arXiv subjects

Tapio T. Rantala

Publications and source records attributed to Tapio T. Rantala.

15 recordsLinked to original sources

arXiv2026

Quantum many-body effects in the optical response of ideal thin films

We study quantum many-body effects in the long-wavelength optical response of confined electrons at finite temperatures. We simulate homogeneous electron gas confined in one dimension into a slab of nanoscale thickness. We demonstrate how the slab boundaries break down the ideal Drude response of free charge carriers, giving rise to scattering effects due to both the surfaces and quantum many-body interactions. We use a recent path-integral Monte Carlo (PIMC) approach developed in [Tiihonen et al. Phys. Rev. A 113, 053711] to quantify these effects in high accuracy. We perform phenomenological fits to Drude and Drude-Lorentz models parameters, manifesting various trends of the optical response with physical parameters like density and temperature, and numerical effects like finite size and the quantum statistics.

physics.optics↗

arXiv2026

Path-integral Monte Carlo estimator for the dipole polarizability of quantum plasma

We present a path-integral Monte Carlo estimator for calculating the dipole polarizability of interacting Coulomb plasma in the long-wavelength limit, i.e., the optical region. We present comprehensive details and method validation studies for our approach based on both collective and one-particle dipole autocorrelation functions in the imaginary time. The simulation of thermal equilibrium in imaginary time has exact Coulomb interactions and Boltzmann quantum statistics. For reference, we use analytically continued Drude model as the long-wavelength limit of the Lindhard response. Our collective response shows perfect match to the analytical reference. The one-particle response is used in systematic studies of physical and numerical parameters, and to discuss the phenomenological Drude scattering model.

cond-mat.mes-hall↗

arXiv2023

Electronic structure calculations with interpolating tensor product wavelet basis

We introduce a basis set consisting of three-dimensional Deslauriers--Dubuc wavelets and solve numerically the Schrödinger equations of H and He atoms and molecules $\mathrm{H}_2$, $\mathrm{H}_2^+$, and $\mathrm{LiH}$ with HF and DFT methods. We also compute the 2s and 2p excited states of hydrogen. The Coulomb singularity at the nucleus is handled by using a pseudopotential. The eigenvalue problem is solved with Arnoldi and Lanczos methods, Poisson equation with GMRES and CGNR methods, and matrix elements are computed using the biorthogonality relations of the interpolating wavelets. Performance is compared with those of CCCBDB and BigDFT.

quant-ph↗

arXiv2021

Path Integrals: From Quantum Mechanics to Photonics

The path integral formulation of quantum mechanics, i.e., the idea that the evolution of a quantum system is determined as a sum over all the possible trajectories that would take the system from the initial to its final state of its dynamical evolution, is perhaps the most elegant and universal framework developed in theoretical physics, second only to the Standard Model of particle physics. In this tutorial, we retrace the steps that led to the creation of such a remarkable framework, discuss its foundations, and present some of the classical examples of problems that can be solved using the path integral formalism, as a way to introduce the readers to the topic, and help them get familiar with the formalism. Then, we focus our attention on the use of path integrals in optics and photonics, and discuss in detail how they have been used in the past to approach several problems, ranging from the propagation of light in inhomogeneous media, to parametric amplification, and quantum nonlinear optics in arbitrary media. To complement this, we also briefly present the Path Integral Monte Carlo (PIMC) method, as a valuable computational resource for condensed matter physics, and discuss its potential applications and advantages if used in photonics.

quant-ph↗

arXiv2017

Real-time Diffusion Monte Carlo method

Direct sampling of multi-dimensional systems with quantum Monte Carlo methods allows exact account of many-body effects or particle correlations. The most straightforward approach to solve the Schrödinger equation, Diffusion Monte Carlo, has been used in several benchmark cases for other methods to pursue. Its robustness is based on direct sampling of a positive probability density for diffusion in imaginary time. It has been argued that the corresponding real time diffusion can not be realised, because the corresponding oscillating complex valued distribution can not be used to drive diffusion. Here, we demonstrate that this can be done with a couple of tricks turning the distribution piecewise positive and normalisable. This study is a proof of concept demonstration using the well-known and transparent case: one-dimensional harmonic oscillator. Furthermore, we show that our novel method can be used to find not only the ground state but also excited states and even the time evolution of a given wave function. Considering fermionic systems, this method may turn out to be feasible for finding the wave function nodes.

