Low-temperature Approximation Research Articles

Bayesian inference of thermal effects in dense matter within the covariant density functional theory

The high temperatures reached in a proto-neutron star or during the post-merger phase of a binary neutron star coalescence lead to non-negligible thermal effects on the equation of state (EOS) of dense nuclear matter (NM). Here we study these effects within the covariant density functional theory employing the posteriors of a Bayesian inference, which encompasses a large sample of EOS models. Different densities and temperatures are considered. We find that for a number of quantities thermal effects are strongly correlated with the Dirac effective mass (m⁎) of the nucleons and/or its logarithmic derivative as a function of density. These results can be explained within the low temperature approximation though they survive beyond this limit.

Substantiating the mechanisms of electronic and phonon friction in the conjugation of materials of samples (parts) by the methods of solid state physics

The article elucidates the essence of the mechanisms of electronic and phonon friction in the coupling of samples (parts) using the methods of solid state physics.
 It is shown that in the triboconjugation of samples made of metallic materials, the flow of fluctuation-electromagnetic and electron-phonon processes should be distinguished. Fluctuation-electromagnetic interactions have long-range effects, and electron-phonon interactions have short-range effects. Based on Lifshitz's fluctuation-electromagnetic theory, the force of friction in moving couplings of metal samples is substantiated, taking into account the frequency ratio in the atomic absorption spectrum and the plasma frequency. A formula for estimating the friction force was obtained, taking into account the dielectric function and the Clausius-Mossotti formula.
 The electronic friction force was estimated using the "jelly" model and the generation of electron-hole pairs in the quantum perturbation theory of solid-state physics.
 The mechanism of electronic friction was discovered based on the phenomenological theory of braking losses of slow ions in solids. The scheme of the model of the electronic friction mechanism is close to the Persson model, which connects the braking force with the electron scattering process. A refined formula for estimating the electronic friction force is proposed.
 The strength of phonon friction is justified on the basis of structural effects that can be induced by the mechanism of breaking adhesive bonds, and perturbation theory. A formula was obtained for estimating the force of phonon friction, taking into account the frequency of phonons, the inverse decay time and the function of the two-dimensional Fourier image of the force of interaction between the atoms of the conjugated surface of the triboelement.
 Cases of static and dynamic phonon friction are considered.
 Electronic and phonon frictional forces are considered at the nanolevel. The Debye low-temperature approximation and refinement of the expressions for estimating the electronic and phonon friction forces are given, taking into account the type of interatomic potential

Ab initio simulations of the surface free energy of TiN(001)

The temperature dependence of the surface free energy of the industrially important TiN(001) system has been investigated by means of an extended two-stage upsampled thermodynamic integration using Langevin dynamics (TU-TILD) methodology, to include the fully anharmonic vibrational contribution, as obtained from ab initio molecular dynamics (AIMD). Inclusion of the fully anharmonic behavior is crucial, since the standard low-temperature quasiharmonic approximation exhibits a severe divergence in the surface free energy due to a high-temperature dynamical instability. The anharmonic vibrations compensate for the quasiharmonic divergence and lead to a modest overall temperature effect on the TiN(001) surface free energy, changing it from around $78\phantom{\rule{0.16em}{0ex}}\mathrm{meV}\phantom{\rule{0.16em}{0ex}}{\AA{}}^{\ensuremath{-}2}$ at 0 K to $73\phantom{\rule{0.16em}{0ex}}\mathrm{meV}\phantom{\rule{0.16em}{0ex}}{\AA{}}^{\ensuremath{-}2}$ at 3000 K. The statistical convergence of the molecular dynamics is facilitated by the use of machine-learning potentials, specifically moment tensor potentials, fitted for TiN(001) at finite temperature. The surface free energy obtained directly from the fitted machine-learning potentials is close to that obtained from the full AIMD simulations.

First-principle investigation of doping effects on mechanical and thermodynamic properties of [formula omitted

We investigate the variation of elastic stiffness moduli and the thermodynamic properties of yttrium orthosilicate (Y2SiO5, YSO) under various doping concentrations of Eu3+ ions. The model is based on a low temperature approximation (T<<θD) , and the plane-wave density functional theory (DFT) is used to carry out the calculations. The results show that the Eu3+ ions primarily occupy the Y1 site of the basic molecule for all applied concentrations. The overall shear, bulk, and Young’s moduli exhibit a decreasing trend with increasing Eu3+ concentration. The overall anisotropy shows a very small increase with increasing concentration. The Debye temperature as well as the Grünesien parameter for each concentration are predicted. Lastly, the predicted heat capacity at constant volume is calculated and compared to experimental values. Our study reveals that there is almost linear relationship between concentration and mechanical properties of YSO. The decrease of the Grünesien parameter with concentration increase might decrease the anharmonic effects in YSO, although this effect is small. In addition, the change in heat capacity with concentration rise is negligible.

