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Lectures on statistical mechanics

Presented here is a transcription of the lecture notes from Professor Allan N. Kaufman’s graduate statistical mechanics course Physics 212A and 212B at the University of California Berkeley from the 1972–1973 academic year. 212A addressed equilibrium statistical mechanics with topics: fundamentals (micro-canonical and sub-canonical ensembles, adiabatic law and action conservation, fluctuations, pressure, and virial theorem), classical fluids and other systems (equation of state, deviations from ideality, virial coefficients and van der Waals potential, canonical ensemble and partition function, quasistatic evolution, grand-canonical ensemble and partition function, chemical potential, simple model of a phase transition, quantum virial expansion, numerical simulation of equations of state, and phase transition), chemical equilibrium (systems with multiple species and chemical reactions, law of mass action, Saha equation, chemical equilibrium including ionization and excited states), and long-range interactions (including Coulomb, dipole, and gravitational interactions, Debye–Hückel theory, and shielding). 212B addressed nonequilibrium statistical mechanics with topics: fundamentals (definitions: realizations, moments, characteristic function, and discrete variables), Brownian motion (Langevin equation, fluctuation–dissipation theorem, spatial diffusion, Boltzmann’s H-theorem), Liouville and Klimontovich equations, Landau equation (derivation, elaboration, and H-theorem, and irreversibility), Markov processes and Fokker–Planck equation (derivations of the Fokker–Planck equation and a master equation), linear response and transport theory (linear Boltzmann equation, linear response theory of Kubo and Mori, relation of entropy production to electrical conductivity, transport relations and coefficients, normal mode solutions of the transport equations, sketch of a generalized Langevin equation method for transport theory), and an introduction to nonequilibrium quantum statistical mechanics.

plasma dynamics

GEOSH: Ideal Gas Chemical Equation of State

We present the framework and methodology for the new Los Alamos National Laboratory (LANL) G as chemical E quation O f S tate at H igher temperatures code (GEOSH) which aims to accurately model the behavior of chemically complex gaseous mixtures in equilibrium. Assuming the ideal gas approximation, GEOSH leverages the recursive nature of the Saha ionization and molecular equations in order to eliminate the molecular and ionic degrees of freedom, thereby reducing the problem size to the number of atomic species plus one for the free electrons if ions are included. This approach allows the chemical species, both molecular and ionic, of the mixture to be expressed in terms of the abundances of the elemental species. As a result, the GEOSH framework achieves a reduction in computational expense, increased processing speed, and the capability to efficiently model large-scale chemical networks. This report provides the necessary physical background and theoretical foundations for the GEOSH code, accompanied by benchmarking studies.

74 ATOMIC AND MOLECULAR PHYSICS

Pressure-Induced Exciton Formation and Superconductivity in Platinum-Based Mineral Sperrylite

We report a comprehensive study of Sperrylite (PtAs 2 ), the main platinum source in natural minerals, as a function of applied pressures up to 150 GPa. While no structural phase transition is detected from pressure-dependent X-ray measurements, the unit cell volume shrinks monotonically with pressure following the third-order Birch–Murnaghan equation of state. The mildly semiconducting behavior found in pure synthesized crystals at ambient pressures becomes more insulating upon increasing the applied pressure before metalizing at higher pressures, giving way to the appearance of an abrupt decrease in resistance near 3 K at pressures above 92 GPa consistent with the onset of a superconducing phase. The pressure evolution of the calculated electronic band structure reveals the same physical trend as our transport measurements, with a non-monotonic evolution explained by a hole band that is pushed below the Fermi energy and an electron band that approaches it as a function of pressure, both reaching a touching point suggestive of an excitonic state. A Lifshitz transition of the electronic structure and an increase in the density of states may naturally explain the onset of superconductivity in this material.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND

Benchmarking fast-neutron response of 7 Li-enriched C 7 LYC scintillators: Simulations and experiment

New insights into the fast neutron response of 7 Li-enriched C 7 LYC scintillators have been obtained through detailed Geant4 simulations of 35 Cl(n,p) and 35 Cl(n, α) reactions that are primarily responsible for the fast neutron response of C 7 LYC. The light output of a 1” x1” C 7 LYC detector was simulated using the Birks equation for light quenching in scintillators. The simulations were benchmarked against neutron scattering data from a 12 C target obtained with a white neutron beam at the Los Alamos LANSCE facility and fourteen 1”x1” C 7 LYC detectors. Incident neutron energies extracted from time-of-flight measurements, and appropriate recoil corrections for the different detector angles were used to map the response of C 7 LYC to mono-energetic neutrons. Resonances in the 35 Cl(n,p) reaction cross-section below 3 MeV incident neutron energy were directly observed in C 7 LYC. The experimental data and simulations are compared with ENDF databases, as well as recent direct cross-section measurements of neutrons scattered from a 35 Cl target. In conclusion, the results suggest a scrutiny of the 35 Cl(n,p) and 35 Cl(n, α) cross sections at low energy in the ENDF library.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS