4,167 research outputs found
Entropy Distance: New Quantum Phenomena
We study a curve of Gibbsian families of complex 3x3-matrices and point out
new features, absent in commutative finite-dimensional algebras: a
discontinuous maximum-entropy inference, a discontinuous entropy distance and
non-exposed faces of the mean value set. We analyze these problems from various
aspects including convex geometry, topology and information geometry. This
research is motivated by a theory of info-max principles, where we contribute
by computing first order optimality conditions of the entropy distance.Comment: 34 pages, 5 figure
Non-Linear N-Parameter Spacetime Perturbations: Gauge Transformations
We introduce N-parameter perturbation theory as a new tool for the study of
non-linear relativistic phenomena. The main ingredient in this formulation is
the use of the Baker-Campbell-Hausdorff formula. The associated machinery
allows us to prove the main results concerning the consistency of the scheme to
any perturbative order. Gauge transformations and conditions for gauge
invariance at any required order can then be derived from a generating
exponential formula via a simple Taylor expansion. We outline the relation
between our novel formulation and previous developments.Comment: 7 pages, no figures, RevTeX 4.0. Revised version to match version
published in PR
Collimation of a spherical collisionless particles stream in Kerr space-time
We examine the propagation of collisionless particles emitted from a
spherical shell to infinity. The number distribution at infinity, calculated as
a function of the polar angle, exhibits a small deviation from uniformity. The
number of particles moving from the polar region toward the equatorial plane is
slightly larger than that of particles in the opposite direction, for an
emission radius in extreme Kerr space-time. This means that the black
hole spin exerts an anti-collimation effect on the particles stream propagating
along the rotation axis. We also confirm this property in the weak field limit.
The quadrupole moment of the central object produces a force toward the
equatorial plane. For a smaller emission radius , the absorption of
particles into the black hole, the non-uniformity and/or the anisotropy of the
emission distribution become much more important.Comment: 11 pages, 8 figures; accepted for publication in CQ
Maxwell-Bloch equation and Correlation function for penetrable Bose gas
We consider the quantum nonlinear Schr\"odinger equation in one space and one
time dimension. We are interested in the non-free-fermionic case. We consider
static temperature-dependent correlation functions. The determinant
representation for correlation functions simplifies in the small mass limit of
the Bose particle. In this limit we describe the correlation functions by the
vacuum expectation value of a boson-valued solution for Maxwell-Bloch
differential equation. We evaluate long-distance asymptotics of correlation
functions in the small mass limit.Comment: LaTEX file, 20 pages, to appear J. Phys. A (1997
Automatically Proving and Disproving Feasibility Conditions
[EN] In the realm of term rewriting, given terms s and t, a reachability condition s>>t is called feasible if there is a substitution O such that O(s) rewrites into O(t) in zero or more steps; otherwise, it is called infeasible. Checking infeasibility of (sequences of) reachability conditions is important in the analysis of computational properties of rewrite systems like confluence or (operational) termination. In this paper, we generalize this notion of feasibility to arbitrary n-ary relations on terms defined by first-order theories. In this way, properties of computational systems whose operational semantics can be given as a first-order theory can be investigated. We introduce a framework for proving feasibility/infeasibility, and a new tool, infChecker, which implements it.Supported by EU (FEDER), and projects RTI2018-094403-B-C32, PROMETEO/2019/098, and SP20180225. Also by INCIBE program "Ayudas para la excelencia de los equipos de investigación avanzada en ciberseguridad" (Raul Gutiérrez).Gutiérrez Gil, R.; Lucas Alba, S. (2020). Automatically Proving and Disproving Feasibility Conditions. Springer Nature. 416-435. https://doi.org/10.1007/978-3-030-51054-1_27S416435Andrianarivelo, N., Réty, P.: Over-approximating terms reachable by context-sensitive rewriting. In: Bojańczyk, M., Lasota, S., Potapov, I. (eds.) RP 2015. LNCS, vol. 9328, pp. 128–139. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24537-9_12Dershowitz, N.: Termination of rewriting. J. Symb. Comput. 3(1/2), 69–116 (1987). https://doi.org/10.1016/S0747-7171(87)80022-6Giesl, J., Thiemann, R., Schneider-Kamp, P., Falke, S.: Mechanizing and improving dependency pairs. J. Autom. Reasoning 37(3), 155–203 (2006). https://doi.org/10.1007/s10817-006-9057-7Goguen, J.A., Meseguer, J.: Models and equality for logical programming. In: Ehrig, H., Kowalski, R., Levi, G., Montanari, U. (eds.) TAPSOFT 1987. LNCS, vol. 250, pp. 1–22. Springer, Heidelberg (1987). https://doi.org/10.1007/BFb0014969Gutiérrez, R., Lucas, S.: Automatic generation of logical models with AGES. In: Fontaine, P. (ed.) CADE 2019. LNCS (LNAI), vol. 11716, pp. 287–299. