47,773 research outputs found
On jump-diffusion processes with regime switching: martingale approach
We study jump-diffusion processes with parameters switching at random times.
Being motivated by possible applications, we characterise equivalent martingale
measures for these processes by means of the relative entropy. The minimal
entropy approach is also developed. It is shown that in contrast to the case of
L\'evy processes, for this model an Esscher transformation does not produce the
minimal relative entropy.Comment: 23 pages, 2 figure
Correlations within the Non-Equilibrium Green's Function Method
Non-equilibrium Green's Function (NGF) method is a powerful tool for studying
the evolution of quantum many-body systems. Different types of correlations can
be systematically incorporated within the formalism. The time evolution of the
single-particle Green's functions is described in terms of the Kadanoff-Baym
equations. The current work initially focuses on introducing the correlations
within infinite nuclear matter in one dimension and then in a finite system in
the NGF approach. Starting from the harmonic oscillator Hamiltonian, by
switching on adiabatically the mean-field and correlations simultaneously, a
correlated state with ground-state characteristics is arrived at within the NGF
method. Furthermore the use of cooling to for improving the adiabatic switching
is explored.Comment: Contribution to Proc. 5th Conference on Nuclei and Mesoscopic
Physics, E Lansing, 6-10 March 2017; 9 pages, 8 figure
Quantum properties of the codirectional three-mode Kerr nonlinear coupler
We investigate the quantum properties for the codirectional three-mode Kerr
nonlinear coupler. We investigate single-, two- and three-mode quadrature
squeezing, Wigner function and purity. We prove that this device can provide
richer nonclassical effects than those produced by the conventional coupler,
i.e. the two-mode Kerr coupler. We show that it can provide squeezing and the
quadrature squeezing exhibiting leaf-revival-collapse phenomenon in dependence
on the values of the interaction parameters. In contrast to the conventional
Kerr coupler two different forms of cat states can be simultaneously generated
in the waveguides. We deduce conditions required for the complete
disentanglement between the components of the system.Comment: 23 pages, 6 figure
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