Sign problems, noise, and chiral symmetry breaking in a QCD-like theory

The Nambu-Jona-Lasinio model reduced to 2+1 dimensions has two different path integral formulations: at finite chemical potential one formulation has a severe sign problem similar to that found in QCD, while the other does not. At large N, where N is the number of flavors, one can compute the probability distributions of fermion correlators analytically in both formulations. In the former case one finds a broad distribution with small mean; in the latter one finds a heavy tailed positive distribution amenable to the cumulant expansion techniques developed in earlier work. We speculate on the implications of this model for QCD.Comment: 16 pages, 5 figures; Published version with minor changes from the origina

Time-dependent Mechanics and Lagrangian submanifolds of Dirac manifolds

A description of time-dependent Mechanics in terms of Lagrangian submanifolds of Dirac manifolds (in particular, presymplectic and Poisson manifolds) is presented. Two new Tulczyjew triples are discussed. The first one is adapted to the restricted Hamiltonian formalism and the second one is adapted to the extended Hamiltonian formalism

A new basis for Hamiltonian SU(2) simulations

Due to rapidly improving quantum computing hardware, Hamiltonian simulations of relativistic lattice field theories have seen a resurgence of attention. This computational tool requires turning the formally infinite-dimensional Hilbert space of the full theory into a finite-dimensional one. For gauge theories, a widely-used basis for the Hilbert space relies on the representations induced by the underlying gauge group, with a truncation that keeps only a set of the lowest dimensional representations. This works well at large bare gauge coupling, but becomes less efficient at small coupling, which is required for the continuum limit of the lattice theory. In this work, we develop a new basis suitable for the simulation of an SU(2) lattice gauge theory in the maximal tree gauge. In particular, we show how to perform a Hamiltonian truncation so that the eigenvalues of both the magnetic and electric gauge-fixed Hamiltonian are mostly preserved, which allows for this basis to be used at all values of the coupling. Little prior knowledge is assumed, so this may also be used as an introduction to the subject of Hamiltonian formulations of lattice gauge theories.Comment: 27 pages, 11 figure

Overcoming exponential volume scaling in quantum simulations of lattice gauge theories

Real-time evolution of quantum field theories using classical computers requires resources that scale exponentially with the number of lattice sites. Because of a fundamentally different computational strategy, quantum computers can in principle be used to perform detailed studies of these dynamics from first principles. Before performing such calculations, it is important to ensure that the quantum algorithms used do not have a cost that scales exponentially with the volume. In these proceedings, we present an interesting test case: a formulation of a compact U(1) gauge theory in 2+1 dimensions free of gauge redundancies. A naive implementation onto a quantum circuit has a gate count that scales exponentially with the volume. We discuss how to break this exponential scaling by performing an operator redefinition that reduces the non-locality of the Hamiltonian. While we study only one theory as a test case, it is possible that the exponential gate scaling will persist for formulations of other gauge theories, including non-Abelian theories in higher dimensions.Comment: 11 pages, 2 figures, Proceedings of the 39th Annual International Symposium on Lattice Field Theory (Lattice 2022), August 8-13 2022, Bonn, German

The Tulczyjew triple for classical fields

The geometrical structure known as the Tulczyjew triple has proved to be very useful in describing mechanical systems, even those with singular Lagrangians or subject to constraints. Starting from basic concepts of variational calculus, we construct the Tulczyjew triple for first-order Field Theory. The important feature of our approach is that we do not postulate {\it ad hoc} the ingredients of the theory, but obtain them as unavoidable consequences of the variational calculus. This picture of Field Theory is covariant and complete, containing not only the Lagrangian formalism and Euler-Lagrange equations but also the phase space, the phase dynamics and the Hamiltonian formalism. Since the configuration space turns out to be an affine bundle, we have to use affine geometry, in particular the notion of the affine duality. In our formulation, the two maps $\alpha$ and $\beta$ which constitute the Tulczyjew triple are morphisms of double structures of affine-vector bundles. We discuss also the Legendre transformation, i.e. the transition between the Lagrangian and the Hamiltonian formulation of the first-order field theor

Neškodljivost kalupnih pjesaka sa bentonitom i svijetlećim nositeljima ugljika

Procedures have been developed to determine the volume, rate and composition (particularly BTEX: benzene, toluene, ethylbenzene and xylenes and PAHs (polycyclic aromatic hydrocarbons)) of gas evolution from moulds and cores prepared with various binders as a means of harmfulness of moulding sands. The rate of gas evolution from green sands with four different lustrous carbon carrier and BTEX content were determined. The gas evolution rates are highest in the range of about 20 to 30 s after contact with molten metal. In practice during the first 200-250 s the total emission of gases generated in investigated samples occurred. The main emitted component from the BTEX group was benzene.Postupci su razvijeni za određivanje volumena, brzine i sastava (posebice BTEX: benzen, toluen, etilbenzen, xilana) i PAH (policiklički automatski hidrokarbonati) plina koji nastaje iz kalupa i jezgri na različitim nosačima u težnji za neškodljivost kalupnih pijesaka. Brzine nastajanja plina iz pripravljenih pijesaka sa 4 različita svijetleća nositelja ugljika i sadržajem BTEX su određeni. Brzine nastajanja plina su najveće u razini 20 do 30 s poslije dodira sa rastopljenim metalom. Praktično, tijekom prvih 200-250 s ostvaruje se ukupna emisija stvorenih plinova u istraživanim uzorcima. Iz BTEX skupine, benzen je glavna emitirajuća komponenta

Artificial Intelligence for Energy Processes and Systems: Applications and Perspectives

In recent years, artificial intelligence has become increasingly popular and is more often used by scientists and entrepreneurs. The rapid development of electronics and computer science is conducive to developing this field of science. Man needs intelligent machines to create and discover new relationships in the world, so AI is beginning to reach various areas of science, such as medicine, economics, management, and the power industry. Artificial intelligence is one of the most exciting directions in the development of computer science, which absorbs a considerable amount of human enthusiasm and the latest achievements in computer technology. This article was dedicated to the practical use of artificial neural networks. The article discusses the development of neural networks in the years 1940–2022, presenting the most important publications from these years and discussing the latest achievements in the use of artificial intelligence. One of the chapters focuses on the use of artificial intelligence in energy processes and systems. The article also discusses the possible directions for the future development of neural networks

Hamiltonian dynamics and constrained variational calculus: continuous and discrete settings

The aim of this paper is to study the relationship between Hamiltonian dynamics and constrained variational calculus. We describe both using the notion of Lagrangian submanifolds of convenient symplectic manifolds and using the so-called Tulczyjew's triples. The results are also extended to the case of discrete dynamics and nonholonomic mechanics. Interesting applications to geometrical integration of Hamiltonian systems are obtained.Comment: 33 page

Classical field theories of first order and lagrangian submanifolds of premultisymplectic manifolds

A description of classical field theories of first order in terms of Lagrangian submanifolds of premultisymplectic manifolds is presented. For this purpose, a Tulczyjew's triple associated with a fibration is discussed. The triple is adapted to the extended Hamiltonian formalism. Using this triple, we prove that Euler-Lagrange and Hamilton-De Donder-Weyl equations are the local equations defining Lagrangian submanifolds of a premultisymplectic manifold.Comment: preprint, 27 page