The Mourre estimate for dispersive 𝑁-body Schrödinger operators

Jan Dereziński

Type: Article

Publication Date: 1990-01-01

Citations: 9

DOI: https://doi.org/10.1090/s0002-9947-1990-0970265-4

Abstract

We prove the Mourre estimate for a certain class of dispersive <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper N"> <mml:semantics> <mml:mi>N</mml:mi> <mml:annotation encoding="application/x-tex">N</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-body Schrödinger operators. Using this estimate we derive some properties of those operators such as the local finiteness of the finite spectrum and the absence of the singular continuous spectrum.

Locations

Transactions of the American Mathematical Society - View - PDF

Similar Works

Action	Title	Year	Authors
+	The Mourre Estimate for Dispersive N-Body Schrodinger Operators	1990	Jan Dereziński
+ PDF Chat	Zero energy scattering for one-dimensional Schrödinger operators and applications to dispersive estimates	2015	Iryna Egorova Markus Holzleitner Gerald Teschl
+	Dispersive estimates for the Schrodinger equation	2010	William Robert Green
+	Dispersive estimates for Schroedinger operators: A survey	2005	Wilhelm Schlag
+	Limiting Absorption Principle for Schrödinger Operators with Oscillating Potential	2016	Thierry Jecko Aiman Mbarek
+	Dispersive and Strichartz estimates for Schrödinger equations	2011	治哉水谷
+ PDF Chat	Dispersive estimates for Schrödinger operators in dimension two with obstructions at zero energy	2013	M. Burak Erdoğan William R. Green
+	Finiteness of the lower spectrum of Schr�dinger operators	1974	John Piepenbrink
+	A new look at Mourre's commutator theory	2006	Sylvain Golénia Thierry Jecko
+	Dispersive estimates for Schr	2012	M. Burak Erdoğan William R. Green
+ PDF Chat	Finiteness of the lower spectrum of Schrödinger operators with singular potentials	1991	Jörg Donig
+	Limiting absorption principle and resonances for the Dirac operator	1992	Erik Balslev Bernard Helffer
+	Limiting Absorption Principle for Schrödinger Operators with Oscillating Potential	2016	Thierry Jecko Aiman Mbarek
+ PDF Chat	Dispersive estimates for inhomogeneous fourth-order Schrödinger operator in 3D with zero energy obstructions	2021	Hongliang Feng
+	A Dispersive Bound for Three-Dimensional Schrödinger Operators with Zero Energy Eigenvalues	2010	Michael Goldberg
+	Dispersive Decay	2021	Alexander Komech Elena Kopylova
+	Dispersive estimates of solutions to the Schrodinger equation in dimensions $n\ge 4$	2006	Georgi Vodev
+ PDF Chat	Semiclassical estimates for the magnetic Schr\"odinger operator on the line	2024	Andrés Larraín-Hubach Jacob N. Shapiro
+ PDF Chat	Semi-classical dispersive estimates	2014	F. F. Cardoso Claudio Cuevas Georgi Vodev
+	Dispersive Estimates for the Dirac–Coulomb Equation	2022	Federico Cacciafesta Éric Séré Junyong Zhang

Works That Cite This (9)

Action	Title	Year	Authors
+	Asymptotic Completeness for Multiparticle Dispersive Charge Transfer Models	1997	Lech Zieliński
+	Dispersive Charge Transfer Model with Long-Range Quantum Interactions	1998	Lech Zieliński
+ PDF Chat	On the spectral analysis of many-body systems	2010	Mondher Damak Vladimir Georgescu
+	Self-adjoint operators affiliated to C*-algebras.	2004	Mondher Damak Vladimir Georgescu
+	Hilbert C*-modules and spectral analysis of many-body systems	2008	Mondher Damak Vladimir Georgescu
+	On the spectral theory of dispersive <i>N</i>-body Hamiltonians	1999	Mondher Damak
+	A Generalized Scaling Limit and its Application to the Semi-Relativistic Particles System Coupled to a Bose Field with Removing Ultraviolet Cutoffs	2010	Toshimitsu Takaesu 俊光高江洲
+ PDF Chat	Scaling Limits for the System of Semi-Relativistic Particles Coupled to a Scalar Bose Field	2011	Toshimitsu Takaesu
+	Multiparticle Quantum Systems in Constant Magnetic Fields	1997	I. S. Laba

Works Cited by This (25)

Action	Title	Year	Authors
+	The analysis of linear partial differential operators	1990	Lars Hörmander
+ PDF Chat	Perturbation Theory for Linear Operators	1995	Tosio Kato
+	Methods of Modern Mathematical Physics	1972	Michael C. Reed Barry Simon
+	Schrodinger Operators: With Application to Quantum Mechanics and Global Geometry	1987	Hans L. Cycon Barry Simon
+	The quantum mechanical virial theorem and the absence of positive energy bound states of Schrödinger operators	1975	Hubert Kalf
+	Exponential bounds and absence of positive eigenvalues forN-body Schr�dinger operators	1982	Richard Froese Ira Herbst
+ PDF Chat	Asymptotic completeness for classes of two, three, and four particle Schrödinger operators	1980	George A. Hagedorn
+ PDF Chat	Absence of singular continuous spectrum for certain self-adjoint operators	1981	E. Mourre
+ PDF Chat	The virial theorem and its application to the spectral theory of Schrödinger operators	1967	Joachim Weidmann
+	Wave Operators and Similarity for Some Non-selfadjoint Operators	1966	Tosio Kato