Quasiperiodic function
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Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering Open
We give a general overview of the high-frequency regime in periodically\ndriven systems and identify three distinct classes of driving protocols in\nwhich the infinite-frequency Floquet Hamiltonian is not equal to the\ntime-averaged Hamilt…
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Nearest Neighbor Tight Binding Models with an Exact Mobility Edge in One Dimension Open
We investigate localization properties in a family of deterministic (i.e., no disorder) nearest neighbor tight binding models with quasiperiodic on site modulation. We prove that this family is self-dual under a generalized duality transfo…
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Interplay of non-Hermitian skin effects and Anderson localization in nonreciprocal quasiperiodic lattices Open
Non-Hermiticity from non-reciprocal hoppings has been shown recently to demonstrate the non-Hermitian skin effect (NHSE) under open boundary conditions (OBCs). Here we study the interplay of this effect and the Anderson localization in a \…
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Single-Particle Mobility Edge in a One-Dimensional Quasiperiodic Optical Lattice Open
A single-particle mobility edge (SPME) marks a critical energy separating extended from localized states in a quantum system. In one-dimensional systems with uncorrelated disorder, a SPME cannot exist, since all single-particle states loca…
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Depinning and nonequilibrium dynamic phases of particle assemblies driven over random and ordered substrates: a review Open
We review the depinning and nonequilibrium phases of collectively interacting particle systems driven over random or periodic substrates. This type of system is relevant to vortices in type-II superconductors, sliding charge density waves,…
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Observation of Slow Dynamics near the Many-Body Localization Transition in One-Dimensional Quasiperiodic Systems Open
In the presence of sufficiently strong disorder or quasiperiodic fields, an interacting many-body system can fail to thermalize and become many-body localized. The associated transition is of particular interest, since it occurs not only i…
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Probing Slow Relaxation and Many-Body Localization in Two-Dimensional Quasiperiodic Systems Open
In a many-body localized (MBL) quantum system, the ergodic hypothesis breaks down, giving rise to a fundamentally new many-body phase. Whether and under which conditions MBL can occur in higher dimensions remains an outstanding challenge b…
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Two Universality Classes for the Many-Body Localization Transition Open
We provide a systematic comparison of the many-body localization (MBL) transition in spin chains with nonrandom quasiperiodic versus random fields. We find evidence suggesting that these belong to two separate universality classes: the fir…
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Observation of Many-Body Localization in a One-Dimensional System with a Single-Particle Mobility Edge Open
We experimentally study many-body localization (MBL) with ultracold atoms in a weak one-dimensional quasiperiodic potential, which in the noninteracting limit exhibits an intermediate phase that is characterized by a mobility edge. We meas…
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One-Dimensional Quasiperiodic Mosaic Lattice with Exact Mobility Edges Open
The mobility edges (MEs) in energy that separate extended and localized states are a central concept in understanding the localization physics. In one-dimensional (1D) quasiperiodic systems, while MEs may exist for certain cases, the analy…
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Discovery of superconductivity in quasicrystal Open
Superconductivity is ubiquitous as evidenced by the observation in many crystals including carrier-doped oxides and diamond. Amorphous solids are no exception. However, it remains to be discovered in quasicrystals, in which atoms are order…
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Interactions and Mobility Edges: Observing the Generalized Aubry-André Model Open
Using synthetic lattices of laser-coupled atomic momentum modes, we experimentally realize a recently proposed family of nearest-neighbor tight-binding models having quasiperiodic site energy modulation that host an exact mobility edge pro…
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Discovery of Nonlinear Multiscale Systems: Sampling Strategies and Embeddings Open
A major challenge in the study of dynamical systems is that of model\ndiscovery: turning data into models that are not just predictive, but provide\ninsight into the nature of the underlying dynamical system that generated the\ndata. This …
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Critical Behavior and Fractality in Shallow One-Dimensional Quasiperiodic Potentials Open
Quasiperiodic systems offer an appealing intermediate between long-range ordered and genuine disordered systems, with unusual critical properties. One-dimensional models that break the so-called self-dual symmetry usually display a mobilit…
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Challenges to observation of many-body localization Open
We study time dynamics of 1D disordered Heisenberg spin-1/2 chain focusing on\na regime of large system sizes and a long time evolution. This regime is\nrelevant for observation of many-body localization (MBL), a phenomenon that is\nexpect…
