On the definition of Quantum Free Particle on Curved Manifolds

A selfconsistent definition of quantum free particle on a generic curved manifold emerges naturally by restricting the dynamics to submanifolds of co-dimension one. PACS 0365 0240Comment: 8 p., phyzzx macropackag

Geometric Phase, Curvature, and Extrapotentials in Constrained Quantum Systems

We derive an effective Hamiltonian for a quantum system constrained to a submanifold (the constraint manifold) of configuration space (the ambient space) by an infinite restoring force. We pay special attention to how this Hamiltonian depends on quantities which are external to the constraint manifold, such as the external curvature of the constraint manifold, the (Riemannian) curvature of the ambient space, and the constraining potential. In particular, we find the remarkable fact that the twisting of the constraining potential appears as a gauge potential in the constrained Hamiltonian. This gauge potential is an example of geometric phase, closely related to that originally discussed by Berry. The constrained Hamiltonian also contains an effective potential depending on the external curvature of the constraint manifold, the curvature of the ambient space, and the twisting of the constraining potential. The general nature of our analysis allows applications to a wide variety of problems, such as rigid molecules, the evolution of molecular systems along reaction paths, and quantum strip waveguides.Comment: 27 pages with 1 figure, submitted to Phys. Rev.

Period-doubling bifurcation in strongly anisotropic Bianchi I quantum cosmology

We solve the Wheeler-DeWitt equation for the minisuperspace of a cosmological model of Bianchi type I with a minimally coupled massive scalar field $\phi$ as source by generalizing the calculation of Lukash and Schmidt [1]. Contrarily to other approaches we allow strong anisotropy. Combining analytical and numerical methods, we apply an adiabatic approximation for $\phi$, and as new feature we find a period-doubling bifurcation. This bifurcation takes place near the cosmological quantum boundary, i.e., the boundary of the quasiclassical region with oscillating $\psi$-function where the WKB-approximation is good. The numerical calculations suggest that such a notion of a ``cosmological quantum boundary'' is well-defined, because sharply beyond that boundary, the WKB-approximation is no more applicable at all. This result confirms the adequateness of the introduction of a cosmological quantum boundary in quantum cosmology.Comment: Latest update of the paper at http://www.physik.fu-berlin.de/~mbach/publics.html#

Effects of eight-quark interactions on the hadronic vacuum and mass spectra of light mesons

The combined effective low energy QCD Lagrangians of Nambu -- Jona-Lasinio (NJL) and 't Hooft are supplemented with eight-quark interactions. This work is a follow-up of recent findings, namely (i) the six quark flavour determinant 't Hooft term destabilizes the NJL vacuum, (ii) the addition of a chiral invariant eight-fermion contact term renders the ground state of the theory globally stable; (iii) stability constrains the values of coupling constants of the model, meaning that even in the presence of eight-quark forces the system can be unstable in a certain parameter region. In the present work we study a phenomenological output of eight-quark interactions considering the mass spectra of pseudoscalar and scalar mesons. Mixing angles are obtained and their equivalence to the two angle approach is derived. We show that the masses of pseudoscalars are almost neutral to the eight-quark forces. The only marked effect of the second order in the SU(3) breaking is found in the $\eta -\eta'$ system. The scalars are more sensitive to the eight-quark interactions. A strong repulsion between the singlet-octet members is the reason for the obtained low mass of the $\sigma$ state within the model considered.Comment: LaTeX, 46 pages, two figure

Quantizing Constrained Systems: New Perspectives

We consider quantum mechanics on constrained surfaces which have non-Euclidean metrics and variable Gaussian curvature. The old controversy about the ambiguities involving terms in the Hamiltonian of order hbar^2 multiplying the Gaussian curvature is addressed. We set out to clarify the matter by considering constraints to be the limits of large restoring forces as the constraint coordinates deviate from their constrained values. We find additional ambiguous terms of order hbar^2 involving freedom in the constraining potentials, demonstrating that the classical constrained Hamiltonian or Lagrangian cannot uniquely specify the quantization: the ambiguity of directly quantizing a constrained system is inherently unresolvable. However, there is never any problem with a physical quantum system, which cannot have infinite constraint forces and always fluctuates around the mean constraint values. The issue is addressed from the perspectives of adiabatic approximations in quantum mechanics, Feynman path integrals, and semiclassically in terms of adiabatic actions.Comment: 11 pages, 2 figure

The Hamiltonian Dynamics of Bounded Spacetime and Black Hole Entropy: The Canonical Method

From first principles, I present a concrete realization of Carlip's idea on the black hole entropy from the conformal field theory on the horizon in any dimension. New formulation is free of inconsistencies encountered in Carlip's. By considering a correct gravity action, whose variational principle is well defined at the horizon, I $derive$ a correct $classical$ Virasoro generator for the surface deformations at the horizon through the canonical method. The existence of the classical Virasoro algebra is crucial in obtaining an operator Virasoro algebra, through canonical quantization, which produce the right central charge and conformal weight $\sim A_+/\hbar G$ for the semiclassical black hole entropy. The coefficient of proportionality depends on the choice of ground state, which has to be put in by hand to obtain the correct numerical factor 1/4 of the Bekenstein-Hawking (BH) entropy. The appropriate ground state is different for the rotating and the non-rotating black holes but otherwise it has a $universality$ for a wide variety of black holes. As a byproduct of my results, I am led to conjecture that {\it non-commutativity of taking the limit to go to the horizon and computing variation is proportional to the Hamiltonian and momentum constraints}. It is shown that almost all the known uncharged black hole solutions satisfy the conditions for the universal entropy formula.Comment: Much details omitted, references added, accepted in Nucl. Phys.

