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

Decomposing generalized measurements into continuous stochastic processes

One of the broadest concepts of measurement in quantum theory is the generalized measurement. Another paradigm of measurement--arising naturally in quantum optics, among other fields--is that of continuous-time measurements, which can be seen as the limit of a consecutive sequence of weak measurements. They are naturally described in terms of stochastic processes, or time-dependent random variables. We show that any generalized measurement can be decomposed as a sequence of weak measurements with a mathematical limit as a continuous stochastic process. We give an explicit construction for any generalized measurement, and prove that the resulting continuous evolution, in the long-time limit, collapses the state of the quantum system to one of the final states generated by the generalized measurement, being decomposed, with the correct probabilities. A prominent feature of the construction is the presence of a feedback mechanism--the instantaneous choice weak measurement at a given time depends on the outcomes of earlier measurements. For a generalized measurement with $n$ outcomes, this information is captured by a real $n$-vector on an $n$-simplex, which obeys a simple classical stochastic evolution.Comment: 9 pages, LaTeX, name changed, typos correcte

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

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 $\Lambda>0$, saddle points can occur only for topologies with vanishing first Betti number and finite fundamental group. For $\Lambda<0$, 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 $\Lambda=0$ 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

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

The Topological Particle and Morse Theory

Canonical BRST quantization of the topological particle defined by a Morse function h is described. Stochastic calculus, using Brownian paths which implement the WKB method in a new way providing rigorous tunnelling results even in curved space, is used to give an explicit and simple expression for the matrix elements of the evolution operator for the BRST Hamiltonian. These matrix elements lead to a representation of the manifold cohomology in terms of critical points of h along lines developed by Witten.Comment: 18 page

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 ℝ 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

Selective Attenuation of Norepinephrine Release and Stress-Induced Heart Rate Increase by Partial Adenosine A1 Agonism

The release of the neurotransmitter norepinephrine (NE) is modulated by presynaptic adenosine receptors. In the present study we investigated the effect of a partial activation of this feedback mechanism. We hypothesized that partial agonism would have differential effects on NE release in isolated hearts as well as on heart rate in vivo depending on the genetic background and baseline sympathetic activity. In isolated perfused hearts of Wistar and Spontaneously Hypertensive Rats (SHR), NE release was induced by electrical stimulation under control conditions (S1), and with capadenoson 6 · 10−8 M (30 µg/l), 6 · 10−7 M (300 µg/l) or 2-chloro-N6-cyclopentyladenosine (CCPA) 10−6 M (S2). Under control conditions (S1), NE release was significantly higher in SHR hearts compared to Wistar (766+/−87 pmol/g vs. 173+/−18 pmol/g, p<0.01). Capadenoson led to a concentration-dependent decrease of the stimulation–induced NE release in SHR (S2/S1 = 0.90±0.08 with capadenoson 6 · 10−8 M, 0.54±0.02 with 6 · 10−7 M), but not in Wistar hearts (S2/S1 = 1.05±0.12 with 6 · 10−8 M, 1.03±0.09 with 6 · 10−7 M). CCPA reduced NE release to a similar degree in hearts from both strains. In vivo capadenoson did not alter resting heart rate in Wistar rats or SHR. Restraint stress induced a significantly greater increase of heart rate in SHR than in Wistar rats. Capadenoson blunted this stress-induced tachycardia by 45% in SHR, but not in Wistar rats. Using a [35S]GTPγS assay we demonstrated that capadenoson is a partial agonist compared to the full agonist CCPA (74+/−2% A1-receptor stimulation). These results suggest that partial adenosine A1-agonism dampens stress-induced tachycardia selectively in rats susceptible to strong increases in sympathetic activity, most likely due to a presynaptic attenuation of NE release

Zebrafish arl6ip1 Is Required for Neural Crest Development during Embryogenesis

BACKGROUND:Although the embryonic expression pattern of ADP ribosylation factor-like 6 interacting protein 1 (Arl6ip1) has been reported, its function in neural crest development is unclear. METHODS/PRINCIPAL FINDINGS:We found that knockdown of Arl6ip1 caused defective embryonic neural crest derivatives that were particularly severe in craniofacial cartilages. Expressions of the ectodermal patterning factors msxb, dlx3b, and pax3 were normal, but the expressions of the neural crest specifier genes foxd3, snai1b, and sox10 were greatly reduced. These findings suggest that arl6ip1 is essential for specification of neural crest derivatives, but not neural crest induction. Furthermore, we revealed that the streams of crestin- and sox10-expressing neural crest cells, which migrate ventrally from neural tube into trunk, were disrupted in arl6ip1 morphants. This migration defect was not only in the trunk neural crest, but also in the enteric tract where the vagal-derived neural crest cells failed to populate the enteric nervous system. We found that this migration defect was induced by dampened Shh signaling, which may have resulted from defective cilia. These data further suggested that arl6ip1 is required for neural crest migration. Finally, by double-staining of TUNEL and crestin, we confirmed that the loss of neural crest cells could not be attributed to apoptosis. CONCLUSIONS/SIGNIFICANCE:Therefore, we concluded that arl6ip1 is required for neural crest migration and sublineage specification