Bold Feynman Diagrams and the Luttinger–Ward Formalism via Gibbs Measures: Perturbative Approach

2021 ◽  
Author(s):  
Lin Lin ◽  
Michael Lindsey
Keyword(s):  
Gibbs Measures ◽  
Feynman Diagrams ◽  
Perturbative Approach

SOME PERTURBATIVE RESULTS FOR TWO-DIMENSIONAL GRAVITY

1990 ◽  
Vol 05 (10) ◽  
pp. 763-770 ◽  
Author(s):  
KRZYSZTOF A. MEISSNER ◽  
JACEK PAWEŁCZYK
Keyword(s):  
Central Charge ◽  
Functional Integration ◽  
Feynman Diagrams ◽  
Two Dimensional ◽  
Moody Algebra ◽  
Perturbative Approach ◽  
Anomalous Dimensions ◽  
Dimensional Gravity ◽  
Wavefunction Renormalization

Perturbative approach to two-dimensional gravity and supergravity is considered. One-loop renormalization of the central charge of SL(2, R) Kac-Moody algebra is calculated perturbatively by functional integration and by explicit calculations of the Feynman diagrams. Also the wavefunction renormalization and the anomalous dimensions in the presence of gravity are calculated.

Translation-Invariant Gibbs Measures for the Blum-Kapel Model on a Cayley Tree

2016 ◽  
Vol 15 (2) ◽  
pp. 239-255 ◽  
Author(s):  
Nosir Khatamov ◽  
◽  
Rustam Khakimov ◽  
Keyword(s):  
Cayley Tree ◽  
Gibbs Measures ◽  
Translation Invariant

scholarly journals On Gibbs Measures and Spectra of Ruelle Transfer Operators

2017 ◽  
Vol 60 (2) ◽  
pp. 411-421
Author(s):  
Luchezar Stoyanov
Keyword(s):  
Spectral Radius ◽  
Spectral Properties ◽  
Gibbs Measures ◽  
Transfer Operator ◽  
Frobenius Theorem ◽  
Transfer Operators

AbstractWe prove a comprehensive version of the Ruelle–Perron–Frobenius Theorem with explicit estimates of the spectral radius of the Ruelle transfer operator and various other quantities related to spectral properties of this operator. The novelty here is that the Hölder constant of the function generating the operator appears only polynomially, not exponentially as in previously known estimates.

scholarly journals Cwebs beyond three loops in multiparton amplitudes

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Neelima Agarwal ◽  
Lorenzo Magnea ◽  
Sourav Pal ◽  
Anurag Tripathi
Keyword(s):  
Gauge Theories ◽  
Anomalous Dimension ◽  
Wilson Line ◽  
Building Blocks ◽  
Feynman Diagrams ◽  
Loop Order ◽  
Abelian Gauge ◽  
Sum Rule ◽  
Combinatorial Properties ◽  
Low Dimensional

Abstract Correlators of Wilson-line operators in non-abelian gauge theories are known to exponentiate, and their logarithms can be organised in terms of collections of Feynman diagrams called webs. In [1] we introduced the concept of Cweb, or correlator web, which is a set of skeleton diagrams built with connected gluon correlators, and we computed the mixing matrices for all Cwebs connecting four or five Wilson lines at four loops. Here we complete the evaluation of four-loop mixing matrices, presenting the results for all Cwebs connecting two and three Wilson lines. We observe that the conjuctured column sum rule is obeyed by all the mixing matrices that appear at four-loops. We also show how low-dimensional mixing matrices can be uniquely determined from their known combinatorial properties, and provide some all-order results for selected classes of mixing matrices. Our results complete the required colour building blocks for the calculation of the soft anomalous dimension matrix at four-loop order.

scholarly journals PHASE TRANSITIONS AND QUANTUM STABILIZATION IN QUANTUM ANHARMONIC CRYSTALS

