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B Hilbert Space Average under Microcanonical Conditions
We consider a space with the Cartesian coordinates {η AB ab ,ξ AB...
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6 Outline of the Present Approach
As already indicated we want to derive the properties of thermodynamic quantities from non-relativistic quantum mechanics, i.e., from starting with a...
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7 System and Environment
In a typical thermodynamic situation we consider a bipartite system with the larger part being called “environment” or “container”, c, whereas the...
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13 Pressure
Technically one could introduce pressure within classical statistical mechanics as an observable, i.e., as a function of the micro state. The...
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21 Summary and Conclusion
This book essentially had two intentions: to define what precisely thermodynamic behavior should be and to show that a certain class of bipartite...
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5 The Program for the Foundation of Thermodynamics
For a foundation of thermodynamics it is tempting to give an abstract but, nevertheless, intuitively appealing definition of entropy, such as:...
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A Hyperspheres
In the following we consider an n tot -dimensional Cartesian space with the coordinates {...
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3 Basics of Thermodynamics and Statistics
After having introduced some central concepts, results, and equations from quantum mechanics, we will now present the main definitions and laws of...
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Method of Invariant Grids
The method of invariant grids is developed for a grid-based computation of invariant manifolds.
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Mathematical Notation and Some Terminology
– The operator L from space W to space E: L : W → E
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Invariance Equation in Differential Form
Definition of invariance in terms of motions and trajectories assumes, at least, existence and uniqueness theorems for solutions of the original...
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Entropy, Quasiequilibrium, and Projectors Field
Projection operators Py contribute both to the invariance equation (3.2), and to the film extension of the dynamics (4.5). Limiting results, exact...
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Probing the Parity and Spin State
Classification into classes of superconductors with singlet and triplet pairing, respectively, needs information on the parity and spin state of the...
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Probing the Vortices: Lattice Symmetry and Internal Structure
A spatial variation of the superconducting properties occurs when a magnetic field is present perpendicular to the surface of a type-II...
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Cu-Mg-Si (Copper - Magnesium - Silicon)
This document is part of Subvolume A4 'Light Metal Systems. Part 4: Selected Systems from Al-Si-Ti to Ni-Si-Ti' of Volume 11 'Ternary Alloy Systems -...
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Basic Theoretical Concepts
Superconductivity is the phenomenon of dissipationless transport which occurs in many metals at su.ciently low temperatures. Metals in the...
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Optical Techniques for Local Measurement
Optical measurement techniques are well suited to many heat transfer problems, insofar as they are non-contact and generally non-invasive. Far-field...
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Molecular Dynamics
The aim in this Chapter is to show how molecular dynamics can be used to study conductive heat transfer in matter in terms of an atomic description...
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Introduction to Radiative Transfer
The aim of this Chapter is to introduce concepts and methods for modelling radiative transfer on short length scales. Electromagnetic radiation...