scholarly journals A cubic scaling algorithm for excited states calculations in particle–particle random phase approximation

2017 ◽  
Vol 340 ◽  
pp. 297-308
Author(s):  
Jianfeng Lu ◽  
Haizhao Yang
Keyword(s):  
Excited States ◽  
Random Phase Approximation ◽  
Random Phase ◽  
Phase Approximation

Quasiparticle nature of excited states in random-phase approximation

2019 ◽  
Vol 99 (1) ◽  
Author(s):  
E. V. Chimanski ◽  
B. V. Carlson ◽  
R. Capote ◽  
A. J. Koning
Keyword(s):  
Excited States ◽  
Random Phase Approximation ◽  
Random Phase ◽  
Phase Approximation

scholarly journals Modified non-Euclidean transformation on the SO(2N+2) U(N+1) Grassmannian and SO(2N + 1) random phase approximation for unified description of Bose and Fermi type collective excitations

2016 ◽  
Vol 13 (04) ◽  
pp. 1650043
Author(s):  
Seiya Nishiyama ◽  
João da Providência
Keyword(s):  
Excited States ◽  
Random Phase Approximation ◽  
Lagrange Equation ◽  
Integrability Condition ◽  
Random Phase ◽  
Phase Approximation ◽  
Zero Curvature ◽  
Geometrical Concept ◽  
Unified Description ◽  
Fermi Type

In a slight different way from the previous one, we propose a modified non-Euclidean transformation on the [Formula: see text] Grassmannian which gives the projected [Formula: see text] Tamm–Dancoff equation. We derive a classical time-dependent (TD) [Formula: see text] Lagrangian which, through the Euler–Lagrange equation of motion for [Formula: see text] coset variables, brings another form of the previous extended-TD Hartree–Bogoliubov (HB) equation. The [Formula: see text] random phase approximation (RPA) is derived using Dyson representation for paired and unpaired operators. In the [Formula: see text] HB case, one boson and two boson excited states are realized. We, however, stress non-existence of a higher RPA vacuum. An integrable system is given by a geometrical concept of zero-curvature, i.e. integrability condition of connection on the corresponding Lie group. From the group theoretical viewpoint, we show the existence of a symplectic two-form [Formula: see text].

scholarly journals Reproduction of exact solutions of Lipkin model by nonlinear higher random-phase approximation

2017 ◽  
Vol 26 (10) ◽  
pp. 1750062 ◽  
Author(s):  
J. Terasaki ◽  
A. Smetana ◽  
F. Šimkovic ◽  
M. I. Krivoruchenko
Keyword(s):  
Exact Solutions ◽  
Excited States ◽  
Random Phase Approximation ◽  
Particle Number ◽  
Random Phase ◽  
Creation Operator ◽  
Phase Approximation ◽  
Many Body ◽  
Lipkin Model ◽  
Number Formula

It is shown that the random-phase approximation (RPA) method with its nonlinear higher generalization, which was previously considered as approximation except for a very limited case, reproduces the exact solutions of the Lipkin model. The nonlinear higher RPA is based on an equation nonlinear on eigenvectors and includes many particle-many hole components in the creation operator of the excited states. We demonstrate the exact character of solutions analytically for the particle number [Formula: see text] and, numerically, for [Formula: see text]. This finding indicates that the nonlinear higher RPA is equivalent to the exact Schrödinger equation, which opens up new possibilities for realistic calculations in many-body problems.

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