Theory and Simulations of Cold atomic Fermi systems: A Quantum Many-Body Laboratory

A special issue of Atoms (ISSN 2218-2004).

Deadline for manuscript submissions: closed (15 September 2021) | Viewed by 2010

Special Issue Editor


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Guest Editor
Department of Physics, California State University Fresno, Fresno, 2345 E. San Ramon Ave. M/S MH37, Fresno, CA 93740, USA
Interests: cold atomic Fermi systems; lattice models for high-temperature superconductors; Quantum Monte Carlo techniques; strongly correlated systems

Special Issue Information

Dear Colleagues,

The amazing experimental control and accuracy that can be currently achieved in cold atoms give us a unique possibility to observe quantum mechanics at work with unprecedented resolution. We are now able to literally engineer quantum Hamiltonians and to shed light into fascinating physical phenomena, such as fermion pairing and superfluidity. The subtle interplay between quantum mechanics, quantum statistics, and interatomic forces frequently gives rise to puzzling and counterintuitive exciting behaviors, resulting in novel phases of matter, such as exotic superfluid phases with possible important topological properties. Moreover, the unique flexibility that is available in cold Fermi gases, where, for example, the interatomic forces can be tuned by controlling an external magnetic field, allows us to mimic the conditions that exist in some of the most mysterious systems in the universe, such as unconventional superconductors and even nuclear matter inside neutron stars. At the same time, Fermi gases can be modeled with relatively simple but still very challenging Hamiltonians, which makes these systems very promising test grounds for many-body theories and numerical simulation methods. Important strongly correlated regimes are known to exist in these systems, making simple approaches fail and calling for advanced correlated methodologies to accurately study the physical properties. In particular, in the last few years, in the petaflops era, we have witnessed an unprecedented progress in numerical methodologies, and cold atoms are an ideal environment to make robust advances in the formidable challenge of solving the fundamental equations of quantum mechanics with the aid of modern supercomputers. In this Special Issue of Atoms, we will collect some of the very important new theoretical and computational research results about fermionic quantum gases. Special emphasis will be dedicated to novel theoretical approaches and novel computational approaches. Reviews of existing important theoretical and computational methods and results will be welcome. Finally, there will be a number of studies involving the importance of cold atoms in condensed matter physics, nuclear physics, and nuclear astrophysics. 

Dr. Ettore Vitali
Guest Editor

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Keywords

  • fermions
  • cold atoms
  • superfluidity
  • fermionic pairing
  • computer simulations of quantum systems
  • strongly correlated systems

Published Papers (1 paper)

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Research

13 pages, 482 KiB  
Article
On the Accuracy of Random Phase Approximation for Dynamical Structure Factors in Cold Atomic Gases
by Patrick Kelly and Ettore Vitali
Atoms 2021, 9(4), 88; https://doi.org/10.3390/atoms9040088 - 26 Oct 2021
Cited by 1 | Viewed by 1440
Abstract
Many-body physics poses one of the greatest challenges to science in the 21st century. Still more daunting is the problem of accurately calculating the properties of quantum many-body systems in the strongly correlated regime. Cold atomic gases provide an excellent test ground, for [...] Read more.
Many-body physics poses one of the greatest challenges to science in the 21st century. Still more daunting is the problem of accurately calculating the properties of quantum many-body systems in the strongly correlated regime. Cold atomic gases provide an excellent test ground, for both experimentalists and theorists, to study the exotic and sometimes counterintuitive behavior of quantum many-body problems. Of particular interest is the appearance of collective excitations in these systems, such as the famous Goldstone mode and the elusive Higgs mode. It is particularly important to assess the robustness of theoretical and computational techniques to study such excitations. We build on the unprecedented opportunity provided by the fact that, in some cases, exact numerical predictions can be obtained through quantum Monte Carlo. We use these predictions to assess the accuracy of the Random Phase Approximation, which is widely considered to be a method of choice for the study of the collective excitations in a cold atomic Fermi gas modeled with a Fermi–Hubbard Hamiltonian. We found good agreement between the two methodologies for the dynamic properties, particularly for the position of the Goldstone mode. We also explored the possibility of using a renormalized, effective potential in place of the physical potential. We determined that using a renormalized potential is likely too simplistic a method for improving the accuracy of generalized Random Phase Approximation and that a more sophisticated approach is needed. Full article
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