scholarly journals Entropic order parameters for the phases of QFT

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Horacio Casini ◽  
Marina Huerta ◽  
Javier M. Magán ◽  
Diego Pontello
Keyword(s):  
Operator Algebras ◽  
Conformal Symmetry ◽  
Quantization Condition ◽  
Order Parameters ◽  
Haag Duality ◽  
Order And Disorder ◽  
Generalized Symmetries ◽  
Dirac Quantization ◽  
Different Types ◽  
Area Law

Abstract We propose entropic order parameters that capture the physics of generalized symmetries and phases in QFT’s. We do it through an analysis of simple properties (additivity and Haag duality) of the net of operator algebras attached to space-time regions. We observe that different types of symmetries are associated with the breaking of these properties in regions of different non-trivial topologies. When such topologies are connected, we show that the non locally generated operators generate an Abelian symmetry group, and their commutation relations are fixed. The existence of order parameters with area law, like the Wilson loop for the confinement phase, or the ’t Hooft loop for the dual Higgs phase, is shown to imply the existence of more than one possible choice of algebras for the same underlying theory. A natural entropic order parameter arises by this non-uniqueness. We display aspects of the phases of theories with generalized symmetries in terms of these entropic order parameters. In particular, the connection between constant and area laws for dual order and disorder parameters is transparent in this approach, new constraints arising from conformal symmetry are revealed, and the algebraic origin of the Dirac quantization condition (and generalizations thereof) is described. A novel tool in this approach is the entropic certainty relation satisfied by dual relative entropies associated with complementary regions, which quantitatively relates the statistics of order and disorder parameters.

scholarly journals Ions, Protons, and Photons as Signatures of Monopoles

Universe ◽  
2018 ◽  
Vol 4 (11) ◽  
pp. 117 ◽  
Author(s):  
Vicente Vento
Keyword(s):  
Magnetic Charge ◽  
Magnetic Monopoles ◽  
Quantization Condition ◽  
Two Photon ◽  
Charge Quantization ◽  
Dirac Quantization ◽  
The Relationship ◽  
Charged Ions

Magnetic monopoles have been a subject of interest since Dirac established the relationship between the existence of monopoles and charge quantization. The Dirac quantization condition bestows the monopole with a huge magnetic charge. The aim of this study was to determine whether this huge magnetic charge allows monopoles to be detected by the scattering of charged ions and protons on matter where they might be bound. We also analyze if this charge favors monopolium (monopole–antimonopole) annihilation into many photons over two photon decays.

Order and disorder in the feldspars, I

1959 ◽  
Vol 32 (246) ◽  
pp. 226-241 ◽  
Author(s):  
Helen D. Megaw
Keyword(s):  
Experimental Observation ◽  
Small Cell ◽  
Order And Disorder ◽  
Different Types ◽  
Diffraction Effects ◽  
Stacking Disorder

SummaryFeldspar structures are classified into small-cell (c ≈ 7 Å.) and largecell (c ≈ 14 Å.) types, as a preliminary to a discussion of the nature of substitution disorder, position disorder, and stacking disorder, and of the relations between them. Diffraction effects characteristic of the different types of disorder are considered and related to experimental observation as far as possible.

OBSERVATIONS ON A U(1) × U(1) VECTOR THEORY

2002 ◽  
Vol 17 (16) ◽  
pp. 2211-2217
Author(s):  
D. G. C. MCKEON
Keyword(s):  
Vector Fields ◽  
Equations Of Motion ◽  
Quantization Condition ◽  
Constraint Condition ◽  
Supersymmetric Version ◽  
Dirac Quantization ◽  
Covariant Gauge ◽  
Vector Theory ◽  
Two Sectors ◽  
Conserved Currents

The symmetry between two sectors of a model containing two U(1) vector fields (related by a constraint condition) and two conserved currents is examined. The equations of motion for the vector fields, once the constraint condition is applied, is similar in form to the Maxwell equations in the presence of both electric and magnetic charge. The Dirac quantization condition need not be applied. The propagators for the vector fields are computed in a covariant gauge, demonstrating that the model is unitary and renormalizable. A supersymmetric version of the model is presented.

scholarly journals Ferroic Multipolar Order and Disorder in Cyanoelpasolite Molecular Perovskites

2018 ◽  
Author(s):  
Chloe Coates ◽  
Harry Gray ◽  
Johnathan Bulled ◽  
Hanna Boström ◽  
Arkadiy Simonov ◽  
...  
Keyword(s):  
Potts Model ◽  
Degrees Of Freedom ◽  
Variable Temperature ◽  
First Order ◽  
Order And Disorder ◽  
Simple Cubic ◽  
Different Types ◽  
Mechanical Models ◽  
Statistical Mechanical ◽  
First Order Transition

<div>We use a combination of variable-temperature high-resolution synchrotron X-ray powder diffraction measurements and Monte Carlo simulations to characterise the evolution of two different types of ferroic multipolar order in a series of cyano elpasolite molecular perovskites. We show that ferroquadrupolar order in [C3N2H5]2Rb[Co(CN)6] is a first-order process that is well described by a 4-state Potts model on the simple cubic lattice. Likewise, ferrooctupolar order in [NMe4]2B[Co(CN)6] (B = K, Rb, Cs) also emerges via a first-order transition that now corresponds to a 6-state Potts model. Hence, for these particular cases, the dominant symmetry breaking mechanisms are well understood in terms of simple statistical mechanical models. By varying composition, we find that the effective coupling between multipolar degrees of freedom—and hence the temperature at which ferromultipolar order emerges—can be tuned in a chemically sensible manner.</div><div><br></div>

scholarly journals High-throughput assessment of hypothetical zeolite materials for their synthesizeability and industrial deployability

