Feynman-Jackson integrals

We introduce perturbative Feynman integrals in the context of q-calculus generalizing the Gaussian q-integrals introduced by Diaz and Teruel. We provide analytic as well as combinatorial interpretations for the Feynman-Jackson integrals.Comment: Final versio

Shifted Power Method for Computing Tensor Eigenpairs

Recent work on eigenvalues and eigenvectors for tensors of order m >= 3 has been motivated by applications in blind source separation, magnetic resonance imaging, molecular conformation, and more. In this paper, we consider methods for computing real symmetric-tensor eigenpairs of the form Ax^{m-1} = \lambda x subject to ||x||=1, which is closely related to optimal rank-1 approximation of a symmetric tensor. Our contribution is a shifted symmetric higher-order power method (SS-HOPM), which we show is guaranteed to converge to a tensor eigenpair. SS-HOPM can be viewed as a generalization of the power iteration method for matrices or of the symmetric higher-order power method. Additionally, using fixed point analysis, we can characterize exactly which eigenpairs can and cannot be found by the method. Numerical examples are presented, including examples from an extension of the method to finding complex eigenpairs

Cosmic Superstring Scattering in Backgrounds

We generalize the calculation of cosmic superstring reconnection probability to non-trivial backgrounds. This is done by modeling cosmic strings as wound tachyon modes in the 0B theory, and the spacetime effective action is then used to couple this to background fields. Simple examples are given including trivial and warped compactifications. Generalization to $(p,q)$ strings is discussed.Comment: 12 pages, 2 figures; v2: references adde

Structural concepts for hydrogen-fueled hypersonic airplanes

Structural concepts for hydrogen-fueled hypersonic aircraf

Optical alignment system Patent

Electro-optical/computer system for aligning large structural members and maintaining correct positio

Multi-Boundary Entanglement in Chern-Simons Theory and Link Invariants

We consider Chern-Simons theory for gauge group $G$ at level $k$ on 3-manifolds $M_n$ with boundary consisting of $n$ topologically linked tori. The Euclidean path integral on $M_n$ defines a quantum state on the boundary, in the $n$-fold tensor product of the torus Hilbert space. We focus on the case where $M_n$ is the link-complement of some $n$-component link inside the three-sphere $S^3$. The entanglement entropies of the resulting states define framing-independent link invariants which are sensitive to the topology of the chosen link. For the Abelian theory at level $k$ ($G= U(1)_k$) we give a general formula for the entanglement entropy associated to an arbitrary $(m|n-m)$ partition of a generic $n$-component link into sub-links. The formula involves the number of solutions to certain Diophantine equations with coefficients related to the Gauss linking numbers (mod $k$) between the two sublinks. This formula connects simple concepts in quantum information theory, knot theory, and number theory, and shows that entanglement entropy between sublinks vanishes if and only if they have zero Gauss linking (mod $k$). For $G = SU(2)_k$, we study various two and three component links. We show that the 2-component Hopf link is maximally entangled, and hence analogous to a Bell pair, and that the Whitehead link, which has zero Gauss linking, nevertheless has entanglement entropy. Finally, we show that the Borromean rings have a "W-like" entanglement structure (i.e., tracing out one torus does not lead to a separable state), and give examples of other 3-component links which have "GHZ-like" entanglement (i.e., tracing out one torus does lead to a separable state).Comment: 37 pages, 19 figure

Simultaneous arrival of information in absorbing wave guides

We demonstrate that the temporal peak generated by specific electromagnetic pulses may arrive at different positions simultaneously in an absorbing wave guide. The effect can be used for triggering several devices all at once at unknown distances from the sender or generally to transmit information so that it arrives at the same time to receivers at different, unknown locations. This simultaneity cannot be realized by the standard transmission methods

First-principles thermoelasticity of bcc iron under pressure

We investigate the elastic and isotropic aggregate properties of ferromagnetic bcc iron as a function of temperature and pressure by computing the Helmholtz free energies for the volume-conserving strained structures using the first-principles linear response linear-muffin-tin-orbital method and the generalized-gradient approximation. We include the electronic excitation contributions to the free energy from the band structures, and phonon contributions from quasi-harmonic lattice dynamics. We make detailed comparisons between our calculated elastic moduli and their temperature and pressure dependences with available experimental and theoretical data.Comment: 5 figures, 2 table

Counterions at charge-modulated substrates

We consider counterions in the presence of a single planar surface with a spatially inhomogeneous charge distribution using Monte-Carlo simulations and strong-coupling theory. For high surface charges, multivalent counterions, or pronounced substrate charge modulation the counterions are laterally correlated with the surface charges and their density profile deviates strongly from the limit of a smeared-out substrate charge distribution, in particular exhibiting a much increased laterally averaged density at the surface.Comment: 7 page

Spin Density Matrix of Spin-3/2 Hole Systems

For hole systems with an effective spin j=3/2, we present an invariant decomposition of the spin density matrix that can be interpreted as a multipole expansion. The charge density corresponds to the monopole moment and the spin polarization due to a magnetic field corresponds to a dipole moment while heavy hole-light hole splitting can be interpreted as a quadrupole moment. For quasi two-dimensional hole systems in the presence of an in-plane magnetic field B the spin polarization is a higher-order effect that is typically much smaller than one even if the minority spin subband is completely depopulated. On the other hand, the field B can induce a substantial octupole moment which is a unique feature of j=3/2 hole systems.Comment: 8 pages, 1 figure, 3 table