Related papers: Absolutely continuous spectrum implies ballistic t…
The presence of chiral modes on the edges of quantum Hall samples is essential to our understanding of the quantum Hall effect. In particular, these edge modes should support ballistic transport and therefore, in a single particle picture,…
We identify a set of quantum graphs with unique and precisely defined spectral properties called {\it regular quantum graphs}. Although chaotic in their classical limit with positive topological entropy, regular quantum graphs are…
In this paper we consider two classes of random Hamiltonians on $L^2(\RR^d)$ one that imitates the lattice case and the other a Schr\"odinger operator with non-decaying, non-sparse potential both of which exhibit a.c. spectrum. In the…
A continuous-time quantum random walk describes the motion of a quantum mechanical particle on an underlying graph. The graph itself is associated with a Hilbert space of dimension equal to the number of vertices. The dynamics of the walk…
We consider the quantum transport in a tight-binding chain with a locally applied potential which is oscillating in time. The steady state for such a driven impurity can be calculated exactly for any energy and applied potential using the…
The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise quantum walks have shown much potential as a frame- work for developing new quantum algorithms.…
We study the Brownian motion of a classical particle in one-dimensional inhomogeneous environments where the transition probabilities follow quasiperiodic or aperiodic distributions. Exploiting an exact correspondence with the…
We explore the tunneling behavior of a quantum particle on a finite graph, in the presence of an asymptotically large potential. Surprisingly the behavior is governed by the local symmetry of the graph around the wells.
Recently, a self-contained trajectory-based formulation of non-relativistic quantum mechanics was developed [Ann. Phys. 315, 505 (2005); Chem. Phys. 370, 4 (2010); J. Chem. Phys. 136, 031102 (2012)], that makes no use of wavefunctions or…
We investigate flows on graphs whose links have random capacities. For binary trees we derive the probability distribution for the maximal flow from the root to a leaf, and show that for infinite trees it vanishes beyond a certain threshold…
Irreversibility is introduced to quantum graphs by coupling the graphs to a bath of harmonic oscillators. The interaction which is linear in the harmonic oscillator amplitudes is localized at the vertices. It is shown that for sufficiently…
In this article we prove existence of the asymptotic capacity of the range of random walks on free products of graphs. In particular, we will show that the asymptotic capacity of the range is almost surely constant and strictly positive.…
We consider viscous two-dimensional steady flows of incompressible fluids past doubly periodic arrays of solid obstacles. In a class of such flows, the autocorrelations for the Lagrangian observables decay in accordance with the power law,…
Quantum fluctuations, through quantum corrections, have the potential to lead to irreversibility in quantum field theory. We consider the virtual ``charge" distribution generated by quantum corrections in the leading log, short range…
It is shown that in many-electron systems quantum transfer amplitudes and thus transfer probabilities may be strongly influenced by fast fluctuating fields, in particular, caused by simultaneous electron transfers. Corresponding mutual…
Do completely unpredictable events exist in nature? Classical theory, being fully deterministic, completely excludes fundamental randomness. On the contrary, quantum theory allows for randomness within its axiomatic structure. Yet, the fact…
A novel transport phenomenon is identified that is induced by inertial Brownian particles which move in simple one-dimensional, symmetric periodic potentials under the influence of both a time periodic and a constant, biasing driving force.…
We investigate quantum and quantum-relativistic effects associated with the noise power spectrum and the fluctuation--dissipation relation between current--noise spectra and linear--response conductance at low frequencies of the…
Quantum random walks have received much interest due to their non-intuitive dynamics, which may hold the key to a new generation of quantum algorithms. What remains a major challenge is a physical realization that is experimentally viable…
We demonstrate numerically that a robust and unusual multifractal regime can emerge in a one-dimensional quantum chain with maximally correlated disorder, above a threshold disorder strength. This regime is preceded by a mixed and an…