Ferdinando de Pasquale

Noise-induced effects in population dynamics

We investigate the role of noise in the nonlinear relaxation of two ecosystems described by generalized Lotka-Volterra equations in the presence of multiplicative noise. Specifically we study two cases: (i) an ecosystem with two interacting species in the presence of periodic driving; (ii) an ecosystem with a great number of interacting species with random interaction matrix. We analyse the interplay between noise and periodic modulation for case (i) and the role of the noise in the transient dynamics of the ecosystem in the presence of an absorbing barrier in case (ii). We find that the presence of noise is responsible for the generation of temporal oscillations and for the appearance of spatial patterns in the first case. In the other case we obtain the asymptotic behaviour of the time average of the ith population and discuss the effect of the noise on the probability distributions of the population and of the local field.

Two-spin entanglement induced by electron scattering in nanostructures

We present a model where two magnetic impurities in a discrete tight-binding ring become entangled because of scattering processes associated to the injection of a conduction electron. We introduce a weak coupling approximation that allows us to solve the problem in a analytical way and compare the theory with the exact numerical results. We obtain the generation of entanglement both in a deterministic way and in a probabilistic one. The first case is intrinsically related to the structure of the two-impurity reduced density matrix, while the second one occurs when a projection on the electron state is performed.

Conditional sign flip via teleportation

We present a model to realize a probabilistic conditional sign flip gate using only linear optics. The gate operates in the space of number-state qubits and is obtained by a nonconventional use of the teleportation protocol. Both a destructive and a nondestructive version of the gate are presented. In the former case an Hadamard gate on the control qubit is combined with a projective teleportation scheme mixing control and target. The success probability is 1/2. In the latter case we need a quantum encoder realized via the interaction of the control qubit with an ancillary state composed of two maximally entangled photons. The success probability is 1/4.

Faithful state transfer through a quantum channel

We study the possibility of realizing perfect quantum state transfer in mesoscopic devices. We discuss the case of the Fano-Anderson model extended to two impurities. For a channel with an infinite number of degrees of freedom, we obtain coherent behavior in the case of strong coupling or in weak coupling off resonance. For a finite number of degrees of freedom, coherent behavior is associated with weak coupling and resonance conditions. Finite-temperature and disorder effects are discussed.

Double-dot chain as a macroscopic quantum bit

We consider an array of N quantum dot pairs interacting via Coulomb interaction between adjacent dots and hopping inside each pair. We show that at the first order in the ratio of hopping and interaction amplitudes, the array maps in an effective two-level system with energy separation becoming exponentially small in the macroscopic (large-N) limit. Decoherence at zero temperature is studied in the limit of weak coupling with phonons. In this case, the macroscopic limit is robust with respect to decoherence. Some possible applications in quantum information processing are discussed.

NONLINEAR RELAXATION IN POPULATION DYNAMICS

We analyze the nonlinear relaxation of a complex ecosystem composed of many interacting species. The ecological system is described by generalized Lotka-Volterra equations with a multiplicative noise. The transient dynamics is studied in the framework of the mean field theory and with random interaction between the species. We focus on the statistical properties of the asymptotic behaviour of the time integral of the i-th population and on the distribution of the population and of the local field.

Entanglement and disorder: a mean field approach

The entanglement of symmetric mean-field (MF) ground states is studied for systems of finite size. While a bare MF approximation amounts to considering factorized states, the symmetrization allows one to restore an amount of entanglement, which survives if finite systems are considered. For the isotropic XY model in the presence of a random transverse field, we calculated the one-site entanglement entropy, which is zero both for vanishing and maximum disorder and reaches a maximum for an intermediate value of disorder.

A new stochastic representation for the decay from a metastable state

We show that a stochastic process on a complex plane can simulate decay from a metastable state. The simplest application of the method to a model in which the approach to equilibrium occurs through transitions over a potential barrier is discussed. The results are compared with direct numerical simulations of the stochastic differential equations describing systems evolution. We have found that the new method is much more efficient from computational point of view than the direct simulations.