6,228 research outputs found
A remark on zeta functions of finite graphs via quantum walks
From the viewpoint of quantum walks, the Ihara zeta function of a finite
graph can be said to be closely related to its evolution matrix. In this note
we introduce another kind of zeta function of a graph, which is closely related
to, as to say, the square of the evolution matrix of a quantum walk. Then we
give to such a function two types of determinant expressions and derive from it
some geometric properties of a finite graph. As an application, we illustrate
the distribution of poles of this function comparing with those of the usual
Ihara zeta function.Comment: 14 pages, 1 figur
Do static sources outside a Schwarzschild black hole radiate?
We show that static sources coupled to a massless scalar field in
Schwarzschild spacetime give rise to emission and absorption of zero-energy
particles due to the presence of Hawking radiation. This is in complete analogy
with the description of the bremsstrahlung by a uniformly accelerated charge
from the coaccelerated observers' point of view. The response rate of the
source is found to coincide with that in Minkowski spacetime as a function of
its proper acceleration. This result may be viewed as restoration of the
equivalence principle by the Hawking effect.Comment: 13 page
Low-frequency absorption cross section of the electromagnetic waves for the extreme Reissner-Nordstrom black holes in higher dimensions
We investigate the low-frequency absorption cross section of the
electromagnetic waves for the extreme Reissner-Nordstrom black holes in higher
dimensions. We first construct the exact solutions to the relevant wave
equations in the zero-frequency limit. In most cases it is possible to use
these solutions to find the transmission coefficients of partial waves in the
low-frequency limit. We use these transmission coefficients to calculate the
low-frequency absorption cross section in five and six spacetime dimensions. We
find that this cross section is dominated by the modes with l=2 in the
spherical-harmonic expansion rather than those with l=1, as might have been
expected, because of the mixing between the electromagnetic and gravitational
waves. We also find an upper limit for the low-frequency absorption cross
section in dimensions higher than six.Comment: 7 pages, 1 figure, Phys. Rev. D (to appear
The Unruh effect and its applications
It has been thirty years since the discovery of the Unruh effect. It has
played a crucial role in our understanding that the particle content of a field
theory is observer dependent. This effect is important in its own right and as
a way to understand the phenomenon of particle emission from black holes and
cosmological horizons. Here, we review the Unruh effect with particular
emphasis to its applications. We also comment on a number of recent
developments and discuss some controversies. Effort is also made to clarify
what seems to be common misconceptions.Comment: 53 pages, 11 figures, submitted to Reviews of Modern Physic
Interaction of Hawking radiation and a static electric charge
We investigate whether the equality found for the response of static scalar
sources interacting (i) with {\em Hawking radiation in Schwarzschild spacetime}
and (ii) with the Fulling-Davies-Unruh thermal bath in the Rindler wedge is
maintained in the case of electric charges. We find a finite result in the
Schwarzschild case, which is computed exactly, in contrast with the divergent
result associated with the infrared catastrophe in the Rindler case, i.e. in
the case of uniformly accelerated charges in Minkowski spacetime. Thus, the
equality found for scalar sources does not hold for electric charges.Comment: 8 pages (REVTEX
SO(4) Invariant States in Quantum Cosmology
The phenomenon of linearisation instability is identified in models of
quantum cosmology that are perturbations of mini-superspace models. In
particular, constraints that are second order in the perturbations must be
imposed on wave functions calculated in such models. It is shown explicitly
that in the case of a model which is a perturbation of the mini-superspace
which has spatial sections these constraints imply that any wave
functions calculated in this model must be SO(4) invariant. (This replaces the
previous corrupted version.)Comment: 15 page
Meteoritic material on the moon
Three types of meteoritic material are found on the moon: micrometeorites, ancient planetesimal debris from the "early intense bombardment," and debris of recent, craterforming projectiles. Their amounts and compositions have been determined from trace element studies. The micrometeorite component is uniformly distributed over the entire lunar surface, but is seen most clearly in mare soils. It has a primitive, C1-chondrite-like composition, and comprises 1 to 1.5 percent of mature soils. Apparently it represents cometary debris. The ancient component is seen in highland breccias and soils. Six varieties have been recognized, differing in their proportions of refractories (Ir, Re), volatiles (Ge, Sb), and Au. All have a fractionated composition, with volatiles depleted relative to siderophiles. The abundance patterns do not match those of the known meteorite classes. These ancient meteoritic components seem to represent the debris of an extinct population of bodies (planetisimals, moonlets) that produced the mare basins during the first 700 Myr of the moon's history. On the basis of their stratigraphy and geographic distribution, five of the six groups are tentatively assigned to specific mare basins: Imbrium, Serenitatis, Crisium, Nectaris, and Humorum or Nubium
Do static sources respond to massive scalar particles from the Hawking radiation as uniformly accelerated ones do in the inertial vacuum?
We revisit the recently found equivalence for the response of a static scalar
source interacting with a {\em massless} Klein-Gordon field when the source is
(i) static in Schwarzschild spacetime, in the Unruh vacuum associated with the
Hawking radiation and (ii) uniformly accelerated in Minkowski spacetime, in the
inertial vacuum, provided that the source's proper acceleration is the same in
both cases. It is shown that this equivalence is broken when the massless
Klein-Gordon field is replaced by a {\em massive} one.Comment: 4 pages, 2 figure
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