Related papers: Higher order deformations of hyperbolic spectra
The basic theory of photoemission, inverse photoemission, Auger-electron and appearance-potential spectroscopy is developed within a unified framework starting from Fermi's golden rule. The spin-resolved and temperature-dependent…
For a hyperbolic surface embedded eigenvalues of the Laplace operator are unstable and tend to become resonances. A sufficient dissolving condition was identified by Phillips-Sarnak and is elegantly expressed in Fermi's Golden Rule. We…
Focusing on the $2\mathrm{p}-1\mathrm{s}$ transition in atomic Hydrogen, we investigate through first order perturbation theory the time evolution of the survival probability of an electron initially taken to be in the excited…
This is the first in a series of papers showing that Haken manifolds have hyperbolic structures; this first was published, the second two have existed only in preprint form, and later preprints were never completed. This eprint is only an…
This is a comment on Phys. Rev. Lett. {\bf 110}, 126405 (2013), showing it biases the ferromagnetic order more than mean field theories would do. With over-biases like this, the theoretical method applied in the given context is called into…
We study the uniqueness of horospheres and equidistant spheres in hyperbolic space under different conditions. First we generalize the Bernstein theorem by Do Carmo and Lawson to the embedded hypersurfaces with constant higher order mean…
Fermi's golden rule is of great importance in quantum dynamics. However, in many textbooks on quantum mechanics, its contents and limitations are obscured by the approximations and arguments in the derivation, which are inevitable because…
I describe the picture by which supersymmetry--the possible symmetry of Nature that converts fermions to bosons and vice versa--accounts for the next stage of physics beyond the Standard Model. I then survey the future experimental program…
These are notes based on a series of talks that the author gave at the "Interactions between hyperbolic geometry and quantum groups" conference held at Columbia University in June of 2009.
The Purcell effect -- stemming directly from the celebrated Fermi's Golden Rule -- links the enhanced emissivity of an emitter to the local density of states (LDoS) of a surrounding cavity. Under typical circumstances the LDoS is assumed to…
This paper shows that every Gromov hyperbolic group can be described by a finite subdivision rule acting on the 3-sphere. This gives a boundary-like sequence of increasingly refined finite cell complexes which carry all quasi-isometry…
Large deviations in the context of first-passage percolation was first studied in the early 1980s by Grimmett and Kesten, and has since been revisited in a variety of studies. However, none of these studies provides a precise relation…
Deformations of complex structures by finite Beltrami differentials are considered on general Riemann surfaces. Exact formulas to any fixed order are derived for the corresponding deformations of the period matrix, Green's functions, and…
We investigate experimentally a Fermi golden rule in two-edge and five-edge microwave networks with preserved time reversal invariance. A Fermi golden rule gives rates of decay of states obtained by perturbing embedded eigenvalues of graphs…
Geometrization theorem, fibered case: Every three-manifold that fibers over the circle admits a geometric decomposition. Double limit theorem: for any sequence of quasi-Fuchsian groups whose controlling pair of conformal structures tends…
This is an extended abstract of a lecture held at the Conference ``Fourier and Radon transformations on symmetric spaces'' in honor of Professor S. Helgason's 65th birthday, Roskilde, Denmark, Sept. 10--12, 1992.
Using, for the first time, configuration-constrained potential-energy-surface calculations with the inclusion of $\beta_6$ deformation, we find remarkable effects of the high order deformation on the high-$K$ isomers in $^{254}$No, the…
The aim of this paper is to demonstrate that very many Dehn fillings on a cusped hyperbolic 3-manifold yield a 3-manifold which is irreducible, atoroidal and not Seifert fibred, and which has infinite, word hyperbolic fundamental group. We…
We analyse the mathematical underpinnings of a mixed hyperbolic-elliptic form of the Einstein equations of motion in which the lapse function is determined by specified mean curvature and the shift is arbitrary. We also examine a new…
The spectral fluctuations of a quantum Hamiltonian system with time-reversal symmetry are studied in the semiclassical limit by using periodic-orbit theory. It is found that, if long periodic orbits are hyperbolic and uniformly distributed…