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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...
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Spin-Based Quantum Dot Quantum Computing
This chapter is an overview of the research on spin-based quantum dot quantum computation, which covers two most prominent architectures, one based...
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Geometry of Irreversibility: The Film of Nonequilibrium States
A geometrical framework of nonequilibrium thermodynamics is developed in this chapter. The notion of macroscopically definable ensembles is...
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Film Extension of the Dynamics: Slowness as Stability
One of the difficulties in the problem of reducing the description is caused by the fact that there exists no commonly accepted formal definition of...
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Slow Invariant Manifolds for Open Systems
Suppose that the slow invariant manifold is found for a dissipative system. What have we constructed it for? First of all, for solving the Cauchy...
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Relaxation Methods
The “large step**” relaxation method for solution of the invariance equation is developed.
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Accuracy Estimation and Post-Processing in Invariant Manifolds Construction
The post-processing algorithms are developed for the accuracy control and enhancement of approximate invariant manifold.
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Method of Natural Projector
P. and T. Ehrenfest introdused in 1911 a model of dynamics with a coarse-graining of the original conservative system in order to introduce...
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Quasi-Chemical Representation
In Chap. 5 we have used the second law of thermodynamics, the existence of the entropy, in order to equip the problem of constructing the slow...
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3 Maximum-Likelihood Methodsin Quantum Mechanics
Maximum Likelihood estimation is a versatile tool covering wide range of applications, but its benefits are apparent particularly in the quantum...
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1 Introduction
Originally, thermodynamics was a purely phenomenological science. Early scientists (Galileo, Santorio, Celsius, Fahrenheit) tried to give definitions...
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17 The Route to Equilibrium
The method we are going to present here also relies, like the approach based on Fermi’s Golden Rule, on a step-wise solution of the Schrödinger...
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16 Theories of Relaxation Behavior
Almost everything stated so far has referred to situations of fully developed equilibrium. We have described means to predict the value that some...
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5 Physically Relevant Representations
From the examples and the discussion of the previous chapter, it appears that for infinite systems the choice of the representation for the algebra...
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10 Appendix
a) $ W(t) \; maps \; {\cal S} \times {\cal S} \; into \; {\cal S} \times {\cal...
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9 Examples
To illustrate the above general ideas we discuss simple concrete models exhibiting spontaneous symmetry breaking.
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2 Spontaneous Symmetry Breaking
One of the most powerful ideas of modern theoretical physics is the mechanism of spontaneous symmetry breaking. It is at the basis of most of the...
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3 Symmetries in Classical Field Theory
As the previous discussion indicates, it is impossible to realize the phenomenon of (spontaneous) breaking of a continuous symmetry in classical...
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10 Constructive Symmetry Breaking
Apart from simple models, like those discussed in the previous section, the existence of a symmetry breaking order parameter is a non-trivial problem...
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5 Stable Structures, Hilbert Sectors, Phases
The mathematical investigation of the existence of solutions for the non-linear (4.6) does not exhaust the problem of the physical interpretation of...