scholarly journals Renormalized spectrum of quasiparticle in limited number of states, strongly interacting with two-mode polarization phonons at T=0 K

2021 ◽  
Vol 24 (1) ◽  
pp. 13705
Author(s):  
M.V. Tkach ◽  
Ju.O. Seti ◽  
O.M. Voitsekhivska
Keyword(s):  
Energy Spectrum ◽  
Ground State ◽  
Green's Functions ◽  
Green’S Functions ◽  
Phonon Modes ◽  
Strongly Interacting ◽  
Renormalized Energy ◽  
Initial States ◽  
Analytical Expressions

Within unitary transformed Hamiltonian of Fröhlich type, using the Green's functions method, exact renormalized energy spectrum of quasiparticle strongly interacting with two-mode polarization phonons is obtained at T=0 K in a model of the system with limited number of its initial states. Exact analytical expressions for the average number of phonons in ground state and in all satellite states of the system are presented. Their dependences on a magnitude of interaction between quasiparticle and both phonon modes are analyzed.

scholarly journals QCD Green's Functions and Phases of Strongly-Interacting Matter

2011 ◽  
Vol 13 ◽  
pp. 01002
Author(s):  
R. Alkofer ◽  
M. Mitter ◽  
B.J. Schaefer
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Strongly Interacting

Degeneracy, Derivative Rule, and Green’s Functions of Anisotropic Elasticity

2004 ◽  
Vol 71 (2) ◽  
pp. 273-282 ◽  
Author(s):  
Wan-Lee Yin
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Direct Proof ◽  
Anisotropic Elasticity ◽  
Higher Order ◽  
Zeroth Order ◽  
Isotropic Elasticity ◽  
Anisotropic Elastic ◽  
Analytical Expressions ◽  
Basic Elasticity

Degenerate and extra-degenerate anisotropic elastic materials have repeated material eigenvalues whose multiplicity is greater than the number of independent eigensolutions. Using basic elasticity relations, a simple, direct proof is given to show that higher-order eigensolutions may be obtained from the analytical expressions of the zeroth-order eigensolutions according to the derivative rule. These higher-order eigensolutions contribute to the complexity of the general solutions of degenerate and extra-degenerate materials, and to the analytical difficulties inherent in such cases including isotropic elasticity. For all types of anisotropic materials, the general solution is given specific forms to obtain Green’s functions of several domains with straight or elliptical boundaries. These results, presented in fully explicit expressions, extend Green’s functions of nondegenerate materials to degenerate and extra-degenerate cases that have not been explored previously.

scholarly journals Eigenvalues, eigenfunctions and Green's functions on a path via Chebyshev polynomials

2009 ◽  
Vol 3 (2) ◽  
pp. 282-302 ◽  
Author(s):  
E. Bendito ◽  
A.M. Encinas ◽  
A. Carmona
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Poisson Equation ◽  
Chebyshev Polynomials ◽  
Ground State ◽  
Green's Functions ◽  
Periodic Boundary ◽  
Green’S Functions ◽  
Boundary Value ◽  
The Poisson Equation

In this work we analyze the boundary value problems on a path associated with Schr?dinger operators with constant ground state. These problems include the cases in which the boundary has two, one or none vertices. In addition, we study the periodic boundary value problem that corresponds to the Poisson equation in a cycle. Moreover, we obtain the Green's function for each regular problem and the eigenvalues and their corresponding eigenfunctions otherwise. In each case, the Green's functions, the eigenvalues and the eigenfunctions are given in terms of first, second and third kind Chebyshev polynomials.

The Scientific Achievements of J. Alberto Ochoa-Tapia

2017 ◽  
Vol 15 (5) ◽  
Author(s):  
Francisco J. Valdés-Parada
Keyword(s):  
Boundary Value Problems ◽  
Green's Functions ◽  
Green’S Functions ◽  
Boundary Value ◽  
Volume Averaging ◽  
Nonlinear Boundary Value Problems ◽  
Efficient Manner ◽  
Convenient Approach ◽  
Analytical Expressions ◽  
Scientific Achievements

Abstract This work is devoted to briefly describe the scientific achievements of J. Alberto Ochoa-Tapia and his research group along almost three decades. The motivation for performing this review is not only to acknowledge his contributions, but also to share with the scientific community a brilliant scientific career. Although an exhaustive and complete review is beyond the scope of this paper, many of Alberto’s scientific contributions are briefly described. In addition, special attention is dedicated to three subjects, namely: Chang’s unit cell, the derivation of boundary conditions between a porous medium and a fluid and the use of Green’s functions to solve boundary-value problems. The first one is a convenient approach to derive analytical expressions of effective-medium coefficients resulting from the volume averaging method. The second one is Alberto’s most referenced work and it is of paramount importance since it provides the means to complete the statement of multiscale modeling. The third focus of attention is about the use of Green’s functions to solve nonlinear boundary-value problems in an efficient manner. Finally, his current and future works are discussed.

Study of the indirect interaction in a non-Fermi liquid within the AdS/CFT correspondence framework

2015 ◽  
Vol 29 (17) ◽  
pp. 1550081
Author(s):  
Alexander V. Zhukov ◽  
Roland Bouffanais ◽  
Anastasiya V. Pak ◽  
Mikhail B. Belonenko
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Liquid System ◽  
Spin Interaction ◽  
De Sitter ◽  
Quantum Liquid ◽  
Excitation Spectra ◽  
Conformal Field ◽  
Analytical Expressions ◽  
Gain Access

The indirect spin–spin interaction between impurities in a non-Fermi quantum liquid system is theoretically investigated in this paper. The poles of the Green’s functions are shown to be responsible for the observed excitation spectra. Specifically, the anti-de Sitter/conformal field theory (AdS/CFT) correspondence is used to gain access to the analytical expressions of the Green’s functions for our particular problem.

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