We propose a new Brownian bridge construction for our newly devised Coherent States Path Integral Monte Carlo algorithm. We apply it to the numerically exact calculation of the thermodynamic properties of the Helium fluid on a plane at low non zero temperature. We find very good agreement with the conventional plane waves path integral Monte Carlo results.
We propose a new Brownian bridge construction for our newly devised Coherent States Path Integral Monte Carlo algorithm. We apply it to the numerically exact calculation of the thermodynamic properties of the Helium fluid on a plane at low non zero temperature. We find very good agreement with the conventional plane waves path integral Monte Carlo results.
By using exact path-integral Monte Carlo methods we calculate the equation of state of an interacting Bose gas as a function of temperature both below and above the superfluid transition. The universal character of the equation of state for dilute systems and low temperatures is investigated by modeling the interatomic interactions using different repulsive potentials corresponding to the same s-wave scattering length. The results obtained for the energy and the pressure are compared to the virial expansion for temperatures larger than the critical temperature. At very low temperatures we find agreement with the ground-state energy calculated using the diffusion Monte Carlo method.
Below Tλ = 2.17 K, bulk 4He is a superfluid and has a non-zero Bose-Einstein condensate fraction. This work will focus primarily on how phenomena such as superfluidity, Bose condensation and superfluid vortices are manifested in microscopic, inhomogeneous helium systems. Path Integral Monte Carlo is a powerful method for calculating the equilibrium properties of quantum systems at finite temperature. We have achieved linear scaling of computer time with number of particles through the use of neighbor lists, allowing us to simulate systems of several thousand atoms. We have derived a local superfluid estimator and used it to examine the microscopic superfluid response around a molecule rotating in a helium nanodroplet. We found that the first solvation layer is well-described by a two dimensional superfluid, with thermal excitations occuring at a lower temperature than in bulk helium. The effective moment of inertia of a linear impurity in a helium droplet is calculated, and compared with experimental scattering results. In addition, we calculated the vortex formation energy for both pure droplets and droplets doped with linear impurities, and found that the linear impurities had a negligible impact on the formation energy. A possible spectroscopic signature of vortices in doped helium droplets was suggested. After deriving a local estimator, we calculated the condensate fraction throughout the free helium surface of a semi-infinite slab. These results, along with densitydensity correlation functions, were used to characterize the surface excitations and calculate the extent to which ripplons are present. In addition, the ripplon dispersion relation was calculated using imaginary-time correlation functions, and found to be lll in good agreement with experimental results. Finally, we have calculated the Dey be-Waller factor in solid helium for a range of temperatures and densities, and compared the scaling behavior with the predictions of harmonic theory. The first non-Gaussian contribution to the density distribution was calculated.
A novel path integral Monte Carlo (PIMC) approach for correlated many-particle systems with arbitrary pair interaction in continuous space at low temperatures is presented. It is based on a representation of the N -particle density operator in a basis of (anti-)symmetrized N -particle states (configurations of occupation numbers). The path integral is transformed into a sum over trajectories with the same topology and, finally, the limit of M →∞ , where M is the number of high-temperature factors, is analytically performed. This yields exact expressions for the thermodynamic quantities and allows to perform efficient simulations for fermions at low temperature and weak to moderate coupling. Our method is expected to be applicable to dense quantum plasmas in the regime of strong degeneracy where conventional PIMC fails due to the fermion sign problem. c
We study the quantum dynamics of a generic model fluid with internal quantum states and classical translational degrees of freedom in two spatial dimensions. The path integral Monte Carlo data for the imaginary time correlation functions are presented and analyzed by the maximum entropy method. A comparison of the frequency distribution with those of a mean field approximation and virial expansion shows good agreement at high and low densities, respectively. \textcopyright{} 1996 The American Physical Society.
