Basic Degrees Of Freedom Research Articles

Bosonic near-CFT1 models from Fock-space fluxes

We construct a family of near-CFT1 models with a conserved U(1) charge, whose basic degrees of freedom are canonical bosons. The Sachdev-Ye-Kitaev (SYK) model — the first microscopic model that realizes the near-CFT1 dynamics — is based on random p-local interactions among fermions. However, a bosonic near-CFT1 model has remained elusive in the p-local approach because such constructions generally suffer from unwanted orderings at low temperatures. Our construction is based on a recent insight that near-CFT1 dynamics can quite generally arise if we place a large amount of random fluxes in a many-body Fock space and p-locality is not essential. All such models are essentially solved by chord diagrams regardless of the nature of the underlying degrees of freedom. We further argue that such bosonic models do not suffer from energetic instablities or unwanted low-temperature orderings. For comparison we also consider a second class of charge-conserving models which are based on qubits. The thermodynamic scalings of these models are very similar to those of the double-scaled complex SYK model but are free of certain singularities the latter suffers from. We also show the level statistics of both models are described by random matrix theory universality down to very low energies.

Confinement in 4D: An Attempt at Classical Understanding

In this review, we revisit our approach to constructing an effective theory for Abelian and Non-Abelian gauge theories in 4D. Our goal is to have an effective theory that provides a simple classical picture of the main qualitatively important features of these theories. We set out to ensure the presence of the massless photons—Goldstone bosons in Abelian theory and their disappearance in the Non-Abelian case—accompanied by the formation of confining strings between charged states. Our formulation avoids using vector fields and instead operates with the basic degrees of freedom that are the scalar fields of a nonlinear σ-model. The Mark 1 model we study turns out to have a large global symmetry group-the 2D diffeomorphism invariance in the Abelian limit, which is isomorphic to the group of all canonical transformations in the classical two dimensional phase space. This symmetry is not present in QED, and we eliminate it by “gauging” this infinite dimensional global group. Introducing additional modifications to the model (Mark 2), we are able to prove that the “Abelian” version is equivalent to the theory of a free photon. Achieving the desired property in the “Non-Abelian” regime turns out to be tricky. We are able to introduce a perturbation that leads to the formation of confining strings in our Mark 1 model. These strings have somewhat unusual properties, in that their profile does not decay exponentially away from the center of the string. In addition, the perturbation explicitly breaks the diffeomorphism invariance. Preserving this invariance in the gauged model as well as achieving confining strings in Mark 2 model remains an open question.

Programmable Stimuli-Responsive Actuators for Complex Motions in Soft Robotics: Concept, Design and Challenges

During the last years, great progress was made in material science in terms of concept, design and fabrication of new composite materials with conferred properties and desired functionalities. The scientific community paid particular interest to active soft materials, such as soft actuators, for their potential as transducers responding to various stimuli aiming to produce mechanical work. Inspired by this, materials engineers today are developing multidisciplinary approaches to produce new active matters, focusing on the kinematics allowed by the material itself more than on the possibilities offered by its design. Traditionally, more complex motions beyond pure elongation and bending are addressed by the robotics community. The present review targets encompassing and rationalizing a framework which will help a wider scientific audience to understand, sort and design future soft actuators and methods enabling complex motions. Special attention is devoted to recent progress in developing innovative stimulus-responsive materials and approaches for complex motion programming for soft robotics. In this context, a challenging overview of the new materials as well as their classification and comparison (performances and characteristics) are proposed. In addition, the great potential of soft transducers are outlined in terms of kinematic capabilities, illustrated by the related application. Guidelines are provided to design actuators and to integrate asymmetry enabling motions along any of the six basic degrees of freedom (translations and rotations), and strategies towards the programming of more complex motions are discussed. As a final note, a series of manufacturing methods are described and compared, from molding to 3D and 4D printing. The review ends with a Perspectives section, from material science and microrobotic points of view, on the soft materials’ future and close future challenges to be overcome.

