Exceptional points of degeneracy and branch points for coupled transmission lines - Linear-algebra and bifurcation theory perspectives

We provide a new angle to investigate exceptional points of degeneracy (EPD) relating the current linear-algebra point of view to bifurcation theory. We apply these concepts to EPDs related to propagation in waveguides supporting two modes (in each direction), described as a coupled transmission line. We show that EPDs are singular points of the dispersion function associated with the fold bifurcation connecting multiple branches of dispersion spectra. This provides an important connection between various modal interaction phenomena known in guided-wave structures with recent interesting effects observed in quantum mechanics, photonics, and metamaterials systems described in terms of the algebraic EPD formalism. Since bifurcation theory involves only eigenvalues, we also establish the connection to the linear-algebra point of view by casting the system eigenvectors in terms of eigenvalues, analytically showing that the coalescence of two eigenvalues results automatically in the coalescence of the two respective eigenvectors. Therefore, for the studied two-coupled transmission-line problem, the eigenvalue degeneracy explicitly implies an EPD. Furthermore, we discuss in some detail the fact that EPDs define branch points in the complex frequency plane, we provide simple formulas for these points, and we show that parity-time (PT) symmetry leads to real-valued EPDs occurring on the real-frequency axis

Heavy Ion Dynamics and Neutron Stars

Some considerations are reported, freely inspired from the presentations and discussions during the Beijing Normal University Workshop on the above Subject, held in July 2007. Of course this cannot be a complete summary but just a collection of personal thougths aroused during the meeting.Comment: 11 pages, no figures, Summary Talk, Int.Workshop on "Nuclear Dynamics in Heavy Ion Collisions and Neutron Stars", Beijing Normal Univ. July 07, to appear in Int.Journ.Modern Physics E (2008

Thermonuclear Burning on the Accreting X-Ray Pulsar GRO J1744-28

We investigate the thermal stability of nuclear burning on the accreting X-ray pulsar GRO J1744-28. The neutron star's dipolar magnetic field is <3\times 10^{11} G if persistent spin-up implies that the magnetospheric radius is less than the co-rotation radius. After inferring the properties of the neutron star, we study the thermal stability of hydrogen/helium burning and show that thermonuclear instabilities are unlikely causes of the hourly bursts seen at very high accretion rates. We then discuss how the stability of the thermonuclear burning depends on both the global accretion rate and the neutron star's magnetic field strength. We emphasize that the appearance of the instability (i.e., whether it looks like a Type I X-ray burst or a flare lasting a few minutes) will yield crucial information on the neutron star's surface magnetic field and the role of magnetic fields in convection. We suggest that a thermal instability in the accretion disk is the origin of the long (~300 days) outburst and that the recurrence time of these outbursts is >50 years. We also discuss the nature of the binary and point out that a velocity measurement of the stellar companion (most likely a Roche-lobe filling giant with m_K>17) will constrain the neutron star mass.Comment: 19 pages, 3 PostScript figures, uses aaspp4.sty and epsfig.sty, to appear in the Astrophysical Journa

On the Possible Common Nature of Double Extensive Air Showers and Aligned Events

Double Extensive Air Showers and aligned events were discovered at energies E {\gtsim} 1016 eV over fourth century back. But up to now there is no sufficiently identical explanation of their nature. In this paper it is expected that both types of events are the result of breakup of the string formed in the collisions of super high energy particles

Longitudinal and transversal spin dynamics of donor-bound electrons in fluorine-doped ZnSe: spin inertia versus Hanle effect

The spin dynamics of the strongly localized, donor-bound electrons in fluorine-doped ZnSe epilayers is studied by pump-probe Kerr rotation techniques. A method exploiting the spin inertia is developed and used to measure the longitudinal spin relaxation time, $T_1$, in a wide range of magnetic fields, temperatures, and pump densities. The $T_1$ time of the donor-bound electron spin of about 1.6 $\mu$s remains nearly constant for external magnetic fields varied from zero up to 2.5 T (Faraday geometry) and in a temperature range $1.8-45$ K. The inhomogeneous spin dephasing time, $T_2^*=8-33$ ns, is measured using the resonant spin amplification and Hanle effects under pulsed and steady-state pumping, respectively. These findings impose severe restrictions on possible spin relaxation mechanisms.Comment: 10 pages, 7 figure

Spin-orbit coupled particle in a spin bath

We consider a spin-orbit coupled particle confined in a quantum dot in a bath of impurity spins. We investigate the consequences of spin-orbit coupling on the interactions that the particle mediates in the spin bath. We show that in the presence of spin-orbit coupling, the impurity-impurity interactions are no longer spin-conserving. We quantify the degree of this symmetry breaking and show how it relates to the spin-orbit coupling strength. We identify several ways how the impurity ensemble can in this way relax its spin by coupling to phonons. A typical resulting relaxation rate for a self-assembled Mn-doped ZnTe quantum dot populated by a hole is 1 $\mu$s. We also show that decoherence arising from nuclear spins in lateral quantum dots is still removable by a spin echo protocol, even if the confined electron is spin-orbit coupled.Comment: 18 pages, 1 figur

The direct evaluation of attosecond chirp from a streaking measurement

We derive an analytical expression, from classical electron trajectories in a laser field, that relates the breadth of a streaked photoelectron spectrum to the group-delay dispersion of an isolated attosecond pulse. Based on this analytical expression, we introduce a simple, efficient and robust procedure to instantly extract the attosecond pulse's chirp from the streaking measurement.Comment: 4 figure