Related papers: Occupation time for classical and quantum walks
We give a technique for calculating the occupation number of quantum fields in time-dependent backgrounds by using the relation between one-dimensional {\em quantum} oscillators and two-dimensional {\em classical} oscillators. We illustrate…
This contribution to the book in honour of J.S. Bell will probably differ from the remaining ones, in particular since only a part of it will be devoted to specific technical arguments. In fact I have considered appropriate to share with…
A new indicator, a real valued $s$-index, is suggested to characterize a quality and impact of the scientific research output. It is expected to be at least as useful as the notorious $h$-index, at the same time avoiding some its obvious…
Quantum information has suggested new forms of quantum logic, called quantum computational logics, where meanings of sentences are represented by pieces of quantum information (generally, density operators of some Hilbert spaces), which can…
A new family of 2D discrete-time quantum walks (DTQWs) is presented and shown to coincide, in the continuous limit, with the Dirac dynamics of a spin 1/2 fermion coupled to a constant and uniform magnetic field. Landau levels are…
The incompatibility between the treatment of time in the classical and in the quantum theory results in the so-called problem of time in canonical quantum gravity. For this reason, attempts have been made to devise algorithms of…
Studying the behaviour of a quantum field in a classical, curved, spacetime is an extraordinary task which nobody is able to take on at present time. Independently by the fact that such problem is not likely to be solved soon, still we…
In recent literature there appeared conflicting claims about whether the Ozsv\'ath-Robinson-R\'ozga family of type N electrovac spacetimes of the Kundt class with $\Lambda$ is complete. We show that indeed it is.
We report on joint work, past and in progress, with K.Fredenhagen and with J.E,Roberts, on the quantum structure of spacetime in the small which is dictated by the principles of Quantum Mechanics and of General Relativity; we comment on how…
The time of arrival at an arbitrary position in configuration space can be given as a function of the phase space variables for the Liouville integrable systems of classical mechanics, but only for them. We review the Jacobi-Lie…
This essay is based on a talk at Advances in Atomic, Molecular, and Optical Sciences 2020 (AAMOS20) in a symposium honoring Prof. S. T. Manson's decades-long contribution to photoabsorption studies. Quantum physics introduced into physics…
Quantum walk models have been used as an algorithmic tool for quantum computation and to describe various physical processes. This paper revisits the relationship between relativistic quantum mechanics and the quantum walks. We show the…
Enumeration of planar lattice walks is a classical topic in combinatorics, at the cross-roads of several domains (e.g., probability, statistical physics, computer science). The aim of this paper is to propose a new approach to obtain some…
This essay presents an accessible introduction to the basic motivations to seek a quantum theory of gravity. It focuses on one approach- loop quantum gravity - as an example of the rich philosophical issues that arise when we try to combine…
Discrete time quantum walks are known to be universal for quantum computation. This has been proven by showing that they can simulate a universal gate set. In this paper we examine computation in terms of language acceptance and present two…
In a purely relational theory there exists a tension between the relational character of the theory and the existence of quantities like distance and duration. We review this issue in the context of the Leibniz-Clarke correspondence. We…
This is an intrusion in the life and the mathematics of Norbert A'Campo, intended to be a tribute to him and an acknowledgement of his impact on those who know him and his work. The final version of this paper appears in the book ``Essays…
The continuous limit of one dimensional discrete-time quantum walks with time- and space-dependent coefficients is investigated. A given quantum walk does not generally admit a continuous limit but some families (1-jets) of quantum walks…
We review attempts by Pascual Jordan and other researchers, most notably Lawrence Biedenharn to generalize quantum mechanics by passing from associative matrix or operator algebras to non-associative algebras. We start with Jordan's work…
Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a…