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Breather Wave Molecules Open
We present both a theoretical description and experimental observation of the nonlinear mutual interactions between a pair of copropagative breathers in the framework of the focusing one-dimensional nonlinear Schrödinger equation. As a gen…
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Noncollinear phases in moiré magnets Open
Significance Moiré patterns, which result when two or more two-dimensional materials with incommensurate or rotated lattices are layered together, create controllable electronic bands that have recently been shown to induce a tremendous we…
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Generalized Aubry-André self-duality and mobility edges in non-Hermitian quasiperiodic lattices Open
We demonstrate the existence of generalized Aubry-André self-duality in a class of non-Hermitian quasiperiodic lattices with complex potentials. From the self-duality relations, the analytical expression of mobility edges is derived. Compa…
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Many-Body Localization in the Presence of a Single-Particle Mobility Edge Open
In one dimension, noninteracting particles can undergo a localization-delocalization transition in a quasiperiodic potential. Recent studies have suggested that this transition transforms into a many-body localization (MBL) transition upon…
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The Fibonacci quasicrystal: case study of hidden dimensions and multifractality Open
The distinctive electronic properties of quasicrystals stem from their long range structural order, with invariance under rotations and under discrete scale change, but without translational invariance. d-dimensional quasicrystals can be d…
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Non-Hermitian mobility edges in one-dimensional quasicrystals with parity-time symmetry Open
We investigate localization-delocalization transition in one-dimensional non-Hermitian quasiperiodic lattices with exponential short-range hopping, which possess parity-time ($\mathcal{PT}$) symmetry. The localization transition induced by…
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Reentrant Localization Transition in a Quasiperiodic Chain Open
Systems with quasiperiodic disorder are known to exhibit a localization transition in low dimensions. After a critical strength of disorder, all the states of the system become localized, thereby ceasing the particle motion in the system. …
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Quasinormal modes, quasiperiodic oscillations, and the shadow of rotating regular black holes in nonminimally coupled Einstein-Yang-Mills theory Open
In this paper we obtain an effective metric describing a regular and rotating\nmagnetic black hole (BH) solution with a Yang-Mills electromagnetic source in\nEinstein-Yang-Mills (EYM) theory using the Newman--Janis algorithm via the\nnon-c…
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Many-body localization in a non-Hermitian quasiperiodic system Open
In the present study, the interplay among interaction, topology, quasiperiodicity, and non-Hermiticity is studied. The hard-core bosons model on a one-dimensional lattice with asymmetry hoppings and quasiperiodic onsite potentials is selec…
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Experimental Observation of Two-Dimensional Anderson Localization with the Atomic Kicked Rotor Open
Dimension 2 is expected to be the lower critical dimension for Anderson localization in a time-reversal-invariant disordered quantum system. Using an atomic quasiperiodic kicked rotor-equivalent to a two-dimensional Anderson-like model-we …
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Quasicrystals: What do we know? What do we want to know? What can we know? Open
More than 35 years and 11 000 publications after the discovery of quasicrystals by Dan Shechtman, quite a bit is known about their occurrence, formation, stability, structures and physical properties. It has also been discovered that quasi…
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Convection roll-driven generation of supra-wavelength periodic surface structures on dielectrics upon irradiation with femtosecond pulsed lasers Open
The significance of the magnitude of Prandtl number of a fluid in the propagation direction of induced convection rolls is elucidated. Specifically, we report on the physical mechanism to account for the formation and orientation of previo…
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Many-body localization transition with power-law interactions: Statistics of eigenstates Open
We study spectral and wavefunction statistics for many-body localization transition in systems with long-range interactions decaying as $1/r^\alpha$ with an exponent $\alpha$ satisfying $ d \le \alpha \le 2d$, where $d$ is the spatial dime…
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Observation of Topological Edge Modes in a Quasiperiodic Acoustic Waveguide Open
Topological boundary and interface modes are generated in an acoustic waveguide by simple quasiperiodic patterning of the walls. The procedure opens many topological gaps in the resonant spectrum and qualitative as well as quantitative ass…
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Localization and topological transitions in non-Hermitian quasiperiodic lattices Open
We investigate the localization and topological transitions in a\none-dimensional (interacting) non-Hermitian quasiperiodic lattice, which is\ndescribed by a generalized Aubry-Andr\\'{e}-Harper model with irrational\nmodulations in the off…