5,004 research outputs found
Sputtering ion source Final report, 29 Mar. - 30 Sep. 1963
Modified sputtering ion source analyses of solid
Toric rings, inseparability and rigidity
This article provides the basic algebraic background on infinitesimal
deformations and presents the proof of the well-known fact that the non-trivial
infinitesimal deformations of a -algebra are parameterized by the
elements of cotangent module of . In this article we focus on
deformations of toric rings, and give an explicit description of in
the case that is a toric ring.
In particular, we are interested in unobstructed deformations which preserve
the toric structure. Such deformations we call separations. Toric rings which
do not admit any separation are called inseparable. We apply the theory to the
edge ring of a finite graph. The coordinate ring of a convex polyomino may be
viewed as the edge ring of a special class of bipartite graphs. It is shown
that the coordinate ring of any convex polyomino is inseparable. We introduce
the concept of semi-rigidity, and give a combinatorial description of the
graphs whose edge ring is semi-rigid. The results are applied to show that for
, is not rigid while for , is
rigid. Here is the complete bipartite graph with one
edge removed.Comment: 33 pages, chapter 2 of the Book << Multigraded Algebra and
Applications>> 2018, Springer International Publishing AG, part of Springer
Natur
Diffusion in an Expanding Plasma using AdS/CFT
We consider the diffusion of a non-relativistic heavy quark of fixed mass M,
in a one-dimensionally expanding and strongly coupled plasma using the AdS/CFT
duality. The Green's function constructed around a static string embedded in a
background with a moving horizon, is identified with the noise correlation
function in a Langevin approach. The (electric) noise decorrelation is of order
1/T(\tau) while the velocity de-correlation is of order MD(\tau)/T(\tau). For
MD>1, the diffusion regime is segregated and the energy loss is Langevin-like.
The time dependent diffusion constant D(\tau) asymptotes its adiabatic limit
2/\pi\sqrt{\lambda} T(\tau) when \tau/\tau_0=(1/3\eta_0\tau_0)^3 where \eta_0
is the drag coefficient at the initial proper time \tau_0.Comment: 19 pages, 2 figures, minor corrections, version to appear in JHE
Quark-Gluon Plasma/Black Hole duality from Gauge/Gravity Correspondence
The Quark-Gluon Plasma (QGP) is the QCD phase of matter expected to be formed
at small proper-times in the collision of heavy-ions at high energy.
Experimental observations seem to favor a strongly coupled QCD plasma with the
hydrodynamic properties of a quasi-perfect fluid, i.e. rapid thermalization (or
isotropization) and small viscosity. The theoretical investigation of such
properties is not obvious, due to the the strong coupling. The Gauge/Gravity
correspondence provides a stimulating framework to explore the strong coupling
regime of gauge theories using the dual string description. After a brief
introduction to Gauge/Gravity duality, and among various existing studies, we
focus on challenging problems of QGP hydrodynamics, such as viscosity and
thermalization, in terms of gravitational duals of both the static and
relativistically evolving plasma. We show how a Black Hole geometry arises
naturally from the dual properties of a nearly perfect fluid and explore the
lessons and prospects one may draw for actual heavy ion collisions from the
Gauge/Gravity duality approach.Comment: 6 pages, 4 figures, invited talk at the EPS HEP 2007 Conference,
Manchester (UK), and at the ``Deuxiemes rencontres PQG-France'', Etretat
(2007); reference adde
Betti numbers for numerical semigroup rings
We survey results related to the magnitude of the Betti numbers of numerical
semigroup rings and of their tangent cones.Comment: 22 pages; v2: updated references. To appear in Multigraded Algebra
and Applications (V. Ene, E. Miller Eds.
Mesoscopic Fermi gas in a harmonic trap
We study the thermodynamical properties of a mesoscopic Fermi gas in view of
recent possibilities to trap ultracold atoms in a harmonic potential. We focus
on the effects of shell closure for finite small atom numbers. The dependence
of the chemical potential, the specific heat and the density distribution on
particle number and temperature is obtained. Isotropic and anisotropic traps
are compared. Possibilities of experimental observations are discussed.Comment: 8 pages, 9 eps-figures included, Revtex, submitted to Phys. Rev. A,
minor changes to figures and captions, corrected typo
The Many Phases of Holographic Superfluids
We investigate holographic superfluids in AdS_{d+1} with d=3,4 in the
non-backreacted approximation for various masses of the scalar field. In d=3
the phase structure is universal for all the masses that we consider: the
critical temperature decreases as the superfluid velocity increases, and as it
is cranked high enough, the order of the phase transition changes from second
to first. Surprisingly, in d=4 we find that the phase structure is more
intricate. For sufficiently high mass, there is always a second order phase
transition to the normal phase, no matter how high the superfluid velocity. For
some parameters, as we lower the temperature, this transition happens before a
first order transition to a new superconducting phase. Across this first order
transition, the gap in the transverse conductivity jumps from almost zero to
about half its maximum value. We also introduce a double scaling limit where we
can study the phase transitions (semi-)analytically in the large velocity
limit. The results corroborate and complement our numerical results. In d=4,
this approach has the virtue of being fully analytically tractable.Comment: 31 pages, 19 figure
Shear Modes, Criticality and Extremal Black Holes
We consider a (2+1)-dimensional field theory, assumed to be holographically
dual to the extremal Reissner-Nordstrom AdS(4) black hole background, and
calculate the retarded correlators of charge (vector) current and
energy-momentum (tensor) operators at finite momentum and frequency. We show
that, similar to what was observed previously for the correlators of scalar and
spinor operators, these correlators exhibit emergent scaling behavior at low
frequency. We numerically compute the electromagnetic and gravitational
quasinormal frequencies (in the shear channel) of the extremal
Reissner-Nordstrom AdS(4) black hole corresponding to the spectrum of poles in
the retarded correlators. The picture that emerges is quite simple: there is a
branch cut along the negative imaginary frequency axis, and a series of
isolated poles corresponding to damped excitations. All of these poles are
always in the lower half complex frequency plane, indicating stability. We show
that this analytic structure can be understood as the proper limit of finite
temperature results as T is taken to zero holding the chemical potential fixed.Comment: 28 pages, 7 figures, added reference
Dielectric (p,q) Strings in a Throat
We calculate the (p,q) string spectrum in a warped deformed conifold using
the dielectric brane method. The spectrum is shown to have the same functional
form as in the dual picture of a wrapped D3-brane with electric and magnetic
fluxes on its world volume. The agreement is exact in the limit where q is
large. We also calculate the dielectric spectrum in the S-dual picture. The
spectrum in the S-dual picture has the same form as in the original picture but
it is not exactly S-dual invariant due to an interchange of Casimirs of the
non-Abelian gauge symmetries. We argue that in order to restore S-duality
invariance the non-Abelian brane action should be refined, probably by a better
prescription for the non-Abelian trace operation
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