相关论文: Quantum and classical localisation, the spin quant…
We present general mappings between classical spin systems and quantum physics. More precisely, we show how to express partition functions and correlation functions of arbitrary classical spin models as inner products between quantum…
We study the classical and quantum transport processes on some finite networks and model them by continuous-time random walks (CTRW) and continuous-time quantum walks (CTQW), respectively. We calculate the classical and quantum transition…
There is considerable experimental evidence for the existence in Quantum Hall systems of an approximate emergent discrete symmetry, $\Gamma_0(2) \subset SL(2,Z)$. The evidence consists of the robustness of the tests of a suite a predictions…
We investigate the localization of electronic states in the integer quantum Hall effect using a magnetic localization landscape (MLL) approach. By studying a continuum Schr\"odinger model with disordered electrostatic potential, we…
We present a method for computing first order asymptotics of semiclassical spectra for 1-D Bogoliubov-de Gennes (BdG) Hamiltonian from Supraconductivity, which models the electron/hole scattering through two SNS junctions. This involves: 1)…
A number of recent studies have investigated the introduction of decoherence in quantum walks and the resulting transition to classical random walks. Interestingly, it has been shown that algorithmic properties of quantum walks with…
In the framework of the semiclassical approach the universal spectral correlations in the Hamiltonian systems with classical chaotic dynamics can be attributed to the systematic correlations between actions of periodic orbits which (up to…
Quantum walks are counterparts of classical random walks. They spread faster, which can be exploited in information processing tasks, and constitute a versatile simulation platform for many quantum systems. Yet, some of their properties can…
We study both the continuous model and the discrete model of the integer quantum Hall effect on the hyperbolic plane in the presence of disorder, extending the results of an earlier paper [CHMM]. Here we model impurities, that is we…
We investigate the properties of a quantum walk which can simulate the behavior of a spin $1/2$ particle in a model with an ordinary spatial dimension, and one extra dimension with warped geometry between two branes. Such a setup…
We apply the semiclassical theory of transport to quantum dots with exact and approximate spatial symmetries; left-right mirror symmetry, up-down mirror symmetry, inversion symmetry or four-fold symmetry. In this work - the first of a pair…
We investigate the impact of decoherence and static disorder on the dynamics of quantum particles moving in a periodic lattice. Our experiment relies on the photonic implementation of a one-dimensional quantum walk. The pure quantum…
We study transport in topologically disordered networks that are subjected to an environment that induces classical diffusion. The dynamics is phenomenologically described within the framework of the recently introduced quantum stochastic…
We review equivariant localization techniques for the evaluation of Feynman path integrals. We develop systematic geometric methods for studying the semi-classical properties of phase space path integrals for dynamical systems, emphasizing…
There is a close analogy between the response of a quantum Hall liquid (QHL) to a small change in the electron density and the response of a superconductor to an externally applied magnetic flux - an analogy which is made concrete in the…
We develop a semiclassical theory for spin-dependent quantum transport in ballistic quantum dots. The theory is based on the semiclassical Landauer formula, that we generalize to include spin-orbit and Zeeman interaction. Within this…
We explore an unusual type of quantum matter that can be realized by qubits having different physical origin. Interactions in this matter are described by essentially different coupling operators for all qubits. We show that at least the…
In previous work we discussed the quantization of paths in spacetime. Building on these ideas we have developed a mathematically coherent theory addressing a number of open questions concerning Loop Quantum Gravity. Our approach develops a…
Quantum chaos of many-body systems has been swiftly developing into a vibrant research area at the interface between various disciplines, ranging from statistical physics to condensed matter to quantum information and to cosmology. In…
Given the extensive application of classical random walks to classical algorithms in a variety of fields, their quantum analogue in quantum walks is expected to provide a fruitful source of quantum algorithms. So far, however, such…