Partition function of interacting calorons ensemble

Deldar, Sedigheh; Kiamari, Motahareh

doi:10.1063/1.4938712

Cited by 2 publications

(2 citation statements)

References 8 publications

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“…As long as the canonical partition function is known, the energy eigenvalue spectrum can be calculated using the method. Many methods for calculating the canonical partition function are developed [1][2][3][4][5][6][7], such as the cluster expansion [8][9][10][11][12]. Canonical partition functions are also calculated through the virial expansion [13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Energy spectrum of interacting gas: cluster expansion method

Li,

Chen

et al. 2022

Preprint

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In this paper, we calculate the energy spectrum of interacting gases by converting the cluster expansion method in statistical mechanics into a method of solving energy eigenvalues. We obtain an explicit expression of the energy eigenvalue, by which we can calculate the eigenvalue of an interacting gas from the interparticle potential directly. As an example, we calculate the energy spectrum for an interacting gas with soft-sphere potentials.

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Section: Introductionmentioning

confidence: 99%

Energy spectrum of interacting gas: cluster expansion method

Li,

Chen

et al. 2022

Preprint

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“…In statistical mechanics, many methods are developed for the calculation of partition functions. For example, the canonical partition function for quon statistics [24], general formulas for the canonical partition function of parastatistical systems [25], the canonical partition function of the freely jointed chain model [26], the partition function of the interacting calorons ensemble [27], the algorithm for computing the exact partition function of lattice polymer models [28], the exact partition function for the q-state Potts Model [29], the partition function for the antiferromagnetic Ising model and the hard-core models [30], and the canonical partition functions for different gaseous systems [31] are investigated.…”

Section: Introductionmentioning

confidence: 99%

Calculating eigenvalues of many-body systems from partition functions

Zhou¹,

Dai²

2018

J. Stat. Mech.

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A method for calculating the eigenvalue of a many-body system without solving the eigenfunction is suggested. In many cases, we only need the knowledge of eigenvalues rather than eigenfunctions, so we need a method solving only the eigenvalue, leaving alone the eigenfunction. In this paper, the method is established based on statistical mechanics. In statistical mechanics, calculating thermodynamic quantities needs only the knowledge of eigenvalues and then the information of eigenvalues is embodied in thermodynamic quantities. The method suggested in the present paper is indeed a method for extracting the eigenvalue from thermodynamic quantities. As applications, we calculate the eigenvalues for some many-body systems. Especially, the method is used to calculate the quantum exchange energies in quantum many-body systems. Using the method, we also calculate the influence of the topological effect on eigenvalues. Moreover, we improve the result of the relation between the counting function and the heat kernel in literature. * daiwusheng@tju.edu.cn.

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Partition function of interacting calorons ensemble

Cited by 2 publications

References 8 publications

Energy spectrum of interacting gas: cluster expansion method

Energy spectrum of interacting gas: cluster expansion method

Calculating eigenvalues of many-body systems from partition functions

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