Diamagnetic behavior of sums Dirichlet eigenvalues

László Erdős, Michael Loss, Vitali Vougalter

Type: Article

Publication Date: 2000-01-01

Citations: 29

DOI: https://doi.org/10.5802/aif.1777

Abstract

The Li-Yau semiclassical lower bound for the sum of the first N eigenvalues of the Dirichlet–Laplacian is extended to Dirichlet– Laplacians with constant magnetic fields. Our method involves a new diamagnetic inequality for constant magnetic fields.

Locations

CiteSeer X (The Pennsylvania State University) - View - PDF
Annales de l’institut Fourier - View - PDF

Similar Works

Action	Title	Year	Authors
+	Inequalities between Dirichlet and Neumann eigenvalues of the magnetic Laplacian	2025	Vladimir Lotoreichik
+	Cheeger Inequalities for the Discrete Magnetic Laplacian	2022	Haitao Yan
+ PDF Chat	Improved Berezin-Li-Yau inequalities with magnetic field	2013	Hynek Kovařík Timo Weidl
+	Estimates for the Lowest Eigenvalue of Magnetic Laplacians	2015	Tomas Ekholm Hynek Kovařík Fabian Portmann
+	Estimates for the Lowest Eigenvalue of Magnetic Laplacians	2015	Tomas Ekholm Hynek Kovařík Fabian Portmann
+	Bounds on eigenvalues of Dirichlet Laplacian	2006	Qing-Ming Cheng Hongcang Yang
+	A reverse Faber-Krahn inequality for the magnetic Laplacian	2024	Bruno Colbois Corentin Léna Luigi Provenzano Alessandro Savo
+	Influence of Robin’s conditions on the spectrum of the magnetic Laplacian	2023	Rayan Fahs
+	Estimates for the lowest eigenvalue of magnetic Laplacians	2016	Tomas Ekholm Hynek Kovařík Fabian Portmann
+ PDF Chat	Inequalities for the lowest magnetic Neumann eigenvalue	2019	Søren Fournais Bernard Helffer
+	Inequalities between Dirichlet and Neumann Eigenvalues	1989	Howard A. Levine Hans F. Weinberger
+ PDF Chat	Limiting absorption principle for the magnetic Dirichlet Laplacian in a half-plane	2016	Nicolas Popoff Éric Soccorsi
+ PDF Chat	Semiclassical bounds in magnetic bottles	2016	Diana Barseghyan Pavel Exner Hynek Kovařík Timo Weidl
+	Inequalities for the lowest magnetic Neumann eigenvalue	2017	Søren Fournais Bernard Helffer
+	Inequalities for the lowest magnetic Neumann eigenvalue	2017	Søren Fournais Bernard Helffer
+ PDF Chat	Improved Berezin—Li—Yau inequalities with magnetic field	2015	Hynek Kovařík Timo Weidl
+	Hardy inequalities for magnetic Dirichlet forms	1999	Ари Лаптев Timo Weidl
+	Generalized Hardy Inequality for the Magnetic Dirichlet Forms	2004	Alexander Balinsky Ари Лаптев Alexander V. Sobolev
+	Kato’s inequality for magnetic Laplacians on graphs	2006	M. Varghese J. Dodziuk
+ PDF Chat	Spectral analysis of the semiclassical magnetic Laplacian : semi-excited states and Birkhoff normal forms	2021	Léo Morin

Works That Cite This (29)

Action	Title	Year	Authors
+ PDF Chat	An Entropic Uncertainty Principle for Positive Operator Valued Measures	2011	Michel Rumin
+	Polya's conjecture in the presence of a constant magnetic field	2007	Rupert L. Frank Michael Loss Timo Weidl
+	Bibliography	2011	József Lőrinczi Fumio Hiroshima Volker Betz
+ PDF Chat	Sums of Magnetic Eigenvalues are Maximal on Rotationally Symmetric Domains	2011	Richard S. Laugesen Jian Liang Arindam Roy
+	Estimates for the lowest eigenvalue of magnetic Laplacians	2016	Tomas Ekholm Hynek Kovařík Fabian Portmann
+	Spectral inequalities for discrete and continuous differential operators	2014	Lukas Schimmer
+	Existence and Nonlinear Stability of Stationary States for the Magnetic Schrödinger–Poisson System	2016	Jean-Marie Barbaroux Vitali Vougalter
+ PDF Chat	Eigenvalue Bounds for Schrödinger Operators with a Homogeneous Magnetic Field	2011	Rupert L. Frank Rikard Olofsson
+	Magnetic spectral bounds on starlike plane domains	2014	Richard S. Laugesen Bartłomiej Siudeja
+ PDF Chat	Sharp Semiclassical Bounds for the Moments of Eigenvalues for Some Schrödinger Type Operators with Unbounded Potentials	2013	Vitali Vougalter

Works Cited by This (14)

Action	Title	Year	Authors
+	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
+	Inequalities for the Moments of the Eigenvalues of the Schrödinger Hamiltonian and Their Relation to Sobolev Inequalities	2006	Élliott H. Lieb Walter Thirring
+	On the Schr�dinger equation and the eigenvalue problem	1983	Peter Li Shing Tung Yau
+	Bound for the Kinetic Energy of Fermions Which Proves the Stability of Matter	1975	Élliott H. Lieb Walter Thirring
+	Domination of semigroups and generalization of Kato’s inequality	1977	Harald Hess Robert Schrader D. A. Uhlenbrock
+	Schrödinger operators with magnetic fields. I. general interactions	1978	J. E. Avron Ira Herbst Barry Simon
+	CONVEX OPERATOR FUNCTIONS	1972	F. A. Berezin
+ PDF Chat	Sharp Lieb-Thirring inequalities in high dimensions	2000	Ари Лаптев Timo Weidl
+	Microlocal Analysis and Precise Spectral Asymptotics	1998	Victor Ivrii