Simulation of dynamical properties of normal and superfluid helium.
22 Mar 2005-Proceedings of the National Academy of Sciences of the United States of America (National Academy of Sciences)-Vol. 102, Iss: 12, pp 4230-4234
TL;DR: This simulation demonstrates that the peak enhancement observed in the neutron scattering experiments below the transition temperature arises exclusively from particle exchange, illuminating the role of Bose-statistical effects on the dynamics of the quantum liquid.
Abstract: The formation of a superfluid when 4He is cooled below the characteristic lambda transition temperature is accompanied by intricate quantum mechanical phenomena, including the emergence of a Bose condensate. A combination of path integral and semiclassical techniques is used to calculate the single-particle velocity autocorrelation function across the normal-to-superfluid transition. We find that the inclusion of particle exchange alters qualitatively the shape of the correlation function below the characteristic transition temperature but has no noticeable effect on the dynamics in the normal phase. The incoherent structure factor extracted from the velocity autocorrelation function is in very good agreement with neutron scattering data, reproducing the width, height, frequency shift, and asymmetry of the curves, as well as the observed increase in peak height characteristic of the superfluid phase. Our simulation demonstrates that the peak enhancement observed in the neutron scattering experiments below the transition temperature arises exclusively from particle exchange, illuminating the role of Bose-statistical effects on the dynamics of the quantum liquid.
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TL;DR: The unique role played by the hydrogen-bond network will be examined, first in liquid water, then in the solvation of model biological compounds, and finally in ice, especially highlighting the important effects related to the quantization of the nuclear motion.
Abstract: The properties of water play a central role in many phenomena of relevance to different areas of science, including physics, chemistry, biology, geology, and climate research. Although well studied for decades, the behavior of water under different conditions and in different environments still remains mysterious and often surprising. In this article, various efforts aimed at providing a comprehensive representation of the water properties at a molecular level through computer modeling and simulation will be described. In particular, the unique role played by the hydrogen-bond network will be examined, first in liquid water, then in the solvation of model biological compounds, and finally in ice, especially highlighting the important effects related to the quantization of the nuclear motion.
212 citations
TL;DR: The performance of both CMD and RPMD for computing vibrational spectra of several simple but representative molecular model systems is investigated systematically as a function of temperature and isotopic substitution.
Abstract: Centroid molecular dynamics (CMD) and ring polymer molecular dynamics (RPMD) are two conceptually distinct extensions of path integral molecular dynamics that are able to generate approximate quantum dynamics of complex molecular systems. Both methods can be used to compute quasiclassical time correlation functions which have direct application in molecular spectroscopy; in particular, to infrared spectroscopy via dipole autocorrelation functions. The performance of both methods for computing vibrational spectra of several simple but representative molecular model systems is investigated systematically as a function of temperature and isotopic substitution. In this context both CMD and RPMD feature intrinsic problems which are quantified and investigated in detail. Based on the obtained results guidelines for using CMD and RPMD to compute infrared spectra of molecular systems are provided.
212 citations
TL;DR: It is found that none of the investigated nanoporous carbon materials satisfy the US Department of Energy goal of volumetric density and mass storage for automotive application at considered storage condition, and geometry of carbon surfaces can enhance the storage capacity only to a limited extent.
Abstract: We used Grand canonical Monte Carlo simulation to model the hydrogen storage in the primitive, gyroid, diamond, and quasi-periodic icosahedral nanoporous carbon materials and in carbon nanotubes. We found that none of the investigated nanoporous carbon materials satisfy the US Department of Energy goal of volumetric density and mass storage for automotive application (6 wt% and 45 kg H2 m−3) at considered storage condition. Our calculations indicate that quasi-periodic icosahedral nanoporous carbon material can reach the 6 wt% at 3.8 MPa and 77 K, but the volumetric density does not exceed 24 kg H2 m−3. The bundle of single-walled carbon nanotubes can store only up to 4.5 wt%, but with high volumetric density of 42 kg H2 m−3. All investigated nanoporous carbon materials are not effective against compression above 20 MPa at 77 K because the adsorbed density approaches the density of the bulk fluid. It follows from this work that geometry of carbon surfaces can enhance the storage capacity only to a limited extent. Only a combination of the most effective structure with appropriate additives (metals) can provide an efficient storage medium for hydrogen in the quest for a source of “clean” energy.
127 citations
TL;DR: A multiple coherent states implementation of the semiclassical approximation is introduced and employed to obtain the power spectra with a few classical trajectories and successfully reproduce anharmonicity and Fermi resonance splittings at a level of accuracy comparable to semiclassicals simulations of thousands of trajectories.
Abstract: A multiple coherent states implementation of the semiclassical approximation is introduced and employed to obtain the power spectra with a few classical trajectories. The method is integrated with the time-averaging semiclassical initial value representation to successfully reproduce anharmonicity and Fermi resonance splittings at a level of accuracy comparable to semiclassical simulations of thousands of trajectories. The method is tested on two different model systems with analytical potentials and implemented in conjunction with the first-principles molecular dynamics scheme to obtain the power spectrum for the carbon dioxide molecule.
102 citations
TL;DR: This represents the first study of dynamical properties of the Ne(13) Lennard-Jones cluster in its liquid-solid phase transition region (temperature from 4 to 14 K) and the force autocorrelation function shows considerable differences from that given by classical mechanics.
