56,234 research outputs found
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 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 at level on
3-manifolds with boundary consisting of topologically linked tori.
The Euclidean path integral on defines a quantum state on the boundary,
in the -fold tensor product of the torus Hilbert space. We focus on the case
where is the link-complement of some -component link inside the
three-sphere . 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 () we give a
general formula for the entanglement entropy associated to an arbitrary
partition of a generic -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 ) 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 ). For , 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
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
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
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