Thermodynamic properties of glassy phonon states induced by strong electron correlations in 𝜃-type organic charge transfer salts

The appearance of electron correlations–induced glassy state of low-energy phonons in the non-dimeric organic charge transfer salt in [Formula: see text]-(BEDT-TTF)2CsZn(SCN)4 is considered as a strong evidence of charge lattice coupling in molecular charge transfer salts. We discuss the temperature and the magnetic field dependences of the heat capacity of this salt in terms of the soft potential model to describe the thermodynamic properties of enhanced phonons that occur in molecular glasses. The evaluated [Formula: see text] term of [Formula: see text]-(BEDT-TTF)2CsZn(SCN)4 is about 30 mJ K[Formula: see text] mol[Formula: see text], which is much larger than other charge transfer salts described by the low-temperature approximation of the Debye model. The magnetic fields dependence of the boson peak is almost negligible, but the low-energy term, for example, in the temperature-linear term of heat capacity shows a slight change, probably due to the small amount of localized spin moments. The comparison with other systems is also performed.

Effect of boundary conditions on fluctuations of the Bose condensate of interacting atoms

For a gas of trapped interacting atoms forming a Bose condensate, we demonstrate a possibility of a significant influence of the boundary conditions on the statistics of the number of particles in the fundamental mode of the system. The analysis is carried out in the Bogoliubov – Popov low-temperature approximation for model homogeneous cubic traps with periodic or combined periodic and zero boundary conditions. It is shown that the effect of the boundary conditions does not weaken even in the region of parameters corresponding to the relatively strong interaction in the Thomas – Fermi asymptotic case, and does not disappear when proceeding to the thermodynamic limit.

Fluctuating temperature and baryon chemical potential in heavy-ion collisions and the position of the critical end point in the effective QCD phase diagram

We use the linear sigma model with quarks to locate the critical end point in the effective QCD phase diagram accounting for fluctuations in temperature and quark chemical potential. For this purpose, we use the non-equilibrium formalism provided by the superstatistics framework. We compute the effective potential in the high- and low-temperature approximations up to sixth order and include the contribution of ring diagrams to account for plasma screening effects. We fix the model parameters from relations between the thermal sigma and pion masses imposing a first order phase transition at zero temperature and a finite critical value for the baryon chemical potential that we take of order of the nucleon mass. We find that the CEP displacement due to fluctuations in temperature and/or quark chemical potential is almost negligible.

On the critical end point in a two-flavor linear sigma model coupled to quarks

We use the linear sigma model coupled to quarks to explore the location of the phase transition lines in the QCD phase diagram from the point of view of chiral symmetry restoration at high temperature and baryon chemical potential. We compute analytically the effective potential in the high- and low-temperature approximations up to sixth order, including the contribution of the ring diagrams to account for the plasma screening properties. We determine the model parameters, namely, the couplings and mass-parameter, from conditions valid at the first order phase transition at vanishing temperature and, using the Hagedorn limiting temperature concept applied to finite baryon density, for a critical baryochemical potential of order of the nucleon mass. We show that when using the set of parameters thus determined, the second order phase transition line (our proxy for the crossover transition) that starts at finite temperature and zero baryon chemical potential converges to the line of first order phase transitions that starts at zero temperature and finite baryon chemical potential to determine the critical end point to lie in the region $$5.02<\mu _B^{\tiny {\text{ CEP }}}/T_c<5.18$$, $$0.14<T^{\tiny {\text{ CEP }}}/T_c<0.23$$, where $$T_c$$ is the critical transition temperature at zero baryon chemical potential.

Thermoelectric transport coefficients of a Dirac electron gas in high magnetic fields

We study the thermoelectric transport properties of a three-dimensional massive relativistic fermion gas with screened Coulomb impurities in high magnetic fields where only the lowest Landau levels contribute to the transport. Our results can be applied to experimental results of gapless and gapped Dirac materials. We focus on the effects of the mass term and we show the main differences that arise compared to the massless Dirac fermions. The different behavior is shown to be relevant at higher magnetic fields. The calculations are performed in the framework of the linear response theory using the exact quantum mechanical solution of the system in a constant magnetic field. We prove that the Mott formula and the Wiedemann-Franz law are valid at low temperatures and use them to calculate the thermoelectric transport coefficients. We show that the temperature range where the low temperature approximation is valid increases with increasing magnetic fields. The magnetic field dependence of measurable quantities (i.e. conductivity, Seebeck coefficient, Nernst coefficient and thermal conductivity) strongly depend on the magnetic field dependence of the scattering rate, thus the result relies on the proper treatment of the impurities. In this work they are included through the first Born approximation using screened charged impurities as impurity potential. We show that the electric conductivity does not change qualitatively in the case of finite mass term. On the other hand we find that the mass term causes significantly different behavior in the Seebeck and Nernst coefficients.

Low temperature gradient thermoelectric generator: Modelling and experimental verification

Internet of Things (IoT) and wearable sensing paradigm assume the sensing devices are available 24/7 and can be accessed from anywhere. This vision implies strict requirements to the power supply and energy harvesting which are expected to guarantee ‘perpetual’ operation of IoT devices. This paper reports on modelling and experimental verification of low temperature gradient thermoelectric generator. Obtained under the conditions of low gradient temperature approximation, the model accounts for the key physical phenomena and enables the accurate output power calculations using a closed-form expression. We perform a comparative study on the state-of-the-art models against the obtained solution and show the simplicity and performance of the proposed approach. For demonstrating practical feasibility of the model, we develop an experimental testbed consisting of the power generator, temperature control and data acquisition units. Experimental results demonstrate the average error 5.5% which improves the state-of-the-art results.

