2,840 research outputs found
The higher grading structure of the WKI hierarchy and the two-component short pulse equation
A higher grading affine algebraic construction of integrable hierarchies,
containing the Wadati-Konno-Ichikawa (WKI) hierarchy as a particular case, is
proposed. We show that a two-component generalization of the Sch\" afer-Wayne
short pulse equation arises quite naturally from the first negative flow of the
WKI hierarchy. Some novel integrable nonautonomous models are also proposed.
The conserved charges, both local and nonlocal, are obtained from the Riccati
form of the spectral problem. The loop-soliton solutions of the WKI hierarchy
are systematically constructed through gauge followed by reciprocal B\" acklund
transformation, establishing the precise connection between the whole WKI and
AKNS hierarchies. The connection between the short pulse equation with the
sine-Gordon model is extended to a correspondence between the two-component
short pulse equation and the Lund-Regge model
The algebraic structure behind the derivative nonlinear Schroedinger equation
The Kaup-Newell (KN) hierarchy contains the derivative nonlinear Schr\"
odinger equation (DNLSE) amongst others interesting and important nonlinear
integrable equations. In this paper, a general higher grading affine algebraic
construction of integrable hierarchies is proposed and the KN hierarchy is
established in terms of a Kac-Moody algebra and principal
gradation. In this form, our spectral problem is linear in the spectral
parameter. The positive and negative flows are derived, showing that some
interesting physical models arise from the same algebraic structure. For
instance, the DNLSE is obtained as the second positive, while the Mikhailov
model as the first negative flows, respectively. The equivalence between the
latter and the massive Thirring model is explicitly demonstrated also. The
algebraic dressing method is employed to construct soliton solutions in a
systematic manner for all members of the hierarchy. Finally, the equivalence of
the spectral problem introduced in this paper with the usual one, which is
quadratic in the spectral parameter, is achieved by setting a particular
automorphism of the affine algebra, which maps the homogeneous into principal
gradation.Comment: references adde
Photon blockade induced Mott transitions and XY spin models in coupled cavity arrays
As photons do not interact with each other, it is interesting to ask whether
photonic systems can be modified to exhibit the phases characteristic of
strongly coupled many-body systems. We demonstrate how a Mott insulator type of
phase of excitations can arise in an array of coupled electromagnetic cavities,
each of which is coupled resonantly to a {\em single} two level system
(atom/quantum dot/Cooper pair) and can be individually addressed from outside.
In the Mott phase each atom-cavity system has the same integral number of net
polaritonic (atomic plus photonic) excitations with photon blockade providing
the required repulsion between the excitations in each site. Detuning the
atomic and photonic frequencies suppresses this effect and induces a transition
to a photonic superfluid. We also show that for zero detuning, the system can
simulate the dynamics of many body spin systems.Comment: 4 pages, 3 figure
Emergent electrodynamics from the Nambu model for spontaneous Lorentz symmetry breaking
After imposing the Gauss law constraint as an initial condition upon the
Hilbert space of the Nambu model, in all its generic realizations, we recover
QED in the corresponding non-linear gauge A_{\mu}A^{\mu}=n^{2}M^{2}. Our result
is non-perturbative in the parameter M for n^{2}\neq 0 and can be extended to
the n^{2}=0 case. This shows that in the Nambu model, spontaneous Lorentz
symmetry breaking dynamically generates gauge invariance, provided the Gauss
law is imposed as an initial condition. In this way electrodynamics is
recovered, with the photon being realized as the Nambu-Goldstone modes of the
spontaneously broken symmetry, which finally turns out to be non-observableComment: 17 page
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