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International Journal of Scientific Research in Physics and Applied Sciences

Static Pair Correlation Functions and Static Structure Factors of Unidirectional Quantum Systems

Grima Dhingra

Published Jun 30, 2019• 0 citations
Publisher

Abstract

Two of the structural functions, static pair correlation function of electrons around positively charged particles and static structure factor, have been theoretically calculated for a one dimensional quantum system with two mobile components occupying same charge density at equal temperatures.The structural functions have been investigated for their density and mass dependence.The reported values of static pair correlation function and structure factors are found to be dependent upon linear density and mass of positive components.Static pair correlation functions for a wide range of temperature, 100K≤T≤ 1500K, has also been generated theoretically.A variation, though diminutive, with temperature has been observed.

DOI
10.26438/ijsrpas/v7i3.15

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Two of the structural functions, static pair correlation function of electrons around positively charged particles and static structure factor, have been theoretically calculated for a one dimensional quantum system with two mobile components occupying same charge density at equal temperatures.The structural functions have been investigated for their density and mass dependence.The reported values of static pair correlation function and structure factors are found to be dependent upon linear density and mass of positive components.Static pair correlation functions for a wide range of temperature, 100K≤T≤ 1500K, has also been generated theoretically.A variation, though diminutive, with temperature has been observed.
We have evaluated the density-density response of the two-dimensional electron gas at zero temperature by solving the Dyson equation for the particle-hole Green's function, including exchange Coulomb matrix elements and short-range contributions in the ladder approximation. We study the effect of these correlations on the total energy, compressibility per particle, local field factor G ( q ), static structure factor and pair-correlation function. Results are compared with the normal random-phase approximation, local field theories and quantum Monte Carlo calculations.
The ground-state correlation properties of a one-dimensional Bose system described by the Lieb-Liniger Hamiltonian are investigated by using exact quantum Monte Carlo techniques. The pair distribution function, static structure factor, one-body density matrix, and momentum distribution of a homogeneous system are calculated for different values of the gas parameter ranging from the Tonks-Girardeau to the mean-field regime. Results for the momentum distribution of a harmonically trapped gas in configurations relevant to experiments are also presented.
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We discuss approximate formulas for the dynamic structure factor of the one-dimensional Bose gas in the Lieb-Liniger model that appear to be applicable over a wide range of the relevant parameters such as the interaction strength, frequency, and wave number. The suggested approximations are consistent with the exact results known in limiting cases. In particular, we encompass exact edge exponents as well as the Luttinger-liquid and perturbation theoretic results. We further discuss derived approximations for the static structure factor and the pair distribution function g(x)g(x)g(x). The approximate expressions show excellent agreement with numerical results based on the algebraic Bethe ansatz.
Abstract In this paper, we theoretically investigate the effect of temperature on spin correlations in an unpolarized quasi-one-dimensional electron gas (Q1DEG). The correlations are treated dynamically within quantum version of the self-consistent mean-field approach of Singwi et al Numerical results for the ↑↑ and ↑↓ components of static structure factor and pair-correlation function, and the wave vector dependent static spin and charge susceptibilities are presented over a wide range of temperature T and electron coupling r s . We find that the recently reported (2020 J. Phys.: Condens. Matter. 32 335403) non-monotonic T -dependence of the contact pair-correlation function g ( r = 0; T ) is driven primarily by an interplay between ↑↓ correlations and thermal effects. At a given temperature, the dynamics of both ↑↑ and ↑↓ correlations is found to become significant with increasing coupling r s , manifesting unambiguously as pronounced peak at 3.5 k F (periodic oscillations) in the corresponding components of the structure factor (pair-correlation function). Analysis of static spin and charge susceptibilities reveals that an imbalance between ↑↑ and ↑↓ correlations may induce a transition to a spin-density wave (SDW) phase of wave vector ∼3.5 k F above a critical coupling for a sufficiently high T , while to a long-wavelength SDW phase at a low T . Higher the temperature, higher is the predicted critical coupling for the SDW phase. Interestingly, transition to the SDW phase is found to precede the recently predicted Wigner crystal instability in the finite- T Q1DEG. Further, if one starts with partially spin-polarized electrons, the SDW instability is found to shift to somewhat higher τ and r s . In addition, we have presented results for the free exchange-correlation energy, free correlation energy, and excess kinetic energy for the unpolarized and fully spin-polarized phases of the finite- T Q1DEG. Wherever interesting, we have compared our results with the predictions of the static version of the mean-field approach.
The static two- and four-spin correlations for the one-dimensional easy-plane Heisenberg spin system with a ferromagnetic coupling, like CsNiF 3 , are investigated in the classical limit by means of the transfer matrix method. They are found to consist essentially of two components which both depend exponentially on the distance between sites. Both in the high- and low-temperature regions, only one component remains and this component still dominates at intermediate temperatures. Analytic forms for the correlation functions are given for asymptotically low temperatures. These are obtained by calculating the second-frequency moment of the dynamical structure factor in three different ways, and by requiring the T=0 limit of the moment to coincide with the square of the spin wave frequency. Generalisations of the Tomita-Mashiyama recursion relations (1972) for the isotropic case are given, valid for low temperatures, Monte Carlo calculations of the correlation functions have also been performed and some results of these are presented as well.