Related papers: Occupation time for classical and quantum walks
This paper gives a constructive answer to the question whether photon states can contain or not, and to what extent, the readings of rulers and clocks. The paper first shows explicitly that, along with the momentum representation, there is…
We extend the theory of quantum time loops introduced by Greenberger and Svozil [1] from the scalar situation (where paths have just an associated complex amplitude) to the general situation where the time traveling system has…
A self-adjoint operator with dimensions of time is explicitly constructed, and it is shown that its complete and orthonormal set of eigenstates can be used to define consistently a probability distribution of the time of arrival at a…
When a physicist performs a quantic measurement, new information about the system at hand is gathered. This paper studies the logical properties of how this new information is combined with previous information. It presents Quantum Logic as…
In a fundamental formulation of the quantum mechanics of a closed system such as the universe as a whole, three forms of information are needed to make predictions for the probabilities of alternative time histories of the closed system .…
A random walk is known as a random process which describes a path including a succession of random steps in the mathematical space. It has increasingly been popular in various disciplines such as mathematics and computer science.…
This paper investigates the mathematical representation of time in physics. In existing theories time is represented by the real numbers, hence their formal properties represent properties of time: these are surveyed. The central question…
Contrary to the conviction expressed by J. Kijowski [Phys. Rev. A 59, 897 (1999)] and shared in some other papers, the reasons to look for the 'time operator' in the context of the standard quantum doctrine of orthogonal projectors and…
This is the extended version of a talk presented at the J.W.Goethe Universitaet Frankfurt a. M. and at the same time a preview at a forthcoming extensive publication on the same subject. It is shown that there is a common background…
We introduce a framework of structural approximation to represent Lorentz-invariant Minkowski space-time as the limit of finite cyclic lattices, each equipped with the action of a finite quasi-Lorentz group. This construction provides a…
In this essay, I argue that modern science is not the dichotomous pairing of theory and experiment that it is typically presented as, and I offer an alternative paradigm defined by its functions as a human endeavor. I also demonstrate how…
We draw a picture of physical systems that allows us to recognize what is this thing called "time" by requiring consistency not only with our notion of time but also with the way time enters the fundamental laws of Physics, independently of…
In previous work we discussed the quantization of paths in spacetime. Building on these ideas we have developed a mathematically coherent theory addressing a number of open questions concerning Loop Quantum Gravity. Our approach develops a…
Experience of time is one of the primordial human experiences which is deeply tied to human consciousness. But despite this intimate relation of time with human conscious experience, time has proved to be very elusive. Particularly in…
We introduce the driven discrete time quantum walk, where walkers are added during the walk instead of only at the beginning. This leads to interference in walker number and very different dynamics when compared to the original quantum…
This note illustrates how a simple random walk with possibly long jumps is related to fractional powers of the Laplace operator. The exposition is elementary and self-contained.
These notes are an elaboration on: (i) a short course that I gave at the IPhT-Saclay in May-June 2012; (ii) a previous letter on reversibility in quantum mechanics. They present an introductory, but hopefully coherent, view of the main…
It is currently widely accepted, as a result of Bell's theorem and related experiments, that quantum mechanics is inconsistent with local realism and there is the so called quantum non-locality. We show that such a claim can be justified…
Despite persistent efforts in revealing the temporal patterns in scientific careers, little attention has been paid to the spatial patterns of scientific activities in the knowledge space. Here, drawing on millions of papers in six…
A quantum walk on a toral phase space involving translations in position and its conjugate momentum is studied in the simple context of a coined walker in discrete time. The resultant walk, with a family of coins parametrized by an angle is…