34,855 research outputs found
Extended Representations of Observables and States for a Noncontextual Reinterpretation of QM
A crucial and problematical feature of quantum mechanics (QM) is
nonobjectivity of properties. The ESR model restores objectivity reinterpreting
quantum probabilities as conditional on detection and embodying the
mathematical formalism of QM into a broader noncontextual (hence local)
framework. We propose here an improved presentation of the ESR model containing
a more complete mathematical representation of the basic entities of the model.
We also extend the model to mixtures showing that the mathematical
representations of proper mixtures does not coincide with the mathematical
representation of mixtures provided by QM, while the representation of improper
mixtures does. This feature of the ESR model entails that some interpretative
problems raising in QM when dealing with mixtures are avoided. From an
empirical point of view the predictions of the ESR model depend on some
parameters which may be such that they are very close to the predictions of QM
in most cases. But the nonstandard representation of proper mixtures allows us
to propose the scheme of an experiment that could check whether the predictions
of QM or the predictions of the ESR model are correct.Comment: 17 pages, standard latex. Extensively revised versio
An algebraic approach to problems with polynomial Hamiltonians on Euclidean spaces
Explicit expressions are given for the actions and radial matrix elements of
basic radial observables on multi-dimensional spaces in a continuous sequence
of orthonormal bases for unitary SU(1,1) irreps. Explicit expressions are also
given for SO(N)-reduced matrix elements of basic orbital observables. These
developments make it possible to determine the matrix elements of polynomial
and a other Hamiltonians analytically, to within SO(N) Clebsch-Gordan
coefficients, and to select an optimal basis for a particular problem such that
the expansion of eigenfunctions is most rapidly convergent.Comment: 19 pages, 8 figure
Temporal and Spatial Dependence of Quantum Entanglement from a Field Theory Perspective
We consider the entanglement dynamics between two Unruh-DeWitt detectors at
rest separated at a distance . This simple model when analyzed properly in
quantum field theory shows many interesting facets and helps to dispel some
misunderstandings of entanglement dynamics. We find that there is spatial
dependence of quantum entanglement in the stable regime due to the phase
difference of vacuum fluctuations the two detectors experience, together with
the interference of the mutual influences from the backreaction of one detector
on the other. When two initially entangled detectors are still outside each
other's light cone, the entanglement oscillates in time with an amplitude
dependent on spatial separation . When the two detectors begin to have
causal contact, an interference pattern of the relative degree of entanglement
(compared to those at spatial infinity) develops a parametric dependence on
. The detectors separated at those with a stronger relative degree of
entanglement enjoy longer disentanglement times. In the cases with weak
coupling and large separation, the detectors always disentangle at late times.
For sufficiently small , the two detectors can have residual entanglement
even if they initially were in a separable state, while for a little
larger, there could be transient entanglement created by mutual influences.
However, we see no evidence of entanglement creation outside the light cone for
initially separable states.Comment: 21 pages, 8 figures. Minor changes. Some plots are re-expressed in
logarithmic negativity. No change in the overall result
Gravity and Nonequilibrium Thermodynamics of Classical Matter
Renewed interest in deriving gravity (more precisely, the Einstein equations)
from thermodynamics considerations [1, 2] is stirred up by a recent proposal
that 'gravity is an entropic force' [3] (see also [4]). Even though I find the
arguments justifying such a claim in this latest proposal rather ad hoc and
simplistic compared to the original one I would unreservedly support the call
to explore deeper the relation between gravity and thermodynamics, this having
the same spirit as my long-held view that general relativity is the
hydrodynamic limit [5, 6] of some underlying theories for the microscopic
structure of spacetime - all these proposals, together with that of [7, 8],
attest to the emergent nature of gravity [9]. In this first paper of two we set
the modest goal of studying the nonequilibrium thermodynamics of classical
matter only, bringing afore some interesting prior results, without invoking
any quantum considerations such as Bekenstein-Hawking entropy, holography or
Unruh effect. This is for the sake of understanding the nonequilibrium nature
of classical gravity which is at the root of many salient features of black
hole physics. One important property of gravitational systems, from
self-gravitating gas to black holes, is their negative heat capacity, which is
the source of many out-of-the ordinary dynamical and thermodynamic features
such as the non-existence in isolated systems of thermodynamically stable
configurations, which actually provides the condition for gravitational
stability. A related property is that, being systems with long range
interaction, they are nonextensive and relax extremely slowly towards
equilibrium. Here we explore how much of the known features of black hole
thermodynamics can be derived from this classical nonequilibrium perspective. A
sequel paper will address gravity and nonequilibrium thermodynamics of quantum
fields [10].Comment: 25 pages essay. Invited Talk at Mariofest, March 2010, Rosario,
Argentina. Festschrift to appear as an issue of IJMP
Improved Color-Temperature Relations and Bolometric Corrections for Cool Stars
We present new grids of colors and bolometric corrections for F-K stars
having 4000 K < Teff < 6500 K, 0.0 < log g < 4.5 and -3.0 < [Fe/H] < 0.0. A
companion paper extends these calculations into the M giant regime. Colors are
tabulated for Johnson U-V and B-V; Cousins V-R and V-I; Johnson-Glass V-K, J-K
and H-K; and CIT/CTIO V-K, J-K, H-K and CO. We have developed these
color-temperature (CT) relations by convolving synthetic spectra with
photometric filter-transmission-profiles. The synthetic spectra have been
computed with the SSG spectral synthesis code using MARCS stellar atmosphere
models as input. Both of these codes have been improved substantially,
especially at low temperatures, through the incorporation of new opacity data.
