Related papers: Occupation time for classical and quantum walks
Recent intriguing discussion of heat death by Kutrovatz is critically examined. It is shown that there exists another way of answering the heat death puzzle, already present in the ancient philosophical tradition. This alternative route…
Why are "analogue spacetimes'' interesting? For the purposes of this workshop the answer is simple: Analogue spacetimes provide one with physically well-defined and physically well-understood concrete models of many of the phenomena that…
We derive the continuous spacetime limit of the one dimensional lazy discrete time quantum walk, obtaining explicit macroscopic evolution equations for a three state model in the presence of decoherence. While continuum limits of two state…
We investigate the distribution of the time spent by a random walker to the right of a boundary moving with constant velocity v. For the continuous-time problem (Brownian motion), we provide a simple alternative proof of Newman's recent…
Inspired by the one-hundredth anniversary of the seminal works of Stern and Gerlach, our contribution is a proposal of how to use their famous experiment in a more contemporary perspective. Our main idea is to re-cast the experiment in the…
An introduction is given to an algebraic formulation and generalisation of the consistent histories approach to quantum theory. The main technical tool in this theory is an orthoalgebra of history propositions that serves as a generalised…
We consider the 2D alternate quantum walk on a cylinder. We concentrate on the study of the motion along the open dimension, in the spirit of looking at the closed coordinate as a small or "hidden" extra dimension. If one starts from…
In this work we present the quantum mechanical computer proposed by Feynman in 1985 and, since then, widely cited but seldom used. The main feature of the model is the presence of a built in clocking mechanism managing for the ordered…
Time-like and space-like invariant space-time intervals are used to analyse measurements of spatial and temporal distances defined by two spatially-separated clocks. The time dilatation effect is confirmed, but not `relativity of…
This note is the written version of conversations with young colleagues on unofficial history, general ideas, unexpected facts and open problems concerning tilting theory.
Quantum walks have emerged as an interesting approach to quantum information processing, exhibiting many unique properties compared to the analogous classical random walk. Here we introduce a model for a discrete-time quantum walk with…
For more than a century lattice random walks have been employed ubiquitously, both as a theoretical laboratory to develop intuition about more complex stochastic processes and as a tool to interpret a vast array of empirical observations.…
As R.Feynman has shown to F. Dyson -- who published it then in 1990 under the name of "Feynman's proof of Maxwell's equations" -- the only interactions compatible with the canonical uncertainty relation (for scalar particles on flat $\R^3$)…
Space-time in quantum mechanics is about bridging Hilbert and configuration space. Thereby, an entirely new perspective is obtained by replacing the Newtonian space-time theater with the image of a presumably high-dimensional Hilbert space,…
A new linear mapping of the linear vector space (LVS) of the octonions is suggested as an approach to the co-ordinatization of space-time. This approach resolves some perplexing issues concerning the validity of certain pre-metric notions…
An extended analysis is made of the Gell-Mann and Hartle axioms for a generalised `histories' approach to quantum theory. Emphasis is placed on finding equivalents of the lattice structure that is employed in standard quantum logic.…
We formulate the transition from decelerated to accelerated expansion as a bounce in connection space and study its quantum cosmology, knowing that reflections are notorious for bringing quantum effects to the fore. We use a formalism for…
The Lindblad equation is widely employed in studies of Markovian quantum open systems. Here, firstly, a simple result is presented on the time evolution of the non Neumann entropy under the Lindblad equation, which enables one to examine if…
Archives are an important source of study for various scholars. Digitization and the web have made archives more accessible and led to the development of several time-aware exploratory search systems. However these systems have been…
A novel approach is suggested for the statistical description of quantum systems of interacting particles. The key point of this approach is that a typical eigenstate in the energy representation (shape of eigenstates, SE) has a well…