Dualities among 1T-Field Theories with Spin, Emerging from a Unifying 2T-Field Theory

The relation between two time physics (2T-physics) and the ordinary one time formulation of physics (1T-physics) is similar to the relation between a 3-dimensional object moving in a room and its multiple shadows moving on walls when projected from different perspectives. The multiple shadows as seen by observers stuck on the wall are analogous to the effects of the 2T-universe as experienced in ordinary 1T spacetime. In this paper we develop some of the quantitative aspects of this 2T to 1T relationship in the context of field theory. We discuss 2T field theory in d+2 dimensions and its shadows in the form of 1T field theories when the theory contains Klein-Gordon, Dirac and Yang-Mills fields, such as the Standard Model of particles and forces. We show that the shadow 1T field theories must have hidden relations among themselves. These relations take the form of dualities and hidden spacetime symmetries. A subset of the shadows are 1T field theories in different gravitational backgrounds (different space-times) such as the flat Minkowski spacetime, the Robertson-Walker expanding universe, AdS(d-k) x S(k) and others, including singular ones. We explicitly construct the duality transformations among this conformally flat subset, and build the generators of their hidden SO(d,2) symmetry. The existence of such hidden relations among 1T field theories, which can be tested by both theory and experiment in 1T-physics, is part of the evidence for the underlying d+2 dimensional spacetime and the unifying 2T-physics structure.Comment: 33 pages, LaTe

Platform Pricing Structure and Moral Hazard

We study pricing by a monopoly platform that matches buyers and sellers in an environment with cross-market externalities. Said platform has no private information, does not set the commodity's price and can only charge trading parties for the transaction. Our innovation consists in introducing moral hazard on the sellers' side and an equilibrium notion of platform reputation in an infinite horizon model. With linear fees the platform can mitigate, but not eliminate, the loss of reputation induced by moral hazard. If lump-sum fees (registration fees) can be levied, moral hazard can be overcome. The upfront payment determines the participation threshold of sellers and extracts them, while (lower) transactions fees provide incentives for good behavior. This breaks the equivalence of lump-sum payments and linear fees (Rochet and Tirole (2006)). We draw implications for the role of subsidies (Caillaud and Jullien (2003)).Platforms; Two-Sided Markets; Reputation; Moral Hazard

Two properties of vectors of quadratic forms in Gaussian random variables

We study distributions of random vectors whose components are second order polynomials in Gaussian random variables. Assuming that the law of such a vector is not absolutely continuous with respect to Lebesgue measure, we derive some interesting consequences. Our second result gives a characterization of limits in law for sequences of such vectors.Comment: 14 page

Non-equilibrium Transport in the Anderson model of a biased Quantum Dot: Scattering Bethe Ansatz Phenomenology

We derive the transport properties of a quantum dot subject to a source-drain bias voltage at zero temperature and magnetic field. Using the Scattering Bethe Anstaz, a generalization of the traditional Thermodynamic Bethe Ansatz to open systems out of equilibrium, we derive exact results for the quantum dot occupation out of equilibrium and, by introducing phenomenological spin- and charge-fluctuation distribution functions in the computation of the current, obtain the differential conductance for large U/\Gamma. The Hamiltonian to describe the quantum dot system is the Anderson impurity Hamiltonian and the current and dot occupation as a function of voltage are obtained numerically. We also vary the gate voltage and study the transition from the mixed valence to the Kondo regime in the presence of a non-equilibrium current. We conclude with the difficulty we encounter in this model and possible way to solve them without resorting to a phenomenological method.Comment: 20 pages, 20 figures, published versio

Magneto-optical response in bimetallic metamaterials

We demonstrate resonant Faraday polarization rotation in plasmonic arrays of bimetallic nano-ring resonators consisting of Au and Ni sections. This metamaterial design allows to optimize the trade-off between the enhancement of magneto-optical effects and plasmonic dissipation. Although Ni sections correspond to as little as ~6% of the total surface of the metamaterial, the resulting magneto-optically induced polarization rotation is equal to that of a continuous film. Such bimetallic metamaterials can be used in compact magnetic sensors, active plasmonic components and integrated photonic circuits

Correlation-based model of artificially induced plasticity in motor cortex by a bidirectional brain-computer interface

