scholarly journals Emergent chiral symmetry in a three-dimensional interacting Dirac liquid

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
András L. Szabó ◽  
Bitan Roy
Keyword(s):  
Fixed Points ◽  
Chiral Symmetry ◽  
Rotational Symmetry ◽  
Three Dimensional ◽  
Spatial Dimension ◽  
Dirac Fermions ◽  
Electronic Interactions ◽  
Emergent Phenomena ◽  
Ordered Phases ◽  
The Stability

Abstract We compute the effects of strong Hubbardlike local electronic interactions on three-dimensional four-component massless Dirac fermions, which in a noninteracting system possess a microscopic global U(1) ⊗ SU(2) chiral symmetry. A concrete lattice realization of such chiral Dirac excitations is presented, and the role of electron-electron interactions is studied by performing a field theoretic renormalization group (RG) analysis, controlled by a small parameter ϵ with ϵ = d−1, about the lower-critical one spatial dimension. Besides the noninteracting Gaussian fixed point, the system supports four quantum critical and four bicritical points at nonvanishing interaction couplings ∼ ϵ. Even though the chiral symmetry is absent in the interacting model, it gets restored (either partially or fully) at various RG fixed points as emergent phenomena. A representative cut of the global phase diagram displays a confluence of scalar and pseudoscalar excitonic and superconducting (such as the s-wave and p-wave) mass ordered phases, manifesting restoration of (a) chiral U(1) symmetry between two excitonic masses for repulsive interactions and (b) pseudospin SU(2) symmetry between scalar or pseudoscalar excitonic and superconducting masses for attractive interactions. Finally, we perturbatively study the effects of weak rotational symmetry breaking on the stability of various RG fixed points.

scholarly journals Unifying description of competing orders in two-dimensional quantum magnets

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
Xue-Yang Song ◽  
Chong Wang ◽  
Ashvin Vishwanath ◽  
Yin-Chen He
Keyword(s):  
Quantum Electrodynamics ◽  
Spatial Dimension ◽  
Magnetic Monopoles ◽  
Two Dimensions ◽  
Dirac Fermions ◽  
Two Dimensional ◽  
Quantum Magnets ◽  
Two Dimensional Materials ◽  
Ordered Phases ◽  
The Stability

Abstract Quantum magnets provide the simplest example of strongly interacting quantum matter, yet they continue to resist a comprehensive understanding above one spatial dimension. We explore a promising framework in two dimensions, the Dirac spin liquid (DSL) — quantum electrodynamics (QED3) with 4 Dirac fermions coupled to photons. Importantly, its excitations include magnetic monopoles that drive confinement. We address previously open key questions — the symmetry actions on monopoles on square, honeycomb, triangular and kagome lattices. The stability of the DSL is enhanced on triangular and kagome lattices compared to bipartite (square and honeycomb) lattices. We obtain the universal signatures of the DSL on triangular and kagome lattices, including those of monopole excitations, as a guide to numerics and experiments on existing materials. Even when unstable, the DSL helps unify and organize the plethora of ordered phases in correlated two-dimensional materials.

scholarly journals Asymptotically Safe Gravity-Fermion Systems on Curved Backgrounds

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 306
Author(s):  
Jesse Daas ◽  
Wouter Oosters ◽  
Frank Saueressig ◽  
Jian Wang
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Chiral Symmetry ◽  
Chiral Symmetry Breaking ◽  
Background Field ◽  
High Energy ◽  
Dirac Fermions ◽  
Dynamical Mechanism ◽  
Asymptotic Safety ◽  
Set Up

We set up a consistent background field formalism for studying the renormalization group (RG) flow of gravity coupled to Nf Dirac fermions on maximally symmetric backgrounds. Based on Wetterich’s equation, we perform a detailed study of the resulting fixed point structure in a projection including the Einstein–Hilbert action, the fermion anomalous dimension, and a specific coupling of the fermion bilinears to the spacetime curvature. The latter constitutes a mass-type term that breaks chiral symmetry explicitly. Our analysis identified two infinite families of interacting RG fixed points, which are viable candidates to provide a high-energy completion through the asymptotic safety mechanism. The fixed points exist for all values of Nf outside of a small window situated at low values Nf and become weakly coupled in the large Nf-limit. Symmetry-wise, they correspond to “quasi-chiral” and “non-chiral” fixed points. The former come with enhanced predictive power, fixing one of the couplings via the asymptotic safety condition. Moreover, the interplay of the fixed points allows for cross-overs from the non-chiral to the chiral fixed point, giving a dynamical mechanism for restoring the symmetry approximately at intermediate scales. Our discussion of chiral symmetry breaking effects provides strong indications that the topology of spacetime plays a crucial role when analyzing whether quantum gravity admits light chiral fermions.

