Bernardo Spagnolo, Università di Palermo #
Fluctuations and nonlinearity in classical and quantum systems #
The role of interplay between noise sources and nonlinearity is 
investigated in three different
classical and quantum systems.
(i) The role of a non-Gaussian Lévy noise on the nonlinear 
transient 
dynamics of a short
overdamped Josephson junction is analyzed. The mean escape time of the 
junction is investigated
considering Gaussian, Cauchy-Lorentz and 
Lévy-Smirnov probability 
distributions of the noise
signals. In these conditions we find resonant activation and the first 
evidence of noise enhanced
stability in a metastable system in the presence of
Lévy
 noise. For 
Cauchy-Lorentz noise source,
trapping phenomena and power law dependence on the noise intensity are 
observed.
(ii) The phenomena of dissonance and consonance in a simple auditory 
sensory model composed
of three neurons are considered. Two of them, here so-called sensory 
neurons, are driven by noise
and subthreshold periodic signals with different ratio of frequencies, and 
its outputs plus noise are
applied synaptically to a third neuron, so-called interneuron. We propose 
a theoretical analysis
with a probabilistic approach to investigate the interspike intervals 
(ISI) statistics of the spike train
generated by the interneuron. We find that at the output of the 
interneuron, inharmonious signals
give rise to blurry spike trains, while the harmonious signals produce 
more regular, less noisy, spike
trains. Theoretical results are compared with numerical simulations.
(iii) Finally the dynamics of a quantum particle subject to an asymmetric 
bistable potential and
interacting with a thermal reservoir is investigated. We obtain the time 
evolution of the population
distributions in the position eigenstates of the particle, for different 
values of the coupling strength
with the thermal bath. The calculation is carried out by using the 
Feynman-Vernon functional under
the discrete variable representation.