quant-ph↗

arXiv2017

Static field-gradient polarizabilities of small atoms and molecules in finite temperature

In this work, we propose new field-free estimators for static field-gradient polarizabilities in finite temperature PIMC simulation. Namely, dipole--quadrupole polarizability $A$, dipole--dipole--quadrupole polarizability $B$ and quadrupole--quadrupole polarizability $C$ are computed for several up to two-electron systems: H, H$^-$, He, Li$^+$, Be$^{2+}$, Ps$_2$, PsH, H$_2^+$, H$_2$, H$_3^+$ and HeH$^+$. We provide complementary data for ground state electronic properties within the adiabatic approximation, and demonstrate good agreement with available values in the literature. More importantly, we present fully non-adiabatic results from 50 K to 1600 K, which allow us to analyze and discuss strong thermal coupling and rovibrational effects in total field-gradient polarizabilities. These phenomena are most relevant but clearly overlooked, e.g., in the construction of modern polarizable force field models. However, our main purpose is demonstrating the accuracy and simplicity of our approach in a problem that is generally challenging.

physics.chem-ph↗

arXiv2015

Numerical path integral solution to strong Coulomb correlation in one dimensional Hooke's atom

We present a new approach based on real time domain Feynman path integrals (RTPI) for electronic structure calculations and quantum dynamics, which includes correlations between particles exactly but within the numerical accuracy. We demonstrate that incoherent propagation by keeping the wave function real is a novel method for finding and simulation of the ground state, similar to Diffusion Monte Carlo (DMC) method, but introducing new useful tools lacking in DMC. We use 1D Hooke's atom, a two-electron system with very strong correlation, as our test case, which we solve with incoherent RTPI (iRTPI) and compare against DMC. This system provides an excellent test case due to exact solutions for some confinements and because in 1D the Coulomb singularity is stronger than in two or three dimensional space. The use of Monte Carlo grid is shown to be efficient for which we determine useful numerical parameters. Furthermore, we discuss another novel approach achieved by combining the strengths of iRTPI and DMC. We also show usefulness of the perturbation theory for analytical approximates in case of strong confinements.

quant-ph↗

arXiv2015

Localized surface plasmon resonance in silver nanoparticles: Atomistic first-principles time-dependent density-functional theory calculations

We observe using ab initio methods that localized surface plasmon resonances in icosahedral silver nanoparticles enter the asymptotic region already between diameters of 1 and 2 nm, converging close to the classical quasistatic limit around 3.4 eV. We base the observation on time-dependent density-functional theory simulations of the icosahedral silver clusters Ag$_{55}$ (1.06 nm), Ag$_{147}$ (1.60 nm), Ag$_{309}$ (2.14 nm), and Ag$_{561}$ (2.68 nm). The simulation method combines the adiabatic GLLB-SC exchange-correlation functional with real time propagation in an atomic orbital basis set using the projector-augmented wave method. The method has been implemented for the electron structure code GPAW within the scope of this work. We obtain good agreement with experimental data and modeled results, including photoemission and plasmon resonance. Moreover, we can extrapolate the ab initio results to the classical quasistatically modeled icosahedral clusters.

cond-mat.mtrl-sci↗

arXiv2014

Numerical path integral approach to quantum dynamics and stationary quantum states

Applicability of Feynman path integral approach to numerical simulations of quantum dynamics in real time domain is examined. Coherent quantum dynamics is demonstrated with one dimensional test cases (quantum dot models) and performance of the Trotter kernel as compared with the exact kernels is tested. A novel approach for finding the ground state and other stationary sates is presented. This is based on the incoherent propagation in real time. For both approaches the Monte Carlo grid and sampling are tested and compared with regular grids and sampling. We asses the numerical prerequisites for all of the above.

physics.comp-ph↗

arXiv2012

Few-body reference data for multicomponent formalisms: Light nuclei molecules

We present full quantum statistical energetics of some electron-light nuclei systems. This is accomplished with the path integral Monte Carlo method. The effects on energetics arising from the change in the nuclear mass are studied. The obtained results may serve as reference data for the multicomponent density functional theory calculations of light nuclei system. In addition, the results reported here will enable better fitting of todays electron-nuclear energy functionals, for which the description of light nuclei is most challenging, in particular.

