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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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2
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Brieuc F, Schran C, Uhl F, Forbert H, Marx D. Converged quantum simulations of reactive solutes in superfluid helium: The Bochum perspective. J Chem Phys 2020; 152:210901. [DOI: 10.1063/5.0008309] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023] Open
Affiliation(s)
- Fabien Brieuc
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, 44780 Bochum, Germany
| | - Christoph Schran
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, 44780 Bochum, Germany
| | - Felix Uhl
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, 44780 Bochum, Germany
| | - Harald Forbert
- Center for Solvation Science ZEMOS, Ruhr-Universität Bochum, 44780 Bochum, Germany
| | - Dominik Marx
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, 44780 Bochum, Germany
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Delaney KT, Orland H, Fredrickson GH. Numerical Simulation of Finite-Temperature Field Theory for Interacting Bosons. PHYSICAL REVIEW LETTERS 2020; 124:070601. [PMID: 32142318 DOI: 10.1103/physrevlett.124.070601] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2019] [Revised: 12/05/2019] [Accepted: 01/15/2020] [Indexed: 06/10/2023]
Abstract
We report a stable and efficient complex Langevin sampling scheme for performing approximation-free numerical simulations directly on the path-integral coherent-states field theory for an assembly of interacting bosons. We apply the method to generate the λ line of critical phase transitions associated with Bose-Einstein condensation in a model ϕ^{4} scalar field theory. The new approach enjoys near-linear scaling in the resolved (d+1) spatial and imaginary-time dimensions and should be particularly efficient for the study of dense systems at low temperature.
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Affiliation(s)
- Kris T Delaney
- Materials Research Laboratory, University of California, Santa Barbara, California 93106-5121, USA
| | - Henri Orland
- Institut de Physique Théorique, CE-Saclay, CEA, F-91191 Gif-sur-Yvette Cedex, France
| | - Glenn H Fredrickson
- Materials Research Laboratory, University of California, Santa Barbara, California 93106-5121, USA
- Departments of Materials and Chemical Engineering, University of California, Santa Barbara, California 93106, USA
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Ramamurti A, Shuryak E. Effective model of QCD magnetic monopoles from numerical study of one- and two-component Coulomb quantum Bose gases. Int J Clin Exp Med 2017. [DOI: 10.1103/physrevd.95.076019] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Comparin T, Krauth W. Momentum Distribution in the Unitary Bose Gas from First Principles. PHYSICAL REVIEW LETTERS 2016; 117:225301. [PMID: 27925718 DOI: 10.1103/physrevlett.117.225301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2016] [Indexed: 06/06/2023]
Abstract
We consider a realistic bosonic N-particle model with unitary interactions relevant for Efimov physics. Using quantum Monte Carlo methods, we find that the critical temperature for Bose-Einstein condensation is decreased with respect to the ideal Bose gas. We also determine the full momentum distribution of the gas, including its universal asymptotic behavior, and compare this crucial observable to recent experimental data. Similar to the experiments with different atomic species, differentiated solely by a three-body length scale, our model only depends on a single parameter. We establish a weak influence of this parameter on physical observables. In current experiments, the thermodynamic instability of our model from the atomic gas towards an Efimov liquid could be masked by the dynamical instability due to three-body losses.
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Affiliation(s)
- Tommaso Comparin
- Laboratoire de Physique Statistique, École Normale Supérieure/PSL Research University, UPMC, Université Paris Diderot, CNRS, 24 rue Lhomond, 75005 Paris, France
| | - Werner Krauth
- Laboratoire de Physique Statistique, École Normale Supérieure/PSL Research University, UPMC, Université Paris Diderot, CNRS, 24 rue Lhomond, 75005 Paris, France
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Nguyen TT, Herrmann AJ, Troyer M, Pilati S. Critical temperature of interacting Bose gases in periodic potentials. PHYSICAL REVIEW LETTERS 2014; 112:170402. [PMID: 24836222 DOI: 10.1103/physrevlett.112.170402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/04/2013] [Indexed: 06/03/2023]
Abstract
The superfluid transition of a repulsive Bose gas in the presence of a sinusoidal potential which represents a simple-cubic optical lattice is investigated using quantum Monte Carlo simulations. At the average filling of one particle per well the critical temperature has a nonmonotonic dependence on the interaction strength, with an initial sharp increase and a rapid suppression at strong interactions in the vicinity of the Mott transition. In an optical lattice the positive shift of the transition is strongly enhanced compared to the homogenous gas. By varying the lattice filling we find a crossover from a regime where the optical lattice has the dominant effect to a regime where interactions dominate and the presence of the lattice potential becomes almost irrelevant.
