A Variational Formulation for Dirac Operators in Bounded Domains. Applications to Spectral Geometric Inequalities
| Autor: | Vladimir Lotoreichik, Rafael D. Benguria, Thomas Ourmières-Bonafos, Pedro R. S. Antunes |
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| Přispěvatelé: | Universidade Aberta [Lisboa], Grupo de Física Matemática - Group of Mathematical Physics (GFM), Universidade de Lisboa = University of Lisbon (ULISBOA), Pontificia Universidad Católica de Chile (UC), Department of Theoretical Physics, Nuclear Physics Institute, Czech Academy of Sciences [Prague] (CAS), Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Universidade de Lisboa (ULISBOA), Centre National de la Recherche Scientifique (CNRS)-École Centrale de Marseille (ECM)-Aix Marseille Université (AMU) |
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Dirac (software) FOS: Physical sciences Dirac operator 01 natural sciences Domain (mathematical analysis) Mathematics - Spectral Theory symbols.namesake Mathematics - Analysis of PDEs Operator (computer programming) [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] Simple (abstract algebra) 0103 physical sciences FOS: Mathematics Boundary value problem 0101 mathematics Spectral Theory (math.SP) Mathematical Physics Eigenvalues and eigenvectors Mathematics 010102 general mathematics Statistical and Nonlinear Physics Mathematical Physics (math-ph) Mathematics::Spectral Theory Bounded function symbols 010307 mathematical physics [MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP] Analysis of PDEs (math.AP) |
| Zdroj: | Communications in Mathematical Physics Communications in Mathematical Physics, 2021, ⟨10.1007/s00220-021-03959-6⟩ Repositório Científico de Acesso Aberto de Portugal Repositório Científico de Acesso Aberto de Portugal (RCAAP) instacron:RCAAP |
| ISSN: | 1432-0916 0010-3616 |
| DOI: | 10.1007/s00220-021-03959-6 |
| Popis: | We investigate spectral features of the Dirac operator with infinite mass boundary conditions in a smooth bounded domain of $\mathbb{R}^2$. Motivated by spectral geometric inequalities, we prove a non-linear variational formulation to characterize its principal eigenvalue. This characterization turns out to be very robust and allows for a simple proof of a Szeg\"o type inequality as well as a new reformulation of a Faber-Krahn type inequality for this operator. The paper is complemented with strong numerical evidences supporting the existence of a Faber-Krahn type inequality. Comment: 34 pages, 4 figures |
| Databáze: | OpenAIRE |
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