arXiv subjects

Mitchell J. Knight

Publications and source records attributed to Mitchell J. Knight.

3 recordsLinked to original sources

arXiv2025

Reduced density matrix approach to one-dimensional ultracold bosonic systems

The variational determination of the two-boson reduced density matrix is described for a one-dimensional system of $N$ (where $N$ ranges from $2$ to $10^4$) harmonically trapped bosons interacting via contact interaction. The ground-state energies are calculated, and compared to existing methods in the field, including the analytic case (for $N=2)$ and mean-field approaches such as the one-dimensional Gross-Pitaevskii equation and its variations. Structural properties including the density and correlation functions are also derived, including the behaviour of the correlation function when boson coordinates coincide, collectively demonstrating the capacity of the reduced density matrix method to accurately calculate ground-state properties of bosonic systems comprising few to many bosons, including the cross-over region between these extremes, across a large range of interaction strengths.

cond-mat.quant-gas↗

arXiv2022

Reduced density matrix approach to ultracold few-fermion systems in one dimension

The variational determination of the two-fermion reduced density matrix is described for harmonically trapped, ultracold few-fermion systems in one dimension with equal spin populations. This is accomplished by formulating the problem as a semi-definite program, with the two-fermion reduced density matrix being subject to well-known $N$-representability conditions. The ground-state energies, as well as the density, pair-correlation function, and lower-order eigenvalues of the two-fermion reduced density matrix of various fermionic systems are found by utilising an augmented Lagrangian method for semi-definite programming. The ground-state energies are found to match well to those determined by full-configuration interaction and coupled-cluster calculations and the density, pair-correlation function, and eigenvalue results demonstrate that the salient features of these systems are well-described by this method. These results collectively demonstrate the utility of the reduced density matrix method firstly in describing strong correlation arising from short-range interactions, suggesting that the well-known N-representability conditions are sufficient to model ultracold fermionic systems, and secondly in illustrating the prospect of treating larger systems currently out of the reach of established methods.

cond-mat.quant-gas↗

arXiv2019

Improved low-dimensional wave equations for cigar-shaped and disk-shaped dipolar Bose-Einstein condensates

Within the formalism of the Gross-Pitaevskii equation, we derive effective one- and two-dimensional equations for cigar- and pancake-shaped dipolar Bose-Einstein condensates with arbitrary polarization angle. These are based on an ansatz for the condensate wavefunction whose width in the tightly-confined direction/s is treated variationally. The equations constitute a coupled partial differential for the low-dimensional wavefunction and algebraic equations for the width parameters. This approach accurately predicts the ground state densities of cigar-shaped and pancake-shaped dipolar Bose-Einstein condensates, and gives strong agreement with the three-dimensional results, even as the trapping is relaxed away from the strict quasi-one- and quasi-two-dimensional regimes. This approach offers a significant improvement over the standard one- and two-dimensional reduction.

cond-mat.quant-gas↗