arXiv subjects

Giovanni Garberoglio

Publications and source records attributed to Giovanni Garberoglio.

At least 19 recordsLinked to original sources

arXiv2026

Determination of fundamental properties of nitrogen from first principles. III. Temperature and frequency dependence of the molecular polarizability and magnetic susceptibility

This work is the third part of the series of papers that focus on the theoretical determination of the properties of nitrogen that are relevant in metrology. Here we present first-principles calculations of the temperature and frequency dependence of the molecular polarizability and magnetic susceptibility of the nitrogen molecule (N$_2$). The purely electronic contributions to the static polarizability, Cauchy coefficients (up to sixth order), and isotropic magnetic susceptibility are computed over a range of internuclear distances using a robust composite scheme combining several electronic structure methods. The temperature dependence, evaluated from $50$~K to $2000$~K, is determined using two independent methods: rovibrational averaging and path integral Monte Carlo (PIMC). The polarizabilities obtained from theory agree with the recent high-precision thermometry measurements, wherever the latter are available, but are significantly less accurate. However, the main usefulness of the theoretical data revolves around combining it with the available experimental results to generate semi-empirical estimates of various quantities that have never been measured thus far. As an example, we determine highly accurate semi-empirical estimates of the static polarizability at key reference temperatures, $α_0(T)=11.735\,962$~a.u.\ at $T=303$~K and $α_0(T)=11.735\,585$~a.u.\ at $T=273.16$~K. Furthermore, we report theoretical values for the magnetic susceptibility, highlighting the importance of the paramagnetic contribution, and address a significant discrepancy with the experimental data for this quantity.

physics.chem-ph↗

arXiv2026

Recommended Second Virial Coefficients for Nitrogen and Oxygen

We provide recommended values for the second virial coefficient, $B(T)$, and its uncertainty, for molecular nitrogen and oxygen. The temperature range covered is $20-3000$ K for nitrogen and $20-2000$ K for oxygen. The recommendations are based on tuning previously published state-of-the-art ab initio pair potentials so that the $B(T)$ calculated from the potentials match selected high-accuracy experimental data; for nitrogen the tuning utilizes values of $B$ derived from literature density data with greatly reduced uncertainty by analyzing the data with the aid of ab initio calculated higher virial coefficients. Quantum effects on $B$ are fully included with the path-integral Monte Carlo method. The resulting $B(T)$ have uncertainties similar to those of the best experimental data, but cover a much wider temperature range.

physics.chem-ph↗

arXiv2026

Third and fourth density and acoustic virial coefficients of neon from first-principles calculations

The third and fourth density and acoustic virial coefficients of neon were determined at temperatures between 10 and 5000 K from first principles employing the path-integral Monte Carlo (PIMC) approach. For these calculations, we used the pair potential of Hellmann $\textit{et al.}$ [J. Chem. Phys. 154, 164304 (2021)], which is based on supermolecular $\textit{ab initio}$ calculations with basis sets of up to octuple-zeta quality and levels of theory up to coupled cluster with single, double, triple, quadruple, and perturbative pentuple excitations [CCSDTQ(P)]. The potential also accounts for relativistic, retardation, and post-Born$-$Oppenheimer effects and is provided with reliable uncertainty estimates. To incorporate nonadditive interactions, we developed a nonadditive three-body potential based on extensive supermolecular CCSD(T), CCSDT, and CCSDT(Q) calculations with basis sets of up to sextuple-zeta quality. This potential also accounts for relativistic effects. The very small nonadditive four-body contributions to the fourth virial coefficients were considered using a relatively simple nonadditive four-body potential based on supermolecular CCSD(T) calculations. We calculated the third and fourth density and third acoustic virial coefficients directly by PIMC and the fourth acoustic virial coefficient indirectly using thermodynamic relations between the density and acoustic virial coefficients. The uncertainties of the pair potential and those estimated for our nonadditive three-body potential were rigorously propagated in the PIMC calculations into uncertainties for the virial coefficients. These uncertainties are distinctly smaller than those of almost all of the corresponding experimental virial coefficient data.

