678 research outputs found
Minkowski space structure of the Higgs potential in 2HDM
The Higgs potential of 2HDM keeps its generic form under the group of
transformation GL(2,C), which is larger than the usually considered
reparametrization group U(2). This reparametrization symmetry induces the
Minkowski space structure in the orbit space of 2HDM. Exploiting this property,
we present a geometric analysis of the number and properties of stationary
points of the most general 2HDM potential. In particular, we prove that
charge-breaking and neutral vacua never coexist in 2HDM and establish
conditions when the most general explicitly CP-conserving Higgs potential has
spontaneously CP-violating minima. Our analysis avoids manipulation with
high-order algebraic equations.Comment: 33 pages, 6 figures; v3: corrected a flaw in the proof of proposition
1
Liquid crystal defects in the Landau-de Gennes theory in two dimensions-beyond the one-constant approximation
We consider the two-dimensional Landau-de Gennes energy with several elastic
constants, subject to general -radially symmetric boundary conditions. We
show that for generic elastic constants the critical points consistent with the
symmetry of the boundary conditions exist only in the case . In this case
we identify three types of radial profiles: with two, three of full five
components and numerically investigate their minimality and stability depending
on suitable parameters. We also numerically study the stability properties of
the critical points of the Landau-de Gennes energy and capture the intricate
dependence of various qualitative features of these solutions on the elastic
constants and the physical regimes of the liquid crystal system
Shifted Power Method for Computing Tensor Eigenpairs
Recent work on eigenvalues and eigenvectors for tensors of order m >= 3 has
been motivated by applications in blind source separation, magnetic resonance
imaging, molecular conformation, and more. In this paper, we consider methods
for computing real symmetric-tensor eigenpairs of the form Ax^{m-1} = \lambda x
subject to ||x||=1, which is closely related to optimal rank-1 approximation of
a symmetric tensor. Our contribution is a shifted symmetric higher-order power
method (SS-HOPM), which we show is guaranteed to converge to a tensor
eigenpair. SS-HOPM can be viewed as a generalization of the power iteration
method for matrices or of the symmetric higher-order power method.
Additionally, using fixed point analysis, we can characterize exactly which
eigenpairs can and cannot be found by the method. Numerical examples are
presented, including examples from an extension of the method to finding
complex eigenpairs
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