1,332 research outputs found
New Shape Invariant Potentials in Supersymmetric Quantum Mechanics
Quantum mechanical potentials satisfying the property of shape invariance are
well known to be algebraically solvable. Using a scaling ansatz for the change
of parameters, we obtain a large class of new shape invariant potentials which
are reflectionless and possess an infinite number of bound states. They can be
viewed as q-deformations of the single soliton solution corresponding to the
Rosen-Morse potential. Explicit expressions for energy eigenvalues,
eigenfunctions and transmission coefficients are given. Included in our
potentials as a special case is the self-similar potential recently discussed
by Shabat and Spiridonov.Comment: 8pages, Te
Results and perspectives from T2K on CPV in the neutrino sector
In the T2K long-baseline neutrino oscilliaton experiment, the J-PARC facility is able to produce a high-intensity muon neutrino (antineutrino) beam, which is sent towards the near detector stations (0.28 km) and the far detector Super-Kamiokande (295 km). The change in the measured intensity and the composition of the beam are used to provide information about the oscillation parameters. A simultaneous analysis of the above neutrino and antineutrino mode data sets leads to the first ever sensitivity to the neutrino-sector CPV based on T2K data alone. Also, it gives the most precise T2K measurements of other neutrino oscillation parameters. The proposal of an extension of the currently approved T2K running from 7.8 × 1021 protons on target to 20 × 1021 protons on target and
aiming at the initial observation of CPV with 3σ or higher significance assuming maximum CP violation, is also presented
Quantum depletion of collapsing Bose-Einstein condensates
We perform the first numerical three-dimensional studies of quantum field
effects in the Bosenova experiment on collapsing condensates by E. Donley et
al. [Nature 415, 39 (2002)] using the exact experimental geometry. In a
stochastic truncated Wigner simulation of the collapse, the collapse times are
larger than the experimentally measured values. We find that a finite
temperature initial state leads to an increased creation rate of uncondensed
atoms, but not to a reduction of the collapse time. A comparison of the
time-dependent Hartree-Fock-Bogoliubov and Wigner methods for the more
tractable spherical trap shows excellent agreement between the uncondensed
populations. We conclude that the discrepancy between the experimental and
theoretical values of the collapse time cannot be explained by Gaussian quantum
fluctuations or finite temperature effects.Comment: 9 pages, 4 figures, replaced with published versio
Zipf's law in Multifragmentation
We discuss the meaning of Zipf's law in nuclear multifragmentation. We remark
that Zipf's law is a consequence of a power law fragment size distribution with
exponent . We also recall why the presence of such distribution
is not a reliable signal of a liquid-gas phase transition
Ballistic deposition patterns beneath a growing KPZ interface
We consider a (1+1)-dimensional ballistic deposition process with
next-nearest neighbor interaction, which belongs to the KPZ universality class,
and introduce for this discrete model a variational formulation similar to that
for the randomly forced continuous Burgers equation. This allows to identify
the characteristic structures in the bulk of a growing aggregate ("clusters"
and "crevices") with minimizers and shocks in the Burgers turbulence, and to
introduce a new kind of equipped Airy process for ballistic growth. We dub it
the "hairy Airy process" and investigate its statistics numerically. We also
identify scaling laws that characterize the ballistic deposition patterns in
the bulk: the law of "thinning" of the forest of clusters with increasing
height, the law of transversal fluctuations of cluster boundaries, and the size
distribution of clusters. The corresponding critical exponents are determined
exactly based on the analogy with the Burgers turbulence and simple scaling
considerations.Comment: 10 pages, 5 figures. Minor edits: typo corrected, added explanation
of two acronyms. The text is essentially equivalent to version
Relativistic shape invariant potentials
Dirac equation for a charged spinor in electromagnetic field is written for
special cases of spherically symmetric potentials. This facilitates the
introduction of relativistic extensions of shape invariant potential classes.
We obtain the relativistic spectra and spinor wavefunctions for all potentials
in one of these classes. The nonrelativistic limit reproduces the usual
Rosen-Morse I & II, Eckart, Poschl-Teller, and Scarf potentials.Comment: Corrigendum: The last statement above equation (1) is now corrected
and replaced by two new statement
Satellite potentials for hypergeometric Natanzon potentials
As a result of the so(2,1) of the hypergeometric Natanzon potential a set of
potentials related to the given one is determined. The set arises as a result
of the action of the so(2,1) generators.Comment: 9 page
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