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Solving the three-body bound-state Bethe-Salpeter equation in Minkowski space
The scalar three-body Bethe-Salpeter equation, with zero-range interaction,
is solved in Minkowski space by direct integration of the four-dimensional
integral equation. The singularities appearing in the propagators are treated
properly by standard analytical and numerical methods, without relying on any
ansatz or assumption. The results for the binding energies and transverse
amplitudes are compared with the results computed in Euclidean space. A fair
agreement between the calculations is found.Comment: 10 pages, 2 figures, version accepted for publication in Phys. Lett.
Non-centro-symmetric superconductors Li2Pd3B and Li2(Pd0.8Pt0.2)3B: amplitude and phase fluctuations analysis of the experimental magnetization data
We report on magnetization data obtained as a function of temperature and
magnetic field in Li2 (Pd0.8Pt0.2)3B and Li2Pd3B non-centro-symmetric
superconductors. Reversible magnetization curves were plotted as M1/2 vs. T.
This allows study of the asymptotic behavior of the averaged order parameter
amplitude (gap) near the superconducting transition. Results of the analysis
show, as expected, a mean field superconducting transition for Li2Pd3B. On
contrary, a large deviation from the mean field behavior is revealed for
Li2(Pd0.8Pt0.2)3B. This is interpreted as due to the strength of the non s-wave
spin-triplet pairing in this Pt-containing compound which produces nodes in the
order parameter and consequently, phase fluctuations. The diamagnetic signal
above Tc(H) in Li2Pd3B is well explained by superconducting Gaussian
fluctuations, which agrees with the observed mean field transition. For
Li2(Pd0.8Pt0.2)3B the diamagnetic signal above Tc(H) is much higher than the
expected Gaussian values and appears to be well explained by three dimensional
critical fluctuations of the lowest-Landau-level type, which somehow agrees
with the scenario of a phase mediated transition.Comment: 7 pages (1 column) 3 figure
Onset of phase correlations in YBa2Cu3O{7-x} as determined from reversible magnetization measurements
Isofield magnetization curves are obtained and analyzed for three single
crystals of YBa2Cu3O{7-x}, ranging from optimally doped to very underdoped, as
well as the BCS superconductor Nb, in the presence of magnetic fields applied
both parallel and perpendicular to the planes. Near Tc, the magnetization
exhibits a temperature dependence \sqrt{M} [Ta(H)-T]^m. In accordance with
recent theories, we associated Ta(H) with the onset of coherent phase
fluctuations of the superconducting order parameter. For Nb and optimally doped
YBaCuO, Ta(H) is essentially identical to the mean-field transition line Tc(H).
The fitting exponent m=0.5 takes its mean-field value for Nb, and varies just
slightly from 0.5 for optimally doped YBaCuO. However, underdoped YBCO samples
exhibit anomalous behavior, with Ta(H)>Tc for H applied parallel to the c axis,
suggesting that the magnetization is probing a region of temperatures above Tc
where phase correlations persist. In this region, the fitting exponent falls in
the range 0.5 < m < 0.8 for H\parallel c, compared with m~0. for $H\parallel ab
planes. The results are interpreted in terms of an anisotropic pairing symmetry
of the order parameter: d-wave along the ab planes and s-wave along the c axis.Comment: 5 pages, 4 figure
Three-body bound states with zero-range interaction in the Bethe-Salpeter approach
The Bethe-Salpeter equation for three bosons with zero-range interaction is
solved for the first time. For comparison the light-front equation is also
solved. The input is the two-body scattering length and the outputs are the
three-body binding energies, Bethe-Salpeter amplitudes and light-front wave
functions. Three different regimes are analyzed: ({\it i}) For weak enough
two-body interaction the three-body system is unbound. ({\it ii}) For stronger
two-body interaction a three-body bound state appears. It provides an
interesting example of a deeply bound Borromean system. ({\it iii}) For even
stronger two-body interaction this state becomes unphysical with a negative
mass squared. However, another physical (excited) state appears, found
previously in light-front calculations. The Bethe-Salpeter approach implicitly
incorporates three-body forces of relativistic origin, which are attractive and
increase the binding energy.Comment: 13 pages, 7 figure
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