Kubo Approach Research Articles

Lattice thermal conductivity of solid LiF based on machine learning force fields and the Green–Kubo approach

Lattice thermal conductivity of solid LiF based on machine learning force fields and the Green–Kubo approach

Uncertainties in the transport properties of helium gas at cryogenic temperatures determined using molecular dynamics simulation

In this study, the transport properties, such as diffusivity, viscosity, and thermal conductivity, of 4He at the gaseous phase are computed for state points in the temperature range of 10 K to 150 K and pressure range of 0.10 MPa (1 atm) to 0.21 MPa using classical and quantum frameworks. Within the classical molecular dynamics simulation (MDS), the Green–Kubo (GK) approach is used. The GK method has an inherent uncertainty associated with it due to the random fluctuations in the flux autocorrelation functions. Moreover, in the temperature range of 10 K to 40 K, the quantum nature of the helium gas particles becomes prominent. The classical MDS performed does not include these effects and hence introduces uncertainties in the calculated results. We discuss efficient ways of time averaging the autocorrelation function to reduce statistical fluctuations and perform the quantum scattering phase shift calculations within the Chapman–Cowling theory to study the quantum effects. Furthermore, this study also provides the transport properties data in the cryogenic temperature limit of 10 K to 150 K, which is scarcely studied in the literature and can be applied in complex systems.

Thermal conductivity tensor of β‐HMX as a function of pressure and temperature from equilibrium molecular dynamics simulations

AbstractWe apply the Green–Kubo (G–K) approach to obtain the thermal conductivity tensor of β‐1,3,5,7‐tetranitro‐1,3,5,7‐tetrazoctane (β‐HMX) as a function of pressure and temperature from equilibrium molecular dynamics (MD) simulations. Direct application of the G–K formula exhibits slow convergence of the integrated thermal conductivity values even for long (120 ns) accumulated simulation times. To partially mitigate this slow convergence, we apply a recently implemented numerical procedure that involves physically justified filtering of the MD‐calculated G–K heat current and fitting the integrated time‐dependent thermal conductivity to a physically motivated double‐exponential function. The thermal conductivity tensor was determined for pressures 0.1 MPa 30 GPa and temperatures 300 K 900 K. The thermal conductivity increases with increasing pressure, by approximately an order of magnitude over the interval considered, and decreases with increasing temperature. The MD predictions are compared to experimental and other theoretically determined values for the thermal conductivity of β‐HMX. A simple, semi‐empirical fitting form is proposed that captures the behavior of over the pressure and temperature intervals studied.

Lattice Thermal Conductivity of Monolayer InSe Calculated by Machine Learning Potential.

The two-dimensional post-transition-metal chalcogenides, particularly indium selenide (InSe), exhibit salient carrier transport properties and evince extensive interest for broad applications. A comprehensive understanding of thermal transport is indispensable for thermal management. However, theoretical predictions on thermal transport in the InSe system are found in disagreement with experimental measurements. In this work, we utilize both the Green-Kubo approach with deep potential (GK-DP), together with the phonon Boltzmann transport equation with density functional theory (BTE-DFT) to investigate the thermal conductivity (κ) of InSe monolayer. The κ calculated by GK-DP is 9.52 W/mK at 300 K, which is in good agreement with the experimental value, while the κ predicted by BTE-DFT is 13.08 W/mK. After analyzing the scattering phase space and cumulative κ by mode-decomposed method, we found that, due to the large energy gap between lower and upper optical branches, the exclusion of four-phonon scattering in BTE-DFT underestimates the scattering phase space of lower optical branches due to large group velocities, and thus would overestimate their contribution to κ. The temperature dependence of κ calculated by GK-DP also demonstrates the effect of higher-order phonon scattering, especially at high temperatures. Our results emphasize the significant role of four-phonon scattering in InSe monolayer, suggesting that combining molecular dynamics with machine learning potential is an accurate and efficient approach to predict thermal transport.