physics.chem-ph↗

arXiv2025

Study of the uniform electron gas through parametrized partition functions

We investigate the energy per particle, static structure factor, and momentum distribution of the uniform electron gas for different conditions defined by the dimensionless temperature $Θ= 0.25 - 1.0$ and average interparticle distance $r_s = 0.5 - 80.0$ using path-integral Monte Carlo (PIMC) simulations. For small $r_\text{s}$ ($r_\text{s}\leq10$) where the sign problem is particularly challenging, we employ a recent approach based on an analytic continuation of the partition function using a real parameter $ξ$, which allows a generalization from bosons ($ξ=1$) to fermions ($ξ=-1$). We show that the results are in good agreement with other state-of-the-art methods while requiring low computational resources. For large $r_\text{s}$ ($r_\text{s}=80$), we use direct PIMC exploiting the good behaviour of the thermodynamic properties for negative $ξ$. In this framework we demonstrate that, for large $r_s$, the small negative region of $ξ$ can be utilized to extract information about the true fermionic limit, where $ξ= -1$.

cond-mat.mtrl-sci↗

arXiv2025

Experimental verification of Threshold Quantum State Tomography on a fully-reconfigurable photonic integrated circuit

Reconstructing the state of a complex quantum system represents a pivotal task for all quantum information applications, both for characterization purposes and for verification of quantum protocols. Recent technological developments have shown the capability of building quantum systems with progressively larger number of qubits in different platforms. The standard approach based on quantum state tomography, while providing a method to completely characterize an unknown quantum state, requires a number of measurements that scales exponentially with the number of qubits. Other methods have been subsequently proposed and tested to reduce the number of measurements, or to focus on specific properties of the output state rather than on its complete reconstruction. Here, we show experimentally the application of an approach, called threshold quantum state tomography, in an advanced hybrid photonic platform with states up to n=4 qubits. This method does not require a priori knowledge on the state, and selects only the informative projectors starting from the measurement of the density matrix diagonal. We show the effectiveness of this approach in a photonic platform, showing that a consistent reduction in the number of measurement is obtained while reconstructing relevant states for quantum protocols, with only very limited loss of information. The advantage of this protocol opens perspective of its application in larger, more complex, systems.

quant-ph↗

arXiv2025

Enhanced Compressive Threshold Quantum State Tomography for Qudit Systems

We propose an efficient quantum state tomography method inspired by compressed sensing and threshold quantum state tomography that can drastically reduce the number of measurement settings to reconstruct the density matrix of an $N$-qudit system. We validate our algorithm with simulations on IBMQ and demonstrate the efficient and accurate reconstruction of $N\leq7$ qubit systems, reproducing GHZ, $W$, and random states with $O(1)$, $O(N^2)$, and $O(N)$ settings.

quant-ph↗

arXiv2025

Normal liquid $^3$He studied by Path Integral Monte Carlo with a parametrized partition function

We compute the energy per particle of normal liquid ${}^3$He in the temperature range $0.15-2$ K using Path Integral Monte Carlo simulations, leveraging a recently proposed method to overcome the sign problem -- a long-standing challenge in many-body fermionic simulations. This approach is based on introducing a parameter $ξ$ into the partition function, which allows a generalization from bosons ($ξ=1$) to fermions ($ξ=-1$). By simulating systems with $ξ\geq 0$, where the sign problem is absent, one can then extrapolate to the fermionic case at $ξ= -1$. Guided by an independent particle model that uncovers non-analytic behavior due to the superfluid transition, which is moderated by finite-size effects, we develop a tailored extrapolation strategy for liquid ${}^3$He that departs from the extrapolation schemes shown to be accurate in those cases were quantum degeneracy effects are weak, and enables accurate results in the presence of Bose-Einstein Condensation and superfluidity for $ξ> 0$. Our approach extends the previously proposed framework and yields energy per particle values in good agreement with experimental data.

