2,485 research outputs found
On the Stringy Hartle-Hawking State
We argue that non-perturbative stringy effects render the
Hartle-Hawking state associated with the eternal black hole
singular at the horizon. We discuss implications of this observation on
firewalls in string theory
Enhancement of the AC RPA
The overall goal of this research project is to improve the response and sensitivity of the AC Retarding Potential Analyzer (RPA). The AC RPA can accurately measure the flux, energy, and energy distribution of charged particles in a space environment. The enhancement of the sensor derives from changes that increase sensitivity of flux measurements through reduction of the baseline noise. The enhanced AC RPA sensor allows diagnosis of required charge particle beams necessary for tests of materials, instruments and subsystems, for future exploration missions
Generalised Bose-Einstein phase transition in large- component spin glasses
It is proposed to understand finite dimensional spin glasses using a
expansion, where is the number of spin components. It is shown that this
approach predicts a replica symmetric state in finite dimensions. The point
about which the expansion is made, the infinite- limit, has been studied in
the mean-field limit in detail and has a very unusual phase transition, rather
similar to a Bose-Einstein phase transition but with macroscopically
occupied low-lying states.Comment: 4 pages (plus a few lines), 3 figures. v2: minor error corrected. v3:
numerics supplemented by analytical arguments, references added, figure of
density of states adde
The geometry of basic, approximate, and minimum-norm solutions of linear equations
AbstractThe basic solutions of the linear equations Ax = b are the solutions of subsystems corresponding to maximal nonsingular submatrices of A. The convex hull of the basic solutions is denoted by C = C(A, b). Given 1 ≤ p ≤ ∞, the lp-approximate solutions of Ax = b, denoted x{p}, are minimizers of ∥Ax − b∥p. Given M ∈ Dm, the set of positive diagonal m × m matrices, the solutions of minx ∥M(Ax − b)∥p are called scaledlp-approximate solutions. For 1 ≤ p1, p2 ≤ ∞, the minimum-lp2-norm lp1-approximate solutions are denoted x{p1}{p2}. Main results: 1.(1) If A ∈ Rm × nm, then C contains all [some] minimum lp-norm solutions, for 1 ≤ p < ∞ [p = ∞].2.(2) For general A and any 1 ≤ p1, p2 < ∞ the set C contains all x{p1}{p2}.3.(3) The set of scaled lp-approximate solutions, with M ranging over Dm, is the same for all 1 < p < ∞.4.(4) The set of scaled least-squares solutions has the same closure as the set of solutions of minx f (|Ax − b|), where f:Rm+ → R ranges over all strictly isotone functions
Characterization of the Oblique Projector with Application to Constrained Least Squares
We provide a full characterization of the oblique projector in the
general case where the range of and the null space of are not
complementary subspaces. We discuss the new result in the context of
constrained least squares minimization.Comment: v1: 6 pages v2: 7 pages. Minor changes (formatting, references) in
sections 1-2. Extra statement in Theorem 3.1. Substantial revision of section
4 v3: 7 pages. A minor change (more explicit formula for \Xi) in Corollary
4.2. Changed + to direct sum at the bottom of p.5 v4: 7 pages. Removed typo
in eq. (17) which was present in v2 and v
An Improved Experiment to Determine the `Past of a Particle' in the Nested Mach-Zehnder Interferometer
We argue that the modification proposed by Li et al. [Chin. Phys. Lett. 32,
050303 (2015)] to the experiment of Danan et al. [Phys. Rev. Lett. 111, 240402
(2013)] does not test the past of the photon as characterised by local weak
traces. Instead of answering the questions: (i) Were the photons in A? (ii)
Were the photons in B? (iii) Were the photons in C? the proposed experiment
measures a degenerate operator answering the questions: (i) Were the photons in
A? (ii) Were the photons in B and C together? A negative answer to the last
question does not tell us if photons were present in B or C. A simple variation
of the modified experiment does provide good evidence for the past of the
photon in agreement with the results Danan et al. obtained.Comment: 3 pages, accepted for publication in Chinese Physics Letter
Asymptotic duality over closed convex sets
AbstractThe asymptotic duality theory of linear programming over closed convex cones [4] is extended to closed convex sets, by embedding such sets in appropriate cones. Applications to convex programming and to approximation theory are given
- …