Related papers: Quantum Interference, Graphs, Walks, and Polynomia…
Quantum walks constitute important tools in different applications, especially in quantum algorithms. To a great extent their usefulness is due to unusual diffusive features, allowing much faster spreading than their classical counterparts.…
We investigate electron transport through azulene molecule with four distinct electrode contact geometries using the non-equilibrium Green's function formalism within the tight-binding Hamiltonian. Employing the Q-matrix approach, we…
Destructive quantum interference (QI) has been a source of interest as a new paradigm for molecular electronics as the electronic conductance is widely dependent on the occurrence or absence of destructive QI effects. In order to interpret…
Quantum interference (QI) in molecular transport junctions can lead to dramatic reductions of the electron transmission at certain energies. In a recent work [Markussen et al., Nano Lett. 2010, 10, 4260] we showed how the presence of such…
We discuss a particular kind of quantum walk on a general graph. We affix two semi-infinite lines to a general finite graph, which we call tails. On the tails, the particle making the walk simply advances one unit at each time step, so that…
A quantum walk is the quantum analogue of a random walk. While it is relatively well understood how quantum walks can speed up random walk hitting times, it is a long-standing open question to what extent quantum walks can speed up the…
We present a method based on graph theory for evaluation of the inelastic propensity rules for molecules exhibiting complete destructive quantum interference in their elastic transmission. The method uses an extended adjacency matrix…
The adjacency matrix of a graph G is the Hamiltonian for a continuous-time quantum walk on the vertices of G. Although the entries of the adjacency matrix are integers, its eigenvalues are generally irrational and, because of this, the…
Quantum walks are accepted as a generic model for quantum transport. The character of the transport crucially depends on the properties of the walk like its geometry and the driving coin. We demonstrate that increasing transport distance…
In this paper we isolate the combinatorial property responsible (at least in part) for the computational speedups recently observed in some quantum walk algorithms. We find that continuous-time quantum walks can exploit the covering space…
We quantitatively differentiate between the spreads of discrete-time quantum and classical random walks on a cyclic graph. Due to the closed nature of any cyclic graph, there is additional "collision"- like interference in the quantum…
Quantum interference (QI) effects in molecular systems are a topic of emerging interest in electron transport studies of single molecule junctions. In a recent Letter, Xia et al. employed a graphical scheme introduced by my colleagues and…
Quantum walks have been employed widely to develop new tools for quantum information processing recently. A natural quantum walk dynamics of interacting particles can be used to implement efficiently the universal quantum computation. In…
We present quantum electron transport theory that incorporates dynamical effects of motion of atoms on electrode-molecule interfaces in the calculations of the electric current. The theory is based on non-equilibrium Green's functions. We…
We study the transition matrix of a quantum walk on strongly regular graphs. It is proposed by Emms, Hancock, Severini and Wilson in 2006, that the spectrum of $S^+(U^3)$, a matrix based on the amplitudes of walks in the quantum walk,…
In the present paper, we study the continuous-time quantum walk on quotient graphs. On such graphs, there is a straightforward reduction of problem to a subspace that can be considerably smaller than the original one. Along the lines of…
We study electron transport properties of some molecular wires and a unconventional disordered thin film within the tight-binding framework using Green's function technique. We show that electron transport is significantly affected by…
Coherent electronic transport through individual molecules is crucially sensitive to quantum interference. Using exact diagonalization techniques, we investigate the zero-bias and zero-temperature conductance through $\pi$-conjugated…
One of the key features of quantum mechanics is the interference of probability amplitudes. The reason for the appearance of interference is mathematically very simple. It is the linear structure of the Hilbert space which is used for the…
If simple guidelines could be established for understanding how quantum interference (QI) can be exploited to control the flow of electricity through single molecules, then new functional molecules, which exploit room-temperature QI could…