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Long A, Eloranta J. Density functional theory of superfluid helium at finite temperatures. J Chem Phys 2021; 155:074102. [PMID: 34418920 DOI: 10.1063/5.0060132] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A density functional theory-based method is developed to describe the static and dynamic response of superfluid helium at finite temperatures. The model relies on the well-established 0 K Orsay-Trento functional, which has been extensively used to study the response of bulk superfluid helium as well as superfluid helium droplets. By including a phenomenological stochastic term in this model, it is possible to obtain thermodynamic equilibrium corresponding to a given temperature by propagating the system in imaginary time. The temperature dependence of thermodynamic quantities, such as the internal energy and entropy, is computed and is compared well with experimental reference data for the bulk liquid up to about 2 K, but begins to gradually deviate above that temperature. Inspection of pseudovorticity during real-time evolution of the system near 2 K reveals the presence of roton quasiparticles, which are suggested to be precursors for quantized vortex rings (Onsager's ghosts), as well as weaker analogs of extended vortex loops.
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Affiliation(s)
- Austin Long
- Department of Physics and Astronomy, California State University at Northridge, 18111 Nordhoff St., Northridge, California 91330, USA
| | - Jussi Eloranta
- Department of Chemistry and Biochemistry, California State University at Northridge, 18111 Nordhoff St., Northridge, California 91330, USA
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de Miguel R, Rubí JM. Statistical Mechanics at Strong Coupling: A Bridge between Landsberg's Energy Levels and Hill's Nanothermodynamics. NANOMATERIALS 2020; 10:nano10122471. [PMID: 33321739 PMCID: PMC7764728 DOI: 10.3390/nano10122471] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/21/2020] [Revised: 12/03/2020] [Accepted: 12/06/2020] [Indexed: 12/27/2022]
Abstract
We review and show the connection between three different theories proposed for the thermodynamic treatment of systems not obeying the additivity ansatz of classical thermodynamics. In the 1950s, Landsberg proposed that when a system comes into contact with a heat bath, its energy levels are redistributed. Based on this idea, he produced an extended thermostatistical framework that accounts for unknown interactions with the environment. A decade later, Hill devised his celebrated nanothermodynamics, where he introduced the concept of subdivision potential, a new thermodynamic variable that accounts for the vanishing additivity of increasingly smaller systems. More recently, a thermostatistical framework at strong coupling has been formulated to account for the presence of the environment through a Hamiltonian of mean force. We show that this modified Hamiltonian yields a temperature-dependent energy landscape as earlier suggested by Landsberg, and it provides a thermostatistical foundation for the subdivision potential, which is the cornerstone of Hill's nanothermodynamics.
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Affiliation(s)
- Rodrigo de Miguel
- Department of Teacher Education, Norwegian University of Science and Technology, 7491 Trondheim, Norway
- Correspondence: ; Tel.: +47-73412115
| | - J. Miguel Rubí
- Department of Condensed Matter Physics, University of Barcelona, 08007 Barcelona, Spain;
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Li H, Liao YD, Chen BB, Zeng XT, Sheng XL, Qi Y, Meng ZY, Li W. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO 4. Nat Commun 2020; 11:1111. [PMID: 32111829 PMCID: PMC7048727 DOI: 10.1038/s41467-020-14907-8] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2019] [Accepted: 02/10/2020] [Indexed: 11/22/2022] Open
Abstract
Frustrated magnets hold the promise of material realizations of exotic phases of quantum matter, but direct comparisons of unbiased model calculations with experimental measurements remain very challenging. Here we design and implement a protocol of employing many-body computation methodologies for accurate model calculations—of both equilibrium and dynamical properties—for a frustrated rare-earth magnet TmMgGaO4 (TMGO), which explains the corresponding experimental findings. Our results confirm TMGO is an ideal realization of triangular-lattice Ising model with an intrinsic transverse field. The magnetic order of TMGO is predicted to melt through two successive Kosterlitz–Thouless (KT) phase transitions, with a floating KT phase in between. The dynamical spectra calculated suggest remnant images of a vanishing magnetic stripe order that represent vortex–antivortex pairs, resembling rotons in a superfluid helium film. TMGO therefore constitutes a rare quantum magnet for realizing KT physics, and we further propose experimental detection of its intriguing properties. TmMgGaO4 is one of a number of recently-synthesized quantum magnets that are proposed to realize important theoretical models. Here the authors demonstrate the agreement between detailed experimental measurements and state-of-the-art predictions based on the 2D transverse-field triangular lattice Ising model.
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Affiliation(s)
- Han Li
- Key Laboratory of Micro-Nano Measurement-Manipulation and Physics (Ministry of Education), School of Physics, Beihang University, Beijing, 100191, China
| | - Yuan Da Liao
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China.,School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100190, China
| | - Bin-Bin Chen
- Key Laboratory of Micro-Nano Measurement-Manipulation and Physics (Ministry of Education), School of Physics, Beihang University, Beijing, 100191, China.,Arnold Sommerfeld Center for Theoretical Physics, Center for NanoScience, and Munich Center for Quantum Science and Technology, Ludwig-Maximilians-Universität München, Fakultät für Physik, D-80333, München, Germany
| | - Xu-Tao Zeng
- Key Laboratory of Micro-Nano Measurement-Manipulation and Physics (Ministry of Education), School of Physics, Beihang University, Beijing, 100191, China
| | - Xian-Lei Sheng
- Key Laboratory of Micro-Nano Measurement-Manipulation and Physics (Ministry of Education), School of Physics, Beihang University, Beijing, 100191, China
| | - Yang Qi
- Center for Field Theory and Particle Physics, Department of Physics and State Key Laboratory of Surface Physics, Fudan University, Shanghai, 200433, China. .,Collaborative Innovation Center of Advanced Microstructures, Nanjing, 210093, China.
| | - Zi Yang Meng
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China. .,Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China. .,Songshan Lake Materials Laboratory, Dongguan, Guangdong, 523808, China.
| | - Wei Li
- Key Laboratory of Micro-Nano Measurement-Manipulation and Physics (Ministry of Education), School of Physics, Beihang University, Beijing, 100191, China. .,International Research Institute of Multidisciplinary Science, Beihang University, Beijing, 100191, China.
