Simulation of dynamical properties of normal and superfluid helium

Abstract

The formation of a superfluid when 4 He 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.semiclassical dynamics ͉ forward-backward ͉ Bose-Einstein condensation ͉ time correlation function ͉ incoherent structure factor T he remarkable properties of superfluids, in particular the observed frictionless flow and heat conduction without a temperature gradient, have fascinated scientists for several decades (1-5). Liquid 4 He has for long served as the paradigm of superfluidity, and the unusual properties of this system around and below the characteristic lambda transition temperature have been the subject of persistent experimental and theoretical investigations. Superfluidity is intimately connected with Bose-Einstein condensation (6, 7) (BEC), but many questions still surround their relationship. A number of experimental properties of superfluid 4 He are consistent with theoretical descriptions that assume the presence of BEC. However, direct observation of BEC in this system has been elusive, owing primarily to strong repulsive interactions associated with the closed-shell electronic structure of 4 He.Theoretical and computational studies have yielded a wealth of information regarding the momentum distribution of superfluid 4 He, from which one can extract the fraction of particles in the zero momentum state (8, 9). These works, the majority of which are based on quantum mechanical simulations such as quantum Monte Carlo (10-14) and path integral Monte Carlo (15) methods, estimate the condensate fraction to be Ϸ7% at saturated vapor pressure (SVP) (12)(13)(14)(15). Experimental studies of these properties are largely based on inelastic neutron scattering measurements (16). At small values of momentum transfer, the differential cross section obtained from these experiments displays characteristics associated with collective response (with a sharp peak that follows the well known phonon-maxon-roton dispersion curve) (3-5, 17, 18). On the other ha...

Test of the consistency of various linearized semiclassical initial value time correlation functions in application to inelastic neutron scattering from liquid para-hydrogen

“…It will be interesting to apply the LSC-IVR to complex systems at even lower temperature (such as normal and superfluid liquid He) where quantum effects are more pronounced, to see how well the Gaussian approximation (Eq. (2.10)) works 52,121 , and its comparison with the direct calculation of the incoherent dynamic structure factor using Eq. (2.6) and also with experimental data [121][122][123][124][125][126] .…”

“…The classical Wigner model is an old idea, but it is important to realize that it is contained within the SC-IVR approach, as a well-defined approximation to it 28,29 . There are other ways to derive the classical Wigner model (or one may simply postulate it) 9,35,40,41 , and we also note that the 'forward-backward semiclassical dynamics' (FBSD) approximation of Makri et al 32,[42][43][44][45][46][47][48][49][50][51][52][53][54][55][56] is very similar to it. The LSC-IVR/classical Wigner model cannot describe true quantum coherence effects in time correlation functions-more accurate SC-IVR approaches, such as the Fourier transform forward-backward IVR (FB-IVR) approach 22,57 (or the still more accurate generalized FB-IVR 58 ) of Miller et al, are needed for this-but it does describe some aspects of the quantum dynamics very well 26,[30][31][32]34,[59][60][61][62] .…”

Linearized semiclassical initial value time correlation functions using the thermal Gaussian approximation: Applications to condensed phase systems

“…The classical Wigner model is an old idea, but it is important to realize that it is contained within the SC-IVR approach, as a well-defined approximation to it. There are other ways to derive the classical Wigner model (or one may simply postulate it) [28][29][30][31] , and we also note that the 'forward-backward semiclassical dynamics' (FBSD) approximation of Makri et al [32][33][34][35][36][37][38][39] is very similar to it. The LSC-IVR/classical Wigner model cannot describe true quantum coherence effects in time correlation functions-more accurate SC-IVR approaches, such as the Fourier transform forward-backward IVR (FB-IVR) approach 40,41 ( 23 .…”

Linearized semiclassical initial value time correlation functions with maximum entropy analytic continuation

“…The classical Wigner model is an old idea, but it is important to realize that it is contained within the SC-IVR approach, as a well-defined approximation to it 39,40 . There are other ways to derive the classical Wigner model (or one may simply postulate it) 6,44,49,50 , and we also note that the 'forward-backward semiclassical dynamics' (FBSD) approximation of Makri et al 24,[28][29][30][51][52][53][54][55][56][57][58][59][60][61][62] is very similar to it. The LSC-IVR/classical Wigner model cannot describe true quantum coherence effects in time correlation functions-more accurate SC-IVR approaches, such as the Fourier transform forward-backward IVR (FB-IVR) approach 22,63 , or the still more accurate generalized FB-IVR 64 and exact FB-IVR 5 of Miller et al , are needed for this-but it does describe some aspects of the quantum dynamics very well [24][25][26][34][35][36][37][38]41,42,[65][66][67] .…”

“…The SC-IVR provides a way for generating the quantum time evolution operator (propagator) by computing an ensemble of classical trajectories, much as is done in standard classical MD simulations. As is well known from SC developments in the early 1970's 1,[18][19][20][21] , such approaches actually contain all quantum effects at least qualitatively, and in molecular systems the description is usually quite quantitative (see reviews [2][3][4][5]14,22,23 and some recent applications [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] ).…”