scholarly journals Sandpile Models in the Large

2021 ◽  
Vol 9 ◽  
Author(s):  
Philippe Ruelle
Keyword(s):  
Field Theory ◽  
Boundary Conditions ◽  
Spanning Tree ◽  
Large Scale ◽  
Two Dimensional ◽  
Critical Systems ◽  
Abelian Sandpile ◽  
Scale Properties ◽  
Sandpile Models ◽  
Theoretic Description

This contribution is a review of the deep and powerful connection between the large-scale properties of critical systems and their description in terms of a field theory. Although largely applicable to many other models, the details of this connection are illustrated in the class of two-dimensional Abelian sandpile models. Bulk and boundary height variables, spanning tree–related observables, boundary conditions, and dissipation are all discussed in this context and found to have a proper match in the field theoretic description.

scholarly journals CONTINUOUS ABELIAN SANDPILE MODEL IN TWO DIMENSIONAL LATTICE

2011 ◽  
Vol 25 (32) ◽  
pp. 4709-4720 ◽  
Author(s):  
N. AZIMI-TAFRESHI ◽  
E. LOTFI ◽  
S. MOGHIMI-ARAGHI
Keyword(s):  
Boundary Conditions ◽  
Small Mass ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
New Model ◽  
Different Boundary Conditions ◽  
Sandpile Model ◽  
Abelian Sandpile Model ◽  
General Properties ◽  
Abelian Sandpile

We investigate a new version of sandpile model which is very similar to Abelian Sandpile Model (ASM), but the height variables are continuous ones. With the toppling rule we define in our model, we show that the model can be mapped to ASM, so the general properties of the two models are identical. Yet the new model allows us to investigate some problems such as the effect of very small mass on the height probabilities, different boundary conditions, etc.

scholarly journals Casimir effect in Horava–Lifshitz-like theories

2015 ◽  
Vol 30 (36) ◽  
pp. 1550220 ◽  
Author(s):  
I. J. Morales Ulion ◽  
E. R. Bezerra de Mello ◽  
A. Yu. Petrov
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Boundary Conditions ◽  
Casimir Force ◽  
Casimir Effect ◽  
Lorentz Symmetry ◽  
Space Time ◽  
Two Dimensional ◽  
Parallel Plates ◽  
Scalar Field Theory

In this paper, we consider a Lorentz-breaking scalar field theory within the Horava–Lifshtz approach. We investigate the changes that a space–time anisotropy produces in the Casimir effect. A massless real quantum scalar field is considered in two distinct situations: between two parallel plates and inside a rectangular two-dimensional box. In both cases, we have adopted specific boundary conditions on the field at the boundary. As we shall see, the energy and the Casimir force strongly depends on the parameter associated with the breaking of Lorentz symmetry and also on the boundary conditions.

scholarly journals The superradiation phenomenon of R-N black holes can be unstable

2020 ◽  
Author(s):  
Wen-Xiang Chen
Keyword(s):  
Black Holes ◽  
Boundary Conditions ◽  
Large Scale ◽  
Astronomical Observation ◽  
Traditional Theory ◽  
Observation Data ◽  
Scale Properties ◽  
The Universe

According to the traditional theory, RN black holes are stable even under superradiation conditions. However, if a total mirror is placed near RN black holes, the black holes may become unstable.Both the theory of inflation and accurate astronomical observation data show that the large-scale properties of the universe are asymptotically uneven, which is the closest approximation to the theory of Sith spacetime.In my research, the boundary conditions of bosons are related to cosmological constants.The conclusion is that the superradiant aperture of RN black may be unstable.

Light front field theory: An advanced Primer

2007 ◽  
Vol 57 (3) ◽  
Author(s):  
L'ubomír Martinovič
Keyword(s):  
Field Theory ◽  
Detailed Comparison ◽  
Light Front ◽  
Two Dimensional ◽  
Schwinger Model ◽  
Initial Space ◽  
Model Hamiltonian ◽  
Spatial Volume ◽  
Hamiltonian Perturbation Theory ◽  
Light Front Quantization

Light front field theory: An advanced PrimerWe present an elementary introduction to quantum field theory formulated in terms of Dirac's light front variables. In addition to general principles and methods, a few more specific topics and approaches based on the author's work will be discussed. Most of the discussion deals with massive two-dimensional models formulated in a finite spatial volume starting with a detailed comparison between quantization of massive free fields in the usual field theory and the light front (LF) quantization. We discuss basic properties such as relativistic invariance and causality. After the LF treatment of the soluble Federbush model, a LF approach to spontaneous symmetry breaking is explained and a simple gauge theory - the massive Schwinger model in various gauges is studied. A LF version of bosonization and the massive Thirring model are also discussed. A special chapter is devoted to the method of discretized light cone quantization and its application to calculations of the properties of quantum solitons. The problem of LF zero modes is illustrated with the example of the two-dimensional Yukawa model. Hamiltonian perturbation theory in the LF formulation is derived and applied to a few simple processes to demonstrate its advantages. As a byproduct, it is shown that the LF theory cannot be obtained as a "light-like" limit of the usual field theory quantized on an initial space-like surface. A simple LF formulation of the Higgs mechanism is then given. Since our intention was to provide a treatment of the light front quantization accessible to postgradual students, an effort was made to discuss most of the topics pedagogically and a number of technical details and derivations are contained in the appendices.

Symbolic computation to estimate two-sided boundary conditions in two-dimensional conduction problems

10.2514/3.920 ◽  
1997 ◽  
Vol 11 ◽  
pp. 472-476
Author(s):  
Henry H. Kerr ◽  
F. C. Frank ◽  
Jae-Woo Lee ◽  
W. H. Mason ◽  
Ching-Yu Yang
Keyword(s):  
Boundary Conditions ◽  
Symbolic Computation ◽  
Two Dimensional

Effective Field Theory in Particle Physics and Cosmology

2020 ◽  
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Particle Physics ◽  
Large Scale ◽  
Effective Field ◽  
Effective Theory ◽  
Soft Collinear Effective Theory ◽  
Multiple Length Scales ◽  
Cosmological Observations ◽  
Standard Models

Effective field theory (EFT) is a general method for describing quantum systems with multiple-length scales in a tractable fashion. It allows us to perform precise calculations in established models (such as the standard models of particle physics and cosmology), as well as to concisely parametrize possible effects from physics beyond the standard models. EFTs have become key tools in the theoretical analysis of particle physics experiments and cosmological observations, despite being absent from many textbooks. This volume aims to provide a comprehensive introduction to many of the EFTs in use today, and covers topics that include large-scale structure, WIMPs, dark matter, heavy quark effective theory, flavour physics, soft-collinear effective theory, and more.

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