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arXiv:nucl-th/0702086 · Journal of Physics A Mathematical and Theoretical

Virtues and flaws of the Pauli potential

Jutri Taruna, J. Piekarewicz, M. Ángeles Pérez-García

Published Jan 4, 2008• 8 citations
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Abstract

Quantum simulations of complex fermionic systems suffer from a variety of challenging problems. In an effort to circumvent these challenges, simpler ‘semi-classical’ approaches have been used to mimic fermionic correlations through a fictitious ‘Pauli potential’ . In this contribution we examine two issues. First, we address some of the inherent difficulties in a widely used version of the Pauli potential. Second, we refine such a potential in a manner consistent with the most basic properties of a cold Fermi gas, such as its momentum distribution and its two-body correlation function.

DOI
10.1088/1751-8113/41/3/035308

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Quantum simulations of complex fermionic systems suffer from a variety of challenging problems. In an effort to circumvent these challenges, simpler ‘semi-classical’ approaches have been used to mimic fermionic correlations through a fictitious ‘Pauli potential’ . In this contribution we examine two issues. First, we address some of the inherent difficulties in a widely used version of the Pauli potential. Second, we refine such a potential in a manner consistent with the most basic properties of a cold Fermi gas, such as its momentum distribution and its two-body correlation function.
The role of Pauli potentials in the semiclassical simulation of Fermi gases at low temperatures is investigated. An alternative Pauli potential to the usual bivariate Gaussian form by Dorso et al. is proposed. This new Pauli potential allows for a simultaneous good reproduction of not only the kinetic energy per particle but also the momentum distribution and the two-body correlation function. The reproduction of the binding energies in finite nuclei in the low and medium mass range is also analyzed. What is found is that given a reasonable short-range atractive nuclear interaction one can include correlation effects in a suitable chosen density dependent Pauli potential.
Confined quantum systems involving NNN identical interacting fermions are found in many areas of physics, including condensed matter, atomic, nuclear, and chemical physics. In a previous series of papers, a many-body perturbation method that is applicable to both weakly and strongly interacting systems of bosons has been set forth by the author and coworkers. A symmetry-invariant perturbation theory was developed that uses group theory coupled with the dimension of space as the perturbation parameter to obtain an analytic correlated wave function through first order for a system under spherical confinement with a general two-body interaction. In the present paper, we extend this formalism to large systems of fermions, circumventing the numerical demands of applying the Pauli principle by enforcing the Pauli principle on paper. The method does not scale in complexity with NNN and has minimal numerical cost. We apply the method to a unitary Fermi gas and compare to recent Monte Carlo values.
In the wake of successful experiments in Fermi condensates, experimental attention is broadening to include resonant interactions in degenerate Bose-Fermi mixtures. In this thesis we wish to study the equilibrium properties of the fermionic molecules that can be created in such a mixture. To this end, we first discuss the two body properties of the system, and introduce the model Hamiltonian we use to describe the resonant physics, highlighting its virtues, as well as its limitations. We then proceed by analyzing the mean field solution of this model, by studying both the equilibrium problem, and the non-equilibrium equations of motion, thus developing a powerful language to discuss the system. We then highlight the limitations of the mean-field approach, and develop a numerically tractable generalized version of this theory, which is able to correctly describe the two-body properties of the system in the low-density limit. Finally, we study the properties of the system using this generalized mean-field theory, by first analyzing the two-body scattering matrix in the many-body environment, assessing its complex poles in order to understand the stability properties of the Feshbach molecules in the gas. Secondly we solve the equilibrium equations self-consistently, to study the molecular populations and density distributions at equilibrium, as a function of external bias magnetic field.
The collective behavior of an ensemble of strongly interacting fermions is central to many physical systems, and its theoretical description is challenging due to the many-body nature of the problem. The ultracold Fermi gas is an ideal model system to shed light on this issue, as it provides excellent controllability, reproducibility, and unique detection methods. One of the problems, however, which complicates the interpretation of such experiments is the inherent density inhomogeneity of the gas due to harmonic confinement. We have developed a technique to overcome this difficulty by selectively probing atoms near the center of a trapped gas while still retaining momentum resolution. In this contribution to the 21th International Conference on Laser Spectroscopy (ICOLS 2013), we give an overview of this technique and some of the observations that have resulted from its implementation.
classical many body models supplemented by repulsive momentum-dependent potentials to simulate the Pauli and Heisenberg principles have been use with some success for nuclear and atomic bound state and collision problems. They are capable of describing mean ground state properties, hydrodynamics, shocks (if warranted by the physics), viscosity, correlations, clustering, fragmentation, etc. We have become interested in the Feldmeier Gaussian packet formulation since it is based on a variational principle using trial wave functions. We discuss some limitations of the model and discuss further directions of investigation.