Wave Chaos in Rotating Optical Cavities

It is shown that, even when the eigenmodes of an optical cavity are wave-chaotic, the frequency splitting due to the rotation of the cavity occurs and the frequency difference is proportional to the angular velocity although the splitting eigenmodes are still wave-chaotic and do not correspond to any unidirectionally-rotating waves.Comment: 4 pages, 6 figure

New detections of isotopic molecular absorption lines: a low ¹²C:¹³C ratio in nearby gas

Molecular absorption line observations towards the background source Sgr B2 `M' are presented. Previous observations have shown that there are ~9 foreground clouds of moderate density along this line of sight, which produce absorption lines that are well spaced in velocity. In two of these clouds, first detections have now been made of the rare isotopomers 12CS, HN13C, HC15N and HC18O+. For a feature at lsr velocities of -4 to +18km s-1, the isotopic ratio 12C:13C has been estimated, from the relative intensities of 12CS and 13CS J=1-0 lines, and also by comparing the strength of the 13CS line with that of C34S J=1-0 observed previously. A convergent solution for the two methods is found if 12CS is optically thick but the isotopomer lines are optically thin. In this case 12C:13C is 24±11, which is surprisingly low if the gas lies near the Sun, as indicated by its velocity. However, it has been suggested that parts of this feature may in fact arise in hot gas close to the Sgr B2 cloud, where a low isotope ratio is expected. If this region of the line is excluded, the 12C:13C ratio for the remaining lsr velocities of +11 to +18kms-1 is only slightly changed, with a value of 22±13. This is the true carbon isotope ratio in some nearby gas, if effects such as peculiar velocities and isotopic fractionation are unimportant. The value found here is well below the local average of ~60-70 in the solar neighbourhood, which suggests that some of the nearby absorbing gas has been recently isotopically enriched by stellar ejecta. This moderate density absorbing gas is then more likely to be material left over after star-formation, rather than a pre-star-for

Observations of five molecular species in absorption towards Sagittarius B2

Seven diffuse molecular clouds have been detected in absorption, using the Sgr B2 star-formation region was used as a source of background continuum emission. Transitions were observed at frequencies around 49, 85 and 98 GHz, from CS, C34S, H13CN, H13CO+, SiO and C3H2. Clouds detected in absorption include the "nuclear disk", the 3 kpc expanding arm, spiral arms in the Galactic Plane, and two unidentified regions. The nuclear disk line profile was found to be inconsistent with homogeneous disk or bar models, instead suggesting irregular perturbations of the gas within a few hundred pc of the Galactic Centre. Absorption in CS was detected in two different rotational transitions, leading to reliable estimates of the physical parameters of the clouds. In particular, exitation temperaturers could be estimated, instead of assumed values being used, as was the case in previous studies. Results from an LTE analysis and from LVG modelling show that the absorption lines are mostly optically thin, with molecular column densities ~1012-14cm-2 per cloud. Excitation temperatures as high as 5K were found, inconsistent with heating by the 2.7K cosmic background radiation alone. Cloud densities were estimated at nH2~104cm-3, or less if the gas is highly subthermalised

Finite geometries and diffractive orbits in isospectral billiards

Several examples of pairs of isospectral planar domains have been produced in the two-dimensional Euclidean space by various methods. We show that all these examples rely on the symmetry between points and blocks in finite projective spaces; from the properties of these spaces, one can derive a relation between Green functions as well as a relation between diffractive orbits in isospectral billiards.Comment: 10 page

Isospectral domains with mixed boundary conditions

We construct a series of examples of planar isospectral domains with mixed Dirichlet-Neumann boundary conditions. This is a modification of a classical problem proposed by M. Kac.Comment: 9 figures. Statement of Theorem 5.1 correcte