scholarly journals Stability of the Discrete Stage–Structure Prey–Predator Model

2020 ◽  
Vol 55 (1) ◽  
Author(s):  
Rehab Noori Shalan ◽  
Shireen R. Jawad ◽  
Alaa Hussien Lafta
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Three Dimensional ◽  
Stage Structure ◽  
Prey Population ◽  
Topological Properties ◽  
Proposed Model ◽  
Predator Model ◽  
The Stability ◽  
Theoretical Results

This paper discusses the discrete stage–structure prey-predator model involved in the Beddington–DeAngelis type of functional response described by differential equation systems proposed as three-dimensional systems. Furthermore, the predators are divided into two types of populations, namely, mature and immature, along with the prey population. The stability of all possible fixed points is demonstrated by solving our proposed model analytically using the standard lemma and topological properties, which give all possible properties to each fixed point. In the same manner, we identify three fixed points, which are as follows: the origin fixed point, which means there are no species; the axial fixed point, which means the prey population increases logistically with the absence of a predator one (mature and immature populations); and the positive fixed point, which signifies the coexistence of all species. We show that the numerical simulations part is used not only to plot the time series of fixed values, but also, to find and illustrate the theoretical results.

scholarly journals Local Stability in 3D Discrete Dynamical Systems: Application to a Ricker Competition Model

2017 ◽  
Vol 2017 ◽  
pp. 1-16
Author(s):  
Rafael Luís ◽  
Elias Rodrigues
Keyword(s):  
Population Dynamics ◽  
Dynamical Systems ◽  
Fixed Points ◽  
Local Stability ◽  
Three Dimensional ◽  
Discrete Dynamical Systems ◽  
Competition Model ◽  
Centre Manifold ◽  
The Stability ◽  
Centre Manifold Theorem

A survey on the conditions of local stability of fixed points of three-dimensional discrete dynamical systems or difference equations is provided. In particular, the techniques for studying the stability of nonhyperbolic fixed points via the centre manifold theorem are presented. A nonlinear model in population dynamics is studied, namely, the Ricker competition model of three species. In addition, a conjecture about the global stability of the nontrivial fixed points of the Ricker competition model is presented.

A Liquid Metal Flow Between Two Coaxial Cylinders System

2019 ◽  
Vol 11 (1) ◽  
pp. 79-86
Author(s):  
Abdelkrim Merah ◽  
Ridha Kelaiaia ◽  
Faiza Mokhtari
Keyword(s):  
Couette Flow ◽  
Metal Flow ◽  
Three Dimensional ◽  
Liquid Sodium ◽  
Taylor Vortex ◽  
Turbulent Regime ◽  
Coaxial Cylinders ◽  
Concentric Cylinders ◽  
Ideal Tool ◽  
The Stability

Abstract The Taylor-Couette flow between two rotating coaxial cylinders remains an ideal tool for understanding the mechanism of the transition from laminar to turbulent regime in rotating flow for the scientific community. We present for different Taylor numbers a set of three-dimensional numerical investigations of the stability and transition from Couette flow to Taylor vortex regime of a viscous incompressible fluid (liquid sodium) between two concentric cylinders with the inner one rotating and the outer one at rest. We seek the onset of the first instability and we compare the obtained results for different velocity rates. We calculate the corresponding Taylor number in order to show its effect on flow patterns and pressure field.

Handheld Laser Scanner Research

2019 ◽  
Vol 952 (10) ◽  
pp. 47-54
Author(s):  
A.V. Komissarov ◽  
A.V. Remizov ◽  
M.M. Shlyakhova ◽  
K.K. Yambaev
Keyword(s):  
Point Cloud ◽  
Three Dimensional ◽  
Laser Scanner ◽  
Test Site ◽  
Optical Systems ◽  
Advantages And Disadvantages ◽  
Site Survey ◽  
Laser Scanners ◽  
Three Dimensional Models ◽  
The Stability

