Quantum simulation of lattice gauge theories in more than one space dimension—requirements, challenges and methods

Over recent years, the relatively young field of quantum simulation of lattice gauge theories, aiming at implementing simulators of gauge theories with quantum platforms, has gone through a rapid development process. Nowadays, it is not only of interest to the quantum information and technology communities. It is also seen as a valid tool for tackling hard, non-perturbative gauge theory problems by particle and nuclear physicists. Along the theoretical progress, nowadays more and more experiments implementing such simulators are being reported, manifesting beautiful results, but mostly on 1 + 1 dimensional physics. In this article, we review the essential ingredients and requirements of lattice gauge theories in more dimensions and discuss their meanings, the challenges they pose and how they could be dealt with, potentially aiming at the next steps of this field towards simulating challenging physical problems in analogue, or analogue-digital ways. This article is part of the theme issue ‘Quantum technologies in particle physics’.

Universality of excited three-body bound states in one dimension

We study a heavy-heavy-light three-body system confined to one space dimension in the regime where an excited state in the heavy-light subsystems becomes weakly bound. The associated two-body system is characterized by (i) the structure of the weakly-bound excited heavy-light state and (ii) the presence of deeply-bound heavy-light states. The consequences of these aspects for the behavior of the three-body system are analyzed. We find a strong indication for universal behavior of both three-body binding energies and wave functions for different weakly-bound excited states in the heavy-light subsystems.

Deiktiskās, prospektīvās un retrospektīvās frāzes zinātnes valodā

The article focuses on the dimensions of space and time in the Latvian language of science. The space dimension is expressed by the deictic constructions of place (demonstrative pronouns and adverbs), and the time dimension is expressed by prospective and retrospective constructions (adverbs and adjectives). The research material consists of the texts of scientific articles included in the project “The Latvian Language of Science in the Intralingual Aspect”. The aim of the present study is to explore research articles written in Latvian and to single out the most frequently used wording expressing the mentioned dimensions. In the present research, content analysis has been carried out to establish the knowledge gap present in the given field. It was found out that very few publications so far exist pertaining to space and time deixis in the Latvian language. The respective wording in the research material has been singled out with the help of AntConc; therefore, the present study is a study in Latvian Linguistics, with the elements of Corpus Linguistics. The content analysis and the study revealed that the deictic space and prospective and retrospective time constructions are present throughout the articles written in the Latvian language of science, i.e. in the introductory parts, in the main bodies, and the conclusions of the mentioned texts and serve the function of creating the joint psychological space of the author and the audience. They facilitate the process of communication between the author and the reader of the given texts.

Deterministic and stochastic models of infection spread and testing in an isolated contingent

The mathematical SIR model generalisation for description of the infectious process dynamics development by adding a testing model is considered. The proposed procedure requires the expansion of states’ space dimension due to variables that cannot be measured directly, but allow you to more adequately describe the processes that occur in real situations. Further generalisation of the SIR model is considered by taking into account randomness in state estimates, forecasting, which is achieved by applying the stochastic differential equations methods associated with the application of the Fokker – Planck – Kolmogorov equations for posterior probabilities. As COVID-19 practice has shown, the widespread use of modern means of identification, diagnosis and monitoring does not guarantee the receipt of adequate information about the individual’s condition in the population. When modelling real epidemic processes in the initial stages, it is advisable to use heuristic modelling methods, and then refine the model using mathematical modelling methods using stochastic, uncertain-fuzzy methods that allow you to take into account the fact that flow, decision-making and control occurs in systems with incomplete information. To develop more realistic models, spatial kinetics must be taken into account, which, in turn, requires the use of systems models with distributed parameters (for example, models of continua mechanics). Obviously, realistic models of epidemics and their control should include models of economic, sociodynamics. The problems of forecasting epidemics and their development will be no less difficult than the problems of climate change forecasting, weather forecast and earthquake prediction.

An evaluation of the data space dimension in phase retrieval: results in Fresnel zone

<div>In this paper, we address the problem of computing the dimension of data space in phase retrieval problem. Starting from the quadratic formulation of the phase retrieval, the analysis is performed in two steps. First, we exploit the lifting technique to obtain a linear representation of the data. Later, we evaluate the dimension of data space by computing analytically the number of relevant singular values of the linear operator that represents the data. The study is done with reference to a 2D scalar geometry consisting of an electric current strip whose square amplitude of the electric radiated field is observed on a two-dimensional extended domain in Fresnel zone.</div>

A Generalized Finite Volume Method for Density Driven Flows in Porous Media

In this article, we consider a time evolution equation for solute transport, coupled with a pressure equation in space dimension 2. For the numerical discretization, we combine the generalized finite volume method SUSHI on adaptive meshes with a time semi-implicit scheme. In the first part of this article, we present numerical simulations for two problems: a rotating interface between fresh and salt water and a well-known test case proposed by Henry. In the second part, we also introduce heat transfer and perform simulations for a system from the documentation of the software SEAWAT.