Implementation of probe rheology simulation technique in atomistically detailed molecular dynamics simulations

The probe rheology simulation technique is a technique for measuring the viscosity of a fluid by measuring the motion of an inserted probe particle. This approach has the benefit of greater potential accuracy at a lower computational cost than other conventional simulation techniques used for the calculation of mechanical properties, such as the Green-Kubo approach and nonequilibrium molecular dynamics simulations, and the potential to allow for sampling local variations of properties. This approach is implemented and demonstrated for atomistically detailed models. The viscosity of four different simple Newtonian liquids is calculated from both the Brownian motion (passive mode) and the forced motion (active mode) of an embedded probe particle. The probe particle is loosely modeled as a nano-sized diamond particle: a rough sphere cut out of an FCC lattice made of carbon atoms. The viscosities obtained from the motion of the probe particle are compared with those obtained from the periodic perturbation method, and good agreement between the two sets of values is observed once the probe-fluid interaction strength (i.e., in the pair-wise Lennard-Jones interaction) is two times higher than their original values, and the artificial hydrodynamic interactions between the probe particle and its periodic images are accounted for. The success of the proposed model opens new opportunities for applying such a technique in the rheological characterization of local mechanical properties in atomistically detailed molecular dynamics simulations, which can be directly compared with or help guide experiments of similar nature.

Theory of Edge Effects and Conductance for Applications in Graphene-Based Nanoantennas

In this paper, we present a theory of edge effects in graphene for its applications to nanoantennas in the THz, infrared, and visible frequency ranges. The novelty of the presented model is reflected in its self-consistency, which is reached due to the formulation in terms of dynamical conductance instead of ordinary surface conductivity. The physical model of edge effects is based on using the concept of the Dirac fermion and the Kubo approach. In contrast with earlier well-known and widely used models, the surface conductance becomes non-homogeneous and non-local. The numerical simulations of the spatial behavior of the surface conductance were performed in a wide range of values, known from the literature, for the graphene ribbon widths and electrochemical potential. It is shown that if the length exceeds 800 nm, our model agrees with the classical Drude conductivity model with a relatively high degree of accuracy. For rather short lengths, the conductance exhibits a new type of spatial oscillations, which are not present in the ordinary conductivity model. These oscillations modify the form of effective boundary conditions and integral equations for electromagnetic field at the surface of graphene-based antenna. The developed theory opens a new way for realizing electrically controlled nanoantennas by changing the electrochemical potential via gate voltage. The obtained results may be applicable for the design of different carbon-based nanodevices in modern quantum technologies.

Heat-current filtering for Green–Kubo and Helfand-moment molecular dynamics predictions of thermal conductivity: Application to the organic crystal [formula omitted]-HMX

The closely related Green–Kubo and Helfand moment approaches are applied to obtain the thermal conductivity tensor of β-1,3,5,7-tetranitro-1,3,5,7-tetrazoctane (β-HMX) at T=300 K and P=1 atm from equilibrium molecular dynamics (MD) simulations. Direct application of the Green–Kubo formula exhibits slow convergence of the integrated thermal conductivity values even for long (120 ns) simulation times. To partially mitigate this slow convergence we developed a numerical procedure that involves filtering of the MD-calculated heat current. The filtering is accomplished by physically justified removal of the heat-current component which is given by a linear function of atomic velocities. A double-exponential function is fitted to the integrated time-dependent thermal conductivity, calculated using the filtered current, to obtain the asymptotic values for the thermal conductivity. In the Helfand moment approach the thermal conductivity is obtained from the rates of change of the averaged squared Helfand moments. Both methods are applied to periodic β-HMX supercells of four different sizes and estimates for the thermal conductivity of the infinitely large crystal are obtained using Matthiessen’s rule. Both approaches yield similar although not identical thermal conductivity values. These predictions are compared to experimental and other theoretically determined values for the thermal conductivity of β-HMX.

Kubo estimation of the electrical conductivity for a hot relativistic fluid in the presence of a magnetic field

We have explored the multi-component structure of electrical conductivity of relativistic Fermionic and Bosonic fluid in presence of magnetic field by using Kubo approach. This is done by explicitly evaluating the thermo-magnetic vector current spectral functions using the real time formalism of finite temperature field theory and the Schwinger proper time formalism. In absence of magnetic field, the one-loop diagramatic representation of Kubo expression of any transport coefficients is exactly same with relaxation time approximation (RTA) based expression, but this equality does not hold for finite magnetic field picture due to lacking of proper implementation of quantum effect in latter approach. We have shown this discrepancy for particular transport coefficient - electrical conductivity, whose starting point in Kubo approach will be electromagnetic current-current correlator and its one-loop skeleton diagram carrying two scalar/Dirac propagators for scalar/Dirac fluid. Through a numerical comparison between RTA and Kubo expressions of conductivity components (parallel and perpendicular), we have attempted to interpret detail quantum field theoretical effect, contained by Kubo expression but not by RTA expression. In classical RTA expression we get magnetic field independent parallel conductivity due to zero Lorentz force but in field theoretical Kubo expression, it decreases and increases with the magnetic field for scalar and Dirac medium respectively due to Landau quantization effect. This parallel component of conductivity can be interpreted as zero momentum limit of quantum fluctuation with same Landau level internal lines. While for perpendicular component of conductivity, fluctuation with Landau level differences $\pm 1$ are noticed, which might be a new realization of transportation in field theoretical sector.

