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We consider a noninteracting disordered system designed to model particle diffusion, relaxation in glasses, and impurity bands of semiconductors. Disorder originates in the random spatial distribution of sites. We find strong numerical…
Disorder plays a crucial role in many systems particularly in solid state physics. However, the disorder in a particular system can usually not be chosen or controlled. We show that the unique control available for ultracold atomic gases…
In previous quantum key distribution (QKD) protocols, information is encoded on either the discrete-variable of single-photon signal or continuous-variables of multi-photon signal. Here, we propose a new QKD protocol by encoding information…
We prove that at large disorder, with large probability and for a set of Diophantine frequencies of large measure, Anderson localization in $\Bbb Z^d$ is {\it stable} under localized time-quasi-periodic perturbations by proving that the…
We analyze the response of a complex quantum-mechanical system (e. g., a quantum dot) to a time-dependent perturbation. Assuming the dot energy spectrum and the perturbation to be described by the Gaussian Orthogonal Ensemble of random…
We study the fingerprint of the Arnol'd diffusion in a quantum system of two coupled nonlinear oscillators with a two-frequency external force. In the classical description, this peculiar diffusion is due to the onset of a weak chaos in a…
We consider the combined influence of disorder, electron-electron interactions and quantum hopping on the properties of electronic systems in a localized phase, approaching an insulator-metal transition. The generic models in this regime…
Anderson localization is a regime in which diffusion is inhibited and waves (also electromagnetic waves) get localized. Here we exploit adaptive optics to achieve focusing in disordered optical fibers in the Anderson regime. By wavefront…
We investigate light transport in three-dimensional disordered media composed of irregular dielectric particles using large scale full-wave simulations. For subwavelength particles with size parameter $kr \approx 1$ and high refractive…
We discuss the role of rare fluctuation effects in quantum condensed matter systems. In particular, we present recent numerical results of the effect of resonant states in Anderson's original model of electron localization. We find that…
Waves propagating in certain one-dimensional quasiperiodic lattices are known to exhibit a sharp localization transition. We theoretically predict and experimentally observe that the localization of light in one-dimensional photonic…
Complex and correlated quantum systems with promise for new functionality often involve entwined electronic degrees of freedom. In such materials, highly unusual properties emerge and could be the result of electron localization. Here, a…
A model of localization based on the Witten Hamiltonian of supersymmetric quantum mechanics is considered. The case where the superpotential $\phi(x)$ is a random telegraph process is solved exactly. Both the localization length and the…
A local impurity usually only strongly affects few single-particle energy levels, thus cannot induce a quantum phase transition (QPT), or any macroscopic quantum phenomena in a many-body system within the Hermitian regime. However, it may…
We demonstrate the extension of coherence between all four two-electron spin ground states of an InAs quantum dot molecule (QDM) via non-local suppression of nuclear spin fluctuations in both constituent quantum dots (QDs), while optically…
This study is concerned with destruction of Anderson localization by a nonlinearity of the power-law type. We suggest using a nonlinear Schr\"odinger model with random potential on a lattice that quadratic nonlinearity plays a dynamically…
We offer theoretical explanations for some recent observations in numerical simulations of quantum random walks (QRW). Specifically, in the case of a QRW on the line with one particle (walker) and two entangled coins, we explain the…
We study electron transmission through a periodic array of quantum dots (QD) sandwiched between doped semiconductor leads. When the Fermi wavelength of tunneling electron exceeds the array lattice constant, the off-resonant per QD…
A technically convenient signature of Anderson localization is exponential decay of the fractional moments of the Green function within appropriate energy ranges. We consider a random Hamiltonian on a lattice whose randomness is generated…
Anderson localization (AL) is a ubiquitous interference phenomenon in which waves fail to propagate in a disordered medium. We observe three-dimensional AL of noninteracting ultracold matter by allowing a spin-polarized atomic Fermi gas to…