physics.chem-ph↗

arXiv2011

Energetics and partition function of H$_3^+$ molecular ion

Full $NVT$ quantum statistics of the H$_3^+$ ion is simulated at low densities using the path integral Monte Carlo approach. For the first time, the molecular total energy, partition function, free energy, entropy and heat capacity are evaluated in temperatures relevant for planetary atmospheric physics. Temperature and density dependent dissociation recombination reaction balance of the molecule and its fragments above 4000 K is described, and also, the density dependence of thermal ionization above $10 000$ K is demonstrated. We introduce a new well-behaving analytical model for the molecular partition function of the H$_3^+$ ion for the temperature range below dissociation and fit the parameters to the energetics from our simulations. The approach presented here can be regarded as an extension of the traditional {\it ab initio} quantum chemistry beyond the Born--Oppenheimer approximation to description of nonadiabatic phenomena, and even further, account of nuclear quantum dynamics.

astro-ph.EP↗

arXiv2010

Finite temperature quantum statistics of H$_3^+$ molecular ion

Full quantum statistical $NVT$ simulation of the five-particle system H$_3^+$ has been carried out using the path integral Monte Carlo method. Structure and energetics is evaluated as a function of temperature up to the thermal dissociation limit. The weakly density dependent dissociation temperature is found to be around $4000$ K. Contributions from the quantum dynamics and thermal motion are sorted out by comparing differences between simulations with quantum and classical nuclei. The essential role of the quantum description of the protons is established.

quant-ph↗

arXiv2009

Comparison of charged-defect finite-size supercell correction methods in a general framework

Starting from the total energy expressions within density functional theory, we are able to perform a comparison of several currently used charged-defect finite-size supercell correction schemes in a unified manner. This approach also provides a framework for a further development of corrections not only for DFT supercell calculations, but also for more advanced methods and for complex geometries. The comparison is performed for three separate defect cases: a gallium vacancy in GaAs, a beryllium interstitial in GaAs and a vacancy in diamond. We found two methods working sufficiently well for all three cases: a method which is very similar to one presented by Freysoldt, and a slightly altered potential alignment method.

cond-mat.mes-hall↗

arXiv2009

Thermal dissociation of dipositronium: path integral Monte Carlo approach

Path integral Monte Carlo simulation of the dipositronium "molecule" Ps$_2$ reveals its surprising thermal instability. Although, the binding energy is $\sim 0.4$ eV, due to the strong temperature dependence of its free energy Ps$_2$ dissociates, or does not form, above $\sim 1000$ K, except for high densities where a small fraction of molecules are in equilibrium with Ps atoms. This prediction is consistent with the recently reported first observation of stable Ps$_2$ molecules by Cassidy & Mills Jr., Nature {\bf 449}, 195 (07), and Phys.Rev.Lett. {\bf 100}, 013401 (08); at temperatures below 1000 K. The relatively sharp transition from molecular to atomic equilibrium, that we find, remains to be experimentally verified. To shed light on the origin of the large entropy factor in free energy we analyze the nature of interatomic interactions of these strongly correlated quantum particles. The conventional diatomic potential curve is given by the van der Waals interaction at large distances, but due to the correlations and high delocalization of constituent particles the concept of potential curve becomes ambiguous at short atomic distances.

physics.comp-ph↗

arXiv2008

Band offset determination of the GaAs/GaAsN interface using the DFT method

The GaAs/GaAsN interface band offset is calculated from first principles. The electrostatic potential at the core regions of the atoms is used to estimate the interface potential and align the band structures obtained from respective bulk calculations. First, it is shown that the present method performs well on the well-known conventional/conventional AlAs/GaAs (001) superlattice system. Then the method is applied to a more challenging nonconventional/conventional GaAsN/GaAs (001) system, and consequently type I band lineup and valence-band offset of about 35 meV is obtained for nitrogen concentration of about 3 %, in agreement with the recent experiments. We also investigate the effect of strain on the band lineup. For the GaAsN layer longitudinally strained to the GaAs lattice constant, the type II lineup with a nearly vanishing band offset is found, suggesting that the anisotropic strain along the interface is the principal cause for the often observed type I lineup.

cond-mat.mtrl-sci↗