4,753 research outputs found
Spectral and Hodge theory of `Witt' incomplete cusp edge spaces
Incomplete cusp edges model the behavior of the Weil-Petersson metric on the compactified Riemann moduli space near the interior of a divisor. Assuming such a space is Witt, we construct a fundamental solution to the heat equation, and using a precise description of its asymptotic behavior at the singular set, we prove that the Hodge-Laplacian on differential forms is essentially self-adjoint, with discrete spectrum satisfying Weyl asymptotics. We go on to prove bounds on the growth of -harmonic forms at the singular set and to prove a Hodge theorem, namely that the space of -harmonic forms is naturally isomorphic to the middle-perversity intersection cohomology. Moreover, we develop an asymptotic expansion for the heat trace near
Quasiclassical Coarse Graining and Thermodynamic Entropy
Our everyday descriptions of the universe are highly coarse-grained,
following only a tiny fraction of the variables necessary for a perfectly
fine-grained description. Coarse graining in classical physics is made natural
by our limited powers of observation and computation. But in the modern quantum
mechanics of closed systems, some measure of coarse graining is inescapable
because there are no non-trivial, probabilistic, fine-grained descriptions.
This essay explores the consequences of that fact. Quantum theory allows for
various coarse-grained descriptions some of which are mutually incompatible.
For most purposes, however, we are interested in the small subset of
``quasiclassical descriptions'' defined by ranges of values of averages over
small volumes of densities of conserved quantities such as energy and momentum
and approximately conserved quantities such as baryon number. The
near-conservation of these quasiclassical quantities results in approximate
decoherence, predictability, and local equilibrium, leading to closed sets of
equations of motion. In any description, information is sacrificed through the
coarse graining that yields decoherence and gives rise to probabilities for
histories. In quasiclassical descriptions, further information is sacrificed in
exhibiting the emergent regularities summarized by classical equations of
motion. An appropriate entropy measures the loss of information. For a
``quasiclassical realm'' this is connected with the usual thermodynamic entropy
as obtained from statistical mechanics. It was low for the initial state of our
universe and has been increasing since.Comment: 17 pages, 0 figures, revtex4, Dedicated to Rafael Sorkin on his 60th
birthday, minor correction
Decoherent Histories Quantum Mechanics with One 'Real' Fine-Grained History
Decoherent histories quantum theory is reformulated with the assumption that
there is one "real" fine-grained history, specified in a preferred complete set
of sum-over-histories variables. This real history is described by embedding it
in an ensemble of comparable imagined fine-grained histories, not unlike the
familiar ensemble of statistical mechanics. These histories are assigned
extended probabilities, which can sometimes be negative or greater than one. As
we will show, this construction implies that the real history is not completely
accessible to experimental or other observational discovery. However,
sufficiently and appropriately coarse-grained sets of alternative histories
have standard probabilities providing information about the real fine-grained
history that can be compared with observation. We recover the probabilities of
decoherent histories quantum mechanics for sets of histories that are recorded
and therefore decohere. Quantum mechanics can be viewed as a classical
stochastic theory of histories with extended probabilities and a well-defined
notion of reality common to all decoherent sets of alternative coarse-grained
histories.Comment: 11 pages, one figure, expanded discussion and acknowledgment
Probing minimal supergravity in the type-I seesaw mechanism with lepton flavour violation at the CERN LHC
The most general supersymmetric seesaw mechanism has too many parameters to
be predictive and thus can not be excluded by any measurements of lepton
flavour violating (LFV) processes. We focus on the simplest version of the
type-I seesaw mechanism assuming minimal supergravity boundary conditions. We
compute branching ratios for the LFV scalar tau decays, , as well as loop-induced LFV decays at low energy, such as
and , exploring their sensitivity to the
unknown seesaw parameters. We find some simple, extreme scenarios for the
unknown right-handed parameters, where ratios of LFV branching ratios correlate
with neutrino oscillation parameters. If the overall mass scale of the left
neutrinos and the value of the reactor angle were known, the study of LFV
allows, in principle, to extract information about the so far unknown
right-handed neutrino parameters.Comment: 29 pages, 27 figures; added explanatory comments, corrected typos,
final version for publicatio
PRDM14 is expressed in germ cell tumors with constitutive overexpression altering human germline differentiation and proliferation.
