7,682 research outputs found
Homogeneous Field and WKB Approximation In Deformed Quantum Mechanics with Minimal Length
In the framework of the deformed quantum mechanics with minimal length, we
consider the motion of a non-relativistic particle in a homogeneous external
field. We find the integral representation for the physically acceptable wave
function in the position representation. Using the method of steepest descent,
we obtain the asymptotic expansions of the wave function at large positive and
negative arguments. We then employ the leading asymptotic expressions to derive
the WKB connection formula, which proceeds from classically forbidden region to
classically allowed one through a turning point. By the WKB connection formula,
we prove the Bohr-Sommerfeld quantization rule up to . We
also show that, if the slope of the potential at a turning point is too steep,
the WKB connection formula fall apart around the turning point.Comment: 31 pages; v2: a new subsection about applications of WKB
approximation and references added, published versio
Testing Holographic Conjectures of Complexity with Born-Infeld Black Holes
In this paper, we use Born-Infeld black holes to test two recent holographic
conjectures of complexity, the "Complexity = Action" (CA) duality and
"Complexity = Volume 2.0" (CV) duality. The complexity of a boundary state is
identified with the action of the Wheeler-deWitt patch in CA duality, while
this complexity is identified with the spacetime volume of the WdW patch in CV
duality. In particular, we check whether the Born-Infeld black holes violate
the Lloyd bound: , where gs stands
for the ground state for a given electrostatic potential. We find that the
ground states are either some extremal black hole or regular spacetime with
nonvanishing charges. Near extremality, the Lloyd bound is violated in both
dualities. Near the charged regular spacetime, this bound is satisfied in CV
duality but violated in CA duality. When moving away from the ground state on a
constant potential curve, the Lloyd bound tend to be saturated from below in CA
duality, while is times as large as the Lloyd bound
in CV duality.Comment: 25 papes, 15 figure
Black Hole Radiation with Modified Dispersion Relation in Tunneling Paradigm: Static Frame
Due to the exponential high gravitational red shift near the event horizon of
a black hole, it might appears that the Hawking radiation would be highly
sensitive to some unknown high energy physics. To study possible deviations
from the Hawking's prediction, the dispersive field theory models have been
proposed, following the Unruh's hydrodynamic analogue of a black hole
radiation. In the dispersive field theory models, the dispersion relations of
matter fields are modified at high energies, which leads to modifications of
equations of motion. In this paper, we use the Hamilton-Jacobi method to
investigate the dispersive field theory models. The preferred frame is the
static frame of the black hole. The dispersion relation adopted agrees with the
relativistic one at low energies but is modified near the Planck mass .
We calculate the corrections to the Hawking temperature for massive and charged
particles to and massless and neutral
particles to all orders. Our results suggest that the thermal spectrum of
radiations near horizon is robust, e.g. corrections to the Hawking temperature
are suppressed by . After the spectrum of radiations near the horizon is
obtained, we use the brick wall model to compute the thermal entropy of a
massless scalar field near the horizon of a 4D spherically symmetric black
hole. We find that the leading term of the entropy depends on how the
dispersion relations of matter fields are modified, while the subleading
logarithmic term does not. Finally, the luminosities of black holes are
computed by using the geometric optics approximation.Comment: 49pages, 2 figures; updated to match journal versio
Set Representations of Linegraphs
Let be a graph with vertex set and edge set . A family
of nonempty sets is a set representation of
if there exists a one-to-one correspondence between the vertices in and the sets in such that if and only if S_i\cap S_j\neq \es. A set representation
is a distinct (respectively, antichain, uniform and simple) set representation
if any two sets and in have the property (respectively, , and ). Let . Two set
representations and are isomorphic if
can be obtained from by a bijection from
to . Let denote a class of set
representations of a graph . The type of is the number of equivalence
classes under the isomorphism relation. In this paper, we investigate types of
set representations for linegraphs. We determine the types for the following
categories of set representations: simple-distinct, simple-antichain,
simple-uniform and simple-distinct-uniform
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