Quantum graphs with singular two-particle interactions

We construct quantum models of two particles on a compact metric graph with singular two-particle interactions. The Hamiltonians are self-adjoint realisations of Laplacians acting on functions defined on pairs of edges in such a way that the interaction is provided by boundary conditions. In order to find such Hamiltonians closed and semi-bounded quadratic forms are constructed, from which the associated self-adjoint operators are extracted. We provide a general characterisation of such operators and, furthermore, produce certain classes of examples. We then consider identical particles and project to the bosonic and fermionic subspaces. Finally, we show that the operators possess purely discrete spectra and that the eigenvalues are distributed following an appropriate Weyl asymptotic law

Chaos-assisted emission from asymmetric resonant cavity microlasers

We study emission from quasi-one-dimensional modes of an asymmetric resonant cavity that are associated with a stable periodic ray orbit confined inside the cavity by total internal reflection. It is numerically demonstrated that such modes exhibit directional emission, which is explained by chaos-assisted emission induced by dynamical tunneling. Fabricating semiconductor microlasers with the asymmetric resonant cavity, we experimentally demonstrate the selective excitation of the quasi-one-dimensional modes by employing the device structure to preferentially inject currents to these modes and observe directional emission in good accordance with the theoretical prediction based on chaos-assisted emission.Comment: 9 pages, 10 figures, some figures are in reduced qualit

Universal behavior of quantum Green's functions

We consider a general one-particle Hamiltonian H = - \Delta_r + u(r) defined in a d-dimensional domain. The object of interest is the time-independent Green function G_z(r,r') = . Recently, in one dimension (1D), the Green's function problem was solved explicitly in inverse form, with diagonal elements of Green's function as prescribed variables. The first aim of this paper is to extract from the 1D inverse solution such information about Green's function which cannot be deduced directly from its definition. Among others, this information involves universal, i.e. u(r)-independent, behavior of Green's function close to the domain boundary. The second aim is to extend the inverse formalism to higher dimensions, especially to 3D, and to derive the universal form of Green's function for various shapes of the confining domain boundary.Comment: 46 pages, the shortened version submitted to J. Math. Phy

Can One Hear the Shape of a Graph?

We show that the spectrum of the Schrodinger operator on a finite, metric graph determines uniquely the connectivity matrix and the bond lengths, provided that the lengths are non-commensurate and the connectivity is simple (no parallel bonds between vertices and no loops connecting a vertex to itself). That is, one can hear the shape of the graph! We also consider a related inversion problem: A compact graph can be converted into a scattering system by attaching to its vertices leads to infinity. We show that the scattering phase determines uniquely the compact part of the graph, under similar conditions as above.Comment: 9 pages, 1 figur

On quantum mechanics with a magnetic field on R^n and on a torus T^n, and their relation

We show in elementary terms the equivalence in a general gauge of a U(1)-gauge theory of a scalar charged particle on a torus T^n = R^n/L to the analogous theory on R^n constrained by quasiperiodicity under translations in the lattice L. The latter theory provides a global description of the former: the quasiperiodic wavefunctions defined on R^n play the role of sections of the associated hermitean line bundle E on T^n, since also E admits a global description as a quotient. The components of the covariant derivatives corresponding to a constant (necessarily integral) magnetic field B = dA generate a Lie algebra g_Q and together with the periodic functions the algebra of observables O_Q . The non-abelian part of g_Q is a Heisenberg Lie algebra with the electric charge operator Q as the central generator; the corresponding Lie group G_Q acts on the Hilbert space as the translation group up to phase factors. Also the space of sections of E is mapped into itself by g in G_Q . We identify the socalled magnetic translation group as a subgroup of the observables' group Y_Q . We determine the unitary irreducible representations of O_Q, Y_Q corresponding to integer charges and for each of them an associated orthonormal basis explicitly in configuration space. We also clarify how in the n = 2m case a holomorphic structure and Theta functions arise on the associated complex torus. These results apply equally well to the physics of charged scalar particles on R^n and on T^n in the presence of periodic magnetic field B and scalar potential. They are also necessary preliminary steps for the application to these theories of the deformation procedure induced by Drinfel'd twists.Comment: Latex2e file, 22 pages. Final version appeared in IJT