Strong Levinson Theorem for the Dirac Equation
نویسندگان
چکیده
منابع مشابه
Spectral Comparison Theorem for the Dirac Equation
We consider a single particle which is bound by a central potential and obeys the Dirac equation. We compare two cases in which the masses are the same but Va < Vb, where V is the time-component of a vector potential. We prove generally that for each discrete eigenvalue E whose corresponding (large and small) radial wave functions have no nodes, it necessarily follows that Ea < Eb. As an illust...
متن کاملSpecial comparison theorem for the Dirac equation.
If a central vector potential V(r,a) in the Dirac equation is monotonic in a parameter a, then a discrete eigenvalue E(a) is monotonic in a. For such a special class of comparisons, this generalizes an earlier comparison theorem that was restricted to node free states. Moreover, the present theorem applies to every discrete eigenvalue.
متن کاملA Local Existence Theorem for the Einstein-Dirac Equation
We study the Einstein-Dirac equation as well as the weak Killing equation on Riemannian spin manifolds with codimension one foliation. We prove that, for any manifold M admitting real Killing spinors (resp. parallel spinors), there exist warped product metrics η on M × R such that (M × R, η) admit Einstein spinors (resp. weak Killing spinors). To prove the result we split the Einstein-Dirac equ...
متن کاملLevinson-like theorem for scattering from a Bose-Einstein condensate.
A relation between the number of bound elementary excitations of an atomic Bose-Einstein condensate and the phase shift of elastically scattered atoms is derived. Within the Bogoliubov model of a weakly interacting Bose gas this relation is exact and generalizes Levinson's theorem. Specific features of the Bogoliubov model such as complex energy and continuum bound states are discussed and a nu...
متن کاملOn Stability and Strong Convergence for the Spatially Homogeneous Boltzmann Equation for Fermi-dirac Particles
ABSTRACT. The paper considers the stability and strong convergence to equilibrium of solutions to the spatially homogeneous Boltzmann equation for Fermi-Dirac particles. Under the usual cut-off condition on the collision kernel, we prove a strong stability in L-topology at any finite time interval, and, for hard and Maxwellian potentials, we prove that the solutions converge strongly in L to eq...
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: Physical Review Letters
سال: 2004
ISSN: 0031-9007,1079-7114
DOI: 10.1103/physrevlett.93.180405