Magnetic generation of normal pseudo-spin polarization in disordered graphene

Spin to pseudo-spin conversion by which the non-equilibrium normal sublattice pseudo-spin polarization could be achieved by magnetic field has been proposed in graphene. Calculations have been performed within the Kubo approach for both pure and disordered graphene including vertex corrections of impurities. Results indicate that the normal magnetic field B_z produces pseudo-spin polarization in graphene regardless of whether the contribution of vertex corrections has been taken into account or not. This is because of non-vanishing correlation between the sigma _z and tau _z provided by the co-existence of extrinsic Rashba and intrinsic spin–orbit interactions which combines normal spin and pseudo-spin. For the case of pure graphene, valley-symmetric spin to pseudo-spin response function is obtained. Meanwhile, by taking into account the vertex corrections of impurities the obtained response function is weakened by several orders of magnitude with non-identical contributions of different valleys. This valley-asymmetry originates from the inversion symmetry breaking generated by the scattering matrix. Finally, spin to pseudo-spin conversion in graphene could be realized as a practical technique for both generation and manipulation of normal sublattice pseudo-spin polarization by an accessible magnetic field in a easy way. This novel proposed effect not only offers the opportunity to selective manipulation of carrier densities on different sublattice but also could be employed in data transfer technology. The normal pseudo-spin polarization which manifests it self as electron population imbalance of different sublattices can be detected by optical spectroscopy measurements.

Spin-current and pseudo-spin density response functions in graphene

Abstract Spin-current and pseudo-spin response to the electric and magnetic fields have been investigated within the Kubo approach. It has been realized that this problem can be regarded as the spin, pseudo-spin correlations and self-correlations. Calculations have been performed within the Dirac cone approximation. Meanwhile, the effect of gate induced Rashba coupling has been considered as a spin-dependent external control parameter where some experimental reports supports that spin–charge correlation can be controlled by the Rashba interaction Ghiasi et al. (2019). Calculations have been performed in the framework of the linear response regime in which the electric and magnetic perturbations are weak. Results of the present study show that the extreme frequencies of response functions could be considered as structural characteristic properties of the sample which are independent of motive and response quantities. Meanwhile, it has been shown that the response functions can effectively be controlled by the Rashba coupling.

Density-dependent finite system-size effects in equilibrium molecular dynamics estimation of shear viscosity: Hydrodynamic and configurational study.

We study the intrinsic nature of the finite system-size effect in estimating shear viscosity of dilute and dense fluids within the framework of the Green-Kubo approach. From extensive molecular dynamics simulations, we observe that the size effect on shear viscosity is characterized by an oscillatory behavior with respect to system size L at high density and by a scaling behavior with an L-1 correction term at low density. Analysis of the potential contribution in the shear-stress autocorrelation function reveals that the former is configurational and is attributed to the inaccurate description of the long-range spatial correlations in finite systems. Observation of the long-time inverse-power decay in the kinetic contribution confirms its hydrodynamic nature. The L-1 correction term of shear viscosity is explained by the sensitive change in the long-time tail obtained from a finite system.

Thermal conductivity of bulk and porous ThO2: Atomistic and experimental study

Thorium dioxide (ThO2) is proposed to play a vital role in the world's future energy needs and is considered a better and safer alternative to the currently used nuclear fuel, uranium dioxide (UO2). Thermo-physical properties of ThO2 are superior to UO2, but the fundamental physics governing the heat transport in ThO2 is still ambiguous, and the available data for the thermal conductivity (k) of ThO2 was scattered. In this article, a systematic investigation regarding the lattice thermal conductivity (kL) of the bulk and porous ThO2 is carried out theoretically and validated with experiments. The phonon transport calculations were done using two different methods; ab-initio calculations combined with the Boltzmann transport equation (BTE) and the equilibrium molecular dynamics (EMD) simulations using Green Kubo (GK) approach. An extensive examination of the phonon mode contribution, available three-phonon scattering phase space modes, Grüneisen parameter, and mean free path (MFP) distributions were analyzed to understand the underlying physics in the thermal transport of ThO2. The effect of porosity on the kL by measurements and molecular dynamics (MD) simulations was explored. The measurements were performed on specimens with different porosity, that were prepared by spark plasma sintering (SPS) using the laser flash (LFA) technique. The results obtained demonstrated that the kL values predicted by both the BTE and the EMD simulations were in excellent agreement with our experimental measurements. Moreover, the model to simulate the 95% theoretical density (TD) using MD simulations also captured the decrease in thermal conductivity with porosity and agreed well with the measured results for 95% TD dense sintered pellets.

