Real Space Triplets in Quantum Condensed Matter: Numerical Experiments Using Path Integrals, Closures, and Hard Spheres
Path integral Monte Carlo and closure computations are utilized to study real space triplet correlations in the quantum hard-sphere system. The conditions cover from the normal fluid phase to the solid phases face-centered cubic (FCC) and cI16 (de Broglie wavelengths <inline-formula><math d...
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MDPI AG
2020-11-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/22/12/1338 |
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| author | Luis M. Sesé |
| author_facet | Luis M. Sesé |
| author_sort | Luis M. Sesé |
| collection | DOAJ |
| description | Path integral Monte Carlo and closure computations are utilized to study real space triplet correlations in the quantum hard-sphere system. The conditions cover from the normal fluid phase to the solid phases face-centered cubic (FCC) and cI16 (de Broglie wavelengths <inline-formula><math display="inline"><semantics><mrow><mn>0.2</mn><mo>≤</mo><msubsup><mi>λ</mi><mi>B</mi><mo>*</mo></msubsup><mo><</mo><mn>2</mn></mrow></semantics></math></inline-formula>, densities <inline-formula><math display="inline"><semantics><mrow><mn>0.1</mn><mo>≤</mo><msubsup><mi>ρ</mi><mi>N</mi><mo>*</mo></msubsup><mo>≤</mo><mn>0.925</mn></mrow></semantics></math></inline-formula>). The focus is on the equilateral and isosceles features of the path-integral centroid and instantaneous structures. Complementary calculations of the associated pair structures are also carried out to strengthen structural identifications and facilitate closure evaluations. The three closures employed are Kirkwood superposition, Jackson–Feenberg convolution, and their average (AV3). A large quantity of new data are reported, and conclusions are drawn regarding (i) the remarkable performance of AV3 for the centroid and instantaneous correlations, (ii) the correspondences between the fluid and FCC salient features on the coexistence line, and (iii) the most conspicuous differences between FCC and cI16 at the pair and the triplet levels at moderately high densities (<inline-formula><math display="inline"><semantics><mrow><msubsup><mi>ρ</mi><mi>N</mi><mo>*</mo></msubsup><mo>=</mo><mn>0.9</mn><mo>,</mo><mo> </mo><mn>0.925</mn><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula>. This research is expected to provide low-temperature insights useful for the future related studies of properties of real systems (e.g., helium, alkali metals, and general colloidal systems). |
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| language | English |
| last_indexed | 2024-03-10T14:35:15Z |
| publishDate | 2020-11-01 |
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| spelling | doaj.art-b2f779d1dae94ad69b5baaab31d3f1bf2023-11-20T22:16:57ZengMDPI AGEntropy1099-43002020-11-012212133810.3390/e22121338Real Space Triplets in Quantum Condensed Matter: Numerical Experiments Using Path Integrals, Closures, and Hard SpheresLuis M. Sesé0Departamento de Ciencias y Técnicas Fisicoquímicas, Facultad de Ciencias, Universidad Nacional de Educación a Distancia (UNED), Avda. Esparta s/n, 28232 Las Rozas, Madrid, SpainPath integral Monte Carlo and closure computations are utilized to study real space triplet correlations in the quantum hard-sphere system. The conditions cover from the normal fluid phase to the solid phases face-centered cubic (FCC) and cI16 (de Broglie wavelengths <inline-formula><math display="inline"><semantics><mrow><mn>0.2</mn><mo>≤</mo><msubsup><mi>λ</mi><mi>B</mi><mo>*</mo></msubsup><mo><</mo><mn>2</mn></mrow></semantics></math></inline-formula>, densities <inline-formula><math display="inline"><semantics><mrow><mn>0.1</mn><mo>≤</mo><msubsup><mi>ρ</mi><mi>N</mi><mo>*</mo></msubsup><mo>≤</mo><mn>0.925</mn></mrow></semantics></math></inline-formula>). The focus is on the equilateral and isosceles features of the path-integral centroid and instantaneous structures. Complementary calculations of the associated pair structures are also carried out to strengthen structural identifications and facilitate closure evaluations. The three closures employed are Kirkwood superposition, Jackson–Feenberg convolution, and their average (AV3). A large quantity of new data are reported, and conclusions are drawn regarding (i) the remarkable performance of AV3 for the centroid and instantaneous correlations, (ii) the correspondences between the fluid and FCC salient features on the coexistence line, and (iii) the most conspicuous differences between FCC and cI16 at the pair and the triplet levels at moderately high densities (<inline-formula><math display="inline"><semantics><mrow><msubsup><mi>ρ</mi><mi>N</mi><mo>*</mo></msubsup><mo>=</mo><mn>0.9</mn><mo>,</mo><mo> </mo><mn>0.925</mn><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula>. This research is expected to provide low-temperature insights useful for the future related studies of properties of real systems (e.g., helium, alkali metals, and general colloidal systems).https://www.mdpi.com/1099-4300/22/12/1338quantum tripletspath integral Monte Carloclosuresquantum hard spheresfluid–solid transitionFCC solid |
| spellingShingle | Luis M. Sesé Real Space Triplets in Quantum Condensed Matter: Numerical Experiments Using Path Integrals, Closures, and Hard Spheres Entropy quantum triplets path integral Monte Carlo closures quantum hard spheres fluid–solid transition FCC solid |
| title | Real Space Triplets in Quantum Condensed Matter: Numerical Experiments Using Path Integrals, Closures, and Hard Spheres |
| title_full | Real Space Triplets in Quantum Condensed Matter: Numerical Experiments Using Path Integrals, Closures, and Hard Spheres |
| title_fullStr | Real Space Triplets in Quantum Condensed Matter: Numerical Experiments Using Path Integrals, Closures, and Hard Spheres |
| title_full_unstemmed | Real Space Triplets in Quantum Condensed Matter: Numerical Experiments Using Path Integrals, Closures, and Hard Spheres |
| title_short | Real Space Triplets in Quantum Condensed Matter: Numerical Experiments Using Path Integrals, Closures, and Hard Spheres |
| title_sort | real space triplets in quantum condensed matter numerical experiments using path integrals closures and hard spheres |
| topic | quantum triplets path integral Monte Carlo closures quantum hard spheres fluid–solid transition FCC solid |
| url | https://www.mdpi.com/1099-4300/22/12/1338 |
| work_keys_str_mv | AT luismsese realspacetripletsinquantumcondensedmatternumericalexperimentsusingpathintegralsclosuresandhardspheres |