Spectral and localization properties of the Dirichlet wave guide with two concentric Neumann discs

Bound states of the Hamiltonian describing a quantum particle living on three dimensional straight strip of width $d$ are investigated. We impose the Neumann boundary condition on the two concentric windows of the radii $a$ and $b$ located on the opposite walls and the Dirichlet boundary condition on the remaining part of the boundary of the strip. We prove that such a system exhibits discrete eigenvalues below the essential spectrum for any $a,b>0$. When $a$ and $b$ tend to the infinity, the asymptotic of the eigenvalue is derived. A comparative analysis with the one-window case reveals that due to the additional possibility of the regulating energy spectrum the anticrossing structure builds up as a function of the inner radius with its sharpness increasing for the larger outer radius. Mathematical and physical interpretation of the obtained results is presented; namely, it is derived that the anticrossings are accompanied by the drastic changes of the wave function localization. Parallels are drawn to the other structures exhibiting similar phenomena; in particular, it is proved that, contrary to the two-dimensional geometry, at the critical Neumann radii true bound states exist.Comment: 25 pages, 7 figure

Homogenization of the planar waveguide with frequently alternating boundary conditions

We consider Laplacian in a planar strip with Dirichlet boundary condition on the upper boundary and with frequent alternation boundary condition on the lower boundary. The alternation is introduced by the periodic partition of the boundary into small segments on which Dirichlet and Neumann conditions are imposed in turns. We show that under the certain condition the homogenized operator is the Dirichlet Laplacian and prove the uniform resolvent convergence. The spectrum of the perturbed operator consists of its essential part only and has a band structure. We construct the leading terms of the asymptotic expansions for the first band functions. We also construct the complete asymptotic expansion for the bottom of the spectrum

Propagation of axions in a strongly magnetized medium

The polarization operator of an axion in a degenerate gas of electrons occupying the ground-state Landau level in a superstrong magnetic field $H\gg H_0=m_e^2c^3/e\hbar =4.41\cdot 10^{13}$ G is investigated in a model with a tree-level axion-electron coupling. It is shown that a dynamic axion mass, which can fall within the allowed range of values $(10^{-5} eV \lesssim m_a\lesssim 10^{-2} eV)$, is generated under the conditions of strongly magnetized neutron stars. As a result, the dispersion relation for axions is appreciably different from that in a vacuum.Comment: RevTex, no figures, 13 pages, Revised version of the paper published in J. Exp. Theor. Phys. {\bf 88}, 1 (1999

Spinors for Spinning p-Branes

The group of the p-brane world volume preserving diffeomorphism is considered. The infinite-dimensional spinors of this group are related, by the nonlinear realization techniques, to the corresponding spinors of its linear subgroup, that are constructed explicitly. An algebraic construction of the Virasoro and Neveu-Schwarz-Ramond algebras, based on this infinite-dimensional spinors and tensors, is demonstrated.Comment: 18 page

Use of accelerated helium-3 ions for determining oxygen and carbon impurities in some pure materials

Methods are developed for the determination of O impurity in Be and Si carbide and concurrent determination of C and O impurities in Si and W by irradiation with accelerated He-3 ions and subsequent activity measurements of C-11 and F-18 formed from C and O with the aid of a gamma-gamma coincidence spectrometer. Techniques for determining O in Ge and Ga arsenide with radiochemical separation of F-18 are also described

Geometric coupling thresholds in a two-dimensional strip

We consider the Laplacian in a strip $\mathbb{R}\times (0,d)$ with the boundary condition which is Dirichlet except at the segment of a length $2a$ of one of the boundaries where it is switched to Neumann. This operator is known to have a non-empty and simple discrete spectrum for any $a>0$. There is a sequence $0<a_1<a_2<...$ of critical values at which new eigenvalues emerge from the continuum when the Neumann window expands. We find the asymptotic behavior of these eigenvalues around the thresholds showing that the gap is in the leading order proportional to $(a-a_n)^2$ with an explicit coefficient expressed in terms of the corresponding threshold-energy resonance eigenfunction

"Doubled" generalized Landau-Lifshiz hierarchies and special quasigraded Lie algebras

Using special quasigraded Lie algebras we obtain new hierarchies of integrable nonlinear vector equations admitting zero-curvature representations. Among them the most interesting is extension of the generalized Landau-Lifshitz hierarchy which we call "doubled" generalized Landau-Lifshiz hierarchy. This hierarchy can be also interpreted as an anisotropic vector generalization of "modified" Sine-Gordon hierarchy or as a very special vector generalization of so(3) anisotropic chiral field hierarchy.Comment: 16 pages, no figures, submitted to Journal of Physics

Microsecond Time-Resolved Absorption Spectroscopy Used to Study CO Compounds of Cytochrome bd from Escherichia coli

Cytochrome bd is a tri-heme (b558, b595, d) respiratory oxygen reductase that is found in many bacteria including pathogenic species. It couples the electron transfer from quinol to O2 with generation of an electrochemical proton gradient. We examined photolysis and subsequent recombination of CO with isolated cytochrome bd from Escherichia coli in oneelectron reduced (MV) and fully reduced (R) states by microsecond time-resolved absorption spectroscopy at 532-nm excitation. Both Soret and visible band regions were examined. CO photodissociation from MV enzyme possibly causes fast (t,1.5 ms) electron transfer from heme d to heme b595 in a small fraction of the protein, not reported earlier. Then the electron migrates to heme b558 (t,16 ms). It returns from the b-hemes to heme d with t,180 ms. Unlike cytochrome bd in the R state, in MV enzyme the apparent contribution of absorbance changes associated with CO dissociation from heme d is small, if any. Photodissociation of CO from heme d in MV enzyme is suggested to be accompanied by the binding of an internal ligand (L) at the opposite side of the heme. CO recombines with heme d (t,16 ms) yielding a transient hexacoordinate state (CO-Fe2+ -L). Then the ligand slowly (t,30 ms) dissociates from heme d. Recombination of CO with a reduced heme b in a fraction of the MV sample may also contribute to the 30-ms phase. In R enzyme, CO recombines to heme d (t,20 ms), some heme b558 (t,0.2–3 ms), and finally migrates from heme d to heme b595 (t,24 ms) in ,5% of the enzyme population. Data are consistent with the recent nanosecond study of Rappaport et al. conducted on the membranes at 640-nm excitation but limited to the Soret band. The additional phases were revealed due to differences in excitation and other experimental conditions

Chaplygin ball over a fixed sphere: explicit integration

We consider a nonholonomic system describing a rolling of a dynamically non-symmetric sphere over a fixed sphere without slipping. The system generalizes the classical nonholonomic Chaplygin sphere problem and it is shown to be integrable for one special ratio of radii of the spheres. After a time reparameterization the system becomes a Hamiltonian one and admits a separation of variables and reduction to Abel--Jacobi quadratures. The separating variables that we found appear to be a non-trivial generalization of ellipsoidal (spheroconical) coordinates on the Poisson sphere, which can be useful in other integrable problems. Using the quadratures we also perform an explicit integration of the problem in theta-functions of the new time.Comment: This is an extended version of the paper to be published in Regular and Chaotic Dynamics, Vol. 13 (2008), No. 6. Contains 20 pages and 2 figure