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DOE OSTI2025

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↗

DOE OSTI2024

Atomic binding corrections for high-energy fixed target experiments

High-energy beams incident on a fixed target may scatter against atomic electrons. To a first approximation, one can treat these electrons as free and at rest. For precision experiments, however, it is important to be able to estimate the size of, and when necessary calculate, subleading corrections. We discuss atomic binding corrections to relativistic lepton-electron scattering. We analyze hydrogen in detail, before generalizing our analysis to multi-electron atoms. Using the virial theorem, and many-body sum rules, we find that the corrections can be reduced to measured binding energies, and the expectation value of a single one-body operator. We comment on the phenomenological impact for neutrino flux normalization and an extraction of hadronic vacuum polarization from elastic muon electron scattering at MUonE.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2026

The Extended Baryonic Tully–Fisher Relation for SDSS MaNGA Galaxies

The baryonic Tully–Fisher relation (BTFR), a relationship between the rotational velocity and baryonic mass in spiral galaxies, probes the relative content of baryonic and total mass in galaxies and thus provides a good test of dark matter content in galaxies. Using Hα kinematics, we model the rotation curves of the Sloan Digital Sky Survey MaNGA DR17 spiral galaxies. To extend the BTFR to higher masses with elliptical galaxies, we estimate their total masses from their stellar velocity dispersions using the virial theorem and define the effective rotational velocity as the velocity a rotation-supported galaxy would exhibit given this mass. The baryonic mass of spiral galaxies is composed of stellar, H I , H 2 , and He mass, while only the stellar mass is used for the baryonic content of ellipticals. We construct joint BTFRs for 5743 MaNGA spiral and elliptical galaxies, TNG100 simulated galaxies with baryonic masses greater than 10 9 M ⊙ , and a cross-matched subsample between these two datasets (3149 spiral and 1423 elliptical galaxies). For the cross-matched subsample, we find agreement in the slopes between observed and simulated galaxies. We find a slope of $3.8{6}_{-0.62}^{+0.92}$ for the full MaNGA sample, which agrees well with the slope of 4.0 predicted by MOND and the fitted slope of $3.5{8}_{-0.38}^{+0.48}$ for the TNG100 galaxies. We find that a sample of lower-mass galaxies is necessary to differentiate between the two models.

79 ASTRONOMY AND ASTROPHYSICS↗