4,161 research outputs found
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
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