A comparative study of imaginary time path integral based methods for quantum dynamics

The recently introduced approximate many-body quantum simulation method, ring polymer molecular dynamics (RPMD), is compared to the centroid molecular dynamics method (CMD). Comparisons of simulation results for liquid para-hydrogen at two state points and liquid ortho-deuterium at one state point are presented. The calculated quantum correlation functions for the two methods are shown to be in good agreement with one another for a large portion of the time spectrum. However, as the quantum mechanical nature of the system increases, RPMD is less accurate in predicting the kinetic energy of the system than is CMD. A simplified and highly efficient algorithm is proposed which largely corrects this deficiency.     

Transport properties of normal liquid helium: comparison of various methodologies

We revisit the problem of self-diffusion in normal liquid helium above the lambda transition. Several different methods are applied to compute the velocity autocorrelation function. Since it is still impossible to determine the exact result for the velocity autocorrelation function from simulation, we appeal to the computation of short-time moments to determine the accuracy of the different approaches at short times. The main conclusion reached from our study is that both the quantum mode-coupling theory and the numerical analytic continuation approach must be regarded as a viable and competitive methods for the computation of dynamical properties of quantum systems.     

A centroid molecular dynamics study of liquid para-hydrogen and ortho-deuterium

Centroid molecular dynamics (CMD) is applied to the study of collective and single-particle dynamics in liquid para-hydrogen at two state points and liquid ortho-deuterium at one state point. The CMD results are compared with the results of classical molecular dynamics, quantum mode coupling theory, a maximum entropy analytic continuation approach, pair-product forward- backward semiclassical dynamics, and available experimental results. The self-diffusion constants are in excellent agreement with the experimental measurements for all systems studied. Furthermore, it is shown that the method is able to adequately describe both the single-particle and collective dynamics of quantum liquids.     

Comparison of approximate quantum simulation methods applied to normal liquid helium at 4 K

The Feynman-Kleinert linearized path integral molecular dynamics (FK-LPI), ring polymer molecular dynamics (RPMD), and centroid molecular dynamics (CMD) methods are applied to the simulation of normal liquid helium. Comparisons of the simulation results at the T = 4 K and rho = 0.01873 A-3 state point are presented. The calculated quantum correlation functions for the three methods show significant differences, both in the short time and in the intermediate regions of the spectrum. Our simulation results are also compared to the recent results of other approximate quantum simulation methods. We find that FK-LPI qualitatively agrees with other approximate quantum simulation results while CMD and RPMD predict a qualitatively different impulsive rebound in the velocity autocorrelation function. Frequency space analysis reveals that RPMD exhibits a broad high-frequency tail similar to that from quantum mode coupling theory and numerical analytic continuation approaches, while FK-LPI provides a somewhat more rapid decay at high frequency than any of these three methods. CMD manifests a high-frequency component that is greatly reduced compared with the other methods.     

A semiclassical study of the thermal conductivity of low temperature liquids

The conventional classical energy current auto-correlation function has been extended into a quantum mechanical version and then approximated by the linearized semiclassical initial value representation approach. Comparison of the thermal conductivity to simulation results shows that about 15% quantum correction to the classical molecular dynamics results for liquid neon are quantitatively predicted. For liquid para-hydrogen the quantum effects are sufficiently large that the linearized semiclassical approach is only 20% accurate, while for both liquid He(4) and He(3) the thermal conductivity disagrees by a factor of 2, although exchange effects appear to play a minor role.     

Symmetrized correlation function for liquid para-hydrogen using complex-time pair-product propagators

We present a simple and efficient method for calculating symmetrized time correlation functions of neat quantum fluids. Using the pair-product approximation to each complex-time quantum mechanical propagator, symmetrized correlation functions are written in terms of a double integral for each degree of freedom with a purely positive integrand. At moderate temperatures and densities, where the pair-product approximation to the Boltzmann operator is sufficiently accurate, the method leads to quantitative results for the early time part of the correlation function. The method is tested extensively on liquid para-hydrogen at 25 K and used to obtain accurate quantum mechanical results for the initial 0.2 ps segment of the symmetrized velocity autocorrelation function of this system, as well as the incoherent dynamic structure factor at certain momentum transfer values.     

Path integral methods for rotating molecules in superfluids

We present a path integral Monte Carlo (PIMC) methodology for quantum simulation of molecular rotations in superfluid environments such as helium and para-hydrogen that combines the sampling of rotational degrees of freedom for a molecular impurity with multilevel Metropolis sampling of Bose permutation exchanges for the solvating species. We show how the present methodology can be applied to the evaluation of imaginary time rotational correlation functions of the molecular impurity, from which the effective rotational constants can be extracted. The combined rotation/permutation sampling approach allows for the first time explicit assessment of the effect of Bose permutations on molecular rotation dynamics, and the converse, i.e., the effect of molecular rotations on permutation exchanges and local superfluidity. We present detailed studies showing that the effect of Bose permutations in the solvating environment is more significant for the dynamics of heavy than light molecules in helium, and that Bose permutation exchanges are slightly enhanced locally by molecular rotation. Finally, the examples studied here reveal a size dependence of rotational excitations for molecules possessing a strongly anisotropic interaction with helium in 4HeN clusters between N approximately 20 and N approximately 10(3).     

