Related papers: Incommensurate standard map
Based on our recently proposed plane wave framework, we theoretically study the localized-extended transition in the one dimensional incommensurate systems with cosine type of potentials, which are in close connection to many recent…
We study the dynamical localization transition in a one-dimensional periodically kicked incommensurate lattice, which is created by perturbing a primary optical lattice periodically with a pulsed weaker incommensurate lattice. The diffusion…
We investigate the mixing properties of a randomized Chirikov standard map on $\mathbb{T}^2$. While the deterministic dynamics exhibit obstructions to global ergodicity, we establish explicit almost-sure quantitative exponential mixing when…
Incommensurate structures can be described by the Frenkel Kontorova model. Aubry has shown that, at a critical value K_c of the coupling of the harmonic chain to an incommensurate periodic potential, the system displays the analyticity…
We report a numerical analysis of the Anderson transition in a quantum-chaotic system, the quasiperiodic kicked rotor with three incommensurate frequencies. It is shown that this dynamical system exhibits the same critical phenomena as the…
In the dynamics of the undamped Frenkel-Kontorova model with kinetic terms, we find a transition between two regimes, a floating incommensurate and a pinned incommensurate phase. This behavior is compared to the static version of the model.…
We performed high-resolution powder neutron diffraction experiments and discovered an elliptic helical incommensurate magnetic structure in the semiconducting rare-earth magnet YbCuS2, featuring effective spin-1/2 Yb$^{3+}$ ions that form a…
A system of quantum computing structures is introduced and proven capable of making emerge, on average, the orbits of classical bounded nonlinear maps on \mathbb{C} through the iterative action of path-dependent quantum gates. The effects…
The relation between classically chaotic dynamics and quantum localization is studied in a system that violates the assumptions of Kolmogorov-Arnold-Moser (KAM) theorem, namely, kicked rotor in a discontinuous potential barrier. We show…
We prove numerically and by dualities the existence of modulated, commensurate and incommensurate states of topological quantum matter in simple systems of parafermions, motivated by recent proposals for the realization of such systems in…
Temperature-dependent x-ray diffraction of the low-dimensional spin 1/2 quantum magnet TiOBr shows that the phase transition at T_{c2} = 47.1 (4) K corresponds to the development of an incommensurate superstructure. Below T_{c1} = 26.8 \pm…
Due to the lack of the translational symmetry, calculating the energy spectrum of an incommensurate system has always been a theoretical challenge. Here, we propose a natural approach to generalize the energy band theory to the…
This paper focuses on distinguishing classes of dynamical behavior for one- and two-dimensional torus maps, in particular between orbits that are incommensurate, resonant, periodic, or chaotic. We first consider Arnold's circle map, for…
A quantum spin-$\frac{1}{2}$ chain with an axial symmetry is normally described by quasiparticles associated with the spins oriented along the axis of rotation. Kinetic constraints can enrich such a description by setting apart different…
The appearance of noncommuting spatial coordinates is studied in quantum systems containing a magnetic monopole and under the influence of a radial potential. We derive expressions for the commutators of the coordinates that have been…
Incommensurability plays a critical role in many strongly correlated systems. In some cases, the origin of such exotic order can be theoretically understood in the framework of 1d line-like topological excitations known as ``quantum…
We characterize the disorder induced localization in momentum space for ultracold atoms in one-dimensional incommensurate lattices, according to the dual Aubry-Andr\'e model. For low disorder the system is localized in momentum space, and…
In the low doping region an incommensurate magnetic phase is observed in LSCO. By means of the composite operator method we show that the single-band 2D Hubbard model describes the experimental situation. In the higher doping region, where…
We investigate precursors of critical behavior in the quasienergy spectrum due to the dynamical instability in the kicked top. Using a semiclassical approach, we analytically obtain a logarithmic divergence in the density of states, which…
We highlight a few recent results on the effect of the diffusion process in deterministic area preserving maps with noncompact phase space, namely the standard map. In more detail, we focus on the anomalous diffusion arising due to the…