On the Absolutely Continuous Spectrum of Dirac Operator
نویسندگان
چکیده
منابع مشابه
Absolutely Continuous Spectrum of a Dirac Operator
where γj are selfadjoint 4× 4matrices satisfying the relations (2) γjγl + γlγj = 2δl,j . Obviously, if the domain of D0 is defined asH1(R3;C4), then D0 is a selfadjoint operator in L2(R3;C4). The spectrum of D0 is absolutely continuous, it coincides with the complement of the interval (−1, 1) as a set: σ(D0) = σa.c.(D0) = (−∞,−1] ∪ [1,∞). The multiplicity of the spectrum is infinite. We see tha...
متن کاملOn the Absolutely Continuous Spectrum of Dirac Operator
We prove that the massless Dirac operator in R with long-range potential has an a.c. spectrum which fills the whole real line. The Dirac operators with matrix-valued potentials are considered as well.
متن کاملAbsolutely Continuous Spectrum of a Schrödinger Operator on a Tree
We give sufficient conditions for the presence of the absolutely continuous spectrum of a Schrödinger operator on a regular rooted tree without loops (also called regular Bethe lattice or Cayley tree). Introduction and results The spectral properties of Schrödinger operators on graphs have numerous applications in physics and they have been intensively studied since late 90’s. We will be mainly...
متن کاملThe Absolutely Continuous Spectrum of the Almost Mathieu Operator
We prove that the spectrum of the almost Mathieu operator is absolutely continuous if and only if the coupling is subcritical. This settles Problem 6 of Barry Simon’s list of Schrödinger operator problems for the twenty-first century.
متن کاملAbsolutely Continuous Spectrum of Dirac Operators with Square Integrable Potentials
We show that the absolutely continuous part of the spectral function of the one-dimensional Dirac operator on a half-line with a constant mass term and a real, square-integrable potential is strictly increasing throughout the essential spectrum (−∞,−1] ∪ [1,∞). The proof is based on estimates for the transmission coefficient for the full-line scattering problem with a truncated potential and a ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Partial Differential Equations
سال: 2005
ISSN: 0360-5302,1532-4133
DOI: 10.1081/pde-200037758