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Affiliation(s)
- T T Nguyen
- The Abdus Salam International Centre for Theoretical Physics, 34151 Trieste, Italy and SISSA-International School for Advanced Studies, 34136 Trieste, Italy
| | - A J Herrmann
- Department of Physics, University of Fribourg, 1700 Fribourg, Switzerland
| | - M Troyer
- Theoretische Physik, ETH Zurich, 8093 Zurich, Switzerland
| | - S Pilati
- The Abdus Salam International Centre for Theoretical Physics, 34151 Trieste, Italy
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Rota R, Boronat J. Onset temperature of Bose-Einstein condensation in incommensurate solid (4)He. PHYSICAL REVIEW LETTERS 2012; 108:045308. [PMID: 22400859 DOI: 10.1103/physrevlett.108.045308] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2011] [Indexed: 05/31/2023]
Abstract
The temperature dependence of the one-body density matrix in (4)He crystals presenting vacancies is computed with path integral Monte Carlo simulations. The main purpose of this study is to estimate the onset temperature T(0) of Bose-Einstein condensation in these systems. We see that T(0) depends on the vacancy concentration X(v) of the simulated system, but not following the law T(0) ~ X(v)(2/3) obtained assuming noninteracting vacancies. For the lowest X(v) we study, that is X(v)= 1/256, we get T(0) = 0.15 ± 0.05 K, close to the temperatures at which a finite fraction of nonclassical rotational inertia is experimentally observed. Below T(0), vacancies do not act as classical point defects becoming completely delocalized entities.
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Affiliation(s)
- R Rota
- Departament de Física i Enginyeria Nuclear, Campus Nord B4-B5, Universitat Politècnica de Catalunya, 08034 Barcelona, Spain
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Pilati S, Giorgini S, Prokof'ev N. Critical temperature of interacting Bose gases in two and three dimensions. PHYSICAL REVIEW LETTERS 2008; 100:140405. [PMID: 18518010 DOI: 10.1103/physrevlett.100.140405] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/22/2008] [Indexed: 05/26/2023]
Abstract
We calculate the superfluid transition temperature of homogeneous interacting Bose gases in three and two spatial dimensions using large-scale path integral Monte Carlo simulations (with up to N=10;{5} particles). In 3D we investigate the limits of the universal critical behavior in terms of the scattering length alone by using different models for the interatomic potential. We find that this type of universality sets in at small values of the gas parameter na3 < or approximately 10(-4). This value is different from the estimate na3 < or approximately 10(-6) for the validity of the asymptotic expansion in the limit of vanishing na3. In 2D we study the Berezinskii-Kosterlitz-Thouless transition of a gas with hard-core interactions. For this system we find good agreement with the classical lattice |psi|4 model up to very large densities. We also explain the origin of the existing discrepancy between previous studies of the same problem.
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Affiliation(s)
- S Pilati
- Dipartimento di Fisica, Università di Trento and CNR-INFM BEC Center, I-38050 Povo, Trento, Italy
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Boninsegni M, Prokof'ev NV, Svistunov BV. Worm algorithm and diagrammatic Monte Carlo: a new approach to continuous-space path integral Monte Carlo simulations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:036701. [PMID: 17025780 DOI: 10.1103/physreve.74.036701] [Citation(s) in RCA: 116] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2006] [Indexed: 05/12/2023]
Abstract
A detailed description is provided of a new worm algorithm, enabling the accurate computation of thermodynamic properties of quantum many-body systems in continuous space, at finite temperature. The algorithm is formulated within the general path integral Monte Carlo (PIMC) scheme, but also allows one to perform quantum simulations in the grand canonical ensemble, as well as to compute off-diagonal imaginary-time correlation functions, such as the Matsubara Green function, simultaneously with diagonal observables. Another important innovation consists of the expansion of the attractive part of the pairwise potential energy into elementary (diagrammatic) contributions, which are then statistically sampled. This affords a complete microscopic account of the long-range part of the potential energy, while keeping the computational complexity of all updates independent of the size of the simulated system. The computational scheme allows for efficient calculations of the superfluid fraction and off-diagonal correlations in space-time, for system sizes which are orders of magnitude larger than those accessible to conventional PIMC. We present illustrative results for the superfluid transition in bulk liquid 4He in two and three dimensions, as well as the calculation of the chemical potential of hcp 4He.
