arXiv subjects

C. Chan

Publications and source records attributed to C. Chan.

57 records · Page 4Linked to original sources

arXiv2012

Magnetic field-induced instability of the cooperative paramagnetic state in Zn$_x$Co$_{4-x}$(OD)$_6$Cl$_2$

Using elastic and inelastic neutron scattering techniques with and without application of an external magnetic field $H$, the magnetic ground states of Zn$_x$Co$_{4-x}$(OD)$_6$Cl$_2$ ($x=0,1$) were studied. Our results show that for $x=0$, the ground state is a magnetic long-range ordered (LRO) state where each tetrahedron forms an "umbrella"-type structure. On the other hand, for $x=1$, no static ordering was observed down to 1.5 K, which resembles the behavior found in the isostructural quantum system Zn$_x$Cu$_{4-x}$(OD)$_6$Cl$_2$. When $H$ field is applied, however the $x=1$ system develops the same LRO state as $x=0$. This indicates that the $x=1$ disordered state is in the vicinity of the $x=0$ ordered state.

cond-mat.str-el↗

arXiv2007

Terahertz detection in single wall carbon nanotubes

It is reported that terahertz radiation from 0.69 THz to 2.54 THz has been sensitively detected in a device consisting of bundles of metallic carbon nanotubes, quasi-optically coupled through a lithographically fabricated antenna, and a silicon lens. The measured data are consistent with a bolometric process and show promise for operation above 4.2 K.

cond-mat.mes-hall↗

arXiv1998

Counting faces of cubical spheres modulo two

Several recent papers have addressed the problem of characterizing the $f$-vectors of cubical polytopes. This is largely motivated by the complete characterization of the $f$-vectors of simplicial polytopes given by Stanley, Billera, and Lee in 1980. Along these lines Blind and Blind have shown that unlike in the simplicial case, there are parity restrictions on the $f$-vectors of cubical polytopes. In particular, except for polygons, all even dimensional cubical polytopes must have an even number of vertices. Here this result is extended to a class of zonotopal complexes which includes simply connected odd dimensional manifolds. This paper then shows that the only modular equations which hold for the $f$-vectors of all d-dimensional cubical polytopes (and hence spheres) are modulo two. Finally, the question of which mod two equations hold for the $f$-vectors of PL cubical spheres is reduced to a question about the Euler characteristics of multiple point loci from codimension one PL immersions into the $d$-sphere. Some results about this topological question are known (Eccles,Herbert,Lannes) and Herbert's result we translate into the cubical setting, thereby removing the PL requirement. A central definition in this paper is that of the derivative complex, which captures the correspondence between cubical spheres and codimension one immersions.

math.CO↗