Germ cell tumors (GCTs) are a heterogeneous group of tumors occurring in gonadal and extragonadal locations. GCTs are hypothesized to arise from primordial germ cells (PGCs), which fail to differentiate. One recently identified susceptibility loci for human GCT is PR (PRDI-BF1 and RIZ) domain proteins 14 (PRDM14). PRDM14 is expressed in early primate PGCs and is repressed as PGCs differentiate. To examine PRDM14 in human GCTs we profiled human GCT cell lines and patient samples and discovered that PRDM14 is expressed in embryonal carcinoma cell lines, embryonal carcinomas, seminomas, intracranial germinomas and yolk sac tumors, but is not expressed in teratomas. To model constitutive overexpression in human PGCs, we generated PGC-like cells (PGCLCs) from human pluripotent stem cells (PSCs) and discovered that elevated expression of PRDM14 does not block early PGC formation. Instead, we show that elevated PRDM14 in PGCLCs causes proliferation and differentiation defects in the germline
Quantum spacetime and the renormalization group: Progress and visions
The quest for a consistent theory which describes the quantum microstructure
of spacetime seems to require some departure from the paradigms that have been
followed in the construction of quantum theories for the other fundamental
interactions. In this contribution we briefly review two approaches to quantum
gravity, namely, asymptotically safe quantum gravity and tensor models, based
on different theoretical assumptions. Nevertheless, the main goal is to find a
universal continuum limit for such theories and we explain how coarse-graining
techniques should be adapted to each case. Finally, we argue that although
seemingly different, such approaches might be just two sides of the same coin.Comment: 14 pages, 4 figures, Proceedings of "Progress and Visions in Quantum
Theory in View of Gravity: Bridging foundations of physics and mathematics",
Leipzig, 201
Singular Instantons Made Regular
The singularity present in cosmological instantons of the Hawking-Turok type
is resolved by a conformal transformation, where the conformal factor has a
linear zero of codimension one. We show that if the underlying regular manifold
is taken to have the topology of , and the conformal factor is taken to
be a twisted field so that the zero is enforced, then one obtains a
one-parameter family of solutions of the classical field equations, where the
minimal action solution has the conformal zero located on a minimal volume
noncontractible submanifold. For instantons with two singularities, the
corresponding topology is that of a cylinder with D=4
analogues of `cross-caps' at each of the endpoints.Comment: 23 pages, compressed and RevTex file, including nine postscript
figure files. Submitted versio
Decoherence of Hydrodynamic Histories: A Simple Spin Model
In the context of the decoherent histories approach to the quantum mechanics
of closed systems, Gell-Mann and Hartle have argued that the variables
typically characterizing the quasiclassical domain of a large complex system
are the integrals over small volumes of locally conserved densities --
hydrodynamic variables. The aim of this paper is to exhibit some simple models
in which approximate decoherence arises as a result of local conservation. We
derive a formula which shows the explicit connection between local conservation
and approximate decoherence. We then consider a class of models consisting of a
large number of weakly interacting components, in which the projections onto
local densities may be decomposed into projections onto one of two alternatives
of the individual components. The main example we consider is a one-dimensional
chain of locally coupled spins, and the projections are onto the total spin in
a subsection of the chain. We compute the decoherence functional for histories
of local densities, in the limit when the number of components is very large.
We find that decoherence requires two things: the smearing volumes must be
sufficiently large to ensure approximate conservation, and the local densities
must be partitioned into sufficiently large ranges to ensure protection against
quantum fluctuations.Comment: Standard TeX, 36 pages + 3 figures (postscript) Revised abstract and
introduction. To appear in Physical Review
Electroweak Baryogenesis from Late Neutrino Masses
Electroweak Baryogenesis, given a first order phase transition, does not work
in the standard model because the quark Yukawa matrices are too hierarchical.
On the other hand, the neutrino mass matrix is apparently not hierarchical. In
models with neutrino mass generation at low scales, the neutrino Yukawa
couplings lead to large CP-violation in the reflection probability of heavy
leptons by the expanding Higgs bubble wall, and can generate the observed
baryon asymmetry of the universe. The mechanism predicts new vector-like
leptons below the TeV scale and sizable mu -> e processes.Comment: 5 pages, 2 figures, references adde
Excited nucleon electromagnetic form factors from broken spin-flavor symmetry
A group theoretical derivation of a relation between the N --> Delta charge
quadrupole transition and neutron charge form factors is presented.Comment: 4 pages, Proc. of the 12 th Int'l. Workshop on the Physics of Excited
Nucleons, NSTAR 2009, Beijing, April 19-22, 200
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