Interference, gravity and gauge fields

Chapter 3 focuses on the physics of quantized vortices in superfluid helium. We begin by introducing the unique properties of 4He, including its phase diagram, the superfluid transition (lambda transition), and the phenomenon of superfluidity. Following this, we will discuss the two-fluid model, a foundational and widely used phenomenological framework. Next, we delve into thermal counterflow, a crucial area that spurred the initial research on quantum turbulence, superfluid turbulence, and quantized vortices. We will then explore the dynamics of quantized vortices, often described by the Vortex Filament Model (VFM), which plays a central role in understanding quantum turbulence. The equations of motion and basic dynamics of vortices will be presented, and since the vortex motion is both nonlinear and nonlocal, numerical simulations are essential for accurately describing quantum turbulence. We will cover the computational methods used in these simulations, including both “two-way” and “one-way” approaches. In addition to quantum turbulence, we will examine the quantized vortex lattice under rotation, another key phenomenon in superfluidity. Early experiments on vortex lattice formation, the realization of rigid-body rotation, and simple examples of vortex dynamics under rotation will be introduced. Finally, we will discuss recent advancements in visualization experiments in superfluid helium, highlighting the results of visualizing quantized vortices, which have greatly enhanced our understanding of vortex dynamics.

Non-perturbative quasi-classical model in a gauge theory with the Yang-Mills (YM) field is developed. The self-consistent solutions of the Dirac equation in the SU(N) gauge field, which is in the eikonal approximation, and the Yang-Mills (YM) equations containing the external fermion current are solved. It shown that the developed model has the self-consistent solutions of the Dirac and Yang-Mills equations at N ≥ 3. In this way, the solutions take place provided that the fermion and gauge fields exist simultaneously, so that the fermion current completely compensates the current generated by the gauge field due to self-interaction of it.\n

Recent experiments have shown that micron-size particles can be trapped in quantized vortices in superfluid helium. We present results of a dynamically self-consistent calculation of the nonlinear interaction of a sphere and a vortex. We find that, depending on the regime, the sphere can be trapped in the vortex or break free from it. We also find that, if trapped, the sphere can travel along the vortex. We analyze the role played by the various forces acting on the sphere during the interaction.

When two vortices cross, each of them breaks into two parts and exchanges part of itself for part of the other. This process, called vortex reconnection, occurs in classical and superfluids, and in magnetized plasmas and superconductors. We present the first experimental observations of reconnection between quantized vortices in superfluid helium. We do so by imaging micrometer-sized solid hydrogen particles trapped on quantized vortex cores and by inferring the occurrence of reconnection from the motions of groups of recoiling particles. We show that the distance separating particles on the just-reconnected vortex lines grows as a power law in time. The average value of the scaling exponent is approximately 1/2, consistent with the self-similar evolution of the vortices.

A dramatic effect of quantized vortices in superfluid helium on the rate of coalescence of suspended impurities has been predicted; such a catalytic process should result in the formation of fiber-like structures having primarily nanothickness. That should be valid for any impurity and it may be used as a basis for a universal method of producing nanowires and nanotubes. Experiments on the imbedding of molecular hydrogen into liquid helium have supported these conclusions. They showed that: (i) in normal liquid He the coalescence led to the formation of spherical microparticles carried by turbulent motion of the liquid; (ii) in the superfluid only very long filaments were observed, which behaved as quantized vortices should do. These filaments are fiber-like hydrogen crystals and survive the transition of the liquid helium to the normal state. The promises for using this phenomenon in basic and applied sciences are outlined.

We show that, when graphene is only subject to strain, the spin connection gauge field that arises plays no measurable role, but when intrinsic curvature is present and strain is small, spin connection dictates most the physics. We do so by showing that the Weyl field associated with strain is a pure gauge field and no constraint on the $(2+1)$-dimensional spacetime appears. On the other hand, for constant intrinsic curvature that also gives a pure-gauge Weyl field, we find a classical manifestation of a quantum Weyl anomaly, descending from a constrained spacetime. We are in the position to do this because we find the equations that the conformal factor in $(2+1)$-dimensions has to satisfy, that is a nontrivial generalization to $(2+1)$-dimensions of the classic Liouville equation of differential geometry of surfaces. Finally, we comment on the peculiarities of the only gauge field that can describe strain, that is the well known {\it pseudogauge field} $A_1 \sim u_{11} - u_{22}$ and $A_2 \sim u_{12}$, and conclude by offering some scenarios of fundamental physics that this peculiar field could help to realize.

