2,595 research outputs found
On the Jacobi-Metric Stability Criterion
We investigate the exact relation existing between the stability equation for
the solutions of a mechanical system and the geodesic deviation equation of the
associated geodesic problem in the Jacobi metric constructed via the
Maupertuis-Jacobi Principle. We conclude that the dynamical and geometrical
approaches to the stability/instability problem are not equivalent.Comment: 14 pages, no figure
The Kink variety in systems of two coupled scalar fields in two space-time dimensions
In this paper we describe the moduli space of kinks in a class of systems of
two coupled real scalar fields in (1+1) Minkowskian space-time. The main
feature of the class is the spontaneous breaking of a discrete symmetry of
(real) Ginzburg-Landau type that guarantees the existence of kink topological
defects.Comment: 12 pages, 5 figures. To appear in Phys. Rev.
Factorization of supersymmetric Hamiltonians in curvilinear coordinates
Planar supersymmetric quantum mechanical systems with separable spectral
problem in curvilinear coordinates are analyzed in full generality. We
explicitly construct the supersymmetric extension of the Euler/Pauli
Hamiltonian describing the motion of a light particle in the field of two heavy
fixed Coulombian centers. We shall also show how the SUSY Kepler/Coulomb
problem arises in two different limits of this problem: either, the two centers
collapse in one center - a problem separable in polar coordinates -, or, one of
the two centers flies to infinity - to meet the Coulomb problem separable in
parabolic coordinates.Comment: 13 pages. Based on the talk presented by M.A. Gonzalez Leon at the
7th International Conference on Quantum Theory and Symmetries (QTS7), August
07-13, 2011, Prague, Czech Republi
Maximum power, ecological function and efficiency of an irreversible Carnot cycle. A cost and effectiveness optimization
In this work we include, for the Carnot cycle, irreversibilities of linear
finite rate of heat transferences between the heat engine and its reservoirs,
heat leak between the reservoirs and internal dissipations of the working
fluid. A first optimization of the power output, the efficiency and ecological
function of an irreversible Carnot cycle, with respect to: internal temperature
ratio, time ratio for the heat exchange and the allocation ratio of the heat
exchangers; is performed. For the second and third optimizations, the optimum
values for the time ratio and internal temperature ratio are substituted into
the equation of power and, then, the optimizations with respect to the cost and
effectiveness ratio of the heat exchangers are performed. Finally, a criterion
of partial optimization for the class of irreversible Carnot engines is herein
presented.Comment: 17 pages, 4 figures. Submitted to Energy Convers. Manag
Two-Dimensional Supersymmetric Quantum Mechanics: Two Fixed Centers of Force
The problem of building supersymmetry in the quantum mechanics of two
Coulombian centers of force is analyzed. It is shown that there are essentially
two ways of proceeding. The spectral problems of the SUSY (scalar) Hamiltonians
are quite similar and become tantamount to solving entangled families of Razavy
and Whittaker-Hill equations in the first approach. When the two centers have
the same strength, the Whittaker-Hill equations reduce to Mathieu equations. In
the second approach, the spectral problems are much more difficult to solve but
one can still find the zero-energy ground states.Comment: This is a contribution to the Proc. of the Seventh International
Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007,
Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA
- …