Search results for " Nonlinear"

showing 10 items of 1224 documents

Kac-Moody group representations and generalization of the Sugawara construction of the Virasoro algebra

1988

We discuss the dynamical structure of the semidirect product of the Virasoro and affine Kac-Moody groups within the framework of a group quantization formalism. This formalism provides a realization of the Virasoro algebra acting on Kac-Moody Fock states which generalizes the Sugawara construction. We also give an explicit construction of the standard Kac-Moody group representations associated with strings on SU(2) and recover, in particular, the ‘renormalization’ β factor of L(z)

Quantum affine algebraPure mathematicsSemidirect productCurrent algebraStatistical and Nonlinear PhysicsUniversal enveloping algebraGroup algebraN = 2 superconformal algebraAlgebraHigh Energy Physics::TheoryMathematics::Quantum AlgebraAlgebra representationVirasoro algebraMathematics::Representation TheoryMathematical PhysicsMathematicsLetters in Mathematical Physics
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Algebraic quantization on a group and nonabelian constraints

1989

A generalization of a previous group manifold quantization formalism is proposed. In the new version the differential structure is circumvented, so that discrete transformations in the group are allowed, and a nonabelian group replaces the ordinary (central)U(1) subgroup of the Heisenberg-Weyl-like quantum group. As an example of the former we obtain the wave functions associated with the system of two identical particles, and the latter modification is used to account for the Virasoro constraints in string theory.

Quantum group58D30Differential structureStatistical and Nonlinear PhysicsString theoryAlgebra58F0622E7081D07Operator algebraUnitary group81E30Algebraic numberQuantum field theoryMathematical PhysicsIdentical particlesMathematicsCommunications in Mathematical Physics
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Influence of pump coherence on the dynamic behavior of a laser

1988

The dynamic behavior of a coherently pumped single-mode unidirectional ring laser with a homogeneously broadened three-level active medium is studied. Our formulation is based on a set often real equations of the plane-wave, mean-field Maxwell–Bloch type. The instability domain in the main control parameters space is determined. Our numerical study of these equations for a parameter range of the type explored in the recent experiments by Weiss Brock [ Phys. Rev. Lett.57, 2804 ( 1986)] reveals some similarities, but striking differences between our theoretical predictions and their experimental observations are also noted.

Quantum opticsPhysicsDynamical systems theorybusiness.industryNonlinear opticsStatistical and Nonlinear PhysicsRing laserLaserInstabilityAtomic and Molecular Physics and Opticslaw.inventionOptical pumpingOpticslawQuantum electrodynamicsbusinessCoherence (physics)Journal of the Optical Society of America B
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Dynamic effects in nonlinear magneto-optics of atoms and molecules: review

2004

A brief review is given of topics relating to dynamical processes arising in nonlinear interactions between light and resonant systems (atoms or molecules) in the presence of a magnetic field.

Quantum opticsPhysicsZeeman effectCondensed matter physicsAtomic Physics (physics.atom-ph)business.industryAtoms in moleculesFOS: Physical sciencesNonlinear opticsStatistical and Nonlinear PhysicsAtomic and Molecular Physics and OpticsPhysics - Atomic PhysicsMagnetic fieldNonlinear systemsymbols.namesakeOpticsQuantum beatssymbolsbusinessMagnetoJournal of the Optical Society of America B
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Quantum repulsive Nonlinear Schrödinger models and their ‘Superconductivity’

1995

Abstract The fundamental role played by the quantum repulsive Nonlinear Schrodinger (NLS) equation in the evolution of our understanding of the phenomenon of superconductivity in appropriate metals at very low temperatures is surveyed. The first major work was that in 1947 by N. N. Bogoliubov, who studied the very physical 3-space-dimensions problem and super fluidity; and the survey takes the form of an actual dedication to that outstanding scientist who died four years ago. The 3-space-dimensions NLS equation is not integrable either classically or quantum mechanically. But a number of recently discovered closely related lattices in one space dimension (one space plus one time dimension) …

Quantum phase transitionPhysicsGeneral MathematicsApplied MathematicsQuantum dynamicsGeneral Physics and AstronomyStatistical and Nonlinear Physicssymbols.namesakeTheoretical physicsQuantum mechanicsQuantum processsymbolsQuantum operationQuantum inverse scattering methodQuantum dissipationQuantumSchrödinger's catChaos, Solitons & Fractals
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Parametric self-trapping in the presence of randomized quasi phase matching

2010

We report on experimental evidence of parametric spatial solitons in a quadratic crystal with randomized periodic ferroelectric poling. Two-color self-focusing via quadratic cascading overcomes the diffractive nature of both fundamental and frequency-doubled beams.