Propensities and Second Order Uncertainty: A Modified Taxi Cab Problem

The study of people’s ability to engage in causal probabilistic reasoning has typically used fixed-point estimates for key figures. For example, in the classic taxi-cab problem, where a witness provides evidence on which of two cab companies (the more common ‘green’/less common ‘blue’) were responsible for a hit and run incident, solvers are told the witness’s ability to judge cab color is 80%. In reality, there is likely to be some uncertainty around this estimate (perhaps we tested the witness and they were correct 4/5 times), known as second-order uncertainty, producing a distribution rather than a fixed probability. While generally more closely matching real world reasoning, a further important ramification of this is that our best estimate of the witness’ accuracy can and should change when the witness makes the claim that the cab was blue. We present a Bayesian Network model of this problem, and show that, while the witness’s report does increase our probability of the cab being blue, it simultaneously decreases our estimate of their future accuracy (because blue cabs are less common). We presented this version of the problem to 131 participants, requiring them to update their estimates of both the probability the cab involved was blue, as well as the witness’s accuracy, after they claim it was blue. We also required participants to explain their reasoning process and provided follow up questions to probe various aspects of their reasoning. While some participants responded normatively, the majority self-reported ‘assuming’ one of the probabilities was a certainty. Around a quarter assumed the cab was green, and thus the witness was wrong, decreasing their estimate of their accuracy. Another quarter assumed the witness was correct and actually increased their estimate of their accuracy, showing a circular logic similar to that seen in the confirmation bias/belief polarization literature. Around half of participants refused to make any change, with convergent evidence suggesting that these participants do not see the relevance of the witness’s report to their accuracy before we know for certain whether they are correct or incorrect

Categorical Updating in a Bayesian Propensity Problem

We present three experiments using a novel problem in which participants update their estimates of propensities when faced with an uncertain new instance. We examine this using two different causal structures (common cause/common effect) and two different scenarios (agent-based/mechanical). In the first, participants must update their estimate of the propensity for two warring nations to successfully explode missiles after being told of a new explosion on the border between both nations. In the second, participants must update their estimate of the accuracy of two early warning tests for cancer when they produce conflicting reports about a patient. Across both experiments, we find two modal responses, representing around one-third of participants each. In the first, "Categorical" response, participants update propensity estimates as if they were certain about the single event, for example, certain that one of the nations was responsible for the latest explosion, or certain about which of the two tests is correct. In the second, "No change" response, participants make no update to their propensity estimates at all. Across the three experiments, the theory is developed and tested that these two responses in fact have a single representation of the problem: because the actual outcome is binary (only one of the nations could have launched the missile; the patient either has cancer or not), these participants believe it is incorrect to update propensities in a graded manner. They therefore operate on a "certainty threshold" basis, whereby, if they are certain enough about the single event, they will make the "Categorical" response, and if they are below this threshold, they will make the "No change" response. Ramifications are considered for the "categorical" response in particular, as this approach produces a positive-feedback dynamic similar to that seen in the belief polarization/confirmation bias literature

Stochastic Gravity: Theory and Applications

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Second, we discuss structure formation from the stochastic gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a black hole and describe the metric fluctuations near the event horizon of an evaporating black holeComment: 100 pages, no figures; an update of the 2003 review in Living Reviews in Relativity gr-qc/0307032 ; it includes new sections on the Validity of Semiclassical Gravity, the Stability of Minkowski Spacetime, and the Metric Fluctuations of an Evaporating Black Hol

Pathogen-induced hatching and population-specific life-history response to water-borne cues in brown trout (Salmo trutta)

Hatching is an important niche shift, and embryos in a wide range of taxa can either accelerate or delay this life-history switch in order to avoid stage-specific risks. Such behavior can occur in response to stress itself and to chemical cues that allow anticipation of stress. We studied the genetic organization of this phenotypic plasticity and tested whether there are differences among populations and across environments in order to learn more about the evolutionary potential of stress-induced hatching. As a study species, we chose the brown trout (Salmo trutta; Salmonidae). Gametes were collected from five natural populations (within one river network) and used for full-factorial in vitro fertilizations. The resulting embryos were either directly infected with Pseudomonas fluorescens or were exposed to waterborne cues from P. fluorescens-infected conspecifics. We found that direct inoculation with P. fluorescens increased embryonic mortality and induced hatching in all host populations. Exposure to waterborne cues revealed population-specific responses. We found significant additive genetic variation for hatching time, and genetic variation in trait plasticity. In conclusion, hatching is induced in response to infection and can be affected by waterborne cues of infection, but populations and families differ in their reaction to the latter