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A one-parameter family of random variables, called the Discrete Action, is de ned for a 2-dimensional Lorentzian spacetime of nite volume. The sin-gle parameter is a discreteness scale.
The present chapter [submitted for publication in "Fourier Transforms, Theory and Applications", G. Nikolic (Ed.), InTech (Open Access Publisher), Vienna, 2011] is concerned with the introduction and ...
An infinite discrete series of solutions of the free Schr\"odinger equation in one dimension is constructed. These solutions are normalizable, expand the whole space of solutions, are spatially multi-...
We study the quantum walk search algorithm of Shenvi, Kempe and Whaley [PRA 67 052307 (2003)] on data structures of one to two spatial dimensions, on which the algorithm is thought to be less efficie...
The general aim of this paper is to supply a method to decide whether a discrete system decoheres or not, and under what conditions decoherence occurs, with no need of appealing to computer simulatio...
We consider crossovers with respect to the weak convergence theorems from a discrete-time quan- tum walk (DTQW). We show that a continuous-time quantum walk (CTQW) and discrete- and continuous-time ...
We consider a discrete-time quantum walk Wt, at time t on a graph with joined half lines J, which is composed of  half lines with the same origin. Our analysis is based on a reduction of the walk o...
In order to construct a quantum theory of gravity, we may have to abandon certain assumptions we were making. In particular, the concept of spacetime as a continuum substratum is questioned. Causal Se...
In this paper, we firstly establish the discrete time and finite state reflected backward stochastic difference equations(DF-RBSDEs for short); then we explore the corresponding basic properties and t...
We analyze the formation and dynamics of bright unstaggered solitons in the disk-shaped dipolar Bose-Einstein condensate, which features the interplay of contact (collisional) and long-range dipole-di...
We report the experimental observation of discrete breathers in a one-dimensional diatomic granular crystal composed of compressed elastic beads that interact via Hertzian contact. We first characteri...
We show that certain types of quantum walks can be modeled as waves that propagate in a medium with phase and group velocities that are explicitly calculable. Since the group and phase velocities indi...
In this paper, we develop spectral analysis of a discrete non-Hermitian quantum system that is a discrete counterpart of some continuous quantum systems on a complex contour. In particular, simple con...
We propose a quantization of linear, volume preserving, maps on the discrete and finite 3-torus T_N^3 represented by elements of the group SL(3,Z_N). These flows can be considered as special motions o...
Reconciliation is an essential part of any secret-key agreement protocol and hence of a Quantum Key Distribution (QKD) protocol, where two legitimate parties are given correlated data and want to agre...

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