Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Quantum_ergodicity> ?p ?o. }
Showing items 1 to 23 of
23
with 100 items per page.
- Quantum_ergodicity abstract "In quantum chaos, a branch of mathematical physics, quantum ergodicity is a property of the quantization of classical mechanical systems that are chaotic in the sense of exponential sensitivity to initial conditions. Quantum ergodicity states, roughly, that in the high-energy limit, the probability distributions associated to energy eigenstates of a quantized ergodic Hamiltonian tend to a uniform distribution in the classical phase space. This is consistent with the intuition that the flows of ergodic systems are equidistributed in phase space. By contrast, classical completely integrable systems generally have periodic orbits in phase space, and this is exhibited in a variety of ways in the high-energy limit of the eigenstates: typically that some form of concentration or "scarring" occurs in the limit.The model case of a Hamiltonian is the geodesic Hamiltonian on the cotangent bundle of a compact Riemannian manifold. The quantization of the geodesic flow is given by the fundamental solution of the Schrödinger equationwhere is the square root of the Laplace-Beltrami operator. The quantum ergodicity theorem of Shnirelman, Yves Colin de Verdière, and Zelditch states that a compact Riemannian manifold whose unit tangent bundle is ergodic under the geodesic flow is also ergodic in the sense that the probability density associated to the nth eigenfunction of the Laplacian tends weakly to the uniform distribution on the unit cotangent bundle as n → ∞.".
- Quantum_ergodicity wikiPageID "23855903".
- Quantum_ergodicity wikiPageRevisionID "574380647".
- Quantum_ergodicity hasPhotoCollection Quantum_ergodicity.
- Quantum_ergodicity subject Category:Chaos_theory.
- Quantum_ergodicity subject Category:Ergodic_theory.
- Quantum_ergodicity subject Category:Modular_forms.
- Quantum_ergodicity subject Category:Quantum_mechanics.
- Quantum_ergodicity type Abstraction100002137.
- Quantum_ergodicity type Form106290637.
- Quantum_ergodicity type LanguageUnit106284225.
- Quantum_ergodicity type ModularForms.
- Quantum_ergodicity type Part113809207.
- Quantum_ergodicity type Relation100031921.
- Quantum_ergodicity type Word106286395.
- Quantum_ergodicity comment "In quantum chaos, a branch of mathematical physics, quantum ergodicity is a property of the quantization of classical mechanical systems that are chaotic in the sense of exponential sensitivity to initial conditions. Quantum ergodicity states, roughly, that in the high-energy limit, the probability distributions associated to energy eigenstates of a quantized ergodic Hamiltonian tend to a uniform distribution in the classical phase space.".
- Quantum_ergodicity label "Quantum ergodicity".
- Quantum_ergodicity sameAs m.07kfyfb.
- Quantum_ergodicity sameAs Q7269044.
- Quantum_ergodicity sameAs Q7269044.
- Quantum_ergodicity sameAs Quantum_ergodicity.
- Quantum_ergodicity wasDerivedFrom Quantum_ergodicity?oldid=574380647.
- Quantum_ergodicity isPrimaryTopicOf Quantum_ergodicity.