444 research outputs found
Exact Methods for Self Interacting Neutrinos
The effective many-body Hamiltonian which describes vacuum oscillations and
self interactions of neutrinos in a two flavor mixing scheme under the single
angle approximation has the same dynamical symmetries as the well known BCS
pairing Hamiltonian. These dynamical symmetries manifest themselves in terms of
a set of constants of motion and can be useful in formulating the collective
oscillation modes in an intuitive way. In particular, we show that a neutrino
spectral split can be simply viewed as an avoided level crossing between the
eigenstates of a mean field Hamiltonian which includes a Lagrange multiplier in
order to fix the value of an exact many-body constant of motion. We show that
the same dynamical symmetries also exist in the three neutrino mixing scheme by
explicitly writing down the corresponding constants of motion.Comment: To appear in the proceedings of CETUP* 201
An Exactly Solvable Model of Interacting Bosons
We introduce a class of exactly solvable boson models. We give explicit
analytic expressions for energy eigenvalues and eigenvectors for an sd-boson
Hamiltonian, which is related to the SO(6) chain of the Interacting Boson Model
Hamiltonian.Comment: 8 pages of LATE
Spectral splits of neutrinos as a BCS-BEC crossover type phenomenon
We show that the spectral split of a neutrino ensemble which initially
consists of electron type neutrinos, is analogous to the BCS-BEC crossover
already observed in ultra cold atomic gas experiments. Such a neutrino ensemble
mimics the deleptonization burst of a core collapse supernova. Although these
two phenomena belong to very different domains of physics, the propagation of
neutrinos from highly interacting inner regions of the supernova to the vacuum
is reminiscent of the evolution of Cooper pairs between weak and strong
interaction regimes during the crossover. The Hamiltonians and the
corresponding many-body states undergo very similar transformations if one
replaces the pair quasispin of the latter with the neutrino isospin of the
former.Comment: 9 pages, 5 figure
Supersymmetry and Nuclear Pairing
We show that nuclear pairing Hamiltonian exhibits supersymmetry in the
strong-coupling limit. The underlying supersymmetric quantum mechanical
structure explains the degeneracies between the energies of the N and Nmax-N+1
pair eigenstates. The supersymmetry transformations connecting these states are
given.Comment: 4 pages of REVTEX, one figur
Symmetry and Supersymmetry in Nuclear Pairing: Exact Solutions
Pairing plays a crucial role in nuclear spectra and attempts to describe it
has a long history in nuclear physics. The limiting case in which all single
particle states are degenerate, but with different s-wave pairing strengths was
only recently solved. In this strong coupling limit the nuclear pairing
Hamiltonian also exhibits a supersymmetry. Another solution away from those
limits, namely two non-degenerate single particle states with different pairing
strengths, was also given. In this contribution these developments are
summarized and difficulties with possible generalizations to more single
particle states and d-wave pairing are discussed.Comment: 6 pages of LATEX, to be published in the Proceedings of the "10th
Int. Spring Seminar on Nuclear Physics: New Quests in Nuclear Structure",
Vietri Sul Mare, May 21-25, 201
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