Encircling an Exceptional Point

We calculate analytically the geometric phases that the eigenvectors of a parametric dissipative two-state system described by a complex symmetric Hamiltonian pick up when an exceptional point (EP) is encircled. An EP is a parameter setting where the two eigenvalues and the corresponding eigenvectors of the Hamiltonian coalesce. We show that it can be encircled on a path along which the eigenvectors remain approximately real and discuss a microwave cavity experiment, where such an encircling of an EP was realized. Since the wavefunctions remain approximately real, they could be reconstructed from the nodal lines of the recorded spatial intensity distributions of the electric fields inside the resonator. We measured the geometric phases that occur when an EP is encircled four times and thus confirmed that for our system an EP is a branch point of fourth order.Comment: RevTex 4.0, four eps-figures (low resolution

Ensembles and experiments in classical and quantum physics

A philosophically consistent axiomatic approach to classical and quantum mechanics is given. The approach realizes a strong formal implementation of Bohr's correspondence principle. In all instances, classical and quantum concepts are fully parallel: the same general theory has a classical realization and a quantum realization. Extending the `probability via expectation' approach of Whittle to noncommuting quantities, this paper defines quantities, ensembles, and experiments as mathematical concepts and shows how to model complementarity, uncertainty, probability, nonlocality and dynamics in these terms. The approach carries no connotation of unlimited repeatability; hence it can be applied to unique systems such as the universe. Consistent experiments provide an elegant solution to the reality problem, confirming the insistence of the orthodox Copenhagen interpretation on that there is nothing but ensembles, while avoiding its elusive reality picture. The weak law of large numbers explains the emergence of classical properties for macroscopic systems.Comment: 56 page

Species abundance distributions: moving beyond single prediction theories to integration within an ecological framework

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75247/1/j.1461-0248.2007.01094.x.pd

SDSS 1507+52: A Halo Cataclysmic Variable?1

We report a photometric and spectroscopic study of the peculiar cataclysmic variable SDSS 1507+52. The star shows very deep eclipses on the 67-minute orbital period, and those eclipses are easily separable into white-dwarf and hot-spot components. This leads to tight constraints on binary parameters, with M1 = 0.83(8) M, M2 = 0.057(8) M, R1 = 0.0097(9) R, R2 = 0.097(4) R, q = 0.069(2), and i = 83.18(13)°. Such numbers suggest possible membership among the WZ Sge stars, a common type of dwarf nova. The spectroscopic behavior (strong and broad H emission, double-peaked and showing a classic rotational disturbance during eclipse) is also typical. But the star’s orbital period is shockingly below the “period minimum” of 77 minutes that is characteristic of hydrogen-rich CVs; producing such a strange binary will require some tinkering with the theory of cataclysmic-variable evolution. The proper motion is also remarkably high for a star of its distance, which we estimate from photometry and trigonometric parallax as 230 ± 40 pc. This suggests a transverse velocity of 164 ± 30 km s-1—uncomfortably high if the star belongs to a Galactic-disk population. These difficulties with understanding its evolution and space velocity can be solved if the star belongs to a Galactic-halo population.<br/