19 research outputs found
Bifurcation structure of two Coupled Periodically driven double-well Duffing Oscillators
The bifurcation structure of coupled periodically driven double-well Duffing
oscillators is investigated as a function of the strength of the driving force
and its frequency . We first examine the stability of the steady
state in linear response, and classify the different types of bifurcation
likely to occur in this model. We then explore the complex behaviour associated
with these bifurcations numerically. Our results show many striking departures
from the behaviour of coupled driven Duffing Oscillators with single
well-potentials, as characterised by Kozlowski et al \cite{k1}. In addition to
the well known routes to chaos already encountered in a one-dimensional Duffing
oscillator, our model exhibits imbricated period-doubling of both types,
symmetry-breaking, sudden chaos and a great abundance of Hopf bifurcations,
many of which occur more than once for a given driving frequency. We explore
the chaotic behaviour of our model using two indicators, namely Lyapunov
exponents and the power spectrum. Poincar\'e cross-sections and phase portraits
are also plotted to show the manifestation of coexisting periodic and chaotic
attractors including the destruction of tori doubling.Comment: 16 pages, 8 figure
Stochastic dissociation of diatomic molecules
The fragmentation of diatomic molecules under a stochastic force is
investigated both classically and quantum mechanically, focussing on their
dissociation probabilities. It is found that the quantum system is more robust
than the classical one in the limit of a large number of kicks. The opposite
behavior emerges for a small number of kicks. Quantum and classical
dissociation probabilities do not coincide for any parameter combinations of
the force. This can be attributed to a scaling property in the classical system
which is broken quantum mechanically.Comment: 5 pages, 1 figure, accepted by J Chem Phy
Femtosecond Photodissociation of Molecules Facilitated by Noise
We investigate the dynamics of diatomic molecules subjected to both a
femtosecond mid-infrared laser pulse and Gaussian white noise. The stochastic
Schr\"odinger equation with a Morse potential is used to describe the molecular
vibrations under noise and the laser pulse. For weak laser intensity, well
below the dissociation threshold, it is shown that one can find an optimum
amount of noise that leads to a dramatic enhancement of the dissociation
probability. The enhancement landscape which is shown as a function of both the
noise and the laser strength, exhibits a global maximum. A frequency-resolved
gain profile is recorded with a pump-probe set-up which is experimentally
realizable. With this profile we identify the linear and nonlinear multiphoton
processes created by the interplay between laser and noise and assess their
relative contribution to the dissociation enhancement.Comment: 5 pages,5 figure
Husimi-Wigner representation of chaotic eigenstates
Just as a coherent state may be considered as a quantum point, its
restriction to a factor space of the full Hilbert space can be interpreted as a
quantum plane. The overlap of such a factor coherent state with a full pure
state is akin to a quantum section. It defines a reduced pure state in the
cofactor Hilbert space. The collection of all the Wigner functions
corresponding to a full set of parallel quantum sections defines the
Husimi-Wigner reresentation. It occupies an intermediate ground between drastic
suppression of nonclassical features, characteristic of Husimi functions, and
the daunting complexity of higher dimensional Wigner functions. After analysing
these features for simpler states, we exploit this new representation as a
probe of numerically computed eigenstates of chaotic Hamiltonians. The
individual two-dimensional Wigner functions resemble those of semiclassically
quantized states, but the regular ring pattern is broken by dislocations.Comment: 21 pages, 7 figures (6 color figures), submitted to Proc. R. Soc.
Dissociation and ionization of small molecules steered by external noise
We show that ionization and dissociation can be influenced separately in a
molecule with appropriate external noise. Specifically we investigate the
hydrogen molecular ion under a stochastic force quantum mechanically beyond the
Born-Oppenheimer approximation. We find that up to 30% of dissociation without
ionization can be achieved by suitably tuning the forcing parameters.Comment: 13 pages, 6 figure
Negativity of the Wigner function as an indicator of nonclassicality
A measure of nonclassicality of quantum states based on the volume of the
negative part of the Wigner function is proposed. We analyze this quantity for
Fock states, squeezed displaced Fock states and cat-like states defined as
coherent superposition of two Gaussian wave packets.Comment: 10 pages, 7 figure