Determination of rarefaction effects on transport properties of nanoscale gas flows using Green–Kubo molecular dynamic simulation

ABSTRACTThis study aimed to investigate the rarefaction effects on thermal conductivity, viscosity, and density of Argon, Neon and Xenon gas flows in a Platinum nanochannel. Green–Kubo approach with Lenard Jones potential function are used for molecular dynamic simulation. Simulations showed that with decrease in number of atoms, density, viscosity and thermal conductivity decreases, while decrease in nanochannel width in same number of gas atoms leads to increase in viscosity and thermal conductivity.

Higher-order fluctuation-dissipation relations in plasma physics: Binary Coulomb systems.

A recent approach that led to compact frequency domain formulations of the cubic and quartic fluctuation-dissipation theorems (FDTs) for the classical one-component plasma (OCP) [Golden and Heath, J. Stat. Phys. 162, 199 (2016)10.1007/s10955-015-1395-6] is generalized to accommodate binary ionic mixtures. Paralleling the procedure followed for the OCP, the basic premise underlying the present approach is that a (k,ω) 4-vector rotational symmetry, known to be a pivotal feature in the frequency domain architectures of the linear and quadratic fluctuation-dissipation relations for a variety of Coulomb plasmas [Golden et al., J. Stat. Phys. 6, 87 (1972)10.1007/BF01023681; J. Stat. Phys. 29, 281 (1982)10.1007/BF01020787; Golden, Phys. Rev. E 59, 228 (1999)10.1103/PhysRevE.59.228], is expected to be a pivotal feature of the frequency domain architectures of the higher-order members of the FDT hierarchy. On this premise, each member, in its most tractable form, connects a single (p+1)-point dynamical structure function to a linear combination of (p+1)-order p density response functions; by definition, such a combination must also remain invariant under rotation of their (k_{1},ω_{1}),(k_{2},ω_{2}),...,(k_{p},ω_{p}), (k_{1}+k_{2}+⋯+k_{p},ω_{1}+ω_{2}+⋯+ω_{p}) 4-vector arguments. Assigned to each 4-vector is a species index that corotates in lock step. Consistency is assured by matching the static limits of the resulting frequency domain cubic and quartic FDTs to their exact static counterparts independently derived in the present work via a conventional time-independent perturbation expansion of the Liouville distribution function in its macrocanonical form. The proposed procedure entirely circumvents the daunting issues of entangled Liouville space paths and nested Poisson brackets that one would encounter if one attempted to use the conventional time-dependent perturbation-theoretic Kubo approach to establish the frequency domain FDTs beyond quadratic order.

Mechanical and thermal properties of graphene random nanofoams via Molecular Dynamics simulations

Graphene foams have recently attracted a great deal of interest for their possible use in technological applications, such as electrochemical storage devices, wearable electronics, and chemical sensing. In this work, we present computational investigations, performed by using molecular dynamics with reactive potentials, of the mechanical and thermal properties of graphene random nanofoams. In particular, we assess the mechanical and thermal performances of four families of random foams characterized by increasing mass density and decreasing average pore size. We find that the foams' mechanical performances under tension cannot be rationalized in terms of mass density, while they are principally related to their topology. Under compression, higher-density foams show the typical slope change in the stress–strain curve at 5−10% strain, moving from linear elasticity to a buckling region. At variance, lower density foams display a quasi-linear behavior up to 35% strain. Furthermore, we assess the thermal conductivity of these random foams using the Green–Kubo approach. While foam thermal conductivity is affected by both connectivity and defects, nevertheless we obtain similar values for all the investigated families, which means that topology is the critical factor affecting thermal transport in these structures.

