Related papers: Disorder, Path Integrals and Localization
The path integral for the propagator is expanded into a perturbation series, which can be exactly summed in the case of $\delta$-function perturbations giving a closed expression for the (energy-dependent) Green function. Making the…
A new paradigm of Anderson localization caused by correlations in the long-range hopping along with uncorrelated on-site disorder is considered which requires a more precise formulation of the basic localization-delocalization principles. A…
The role of disorder on wave propagation through the universe is studied. Assuming space fluctuations of the order of the Planck length and the size of the universe as the corresponding localization length for the background radiation, we…
Quantum walks are promising for information processing tasks because on regular graphs they spread quadratically faster than random walks. Static disorder, however, can turn the tables: unlike random walks, quantum walks can suffer Anderson…
We study the effect of Anderson localization on the expansion of a Bose-Einstein condensate, released from a harmonic trap, in a 3D random potential. We use scaling arguments and the self-consistent theory of localization to show that the…
Diffusive transport is among the most common phenomena in nature [1]. However, as predicted by Anderson [2], diffusion may break down due to interference. This transition from diffusive transport to localization of waves should occur for…
While Anderson localisation is largely well-understood, its description has traditionally been rather cumbersome. A recently-developed theory -- Localisation Landscape Theory (LLT) -- has unparalleled strengths and advantages, both…
We investigate disorder induced localization in the presence of nonlinearity and curvature. We numerically analyze the time-resolved three-dimensional expansion of a wave-packet in a bended cigar shaped potential with a focusing Kerr-like…
The periodically $\delta$-kicked quantum linear rotor is known to experience non-classical bounded energy growth due to quantum dynamical localization in angular momentum space. We study the effect of random deviations of the kick period in…
We investigate the transition induced by disorder in a periodically-driven one-dimensional model displaying quantized topological transport. We show that, while instantaneous eigenstates are necessarily Anderson localized, the periodic…
The interplay between disorder and quantum interference leads to a wide variety of physical phenomena including celebrated Anderson localization -- the complete absence of diffusive transport due to quantum interference between different…
For a Hamiltonian ${\hat H}$ containing a position-dependent (disordered) potential, we introduce a sequence of landscape functions $u_n(\vec{r})$ obeying ${\hat H} u_n(\vec{r}) = u_{n-1}(\vec{r})$ with $u_0(\vec{r}) = 1$. For $n \to…
Anderson localization is a consequence of coherent interference of multiple scattering events in the presence of disorder, which leads to an exponential suppression of the transmission. The decay of the transmission is typically probed at a…
A one-dimensional boundary of a two-dimensional topological superconductor can host a number of topologically protected chiral modes. Combining two topological superconductors with different topological indices, it is possible to achieve a…
Quantum walks have been shown to have impressive transport properties compared to classical random walks. However, imperfections in the quantum walk algorithm can destroy any quantum mechanical speed-up due to Anderson localization. We…
We present a self-consistent theory of Anderson localization that yields a simple algorithm to obtain \emph{typical local density of states} as an order parameter, thereby reproducing the essential features of a phase-diagram of…
We calculated numerically the localization length of one-dimensional Anderson model with correlated diagonal disorder. For zero energy point in the weak disorder limit, we showed that the localization length changes continuously as the…
Quantum particles in a disordered potential, photons or classical waves in a random medium, or the universe expansion in a fluctuating cosmic field, all share Anderson localization as a communality. In general, localization is enhanced for…
We study analytically the metal-insulator transition in a disordered conductor by combining the self-consistent theory of localization with the one parameter scaling theory. We provide explicit expressions of the critical exponents and the…
The self-consistent theory of Anderson localization of quantum particles or classical waves in disordered media is reviewed. After presenting the basic concepts of the theory of Anderson localization in the case of electrons in disordered…