Trace asymptotics for fractional Schrödinger operators
نویسندگان
چکیده
منابع مشابه
Nonclassical Eigenvalue Asymptotics for Operators of Schrödinger
which depends on the volume u)n of the unit sphere in R n and the beta function. Assuming /3 < 2 we see that integral (2) becomes divergent if V (x) vanishes to a sufficiently high order. The simplest such potential is V(x,y) = \x\\y\P o n R n + R m . The Weyl (volume counting) principle, when applied to the corresponding Schrödinger operator — A-hV(x), fails to predict discrete spectrum below ...
متن کاملAsymptotics and Gaps in the Spectra of Magnetic Schrödinger Operators
In this paper, we study an L version of the semiclassical approximation of magnetic Schrödinger operators with invariant Morse type potentials on covering spaces of compact manifolds. In particular, we are able to establish the existence of an arbitrary large number of gaps in the spectrum of these operators, in the semiclassical limit as the coupling constant μ goes to zero.
متن کاملTrace Asymptotics for Subordinate Semigroups
We address a conjecture of D. Applebaum on small time trace asymptotics for subordinate Brownian motion on compact manifolds. In [1], heat trace asymptotics are computed for the semigroup of the square root of the Laplacian (the generator of the Cauchy process) on the n-dimensional torus, SU(2) and SO(3), and a conjecture is made [1, pp. 2493-2494] that such asymptotics should hold for all α-st...
متن کاملFractional Schrödinger equation.
Some properties of the fractional Schrödinger equation are studied. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics. As physical applications of the fractional Schrödinger equation we find the energy spectra of a hydrogenlike atom (fractional "Bohr atom") and of a fractional oscillator in the semiclassical a...
متن کاملEquivariant asymptotics for Toeplitz operators
In recent years, the Tian-Zelditch asymptotic expansion for the equivariant components of the Szegö kernel of a polarized complex projective manifold, and its subsequent generalizations in terms of scaling limits, have played an important role in algebraic, symplectic, and differential geometry. A natural question is whether there exist generalizations in which the projector onto the spaces of ...
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: Journal of Functional Analysis
سال: 2014
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2013.10.021