64 research outputs found
Quantum Entanglement and fixed point Hopf bifurcation
We present the qualitative differences in the phase transitions of the
mono-mode Dicke model in its integrable and chaotic versions. We show that a
first order phase transition occurs in the integrable case whereas a second
order in the chaotic one. This difference is also reflected in the classical
limit: for the integrable case the stable fixed point in phase space suffers a
bifurcation of Hopf type whereas for the second one a pitchfork type
bifurcation has been reported
Classical bifurcations and entanglement in smooth Hamiltonian system
We study entanglement in two coupled quartic oscillators. It is shown that
the entanglement, as measured by the von Neumann entropy, increases with the
classical chaos parameter for generic chaotic eigenstates. We consider certain
isolated periodic orbits whose bifurcation sequence affects a class of quantum
eigenstates, called the channel localized states. For these states, the
entanglement is a local minima in the vicinity of a pitchfork bifurcation but
is a local maxima near a anti-pitchfork bifurcation. We place these results in
the context of the close connections that may exist between entanglement
measures and conventional measures of localization that have been much studied
in quantum chaos and elsewhere. We also point to an interesting near-degeneracy
that arises in the spectrum of reduced density matrices of certain states as an
interplay of localization and symmetry.Comment: 7 pages, 6 figure
From travelling waves to mild chaos: a supercritical bifurcation cascade in pipe flow
We study numerically a succession of transitions in pipe Poiseuille flow that
leads from simple travelling waves to waves with chaotic time-dependence. The
waves at the origin of the bifurcation cascade possess a shift-reflect symmetry
and are both axially and azimuthally periodic with wave numbers {\kappa} = 1.63
and n = 2, respectively. As the Reynolds number is increased, successive
transitions result in a wide range of time dependent solutions that includes
spiralling, modulated-travelling, modulated-spiralling,
doubly-modulated-spiralling and mildly chaotic waves. We show that the latter
spring from heteroclinic tangles of the stable and unstable invariant manifolds
of two shift-reflect-symmetric modulated-travelling waves. The chaotic set thus
produced is confined to a limited range of Reynolds numbers, bounded by the
occurrence of manifold tangencies. The states studied here belong to a subspace
of discrete symmetry which makes many of the bifurcation and path-following
investigations presented technically feasible. However, we expect that most of
the phenomenology carries over to the full state-space, thus suggesting a
mechanism for the formation and break-up of invariant states that can sustain
turbulent dynamics.Comment: 38 pages, 35 figures, 1 tabl
Comparative exploration on bifurcation behavior for integer-order and fractional-order delayed BAM neural networks
In the present study, we deal with the stability and the onset of Hopf bifurcation of two type delayed BAM neural networks (integer-order case and fractional-order case). By virtue of the characteristic equation of the integer-order delayed BAM neural networks and regarding time delay as critical parameter, a novel delay-independent condition ensuring the stability and the onset of Hopf bifurcation for the involved integer-order delayed BAM neural networks is built. Taking advantage of Laplace transform, stability theory and Hopf bifurcation knowledge of fractional-order differential equations, a novel delay-independent criterion to maintain the stability and the appearance of Hopf bifurcation for the addressed fractional-order BAM neural networks is established. The investigation indicates the important role of time delay in controlling the stability and Hopf bifurcation of the both type delayed BAM neural networks. By adjusting the value of time delay, we can effectively amplify the stability region and postpone the time of onset of Hopf bifurcation for the fractional-order BAM neural networks. Matlab simulation results are clearly presented to sustain the correctness of analytical results. The derived fruits of this study provide an important theoretical basis in regulating networks
Analysis of quantum phase transition in some different Curie-Weiss models: a unified approach
A unified approach to the analysis of quantum phase transitions in some
different Curie-Weiss models is proposed such that they are treated and
analyzed under the same general scheme. This approach takes three steps:
balancing the quantum Hamiltonian by an appropriate factor, rewriting the
Hamiltonian in terms of operators only, and obtention of a classical
Hamiltonian. operators are obtained from creation and annihilation
operators as linear combinations in the case of fermions and as an inverse
Holstein-Primakoff transformation in the case of bosons. This scheme is
successfully applied to Lipkin, pairing, Jaynes-Cummings, bilayer, and
Heisenberg models.Comment: 24 pages, 6 figures, submitted for publication on August 29, 2017
Some errors concerning the Jaynes-Cummings model need to be fixe
Quantum correlations and synchronization measures
The phenomenon of spontaneous synchronization is universal and only recently
advances have been made in the quantum domain. Being synchronization a kind of
temporal correlation among systems, it is interesting to understand its
connection with other measures of quantum correlations. We review here what is
known in the field, putting emphasis on measures and indicators of
synchronization which have been proposed in the literature, and comparing their
validity for different dynamical systems, highlighting when they give similar
insights and when they seem to fail.Comment: book chapter, 18 pages, 7 figures, Fanchini F., Soares Pinto D.,
Adesso G. (eds) Lectures on General Quantum Correlations and their
Applications. Quantum Science and Technology. Springer (2017
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