Pairing of the Pöschl–Teller gas

Fan, Hsuan-Hao

doi:10.1007/s10909-018-02117-y

Cited by 2 publications

(4 citation statements)

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“…The essential difference compared with what we have discussed in previous work [35,129] is the operator form (6.1) of the interaction. Instead of a local W (r), we have the spin-dependent interactionW…”

Section: Energeticsmentioning

confidence: 58%

“…125 to study pairing in the unitary limit. We have recently examined the ground state and pairing properties of the Pöschl-Teller gas [129]; in this work we have improved these calculations by applying the improvements outlined above. Since many techical details have been discussed in the preceding sections, we can restrict ourselves to display just the new aspects of our calculations.…”

Section: Pöschl-teller Interactionmentioning

confidence: 99%

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Variational and Parquet-diagram theory for strongly correlated normal and superfluid systems

Fan

Krotscheck

2019

Physics Reports

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We develop the variational and correlated basis functions/parquet-diagram theory of strongly interacting normal and superfluid systems. The first part of this contribution is devoted to highlight the connections between the Euler equations for the Jastrow-Feenberg wave function on the one hand side, and the ring, ladder, and self-energy diagrams of parquet-diagram theory on the other side. We will show that these subsets of Feynman diagrams are contained, in a local approximation, in the variational wave function.In the second part of this work, we derive the fully optimized Fermi-Hypernetted Chain (FHNC-EL) equations for a superfluid system. Close examination of the procedure reveals that the naïve application of these equations exhibits spurious unphysical properties for even an infinitesimal superfluid gap. We will conclude that it is essential to go beyond the usual Jastrow-Feenberg approximation and to include the exact particle-hole propagator to guarantee a physically meaningful theory and the correct stability range.We will then implement this method and apply it to neutron matter and low density Fermi liquids interacting via the Lennard-Jones model interaction and the Pöschl-Teller interaction. While the quantitative changes in the magnitude of the superfluid gap are relatively small, we see a significant difference between applications for neutron matter and the Lennard-Jones and Pöschl-Teller systems. Despite the fact that the gap in neutron matter can be as large as half the Fermi energy, the corrections to the gap are relatively small. In the Lennard-Jones and Pöschl-Teller models, the most visible consequence of the self-consistent calculation is the change in stability range of the system. 7 Discussion 75 Appendix A Cluster expansions for the generating function. Diagonal terms 76 Appendix B Cluster expansions for the generating function. Off-diagonal terms 78 Appendix C Cluster expansions for the energy numerator terms 79 Appendix D Calculation of exchange diagrams 84 1. IntroductionThe repertoire of methods for the quantitative microscopic description of normal quantum many-body systems has condensed, over the past few decades, to a relatively small number of techniques. These can be roughly classified on the one hand side as various shades of large-scale numerical simulation methods and, on the other hand, diagrammatic approaches summing, in some approximation, the parquet class of Feynman diagrams. Numerical simulations are capable of high precision but are computationally demanding and limited to relatively simple Hamiltonians and mostly ground state properties. They also need the physical intuition of the user about the possible state of the system. Semi-analytic, diagrammatic approaches lead to a better understanding of the underlying physical mechanisms, but have limited accuracy due to some necessary approximations. These diagrammatic approaches are versions of Green's function methods [1], Coupled Cluster theory [2], and variational methods [3]. The interconnections between the various me...

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Section: Energeticsmentioning

confidence: 58%

Section: Pöschl-teller Interactionmentioning

confidence: 99%

Variational and Parquet-diagram theory for strongly correlated normal and superfluid systems

Fan

Krotscheck

2019

Physics Reports

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“…Yang and Sun [20] employed both terraced and sloped layouts for a 20 MW PV project site and found that the terraced layout had certain economic advantages over the sloped layout. Fan [21] used manual grid division and manual assignment to optimize the site leveling design of the same project. The results displayed significant improvements over the original design from FastTFT [14].…”

Section: Introductionmentioning

confidence: 99%

“…Some optimization research in civil engineering and agriculture can provide valuable insights for designing the leveling of PV slopes. Currently, the most researched method is the plane method [22], which includes approaches based on least squares [16,21] and improved least square methods [23]. However, these methods tend to produce non-optimal results as they only provide a plane-fitting surface.…”

Section: Introductionmentioning

confidence: 99%

A Linear Optimization for Slope Leveling of Ground-Mounted Centralized Photovoltaic Sites

Tao,

Zheng,

Cheng

et al. 2024

Buildings

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Slope leveling is essential for the successful implementation of ground-mounted centralized photovoltaic (PV) plants, but currently, there is a lack of optimization methods available. To address this issue, a linear programming approach has been proposed to optimize PV slope leveling. This method involves dividing the field into blocks and grids and using hyperbolic paraboloids to simulate the design surface. By programming in MATLAB, the globally optimal solution for PV slope leveling can be calculated. Engineering case studies have demonstrated that this optimization method can achieve significant cut-and-fill volume savings ranging from 58% to 78%, when compared to the traditional segmented plane method. Additionally, the effectiveness of the optimization method improves with larger site areas and more complex terrains. A parameter analysis considering slope ratio, grid size, and block size reveals that grid size has a minimal impact on cut-and-fill volume, while slope ratio and block size have a significant influence. For typical PV projects, the recommended ranges of slope ratio, grid size, and block size are 3–7%, 5–20 m, and 30–50 m, respectively, for slope leveling design. In summary, the proposed linear optimization method provides an optimal slope leveling scheme for ground-mounted centralized PV plants, with convenient operation and fast computation.

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Pairing of the Pöschl–Teller gas

Cited by 2 publications

References 20 publications

Variational and Parquet-diagram theory for strongly correlated normal and superfluid systems

Variational and Parquet-diagram theory for strongly correlated normal and superfluid systems

A Linear Optimization for Slope Leveling of Ground-Mounted Centralized Photovoltaic Sites

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