2,742 research outputs found
Making an IDEA a Reality: Providing a Free and Appropriate Public Education for Children with Disabilities Under the Individuals with Disabilities Education Act
Quantum back-reaction in a universe with positive cosmological constant
Semiclassical techniques have proven to be a very powerful method to extract
physical effects from different quantum theories. Therefore, it is expected
that in the near future they will play a very prominent role in the context of
quantum gravity. In this work we develop systematic tools to derive
semiclassical approximations for any quantum theory with one degree of freedom.
In our approach, the wave function is decomposed in terms of an infinite set of
moments, which encode the complete quantum information of the system.
Semiclassical regimes can then be properly described by truncation of this
infinite system. The use of efficient computer algebra tools allows us to
compute the equations of motion up to a very high order. In this way, we can
study very precisely the quantum back reaction of the system as well as the
convergence of the method with the considered order. Finally, these tools are
applied to the particular case of a homogeneous universe filled with a massless
scalar field and positive cosmological constant, which provide interesting
physical results.Comment: 4 pages. Proceedings of the Loops'11 conference. Submitted to Journal
of Physics: Conference Serie
Statistical moments for classical and quantum dynamics: formalism and generalized uncertainty relations
The classical and quantum evolution of a generic probability distribution is
analyzed. To that end, a formalism based on the decomposition of the
distribution in terms of its statistical moments is used, which makes explicit
the differences between the classical and quantum dynamics. In particular,
there are two different sources of quantum effects. Distributional effects,
which are also present in the classical evolution of an extended distribution,
are due to the fact that all moments can not be vanishing because of the
Heisenberg uncertainty principle. In addition, the non-commutativity of the
basic quantum operators add some terms to the quantum equations of motion that
explicitly depend on the Planck constant and are not present in the classical
setting. These are thus purely-quantum effects. Some particular Hamiltonians
are analyzed that have very special properties regarding the evolution they
generate in the classical and quantum sector. In addition, a large class of
inequalities obeyed by high-order statistical moments, and in particular
uncertainty relations that bound the information that is possible to obtain
from a quantum system, are derived.Comment: 14 pages. Minor change
Quantum-gravitational effects on gauge-invariant scalar and tensor perturbations during inflation: The de Sitter case
We present detailed calculations for quantum-gravitational corrections to the
power spectra of gauge-invariant scalar and tensor perturbations during
inflation. This is done by performing a semiclassical Born-Oppenheimer type of
approximation to the Wheeler-DeWitt equation, from which we obtain a
Schroedinger equation with quantum-gravitational correction terms. As a first
step, we perform our calculation for a de Sitter universe and find that the
correction terms lead to an enhancement of power on the largest scales.Comment: 21 pages, 5 figures, clarifications and references added, version
accepted for publication in Physical Review
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