On a geometric framework for Lagrangian supermechanics

We re-examine classical mechanics with both commuting and anticommuting degrees of freedom. We do this by defining the phase dynamics of a general Lagrangian system as an implicit differential equation in the spirit of Tulczyjew. Rather than parametrising our basic degrees of freedom by a specified Grassmann algebra, we use arbitrary supermanifolds by following the categorical approach to supermanifolds.

A continuity re-relaxed thin shell formulation for static and dynamic analyses of linear problems

This paper presents a curvature-constructed triangular element for static, free vibration and explicit dynamic analyses of shell structures by using a continuity re-relaxed technique. In the present method, the formulation is based on the classical thin shell theory, and only the translational displacements are treated as the filed variables that are assumed piecewisely linear. A set of three-node triangular background cells is adopted to discretize the problem domain. The curvature field in an element is constructed using the continuity re-relaxed technique, which can relax the continuity requirement of the trial function. The membrane strain filed is formulated same as the practice of standard FEM. Based on the principle of virtual work, the discertized system equations are finally formed. As the rotational displacements are not considered as the basic degrees of freedom, the essential boundary conditions of this part are imposed in the process of forming the curvature field. In order to validate the efficiency and accuracy of the present method, several numerical examples are studied. The results demonstrate that the present formulation can achieve very stable and accurate solutions with the less consuming of CPU time.

Partition Function in One, Two, and Three Spatial Dimensions from Effective Lagrangian Field Theory

The systematic effective Lagrangian method was first formulated in the context of the strong interaction; chiral perturbation theory (CHPT) is the effective theory of quantum chromodynamics (QCD). It was then pointed out that the method can be transferred to the nonrelativistic domain—in particular, to describe the low-energy properties of ferromagnets. Interestingly, whereas for Lorentz-invariant systems the effective Lagrangian method fails in one spatial dimension (ds=1), it perfectly works for nonrelativistic systems in ds=1. In the present brief review, we give an outline of the method and then focus on the partition function for ferromagnetic spin chains, ferromagnetic films, and ferromagnetic crystals up to three loops in the perturbative expansion—an accuracy never achieved by conventional condensed matter methods. We then compare ferromagnets in ds=1, 2, 3 with the behavior of QCD at low temperatures by considering the pressure and the order parameter. The two apparently very different systems (ferromagnets and QCD) are related from a universal point of view based on the spontaneously broken symmetry. In either case, the low-energy dynamics is described by an effective theory containing Goldstone bosons as basic degrees of freedom.

Compton Scattering on Light Nuclei

Compton scattering on light nuclei ($A=2,3$) has emerged as an effective avenue to search for signatures of neutron polarizabilities, both spin--independent and spin--dependent ones. In this discussion I will focus on the theoretical aspect of Compton scattering on light nuclei; giving first a brief overview and therafter concentrating on our Compton scattering calculations based on Chiral effective theory at energies of the order of pion mass. These elastic $\gamma$d and $\gamma$He-3 calculations include nucleons, pions as the basic degrees of freedom. I will also discuss $\gamma$d results where the $\Delta$-isobar has been included explicitly. Our results on unpolarized and polarization observables suggest that a combination of experiments and further theoretical efforts will provide an extraction of the neutron polarizabilities.

Polyakov loop in chiral quark models at finite temperature

We describe how the inclusion of the gluonic Polyakov loop incorporates large gauge invariance and drastically modifies finite temperature calculations in chiral quark models after color neutral states are singled out. This generates an effective theory of quarks and Polyakov loops as basic degrees of freedom. We find a strong suppression of finite temperature effects in hadronic observables triggered by approximate triality conservation (Polyakov cooling), so that while the center symmetry breaking is exponentially small with the constituent quark mass, chiral symmetry restoration is exponentially small with the pion mass. To illustrate the point we compute some low energy observables at finite temperature and show that the finite temperature corrections to the low energy coefficients are $N_c$ suppressed due to color average of the Polyakov loop. Our analysis also shows how the phenomenology of chiral quark models at finite temperature can be made compatible with the expectations of chiral perturbation theory. The implications for the simultaneous center symmetry breaking-chiral symmetry restoration phase transition are also discussed.