2008 ◽  
Vol 20 (05) ◽  
pp. 529-595 ◽  
Author(s):  
ALINA KARGOL ◽  
YURI KONDRATIEV ◽  
YURI KOZITSKY
Keyword(s):  
Phase Transitions ◽  
Gibbs Measures ◽  
Quantum Effects ◽  
Gibbs States ◽  
Translation Invariance ◽  
Unified Theory ◽  
The Relationship ◽  
Anharmonic Crystals

A unified theory of phase transitions and quantum effects in quantum anharmonic crystals is presented. In its framework, the relationship between these two phenomena is analyzed. The theory is based on the representation of the model Gibbs states in terms of path measures (Euclidean Gibbs measures). It covers the case of crystals without translation invariance, as well as the case of asymmetric anharmonic potentials. The results obtained are compared with those known in the literature.

scholarly journals Effects of magnetic perturbations and radiation on the runaway avalanche

2021 ◽  
Vol 87 (2) ◽  
Author(s):  
P. Svensson ◽  
O. Embreus ◽  
S. L. Newton ◽  
K. Särkimäki ◽  
O. Vallhagen ◽  
...  
Keyword(s):  
Growth Rate ◽  
Runaway Electrons ◽  
Plasma Parameters ◽  
Perturbative Approach ◽  
Efficient Simulation ◽  
Strong Current ◽  
Magnetic Perturbations ◽  
Space Dynamics ◽  
Stochastic Magnetic Fields ◽  
Mitigation Methods

The electron runaway phenomenon in plasmas depends sensitively on the momentum- space dynamics. However, efficient simulation of the global evolution of systems involving runaway electrons typically requires a reduced fluid description. This is needed, for example, in the design of essential runaway mitigation methods for tokamaks. In this paper, we present a method to include the effect of momentum-dependent spatial transport in the runaway avalanche growth rate. We quantify the reduction of the growth rate in the presence of electron diffusion in stochastic magnetic fields and show that the spatial transport can raise the effective critical electric field. Using a perturbative approach, we derive a set of equations that allows treatment of the effect of spatial transport on runaway dynamics in the presence of radial variation in plasma parameters. This is then used to demonstrate the effect of spatial transport in current quench simulations for ITER-like plasmas with massive material injection. We find that in scenarios with sufficiently slow current quench, owing to moderate impurity and deuterium injection, the presence of magnetic perturbations reduces the final runaway current considerably. Perturbations localised at the edge are not effective in suppressing the runaways, unless the runaway generation is off-axis, in which case they may lead to formation of strong current sheets at the interface of the confined and perturbed regions.

scholarly journals A unified perturbative approach to electrocaloric effects

2021 ◽  
Vol 2 (1) ◽  
Author(s):  
Mónica Graf ◽  
Jorge Íñiguez
Keyword(s):  
External Field ◽  
Taylor Series ◽  
Physical Interpretation ◽  
Applied Field ◽  
Atomistic Simulations ◽  
Small Field ◽  
Electrocaloric Effect ◽  
Perturbative Approach ◽  
Similarities And Differences ◽  
Straightforward Interpretation

AbstractThe electrocaloric effect, that is, the temperature change experienced by an insulator upon application of an electric field, offers promising ecofriendly alternatives to refrigeration. However, the theoretical treatments of this response are mostly case specific and lack a unified picture revealing the similarities and differences among the various known effects. Here, we show that the electrocaloric effect lends itself to a straightforward interpretation when expressed as a Taylor series in the external field. Our formalism explains in a unified and simple way the most notable small-field effects reported in the literature, namely the so-called normal and inverse electrocaloric responses, corresponding to an increase or decrease of temperature under applied field, as usually found in ferroelectrics or antiferroelectrics, respectively. This helps us to clarify their physical interpretation. We then discuss in detail atomistic simulations for the prototype ferroelectric PbTiO3, explicitly evaluating subtle predictions of the theory, such as the occurrence of competing contributions to the electrocaloric response.

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