Related papers: Detection of discrete spacetime by matter interfer…
This survey article reviews recent results on fermion system in discrete space-time and corresponding systems in Minkowski space. After a basic introduction to the discrete setting, we explain a mechanism of spontaneous symmetry breaking…
The Dirac equation can be modelled as a quantum walk, with the quantum walk being: discrete in time and space (i.e. a unitary evolution of the wave-function of a particle on a lattice); homogeneous (i.e. translation-invariant and…
For purposes of regularization as well as numerical simulation, the discretization of Lorentz invariant continuum field theories on a space-time lattice is often convenient. In general, this discretization destroys the rotational or…
It is shown that discrete-time quantum walks can be used to digitize, i.e., to time discretize fermionic models of continuous-time lattice gauge theory. The resulting discrete-time dynamics is thus not only manifestly unitary, but also…
In papers on primary state diffusion (Percival 1994, 1995), numerical estimates suggested that fluctuations in the space-time metric on the scale of the Planck time (10^-44s) could be detected using atom interferometers. In this paper we…
Lattice gauge theory's discretization of spacetime suffers from a drawback in that Lorentz covariance is lost because the axes of the lattice create preferred directions in spacetime. Smaller and smaller lattice spacings decrease the effect…
One of the most striking predictions of quantum electrodynamics is that vacuum fluctuations of the electromagnetic field can lead to spontaneous emission of atoms as well as photon-mediated interactions among them. Since these processes…
We propose a lattice model for Dirac fermions which allows us to break the degeneracy of the node structure. In the presence of a random gap we analyze the scaling behavior of the localization length as a function of the system width within…
Recent work has demonstrated that discrete quantum walks, when extended to quantum cellular automata (QCA), can, in the continuum limit, reproduce relativistic wave equations and quantum field theories (QFTs), including free quantum…
The hypothesis of a discrete fabric of the universe--the "Planck scale"--is always on stage, since it solves mathematical and conceptual problems in the infinitely small. However, it clashes with special relativity, which is designed for…
In this paper we propose a continuum variational model for a two-dimensional deformable lattice of atoms interacting with a two-dimensional rigid lattice. The two lattices have slightly different lattice parameters and there is a small…
A model in which pointlike defects are randomly embedded in Minkowski spacetime is considered. The distribution of spacetime defects is constructed to be Lorentz-invariant. It does not introduce a preferred reference frame, because it is…
Gauge invariance is one of the more important concepts in physics. We discuss this concept in connection with the unitary evolution of discrete-time quantum walks in one and two spatial dimensions, when they include the interaction with…
We introduce a lattice model for a static and isotropic system of relativistic fermions. An action principle is formulated, which describes a particle-particle interaction of all fermions. The model is designed specifically for a numerical…
Presented is a quantum lattice gas algorithm to efficiently model a system of Dirac particles interacting through an intermediary gauge field. The algorithm uses a fixed qubit array to represent both the spacetime and the particles…
We consider a tracer particle performing a random walk on a two-dimensional lattice in the presence of immobile hard obstacles. Starting from equilibrium, a constant force pulling on the particle is switched on, driving the system to a new…
Atom interferometers provide a powerful tool for measuring physical constants and testifying fundamental physics with unprecedented precision. Conventional atom interferometry focuses on the phase difference between two paths and utilizes…
New quantum degrees of freedom of space-time, originating at the Planck scale, could create a coherent indeterminacy and noise in the transverse position of massive bodies on macroscopic scales. An experiment is under development at…
The interest of part of the quantum-gravity community in the possibility of Planck-scale-deformed Lorentz symmetry is also fueled by the opportunities for testing the relevant scenarios with analyses, from a signal-propagation perspective,…
In one-dimensional random walks, the waiting time for each direction transitions is the same, even in the presence of bias, as a consequence of the microscopic-reversibility. We study the symmetry breaking of forward/ backward transition…