cond-mat.quant-gas↗

arXiv2025

Revisiting the properties of superfluid and normal liquid ${}^4$He using ab initio potentials

We investigate the properties of liquid ${}^4$He in both the normal and superfluid phases using path integral Monte Carlo simulations and recently developed ab initio potentials that incorporate pair, three-body, and four-body interactions. By focusing on the energy per particle as a representative observable, we use a perturbative approach to quantify the individual contributions of the many-body potentials and systematically propagate their associated uncertainties. Our findings indicate that the three-body and four-body potentials contribute to the total energy by approximately 4% and 0.4%, respectively. However, the primary limitation in achieving highly accurate first-principles calculations arises from the uncertainty in the four-body potential, which currently dominates the propagated uncertainty. In addition to the energy per particle, we analyze other key observables, including the superfluid fraction, condensed fraction, and pair distribution function, all of which demonstrate excellent agreement with experimental measurements.

cond-mat.other↗

arXiv2024

Path-integral calculation of the third dielectric virial coefficient of helium based on ab initio three-body polarizability and dipole surfaces

We develop a surface for the electric dipole moment of three interacting helium atoms and use it, together with state-of-the-art potential and polarizability surfaces, to compute the third dielectric virial coefficient, $C_\varepsilon$, for both $^4$He and $^3$He isotopes. Our results agree with previously published data computed using an approximated form for the three-body polarizability, and are extended to the low-temperature regime by including exchange effects. Additionally, the uncertainty of $C_\varepsilon$ is rigorously determined for the first time by propagating the uncertainties of the potential and polarizability surfaces; this uncertainty is much larger than the contribution from the dipole-moment surface to $C_\varepsilon$. Our results compare reasonably well with the limited experimental data. The first-principles values of $C_ε$ computed in this work will enhance the accuracy of primary temperature and pressure metrology based on measurements of the dielectric constant of helium.

physics.chem-ph↗

arXiv2024

A Tailor-made Quantum State Tomography Approach

Quantum state tomography (QST) aims at reconstructing the state of a quantum system. However in conventional QST the number of measurements scales exponentially with the number of qubits. Here we propose a QST protocol, in which the introduction of a threshold allows one to drastically reduce the number of measurements required for the reconstruction of the state density matrix without compromising the result accuracy. In addition, one can also use the same approach to reconstruct an approximated density matrix depending on the available resources. We experimentally demonstrate this protocol by performing the tomography of states up to 7 qubits. We show that our approach can lead to the same accuracy of QST even when the number of measurements is reduced by more than two orders of magnitudes.

quant-ph↗

arXiv2024

Third density and acoustic virial coefficients of helium isotopologues from ab initio calculations

Improved two-body and three-body potentials for helium have been used to calculate from first principles the third density and acoustic virial coefficients for both $^4$He and $^3$He. For the third density virial coefficient $C(T)$, uncertainties have been reduced by a factor of 4--5 compared to the previous state of the art; the accuracy of first-principles $C(T)$ now exceeds that of the best experiments by more than two orders of magnitude. The range of calculations has been extended to temperatures as low as 0.5~K. For the third acoustic virial coefficient $γ_a(T)$, we applied the Schlessinger Point Method, which can calculate $γ_a$ and its uncertainty based on the $C(T)$ data, overcoming some limitations of direct path-integral calculation. The resulting $γ_a$ are calculated at temperatures down to 0.5~K; they are consistent with available experimental data but have much smaller uncertainties. The first-principles data presented here will enable improvement of primary temperature and pressure metrology based on gas properties.

physics.chem-ph↗

arXiv2023

Comprehensive Quantum Calculation of the First Dielectric Virial Coefficient of Water

