دانلود کتاب فیزیک نظری فشرده چهارم – آمار کوانتومی و ترمودینامیک

This book provides a textbook on quantum statistics and thermodynamics and is in particular suited for bachelor students in their last year of bachelor studies in theoretical physics. Prerequisites are a knowledge of classical Hamilton dynamics, quantum mechanics and its formulations in different representations. Elementary knowledge about electrodynamics is welcome in particular about elementary electric and magnetic dipoles and their interactions with external electromagnetic ields. Somewhat contrary to standard books about thermodynamics we will not start with the phenomenological thermodynamics, but directly from quantum dynamics with the deinition of the statistical operator in the many-particle Hilbert space. This opens up the possibility to deine the entropy as the statistical average of the negative logarithm of the statistical operator and to set up the framework for irreversible processes in macro-systems even if the basic equations of motion for elementary particles obey micro-reversibility. Statistical ensembles then are speciied by the postulate of maximum entropy and microcanonical, canonical, grand-canonical and general ensembles are deined, which depend on the knowledge about energy, particle number and volume. If some of these quantities are only known on average, then corresponding Lagrange parameters are introduced, that guarantee the average values, respectively. These Lagrange parameters will be related to temperature, chemical potential and pressure later on. Another important issue of quantum mechanics is the exchange symmetry of many-body states of identical particles, which has no counterpart in classical mechanics, i.e. the exchange symmetry with respect to particle exchange: the wave functions have to be symmetric or antisymmetric with respect to particle exchange, which leads to the separation of bosons and fermions with different quantization rules for the deinition of creation and annihilation operators. This splitting of the Hilbert space in bosons and fermions has important consequences e.g. for the speciic heat, the thermal expansion coeficient and the single-particle occupation numbers at low temperatures. Only in case of low densities and/or high temperatures these different quantities merge to the classical limit. Independently, the different ensembles go over to the classical distribution functions, if the particle number N becomes large, since the relative luctuations in energy and particle number scale as 1/√N. In line with the different ensembles thermodynamic potentials are deined as a function of the natural variables and their total differentials are speciied. This leads to a couple of Maxwell relations that can be employed to compute thermodynamic quantities. The three laws of thermodynamics are formulated and proven and it is shown that the classical ideal gas violates the 3rd law of thermodynamics at low temperatures. Isochoric, isobaric, isothermal and adiabatic changes of state are discussed and employed for the thermodynamics of the Carnot cycle and the Otto engine. Furthermore, small deviations from equilibrium are investigated and the connection between spontaneous luctuations of physical quantities around their average values in statistical equilibrium and forced deviations from the average values due to disturbances of the balance by external perturbations. It is shown that these two phenomena are closely linked for weak external perturbations and ind their expression in the luctuation-dissipation theorem. To this aim we will introduce the thermodynamic perturbation theory and compute response functions for various examples like the electric conductivity or the resistance noise.