Optimal heat kernel estimates for Schrödinger operators with magnetic fields in two dimensions

DOI10.1007/BF02885674zbMath0873.35078OpenAlexW2169915528MaRDI QIDQ1360568

Michael Loss, Bernd Thaller

Publication date: 2 November 1997

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02885674

zbMATH Keywords

smoothing estimatesMehler kernelmagnetic Schrödinger semigroups

Mathematics Subject Classification ID

Groups and semigroups of linear operators (47D03) General theory of partial differential operators (47F05) PDEs in connection with quantum mechanics (35Q40) Schrödinger operator, Schrödinger equation (35J10)

Related Items

Magnetic Energies and Feynman–Kac–Itô Formulas for Symmetric Markov Processes, A rigorous mathematical construction of Feynman path integrals for the Schrödinger equation with magnetic field, Heat kernels of two-dimensional magnetic Schrödinger and Pauli operators, The nonexistence of vortices for rotating Bose-Einstein condensates with attractive interactions, Heat kernel estimates and spectral properties of a pseudorelativistic operator with magnetic field, Interpolation inequalities and spectral estimates for magnetic operators, Heat kernel asymptotics for magnetic Schrödinger operators, Strong diamagnetism for general domains and application, ON THE LOCATION OF SPIKES FOR THE SCHRÖDINGER EQUATION WITH ELECTROMAGNETIC FIELD, Behaviour of heat kernels of Schrödinger operators and applications to certain semilinear parabolic equations, Sharp Gaussian bounds and 𝐿^{𝑝}-growth of semigroups associated with elliptic and Schrödinger operators

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Gaussian kernels have only Gaussian maximizers
• Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians
• Best constants in Young's inequality, its converse, and its generalization to more than three functions
• Inequalities in Fourier analysis
• Domination of semigroups and generalization of Kato's inequality
• Schrödinger operators with magnetic fields. I: General interactions
• Lower bounds for the spectra of Schrödinger operators with magnetic fields
• Estimates on stochastic oscillatory integrals and on the heat kernel of the magnetic Schrödinger operator
• Optimal smoothing and decay estimates for viscously damped conservation laws, with applications to the 2-D Navier-Stokes equation
• Schrödinger operators with singular potentials
• Schrödinger semigroups
• Logarithmic Sobolev Inequalities
• Logarithmic Sobolev Inequalities for the Heat-Diffusion Semigroup
• Partially Alternate Derivation of a Result of Nelson
• Schrödinger operators with singular magnetic vector potentials