Computation of Dynamic Polarizabilities and van der Waals Coefficients from Path-Integral Monte Carlo

Abstract

We demonstrate computation of total dynamic multipole polarizabilities using path-integral Monte Carlo method (PIMC). The PIMC approach enables accurate thermal and nonadiabatic mixing of electronic, rotational, and vibrational degrees of freedom. Therefore, we can study the thermal effects, or lack thereof, in the full multipole spectra of the chosen one- and two-electron systems: H, Ps, He, Ps2, H2, and HD+. We first compute multipole–multipole correlation functions up to octupole order in imaginary time. The real-domain spectral function is then obtained by analytical continuation with the maximum entropy method. In general, sharpness of the active spectra is limited, but the obtained off-resonant polarizabilities are in good agreement with the existing literature. Several weak and strong thermal effects are observed. Furthermore, the polarizabilities of Ps2 and some higher multipole and higher frequency data have not been published before. In addition, we compute isotropic dispersion coefficients C 6, C 8, and C 10 between pairs of species using the simplified Casimir–Polder formulas.

Path Integrals: From Quantum Mechanics to Photonics

“…There, however, only very simple systems were studied, such as the hydrogen (H) and hydrogen-like (Li + and Be + 2 ) atoms, the helium atoms He and He + , the hydrogen molecule H 2 and H + 2 , hydrogenhelium (HeH + ) and hydrogen-deuterium (HD + ) molecules, and the positronium atom. These systems have been studied employing different methods, including finite-field simulations for static polarisabilities 64 , polarisability estimators for simulation without the external field 73 , static field-gradient polarisabilities 65 , and finally, dynamic polarisabilities and van der Waals coefficients 72 . The last one, in particular, is of great interest, as the macroscopic electric susceptibility is constructed starting from the dynamic frequency dependent polarisabilities.…”

“…7) and one small (dotted green and blue lines in Fig. 7), to rule out possible numerical artefacts 72 . The results have been then compared with polarisability data available in literature, and obtained using a T = 0 K approach, with methods other than PIMC 108 .…”

“…In recent years, one of the authors of this tutorial (TTR) has significantly contributed to taking PIMC simulations to new though simple quantum particle systems, such as small atoms 60,61 , molecules [62][63][64][65] , a chemical reaction 66 and quantum dots [67][68][69] , with the ultimate goal of providing a more accurate description of their electronic structure and related properties including many-body effects, and how they change with temperature 61,70,71 . In this context, PIMC has proven to be a very reliable and excellent method to calculate the electric polarisabilities of atomic and molecular systems, leading therefore to an accurate estimation of the optical properties of both individual small quantum systems and collections of them, in the form of dilute gases 65,72,73 .…”

“…A different approach, based on a real, rather than imaginary, time path integral (RTPI) has been recently proposed as a way to describe the full quantum dynamics of a quantum system at zero-Kelvin, and to also characterise the evolution of its eigenstates 68,72,[74][75][76][77] . A combination of PIMC and RTPI therefore gives the possibility to have a comprehensive tool to study the properties of complex systems and their classical and quantum evolution.…”

Diamagnetic susceptibility from a nonadiabatic path-integral simulation of few-electron systems

“…The PIMC approach enables statistically exact simulation of thermal density matrices [15] but also various response properties [16][17][18] of real few-body Coulomb systems, as long as the particles are distinguishable. Much larger systems [21] with indistinguishable fermions can also be simulated exactly, but only with exponentially decreasing numerical efficiency.…”