The individual particle theory of many body systems was studied starting from a microscopic point of view. A technique which is equivalent to a generalized thermodynamics was used to show that, under the appropriate conditions of temperature and external field, the quasi-particle approach is correct for three very dissimilar systemsi the normal degenerate Fermi system, the metallic electron-phonon system, and the polaron. The fact that an approach like this works for such dissimilar systems emphasizes the underlying unity of the quasi-particle models. The concept that the real t~me non-equilibrium self-energy and the incoherent part of the density-density correlation function may be generated as functional derivatives of a generalized thermodynamic potential (~), together with local translational and rotational invariance and Galilean relativity, leads to a transformation from the microscopic particle density variables g«p,m,R,T) to those of the quasi-particle theory n (R,T). ~ - p- It was shown that, for zero temperature, such a ~ derivability is exact; at low temperature and for slowly varying fields, this ~ derivability is approximately true. This was shown by a procedure which is eqUivalent to an expansion in terms of the real scattering probability for quasiparticles. At low temperature and for slowly varying fields, such real scattering is very improbable and the expansion parameter is small. Perturbation theory was used only to determine the actual size of terms which, on physical grounds are necessarily small. As such, this approach is non-perturbative, depending only on properties of the exact selfenergies and correlation functions. In addition to demonstrating that the quasi-particle models are correct, information on the regions of validity for ~hese models is obtained. .As by-products of these derivations, microscopic expressions for the parameters of the quasi-particle theory and simple microscopic expressions for the currents in degenerate Fermi systems and the electron-phonon system are obtained.The individual particle theory of many body systems was studied starting from a microscopic point of view. A technique which is equivalent to a generalized thermodynamics was used to show that, under the appropriate conditions of temperature and external field, the quasi-particle approach is correct for three very dissimilar systemsi the normal degenerate Fermi system, the metallic electron-phonon system, and the polaron. The fact that an approach like this works for such dissimilar systems emphasizes the underlying unity of the quasi-particle models. The concept that the real t~me non-equilibrium self-energy and the incoherent part of the density-density correlation function may be generated as functional derivatives of a generalized thermodynamic potential (~), together with local translational and rotational invariance and Galilean relativity, leads to a transformation from the microscopic particle density variables g«p,m,R,T) to those of the quasi-particle theory n (R,T). ~ - p- It was shown that, for zero temperature, such a ~ derivability is exact; at low temperature and for slowly varying fields, this ~ derivability is approximately true. This was shown by a procedure which is eqUivalent to an expansion in terms of the real scattering probability for quasiparticles. At low temperature and for slowly varying fields, such real scattering is very improbable and the expansion parameter is small. Perturbation theory was used only to determine the actual size of terms which, on physical grounds are necessarily small. As such, this approach is non-perturbative, depending only on properties of the exact selfenergies and correlation functions. In addition to demonstrating that the quasi-particle models are correct, information on the regions of validity for ~hese models is obtained. .As by-products of these derivations, microscopic expressions for the parameters of the quasi-particle theory and simple microscopic expressions for the currents in degenerate Fermi systems and the electron-phonon system are obtained.

