Related papers: Lattice radial quantization by cubature
The engineering of specialty lasers with unconventional mode structures is one of the modern challenges in the development of integrated coherent sources. Examples include the use of bound states in the continuum, microlasers with orbital…
Aiming at the study of critical phenomena in the presence of boundaries with a non-trivial shape we discuss how lattices with an adaptive lattice spacing can be implemented. Since the parameters of the Hamiltonian transform non-trivially…
We give a lattice theory treatment of certain one and two dimensional quantum field theories. In one dimension we construct a combinatorial version of a non-trivial field theory on the circle which is of some independent interest in itself…
This paper is a survey of author's mathematical and logical study of the problem of quantization of fields.
We explore the mathematical consequences of the assumption of a discrete space-time. The fundamental laws of physics have to be translated into the language of discrete mathematics. We find integral transformations that leave the lattice of…
The physical properties induced by a quenched surface magnetic field in the Ising model are investigated by means of boundary quantum field theory in replica space. Exact boundary scattering amplitudes are proposed and used to study the…
The Berry curvature is a fundamental concept describing topological order of quantum systems. While it can be analytically tractable in non-interacting systems, numerical simulations are necessary in interacting systems. We present a…
The partition function of the 2d Ising model with random nearest neighbor coupling is expressed in the dual lattice made of square plaquettes. The dual model is solved in the the mean field and in different types of Bethe-Peierls…
We prepare arbitrary patterns of neutral atoms in a one-dimensional (1D) optical lattice with single-site precision using microwave radiation in a magnetic field gradient. We give a detailed account of the current limitations and propose…
In a way similar to the continuous case formally, we define in different but equivalent manners the difference discrete connection and curvature on discrete vector bundle over the regular lattice as base space. We deal with the difference…
We propose an ion trap configuration such that individual traps can be stacked together in a three dimensional simple cubic arrangement. The isolated trap as well as the extended array of ion traps are characterized for different locations…
These two lectures give a pedagogical introduction to the ``string-inspired'' worldline technique for perturbative calculations in quantum field theory. This includes an overview over the present range of its applications. Several examples…
We describe a new viewpoint on canonical quantization of linear fields on a general curved background that encompasses and generalizes the standard treatment of canonical QFT given in textbooks. Our method permits the construction of pure…
We introduce a lattice structure as a generalization of meet-continuous lattices and quantales. We develop a point-free approach to these new lattices and apply these results to $R$-modules. In particular, we give the module counterpart of…
There has been major progress in recent years in the development of improved discretizations of the QCD action, current operators, etc for use in numerical simulations that employ very coarse lattices. These lectures review the field…
Complex bases, along with direct-sums defined by rings of imaginary quadratic integers, induce algebraic lattices. In this work, we study such lattices and their reduction algorithms. Firstly, when the lattice is spanned over a two…
This is a series of lectures on Monte Carlo results on the non-perturbative, lattice formulation approach to quantum field theory. Emphasis is put on 4D scalar quantum field theory. I discuss real space renormalization group, fixed point…
Three-dimensional lattices are fundamental to solid-state physics. The description of a lattice with an atomic basis constitutes the necessary information to predict solid phase properties and evolution. Here, we present a new algorithm for…
We study the phase diagram of scalar field theory on a three dimensional Euclidean spacetime whose spatial component is a fuzzy sphere. The corresponding model is an ordinary one-dimensional matrix model deformed by terms involving fixed…
We propose an orbifold lattice formulation of QCD suitable for quantum simulations. We show explicitly how to encode gauge degrees of freedom into qubits using noncompact variables, and how to write down a simple truncated Hamiltonian in…