Related papers: Automorphic Bloch theorems for hyperbolic lattices
We experimentally investigate the quantum motion of an impurity atom that is immersed in a strongly interacting one-dimensional Bose liquid and is subject to an external force. We find that the momentum distribution of the impurity exhibits…
Exceptional points (EPs) are prominent non-Hermitian band degeneracies that give rise to a variety of intriguing and unconventional phenomena. Similar to Weyl and Dirac points, EPs carry topological charges and comply with the celebrated…
We study bootstrap percolation (BP) on hyperbolic lattices obtained by regular tilings of the hyperbolic plane. Our work is motivated by the connection between the BP transition and the dynamical transition of kinetically constrained…
The topological characteristics of energy bands in crystalline systems are encapsulated in the Berry curvature of the bulk Bloch states. In photonic crystal slabs, far-field emission from guided resonances naturally provides a non-invasive…
Considering the dynamics of non-interacting particles randomly moving on a lattice, the occurrence of a discontinuous transition in the values of the lattice parameters (lattice spacing and hopping times) determines the uprisal of two…
We study the dynamics of nonlinear localized excitations (solitons) in two-dimensional (2D) Bose-Einstein condensates (BECs) with repulsive interactions, loaded into an optical lattice (OL), which is combined with an external parabolic…
The link between chemical orbitals described by local degrees of freedom and band theory, which is defined in momentum space, was proposed by Zak several decades ago for spinless systems with and without time-reversal in his theory of…
Let $\Gamma$ be a non-elementary hyperbolic group and $\mu$ be a probability on $\Gamma$. We study the $\mu$-proximal, stationary actions, also known as boundary actions, of $\Gamma$. In particular, we are interested in the spectrum of…
In this thesis, I am going to consider Bernoulli percolation on graphs admitting vertex-transitive actions of groups of isometries of d-dimensional hyperbolic spaces H^d. In the first chapter, I give an overview concerning percolation and…
We study quantum dynamics of a wave packet on a class of one dimensional decorated aperiodic lattices, described within a tight binding formalism. We look for the possibility of finding extended single particle states even in the absence of…
It is well known that the orbit of a lattice in hyperbolic $n$-space is uniformly distributed when projected radially onto the unit sphere. In the present work, we consider the fine-scale statistics of the projected lattice points, and…
Topological flat bands (TFBs) provide a promising platform to investigate intriguing fractionalization phenomena, such as the fractional Chern insulators (FCIs). Most of TFB models are established in two-dimensional Euclidean lattices with…
The presence of flat bands is a source of localization in lattice systems. While flat bands are often unstable with respect to interactions between the particles, they can persist in certain cases. We consider a diamond ladder with…
We study tight-binding models in the crossover from hyperbolic to Euclidean lattices, realized through the successive insertion of Euclidean defects into hyperbolic lattices. We analyze how the holographic two-point boundary correlation…
Recent discoveries in semi-metallic multi-gap systems featuring band singularities have galvanized enormous interest in particular due to the emergence of non-Abelian braiding properties of band nodes. This previously uncharted set of…
We theoretically investigate Bloch oscillations in a one-dimensional Bose-Hubbard chain, with single-particle losses from the odd lattice sites described by the Lindblad equation. For a single particle the time evolution of the state is…
In this work we first discuss systematically three general approaches to construct a non-Hermitian flat band, defined by its dispersionless real part. They resort to, respectively, spontaneous restoration of non-Hermitian particle-hole…
The nature of space-time at high energy is an open question and the link between extra-dimensional theories with the physics of the Standard Model can not be established in a unique way. The compactification path is not unique and…
Motivated by recent theoretical and experimental developments in the physics of hyperbolic crystals, we study the noncommutative Bloch transform of Fuchsian groups that we call the hyperbolic Bloch transform. First, we prove that the…
Going beyond the conventional theory, non-Abelian band topology uncovers the global quantum geometry of Bloch bands with multiple gaps and thus unveil a new paradigm for topological physics. However, to date, all non-Abelian topological…