Related papers: Random matrix approach to `nonuniversal' conductan…
This is a cursory overview of applications of concepts from random matrix theory (RMT) to quantum electronics and classical & quantum optics. The emphasis is on phenomena, predicted or explained by RMT, that have actually been observed in…
We investigate if the degradation of a quantum directional reference frame through repeated use can be modeled as a classical direction undergoing a random walk on a sphere. We demonstrate that the behaviour of the fidelity for a degrading…
We present a theoretical analysis of recent experimental results of Yacoby et al. on transport properties of high quality quantum wires. We suggest an explanation of observed deviations of the conductance from the universal value $2e^2/h$…
This letter treats the quantum random walk on the line determined by a 2 times 2 unitary matrix U. A combinatorial expression for the mth moment of the quantum random walk is presented by using 4 matrices, P, Q, R and S given by U. The…
Random matrix theory of the transition strengths is applied to transport in the strongly localized regime. The crossover distribution function between the different ensembles is derived and used to predict quantitatively the {\sl universal}…
Quantum process tomography, the standard procedure to characterize any quantum channel in nature, is affected by a circular argument: in order to characterize the channel, the tomographic preparation and measurement need in turn to be…
We propose a simple formalism to calculate the conductance of any quantum network made of one-dimensional quantum wires. We apply this method to analyze, for two periodic systems, the modulation of this conductance with respect to the…
A quantum finite multi-barrier system, with a periodic potential, is considered and exact expressions for its plane wave amplitudes are obtained using the Transfer Matrix method [10]. This quantum model is then associated with a stochastic…
Recent progress on the understanding of the Random Conductance Model is reviewed and commented. A particular emphasis is on the results on the scaling limit of the random walk among random conductances for almost every realization of the…
We characterize quantumness of the so-called quantum walks (whose dynamics is governed by quantum mechanics) by introducing two computable measures which are stronger than the variance of the walker's position probability distribution. The…
It is shown that, in the scaling regime, transport properties of quantum wires with off-diagonal disorder are described by a family of scaling equations that depend on two parameters: the mean free path and an additional continuous…
We use the technique of bosonization to understand a variety of recent experimental results on the conductivity of a quantum wire. The quantum wire is taken to be a finite-length Luttinger liquid connected on two sides to semi-infinite…
The possibility of determining the state of a quantum system after a continuous measurement of position is discussed in the framework of quantum trajectory theory. Initial lack of knowledge of the system and external noises are accounted…
In a quantum wire with ideal helical modes, the conductance is quantized in units of e^2/h, provided the wire is connected to Fermi liquid leads. We show that this universality does not hold in partially gapped quasi-helical systems such as…
Measurements of quantum systems can be used to generate classical data that is truly unpredictable for every observer. However, this true randomness needs to be discriminated from randomness due to ignorance or lack of control of the…
Changing some of its parameters over time is a paradigmatic way of driving an otherwise isolated many-body quantum system out of equilibrium, and a vital ingredient for building quantum computers and simulators. Here, we further develop a…
A quantum phase transition is an unequivocal signature of strongly correlated many-body physics. Signatures of such phenomena are yet to be observed in ballistic transport through quantum wires. Recent developments in quantum wires have…
In many experiments on microscopic quantum systems, it is implicitly assumed that when a macroscopic procedure or "instruction" is repeated many times -- perhaps in different contexts -- each application results in the same microscopic…
A small quantum scattering system (the microsystem) is studied in interaction with a large system (the macrosystem) described by unknown stochastic variables. The interaction between the two systems is diagonal for the microsystem in a…
We have developed a multi-scale self-consistent method to study the charge conductivity of a porous system or a metallic matrix alloyed by randomly distributed nonmetallic grains and vacancies by incorporating Schr\"{o}dinger's equation and…