205,291 research outputs found
A moment-equation-copula-closure method for nonlinear vibrational systems subjected to correlated noise
We develop a moment equation closure minimization method for the inexpensive
approximation of the steady state statistical structure of nonlinear systems
whose potential functions have bimodal shapes and which are subjected to
correlated excitations. Our approach relies on the derivation of moment
equations that describe the dynamics governing the two-time statistics. These
are combined with a non-Gaussian pdf representation for the joint
response-excitation statistics that has i) single time statistical structure
consistent with the analytical solutions of the Fokker-Planck equation, and ii)
two-time statistical structure with Gaussian characteristics. Through the
adopted pdf representation, we derive a closure scheme which we formulate in
terms of a consistency condition involving the second order statistics of the
response, the closure constraint. A similar condition, the dynamics constraint,
is also derived directly through the moment equations. These two constraints
are formulated as a low-dimensional minimization problem with respect to
unknown parameters of the representation, the minimization of which imposes an
interplay between the dynamics and the adopted closure. The new method allows
for the semi-analytical representation of the two-time, non-Gaussian structure
of the solution as well as the joint statistical structure of the
response-excitation over different time instants. We demonstrate its
effectiveness through the application on bistable nonlinear
single-degree-of-freedom energy harvesters with mechanical and electromagnetic
damping, and we show that the results compare favorably with direct Monte-Carlo
Simulations
Higher order nonclassicalities of finite dimensional coherent states: A comparative study
Conventional coherent states (CSs) are defined in various ways. For example,
CS is defined as an infinite Poissonian expansion in Fock states, as displaced
vacuum state, or as an eigenket of annihilation operator. In the infinite
dimensional Hilbert space, these definitions are equivalent. However, these
definitions are not equivalent for the finite dimensional systems. In this
work, we present a comparative description of the lower- and higher-order
nonclassical properties of the finite dimensional CSs which are also referred
to as qudit CSs (QCSs). For the comparison, nonclassical properties of two
types of QCSs are used: (i) nonlinear QCS produced by applying a truncated
displacement operator on the vacuum and (ii) linear QCS produced by the
Poissonian expansion in Fock states of the CS truncated at (d-1)-photon Fock
state. The comparison is performed using a set of nonclassicality witnesses
(e.g., higher order antiubunching, higher order sub-Poissonian statistics,
higher order squeezing, Agarwal-Tara parameter, Klyshko's criterion) and a set
of quantitative measures of nonclassicality (e.g., negativity potential,
concurrence potential and anticlassicality). The higher order nonclassicality
witness have found to reveal the existence of higher order nonclassical
properties of QCS for the first time.Comment: A comparative description of the higher-order nonclassical properties
of the finite dimensional coherent state
Higher order nonclassicalities in a codirectional nonlinear optical coupler: Quantum entanglement, squeezing and antibunching
Higher order nonclassical properties of fields propagating through a
codirectional asymmetric nonlinear optical coupler which is prepared by
combining a linear wave guide and a nonlinear (quadratic) wave guide operated
by second harmonic generation are studied. A completely quantum mechanical
description is used here to describe the system. Closed form analytic solutions
of Heisenberg's equations of motion for various modes are used to show the
existence of higher order antibunching, higher order squeezing, higher order
two-mode and multi-mode entanglement in the asymmetric nonlinear optical
coupler. It is also shown that nonclassical properties of light can transfer
from a nonlinear wave guide to a linear wave guide.Comment: 9 pages 5 figure
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