The resulting synthetic colors have been put onto the observational systems by
applying color calibrations derived from models and photometry of field stars
which have Teffs determined by the infrared-flux method. The color calibrations
have zero points and slopes which change most of the original synthetic colors
by less than 0.02 mag and 5%, respectively. The adopted Teff scale (Bell &
Gustafsson 1989) is confirmed by the extraordinary agreement between the
predicted and observed angular diameters of the field stars. We have also
derived empirical CT relations from the field-star photometry. Except for the
coolest dwarfs (Teff < 5000 K), our calibrated, solar-metallicity model colors
are found to match these and other empirical relations quite well. Our
calibrated, 4 Gyr, solar-metallicity isochrone also provides a good match to
color-magnitude diagrams of M67. We regard this as evidence that our calibrated
colors can be applied to many astrophysical problems, including modelling the
integrated light of galaxies. (abridged)Comment: To appear in the March 2000 issue of the Astronomical Journal. 72
pages including 16 embedded postscript figures (one page each) and 6 embedded
postscript tables (18 pages total
Low frequency m=1 normal mode oscillations of a self-gravitating disc
A continuous system such as a galactic disc is shown to be well approximated
by an N-ring differentially rotating self-gravitating system. Lowest order
(m=1) non-axisymmetric features such as lopsidedness and warps are global in
nature and quite common in the discs of spiral galaxies. Apparently these two
features of the galactic discs have been treated like two completely disjoint
phenomena. The present analysis based on an eigenvalue approach brings out
clearly that these two features are fundamentally similar in nature and they
are shown to be very Low frequency Normal Mode (LNM) oscillations manifested in
different symmetry planes of the galactic disc. Our analysis also show that
these features are actually long-lived oscillating pattern of the N-ring
self-gravitating system.Comment: 5 figures. Accepted for publication in MNRAS Letter
Quantum theory of successive projective measurements
We show that a quantum state may be represented as the sum of a joint
probability and a complex quantum modification term. The joint probability and
the modification term can both be observed in successive projective
measurements. The complex modification term is a measure of measurement
disturbance. A selective phase rotation is needed to obtain the imaginary part.
This leads to a complex quasiprobability, the Kirkwood distribution. We show
that the Kirkwood distribution contains full information about the state if the
two observables are maximal and complementary. The Kirkwood distribution gives
a new picture of state reduction. In a nonselective measurement, the
modification term vanishes. A selective measurement leads to a quantum state as
a nonnegative conditional probability. We demonstrate the special significance
of the Schwinger basis.Comment: 6 page
Classical statistical distributions can violate Bell-type inequalities
We investigate two-particle phase-space distributions in classical mechanics
characterized by a well-defined value of the total angular momentum. We
construct phase-space averages of observables related to the projection of the
particles' angular momenta along axes with different orientations. It is shown
that for certain observables, the correlation function violates Bell's
inequality. The key to the violation resides in choosing observables impeding
the realization of the counterfactual event that plays a prominent role in the
derivation of the inequalities. This situation can have statistical (detection
related) or dynamical (interaction related) underpinnings, but non-locality
does not play any role.Comment: v3: Extended version. To be published in J. Phys.
Quantum Equilibrium and the Origin of Absolute Uncertainty
The quantum formalism is a ``measurement'' formalism--a phenomenological
formalism describing certain macroscopic regularities. We argue that it can be
regarded, and best be understood, as arising from Bohmian mechanics, which is
what emerges from Schr\"odinger's equation for a system of particles when we
merely insist that ``particles'' means particles. While distinctly
non-Newtonian, Bohmian mechanics is a fully deterministic theory of particles
in motion, a motion choreographed by the wave function. We find that a Bohmian
universe, though deterministic, evolves in such a manner that an {\it
appearance} of randomness emerges, precisely as described by the quantum
formalism and given, for example, by ``\rho=|\psis|^2.'' A crucial ingredient
in our analysis of the origin of this randomness is the notion of the effective
wave function of a subsystem, a notion of interest in its own right and of
relevance to any discussion of quantum theory. When the quantum formalism is
regarded as arising in this way, the paradoxes and perplexities so often
associated with (nonrelativistic) quantum theory simply evaporate.Comment: 75 pages. This paper was published a long time ago, but was never
archived. We do so now because it is basic for our recent article
quant-ph/0308038, which can in fact be regarded as an appendix of the earlier
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