1,142 research outputs found
Intertwining relations of non-stationary Schr\"odinger operators
General first- and higher-order intertwining relations between non-stationary
one-dimensional Schr\"odinger operators are introduced. For the first-order
case it is shown that the intertwining relations imply some hidden symmetry
which in turn results in a -separation of variables. The Fokker-Planck and
diffusion equation are briefly considered. Second-order intertwining operators
are also discussed within a general approach. However, due to its complicated
structure only particular solutions are given in some detail.Comment: 18 pages, LaTeX20
Factorization of non-linear supersymmetry in one-dimensional Quantum Mechanics. II: proofs of theorems on reducibility
In this paper, we continue to study factorization of supersymmetric (SUSY)
transformations in one-dimensional Quantum Mechanics into chains of elementary
Darboux transformations with nonsingular coefficients. We define the class of
potentials that are invariant under the Darboux - Crum transformations and
prove a number of lemmas and theorems substantiating the formulated formerly
conjectures on reducibility of differential operators for spectral equivalence
transformations. Analysis of the general case is performed with all the
necessary proofs.Comment: 13 page
Vector meson decays from the Extended Chiral Quark Model
We derive the the effective lagrangian that describes the interactions among
vector, axial-vector mesons and pseudoscalars starting from the extended chiral
quark model (ECQM). The results for the low-energy constants of this effective
lagrangian have a parametric resemblance with existing predictions based on the
Nambu-Jona-Lasinio model (except for some overall signs that we correct), but
are numerically different. Therefore a precise measurement of these decay
constants can shed some light on the way chiral symmetry breaking is modelled
in QCD. Although most of the constants are poorly measured, comparison with
phenomenology allows us to determine one of the parameters of the ECQM that
could not be fully determined in previous analyses.Comment: 7 pages, revtex
New Two-Dimensional Quantum Models Partially Solvable by Supersymmetrical Approach
New solutions for second-order intertwining relations in two-dimensional SUSY
QM are found via the repeated use of the first order supersymmetrical
transformations with intermediate constant unitary rotation. Potentials
obtained by this method - two-dimensional generalized P\"oschl-Teller
potentials - appear to be shape-invariant. The recently proposed method of
separation of variables is implemented to obtain a part of their
spectra, including the ground state. Explicit expressions for energy
eigenvalues and corresponding normalizable eigenfunctions are given in analytic
form. Intertwining relations of higher orders are discussed.Comment: 21 pages. Some typos corrected; imrovements added in Subsect.4.2;
some references adde
Factorization of nonlinear supersymmetry in one-dimensional Quantum Mechanics. I: general classification of reducibility and analysis of the third-order algebra
We study possible factorizations of supersymmetric (SUSY) transformations in
the one-dimensional quantum mechanics into chains of elementary Darboux
transformations with nonsingular coefficients. A classification of irreducible
(almost) isospectral transformations and of related SUSY algebras is presented.
The detailed analysis of SUSY algebras and isospectral operators is performed
for the third-order case.Comment: 16 page
Higher Order Matrix SUSY Transformations in Two-Dimensional Quantum Mechanics
The iteration procedure of supersymmetric transformations for the
two-dimensional Schroedinger operator is implemented by means of the matrix
form of factorization in terms of matrix 2x2 supercharges. Two different types
of iterations are investigated in detail. The particular case of diagonal
initial Hamiltonian is considered, and the existence of solutions is
demonstrated. Explicit examples illustrate the construction.Comment: 15
Dirac fields in f(R)-gravity with torsion
We study f(R)-gravity with torsion in presence of Dirac massive fields. Using
the Bianchi identities, we formulate the conservation laws of the theory and we
check the consistency with the matter field equations. Further, we decompose
the field equations in torsionless and torsional terms: we show that the
non-linearity of the gravitational Lagrangian reduces to the presence of a
scalar field that depends on the spinor field; this additional scalar field
gives rise to an effective stress-energy tensor and plays the role of a scale
factor modifying the normalization of Dirac fields. Problems for fermions
regarding the positivity of energy and the particle-antiparticle duality are
discussed.Comment: 14 page
Lorentz Symmetry Breaking in Abelian Vector-Field Models with Wess-Zumino Interaction
We consider the abelian vector-field models in the presence of the
Wess-Zumino interaction with the pseudoscalar matter. The occurence of the
dynamic breaking of Lorentz symmetry at classical and one-loop level is
described for massless and massive vector fields. This phenomenon appears to be
the non-perturbative counterpart of the perturbative renormalizability and/or
unitarity breaking in the chiral gauge theories.Comment: 11 pages,LaTeX, Preprint DFUB/94 - 1
The Standard Quantum Limit of Coherent Beam Combining
Coherent beam combining refers to the process of generating a bright output
beam by merging independent input beams with locked relative phases. We report
the first quantum mechanical noise limit calculations for coherent beam
combining and compare our results to quantum-limited amplification. Our
coherent beam combining scheme is based on an optical Fourier transformation
which renders the scheme compatible with integrated optics. The scheme can be
layed out for an arbitrary number of input beams and approaches the shot noise
limit for a large number of inputs
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