Related papers: The Quantum Darboux Theorem,
Based on an observation that the basic mode of a common microwave waveguide is a solution to the Klein-Gordon equation, quantum mechanics is modeled as the wave-function propagated inside a waveguide. The guide width is determined by the…
Recent work has revealed a general procedure for incorporating disorder into the semiclassical model of carrier transport, whereby the predictions of quantum linear response theory can be recovered within a quantum kinetic approach based on…
Quantum walk (QW) provides a versatile tool to study fundamental physics and also to make a variety of practical applications. We here start with the recent idea of {\it nonlinear} QW and show that introducing {\it nonlinearity} to QW can…
The issue of non-locality in quantum mechanics can potentially be resolved by considering relativistically covariant diffusion in four-dimensional spacetime. Stochastic particles described by the Klein-Gordon equation are shown to undergo a…
In this first of a series of four articles, it is shown how a hamiltonian quantum dynamics can be formulated based on a generalization of classical probability theory using the notion of quasi-invariant measures on the classical phase space…
We have studied quantum systems on finite-dimensional Hilbert spaces and found that all these systems are connected through local transformations. Actually, we have shown that these transformations give rise to a gauge group that connects…
We demonstrate an alternative method for calculating the asymptotic behaviour of the discrete one-coin quantum walk on the infinite line, via the Jacobi polynomials that arise in the path integral representation. This is significantly…
A particular example is produced to prove that quantum walks can be used to simulate full-fledged discrete gauge theories. A new family of $2D$ walks is introduced and its continuous limit is shown to coincide with the dynamics of a Dirac…
Here I present a new discrete model of quantum mechanics for relativistic 1-electron systems, in which particle movement is described by a directed space-time graph with attached 4-spinors, but without any continuous wave functions. These…
The classical spectral theorem completely describes self-adjoint operators on finite dimensional inner product vector spaces as linear combinations of orthogonal projections onto pairwise orthogonal subspaces. We prove a similar theorem for…
In a topological quantum computer, universal quantum computation is performed by dragging quasiparticle excitations of certain two dimensional systems around each other to form braids of their world lines in 2+1 dimensional space-time. In…
We describe a multi-scale resolution approach to analyzing problems in Quantum Mechanics using Daubechies wavelet basis. The expansion of the wavefunction of the quantum system in this basis allows a natural interpretation of each basis…
We develop the continuum mechanics of quantum many-body systems in the linear response regime. The basic variable of the theory is the displacement field, for which we derive a closed equation of motion under the assumption that the…
Herein, we propose a novel strategy for implementing a direct readout of the symmetric characteristic function of the quantum states of quantum fields without the involvement of idealized measurements, an aspect that has always been deemed…
We propose a new family of discrete-spacetime quantum walks capable to propagate on any arbitrary triangulations. Moreover we also extend and generalize the duality principle introduced by one of the authors, linking continuous local…
We examine in detail the possibilty of applying Darboux transformation to non Hermitian hamiltonians. In particular we propose a simple method of constructing exactly solvable PT symmetric potentials by applying Darboux transformation to…
"Quantum Topology" deals with the general quantum theory as the theory of the functional quantum space; space time and energy momentum forms form a connected manifold; a functional quantum space on the quantum level. The general quantum…
An approach to the quantum-classical mechanics of phase space dependent operators, which has been proposed recently, is remodeled as a formalism for wave fields. Such wave fields obey a system of coupled non-linear equations that can be…
We reconsider differential geometry from the point of view of the quantum theory of non-relativistic spinning particles, which provides examples of supersymmetric quantum mechanics. This enables us to encode geometrical structure in…
This paper is an introduction to diagrammatic methods for representing quantum processes and quantum computing. We review basic notions for quantum information and quantum computing. We discuss topological diagrams and some issues about…