Analytic Evaluation of the 1-Hole Spectral Function for the 1-D t-J Model in the Limit J → 0

Author(s):  
Michael Ziegler ◽  
Peter Horsch

2008 ◽  
Author(s):  
Steven K. Huprich ◽  
Thomas A. Schmitt ◽  
Iwona Chelminski ◽  
Mark Zimmerman




Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 477
Author(s):  
Katarzyna Górska ◽  
Andrzej Horzela

In this paper, we show that spectral functions relevant for commonly used models of the non-Debye relaxation are related to the Stieltjes functions supported on the positive semi-axis. Using only this property, it can be shown that the response and relaxation functions are non-negative. They are connected to each other and obey the time evolution provided by integral equations involving the memory function M(t), which is the Stieltjes function as well. This fact is also due to the Stieltjes character of the spectral function. Stochastic processes-based approach to the relaxation phenomena gives the possibility to identify the memory function M(t) with the Laplace (Lévy) exponent of some infinitely divisible stochastic processes and to introduce its partner memory k(t). Both memories are related by the Sonine equation and lead to equivalent evolution equations which may be freely interchanged in dependence of our knowledge on memories governing the process.



2021 ◽  
Vol 126 (6) ◽  
Author(s):  
J. Settino ◽  
N. Lo Gullo ◽  
F. Plastina ◽  
A. Minguzzi
Keyword(s):  


2020 ◽  
Vol 102 (6) ◽  
Author(s):  
A. B. Larionov ◽  
U. Mosel ◽  
L. von Smekal


1969 ◽  
Vol 10 (2) ◽  
pp. 208-212 ◽  
Author(s):  
R. Acharya
Keyword(s):  


1997 ◽  
Vol 20 (2) ◽  
pp. 397-402 ◽  
Author(s):  
E. M. E. Zayed

The spectral functionΘ(t)=∑i=1∞exp(−tλj), where{λj}j=1∞are the eigenvalues of the negative Laplace-Beltrami operator−Δ, is studied for a compact Riemannian manifoldΩof dimension “k” with a smooth boundary∂Ω, where a finite number of piecewise impedance boundary conditions(∂∂ni+γi)u=0on the parts∂Ωi(i=1,…,m)of the boundary∂Ωcan be considered, such that∂Ω=∪i=1m∂Ωi, andγi(i=1,…,m)are assumed to be smooth functions which are not strictly positive.



1998 ◽  
Vol 57 (18) ◽  
pp. R11089-R11092 ◽  
Author(s):  
M. R. Norman ◽  
H. Ding


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