Levinson-Theorem

Physik Online ◽  
2018 ◽  
Author(s):  
Hugo Reinhardt
Keyword(s):  
Levinson Theorem

scholarly journals Quark Cluster Expansion Model for Interpreting Finite-T Lattice QCD Thermodynamics

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 514
Author(s):  
David Blaschke ◽  
Kirill A. Devyatyarov ◽  
Olaf Kaczmarek
Keyword(s):  
Lattice Qcd ◽  
Cluster Expansion ◽  
Quark Gluon Plasma ◽  
Degrees Of Freedom ◽  
Gluon Plasma ◽  
Polyakov Loop ◽  
Unified Approach ◽  
Narrow Temperature Interval ◽  
Levinson Theorem ◽  
Expansion Model

In this work, we present a unified approach to the thermodynamics of hadron–quark–gluon matter at finite temperatures on the basis of a quark cluster expansion in the form of a generalized Beth–Uhlenbeck approach with a generic ansatz for the hadronic phase shifts that fulfills the Levinson theorem. The change in the composition of the system from a hadron resonance gas to a quark–gluon plasma takes place in the narrow temperature interval of 150–190 MeV, where the Mott dissociation of hadrons is triggered by the dropping quark mass as a result of the restoration of chiral symmetry. The deconfinement of quark and gluon degrees of freedom is regulated by the Polyakov loop variable that signals the breaking of the Z(3) center symmetry of the color SU(3) group of QCD. We suggest a Polyakov-loop quark–gluon plasma model with O(αs) virial correction and solve the stationarity condition of the thermodynamic potential (gap equation) for the Polyakov loop. The resulting pressure is in excellent agreement with lattice QCD simulations up to high temperatures.

scholarly journals SCATTERING THEORY FOR LATTICE OPERATORS IN DIMENSION d ≥ 3

2012 ◽  
Vol 24 (08) ◽  
pp. 1250020 ◽  
Author(s):  
JEAN BELLISSARD ◽  
HERMANN SCHULZ-BALDES
Keyword(s):  
Scattering Theory ◽  
Tight Binding ◽  
Gradient Flow ◽  
Index Theorem ◽  
Finite Range ◽  
Dilation Operator ◽  
Classical Energy ◽  
Energy Gradient ◽  
Embedded Eigenvalues ◽  
Levinson Theorem

This paper analyzes the scattering theory for periodic tight-binding Hamiltonians perturbed by a finite range impurity. The classical energy gradient flow is used to construct a conjugate (or dilation) operator to the unperturbed Hamiltonian. For dimension d ≥ 3, the wave operator is given by an explicit formula in terms of this dilation operator, the free resolvent and the perturbation. From this formula, the scattering and time delay operators can be read off. Using the index theorem approach, a Levinson theorem is proved which also holds in the presence of embedded eigenvalues and threshold singularities.

scholarly journals Globally Analytic Simplification and the Levinson Theorem

1994 ◽  
Vol 182 (1) ◽  
pp. 269-286 ◽  
Author(s):  
H. Gingold ◽  
P.F. Hsieh ◽  
Y. Sibuya
Keyword(s):  
Levinson Theorem

Levinson theorem for the Dirac equation inD+1dimensions

2003 ◽  
Vol 67 (6) ◽  
Author(s):  
Xiao-Yan Gu ◽  
Zhong-Qi Ma ◽  
Shi-Hai Dong
Keyword(s):  
Dirac Equation ◽  
Levinson Theorem

scholarly journals Relativistic Levinson theorem in two dimensions

1998 ◽  
Vol 58 (3) ◽  
pp. 2160-2167 ◽  
Author(s):  
Shi-Hai Dong ◽  
Xi-Wen Hou ◽  
Zhong-Qi Ma
Keyword(s):  
Two Dimensions ◽  
Levinson Theorem
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