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Affiliation(s)
- M Boninsegni
- Department of Physics, University of Alberta, Edmonton, Alberta, Canada T6G 2J1
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Rosenblit M, Jortner J. Electron bubbles in helium clusters. II. Probing superfluidity. J Chem Phys 2006; 124:194506. [PMID: 16729824 DOI: 10.1063/1.2192782] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023] Open
Abstract
In this paper we present calculations of electron tunneling times from the ground electronic state of excess electron bubbles in ((4)He)(N) clusters (N=6500-10(7), cluster radius R=41.5-478 A), where the equilibrium bubble radius varies in the range R(b)=13.5-17.0 A. For the bubble center located at a radial distance d from the cluster surface, the tunneling transition probability was expressed as A(0)phi(d,R)exp(-betad), where beta approximately 1 A(-1) is the exponential parameter, A(0) is the preexponential factor for the bubble located at the cluster center, and phi(d,R) is a correction factor which accounts for cluster curvature effects. Electron tunneling dynamics is grossly affected by the distinct mode of motion of the electron bubble in the image potential within the cluster, which is dissipative (i.e., tau(D)<tau(0)) in normal fluid ((4)He)(N) and ((3)He)(N) clusters, while it is undamped (i.e., tau(D)>>tau(0)) in superfluid ((4)He)(N) clusters, where tau(D) is the bubble motional damping time (tau(D) approximately 4 x 10(-12) s for normal fluid clusters and tau(D) approximately 10 s for superfluid clusters), while tau(0) approximately 10(-9)-10(-10) s is the bubble oscillatory time. Exceedingly long tunneling lifetimes, which cannot be experimentally observed, are manifested from bubbles damped to the center of the normal fluid cluster, while for superfluid clusters electron tunneling occurs from bubbles located in the vicinity of the initial distance d near the cluster boundary. Model calculations of the cluster size dependence of the electron tunneling time (for a fixed value of d=38-39 A), with lifetimes increasing in the range of 10(-3)-0.3 s for N=10(4)-10(7), account well for the experimental data [M. Farnik and J. P. Toennies, J. Chem. Phys. 118, 4176 (2003)], manifesting cluster curvature effects on electron tunneling dynamics. The minimal cluster size for the dynamic stability of the bubble was estimated to be N=3800, which represents the threshold cluster size for which the excess electron bubble in ((4)He)(N) (-) clusters is amenable to experimental observation.
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Affiliation(s)
- Michael Rosenblit
- School of Chemistry, Tel Aviv University, Ramat Aviv, 69978 Tel Aviv, Israel
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Kleinert H, Schmidt S, Pelster A. Reentrant phenomenon in the quantum phase transitions of a gas of bosons trapped in an optical lattice. PHYSICAL REVIEW LETTERS 2004; 93:160402. [PMID: 15524958 DOI: 10.1103/physrevlett.93.160402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2003] [Indexed: 05/24/2023]
Abstract
We calculate the location of the quantum phase transitions of a Bose gas trapped in an optical lattice as a function of effective scattering length a(eff) and temperature T. Knowledge of recent high-loop results on the shift of the critical temperature at weak couplings is used to locate a nose in the phase diagram above the free Bose-Einstein critical temperature T((0))(c), thus predicting the existence of a reentrant transition above T((0))(c), where a condensate should form when increasing a(eff). At zero temperature, the transition to the normal phase produces the experimentally observed Mott insulator.
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Affiliation(s)
- H Kleinert
- Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
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Gordillo MC, Ceperley DM. Effect of disorder on the critical temperature of a dilute hard-sphere Gas. PHYSICAL REVIEW LETTERS 2000; 85:4735-4738. [PMID: 11082639 DOI: 10.1103/physrevlett.85.4735] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2000] [Indexed: 05/23/2023]
Abstract
We have performed path integral Monte Carlo calculations to determine the effect of quenched disorder on the superfluid density of a dilute 3D hard-sphere gas. The disorder was introduced by locating hard cylinders randomly inside the simulation cell. Our results indicate that the disorder does not strongly affect the superfluid critical temperature. There is a reduction of rho(s)/rho with increasing disorder and with excluded volume for similar disorders and a possible change of universality class (as evidenced by the correlation length exponent) at high disorder. Comparison to experiments of helium in Vycor is made.
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Affiliation(s)
- MC Gordillo
- Departament de Fisica i Enginyeria Nuclear, Campus Nord B4-B5, Universitat Politecnica de Catalunya, E-08034 Barcelona, Spain
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Hunter JE, Reinhardt WP. Finite‐size scaling behavior of the free energy barrier between coexisting phases: Determination of the critical temperature and interfacial tension of the Lennard‐Jones fluid. J Chem Phys 1995. [DOI: 10.1063/1.470121] [Citation(s) in RCA: 50] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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