Abstract: The linearized approximation to the semiclassical initial value representation (LSC-IVR) has been used together with the thermal Gaussian approximation (TGA) (TGA/LSC-IVR) to simulate quantum dynamical effects in realistic models of two condensed phase systems. This represents the first study of dynamical properties of the Ne13 Lennard-Jones (LJ) cluster in its liquid-solid phase transition region (temperature from 4 K to 14 K). Calculation of the force autocorrelation function shows considerable differences from that given by classical mechanics, namely that the cluster is much more mobile (liquid-like) than in the classical case. Liquid para-hydrogen at two thermodynamic state points (25 K and 14 K under nearly zero external pressure) has also been studied. The momentum autocorrelation function obtained from the TGA/LSC-IVR approach shows very good agreement with recent accurate path integral Monte Carlo (PIMC) results at 25 K. The self-diffusion constants calculated by the TGA/LSC-IVR are in reasonable agreement with those from experiment and from other theoretical calculations. These applications demonstrate the TGA/LSC-IVR to be a practical and versatile method for quantum dynamics simulations of condensed phase systems.
96 citations
References
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TL;DR: The Bose-Einstein condensation (BEC) phenomenon was first introduced by Bose as discussed by the authors, who derived the Planck law for black-body radiation by treating the photons as a gas of identical particles.
Abstract: In 1924 the Indian physicist Satyendra Nath Bose sent Einstein a paper in which he derived the Planck law for black-body radiation by treating the photons as a gas of identical particles. Einstein generalized Bose's theory to an ideal gas of identical atoms or molecules for which the number of particles is conserved and, in the same year, predicted that at sufficiently low temperatures the particles would become locked together in the lowest quantum state of the system. We now know that this phenomenon, called Bose-Einstein condensation (BEC), only happens for "bosons" – particles with a total spin that is an integer multiple of h, the Planck constant divided by 2π.
3,298 citations
05 Mar 2018
TL;DR: In this article, the two-fluid model is used to model elementary excitement in He II and the response to a transverse probe is described as a superfluid flow.
Abstract: * Introduction * Experimental and Theoretical Background on He II. * Elementary Excitations * Elementary Excitations in He II * Superfulid Behavior: Response to a Transverse Probe. Qualitative Behavior of a Superfluid * Superfluid Flow: Macroscopic Limit * Basis for the Two-Fluid Model * First, Second, and Quasi-Particle sound * Vortex Lines * Microscopic Theory: Uniform Condensate * Microscopic Theory: Non-Uniform Condensate * Conclusion
2,717 citations
TL;DR: In this paper, the two-fluid model is used to describe the behavior of a superfluid in response to a transverse probe in a two-fluid model.
Abstract: Special Preface -- Preface -- Special Preface -- Preface -- Introduction -- Neutral Fermi Liquids -- Response and Correlation in Neutral Systems -- Charged Fermi Liquids -- Response and Correlation in Homogeneous Electron Systems -- Microscopic Theories of the Electron Liquid -- Introduction -- Experimental And Theoretical Background On He II -- Elementary Excitations -- Elementary Excitations in He II -- Superfluid Behavior: Response To A Transverse Probe. Qualitative Behavior Of A Superfluid -- Superfluid Flow: Macroscopic Limit -- Basis for the Two-Fluid Model -- First, Second, And Quasi-Particle Sound -- Vortex Lines -- Microscopic Theory: Uniform Condensate -- Microscopic Theory: Non-Uniform Condensate -- Conclusion -- * Second Quantization
2,494 citations
TL;DR: In this paper, the authors introduce a picture of a boson superfluid and show how superfluidity and Bose condensation manifest themselves, showing the excellent agreement between simulations and experimental measurements on liquid and solid helium for such quantities as pair correlations, the superfluid density, the energy, and the momentum distribution.
Abstract: One of Feynman's early applications of path integrals was to superfluid $^{4}\mathrm{He}$. He showed that the thermodynamic properties of Bose systems are exactly equivalent to those of a peculiar type of interacting classical "ring polymer." Using this mapping, one can generalize Monte Carlo simulation techniques commonly used for classical systems to simulate boson systems. In this review, the author introduces this picture of a boson superfluid and shows how superfluidity and Bose condensation manifest themselves. He shows the excellent agreement between simulations and experimental measurements on liquid and solid helium for such quantities as pair correlations, the superfluid density, the energy, and the momentum distribution. Major aspects of computational techniques developed for a boson superfluid are discussed: the construction of more accurate approximate density matrices to reduce the number of points on the path integral, sampling techniques to move through the space of exchanges and paths quickly, and the construction of estimators for various properties such as the energy, the momentum distribution, the superfluid density, and the exchange frequency in a quantum crystal. Finally the path-integral Monte Carlo method is compared to other quantum Monte Carlo methods.
1,908 citations
TL;DR: In this paper, the authors present a tutorial review of some ideas that are basic to our current understanding of Bose-Einstein condensation in the dilute atomic alkali gases, with special emphasis on the case of two or more coexisting hyperfine species.
Abstract: The author presents a tutorial review of some ideas that are basic to our current understanding of the phenomenon of Bose-Einstein condensation (BEC) in the dilute atomic alkali gases, with special emphasis on the case of two or more coexisting hyperfine species. Topics covered include the definition of and conditions for BEC in an interacting system, the replacement of the true interatomic potential by a zero-range pseudopotential, the time-independent and time-dependent Gross-Pitaevskii equations, superfluidity and rotational properties, the Josephson effect and related phenomena, and the Bogoliubov approximation.
1,695 citations