arXiv subjects

Yanghyun Byun

Publications and source records attributed to Yanghyun Byun.

4 recordsLinked to original sources

arXiv2020

Vector fields on projective Stiefel manifolds and the Browder-Dupont invariant

We develop strong lower bounds for the span of the projective Stiefel manifolds $X_{n,r}=O(n)/(O(n-r)\times \mathbb Z/2)$, which enable very accurate (in many cases exact) estimates of the span. The technique, for the most part, involves elementary stability properties of vector bundles. However, the case $X_{n,2}$ with $n$ odd presents extra difficulties, which are partially resolved using the Browder-Dupont invariant. In the process, we observe that the symmetric lift due to Sutherland does not necessarily exist for all odd dimensional closed manifolds, and therefore the Browder-Dupont invariant, as he formulated it, is not defined in general. We will characterize those $n$'s for which the Browder-Dupont invariant is well-defined on $X_{n,2}$. Then the invariant will be used in this case to obtain the lower bounds for the span as a corollary of a stronger result.

math.GT↗

arXiv2016

On the charged boson gas model as a theory of high Tc superconductivity

We consider a hypothetical bound state of two electrons even if we leave the binding mechanism unknown. The bound electron pairs should behave as bosons and we conclude that the paired electrons are 'apparently' in the highest energy states of all the occupied states. We call this multi-particle state an 'apparent' Fermi surface. Then the solid in concern must be a type 2 superconductor for a charged boson fluid is theoretically known to be as such. Moreover the Bose-Einstein condensation is known to be closely related to the critical temperatures of high Tc superconductors, which is consistent with our model. Most notably the model may describe a superconductor either with or without a Fermi surface. We propose two experimental methods to detect a bound electron pair, low energy electron-electron scattering and photoemission from high Tc superconductors.

cond-mat.supr-con↗

arXiv2014

Cohomology of flat bundles and a Chern-Simons functional

We show that a flat principal bundle with compact connected structure group and its adjoint bundles of Lie groups have the same cohomology as the trivial bundle, which is done by proving they satisfy the condition for the Leray-Hirsch theorem. This information has been used to construct a cohomology class of the adjoint bundle of a flat bundle whose restriction to each fiber is the class of the Maurer-Cartan 3-form. Then we use this result to define an invariant of a gauge transformation of a flat bundle which describes the effect of the gauge transformation on a Chern-Simons functional.

math.DG↗

arXiv2013

An exotic proposal on Cooper pairing in high-$T_c$ supercondutors

We propose that a Cooper pair in a high-$T_c$ superconductor might be in fact a bound system $\rm eex\bar x$ of two electrons, a particle $\rm x$ and its antiparticle. We assume $\rm eex\bar x$ is more massive than two free electrons. We observe that $\rm eex\bar x$ should be stable in a solid if it is in a low enough state in the solid. A solid which admits such a low state for $\rm eex\bar x$ has some properties which seem closely related to the behavior of HTS materials. The interaction of the $\rm x$-particle which binds the four particles into $\rm eex\bar x$ has been discussed. We also discuss the scale of the mass excess of $\rm eex\bar x$ relative to two free electrons. An experiment designed to detect a bound system of two electrons with a mass excess has been proposed.

physics.gen-ph↗