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Statistical Physics and Thermodynamics Primer
Published in Thomas M. Nordlund, Peter M. Hoffmann, Quantitative Understanding of Biosystems, 2019
Thomas M. Nordlund, Peter M. Hoffmann
Particles are distinguished according to their intrinsic spin properties. If the particle total spin is half-integer, the particle is a fermion and the Pauli Exclusion Principle applies. If spin is zero or integral, the particle is a boson and the exclusion principle does not apply. The implications are that we should use Fermi–Dirac (F–D) statistics for fermions and Bose–Einstein (B–E) statistics for bosons, or maybe we ignore quantum mechanics and use Boltzmann statistics if we’re not in a physics course or research lab. Do we actually need to decide which quantum statistics applies to our biosystems? Rarely. Quantum statistics (e.g., the exclusion principle) applies when two identical particles effectively compete to occupy the same state. This is (virtually) never the case for an ideal gas at room temperature, a solution of protein molecules, or lipids in a cell membrane. The number of quantum states (e.g., location and speeds of all atoms, vibrational states, and random changes) available to a protein molecule in solution is so vast that two molecules will not attempt to occupy the same state in the age of the universe. During our lifetime, or during the time course of a measurement, we are safe using Boltzmann and ignoring F–D and B–E. You are always welcome to use either of those latter two statistical distributions and show that they reduce to the Boltzmann distribution when applied to an ideal gas or DNA solution.
Symmetry, Spin, and Statistics, 1926-1930
Published in John C.D. Brand, Lines of Light, 2017
Electron and nuclear spin leave distinctive signatures on spectra. Electron spin came first,1 so that, to a degree, the effects of nuclear spin could be treated by analogy, but the nucleus was a complex entity compared to an electron and raised new questions. A solution called for insights from quantum mechanics, molecular orbital theory, quantum statistics, group theory, and thermodynamics, all except the last being recent additions to the armory of physical theory. The consequences of electron and nuclear spin were worked out in principle in five years, between 1926 and 1930, though the task of unraveling the practical implications for optical spectra, or cataloging the spin of all nuclei, isotopes included, went on much longer.
Quantum Dynamics of Tribosystems
Published in Dmitry N. Lyubimov, Kirill N. Dolgopolov, L.S. Pinchuk, Quantum Effects in Tribology, 2017
Dmitry N. Lyubimov, Kirill N. Dolgopolov, L.S. Pinchuk
The fact that quasiparticles have a spin suggests that quasiparticles should obey the laws of quantum statistics, which divide them into two big classes bosons and fermions. Fermions are particles or quasiparticles that have spin 1/2, are described by asymmetric wave functions and obey the Pauli exclusion principle, according to which, in a quantum system there cannot be more than one fermion [31]. That is, between fermions there are distinctive forces of ‘quantum repulsion’ that do not allow Fermi particles to form compact structures. These forces determined the specifics of atomic shells structure, hence all chemical properties of substances in the nature.
Quantum inertial Alfvén solitary waves: the effect of exchange-correlation and spin magnetization
Published in Waves in Random and Complex Media, 2021
Marklund et al. have studied the characteristics of nonlinear magnetosonic waves in strongly magnetized quantum plasma with quantum Bohm potential and electron spin- effects. In the momentum equation, an additional negative pressure like term was added due to spin effects, as a result, the nonlinear waves become wider and have ?>shallower density depletions for a larger value of magnetization energy (i.e. Zeeman energy) They observed that the spin of the electrons collectively modifies the quantum dynamics of the MHD plasma [19]. Mushtaq and Vladimirov have studied the nonlinear magnetosonic along with shock waves in quantum plasmas including the quantum diffraction and spin effects [20]. They further studied arbitrary nonlinear magnetosonic waves in degenerate plasmas by considering the quantum statistics, diffraction and spin effects [21].
Formation of ultralong-range fermionic Rydberg molecules in 87Sr: role of quantum statistics
Published in Molecular Physics, 2019
J. D. Whalen, R. Ding, S. K. Kanungo, T. C. Killian, S. Yoshida, J. Burgdörfer, F. B. Dunning
87Sr atoms have a sizable nuclear spin, , resulting in a total angular momentum for the 5s 21S ground state, and a large number of magnetic sub-levels . However, only if two atoms are in the same (identical) internal state, i.e. the same magnetic sub-level, do they show Pauli exclusion effects, i.e. an exchange hole, at short ranges. Therefore, to clearly observe the effects of quantum statistics the Fermi gas must be spin polarised, i.e. must be transferred to the same magnetic sub-level (say, ).