173 research outputs found
A Rigorous Approach to the Feynman-Vernon Influence Functional and its Applications. I
A rigorous representation of the Feynman-Vernon influence functional used to describe open quantum systems is given, based on the theory of infinite dimensional oscillatory integrals. An application to the case of the density matrices describing the Caldeira-Leggett model of two quantum systems with a quadratic interaction is treated
Time separation as a hidden variable to the Copenhagen school of quantum mechanics
The Bohr radius is a space-like separation between the proton and electron in
the hydrogen atom. According to the Copenhagen school of quantum mechanics, the
proton is sitting in the absolute Lorentz frame. If this hydrogen atom is
observed from a different Lorentz frame, there is a time-like separation
linearly mixed with the Bohr radius. Indeed, the time-separation is one of the
essential variables in high-energy hadronic physics where the hadron is a bound
state of the quarks, while thoroughly hidden in the present form of quantum
mechanics. It will be concluded that this variable is hidden in Feynman's rest
of the universe. It is noted first that Feynman's Lorentz-invariant
differential equation for the bound-state quarks has a set of solutions which
describe all essential features of hadronic physics. These solutions explicitly
depend on the time separation between the quarks. This set also forms the
mathematical basis for two-mode squeezed states in quantum optics, where both
photons are observable, but one of them can be treated a variable hidden in the
rest of the universe. The physics of this two-mode state can then be translated
into the time-separation variable in the quark model. As in the case of the
un-observed photon, the hidden time-separation variable manifests itself as an
increase in entropy and uncertainty.Comment: LaTex 10 pages with 5 figure. Invited paper presented at the
Conference on Advances in Quantum Theory (Vaxjo, Sweden, June 2010), to be
published in one of the AIP Conference Proceedings serie
G-Brownian Motion as Rough Paths and Differential Equations Driven by G-Brownian Motion
The present paper is devoted to the study of sample paths of G-Brownian
motion and stochastic differential equations (SDEs) driven by G-Brownian motion
from the view of rough path theory. As the starting point, we show that
quasi-surely, sample paths of G-Brownian motion can be enhanced to the second
level in a canonical way so that they become geometric rough paths of roughness
2 < p < 3. This result enables us to introduce the notion of rough differential
equations (RDEs) driven by G-Brownian motion in the pathwise sense under the
general framework of rough paths. Next we establish the fundamental relation
between SDEs and RDEs driven by G-Brownian motion. As an application, we
introduce the notion of SDEs on a differentiable manifold driven by GBrownian
motion and construct solutions from the RDE point of view by using pathwise
localization technique. This is the starting point of introducing G-Brownian
motion on a Riemannian manifold, based on the idea of Eells-Elworthy-Malliavin.
The last part of this paper is devoted to such construction for a wide and
interesting class of G-functions whose invariant group is the orthogonal group.
We also develop the Euler-Maruyama approximation for SDEs driven by G-Brownian
motion of independent interest
Brownian bridges to submanifolds
We introduce and study Brownian bridges to submanifolds. Our method involves
proving a general formula for the integral over a submanifold of the minimal
heat kernel on a complete Riemannian manifold. We use the formula to derive
lower bounds, an asymptotic relation and derivative estimates. We also see a
connection to hypersurface local time. This work is motivated by the desire to
extend the analysis of path and loop spaces to measures on paths which
terminate on a submanifold
On arbitrages arising from honest times
In the context of a general continuous financial market model, we study
whether the additional information associated with an honest time gives rise to
arbitrage profits. By relying on the theory of progressive enlargement of
filtrations, we explicitly show that no kind of arbitrage profit can ever be
realised strictly before an honest time, while classical arbitrage
opportunities can be realised exactly at an honest time as well as after an
honest time. Moreover, stronger arbitrages of the first kind can only be
obtained by trading as soon as an honest time occurs. We carefully study the
behavior of local martingale deflators and consider no-arbitrage-type