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de Miguel R, Rubi JM. Finite Systems in a Heat Bath: Spectrum Perturbations and Thermodynamics. J Phys Chem B 2016; 120:9180-6. [DOI: 10.1021/acs.jpcb.6b05591] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Rodrigo de Miguel
- Section for Natural Science,
FLT Faculty, Norwegian University of Science and Technology, 7491 Trondheim, Norway
| | - J. Miguel Rubi
- Departament de
Fisica Fonamental,
Facultat de Fisica, Universitat de Barcelona, 08029 Barcelona, Spain
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MAYNARD J. PRECISION, SELF-CONSISTENT THERMODYNAMICS FOR SUPERFLUID HELIUM FROM SOUND VELOCITY MEASUREMENTS. CHEM ENG COMMUN 2007. [DOI: 10.1080/00986448008912530] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- J.D. MAYNARD
- a Department of Physics , The Pennsylvania State University , University Park, PA, 16802
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Abstract
The problem of the appearance of quantized vortex lines and rings in superflow and the modification of that flow by the vortices , is examined in the light of a suggestion by lordanskii, namely that thermal fluctuations may play a vital role in the nudeation process. The view is taken that there exists a distribution of quantized vortex rings in liquid helium and that the smallest of these is a roton. The evolution of these rings in a counterflow is examined by means of a Langevin equation. A Fokker-Planck equation is developed, and a number of examples are presented which illustrate the features of such include nucleation of vortices in an unbounded fluid, nucleation in a finite channel, the thermally activated vortex mill, nucleation of vortices by ions and phonon-roton relaxation times.
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Lemmens LF, Witters J, Brosens F, Devreese JT. Polaron-type theory for the specific heat of 3He in superfluid 4He. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 48:9669-9672. [PMID: 10007213 DOI: 10.1103/physrevb.48.9669] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Um CI, Nam ST, Lee SY, George TF. Temperature variation of the elementary excitation spectrum of thin liquid-4He films. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 46:6346-6360. [PMID: 10002321 DOI: 10.1103/physrevb.46.6346] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Temperature Dependence of S(Q, ω) for Liquid 4He. ACTA ACUST UNITED AC 1989. [DOI: 10.1007/978-3-642-83428-8_6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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Lu P, Suebka P. Mechanism of the anomalous increase of the specific heat of helium II near the lambda point. PHYSICAL REVIEW. B, CONDENSED MATTER 1987; 36:760-762. [PMID: 9942103 DOI: 10.1103/physrevb.36.760] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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13. Solid and Liquid Helium. ACTA ACUST UNITED AC 1987. [DOI: 10.1016/s0076-695x(08)60573-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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Suebka P, Lu P. Temperature dependence of the excitation energy spectrum of He II. PHYSICAL REVIEW. B, CONDENSED MATTER 1985; 31:1603-1604. [PMID: 9935939 DOI: 10.1103/physrevb.31.1603] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Reatto L, Straley JP. Phase Transition in the Pair-Hamiltonian Model for Liquid Helium. ACTA ACUST UNITED AC 1969. [DOI: 10.1103/physrev.183.321] [Citation(s) in RCA: 26] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Bruschi L, Mazzoldi P, Santini M. Periodic Critical Velocities of Ions in Liquid Helium II. Temperature Dependence. ACTA ACUST UNITED AC 1968. [DOI: 10.1103/physrev.167.203] [Citation(s) in RCA: 49] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Boghosian C, Meyer H. Density, Coefficient of Thermal Expansion, and Entropy of Compression of LiquidHe4under Pressure Below 1.4°K. ACTA ACUST UNITED AC 1966. [DOI: 10.1103/physrev.152.200] [Citation(s) in RCA: 46] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Webeler R, Hammer D. Viscosity coefficients and the phonon density temperature dependence in liquid 4He. ACTA ACUST UNITED AC 1965. [DOI: 10.1016/0031-9163(65)90761-4] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Hammel E, Keller W. On the existence of a maximum in the fountain pressure vs temperature relationship in liquid helium II. ACTA ACUST UNITED AC 1965. [DOI: 10.1016/0031-8914(65)90108-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Henshaw DG, Woods ADB. Modes of Atomic Motions in Liquid Helium by Inelastic Scattering of Neutrons. ACTA ACUST UNITED AC 1961. [DOI: 10.1103/physrev.121.1266] [Citation(s) in RCA: 343] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Cohen M. Relation between Inelastic Neutron Scattering and Thermodynamic Functions of Liquid Helium. ACTA ACUST UNITED AC 1960. [DOI: 10.1103/physrev.118.27] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Yarnell JL, Arnold GP, Bendt PJ, Kerr EC. Excitations in Liquid Helium: Neutron Scattering Measurements. ACTA ACUST UNITED AC 1959. [DOI: 10.1103/physrev.113.1379] [Citation(s) in RCA: 155] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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