47,284 research outputs found
Conservation laws arising in the study of forward-forward Mean-Field Games
We consider forward-forward Mean Field Game (MFG) models that arise in
numerical approximations of stationary MFGs. First, we establish a link between
these models and a class of hyperbolic conservation laws as well as certain
nonlinear wave equations. Second, we investigate existence and long-time
behavior of solutions for such models
Constraints on neutrino decay lifetime using long-baseline charged and neutral current data
We investigate the status of a scenario involving oscillations and decay for
charged and neutral current data from the MINOS and T2K experiments. We first
present an analysis of charged current neutrino and anti-neutrino data from
MINOS in the framework of oscillation with decay and obtain a best fit for
non-zero decay parameter . The MINOS charged and neutral current data
analysis results in the best fit for ~eV, and zero decay parameter, which
corresponds to the limit for standard oscillations. Our combined MINOS and T2K
analysis reports a constraint at the 90\% confidence level for the neutrino
decay lifetime ~s/eV. This is the best limit
based only on accelerator produced neutrinos
Back to Parmenides
After a brief introduction to issues that plague the realization of a theory
of quantum gravity, I suggest that the main one concerns a quantization of the
principle of relative simultaneity. This leads me to a distinction between time
and space, to a further degree than that present in the canonical approach to
general relativity. With this distinction, one can make sense of superpositions
as interference between alternative paths in the relational configuration space
of the entire Universe. But the full use of relationalism brings us to a
timeless picture of Nature, as it does in the canonical approach (which
culminates in the Wheeler-DeWitt equation). After a discussion of Parmenides
and the Eleatics' rejection of time, I show that there is middle ground between
their view of absolute timelessness and a view of physics taking place in
timeless configuration space. In this middle ground, even though change does
not fundamentally exist, the illusion of change can be recovered in a way not
permitted by Parmenides. It is recovered through a particular density
distribution over configuration space which gives rise to 'records'.
Incidentally, this distribution seems to have the potential to dissolve further
aspects of the measurement problem that can still be argued to haunt the
application of decoherence to Many-Worlds quantum mechanics. I end with a
discussion indicating that the conflict between the conclusions of this paper
and our view of the continuity of the self may still intuitively bother us.
Nonetheless, those conclusions should be no more challenging to our intuition
than Derek Parfit's thought experiments on the subject.Comment: 25 pages, 1 figure. Winner of the essay contest: "Space-time after
quantum gravity" (University of Illinois and Universit\'e de Geneve). To be
published in special editio
Atom-field transfer of coherence in a two-photon micromaser assisted by a classical field
We investigate the transfer of coherence from atoms to a cavity field
initially in a statistical mixture in a two-photon micromaser arrangement. The
field is progressively modified from a maximum entropy state (thermal state)
towards an almost pure state (entropy close to zero) due to its interaction
with atoms sent across the cavity. We trace over the atomic variables, i.e.,
the atomic states are not collapsed by a detector after they leave the cavity.
We find that by applying an external classical driving field it is possible to
substantially increase the field purity without the need of previously
preparing the atoms in a superposition of their energy eigenstates. We also
discuss some of the nonclassical features of the resulting field.Comment: 10 pages, 7 figures, LaTe
The Hessian Riemannian flow and Newton's method for Effective Hamiltonians and Mather measures
Effective Hamiltonians arise in several problems, including homogenization of
Hamilton--Jacobi equations, nonlinear control systems, Hamiltonian dynamics,
and Aubry--Mather theory. In Aubry--Mather theory, related objects, Mather
measures, are also of great importance. Here, we combine ideas from mean-field
games with the Hessian Riemannian flow to compute effective Hamiltonians and
Mather measures simultaneously. We prove the convergence of the Hessian
Riemannian flow in the continuous setting. For the discrete case, we give both
the existence and the convergence of the Hessian Riemannian flow. In addition,
we explore a variant of Newton's method that greatly improves the performance
of the Hessian Riemannian flow. In our numerical experiments, we see that our
algorithms preserve the non-negativity of Mather measures and are more stable
than {related} methods in problems that are close to singular. Furthermore, our
method also provides a way to approximate stationary MFGs.Comment: 24 page
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