Time Decay of Quantum Waves on Riemannian Manifolds – Recent Development

Shijun Zheng

Time Decay of Quantum Waves on Riemannian Manifolds – Recent Development

Mathematical Sciences

Research output: Contribution to conference › Presentation

Abstract

It is a quest to understand the behavior of waves or particles traveling in a quantum-mechanical background. We give a survey on some aspects of recent development concerning the decay of solutions to dispersive equations on Euclidean spaces and Riemannian manifolds. The problems and techniques are mainly from harmonic analysis and PDE. We will observe that the spectral multiplier theorem, Strichartz estimates and restriction phenomenon occur on manifolds as well as p-adic number fields.

Original language	American English
State	Published - Mar 3 2007
Event	Spring Southeastern Sectional Meeting of the American Mathematical Society (AMS) - Statesboro, GA Duration: Mar 12 2011 → …

Conference

Conference	Spring Southeastern Sectional Meeting of the American Mathematical Society (AMS)
Period	03/12/11 → …

Disciplines

Mathematics
Physical Sciences and Mathematics

Keywords

Quantum Waves
Riemannian Manifolds
Time Decay

Access to Document

http://www.ams.org/meetings/sectional/1024-35-81.pdf

Cite this

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title = "Time Decay of Quantum Waves on Riemannian Manifolds – Recent Development",

abstract = " It is a quest to understand the behavior of waves or particles traveling in a quantum-mechanical background. We give a survey on some aspects of recent development concerning the decay of solutions to dispersive equations on Euclidean spaces and Riemannian manifolds. The problems and techniques are mainly from harmonic analysis and PDE. We will observe that the spectral multiplier theorem, Strichartz estimates and restriction phenomenon occur on manifolds as well as p-adic number fields.",

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author = "Shijun Zheng",

year = "2007",

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note = "Spring Southeastern Sectional Meeting of the American Mathematical Society (AMS) ; Conference date: 12-03-2011",

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AU - Zheng, Shijun

PY - 2007/3/3

Y1 - 2007/3/3

N2 - It is a quest to understand the behavior of waves or particles traveling in a quantum-mechanical background. We give a survey on some aspects of recent development concerning the decay of solutions to dispersive equations on Euclidean spaces and Riemannian manifolds. The problems and techniques are mainly from harmonic analysis and PDE. We will observe that the spectral multiplier theorem, Strichartz estimates and restriction phenomenon occur on manifolds as well as p-adic number fields.

AB - It is a quest to understand the behavior of waves or particles traveling in a quantum-mechanical background. We give a survey on some aspects of recent development concerning the decay of solutions to dispersive equations on Euclidean spaces and Riemannian manifolds. The problems and techniques are mainly from harmonic analysis and PDE. We will observe that the spectral multiplier theorem, Strichartz estimates and restriction phenomenon occur on manifolds as well as p-adic number fields.

KW - Quantum Waves

KW - Riemannian Manifolds

KW - Time Decay

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpres/422

UR - http://www.ams.org/meetings/sectional/1024-35-81.pdf

M3 - Presentation

T2 - Spring Southeastern Sectional Meeting of the American Mathematical Society (AMS)

Y2 - 12 March 2011

ER -

Time Decay of Quantum Waves on Riemannian Manifolds – Recent Development

Abstract

Conference

Disciplines

Keywords

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