Search results for "Integrable system"
showing 10 items of 354 documents
Linear confinement in momentum space: singularity-free bound-state equations
2014
Relativistic equations of Bethe-Salpeter type for hadron structure are most conveniently formulated in momentum space. The presence of confining interactions causes complications because the corresponding kernels are singular. This occurs not only in the relativistic case but also in the nonrelativistic Schr\"odinger equation where this problem can be studied more easily. For the linear confining interaction the singularity reduces to one of Cauchy principal value form. Although this singularity is integrable, it still makes accurate numerical solutions difficult. We show that this principal value singularity can be eliminated by means of a subtraction method. The resulting equation is much…
Momentum space integral equations for three charged particles: Nondiagonal kernels
2000
Standard solution methods are known to be applicable to Faddeev-type momentum space integral equations for three-body transition amplitudes, not only for purely short-range interactions but also, after suitable modifications, for potentials possessing Coulomb tails provided the total energy is below the three-body threshold. For energies above that threshold, however, long-range Coulomb forces have been suspected to give rise to such severe singularities in the kernels, even of the modified equations, that their compactness properties are lost. Using the rigorously equivalent formulation in terms of an effective-two-body theory we prove that, for all energies, the nondiagonal kernels occurr…
SUPERFIELDS AND CANONICAL METHODS IN SUPERSPACE
1986
We consider the “supersymmetric roots” of the Heisenberg evolution equation as describing the dynamics of superfields in superspace. We investigate the superfield commutators and their equal time limits and exhibit their noncanonical character even for free superfields. For simplicity, we concentrate on the D=1 case, i.e., the superfield formulation of supersymmetric quantum mechanics in the Heisenberg picture and, as a soluble example, the supersymmetric oscillator. Finally, we express Noether’s theorem in superspace and give the definition of the global conserved supercharges.
Testing the mechanism of R-parity breaking with slepton LSP decays
2003
In supersymmetric models R-parity can be violated through either bilinear or trilinear terms in the superpotential, or both. If charged scalar leptons are the lightest supersymmetric particles, their decay properties can be used to obtain information about the relative importance of these couplings. We show that in some specific scenarios it is even possible to decide whether bilinear or trilinear terms give the dominant contribution to the neutrino mass matrix.
R-parity violating sneutrino decays
2004
R-parity can be violated through either bilinear and/or trilinear terms in the superpotential. The decay properties of sneutrinos can be used to obtain information about the relative importance of these couplings provided sneutrinos are the lightest supersymmetric particles. We show that in some specific scenarios it is even possible to decide whether bilinear or trilinear terms give the dominant contribution to the neutrino mass matrix.
Status and Prospects of Top-Quark Physics
2009
The top quark is the heaviest elementary particle observed to date. Its large mass of about 173 GeV/c^2 makes the top quark act differently than other elementary fermions, as it decays before it hadronises, passing its spin information on to its decay products. In addition, the top quark plays an important role in higher-order loop corrections to standard model processes, which makes the top quark mass a crucial parameter for precision tests of the electroweak theory. The top quark is also a powerful probe for new phenomena beyond the standard model. During the time of discovery at the Tevatron in 1995 only a few properties of the top quark could be measured. In recent years, since the star…
Corrections for positon annihilation in flight in nuclear spectrometry
1973
Abstract Theories of positon single- and two-quanta annihilation in flight, the Fermi beta-decay theory, and theories of positon energy loss are used in calculations of total probabilities of annihilation in flight of positons in continuous spectra. The results are given in a nomogram useful in correcting for positon annihilation in flight in various nuclear-spectrometry experiments. Confirmation of the theoretical basis employed was obtained by comparing total absolute probabilities for annihilation in flight of 62 Cu positons in Perspex, copper, cadmium and lead, using a new differential method. The agreement with the theory was found to be excellent. A method for obtaining “correct” posi…
Kuznetsov-Ma Soliton Dynamics in Nonlinear Fiber Optics
2012
The Kuznetzov-Ma (KM) soliton is a solution of the nonlinear Schrodinger equation derived in 1977 but never observed experimentally. Here we report experiments showing KM soliton dynamics in nonlinear breather evolution in optical fiber.
Spectral incoherent solitons: a localized soliton behavior in the frequency domain
2008
We show both theoretically and experimentally in an optical fiber system that a noninstantaneous nonlinear environment supports the existence of spectral incoherent solitons. Contrary to conventional solitons, spectral incoherent solitons do not exhibit a confinement in the spatiotemporal domain, but exclusively in the frequency domain. The theory reveals that the causality condition inherent to the nonlinear response function is the key property underlying the existence of spectral incoherent solitons. These solitons constitute nonequilibrium stable states of the incoherent field and are shown to be robust with respect to binary collisions.
An exact soliton solution for an averaged dispersion-managed fibre system equation
2001
We consider the nonlinear wave propagation in an averaged dispersion-managed (DM) fibre system. We present the explicit Lax pair with a variable spectral parameter and derive the exact soliton solution using the Backlund transformation. A similar study is also carried out for simultaneous propagation of N nonlinear pulses in the averaged DM fibre system.