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Bosons in a trap: A rigorous derivation of the Gross-Pitaevskii energy functional
The ground-state properties of interacting Host gases in external potentials, as considered in recent exptriments, are usually described by means of the Gross-Pitaevskii energy functional. We present…
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The physics and mathematics of the second law of thermodynamics (Physics Reports 310 (1999) 1–96)☆
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The Mathematics of the Bose Gas and its Condensation
The Dilute Bose Gas in 3D.- The Dilute Bose Gas in 2D.- Generalized Poincare Inequalities.- Bose-Einstein Condensation and Superfluidity for Homogeneous Gases.- Gross-Pitaevskii Equation for Trapped…
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Ground State Energy of the Low Density Bose Gas
Now that the properties of low temperature Bose gases at low density, ρ, can be examined exprimentally it is appropriate to revisit some of the formulas deduced by many authors four to five decades…
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The entropy concept for non-equilibrium states
TLDR
The conclusion is that it is generally not possible to find a unique entropy that has all relevant physical properties, but it is shown that one can define two entropy functions, called S− and S+, which, taken together, delimit the range of adiabatic processes that can occur between non-equilibrium states.
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Asymptotics of heavy atoms in high magnetic fields: II. Semiclassical regions
The ground state energy of an atom of nuclear chargeZe in a magnetic fieldB is exactly evaluated to leading order asZ→∞ in the following three regions:B≪Z4/3,B≈Z4/3 andZ4/3≪B≪Z3. In each case this is…
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String-Localized Quantum Fields and Modular Localization
We study free, covariant, quantum (Bose) fields that are associated with irreducible representations of the Poincaré group and localized in semi-infinite strings extending to spacelike infinity.…
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Integral representations for Schwinger functionals and the moment problem over nuclear spaces
It is shown that a continuous positive linear functional on a commutative nuclear *-algebra has an integral decomposition into characters if and only if the functional is strongly positive, i.e.…
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A Fresh Look at Entropy and the Second Law of Thermodynamics
In days long gone, the second law of thermodynamics (which predated the first law) was regarded as perhaps the most perfect and unassailable law in physics. It was even supposed to have philosophical…
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A Rigorous Derivation¶of the Gross–Pitaevskii Energy Functional¶for a Two-dimensional Bose Gas
Abstract: We consider the ground state properties of an inhomogeneous two-dimensional Bose gas with a repulsive, short range pair interaction and an external confining potential. In the limit when…
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