Classical and Quantum Gases on a Semiregular Mesh
The main objective of a statistical mechanical calculation is drawing the phase diagram of a many-body system. In this respect, discrete systems offer the clear advantage over continuum systems of an easier enumeration of microstates, though at the cost of added abstraction. With this in mind, we ex...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-10-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/11/21/10053 |
| _version_ | 1827678305117011968 |
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| author | Davide De Gregorio Santi Prestipino |
| author_facet | Davide De Gregorio Santi Prestipino |
| author_sort | Davide De Gregorio |
| collection | DOAJ |
| description | The main objective of a statistical mechanical calculation is drawing the phase diagram of a many-body system. In this respect, discrete systems offer the clear advantage over continuum systems of an easier enumeration of microstates, though at the cost of added abstraction. With this in mind, we examine a system of particles living on the vertices of the (biscribed) pentakis dodecahedron, using different couplings for first and second neighbor particles to induce a competition between icosahedral and dodecahedral orders. After working out the phases of the model at zero temperature, we carry out Metropolis Monte Carlo simulations at finite temperature, highlighting the existence of smooth transitions between distinct “phases”. The sharpest of these crossovers are characterized by hysteretic behavior near zero temperature, which reveals a bottleneck issue for Metropolis dynamics in state space. Next, we introduce the quantum (Bose-Hubbard) counterpart of the previous model and calculate its phase diagram at zero and finite temperatures using the decoupling approximation. We thus uncover, in addition to Mott insulating “solids”, also the existence of supersolid “phases” which progressively shrink as the system is heated up. We argue that a quantum system of the kind described here can be realized with programmable holographic optical tweezers. |
| first_indexed | 2024-03-10T06:06:27Z |
| format | Article |
| id | doaj.art-51c2e2907b4245c086c97e05785f0dba |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-10T06:06:27Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-51c2e2907b4245c086c97e05785f0dba2023-11-22T20:27:21ZengMDPI AGApplied Sciences2076-34172021-10-0111211005310.3390/app112110053Classical and Quantum Gases on a Semiregular MeshDavide De Gregorio0Santi Prestipino1Dipartimento di Scienze Matematiche ed Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, Viale F. Stagno d’Alcontres 31, 98166 Messina, ItalyDipartimento di Scienze Matematiche ed Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, Viale F. Stagno d’Alcontres 31, 98166 Messina, ItalyThe main objective of a statistical mechanical calculation is drawing the phase diagram of a many-body system. In this respect, discrete systems offer the clear advantage over continuum systems of an easier enumeration of microstates, though at the cost of added abstraction. With this in mind, we examine a system of particles living on the vertices of the (biscribed) pentakis dodecahedron, using different couplings for first and second neighbor particles to induce a competition between icosahedral and dodecahedral orders. After working out the phases of the model at zero temperature, we carry out Metropolis Monte Carlo simulations at finite temperature, highlighting the existence of smooth transitions between distinct “phases”. The sharpest of these crossovers are characterized by hysteretic behavior near zero temperature, which reveals a bottleneck issue for Metropolis dynamics in state space. Next, we introduce the quantum (Bose-Hubbard) counterpart of the previous model and calculate its phase diagram at zero and finite temperatures using the decoupling approximation. We thus uncover, in addition to Mott insulating “solids”, also the existence of supersolid “phases” which progressively shrink as the system is heated up. We argue that a quantum system of the kind described here can be realized with programmable holographic optical tweezers.https://www.mdpi.com/2076-3417/11/21/10053lattice-gas modelsspherical boundary conditionsultracold quantum gasesdecoupling approximationsupersolid phases |
| spellingShingle | Davide De Gregorio Santi Prestipino Classical and Quantum Gases on a Semiregular Mesh Applied Sciences lattice-gas models spherical boundary conditions ultracold quantum gases decoupling approximation supersolid phases |
| title | Classical and Quantum Gases on a Semiregular Mesh |
| title_full | Classical and Quantum Gases on a Semiregular Mesh |
| title_fullStr | Classical and Quantum Gases on a Semiregular Mesh |
| title_full_unstemmed | Classical and Quantum Gases on a Semiregular Mesh |
| title_short | Classical and Quantum Gases on a Semiregular Mesh |
| title_sort | classical and quantum gases on a semiregular mesh |
| topic | lattice-gas models spherical boundary conditions ultracold quantum gases decoupling approximation supersolid phases |
| url | https://www.mdpi.com/2076-3417/11/21/10053 |
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