scholarly journals A Note on the Calculation of the Long-Wavelength Limit of the Bosonic Excitation Spectrum

2015 ◽  
Vol 70 (1) ◽  
pp. 73-78 ◽  
Author(s):  
Andrij Rovenchak
Keyword(s):  
Excitation Spectrum ◽  
Green's Functions ◽  
Green’S Functions ◽  
Good Description ◽  
Equations Of Motion ◽  
Elementary Excitation ◽  
Collective Variables ◽  
Long Wavelength ◽  
Wavelength Limit ◽  
Bose Liquid

AbstractAn approach is proposed to analyse an interacting bosonic system using two-time temperature Green’s functions on the collective variables. Two systems are studied: liquid helium-4 and the Yukawa Bose liquid being a model of the nuclear matter. The suggested decoupling in the equations of motion for Green’s functions yields a good description of the elementary excitation spectrum in the long-wavelength limit.

Wick-Regeln mit Zwischenzuständen und die Neue Tamm-Dancoff-Methode mit Zwischenzuständen / On Wick Rules with Intermediate States and the New Tamm-Dancoff Method with Intermediate States

1976 ◽  
Vol 31 (8) ◽  
pp. 872-886 ◽  
Author(s):  
A. Friederich ◽  
W. Gerling
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Equations Of Motion ◽  
Random Phase ◽  
Dimensional Subspace ◽  
Finite Dimensional Subspace ◽  
Great Success ◽  
Hartree Fock ◽  
Intermediate States ◽  
Many Body Systems

AbstractInstead of emphasizing the ground state as is done in Green's function method, we take a finite-dimensional subspace of the Hilbert space: the space of the "intermediate states". A systematic introduction of intermediate states is effected by an extension of the method of generating functionals: we combine the generating functionals of the n-point Green's functions to a "matrix functional" T, and form new matrix functionals, which are matrix functions of T. The aim of this paper is to develop the functional calculus in such a way that the transition from scalar functionals to matrix functionals is straightforward, and the method of obtaining further results becomes clear. Following the lines of Dürr and Wagner we get u η-and ζ-rules with intermediate states". Using them we define a truncation procedure for the equations of motion of the n-point Green's functions, the "New Tamm-Dancoff method with intermediate states". This extension makes it possible to treat the effect of nearby levels in many body systems with Green's functions. In ad-dition to well-known approximations, such as the Hartree-Fock and the Hartree-Bogoliubov theory, the RPA and the quasiparticle RPA, we obtain a series of new approximations. Among these are the "Hartree-Fock theory with intermediate states" and the "random-phase approximation with intermediate states", which we already applied with great success to some exactly soluble models.

Local conservation laws and equations of motion for Green’s functions

1988 ◽  
Vol 38 (3) ◽  
pp. 1641-1644 ◽  
Author(s):  
K. Gütter ◽  
P.-G. Reinhard ◽  
C. Toepffer
Keyword(s):  
Conservation Laws ◽  
Green's Functions ◽  
Green’S Functions ◽  
Equations Of Motion ◽  
Local Conservation

scholarly journals Equation of motion truncation scheme based on partial orthogonalization

2021 ◽  
Vol 94 (1) ◽  
Author(s):  
Francesco Catalano ◽  
Johan Nilsson
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
General Scheme ◽  
Equations Of Motion ◽  
Mean Field ◽  
Test Case ◽  
Excitation Energies ◽  
Fermi Surfaces ◽  
Truncation Scheme ◽  
Half Filling

Abstract We introduce a general scheme to consistently truncate equations of motion for Green’s functions. Our scheme is guaranteed to generate physical Green’s functions with real excitation energies and positive spectral weights. There are free parameters in our scheme akin to mean field parameters that may be determined to get as good an approximation to the physics as possible. As a test case we apply our scheme to a two-pole approximation for the 2D Hubbard model. At half-filling we find an insulating solution with several interesting properties: it has low expectation value of the energy and it gives upper and lower Hubbard bands with the full non-interacting bandwidth in the large U limit. Away from half-filling, in particular in the intermediate interaction regime, our scheme allows for several different phases with different number of Fermi surfaces and topologies. Graphic abstract

Theoretical Models for Magnetic Properties of Iron Pnictides Part I: Spin Formalism

2011 ◽  
Vol 35 (1) ◽  
pp. 29-43 ◽  
Author(s):  
M. Vujinović ◽  
M. Pantić ◽  
D. Kapor ◽  
S. Radošević
Keyword(s):  
Magnetic Properties ◽  
Random Phase Approximation ◽  
Green's Functions ◽  
Green’S Functions ◽  
Equations Of Motion ◽  
Random Phase ◽  
Theoretical Models ◽  
Wave Dispersion ◽  
Iron Pnictides ◽  
Model Hamiltonian

Theoretical Models for Magnetic Properties of Iron Pnictides Part I: Spin FormalismWe attempt to describe the magnetic properties of parent pnictide compounds by using theJ1-J2-JcHeisenberg model Hamiltonian. In order to obtain the ground state magnetization and spin wave dispersion we use the Green's functions method for spin operators. The equations of motion for Green's functions are decoupled by employing the random phase approximation. We analyze the results numerically and after comparison with experimental data we conclude that the model is to be modified to make it more relevant to iron pnictides.

Decoherence of Kondo singlet caused by phase-sensitive detection of Aharonov–Bohm interferometer

2014 ◽  
Vol 28 (11) ◽  
pp. 1450084
Author(s):  
Ming-Lun Chen ◽  
Shun-Jin Wang
Keyword(s):  
Quantum Dot ◽  
Cluster Expansion ◽  
Green's Functions ◽  
Green’S Functions ◽  
Equations Of Motion ◽  
Sensitive Detection ◽  
Qualitative Explanation ◽  
Phase Sensitive ◽  
Phase Sensitive Detection ◽  
Aharonov Bohm

To investigate the decoherence of Kondo singlet, we once again check a model, an Aharonov–Bohm interferometer with a quantum dot coupling to left–right electrodes, which is designed by Yacoby to measure phase-sensitive of a quantum dot. By employing the cluster expansion, the equations of motion of Green's functions are transformed into the corresponding equations of connected Green's functions, which contain the correlation of two conducting electrons. With the method, we show that the Kondo singlet is suppressed by phase-sensitive detection of Aharonov–Bohm interferometer. Our numerical results have provided a qualitative explanation with the anomalous features observed in an experiment by Avinun-Kalish et al. [Phys. Rev. Lett.92 (2004) 156801].

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