Levinson's theorems and the quantum-mechanical partition function for plasmas

In this paper, we study two generalized uncertainty principles (GUPs) including [Formula: see text] and [Formula: see text] which imply minimal measurable lengths. Using two momentum representations, for the former GUP, we find eigenvalues and eigenfunctions of the free particle and the harmonic oscillator in terms of generalized trigonometric functions. Also, for the latter GUP, we obtain quantum mechanical solutions of a particle in a box and harmonic oscillator. Finally we investigate the statistical properties of the harmonic oscillator including partition function, internal energy, and heat capacity in the context of the first GUP.

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$$ T\overline{T} $$ and $$ J\overline{T} $$ deformations in quantum mechanics

Journal of High Energy Physics ◽

10.1007/jhep11(2020)099 ◽

2020 ◽

Vol 2020 (11) ◽

Author(s):

Soumangsu Chakraborty ◽

Amiya Mishra

Keyword(s):

Quantum Mechanics ◽

Gauge Theory ◽

Partition Function ◽

Linear Combination ◽

Mechanical Systems ◽

General Linear ◽

Quantum Mechanical ◽

Partition Functions ◽

Flow Equations ◽

Quantum Mechanical Systems

Abstract In this paper, we continue the study of $$ T\overline{T} $$ T T ¯ deformation in d = 1 quantum mechanical systems and propose possible analogues of $$ J\overline{T} $$ J T ¯ deformation and deformation by a general linear combination of $$ T\overline{T} $$ T T ¯ and $$ J\overline{T} $$ J T ¯ in quantum mechanics. We construct flow equations for the partition functions of the deformed theory, the solutions to which yields the deformed partition functions as integral of the undeformed partition function weighted by some kernels. The kernel formula turns out to be very useful in studying the deformed two-point functions and analyzing the thermodynamics of the deformed theory. Finally, we show that a non-perturbative UV completion of the deformed theory is given by minimally coupling the undeformed theory to worldline gravity and U(1) gauge theory.

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Free-Bound Model of the Plasma in Equilibrium

Zeitschrift für Naturforschung A ◽

10.1515/zna-1966-1202 ◽

1966 ◽

Vol 21 (12) ◽

pp. 2012-2022 ◽

Cited By ~ 13

Author(s):

G. Ecker ◽

W. Kröll

Keyword(s):

Partition Function ◽

Thermodynamic Equilibrium ◽

Mechanical Treatment ◽

Quantum Mechanical ◽

Level Shift ◽

Partition Functions ◽

Quantum Mechanical Treatment ◽

Classical Approximation ◽

Free Particles ◽

Simple Models

The plasma in thermodynamic equilibrium has been extensively discussed under the assumption that all particles can be classified as “bound” or “classically free”. Under this assumption simple models led to divergencies of the partition functions of bound and free particles as well as to discrepancies of the predicted level shift. On the basis of a quantum-mechanical treatment we develop an “adapted free-bound approximation” for the eigenstates and a classical approximation for the partition function of the free particles. It is a decisive feature of the analysis that it takes freebound interaction into account. The results produce values for the free-bound limit and the limit of the series continuum. They also remove the divergence difficulties.

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