Cavity Volume and Free Energy in Many-Body Systems

We present an inequality that gives a lower bound on the expectation value of certain two-body interaction potentials in a general state on Fock space in terms of the corresponding expectation value for thermal equilibrium states of non-interacting systems and the difference in the free energy. This bound can be viewed as a rigorous version of first-order perturbation theory for many-body systems at positive temperature. As an application, we give a proof of the first two terms in a high density (and high temperature) expansion of the free energy of jellium with Coulomb interactions, both in the fermionic and bosonic case. For bosons, our method works above the transition temperature (for the non-interacting gas) for Bose–Einstein condensation.

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Inequalities for the Free Energy of Certain Many-Body Systems

Physical Review Letters ◽

10.1103/physrevlett.22.587 ◽

1969 ◽

Vol 22 (12) ◽

pp. 587-590 ◽

Cited By ~ 3

Author(s):

Peter Kleban

Keyword(s):

Free Energy ◽

Many Body ◽

Many Body Systems

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Inequalities for the Energy and Free Energy of Many-Body Systems

Physical Review Letters ◽

10.1103/physrevlett.22.1413.2 ◽

1969 ◽

Vol 22 (25) ◽

pp. 1413-1413

Author(s):

Peter Kleban ◽

R. V. Lange

Keyword(s):

Free Energy ◽

Many Body ◽

Many Body Systems

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Variational structure of Luttinger–Ward formalism and bold diagrammatic expansion for Euclidean lattice field theory

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1720782115 ◽

2018 ◽

Vol 115 (10) ◽

pp. 2282-2286

Author(s):

Lin Lin ◽

Michael Lindsey

Keyword(s):

Field Theory ◽

Free Energy ◽

Infinite Order ◽

Many Body ◽

Lattice Field Theory ◽

Numerical Evidence ◽

Lattice Field ◽

Variational Structure ◽

Euclidean Lattice ◽

Many Body Systems

The Luttinger–Ward functional was proposed more than five decades ago and has been used to formally justify most practically used Green’s function methods for quantum many-body systems. Nonetheless, the very existence of the Luttinger–Ward functional has been challenged by recent theoretical and numerical evidence. We provide a rigorously justified Luttinger–Ward formalism, in the context of Euclidean lattice field theory. Using the Luttinger–Ward functional, the free energy can be variationally minimized with respect to Green’s functions in its domain. We then derive the widely used bold diagrammatic expansion rigorously, without relying on formal arguments such as partial resummation of bare diagrams to infinite order.

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REGULAR STRUCTURE OF LOW-LYING STATES FOR ATOMIC NUCLEI UNDER RANDOM INTERACTIONS

International Journal of Modern Physics E ◽

10.1142/s021830130801194x ◽

2008 ◽

Vol 17 (supp01) ◽

pp. 304-317

Author(s):

Y. M. ZHAO

Keyword(s):

Ground State ◽

Collective Motion ◽

Regular Structure ◽

Positive Parity ◽

Many Body ◽

Random Interactions ◽

Atomic Nuclei ◽

Many Body Systems

In this paper we review regularities of low-lying states for many-body systems, in particular, atomic nuclei, under random interactions. We shall discuss the famous problem of spin zero ground state dominance, positive parity dominance, collective motion, odd-even staggering, average energies, etc., in the presence of random interactions.

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