
Statistical Physics of Condensed Matter Systems
Description
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The macroscopic properties of gases, liquids or solids emerge as an average of the characteristics of their elementary constituents (either atoms or molecules). Accordingly, the statistical description of aggregates is based on the concept that macroscopic properties can be predicted by calculating the average value of any given physical observable which can be represented by microscopic (atomic or molecular) quantities.
The statistical approach aims at describing condensed matter at the most fundamental level (i.e. by taking explicit account of its atomic-scale structure), without however claiming to describe in detail all the degrees of freedom associated with its elementary constituents. This is an effective approach since it provides results of paradigmatic importance through a robust mathematical formalism; it is also an efficient means of predicting the emergent phenomena occurring in aggregates, providing their most fundamental explanation.
This Primer is divided into two parts, respectively focused on the statistical physics of classical and quantum systems. Each part contains a general chapter where basic concepts and related mathematics are developed leading to the Boltzmann, Fermi-Dirac, and Bose-Einstein distribution laws, which are the three cornerstones of statistical physics. Following this, distribution laws are applied to a thorough investigation of the thermal properties of paradigmatically important systems such as classical ideal gas, electron gas and phonon gas. Some specific phenomenologies are also discussed, the statistical foundations of which are treated in detail. These include, paramagnetism, blackbody radiation (photon gas), and the Bose-Einstein condensation.
This is a textbook for a standard introductory bachelor-level course in statistical physics and 2nd or 3rd year condensed matter and solid state courses.
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Luciano Colombo is a professor of theoretical condensed matter physics at the University of Cagliari and fellow of the Istituto Lombardo Accademia di Scienze e Lettere. He has been doing theoretical and computational research on materials physics for more than 30 years, publishing more than 250 scientific papers and leading several research projects.
Content
I Classical statistical physics
1 The statistical description of a classical system
2 Thermal properties of classical gases
II Quantum statistical physics
3 The statistical description of a quantum system
4 Thermal properties of quantum gases
5 Other quantum systems and phenomena
III Concluding remarks
6 What is missing in this "Primer"
IV Appendices
A Mathematical tools
B Gibbs entropy
C Thermodynamic potentials
D Calculating the grand partition function of a real gas
E Fermi-Dirac distribution law: a phenomenological derivation
F The conceptual framework for solid-state physics
G Bose-Einstein distribution law: a phenomenological derivation
H Density of states of the blackbody radiation
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