We present a complete calculation, fully accounting for quantum effects and for molecular flexibility, of the first dielectric virial coefficient of water and its isotopologues. The contribution of the electronic polarizability is computed from a state-of-the-art intramolecular potential and polarizability surface from the literature, and its small temperature dependence is quantified. The dipolar polarizability is calculated in a similar manner with an accurate literature dipole-moment surface; it differs from the classical result both due to the different molecular geometries sampled at different temperatures and due to the quantization of rotation. We calculate the dipolar contribution independently from spectroscopic information in the HITRAN2020 database and find that the two methods yield consistent results. The resulting first dielectric virial coefficient provides a complete description of the dielectric constant at low density that can be used in humidity metrology and as a boundary condition for new formulations for the static dielectric constant of water and heavy water.

physics.chem-ph↗

arXiv2023

Ab initio Calculation of Fluid Properties for Precision Metrology

Recent advances regarding the interplay between ab initio calculations and metrology are reviewed, with particular emphasis on gas-based techniques used for temperature and pressure measurements. Since roughly 2010, several thermophysical quantities - in particular, virial and transport coefficients - can be computed from first principles without uncontrolled approximations and with rigorously propagated uncertainties. In the case of helium, computational results have accuracies that exceed the best experimental data by at least one order of magnitude and are suitable to be used in primary metrology. The availability of ab initio virial and transport coefficients contributed to the recent SI definition of temperature by facilitating measurements of the Boltzmann constant with unprecedented accuracy. Presently, they enable the development of primary standards of temperature in the range 2.5-552 K and pressure up to 7 MPa using acoustic gas thermometry, dielectric constant gas thermometry, and refractive index gas thermometry. These approaches will be reviewed, highlighting the effect of first-principles data on their accuracy. The recent advances in electronic structure calculations that enabled highly accurate solutions for the many-body interaction potentials and polarizabilities of atoms - particularly helium - will be described, together with the subsequent computational methods, most often based on quantum statistical mechanics and its path-integral formulation, that provide thermophysical properties and their uncertainties. Similar approaches for molecular systems, and their applications, are briefly discussed. Current limitations and expected future lines of research are assessed.

cond-mat.stat-mech↗

arXiv2023

Three-body potential and third virial coefficients for helium including relativistic and nuclear-motion effects

The non-additive three-body interaction potential for helium was computed using the coupled-cluster theory and the full configuration interaction method. The obtained potential comprises an improved nonrelativistic Born--Oppenheimer energy and the leading relativistic and nuclear-motion corrections. The mean absolute uncertainty of our calculations due to the incompleteness of the orbital basis set was determined employing complete-basis-set extrapolation techniques and was found to be 1.2%. For three helium atoms forming an equilateral triangle with the side length of 5.6~bohr our three-body potential amounts to $-$90.6~mK, with an estimated uncertainty of 0.5~mK. An analytic function, developed to accurately fit the computed three-body interaction energies, was chosen to correctly describe the asymptotic behavior of the three-body potential for trimer configurations corresponding to both the three-atomic and the atom-diatom fragmentation channels. For large triangles with sides $r_{12}$, $r_{23}$, and $r_{31}$, the potential takes correctly into account all angular terms decaying as $r_{12}^{-l} r_{23}^{-m} r_{31}^{-n}$ with $l+m+n \le 14$ for the nonrelativistic Born--Oppenheimer energy and $l+m+n \le 9$ for the post-Born--Oppenheimer corrections. We also developed a short-range analytic function describing the local behavior of the total uncertainty of the computed three-body interaction energies. Using both fits we calculated the third pressure and acoustic virial coefficients for helium and their uncertainties for a wide range of temperatures. The results of these calculations were compared with available experimental data and with previous theoretical determinations. The estimated uncertainties of present calculations are 3-5 times smaller than those reported in the best previous work.

physics.chem-ph↗

arXiv2021

Understanding Anharmonic Effects on Hydrogen Desorption Characteristics of Mg$_n$H$_{2n}$ Nanoclusters by ab initio trained Deep Neural Network