We review numerical studies of quantum turbulence. Quantum turbulence is currently one of the most important problems in low temperature physics and is actively studied for superfluid helium and atomic Bose--Einstein condensates. A key aspect of quantum turbulence is the dynamics of condensates and quantized vortices. The dynamics of quantized vortices in superfluid helium are described by the vortex filament model, while the dynamics of condensates are described by the Gross--Pitaevskii model. Both of these models are nonlinear, and the quantum turbulent states of interest are far from equilibrium. Hence, numerical studies have been indispensable for studying quantum turbulence. In fact, numerical studies have contributed in revealing the various problems of quantum turbulence. This article reviews the recent developments in numerical studies of quantum turbulence. We start with the motivation and the basics of quantum turbulence and invite readers to the frontier of this research. Though there are many important topics in the quantum turbulence of superfluid helium, this article focuses on inhomogeneous quantum turbulence in a channel, which has been motivated by recent visualization experiments. Atomic Bose--Einstein condensates are a modern issue in quantum turbulence, and this article reviews a variety of topics in the quantum turbulence of condensates e.g. two-dimensional quantum turbulence, weak wave turbulence, turbulence in a spinor condensate, $etc.$, some of which has not been addressed in superfluid helium and paves the novel way for quantum turbulence researches. Finally we discuss open problems.

It is shown that in an algebraically special space-time that admits a congruence of null strings, the Yang–Mills equations with sources reduce to a pair of nonlinear first-order differential equations for two matrices, provided that the gauge field is aligned with the congruence. In the case where the current is tangent to the null strings, the gauge field is determined by a matrix potential that has to satisfy a second-order differential equation with quadratic nonlinearities. As an example of this case, the Yang–Mills–Weyl equations are reduced, assuming that the multiplet of Weyl neutrino fields are also aligned with the congruence, and a reduced form of the Einstein–Yang–Mills–Weyl equations is also given.

We study theoretically and numerically the dynamics of quantized vortices in superfluid helium and rotating Bose-Einstein condensates. After reviewing briefly the recent motivation, we discuss these topics with the emphasis on the research done by our group. One of the modern important problems is how superfluid turbulence relates to classical turbulence. First, we show that superfluid turbulence consisting of a vortex tangle has an energy spectrum consistent with the Kolmogorov law. Second, we discuss the vortex states that appear in a rotating channel with counterflow. In the field of atomic-gas Bose-Einstein condensation, the dramatic observations of quantized vortices were made for rotating condensates. By solving numerically the Gross-Pitaevskii equation, we found a whole story of the vortex lattice formation consistent with the observations.

Minimum uncertainty states in angular momentum and angle variables for charged particles in structured electromagnetic fields

Aspects of the refined Gribov–Zwanziger action in linear covariant gauges

The model of dark matter is presented where the dark matter is a classical gauge field. A spherical symmetric solution of Yang-Mills equation is obtained. The asymptotic behavior of the gauge fields and matter density is investigated. It is shown that the distribution of the matter density allows us interpret it as the dark matter. The fitting of a typical rotational curve with the rotational curve created by the spherical solution of SU(3) Yang-Mills equation is made

Gauge field interactions in spaces with arbitrary torsion

Mathematical aspects of Kaluza–Klein gravity

Building a universal quantum computer is a central goal of emerging quantum technologies and it is expected to revolutionize science and technology. Unfortunately, this future does not seem very close, however, quantum computers built for a special purpose, i.e., quantum simulators, are currently being developed in many leading laboratories. Numerous schemes for quantum simulation have been proposed and realized using, e.g., ultracold atoms in optical lattices, ultracold trapped ions, atoms in arrays of cavities, atoms/ions in arrays of traps, quantum dots or superconducting circuits. The progress in experimental implementations is more than spectacular.Particularly interesting are those systems that simulate quantum matter evolving in artificial, or synthetic, Abelian or even non-Abelian gauge fields. Abelian gauge fields are analogues to the standard magnetic field and lead to fascinating effects such as the integer or fractional quantum Hall effects (IQHE, FQHE) and vortex lattices. Non-Abelian gauge fields couple the motional states of the particles to their internal degrees of freedom (such as hyperfine states for atoms or ions, electronic spins for electrons, etc). In this sense, external non-Abelian fields extend the concept of spin–orbit coupling, which is familiar from AMO and condensed matter physics. They lead to yet another variety of fascinating novel phenomena such as the quantum spin Hall effect (QSHE), 3D topological insulators, topological superconductors and superfluids of various kinds.Even more fascinating is the possibility of generating synthetic gauge fields that are dynamical, i.e., that evolve in time according to the corresponding lattice gauge theory (LGT). These dynamical gauge fields can also couple to matter fields, allowing the quantum simulation of such complex systems (notoriously hard to simulate using 'traditional' computers), which are particularly relevant for modern high-energy physics. So far there are only theoretical proposals for simulating Abelian LGTs, but many groups are working on extensions to the non-Abelian scenarios.The scope of this special issue of Journal of Physics B: Atomic, Molecular and Optical Physics is on all of these developments, with particular emphasis on the non-Abelian case. We invite the leading theory and experimental groups to contribute to this very special issue of the journal in order to provide a reference collection for quantum simulations of gauge fields.To summarize the key features should be Synthetic spin–orbit coupling and the physics of topological insulating phases Strongly correlated phases in non-Abelian gauge potentials Dynamical non-Abelian gauge fields and the simulation of lattice gauge theories Spin–orbit coupled BEC and vortex physics Simulators of Abelian LGTs Simulators of non-Abelian LGTsYou are invited to submit your article by 15 December 2012. Expected publication: Summer 2013.Corrections were made to this article on 7 November 2012. A change was made to the affiliations.