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-29436-6_17Kojima, Y., Sakai, M.: Innermost reachability and context sensitive reachability properties are decidable for linear right-shallow term rewriting systems. In: Voronkov, A. (ed.) RTA 2008. LNCS, vol. 5117, pp. 187–201. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-70590-1_13Kojima, Y., Sakai, M., Nishida, N., Kusakari, K., Sakabe, T.: Context-sensitive innermost reachability is decidable for linear right-shallow term rewriting systems. Inf. Media Technol. 4(4), 802–814 (2009)Kojima, Y., Sakai, M., Nishida, N., Kusakari, K., Sakabe, T.: Decidability of reachability for right-shallow context-sensitive term rewriting systems. IPSJ Online Trans. 4, 192–216 (2011)Lucas, S.: Analysis of rewriting-based systems as first-order theories. In: Fioravanti, F., Gallagher, J.P. (eds.) LOPSTR 2017. LNCS, vol. 10855, pp. 180–197. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-94460-9_11Lucas, S.: Context-sensitive computations in functional and functional logic programs. J. Funct. Logic Program. 1998(1) (1998). http://danae.uni-muenster.de/lehre/kuchen/JFLP/articles/1998/A98-01/A98-01.htmlLucas, S.: Proving semantic properties as first-order satisfiability. Artif. Intell. 277 (2019). https://doi.org/10.1016/j.artint.2019.103174Lucas, S.: Using well-founded relations for proving operational termination. J. Autom. Reasoning 64(2), 167–195 (2019). https://doi.org/10.1007/s10817-019-09514-2Lucas, S., Gutiérrez, R.: Use of logical models for proving infeasibility in term rewriting. Inf. Process. Lett. 136, 90–95 (2018). https://doi.org/10.1016/j.ipl.2018.04.002Lucas, S., Marché, C., Meseguer, J.: Operational termination of conditional term rewriting systems. Inf. Process. Lett. 95(4), 446–453 (2005). https://doi.org/10.1016/j.ipl.2005.05.002Lucas, S., Meseguer, J.: Proving operational termination of declarative programs in general logics. In: Chitil, O., King, A., Danvy, O. (eds.) Proceedings of the 16th International Symposium on Principles and Practice of Declarative Programming, Kent, Canterbury, United Kingdom, 8–10 September 2014, pp. 111–122. ACM (2014). https://doi.org/10.1145/2643135.2643152Lucas, S., Meseguer, J., Gutiérrez, R.: The 2D dependency pair framework for conditional rewrite systems. Part I: definition and basic processors. J. Comput. Syst. Sci. 96, 74–106 (2018). https://doi.org/10.1016/j.jcss.2018.04.002Lucas, S., Meseguer, J., Gutiérrez, R.: The 2D dependency pair framework for conditional rewrite systems—Part II: advanced processors and implementation techniques. J. Autom. Reasoning (2020, in press)McCune, W.: Prover9 and Mace4. https://www.cs.unm.edu/~mccune/mace4/Meßner, F., Sternagel, C.: nonreach – a tool for nonreachability analysis. In: Vojnar, T., Zhang, L. (eds.) TACAS 2019. LNCS, vol. 11427, pp. 337–343. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17462-0_19Middeldorp, A., Nagele, J., Shintani, K.: Confluence competition 2019. In: Beyer, D., Huisman, M., Kordon, F., Steffen, B. (eds.) TACAS 2019. LNCS, vol. 11429, pp. 25–40. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17502-3_2Nishida, N., Maeda, Y.: Narrowing trees for syntactically deterministic conditional term rewriting systems. In: Kirchner, H. (ed.) Proceedings of the 3rd International Conference on Formal Structures for Computation and Deduction. FSCD 2018. Leibniz International Proceedings in Informatics (LIPIcs), vol. 108, pp. 26:1–26:20. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik (2018). https://doi.org/10.4230/LIPIcs.FSCD.2018.26Ohlebusch, E.: Advanced Topics in Term Rewriting. Springer, Heidelberg (2002). http://www.springer.com/computer/swe/book/978-0-387-95250-5Prawitz, D.: Natural Deduction: A Proof-Theoretical Study. Dover, New York (2006)Sternagel, C., Sternagel, T., Middeldorp, A.: CoCo 2018 Participant: ConCon 1.5. In: Felgenhauer, B., Simonsen, J. (eds.) Proceedings of the 7th International Workshop on Confluence. IWC 2018, p. 66 (2018). http://cl-informatik.uibk.ac.at/events/iwc-2018/Sternagel, C., Yamada, A.: Reachability analysis for termination and confluence of rewriting. In: Vojnar, T., Zhang, L. (eds.) TACAS 2019. LNCS, vol. 11427, pp. 262–278. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17462-0_15Winkler, S., Moser, G.: MædMax: a maximal ordered completion tool. In: Galmiche, D., Schulz, S., Sebastiani, R. (eds.) IJCAR 2018. LNCS (LNAI), vol. 10900, pp. 472–480. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-94205-6_3
Gravitational waves from a test particle scattered by a neutron star: Axial mode case
Using a metric perturbation method, we study gravitational waves from a test
particle scattered by a spherically symmetric relativistic star. We calculate
the energy spectrum and the waveform of gravitational waves for axial modes.