Magnesium hydride (MgH$_2$) has been widely studied for effective hydrogen storage. However, its bulk desorption temperature (553 K) is deemed too high for practical applications. Besides doping, a strategy to decrease such reaction energy for releasing hydrogen is the use of MgH$_2$-based nanoparticles (NPs). Here, we investigate first the thermodynamic properties of Mg$_n$H$_{2n}$ NPs ($n<10$) from first-principles, in particular by assessing the anharmonic effects on the enthalpy, entropy and thermal expansion by means of the Stochastic Self Consistent Harmonic Approximation (SSCHA). The latter method goes beyond previous approaches, typically based on molecular mechanics and the quasi-harmonic approximation, allowing the ab initio calculation of the fully-anharmonic free energy. We find an almost linear dependence on temperature of the interatomic bond lengths - with a relative variation of few percent over 300K -, alongside with a bond distance decrease of the Mg-H bonds. In order to increase the size of NPs toward experiments of hydrogen desorption from MgH$_2$ we devise a computationally effective Machine Learning model trained to accurately determine the forces and total energies (i.e. the potential energy surfaces), integrating the latter with the SSCHA model to fully include the anharmonic effects. We find a significative decrease of the H-desorption temperature for sub-nanometric clusters Mg$_n$H$_{2n}$ with $n \leq 10$, with a non-negligible, although little effect due to anharmonicities (up to 10%).

cond-mat.mtrl-sci↗

arXiv2021

Stochastic Dynamics and Bound States of Heavy Impurities in a Fermi Bath

We investigate the dynamics of heavy impurities embedded in an ultra-cold Fermi gas by using a Generalized Langevin equation. The latter -- derived by means of influence functional theory -- describes the stochastic classical dynamics of the impurities and the quantum nature of the fermionic bath manifests in the emergent interaction between the impurities and in the viscosity tensor. By focusing on the two-impurity case, we predict the existence of bound states, in different conditions of coupling and temperature, and whose life-time can be analytically estimated. Our predictions should be testable using cold-gases platforms within current technology.

cond-mat.quant-gas↗

arXiv2021

Path-integral calculation of the third dielectric virial coefficient of noble gases

We present the first framework for fully quantum calculation of the third dielectric virial coefficient $C_\varepsilon(T)$ of noble gases, including exchange effects. The quantum effects are taken into account with the path-integral Monte Carlo method. Calculations employing state-of-the-art pair and three-body potentials and pair polarizabilities yield results generally consistent with the few scattered experimental data available for helium, neon, and argon, but rigorous calculations with well-described uncertainties will require the development of surfaces for the three-body nonadditive polarizability and the three-body dipole moment. The framework developed here will enable new approaches to primary temperature and pressure metrology based on first-principles calculations of gas properties.

cond-mat.stat-mech↗

arXiv2021

Path-integral calculation of the fourth virial coefficient of helium isotopes

We use the path-integral Monte Carlo (PIMC) method and state-of-the-art two-body and three-body potentials to calculate the fourth virial coefficients $D(T)$ of $^4$He and $^3$He as functions of temperature from 2.6K to 2000K. We derive expressions for the contributions of exchange effects due to the bosonic or fermionic nature of the helium isotope; these effects have been omitted from previous calculations. The exchange effects are relatively insignificant for $^4$He at the temperatures considered, but for $^3$He they are necessary for quantitative accuracy below about 4K. Our results are consistent with previous theoretical work (and with some of the limited and scattered experimental data) for $^4$He; for $^3$He there are no experimental values and this work provides the first values of $D(T)$ calculated at this level. The uncertainty of the results depends on the statistical uncertainty of the PIMC calculation, the estimated effect of omitting four-body and higher terms in the potential energy, and the uncertainty contribution propagated from the uncertainty of the potentials. At low temperatures, the uncertainty is dominated by the statistical uncertainty of the PIMC calculations, while at high temperatures the uncertainties related to the three-body potential and to omitted higher-order contributions become dominant.

physics.atm-clus↗