Search
Search Results
-
9 The Goldstone Theorem
The mechanism of SSB does not only provide a general strategy for unifying the description of apparently different systems, but it also provide...
-
Introduction to Part II
These notes arose from courses given at the International School for Advanced Studies (Trieste) and at the Scuola Normale Superiore (Pisa) in various...
-
6 Sectors with Energy-Momentum Density
We shall now discuss the requirement III of finite energy-momentum, briefly mentioned in the previous section. Clearly, the possibility of using...
-
Coupled Map Lattices: at the Age of Maturity
Coupled Map Lattices (CML) were simultaneously and independently introduced by K. Kaneko, R. Kapral and S. Kuznetsov in 1983–84 [1, 2, 3, 4, 5, 6]....
-
The Four–Dimensional Spacetime
Physics theories are made by building mathematical models that correspond to physical systems. General Relativity, the physical theory of...
-
13 Fermi and Bose Gas at Non-zero Temperature
As an example of symmmetry breaking at non-zero temperature we discuss the free Fermi and Bose gas, starting from finite volume and then discussing...
-
1 Symmetries of a Classical System
The realization of symmetries in physical systems has proven to be of help in the description of physical phenomena: it makes it possible to relate...
-
14 Quantum Fields at Non-zero Temperature
The general structure discussed above provides a neat and unique prescription for the quantization of relativistic fields at non-zero temperature...
-
8 Examples
The model describes the simplest non-linear field theory and it can be regarded as a prototype of field theories in one space dimension (s=1). The...
-
Momentum and Energy Relations
The equations of motion (5.12) for the charged insulating sphere of radius a moving with arbitrary center velocity u(t) can be rewritten in...
-
Desynchronization and Chaos in the Kuramoto Model
Abstract. The Kuramoto model of N globally coupled phase oscillators is an essentially non-linear dynamical system with a rich dynamical behavior and...
-
Spatially Extended Monotone Map**s
This chapter deals with the study of travelling waves in discrete time spatially extended systems with monotone dynamics. Such systems appear for...
-
Boundary Conditions
Most Numerical Relativity simulations are devised to approximate the time evolution of the dynamical fields starting from data given on an initial...
-
Dynamical Frustration in ANNNI Model and Annealing
Simulated annealing is usually applied to systems with frustration, like spin glasses and optimisation problems, where the energy landscape is...
-
Derivation of Force and Power Equations
The inconsistency between the power and force equations of motion, (2.4) and (2.1) or (2.5), is so surprising that one is tempted to question the...
-
Internal Binding Forces
In Appendix B, we have critically confirmed the evaluation of the self electromagnetic force and power, (3.1) and (3.2), leading to the force and...
-
The CML2004 Project
Coupled map lattices (CML) are basic models for the time evolution of nonlinear systems which, above all, are extended in space or involve many...
-
The Frenkel–Kontorova Model
In the preface to his monograph on the structure of Evolutionary Theory [1], the late professor Stephen Jay Gould attributes to the philosopher...
-
On Phase Transitions in Coupled Map Lattices
Coupled map lattices are a paradigm for studying fundamental questions in spatially extended dynamical systems. Within this tutorial we focus on...
-
Combinatorial Optimization and the Physics of Disordered Systems
The purpose of this chapter of this monograph is to confront the reader with a number of optimization algorithms that are exact and polynomial in...