Experiments show that spike-triggered stimulation performed with Bidirectional Brain-Computer-Interfaces (BBCI) can artificially strengthen connections between separate neural sites in motor cortex (MC). What are the neuronal mechanisms responsible for these changes and how does targeted stimulation by a BBCI shape population-level synaptic connectivity? The present work describes a recurrent neural network model with probabilistic spiking mechanisms and plastic synapses capable of capturing both neural and synaptic activity statistics relevant to BBCI conditioning protocols. When spikes from a neuron recorded at one MC site trigger stimuli at a second target site after a fixed delay, the connections between sites are strengthened for spike-stimulus delays consistent with experimentally derived spike time dependent plasticity (STDP) rules. However, the relationship between STDP mechanisms at the level of networks, and their modification with neural implants remains poorly understood. Using our model, we successfully reproduces key experimental results and use analytical derivations, along with novel experimental data. We then derive optimal operational regimes for BBCIs, and formulate predictions concerning the efficacy of spike-triggered stimulation in different regimes of cortical activity.Comment: 35 pages, 9 figure

Classical mechanics as nonlinear quantum mechanics

All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schrodinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a linear equation is real and positive, rather than complex. This has profound implications on the role of the Bohmian classical-like interpretation of linear quantum mechanics, as well as on the possibilities to find a consistent interpretation of arbitrary nonlinear generalizations of quantum mechanics.Comment: 7 pages, invited talk given at conference Quantum Theory: Reconsideration of Foundations 4, Vaxjo, Sweden, June 11-16, 200

EPR Paradox,Locality and Completeness of Quantum Theory

The quantum theory (QT) and new stochastic approaches have no deterministic prediction for a single measurement or for a single time -series of events observed for a trapped ion, electron or any other individual physical system. The predictions of QT being of probabilistic character apply to the statistical distribution of the results obtained in various experiments. The probability distribution is not an attribute of a dice but it is a characteristic of a whole random experiment : '' rolling a dice''. and statistical long range correlations between two random variables X and Y are not a proof of any causal relation between these variable. Moreover any probabilistic model used to describe a random experiment is consistent only with a specific protocol telling how the random experiment has to be performed.In this sense the quantum theory is a statistical and contextual theory of phenomena. In this paper we discuss these important topics in some detail. Besides we discuss in historical perspective various prerequisites used in the proofs of Bell and CHSH inequalities concluding that the violation of these inequalities in spin polarization correlation experiments is neither a proof of the completeness of QT nor of its nonlocality. The question whether QT is predictably complete is still open and it should be answered by a careful and unconventional analysis of the experimental data. It is sufficient to analyze more in detail the existing experimental data by using various non-parametric purity tests and other specific statistical tools invented to study the fine structure of the time-series. The correct understanding of statistical and contextual character of QT has far reaching consequences for the quantum information and quantum computing.Comment: 16 pages, 59 references,the contribution to the conference QTRF-4 held in Vaxjo, Sweden, 11-16 june 2007. To be published in the Proceeding

A Curious Geometrical Fact About Entanglement

I sketch how the set of pure quantum states forms a phase space, and then point out a curiousity concerning maximally entangled pure states: they form a minimal Lagrangian submanifold of the set of all pure states. I suggest that this curiousity should have an interesting physical interpretation.Comment: Talk at the Vaxjo conference on Quantum Theory: Reconsideration of Foundations -

Geometrization of Classical Wave Fields

Geometrical model for material Dirac wave field and for Maxwell electromagnetic field is suggested where above fields are considered as propagating regions of the space itself with distorted euclidean geometry. It is shown that equations for these fields can be considered as relations describing the space topological defects. These defects, being closed topological manifolds, are embedded in the outer five-dimensional space, and observable objects appear to be intersections of above defects with the physical space. This interpretation explains irrational properties of quantum objects such as wave-corpuscular duality, stochastic behavior, instantaneous nonlocal correlation in EPR-paradox, the light velocity invariance and so on. Wave-corpuscular properties arise as a result of the defect periodical movement in the outer space relative to its intersection with the physical space, and just this periodical movement attributes phase to the propagating object. Appearance of probabilities within the formalism is a consequence of uncertainty of the closed topological manifold shape, and ensemble of all possible shapes for the same object can be considered as an ensemble of hidden variables that leads to probabilistic description. Embedded in the outer space topological defects provide channels for nonlocal correlations between their intersections-- noninteracting particles in EPR-experiments, and this means that the proposed approach can be considered as a nonlocal model with hidden variables.Comment: 7 pages, Int.Conf.,Quantum Theory: Reconsideration of Foundations-4, Vaxjo, Sweden. 11-16 June 200