2019 ◽  
Vol 234 (7-8) ◽  
pp. 437-450 ◽  
Author(s):  
Jose Luis Salcedo Perez ◽  
Maciej Haranczyk ◽  
Nils Edvin Richard Zimmermann
Keyword(s):  
Detailed Analysis ◽  
High Throughput ◽  
Lattice Energy ◽  
Order Parameters ◽  
Interatomic Distances ◽  
3 Dimensional ◽  
Framework Materials ◽  
Different Types ◽  
Future Direction ◽  
New Criteria

Abstract Zeolites are important microporous framework materials, where 200+ structures are known to exist and many millions so-called hypothetical materials can be computationally created. Here, we screen the “Deem” database of hypothetical zeolite structures to find experimentally feasible and industrially relevant materials. We use established and existing criteria and structure descriptors (lattice energy, local interatomic distances, TTT angles), and we develop new criteria which are based on 5-th neighbor distances to T-atoms, tetrahedral order parameters (or, tetrahedrality), and porosity and channel dimensionality. Our filter funnel for screening the most attractive zeolite materials that we construct consists of nine different types of criteria and a total of 53 subcriteria. The funnel reduces the pool of candidate materials from initially >300,000 to 70 and 33, respectively, depending on the channel dimensionality constraint applied (2- and 3-dimensional vs. only 3-dimensional channels). We find that it is critically important to define longer range and more stringent criteria such as the new 5-th neighbor distances to T-atoms and the tetrahedrality descriptor in order to succeed in reducing the huge pool of candidates to a manageable number. Apart from four experimentally achieved structures (BEC, BOG, ISV, SSF), all other candidates are hypothetical frameworks, thus, representing most valuable targets for synthesis and application. Detailed analysis of the screening data allowed us to also propose an exciting future direction how such screening studies as ours could be improved and how framework generating algorithms could be competitively optimized.

scholarly journals Dirac quantization condition for monopole in noncommutative space-time

2009 ◽  
Vol 79 (12) ◽  
Author(s):  
Masud Chaichian ◽  
Subir Ghosh ◽  
Miklos Långvik ◽  
Anca Tureanu
Keyword(s):  
Space Time ◽  
Quantization Condition ◽  
Noncommutative Space ◽  
Dirac Quantization

scholarly journals DUALITY IN EQUATIONS OF MOTION FROM SPACE–TIME DEPENDENT LAGRANGIANS

2000 ◽  
Vol 15 (14) ◽  
pp. 901-911 ◽  
Author(s):  
RAJSEKHAR BHATTACHARYYA ◽  
DEBASHIS GANGOPADHYAY
Keyword(s):  
Equations Of Motion ◽  
Space Time ◽  
Quantization Condition ◽  
Time Dependent ◽  
Classical Solutions ◽  
String Solution ◽  
Yang Mills ◽  
Dirac Quantization ◽  
Lagrangian Field Theory ◽  
Condition C

Starting from Lagrangian field theory and the variational principle, we show that duality in equations of motion can also be obtained by introducing explicit space–time dependence of the Lagrangian. Poincaré invariance is achieved precisely when the duality conditions are satisfied in a particular way. The same analysis and criteria are valid for both Abelian and non-Abelian dualities. We illustrate how (a) Dirac string solution, (b) Dirac quantization condition, (c) 't Hooft–Polyakov monopole solutions and (d) a procedure emerges for obtaining new classical solutions of Yang–Mills (YM) theory. Moreover, these results occur in a way that is strongly reminiscent of the holographic principle.

scholarly journals SUPERSYMMETRIC QUANTUM MECHANICAL GENERALIZED MIC–KEPLER SYSTEM

2008 ◽  
Vol 23 (12) ◽  
pp. 895-904 ◽  
Author(s):  
PULAK RANJAN GIRI
Keyword(s):  
Ground State ◽  
Quantization Condition ◽  
Quantum Mechanical ◽  
Dirac Quantization ◽  
Kepler System

We construct supersymmetric (SUSY) generalized MIC–Kepler system and show that the systems with half integral Dirac quantization condition [Formula: see text] belong to an SUSY family (hierarchy of Hamiltonian) with same spectrum between the respective partner Hamiltonians except for the ground state. Similarly, the systems with integral Dirac quantization condition μ=±1,±2,±3,… belong to another family. We show that, it is necessary to introduce additional potential to MIC–Kepler system in order to unify the two families into one. We also reproduce the results of the (supersymmetric) Hydrogenic problem in our study.

Order and disorder in NMC layered materials: a FAULTS simulation analysis

2017 ◽  
Vol 32 (S1) ◽  
pp. S213-S220 ◽  
Author(s):  
Marine Reynaud ◽  
Montse Casas-Cabanas
Keyword(s):  
Powder Diffraction ◽  
Simulation Analysis ◽  
Structural Information ◽  
Stacking Faults ◽  
Structural Models ◽  
Layered Materials ◽  
Neutron Powder Diffraction ◽  
X Ray ◽  
Order And Disorder ◽  
Different Types

The program FAULTS has been used to simulate the X-ray powder diffraction (XRD), neutron powder diffraction (NPD), and electron diffraction (ED) patterns of several structural models for LiNi1/3Mn1/3Co1/3O2, including different types of ordering of the transition metal (TM) cations in the TM slabs, different amounts of Li+/NiII+ cation mixing and different amounts of stacking faults. The results demonstrate the relevance of the structural information provided by NPD and ED data as compared with XRD to characterize the microstructure of NMC (LiNi1−y-zMnyCozO2) compounds.

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