Polar solvation dynamics in supercritical fluids: a mode-coupling treatment

A mode-coupling treatment of polar solvation dynamics in supercritical fluids is presented. The equilibrium solvation time correlation function for the solute fluctuating transition frequency is obtained from the mode-coupling theory method and from molecular-dynamics simulations. The theory is shown to be in good agreement with the simulation. The solvation time correlation function exhibits three distinct time scales, with rapid initial decay, followed by a recurrence at intermediate times, and a slowly decaying long-time tail. Our theoretical analysis shows that the short-time decay arises from the coupling of the solute energy gap to the solvent polarization modes, the recurrence at intermediate times is due to the energy modes, while the slow long-time decay reflects the coupling to the number density modes.     

Thermal Gaussian molecular dynamics for quantum dynamics simulations of many-body systems: application to liquid para-hydrogen

A new method, here called thermal Gaussian molecular dynamics (TGMD), for simulating the dynamics of quantum many-body systems has recently been introduced [I. Georgescu and V. A. Mandelshtam, Phys. Rev. B 82, 094305 (2010)]. As in the centroid molecular dynamics (CMD), in TGMD the N-body quantum system is mapped to an N-body classical system. The associated both effective Hamiltonian and effective force are computed within the variational Gaussian wave-packet approximation. The TGMD is exact for the high-temperature limit, accurate for short times, and preserves the quantum canonical distribution. For a harmonic potential and any form of operator A?, it provides exact time correlation functions C(AB)(t) at least for the case of B, a linear combination of the position, x, and momentum, p, operators. While conceptually similar to CMD and other quantum molecular dynamics approaches, the great advantage of TGMD is its computational efficiency. We introduce the many-body implementation and demonstrate it on the benchmark problem of calculating the velocity time auto-correlation function for liquid para-hydrogen, using a system of up to N = 2592 particles.     

Computation of the properties of liquid neon, methane, and gas helium at low temperature by the Feynman-Hibbs approach

The properties of liquid methane, liquid neon, and gas helium are calculated at low temperatures over a large range of pressure from the classical molecular-dynamics simulations. The molecular interactions are represented by the Lennard-Jones pair potentials supplemented by quantum corrections following the Feynman-Hibbs approach. The equations of state, diffusion, and shear viscosity coefficients are determined for neon at 45 K, helium at 80 K, and methane at 110 K. A comparison is made with the existing experimental data and for thermodynamical quantities, with results computed from quantum numerical simulations when they are available. The theoretical variation of the viscosity coefficient with pressure is in good agreement with the experimental data when the quantum corrections are taken into account, thus reducing considerably the 60% discrepancy between the simulations and experiments in the absence of these corrections.     

Mode-coupling theory for reaction dynamics in liquids

A theory for chemical reaction dynamics in condensed phase systems based on the generalized Langevin formalism of Grote and Hynes [J. Chem. Phys. 73, 2715 (1980)] is presented. A microscopic approach to calculate the dynamic friction is developed within the framework of a combination of kinetic and mode-coupling theories. The approach provides a powerful analytic tool to study chemical reactions in realistic condensed phase environments. The accuracy of the approach is tested for a model isomerization reaction in a Lennard-Jones fluid. Good agreement is obtained for the transmission coefficient at different solvent densities, in comparison with numerical simulations based on the reactive-flux approach.     

Quantum mode-coupling theory for binary mixtures

We extend the quantum mode-coupling theory of neat liquids to the case of binary mixtures, in order to study supercooled liquids where quantum fluctuations may compete with thermal fluctuations. We apply the theory to a generic model of a binary mixture of Lennard-Jones particles. Our treatment may be used to study quantum aging and exotic glass melting scenarios in structural supercooled quantum liquids.     

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

The linearized approximation to the semiclassical initial value representation (LSC-IVR) is used to calculate time correlation functions relevant to the incoherent dynamic structure factor for inelastic neutron scattering from liquid para-hydrogen at 14 K. Various time correlations functions were used which, if evaluated exactly, would give identical results, but they do not because the LSC-IVR is approximate. Some of the correlation functions involve only linear operators, and others involve nonlinear operators. The consistency of the results obtained with the various time correlation functions thus provides a useful test of the accuracy of the LSC-IVR approximation and its ability to treat correlation functions involving both linear and nonlinear operators in realistic anharmonic systems. The good agreement of the results obtained from different correlation functions, their excellent behavior in the spectral moment tests based on the exact moment constraints, and their semiquantitative agreement with the inelastic neutron scattering experimental data all suggest that the LSC-IVR is indeed a good short-time approximation for quantum mechanical correlation functions.     

