4 figure

Poincare series of collections of plane valuations

In earlier papers there were given formulae for the Poincare series of multi-index filtrations on the ring of germs of functions of two variables defined by collections of valuations corresponding to (reducible) plane curve singularities and by collections of divisorial ones. It was shown that the Poincare series of a collection of divisorial valuations determines the topology of the collection of divisors. Here we give a formula for the Poincare series of a general collection of valuations on the ring of germs of functions of two variables centred at the origin and prove a generalization of the statement that the Poincare series determines the topology of the collection

Continuous-variable phase-estimation with unitary and random linear disturbance

We address the problem of continuous-variable quantum phase estimation in the presence of linear disturbance at the Hamiltonian level, by means of Gaussian probe states. In particular we discuss both unitary and random disturbance, by considering the parameter which characterizes the unwanted linear term present in the Hamiltonian as fixed (unitary disturbance) or random with a given probability distribution (random disturbance). We derive the optimal input Gaussian states at fixed energy, maximizing the quantum Fisher information over the squeezing angle and the squeezing energy fraction, and we discuss the scaling of the quantum Fisher information in terms of the output number of photons $n_{out}$. We observe that in the case of unitary disturbance the optimal state is a squeezed vacuum state and the quadratic scaling is conserved. As regards the random disturbance, we observe that the optimal squeezing fraction may not be equal to one, and, for any non-zero value of the noise parameter, the quantum Fisher information scales linearly with the average number of photons. We finally discuss the performance of homodyne measurement, comparing the achievable precision with the ultimate limit posed by the quantum Cram\'er-Rao bound.Comment: 7 pages, 6 figure