9 research outputs found
Anisotropic Bose-Einstein condensates and completely integrable dynamical systems
A Gaussian ansatz for the wave function of two-dimensional harmonically
trapped anisotropic Bose-Einstein condensates is shown to lead, via a
variational procedure, to a coupled system of two second-order, nonlinear
ordinary differential equations. This dynamical system is shown to be in the
general class of Ermakov systems. Complete integrability of the resulting
Ermakov system is proven. Using the exact solution, collapse of the condensate
is analyzed in detail. Time-dependence of the trapping potential is allowed
A geometric approach to time evolution operators of Lie quantum systems
Lie systems in Quantum Mechanics are studied from a geometric point of view.
In particular, we develop methods to obtain time evolution operators of
time-dependent Schrodinger equations of Lie type and we show how these methods
explain certain ad hoc methods used in previous papers in order to obtain exact
solutions. Finally, several instances of time-dependent quadratic Hamiltonian
are solved.Comment: Accepted for publication in the International Journal of Theoretical
Physic
Δr in the Two-Higgs-Doublet Model at full one loop level—and beyond
After the recent discovery of a Higgs-like boson particle at the CERN
LHC-collider, it becomes more necessary than ever to prepare ourselves for
identifying its standard or non-standard nature. The Electroweak parameter
Delta r relating the values of the gauge boson masses [MW,MZ] and the Fermi
constant [G_F] is the traditional observable encoding high precision
information of the electroweak physics at the quantum level. In this work we
present a complete quantitative study of Delta r in the framework of the
general (unconstrained) Two-Higgs-Doublet Model (2HDM). First of all we report
on a systematic analysis of Delta r at the full one loop level in the general
2HDM, which to our knowledge was missing in the literature. Thereby we extract
a theoretical prediction for the mass of the W-boson in this model, taking MZ,
\alpha_{em} and G_F as experimental inputs. We find typical corrections leading
to mass shifts which help to improve the agreement
with the experimentally measured value, in a degree no less significant than in
the MSSM case. In the second part of our study we extend our calculation beyond
the mere one-loop order. We devise an effective Lagrangian approach that
captures the dominant higher order quantum effects on delta rho (viz. that part
of Delta r describing the breaking of the approximate SU(2) custodial symmetry)
in the limit of large Higgs boson self-interactions. This limit constitutes a
telltale property of the general 2HDM which is unmatched by e.g. the MSSM. Our
conclusion is that the Electroweak precision program to be conducted at the
LHC, and maybe at a future linear collider, can nicely complement the direct
searches. Should these distinctive loop effects be eventually found they would
signal a smoking gun hinting at non-standard Higgs physics.Comment: LaTeX, 12 figures, 4 tables. Extended discussion, references added.
Version accepted in Eur. Phys. J.