The authors consider hand-held laser scanners, as a new photogrammetric tool for obtaining three-dimensional models of objects. The principle of their work and the newest optical systems based on various sensors measuring the depth of space are described in detail. The method of simultaneous navigation and mapping (SLAM) used for combining single scans into point cloud is outlined. The formulated tasks and methods for performing studies of the DotProduct (USA) hand-held laser scanner DPI?8X based on a test site survey are presented. The accuracy requirements for determining the coordinates of polygon points are given. The essence of the performed experimental research of the DPI?8X scanner is described, including scanning of a test object at various scanner distances, shooting a test polygon from various scanner positions and building point cloud, repeatedly shooting the same area of the polygon to check the stability of the scanner. The data on the assessment of accuracy and analysis of research results are given. Fields of applying hand-held laser scanners, their advantages and disadvantages are identified.

scholarly journals Gum Tragacanth (GT): A Versatile Biocompatible Material beyond Borders

Molecules ◽  
2021 ◽  
Vol 26 (6) ◽  
pp. 1510 ◽  
Author(s):  
Mohammad Ehsan Taghavizadeh Yazdi ◽  
Simin Nazarnezhad ◽  
Seyed Hadi Mousavi ◽  
Mohammad Sadegh Amiri ◽  
Majid Darroudi ◽  
...  
Keyword(s):  
Tissue Engineering ◽  
Food Packaging ◽  
Three Dimensional ◽  
Great Promise ◽  
Anionic Polymer ◽  
Gum Tragacanth ◽  
New Horizons ◽  
Tissue Healing ◽  
The Stability ◽  
Therapeutic Substance

The use of naturally occurring materials in biomedicine has been increasingly attracting the researchers’ interest and, in this regard, gum tragacanth (GT) is recently showing great promise as a therapeutic substance in tissue engineering and regenerative medicine. As a polysaccharide, GT can be easily extracted from the stems and branches of various species of Astragalus. This anionic polymer is known to be a biodegradable, non-allergenic, non-toxic, and non-carcinogenic material. The stability against microbial, heat and acid degradation has made GT an attractive material not only in industrial settings (e.g., food packaging) but also in biomedical approaches (e.g., drug delivery). Over time, GT has been shown to be a useful reagent in the formation and stabilization of metal nanoparticles in the context of green chemistry. With the advent of tissue engineering, GT has also been utilized for the fabrication of three-dimensional (3D) scaffolds applied for both hard and soft tissue healing strategies. However, more research is needed for defining GT applicability in the future of biomedical engineering. On this object, the present review aims to provide a state-of-the-art overview of GT in biomedicine and tries to open new horizons in the field based on its inherent characteristics.

scholarly journals $$ \mathcal{N} $$ = 1 QED in 2 + 1 dimensions: dualities and enhanced symmetries

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Francesco Benini ◽  
Sergio Benvenuti
Keyword(s):  
Fixed Points ◽  
Three Dimensional ◽  
Global Symmetry ◽  
Mass Terms

Abstract We consider three-dimensional sQED with 2 flavors and minimal supersymmetry. We discuss various models which are dual to Gross-Neveu-Yukawa theories. The U(2) ultraviolet global symmetry is often enhanced in the infrared, for instance to O(4) or SU(3). This is analogous to the conjectured behaviour of non-supersymmetric QED with 2 flavors. A perturbative analysis of the Gross-Neveu-Yukawa models in the D = 4 − ε expansion shows that the U(2) preserving superpotential deformations of the sQED (mod- ulo tuning mass terms to zero) are irrelevant, therefore the fixed points with enhanced symmetry are stable. We also construct an example of $$ \mathcal{N} $$ N = 2 sQED with 4 flavors that exhibits enhanced SO(6) symmetry.

Stability and instability of some nonlinear dispersive solitary waves in higher dimension

1996 ◽  
Vol 126 (1) ◽  
pp. 89-112 ◽  
Author(s):  
Anne de Bouard
Keyword(s):  
Solitary Waves ◽  
Acoustic Waves ◽  
Vries Equation ◽  
Three Dimensional ◽  
Higher Dimension ◽  
Ion Acoustic Waves ◽  
Stability And Instability ◽  
Ion Acoustic ◽  
De Vries ◽  
The Stability

We study the stability of positive radially symmetric solitary waves for a three dimensional generalisation of the Korteweg de Vries equation, which describes nonlinear ion-acoustic waves in a magnetised plasma, and for a generalisation in dimension two of the Benjamin–Bona–Mahony equation.

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