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In this paper, we establish the Anderson localization, strong dynamical localization and the (1 2 -) -Hölder continuity of the integrated density of states (IDS) for some multi-dimensional discrete quasi-periodic (QP) Schrödinger operators with asymmetric C 2 -cosine type potentials. We extend both the iteration scheme of Cao-Shi-Zhang (Commun Math Phys 404(1):495–561, 2023) and the interlacing method of Forman and VandenBoom (Localization and Cantor spectrum for quasiperiodic discrete Schrödinger operators with asymmetric, smooth, cosine-like sampling functions. arXiv:2107.05461, 2021) to handle asymmetric Rellich functions with collapsed gaps. [ABSTRACT FROM AUTHOR]

In this paper, we study the multidimensional lattice Schrödinger operators with C 2 -cosine like quasi-periodic (QP) potential. We establish quantitative Green's function estimates, the arithmetic version of Anderson (and dynamical) localization, and the finite volume version of (1 2 -) -Hölder continuity of the integrated density of states for such QP Schrödinger operators. Our proof is based on an extension of the fundamental multi-scale analysis type method of Fröhlich–Spencer–Wittwer (Commun Math Phys 132(1), 5–25, 1990) to the higher lattice dimensions. We resolve the level crossing issue on eigenvalues parameterizations in the case of both higher lattice dimension and C 2 regular potential. [ABSTRACT FROM AUTHOR]