Related papers: Quantum Interference, Graphs, Walks, and Polynomia…
We show that the coined quantum walk on a line can be understood as an interference phenomenon, can be classically implemented, and indeed already has been. The walk is essentially two independent walks associated with the different coin…
Quantum interference in coherent transport through single molecular rings may provide a mechanism to control current in molecular electronics. We investigate its applicability by using a single-particle Green function method combined with…
Quantum transport properties through single polycyclic hydrocarbon molecules attached to two metallic electrodes are studied by the use of Green's function technique. A parametric approach based on the tight-binding model is introduced to…
Non-equilibrium Green's function theory for non-adiabatic effects in quantum transport [Kershaw and Kosov, J.Chem. Phys. 2017, 147, 224109 and J. Chem. Phys. 2018, 149, 044121] is extended to the case of interacting electrons. We consider a…
The continuous-time quantum walk is a particle evolving by Schr\"odinger's equation in discrete space. Encoding the space as a graph of vertices and edges, the Hamiltonian is proportional to the discrete Laplacian. In some physical systems,…
Quantum walks, both discrete and continuous, serve as fundamental tools in quantum information processing with diverse applications. This work introduces a hybrid quantum walk model that integrates the coin mechanism of discrete walks with…
The method of the quantum probability theory only requires simple structural data of graph and allows us to avoid a heavy combinational argument often necessary to obtain full description of spectrum of the adjacency matrix. In the present…
A continuous-time quantum walk is modelled using a graph. In this short paper, we provide lower bounds on the size of a graph that would allow for some quantum phenomena to occur. Among other things, we show that, in the adjacency matrix…
Destructive quantum interference in electron transport through molecules provides an unconventional route for suppressing electric current. In this work we introduce "interference vectors" for each interference and use them to characterize…
A quantum walk places a traverser into a superposition of both graph location and traversal "spin." The walk is defined by an initial condition, an evolution determined by a unitary coin/shift-operator, and a measurement based on the…
Random walk algorithms are crucial for sampling and approximation problems in statistical physics and theoretical computer science. The mixing property is necessary for Markov chains to approach stationary distributions and is facilitated…
We set the ground for a theory of quantum walks on graphs- the generalization of random walks on finite graphs to the quantum world. Such quantum walks do not converge to any stationary distribution, as they are unitary and reversible.…
Quantum interference, be it destructive or constructive, has a substantial influence on the magnitude of molecular conductance and consequently there is significant interest in predicting these effects. It is commonly thought that…
We discuss the general form of the transmission spectrum through a molec- ular junction in terms of the Green function of the isolated molecule. By introducing a tight binding method, we are able to translate the Green func- tion properties…
We provide a simple set of rules for predicting interference effects in off-resonant transport through single-molecule junctions. These effects fall in two classes, showing respectively an odd or an even number of nodes in the linear…
Quantum walks on graphs can model physical processes and serve as efficient tools in quantum information theory. Once we admit random variations in the connectivity of the underlying graph, we arrive at the problem of percolation, where the…
We study quantum interference effects due to electron motion on the Kagom\'e lattice in a perpendicular magnetic field. These effects arise from the interference between phase factors associated with different electron closed-paths. From…
This paper investigates continuous-time quantum walks on directed bipartite graphs based on a graph's adjacency matrix. We prove that on bipartite graphs, probability transport between the two node partitions can be completely suppressed by…
We look for manifestations of quantum interference effects in the Seebeck coefficient of a molecular junction, when the electronic conductance exhibits pronounced destructive interference features due to the presence of quasi-degenerate…
Using the tight-binding model and the generalized Green's function formalism, the effect of quantum interference on the electron transport through the benzene molecule in a semiconductor/benzene/semiconductor junction is numerically…