Construction of theory of a binary mixture of nonideal bose gases (or liquids) by the method of collective variables. II. The s-particle density matrices at T=0. Variational calculation of the ground-state energy and density-density correlation functions

1987 ◽  
Vol 71 (1) ◽  
pp. 418-428
Author(s):  
G. O. Balabanya
Keyword(s):  
Binary Mixture ◽  
Ground State ◽  
Correlation Functions ◽  
State Energy ◽  
Particle Density ◽  
Variational Calculation ◽  
Density Matrices ◽  
Bose Gases ◽  
Collective Variables ◽  
Density Correlation

THE ANGULAR MOMENTUM DEPENDENT CALCULATION OF THE GROUND STATE ENERGY OF LIQUID 3He

2005 ◽  
Vol 19 (30) ◽  
pp. 1793-1802 ◽  
Author(s):  
M. MODARRES
Keyword(s):  
Angular Momentum ◽  
Ground State Energy ◽  
Ground State ◽  
Correlation Functions ◽  
State Energy ◽  
Interatomic Potentials ◽  
Channel Correlation ◽  
P Waves ◽  
Effective Interactions ◽  
Three Body

We investigate the possible angular momentum, l, dependence of the ground state energy of normal liquid 3 He . The method of lowest order constrained variational (LOCV) which includes the three-body cluster energy and normalization constraint (LOCVE) is used with angular momentum dependent two-body correlation functions. A functional minimization is performed with respect to each l-channel correlation function. It is shown that this dependence increases the binding energy of liquid 3 He by 8% with respect to calculations without angular momentum dependent correlation functions. The l=0 state has completely different behavior with respect to other l-channels. It is also found that the main contribution from potential energy comes from the l=1 state (p-waves) and the effect of l≥11 is less than about 0.1%. The effective interactions and two-body correlations in different channels are being discussed. Finally we conclude that this l-dependence can be verified experimentally by looking into the magnetization properties of liquid helium 3 and interatomic potentials.

Is it Reasonable to Obtain Information on the Polarizability and Hyperpolarizability Only from the Electron Density?

2018 ◽  
Vol 71 (4) ◽  
pp. 295 ◽  
Author(s):  
Dylan Jayatilaka ◽  
Kunal K. Jha ◽  
Parthapratim Munshi
Keyword(s):  
Density Matrix ◽  
Electron Density ◽  
Ground State ◽  
Density Functional ◽  
Particle Density ◽  
Density Matrices ◽  
Hartree Fock ◽  
Electron Density Matrix ◽  
Ground State Electron ◽  
Side Result

Formulae for the static electronic polarizability and hyperpolarizability are derived in terms of moments of the ground-state electron density matrix by applying the Unsöld approximation and a generalization of the Fermi-Amaldi approximation. The latter formula for the hyperpolarizability appears to be new. The formulae manifestly transform correctly under rotations, and they are observed to be essentially cumulant expressions. Consequently, they are additive over different regions. The properties of the formula are discussed in relation to others that have been proposed in order to clarify inconsistencies. The formulae are then tested against coupled-perturbed Hartree-Fock results for a set of 40 donor-π-acceptor systems. For the polarizability, the correlation is reasonable; therefore, electron density matrix moments from theory or experiment may be used to predict polarizabilities. By constrast, the results for the hyperpolarizabilities are poor, not even within one or two orders of magnitude. The formula for the two- and three-particle density matrices obtained as a side result in this work may be interesting for density functional theories.

Variational calculation on ground-state energy of bound polarons in parabolic quantum wires

2001 ◽  
Vol 10 (5) ◽  
pp. 437-442 ◽  
Author(s):  
Wang Zhuang-bing ◽  
Wu Fu-li, Chen Qing-hu ◽  
Jiao Zheng-kuan
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Quantum Wires ◽  
Variational Calculation

Ground State Energy of Polaron Bound in a Coulomb Potential

1974 ◽  
Vol 52 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Mitsuru Matsuura
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
Present Method ◽  
State Energy ◽  
Variational Calculation ◽  
Effective Potentials ◽  
Important Region ◽  
Electron Phonon Coupling ◽  
Wide Range ◽  
Path Integral Method

The path integral method is used to obtain an expression, involving a sum over the complete set of solutions for the effective trial Hamiltonian, for the ground state energy of the bound polaron. The numerical calculations of this expression are performed for the hydrogenic and harmonic oscillator effective potentials. The present method together with several previous theories and their numerical results are discussed over a wide range of the electron–phonon coupling constant α and the electron–massive hole coupling β. It is shown that, for the experimentally important region, the present method with the hydrogenic potential yields the lowest energy—slightly lower than obtained by the Larsen's variational calculation.

AN EXACTLY SOLVABLE ONE-DIMENSIONAL MODEL OF FERMIONS WITH CORRELATED HOPPING

1996 ◽  
Vol 10 (27) ◽  
pp. 3673-3683 ◽  
Author(s):  
IGOR N. KARNAUKHOV
Keyword(s):  
Critical Exponents ◽  
Ground State ◽  
Correlation Functions ◽  
State Energy ◽  
One Dimension ◽  
Supersymmetric Model ◽  
Dimensional Model ◽  
Long Distance ◽  
One Dimensional ◽  
Exactly Solvable

A new solution of supersymmetric model of electrons with correlated hopping which generalizes those obtained earlier is formulated. The model is solved in one dimension by the Bethe ansatz. The ground state energy is calculated, and the critical exponents describing the decrease of the correlation functions on long distance are derived.

scholarly journals The Inhomogeneous Gaussian Free Field, with application to ground state correlations of trapped 1d Bose gases

2018 ◽  
Vol 4 (6) ◽  
Author(s):  
Yannis Brun ◽  
Jerome Dubail
Keyword(s):  
Ground State ◽  
Correlation Functions ◽  
Particle Density ◽  
Free Field ◽  
Form Factors ◽  
Gaussian Free Field ◽  
Luttinger Liquids ◽  
Model Combining ◽  
Ground State Correlation ◽  
Trapped Gas

This formalism is then applied to the study of ground state correlations of the Lieb-Liniger gas trapped in an external potential V(x)V(x). Relations with previous works on inhomogeneous Luttinger liquids are discussed. The main innovation here is in the identification of local observables \hat{O} (x)Ô(x) in the microscopic model with their field theory counterparts \partial_x h, e^{i h(x)}, e^{-i h(x)}∂xh,eih(x),e−ih(x), etc., which involve non-universal coefficients that themselves depend on position — a fact that, to the best of our knowledge, was overlooked in previous works on correlation functions of inhomogeneous Luttinger liquids —, and that can be calculated thanks to Bethe Ansatz form factors formulae available for the homogeneous Lieb-Liniger model. Combining those position-dependent coefficients with the correlation functions of the IGFF, ground state correlation functions of the trapped gas are obtained. Numerical checks from DMRG are provided for density-density correlations and for the one-particle density matrix, showing excellent agreement.

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