scholarly journals Thermodynamic limit of correlation functions in a system of gravitating fermions

1976 ◽  
Vol 48 (3) ◽  
pp. 207-213 ◽  
Author(s):  
Bernhard Baumgartner
Keyword(s):  
Thermodynamic Limit ◽  
Correlation Functions

scholarly journals Correlation functions by separation of variables: the XXX spin chain

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Giuliano Niccoli ◽  
Hao Pei ◽  
Véronique Terras
Keyword(s):  
Integral Representation ◽  
Boundary Conditions ◽  
Thermodynamic Limit ◽  
Correlation Functions ◽  
Periodic Boundary ◽  
Separation Of Variables ◽  
Periodic Boundary Conditions ◽  
Multiple Integral ◽  
Periodic Case ◽  
Zero Temperature

We explain how to compute correlation functions at zero temperature within the framework of the quantum version of the Separation of Variables (SoV) in the case of a simple model: the XXX Heisenberg chain of spin 1/2 with twisted (quasi-periodic) boundary conditions. We first detail all steps of our method in the case of anti-periodic boundary conditions. The model can be solved in the SoV framework by introducing inhomogeneity parameters. The action of local operators on the eigenstates are then naturally expressed in terms of multiple sums over these inhomogeneity parameters. We explain how to transform these sums over inhomogeneity parameters into multiple contour integrals. Evaluating these multiple integrals by the residues of the poles outside the integration contours, we rewrite this action as a sum involving the roots of the Baxter polynomial plus a contribution of the poles at infinity. We show that the contribution of the poles at infinity vanishes in the thermodynamic limit, and that we recover in this limit for the zero-temperature correlation functions the multiple integral representation that had been previously obtained through the study of the periodic case by Bethe Ansatz or through the study of the infinite volume model by the q-vertex operator approach. We finally show that the method can easily be generalized to the case of a more general non-diagonal twist: the corresponding weights of the different terms for the correlation functions in finite volume are then modified, but we recover in the thermodynamic limit the same multiple integral representation than in the periodic or anti-periodic case, hence proving the independence of the thermodynamic limit of the correlation functions with respect to the particular form of the boundary twist.

scholarly journals Thermodynamic Limit of Time‐Dependent Correlation Functions for One‐Dimensional Systems

1970 ◽  
Vol 11 (9) ◽  
pp. 2898-2905 ◽  
Author(s):  
G. Gallavotti ◽  
O. E. Lanford ◽  
Joel L. Lebowitz
Keyword(s):  
Thermodynamic Limit ◽  
Correlation Functions ◽  
Time Dependent ◽  
One Dimensional ◽  
Dependent Correlation

Correlation functions in the twisted N = 4 model

1997 ◽  
Vol 508 (1-2) ◽  
pp. 468-482
Author(s):  
W Pei
Keyword(s):  
Correlation Functions

Linearized hydrodynamics of 3 He-A1 : correlation functions and hydrodynamic parameters

1982 ◽  
Vol 43 (2) ◽  
pp. 369-380 ◽  
Author(s):  
H. Brand ◽  
H. Pleiner
Keyword(s):  
Correlation Functions ◽  
Hydrodynamic Parameters
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