Mini-Workshop: Multiscale Modeling in Epitaxial Growth

Thin film epitaxy is a modern technology of growing single crystals that inherit atomic structures from substrates. Various mathematical models and numerical algorithms are proposed to be used for describing epitaxial growth processes. Due to the underlying multiscale phenomena, which range from the interaction of single atoms at steps up to an engineering scale, on which the transport of material to the surface in a MBE (molecular beam epitaxy) furnace needs to be described, the models can be distinguished by the relevant length scales they are living on (a) discrete atomic models: Individual atoms are the basic degrees of freedom and single hoppings to neighbouring lattice sites are simulated by kinetic Monte Carlo methods. A n example are the so-called Solid-on-Solid models. (b) discrete-continuous models: The atomic distance in the growth direction is discrete, but the atomic distance in the lateral direction is coarse grained. The steps are assumed to be smooth curves and serve as free boundaries for an adatom diffusion equation on terraces. These models are known as Burton-Cabrera-Frank models. (c) continuous models: The atomic processes at steps are neglected , the overall surface is assumed to be smooth and phenomenological equations describe directly the height of the growing film. An example is the Villain equation. The main goal in modelling epitaxial growth is to bridge the gap between these different models and to describe growth process on a continuous scale by incorporating atomic effects. The focus of this workshop was to bring together materials scientists, theoretical physicists and applied mathematicians to exchange ideas on the three different regimes (a),(b) and (c). The mini-workshop consisted of three introducing lectures, one for each approach and several lectures which focus on connections both in an analytical and numerical fashion. The contributions ranged from quantum-chemistry, molecular dynamics and kinetic Monte Carlo to step flow and continuum models. Several multiscale approaches have been considered to combine at least two of these models. Besides the mathematical aspects of modelling epitaxial growth also the connection to experimental results was dealt with in order to drive the recent theoretical developments into a direction which is relevant for a large variety of industrial applications. The mini-workshop was also used to give young researchers the opportunity to be introduced into such an actual interdisciplinary field.

Schematic model for QCD. III. Hadronic states

The hadronic spectrum obtained in the framework of a QCD-inspired schematic model, is presented. The model is the extension of a previous version, whose basic degrees of freedom are constituent quarks and antiquarks, and gluons. The interaction between quarks and gluons is a phenomenological interaction and its parameters are fixed from data. The classification of the states, in terms of quark and antiquark and gluon configurations is based on symmetry considerations, and it is independent of the chosen interaction. Following this procedure, nucleon and $\Delta$ resonances are identified, as well as various penta- and hepta-quarks states. The lowest pentaquarks state is predicted at 1.5 GeV and it has negative parity, while the lowest hepta-quarks state has positive parity and its energy is of the order of 2.5 GeV.

A thick–thin triangular plate element

AbstractA simple and efficient triangular finite element is introduced for plate bending applications. The element is a three‐node triangular one with three basic degrees of freedom per node and two internal rotation degrees of freedom, using selective reduced integration. Numerical examples indicate that, despite its simplicity, the element is not only competitively accurate, but also useful as a thick‐thin triangular plate bending element. It is also pointed out that this element using selective reduced integration is in fact a mixed element.

A simple and efficient triangular finite element for plate bending

A simple and efficient triangular finite element is introduced for plate bending application. The element is a three-node triangular one with three basic degrees of freedom per node and two internal rotation degrees of freedom, using selective reduced integration. Numerical examples indicate that, despite its simplicity, the element is not only competitively accurate, but also useful as a thick/thin triangular plate bending element. It is also pointed out that this element using selective reduced integration is in fact a mixed element.