Related papers: The Dry Ten Martini Problem at Criticality

We develop two approximation schemes for solving the cell equation and the discounted cell equation using Aubry-Mather-Fathi theory. The Hamiltonian is supposed to be Tonelli, time-independent , and periodic in space. By Legendre transform…

The almost periodic eigenvalue problem described by the Harper equation is connected to other classes of quasiperiodic behaviour: the dissipative dynamics on critical invariant tori and quasiperiodically driven maps. Firstly, the strong…

In this study, we investigate the localization transition and quantum criticality {in the ground state of the} disordered Aubry-Andr\'{e}-Harper (AAH) model, where a quasiperiodic potential is hybridized with a disordered potential. In the…

Aubry-Andre Harper (AAH) lattice models, characterized by reflection-asymmetric, sinusoidally varying nearest-neighbor tunneling profile, are well-known for their topological properties. We consider the fate of such models in the presence…

We theoretically study a one-dimensional quasi-periodic Fermi system with topological $p$-wave superfluidity, which can be deduced from a topologically non-trivial tight-binding model on the square lattice in a uniform magnetic field and…

In this article we develop an analogue of Aubry-Mather theory for a class of dissipative systems, namely conformally symplectic systems, and prove the existence of interesting invariant sets, which, in analogy to the conservative case, will…

There has been interest in the spin transport properties of the Aubry-Andre-Harper model at high temperatures under weak integrability breaking, in particular for small interactions or small fields. We present old unpublished and new…

We clarify the algebraic structure of continuous and discrete quasi-exactly solvable spectral problems by embedding them into the framework of the quantum inverse scattering method. The quasi-exactly solvable hamiltonians in one dimension…

One dimensional tight binding models such as Aubry-Andre-Harper (AAH) model (with onsite cosine potential) and the integrable Maryland model (with onsite tangent potential) have been the subject of extensive theoretical research in…

In this paper we use results on reducibility, localization and duality for the Almost Mathieu operator, \[ (H_{b,\phi} x)_n= x_{n+1} +x_{n-1} + b \cos(2 \pi n \omega + \phi)x_n \] on $l^2(\mathbb{Z})$ and its associated eigenvalue equation…

We discuss the systematic engineering of quasicrystals in open quantum systems where quasiperiodicity is introduced through purely dissipative processes. While the resulting short-time dynamics is governed by non-Hermitian variants of the…

By exploiting the contact Hamiltonian dynamics $(T^*M\times\mathbb R,\Phi_t)$ around the Aubry set of contact Hamiltonian systems, we provide a relation among the Mather set, the $\Phi_t$-recurrent set, the strongly static set, the Aubry…

We report on a direct connection between quasi-periodic topology and the Almost Mathieu (Andre-Aubry) metal insulator transition (MIT). By constructing quasi-periodic transfer matrix equations from the limit of rational approximate…

We propose a solvable class of 1D quasiperiodic tight-binding models encompassing extended, localized, and critical phases, separated by nontrivial mobility edges. Limiting cases include the Aubry-Andr\'e model and the models of PRL 114,…

The transfer matrix is a powerful technique that can be applied to statistical mechanics systems as, for example, in the calculus of the entropy of the ice model. One interesting way to study such systems is to map it onto a 3-color…

The front dynamics in the Harper (or Aubry-Andr\'e) model (which has a localization transition) is investigated using two different settings, particle number front where the system is at zero temperature, and initially, the particle numbers…

We propose a realization of the two-impurity Anderson model in a double quantum-dot device. When charge transfer between the dots is suppressed the system exhibits a quantum phase transition, controlled by a surface of non-Fermi liquid…

Quasicrystals are fascinating and important because of their unconventional atomic arrangements, which challenge traditional notions of crystalline structures. Unlike regular crystals, they lack translational symmetry and generate unique…

Pendry and MacKinnon meaningful discretization of Maxwell's equations was put forward specifically as part of a finite-element numerical algorithm. By contrast with a numerical approach, in the same spirit evoked by the relationships…

We explore an asymmetric two-fermion Hubbard dimer to test the accuracy of the adiabatic approximation of time-dependent density functional theory in modelling time-resolved charge transfer. We show that the model shares essential features…