Quantum fluctuations increase the self-diffusive motion of para-hydrogen in narrow carbon nanotubes

Quantum fluctuations significantly increase the self-diffusive motion of para-hydrogen adsorbed in narrow carbon nanotubes at 30 K comparing to its classical counterpart. Rigorous Feynman's path integral calculations reveal that self-diffusive motion of para-hydrogen in a narrow (6,6) carbon nanotube at 30 K and pore densities below ～29 mmol cm(-3) is one order of magnitude faster than the classical counterpart. We find that the zero-point energy and tunneling significantly smoothed out the free energy landscape of para-hydrogen molecules adsorbed in a narrow (6,6) carbon nanotube. This promotes a delocalization of the confined para-hydrogen at 30 K (i.e., population of unclassical paths due to quantum effects). Contrary the self-diffusive motion of classical para-hydrogen molecules in a narrow (6,6) carbon nanotube at 30 K is very slow. This is because classical para-hydrogen molecules undergo highly correlated movement when their collision diameter approached the carbon nanotube size (i.e., anomalous diffusion in quasi-one dimensional pores). On the basis of current results we predict that narrow single-walled carbon nanotubes are promising nanoporous molecular sieves being able to separate para-hydrogen molecules from mixtures of classical particles at cryogenic temperatures.     

Non-markovian theory of diffusion-controlled excitation transfer

The non-markovian encounter theory is extended to kinetic calculations of an exciton (electron) contact transfer between an energy (charge) donor and acceptor. This process is shown to be non-stationary from the beginning to the end if the donor state relaxation time is shorter than the encounter time. The theory is applied to calculations of hot luminescence quantum yield in liquid solutions with a quenching impurity.     

Connection between the observable and centroid structural properties of a quantum fluid: application to liquid para-hydrogen

It is shown that the discrepancy between path integral Monte Carlo [M. Zoppi et al., Phys. Rev. B 65, 092204 (2002)] and path integral centroid molecular dynamics [F. J. Bermejo et al., Phys. Rev. Lett. 84, 5359 (2000)] calculations of the static structure factor of liquid para-hydrogen can be explained based on a deconvolution equation connecting centroid and physical radial distribution functions. An explicit expression for the kernel of the deconvolution equation has been obtained using functional derivative techniques. In the superposition approximation, this kernel is given by the functional derivative of the effective potential with respect to the pairwise classical potential. Results of path integral Monte Carlo calculations for the radial distribution function and the static structure factor of liquid para-hydrogen are presented.     

Fragmentation of ionized doped helium nanodroplets: theoretical evidence for a dopant ejection mechanism

We report a theoretical study of the effect induced by a helium nanodroplet environment on the fragmentation dynamics of a dopant. The dopant is an ionized neon cluster Ne(n) (+) (n=4-6) surrounded by a helium nanodroplet composed of 100 atoms. A newly designed mixed quantum/classical approach is used to take into account both the large helium cluster zero-point energy due to the light mass of the helium atoms and all the nonadiabatic couplings between the Ne(n) (+) potential-energy surfaces. The results reveal that the intermediate ionic dopant can be ejected from the droplet, possibly with some helium atoms still attached, thereby reducing the cooling power of the droplet. Energy relaxation by helium atom evaporation and dissociation, the other mechanism which has been used in most interpretations of doped helium cluster dynamics, also exhibits new features. The kinetic energy distribution of the neutral monomer fragments can be fitted to the sum of two Boltzmann distributions, one with a low kinetic energy and the other with a higher kinetic energy. This indicates that cooling by helium atom evaporation is more efficient than was believed so far, as suggested by recent experiments. The results also reveal the predominance of Ne(2) (+) and He(q)Ne(2) (+) fragments and the absence of bare Ne(+) fragments, in agreement with available experimental data (obtained for larger helium nanodroplets). Moreover, the abundance in fragments with a trimeric neon core is found to increase with the increase in dopant size. Most of the fragmentation is achieved within 10 ps and the only subsequent dynamical process is the relaxation of hot intermediate He(q)Ne(2) (+) species to Ne(2) (+) by helium atom evaporation. The dependence of the ionic fragment distribution on the parent ion electronic state reached by ionization is also investigated. It reveals that He(q)Ne(+) fragments are produced only from the highest electronic state, whereas He(q)Ne(2) (+) fragments originate from all the electronic states. Surprisingly, the highest electronic states also lead to fragments that still contain the original ionic dopant species. A mechanism is conjectured to explain this fragmentation inhibition.