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We describe how to engineer wavefunction delocalization in disordered systems modelled by tight-binding Hamiltonians in d>1 dimensions. We show analytically that a simple product structure for the random onsite potential energies, together…
Localization phenomena during transport are typically driven by disordered scalar potentials. Here, we predict a universal pseudospin localization phenomenon induced by a disordered vectorial potential and demonstrate it experimentally in…
Localization of waves by disorder is a fundamental physical problem encompassing a diverse spectrum of theoretical, experimental and numerical studies in the context of metal-insulator transition, quantum Hall effect, light propagation in…
The specific problem we address in these lectures is the problem of transport and localization in disordered systems, when interference is present, as characteristic for waves, with a focus on realizations with ultracold atoms.
Recent advances in transport properties measurements of disordered materials and lattice simulations, using superconducting qubits, have rekindled interest in Anderson localization, motivating our study of highly disordered quantum…
Controlling the flow of energy in a random medium is a research frontier with a wide range of applications. As recently demonstrated, the effect of disorder on the transmission of optical beams, may be partially compensated by wavefront…
We review some recent (mostly ours) results on the Anderson localization of light and electron waves in complex disordered systems, including: (i) left-handed metamaterials, (ii) magneto-active optical structures, (iii) graphene…
We propose a concept of disordered resonant media, which are characterized by random variations of their parameters along the light propagation direction. In particular, a simple model of disorder considered in the paper implies random…
The use of coherent wave phenomena to enhance device performance is a cornerstone of modern optics. In juxtaposition to (locally) periodic metasurfaces, their disordered counterparts exhibit an interplay of destructive and constructive…
Systems with purely off-diagonal disorder have peculiar features such as the localization-delocalization transition and long-range correlations in their wavefunctions. To motivate possible experimental studies of the physics of off-diagonal…
A metamaterial formed by superconducting circuits or quantum dots can serve as active lasing medium when coupled to a microwave resonator. For these artificial atoms, in contrast to real atoms, variations in their parameters cannot be…
In one dimension, any disorder is traditionally believed to localize all states. We show that this paradigm breaks down under hyperuniform disorder, which suppresses long-wavelength fluctuations and interpolates between random and periodic…
Localization of waves by disorder is a fundamental physical problem encompassing a diverse spectrum of theoretical, experimental and numerical studies in the context of metal-insulator transitions, the quantum Hall effect, light propagation…
Connections between the electron eigenstates and conductivity of one-dimensional disordered electron systems is studied in the framework of the tight-binding model. We show that for weak disorder only part of the states exhibit resonant…
We study charge transport in one-dimensional graphene superlattices created by applying layered periodic and disordered potentials. It is shown that the transport and spectral properties of such structures are strongly anisotropic. In the…
The propagation of light through samples with random inhomogeneities can be described by way of transmission eigenchannels, which connect incoming and outgoing external propagating modes. Although the detailed structure of a disordered…
Localization due to disorder has been one of the most intriguing theoretical concepts evolved in condensed matter. Here, we expand the theory of localization by considering two types of disorder at the same time, namely the original…
Understanding the ability of particles to maneuver through disordered environments is a central problem in innumerable settings, from active matter and biology to electronics. Macroscopic particles ultimately exhibit diffusive motion when…
Localized waves in disordered one-dimensional materials have been studied for decades, including white-noise and correlated disorder, as well as quasi-periodic disorder. How these wave phenomena relate to those in crystalline (periodic…
Photonic metasurfaces are ultrathin electromagnetic wave-molding metamaterials providing the missing link for the integration of nanophotonic chips with nanoelectronic circuits. An extra twist in this field originates from spin-optical…