Surface Phonons and Other Localized Excitations

The diatomic linear chain of masses coupled by harmonic springs is a textboook model for vibrational normal modes (phonons) in crystals. In addition to propagating acoustic and optic branches, this model is known to support a ``gap mode'' localized at the surface, provided the atom at the surface has light rather than heavy mass. An elementary argument is given which explains this mode and provides values for the frequency and localization length. By reinterpreting this mode in different ways, we obtain the frequency and localization lengths for three other interesting modes: (1) the surface vibrational mode of a light mass impurity at the surface of a monatomic chain; (2) the localized vibrational mode of a stacking fault in a diatomic chain; and (3) the localized vibrational mode of a light mass impurity in a monatomic chain.Comment: 5 pages with 4 embedded postscript figures. This paper will appear in the American Journal of Physic

Localized Modes in Open One-Dimensional Dissipative Random Systems

We consider, both theoretically and experimentally, the excitation and detection of the localized quasi-modes (resonances) in an open dissipative 1D random system. We show that even though the amplitude of transmission drops dramatically so that it cannot be observed in the presence of small losses, resonances are still clearly exhibited in reflection. Surprisingly, small losses essentially improve conditions for the detection of resonances in reflection as compared with the lossless case. An algorithm is proposed and tested to retrieve sample parameters and resonances characteristics inside the random system exclusively from reflection measurements.Comment: 5 pages, 3 figures, to appear in Phys. Rev. Let

Phase randomness in a one-dimensional disordered absorbing medium

Analytical study of the distribution of phase of the transmission coefficient through 1D disordered absorbing system is presented. The phase is shown to obey approximately Gaussian distribution. An explicit expression for the variance is obtained, which shows that absorption suppresses the fluctuations of the phase. The applicability of the random phase approximation is discussed.Comment: submitted to Phys.Rev.

Boundary Energies and the Geometry of Phase Separation in Double--Exchange Magnets

We calculate the energy of a boundary between ferro- and antiferromagnetic regions in a phase separated double-exchange magnet in two and three dimensions. The orientation dependence of this energy can significantly affect the geometry of the phase-separated state in two dimensions, changing the droplet shape and possibly stabilizing a striped arrangement within a certain range of the model parameters. A similar effect, albeit weaker, is also present in three dimensions. As a result, a phase-separated system near the percolation threshold is expected to possess intrinsic hysteretic transport properties, relevant in the context of recent experimental findings.Comment: 6 pages, including 4 figures; expanded versio

Expansion of a Bose-Einstein Condensate in the Presence of Disorder

Expansion of a Bose-Einstein condensate (BEC) is studied, in the presence of a random potential. The expansion is controlled by a single parameter, $(\mu\tau_{eff} /\hbar)$, where $\mu$ is the chemical potential, prior to the release of the BEC from the trap, and $\tau_{eff}$ is a transport relaxation time which characterizes the strength of the disorder. Repulsive interactions (nonlinearity) facilitate transport and can lead to diffusive spreading of the condensate which, in the absence of interactions, would have remained localized in the vicinity of its initial location

Quantum oscillations in graphene in the presence of disorder and interactions

Quantum oscillations in graphene is discussed. The effect of interactions are addressed by Kohn's theorem regarding de Haas-van Alphen oscillations, which states that electron-electron interactions cannot affect the oscillation frequencies as long as disorder is neglected and the system is sufficiently screened, which should be valid for chemical potentials not very close to the Dirac point. We determine the positions of Landau levels in the presence of potential disorder from exact transfer matrix and finite size diagonalization calculations. The positions are shown to be unshifted even for moderate disorder; stronger disorder, can, however, lead to shifts, but this also appears minimal even for disorder width as large as one-half of the bare hopping matrix element on the graphene lattice. Shubnikov-de Haas oscillations of the conductivity are calculated analytically within a self-consistent Born approximation of impurity scattering. The oscillatory part of the conductivity follows the widely invoked Lifshitz-Kosevich form when certain mass and frequency parameters are properly interpreted.Comment: Appendix A was removed, as the content of it is already contained in Ref. 17. Thanks to M. A. H. Vozmedian

Comment on "Clock Shift in High Field Magnetic Resonance of Atomic Hydrogen"

In this Comment, we reanalyze the experiments on the collision frequency shift of the b-c and a-d hyperfine transitions in three-dimensional atomic hydrogen in the presence of, respectively, a and b-state atoms. Accurate consideration of the symmetry of the spatial and spin part of the diatomic wavefunction yields the difference a_T-a_S=0.30(5) \AA between the triplet and singlet s-wave scattering lengths of hydrogen atoms. This corrects the factor-of two error of the commented work [Phys. Rev. Lett. 101, 263003 (2008)].Comment: 1 pag

Recent developments in the determination of the amplitude and phase of quantum oscillations for the linear chain of coupled orbits

De Haas-van Alphen oscillations are studied for Fermi surfaces (FS) illustrating the model proposed by Pippard in the early sixties, namely the linear chain of orbits coupled by magnetic breakdown. This FS topology is relevant for many multiband quasi-two dimensional (q-2D) organic metals such as $\kappa$-(BEDT-TTF)$_2$Cu(NCS)$_2$ and $\theta$-(BEDT-TTF)$_4$CoBr$_4$(C$_6$H$_4$Cl$_2$) which are considered in detail. Whereas the Lifshits-Kosevich model only involves a first order development of field- and temperature-dependent damping factors, second order terms may have significant contribution on the Fourier components amplitude for such q-2D systems at high magnetic field and low temperature. The strength of these second order terms depends on the relative value of the involved damping factors, which are in turns strongly dependent on parameters such as the magnetic breakdown field, effective masses and, most of all, effective Land\'{e} factors. In addition, the influence of field-dependent Onsager phase factors on the oscillation spectra is considered.Comment: arXiv admin note: text overlap with arXiv:1304.665

Extended quasimodes within nominally localized random waveguides

We have measured the spatial and spectral dependence of the microwave field inside an open absorbing waveguide filled with randomly juxtaposed dielectric slabs in the spectral region in which the average level spacing exceeds the typical level width. Whenever lines overlap in the spectrum, the field exhibits multiple peaks within the sample. Only then is substantial energy found beyond the first half of the sample. When the spectrum throughout the sample is decomposed into a sum of Lorentzian lines plus a broad background, their central frequencies and widths are found to be essentially independent of position. Thus, this decomposition provides the electromagnetic quasimodes underlying the extended field in nominally localized samples. When the quasimodes overlap spectrally, they exhibit multiple peaks in space.Comment: 4 pages, submitted to PRL (23 December 2005