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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Autores principales:	Davide De Gregorio, Santi Prestipino
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	lattice-gas models spherical boundary conditions ultracold quantum gases decoupling approximation supersolid phases Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999
Acceso en línea:	https://doaj.org/article/51c2e2907b4245c086c97e05785f0dba
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spelling	oai:doaj.org-article:51c2e2907b4245c086c97e05785f0dba2021-11-11T15:08:34ZClassical and Quantum Gases on a Semiregular Mesh10.3390/app1121100532076-3417https://doaj.org/article/51c2e2907b4245c086c97e05785f0dba2021-10-01T00:00:00Zhttps://www.mdpi.com/2076-3417/11/21/10053https://doaj.org/toc/2076-3417The 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.Davide De GregorioSanti PrestipinoMDPI AGarticlelattice-gas modelsspherical boundary conditionsultracold quantum gasesdecoupling approximationsupersolid phasesTechnologyTEngineering (General). Civil engineering (General)TA1-2040Biology (General)QH301-705.5PhysicsQC1-999ChemistryQD1-999ENApplied Sciences, Vol 11, Iss 10053, p 10053 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	lattice-gas models spherical boundary conditions ultracold quantum gases decoupling approximation supersolid phases Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999
spellingShingle	lattice-gas models spherical boundary conditions ultracold quantum gases decoupling approximation supersolid phases Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999 Davide De Gregorio Santi Prestipino Classical and Quantum Gases on a Semiregular Mesh
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.
format	article
author	Davide De Gregorio Santi Prestipino
author_facet	Davide De Gregorio Santi Prestipino
author_sort	Davide De Gregorio
title	Classical and Quantum Gases on a Semiregular Mesh
title_short	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_sort	classical and quantum gases on a semiregular mesh
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/51c2e2907b4245c086c97e05785f0dba
work_keys_str_mv	AT davidedegregorio classicalandquantumgasesonasemiregularmesh AT santiprestipino classicalandquantumgasesonasemiregularmesh
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Classical and Quantum Gases on a Semiregular Mesh

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