Quasi-phase-matchingAnderson localizationNonlinear opticsSpatial solitons01 natural sciences010309 opticsQuadratic equationOpticsdisordered systems0103 physical sciencescomplex systems; disordered systems; nonlinear optics; nonlinear waves; second harmonic generation; solitonssolitonscomplex systems010306 general physicsParametric statisticsPhysicsComputer simulationsecond harmonic generationbusiness.industryPolingParametric processesnonlinear wavesFerroelectricityAtomic and Molecular Physics and OpticsbusinessRefractive indexSpatial solitons Nonlinear optics Parametric processesOptics Letters
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Ultraviolet quasi-phase-matched second harmonic generation in surface periodically poled lithium niobate optical waveguides

2007

The compatibility of low concentration (alpha-phase) proton exchange channel waveguides with electric field surface periodic poling of congruent lithium niobate (SPPLN) crystals has been experimentally demonstrated. With such waveguides, we obtained ultraviolet second harmonic generation (SHG) by first order quasi-phase-matching (QPM), a result made possible by the fabrication, on Z-cut LN crystals, of periodic structures with a pitch down to 750 nm. Nonlinear copropagating QPM-SHG measurements have been carried out on such structures. The pump source was a Ti:sapphire laser with a tunability range of 700-980 nm and a 40 GHz linewidth. We have measured UV continuous wave light at 390 nm by …

Quasi-phase-matchingMaterials sciencebusiness.industryLithium niobateSecond-harmonic generationNonlinear opticsCondensed Matter PhysicsLaserIndustrial and Manufacturing EngineeringAtomic and Molecular Physics and Opticslaw.inventionQPM SHG PPLN Optical Waveguides Nonlinear Opticschemistry.chemical_compoundLaser linewidthOpticschemistryPeriodic polinglawContinuous wavebusinessInstrumentationLaser Physics
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Growth, percolation, and correlations in disordered fiber networks

1997

This paper studies growth, percolation, and correlations in disordered fiber networks. We start by introducing a 2D continuum deposition model with effective fiber-fiber interactions represented by a parameter $p$ which controls the degree of clustering. For $p=1$, the deposited network is uniformly random, while for $p=0$ only a single connected cluster can grow. For $p=0$, we first derive the growth law for the average size of the cluster as well as a formula for its mass density profile. For $p>0$, we carry out extensive simulations on fibers, and also needles and disks to study the dependence of the percolation threshold on $p$. We also derive a mean-field theory for the threshold ne…

Random graphPhysicsStatistical Mechanics (cond-mat.stat-mech)Degree (graph theory)Continuum (topology)FOS: Physical sciencesPair distribution functionStatistical and Nonlinear PhysicsPercolation threshold01 natural sciences010305 fluids & plasmasCorrelation function (statistical mechanics)Percolation0103 physical sciencesCluster (physics)Statistical physics010306 general physicsCondensed Matter - Statistical MechanicsMathematical Physics
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COST 241 intercomparison of nonlinear refractive index measurements in dispersion shifted optical fibres at =1550 nm

1997

COST 241 measurements of the nonlinear refractive index, n/sub 2/, exhibit a large scatter depending on the specific measurement technique. This is largely due to the electrostrictive contribution to the Kerr nonlinearity, as is revealed by the resonant behaviour of n/sub 2/ (with peak values up to 3.9 10/sup -20/ m/sup 2/ W/sup -1/) observed with signal modulation frequencies in the 0.11 GHz range.

Range (particle radiation)Optical fiberMaterials scienceElectrostrictionKerr nonlinearitybusiness.industrySignal modulationResonanceNonlinear refractive indexlaw.inventionOpticslawDispersion (optics)Electrical and Electronic EngineeringAtomic physicsbusinessElectronics Letters
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AKNS and NLS hierarchies, MRW solutions, $P_n$ breathers, and beyond

2018

We describe a unified structure of rogue wave and multiple rogue wave solutions for all equations of the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy and their mixed and deformed versions. The definition of the AKNS hierarchy and its deformed versions is given in the Sec. II. We also consider the continuous symmetries of the related equations and the related spectral curves. This work continues and summarises some of our previous studies dedicated to the rogue wave-like solutions associated with AKNS, nonlinear Schrodinger, and KP hierarchies. The general scheme is illustrated by the examples of small rank n, n ⩽ 7, rational or quasi-rational solutions. In particular, we consider rank-2 and …

Rank (linear algebra)BreatherStructure (category theory)Statistical and Nonlinear PhysicsWave equation01 natural sciences010305 fluids & plasmasNonlinear systemsymbols.namesakeNonlinear Sciences::Exactly Solvable and Integrable Systems[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]0103 physical sciencesHomogeneous spacesymbolsRogue wave010306 general physicsNonlinear Sciences::Pattern Formation and SolitonsMathematical PhysicsSchrödinger's catMathematicsMathematical physics
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