Subcritical behavior for quasi-periodic Schrödinger cocycles with trigonometric potentials
نویسندگان
چکیده
منابع مشابه
Lyapunov Exponents For Some Quasi-Periodic Cocycles
We consider SL(2,R)-valued cocycles over rotations of the circle and prove that they are likely to have Lyapunov exponents ≈ ± logλ if the norms of all of the matrices are ≈ λ. This is proved for λ sufficiently large. The ubiquity of elliptic behavior is also observed. Consider an area preserving diffeomorphism f of a compact surface. Assume that f is not uniformly hyperbolic, but that it has o...
متن کاملExistence of non-trivial solutions for fractional Schrödinger-Poisson systems with subcritical growth
In this paper, we are concerned with the following fractional Schrödinger-Poisson system: (−∆s)u + u + λφu = µf(u) +|u|p−2|u|, x ∈R3 (−∆t)φ = u2, x ∈R3 where λ,µ are two parameters, s,t ∈ (0,1] ,2t + 4s > 3 ,1 < p ≤ 2∗ s and f : R → R is continuous function. Using some critical point theorems and truncation technique, we obtain the existence and multiplicity of non-trivial solutions with ...
متن کاملSchrödinger Operators with Singular Potentials †
We describe classical and recent results on the spectral theory of Schrödinger and Pauli operators with singular electric and magnetic potentials
متن کاملBloch decomposition-based Gaussian beam method for the Schrödinger equation with periodic potentials
The linear Schrödinger equation with periodic potentials is an important model in solid state physics. The most efficient direct simulation using a Bloch decomposition based time-splitting spectral method [18] requires the mesh size to be O(ε) where ε is the scaled semiclassical parameter. In this paper, we generalize the Gaussian beam method introduced in [23] to solve this problem asymptotica...
متن کاملSchrödinger operators with oscillating potentials ∗
Schrödinger operators H with oscillating potentials such as cos x are considered. Such potentials are not relatively compact with respect to the free Hamiltonian. But we show that they do not change the essential spectrum. Moreover we derive upper bounds for negative eigenvalue sums of H.
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 Spectral Theory
سال: 2018
ISSN: 1664-039X
DOI: 10.4171/jst/192