Diffusion of Dirac fermions across a topological merging transition in two dimensions

A continuous deformation of a Hamiltonian possessing at low energy two Dirac points of opposite chiralities can lead to a gap opening by merging of the two Dirac points. In two dimensions, the critical Hamiltonian possesses a semi-Dirac spectrum: linear in one direction but quadratic in the other. We study the transport properties across such a transition, from a Dirac semi-metal through a semi-Dirac phase towards a gapped phase. Using both a Boltzmann approach and a diagrammatic Kubo approach, we describe the conductivity tensor within the diffusive regime. In particular, we show that both the anisotropy of the Fermi surface and the Dirac nature of the eigenstates combine to give rise to anisotropic transport times, manifesting themselves through an unusual matrix self-energy.

Appraisal of Surface Hopping as a Tool for Modeling Condensed Phase Linear Absorption Spectra.

Whereas surface hopping is usually used to study populations and mean-field dynamics to study coherences, in two recent papers, we described a procedure for calculating dipole-dipole correlation functions (and therefore absorption spectra) directly from ensembles of surface hopping trajectories. We previously applied this method to a handful of one-dimensional model problems intended to mimic the gas phase. In this article, we now benchmark this new procedure on a set of multidimensional model problems intended to mimic the condensed phase and compare our results against other standard semiclassical methods. By comparison, we demonstrate that methods that include only dynamical information from one PES (the standard Kubo approaches) exhibit large discrepancies with the results of exact quantum dynamics. Furthermore, for model problems with nonadiabatic excited state dynamics but no quantized vibrational structure in the spectra, our surface hopping approach performs comparably to using Ehrenfest dynamics to calculate the electronic coherences. That being said, however, when quantized vibrational structures are present in the spectra but the electronic states are uncoupled, performing the dynamics on the mean PES still outperforms our present method. These benchmark results should influence future studies that use ensembles of independent semiclassical trajectories to model linear as well as multidimensional spectra in the condensed phase.

Golden Ratio Autocorrelation Function and the Exponential Decay

An autocorrelation function is obtained on the base of the recurrence relation formalism, whose continued fraction form corresponds to that of the golden ratio. It turns out that this Golden Ratio (GR) autocorrelation is known in science and obeys all necessary conditions, in contrast to the exponential autocorrelation function. Using the Kubo approach it is shown how exponential correlations appear in the linear response theory as a result of non-Hermitian relaxation of the system.

Lenard‐Balescu Calculations and Classical Molecular Dynamics Simulations of Electrical and Thermal Conductivities of Hydrogen Plasmas

AbstractWe present a discussion of kinetic theory treatments of linear electrical and thermal transport in hydrogen plasmas, for a regime of interest to inertial confinement fusion applications. In order to assess the accuracy of one of the more involved of these approaches, classical Lenard‐Balescu theory, we perform classical molecular dynamics simulations of hydrogen plasmas using 2‐body quantum statistical potentials and compute both electrical and thermal conductivity from our particle trajectories using the Kubo approach. Our classical Lenard‐Balescu results employing the identical statistical potentials agree well with the simulations. Comparison between quantum Lenard‐Balescu and classical Lenard‐Balescu for conductivities then allows us to both validate and critique the use of various statistical potentials for the prediction of plasma transport properties. These findings complement our earlier MD/kinetic theory work on temperature equilibration [1], and reach similar conclusions as to which forms of statistical potentials best reproduce true quantum behavior. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Shear viscosity and imperfect fluidity in bosonic and fermionic superfluids

In this paper we address the ratio of the shear viscosity to entropy density $\eta/s$ in bosonic and fermionic superfluids. A small $\eta/s$ is associated with nearly perfect fluidity, and more general measures of the fluidity perfection/imperfection are of wide interest to a number of communities. We use a Kubo approach to concretely address this ratio via low temperature transport associated with the quasi-particles. Our analysis for bosonic superfluids utilizes the framework of the one-loop Bogoliubov approximation, whereas for fermionic superfluids we apply BCS theory and its BCS-BEC extension. Interestingly, we find that the transport properties of strict BCS and Bogoliubov superfluids have very similar structures, albeit with different quasi-particle dispersion relations. While there is a dramatic contrast between the power law and exponential temperature dependence for $\eta$ alone, the ratio $\eta/s$ for both systems is more similar. Specifically we find the same linear dependence (on the ratio of temperature $T$ to inverse lifetime $\gamma(T)$) with $\eta/s \propto T/\gamma(T)$, corresponding to imperfect fluidity. By contrast, near the unitary limit of BCS-BEC superfluids a very different behavior results, which is more consistent with near-perfect fluidity.