Jan 1, 19660 citations

Analytic properties of thermodynamic functions and phase transitions

Siegfried Großmann

Advances in Solid State PhysicsDec 21, 20079 citations

Elements of Statistical Mechanics

Sergei Vladimirovich Tyablikov

Springer eBooksJan 1, 19676 citations

Very Low-Temperature Fermi Gas

Franz Mohling

The momentum distribution in a low-temperature Fermi gas is investigated using the methods of quantum statistics developed by Lee and Yang together with the linked-pair expansions of the previous paper. It is shown that in order to determine the momentum distribution at very low temperatures two coupled integral equations must be considered, one in momentum variables and due to Lee and Yang, and the other in temperature variables. It is also shown that the dominant low-temperature behavior of the momentum distribution can be extracted in terms of a certain function ${\ensuremath{\nu}}^{\ensuremath{'}}(\mathrm{k})$. For a low-density Fermi gas with strong, short-range, two-body interactions, it is shown to third order in the scattering parameters of the interaction that at $T=0$ the function ${\ensuremath{\nu}}^{\ensuremath{'}}(\mathrm{k})$ is equal to the free particle momentum distribution. Also, the energy and other thermodynamic quantities are expressed in terms of ${\ensuremath{\nu}}^{\ensuremath{'}}(\mathrm{k})$, so that the theory permits a generalization of perturbation theoretic results to nonzero temperatures. The ground-state energy, momentum distribution, and thermodynamic potential are calculated to third order in the scattering parameters.The momentum distribution in a low-temperature Fermi gas is investigated using the methods of quantum statistics developed by Lee and Yang together with the linked-pair expansions of the previous paper. It is shown that in order to determine the momentum distribution at very low temperatures two coupled integral equations must be considered, one in momentum variables and due to Lee and Yang, and the other in temperature variables. It is also shown that the dominant low-temperature behavior of the momentum distribution can be extracted in terms of a certain function ${\ensuremath{\nu}}^{\ensuremath{'}}(\mathrm{k})$. For a low-density Fermi gas with strong, short-range, two-body interactions, it is shown to third order in the scattering parameters of the interaction that at $T=0$ the function ${\ensuremath{\nu}}^{\ensuremath{'}}(\mathrm{k})$ is equal to the free particle momentum distribution. Also, the energy and other thermodynamic quantities are expressed in terms of ${\ensuremath{\nu}}^{\ensuremath{'}}(\mathrm{k})$, so that the theory permits a generalization of perturbation theoretic results to nonzero temperatures. The ground-state energy, momentum distribution, and thermodynamic potential are calculated to third order in the scattering parameters.

Physical ReviewMay 15, 196135 citations

A Schrödinger-like equation for the Thermodynamics of a particle in a box

Adrian Faigon

The particle in an expanding/contracting 1-dimension box is revisited in action-angle like variables with direct thermodynamic interpretation. An angle dependent potential is proposed accurately describing the mechanical behavior while also capturing thermodynamic evolution -- entropy production -- within a canonical Hamiltonian framework. Heat transfer at constant volume is analyzed, and the derived thermal conductance matches the universal quantum of heat conductance $G_{Q}$ in the quantum limit. Having a Hamiltonian scheme interpretable in thermodynamic terms, a Schrödinger-like wave equation is formulated whose wavefunction solutions contain the information about the entropy evolution. The results show exact agreement with 'classical' results for non abrupt changes. Finally, comparisons with a pure quantum mechanical treatment of the wave function in an expanding box confirm consistency in quasi-static regimes and reveal adiabaticity breakdown under far-from-equilibrium conditions.The particle in an expanding/contracting 1-dimension box is revisited in action-angle like variables with direct thermodynamic interpretation. An angle dependent potential is proposed accurately describing the mechanical behavior while also capturing thermodynamic evolution -- entropy production -- within a canonical Hamiltonian framework. Heat transfer at constant volume is analyzed, and the derived thermal conductance matches the universal quantum of heat conductance $G_{Q}$ in the quantum limit. Having a Hamiltonian scheme interpretable in thermodynamic terms, a Schrödinger-like wave equation is formulated whose wavefunction solutions contain the information about the entropy evolution. The results show exact agreement with 'classical' results for non abrupt changes. Finally, comparisons with a pure quantum mechanical treatment of the wave function in an expanding box confirm consistency in quasi-static regimes and reveal adiabaticity breakdown under far-from-equilibrium conditions.

physics.class-phCross-listedarXiv:2603.28820Mar 31, 20260 citations

Statistical quasi-particles and the thermodynamics of hot dense matter

Ch.G. van Weert, M.C.J. Leermakers

Physica A Statistical Mechanics and its ApplicationsJul 1, 19857 citations

T=0

the function ${\ensuremath{\nu}}^{\ensuremath{'}}(\mathrm{k})$ is equal to the free particle momentum distribution. Also, the energy and other thermodynamic quantities are expressed in terms of ${\ensuremath{\nu}}^{\ensuremath{'}}(\mathrm{k})$, so that the theory permits a generalization of perturbation theoretic results to nonzero temperatures. The ground-state energy, momentum distribution, and thermodynamic potential are calculated to third order in the scattering parameters.

G_{Q}

in the quantum limit. Having a Hamiltonian scheme interpretable in thermodynamic terms, a Schrödinger-like wave equation is formulated whose wavefunction solutions contain the information about the entropy evolution. The results show exact agreement with 'classical' results for non abrupt changes. Finally, comparisons with a pure quantum mechanical treatment of the wave function in an expanding box confirm consistency in quasi-static regimes and reveal adiabaticity breakdown under far-from-equilibrium conditions.