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12 Temperature
If it is hard to define entropy as a function of the micro state on the basis of classical mechanics, it is even harder to do so for the temperature....
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11 Typical Spectra of Large Systems
If a set of axioms is formulated as a basis of thermodynamics, one is usually told that entropy has to be an extensive quantity. This basically means...
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E Local Temperature Conditions for a Spin Chain
In this chapter we present the technical details of the application of the local temperature conditions (18.32) and (18.34) to a spin chain (18.38).
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4 Brief Review of Pertinent Concepts
In spite of the fact that phenomenological thermodynamics works very well, as outlined in the previous chapter, there have been many attempts to...
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19 Heat Conduction
In Chap. 17 we have considered the route of a system into its global equilibrium state due to the coupling to an environment - the way from a...
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Numerical Investigations of Scaling at the Anderson Transition
At low temperature T, a significant difference between the behavior of crystals on the one hand and disordered solids on the other is seen:...
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Frequency Dependent Electrical Transport in the Integer Quantum Hall Effect
It is well established to view the integer quantum Hall effect (QHE) as a sequence of quantum phase transitions associated with critical points that...
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Quantum Tunneling of an Acoustic Polaron in One-Dimensional Electron-Lattice System
More than two decades ago, Donovan and Wilson [1] found peculiar charge carriers with an anomalously high mobility in photo-conduction experiments on...
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Transfer Matrix Studies of Left-Handed Materials
Photonic band gap (PBG) materials are by definition composites, whose properties are not determined by the fundamental physical properties of their...
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Conductance Quasi-quantization of Quantum Point Contacts: Why Tight Binding Models Are Insufficient
Recent advances in miniaturization techniques have proliferated the theoretical and experimental interest in controlling transport through contacts...
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Introduction to Part I
These notes essentially reproduce lectures given at the International School for Advanced Studies (Trieste) and at the Scuola Normale Superiore...
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7 Examples
As mentioned before, the quantum mechanics of infinite systems is not under mathematical control as it is in the finite dimensional case. A...
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1 Quantum Mechanics. Algebraic Structure and States
We briefly review the basic structure of Quantum Mechanics (QM) with the aim of covering both the case of systems with a finite number of degrees of...
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15 Breaking of Continuous Symmetries. Goldstone’s Theorem
For a long time, the mechanism of spontaneous breaking of continuous symmetries has been recognized to be at the basis of many collective phenomena...
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4 General Properties of Solutions of Classical Field Equations
The first basic question is to identify the possible configurations of the systems (3.1), namely the set X of initial data for which the time...
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2 Fock Representation
The general lesson from the GNS theorem is that a state Ω on the algebra of observables, namely a set of expectations, defines a realization of the...
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8 Symmetry Breaking in Quantum Systems
Most of the wisdom on spontaneous symmetry breaking (SSB), especially for elementary particle theory, relies on approximations and/or a perturbative...
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3 Non-Fock Representations
As anticipated in the previous discussions, the Fock representation is very special to the finite dimensional case and to free fields. Actually, as a...
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16 * The Goldstone Theorem at Non-zero Temperature
The proof of the Goldstone theorem can be easily extended to the case of non-zero temperature T = 1/β, i.e. to representations defined by KMS states....
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Low-Temperature Conduction of a Quantum Dot
We review mechanisms of low-temperature electronic transport through a quantum dot weakly coupled to two conducting leads. Transport in this case is...