Since metric perturbations in axial modes do not couple to the matter fluid of
the star, emitted waves for a normal neutron star show only one peak in the
spectrum, which corresponds to the orbital frequency at the turning point,
where the gravitational field is strongest. However, for an ultracompact star
(the radius ), another type of resonant periodic peak appears in
the spectrum. This is just because of an excitation by a scattered particle of
axial quasinormal modes, which were found by Chandrasekhar and Ferrari. This
excitation comes from the existence of the potential minimum inside of a star.
We also find for an ultracompact star many small periodic peaks at the
frequency region beyond the maximum of the potential, which would be due to a
resonance of two waves reflected by two potential barriers (Regge-Wheeler type
and one at the center of the star). Such resonant peaks appear neither for a
normal neutron star nor for a Schwarzschild black hole. Consequently, even if
we analyze the energy spectrum of gravitational waves only for axial modes, it
would be possible to distinguish between an ultracompact star and a normal
neutron star (or a Schwarzschild black hole).Comment: 21 pages, revtex, 11 figures are attached with eps files Accepted to
Phys. Rev.
All the Exact Solutions of Generalized Calogero-Sutherland Models
A collective field method is extended to obtain all the explicit solutions of
the generalized Calogero-Sutherland models that are characterized by the roots
of all the classical groups, including the solutions corresponding to spinor
representations for and cases.Comment: Latex, 17 pages. Title and abstract slightly changed, plus minor
correction
Resonant inelastic x-ray scattering study of holon-antiholon continuum in SrCuO2
We report a resonant inelastic x-ray scattering study of charge excitations
in the quasi-one-dimensional Mott insulator SrCuO2. We observe a continuum of
low-energy excitations, in which a highly dispersive feature with a large
sinusoidal dispersion (~1.1 eV) resides. We have also measured the optical
conductivity, and studied the dynamic response of the extended Hubbard model
with realistic parameters, using a dynamical density-matrix renormalization
group method. In contrast to earlier work, we do not find a long-lived exciton,
but rather these results suggest that the excitation spectrum comprises a
holon-antiholon continuum together with a broad resonance.Comment: Final version to be published in Phys. Rev. Let
Gravitational Radiation from the radial infall of highly relativistic point particles into Kerr black holes
In this paper, we consider the gravitational radiation generated by the
collision of highly relativistic particles with rotating Kerr black holes. We
use the Sasaki-Nakamura formalism to compute the waveform, energy spectra and
total energy radiated during this process. We show that the gravitational
spectrum for high-energy collisions has definite characteristic universal
features, which are independent of the spin of the colliding objects. We also
discuss possible connections between these results and the black hole-black
hole collision at the speed of light process. With these results at hand, we
predict that during the high speed collision of a non-rotating hole with a
rotating one, about 35% of the total energy can get converted into
gravitational waves. Thus, if one is able to produce black holes at the Large
Hadron Collider, as much as 35% of the partons' energy should be emitted during
the so called balding phase. This energy will be missing, since we don't have
gravitational wave detectors able to measure such amplitudes. The collision at
the speed of light between one rotating black hole and a non-rotating one or
two rotating black holes turns out to be the most efficient gravitational wave
generator in the Universe.Comment: 15 pages, REVTEX4. Some comments and references adde
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