conditions weaker than NFLVR.Comment: 25 pages, revised versio
Dominant Topologies in Euclidean Quantum Gravity
The dominant topologies in the Euclidean path integral for quantum gravity
differ sharply according on the sign of the cosmological constant. For
, saddle points can occur only for topologies with vanishing first
Betti number and finite fundamental group. For , on the other hand,
the path integral is dominated by topologies with extremely complicated
fundamental groups; while the contribution of each individual manifold is
strongly suppressed, the ``density of topologies'' grows fast enough to
overwhelm this suppression. The value is thus a sort of boundary
between phases in the sum over topologies. I discuss some implications for the
cosmological constant problem and the Hartle-Hawking wave function.Comment: 14 pages, LaTeX. Minor additions (computability, relation to
``minimal volume'' in topology); error in eqn (3.5) corrected; references
added. To appear in Class. Quant. Gra
Gfi1aa and Gfi1b set the pace for primitive erythroblast differentiation from hemangioblasts in the zebrafish embryo
The transcriptional repressors G
fi
1(a) and G
fi
1b are epigenetic regulators with unique and
overlapping roles in hematopoiesis. In different contexts, G
fi
1 and G
fi
1b restrict or promote
cell proliferation, prevent apoptosis, in
fl
uence cell fate decisions, and are essential for
terminal differentiation. Here, we show in primitive red blood cells (prRBCs) that they can
also set the pace for cellular differentiation. In zebra
fi
sh, prRBCs express 2 of 3 zebra
fi
sh G
fi
1/
1bparalogs,G
fi
1aaandG
fi
1b.Therecentlyidenti
fi
edzebra
fi
sh
gfi1aa
gene trap allele
qmc551
drives erythroid green
fl
uorescent protein (GFP) instead of G
fi
1aa expression, yet
homozygous carriers have normal prRBCs. prRBCs display a maturation defect only after
splice morpholino-mediated knockdown of G
fi
1b in
gfi1aa
qmc551
homozygous embryos. To study
the transcriptome of the G
fi
1aa/1b double-depleted cells, we performed an RNA-Seq experi-
ment on GFP-positive prRBCs sorted from 20-h
our-old embryos that were heterozygous or
homozygous for
gfi1aa
qmc551
,aswellas
wt
or morphant for
gfi1b
.Wesubsequentlycon
fi
rmed
and extended these data in whole-mount in situ hybridization experiments on newly generated
single- and double-mutant embryos. Combi
ned, the data showed that in the absence of G
fi
1aa,
the synchronously developing prRBCs were delayed
in activating late erythr
oid differentiation,
as they struggled to suppress early erythroid and
endothelial transcripti
on programs. The latter
highlighted the bipotent natu
re of the progenitors from which prRBCs arise. In the absence
of G
fi
1aa, G
fi
1b promoted erythroid differentiation as stepwise loss of
wt gfi1b
copies
progressively delayed G
fi
1aa-depleted prRBCs even
further, showing that G
fi
1aa and G
fi
1b
together set the pace for prRBC diffe
rentiation from hemangioblasts
Laplace Operators on Fractals and Related Functional Equations
We give an overview over the application of functional equations, namely the
classical Poincar\'e and renewal equations, to the study of the spectrum of
Laplace operators on self-similar fractals. We compare the techniques used to
those used in the euclidean situation. Furthermore, we use the obtained
information on the spectral zeta function to define the Casimir energy of
fractals. We give numerical values for this energy for the Sierpi\'nski gasket
Functional inequalities on manifolds with non-convex boundary
In this article, new curvature conditions are introduced to establish functional inequalities including gradient estimates, Harnack inequalities and transportation-cost inequalities on manifolds with non-convex boundary
Necessary and sufficient conditions for path-independence of Girsanov transformation for infinite-dimensional stochastic evolution equations
Based on a recent result on linking stochastic differential equations on â d to (finite-dimensional) Burger-KPZ type nonlinear parabolic partial differential equations, we utilize Galerkin type finite-dimensional approximations to characterize the path-independence of the density process of Girsanov transformation for the infinite-dimensional stochastic evolution equations. Our result provides a link of infinite-dimensional semi-linear stochastic differential equations to infinite-dimensional Burgers-KPZ type nonlinear parabolic partial differential equations. As an application, this characterization result is applied to stochastic heat equation in one space dimension over the unit interval
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