Several microscopic theories point out that Bose-Einstein condensation (BEC), i.e., a macroscopic occupation of the lowest energy single particle state in many-boson systems, may appear also in quantum fluids and solids and that it is at the origin of the phenomenon of superfluidity. Nevertheless, the connection between BEC and superfluidity is still matter of debate, since the experimental evidences indicating a non zero condensate fraction in superfluid helium are only indirect. In the theoretical study of BEC in quantum fluids and solids, perturbative approaches are useless because of the strong correlations between the atoms, arising both from the interatomic potential and from the quantum nature of the system. Microscopic Quantum Monte Carlo simulations provide a reliable description of these systems. In particular, the Path Integral Monte Carlo (PIMC) method is very suitable for this purpose. This method is able to provide exact results for the properties of the quantum system, both at zero and finite temperature, only with the definition of the Hamiltonian and of the symmetry properties of the system, giving an easy picture for superfluidity and BEC in many-boson systems. In this thesis, we apply PIMC methods to the study of several quantum fluids and solids. We describe in detail all the features of PIMC, from the sampling methods to the estimators of the physical properties. We present also the most recent techniques, such as the high-order approximations for the thermal density matrix and the worm algorithm, used in PIMC to provide reliable simulations. We study the liquid phase of condensed 4He, providing unbiased estimations of the one-body density matrix g1(r). We analyze the model for g1(r) used to fit the experimental data, highlighting its merits and its faults. In particular we see that, even if it presents some difficulties in the description of the overall behavior of g1(r), it can provide an accurate estimation of the kinetic energy K and of the condensate fraction n0 of the system. Furthermore, we show that our results for n0 as a function of the pressure are in a good agreement with the most recent experimental results. The study of the solid phase of 4He is the most significant part of this thesis. The recent observation of non classical rotational inertia (NCRI) effects in solid helium has generated big interest in the study of an eventual supersolid phase, characterized at the same time by crystalline order and superfluidity. Nevertheless, until now it has been impossible to give a theoretical model able to describe all the experimental evidences. In this work, we perform PIMC simulations of 4He at high densities, according to different microscopic configurations of the atoms. In commensurate crystals we see that BEC does not appear, our model being able to reproduce the momentum distribution obtained form neutron scattering experiments. In a crystal with vacancies, we have been able to see a transition to a superfluid phase at temperatures in agreement with experimental results if the vacancy concentration is low enough. In amorphous solids, superfluid effects are enhanced but appear at temperatures higher than the experimental estimation for the transition temperature. Finally, we study also metastable disordered configurations in molecular para-hydrogen at low temperature. The aim of this study is to investigate if a Bose liquid other than helium can display superfluidity. Choosing accurately a ¿quantum liquid¿ initial configuration and the dimensions of the simulation box, we have been able to frustrate the formation of the crystal and to calculate the temperature dependence of the superfluid density, showing a transition to a superfluid phase at temperatures close to 1 K.
It is shown from first principles that, in spite of the large interatomic forces, liquid 4 He should exhibit a transition analogous to the transition in an ideal Bose–Einstein gas. The exact partition function is written as an integral over trajectories, using the space-time approach to quantum mechanics. R.P. Feynman, 1953 Summary In this chapter we discuss imaginary-time path integrals and the path-integral Monte Carlo method for the calculation of properties of quantum systems at non-zero temperature. We discuss how Fermi and Bose statistics enter, and how to generalize the fixed-node procedure to non-zero temperature. We then discuss an auxiliary-field method for the Hubbard model. The path-integral method can be used to perform ground-state calculations, allowing calculations of properties with less bias than the projector Monte Carlo method. We also discuss the problem of estimating real-time response functions using information from imaginary-time correlation functions. In previous chapters we described two QMC methods, namely variational QMC and projector (diffusion) QMC. Both of these methods are zero temperature, or, more properly, are formulated for single states. In this chapter we discuss the path-integral Monte Carlo (PIMC) method, which is explicitly formulated at non-zero temperature. Directly including temperature is important because many, if not most, measurements and practical applications involve significant thermal effects. One might think that to do calculations at a non-zero temperature we would have to explicitly sum over excited states. Such a summation would be difficult to accomplish once the temperature is above the energy gap, because there are so many possible many-body excitations. In addition, the properties for each excitation are more difficult to calculate than those for the ground state. As we will see, path-integral methods do not require an explicit sum over excitations. As an added bonus, they provide an interesting and enlightening window through which to view quantum systems. However, the sign problem, introduced in the previous chapter, is still present for fermion systems. The fixed-node approximation is used again. An advantage of PIMC is the absence of a trial wavefunction. As a result, quantum expectation values, including ones not involving the energy, can be computed directly. For the expert, the lack of an importance function may seem a disadvantage; without it one cannot push the simulation in a preferred direction.