Random field Ising-like effective theory of the glass transition. II. Finite-dimensional models

As in the preceding paper we aim at identifying the effective theory that describes the fluctuations of the local overlap with an equilibrium reference configuration close to a putative thermodynamic glass transition. We focus here on the case of finite-dimensional glass-forming systems, in particular supercooled liquids. The main difficulty for going beyond the mean-field treatment comes from the presence of diverging point-to-set spatial correlations. We introduce a variational low-temperature approximation scheme that allows us to account, at least in part, for the effect of these correlations. The outcome is an effective theory for the overlap fluctuations in terms of a random-field + random-bond Ising model with additional, power-law decaying, pair and multi-body interactions generated by the point-to-set correlations. This theory is much more tractable than the original problem. We check the robustness of the approximation scheme by applying it to a fully connected model already studied in the companion paper. We discuss the physical implications of this mapping for glass-forming liquids and the possibility it offers to determine the presence or not of a finite-temperature thermodynamic glass transition.

Temperature dependence of the Gibbs energy of vacancy formation of fcc Ni

Quantum-mechanical calculations are used to determine the temperature dependence of the Gibbs energy of vacancy formation in nickel. Existing data reveal a discrepancy between the high-temperature estimates from experiments and low-temperature approximations from density functional theory. Our finite-temperature calculations - which include the effects of magnetism and fully interacting phonon vibrations - demonstrate that this discrepancy is mostly caused by the previously neglected explicit anharmonic contribution.

Relaxation Rate and Mobility of a Two-dimensional Electron Gas in MgZnO/ZnO Heterostructures Including Exchange and Correlation Effects

We investigate the relaxation rate and mobility of a two-dimensional electron gas (2DEG) confined in MgZnO/ZnO heterostructures (HSs) for temperatures , taking into account exchange and correlation effects. We use the variational-subband-wave-function model for carrier confinement and assume that the electrons are confined to the lowest subband and scattered by acoustic phonons via deformation potential (DP) and piezoelectric (PE) fields, polar LO phonons, interface roughness (IRS), interface charges (IFCs) and the background impurities (BIs). The calculations are based on the linearized Boltzmann equation (BE) and the relaxation time approximation, assuming the scattering by acoustic phonons to be quasi-elastic. We consider three physically distinct temperature ranges with respect to phonon scattering: the Bloch-Grüneisen (BG), equipartition (EP), and inelastic regimes. In the inelastic regime at high temperatures, where the scattering from polar LO phonons becomes important, we solve directly the linearized BE by an iterative method and compare the obtained results with those of the low-temperature and high-energy relaxation-time approximation. Our calculated low-temperature mobility is in good agreement with the recent experiment.

Spin-diffusions and diffusive molecular dynamics

Metastable configurations in condensed matter typically fluctuate about local energy minima at the femtosecond time scale before transitioning between local minima after nanoseconds or microseconds. This vast scale separation limits the applicability of classical molecular dynamics (MD) methods and has spurned the development of a host of approximate algorithms. One recently proposed method is diffusive MD which aims at integrating a system of ordinary differential equations describing the likelihood of occupancy by one of two species, in the case of a binary alloy, while quasistatically evolving the locations of the atoms. While diffusive MD has shown itself to be efficient and provide agreement with observations, it is fundamentally a model, with unclear connections to classical MD. In this work, we formulate a spin-diffusion stochastic process and show how it can be connected to diffusive MD. The spin-diffusion model couples a classical overdamped Langevin equation to a kinetic Monte Carlo model for exchange amongst the species of a binary alloy. Under suitable assumptions and approximations, spin-diffusion can be shown to lead to diffusive MD type models. The key assumptions and approximations include a well-defined time scale separation, a choice of spin-exchange rates, a low temperature approximation, and a mean field type approximation. We derive several models from different assumptions and show their relationship to diffusive MD. Differences and similarities amongst the models are explored in a simple test problem.

The behavior of three-dimensional ultimately short optical pulses in a system of carbon nanotubes in the presence of an external magnetic field

The character of the behavior of three-dimensional ultimately short optical pulses propagating in a system of carbon nanotubes in the presence of an external magnetic field perpendicular to both the nanotubes’ axis and the direction of pulse propagation is investigated. Electromagnetic-field evolution is analyzed within the framework of the Maxwell’s equations, while the electronic system of the carbon nanotubes is investigated in the low-temperature approximation.

Three-dimensional extremely-short optical pulses in carbon nanotube arrays in the presence of an external magnetic field

In this paper, we study the behavior of three-dimensional extremely-short optical pulses propagating in a system made of carbon nanotubes in the presence of an external magnetic field applied perpendicular both to the nanotube axis and to the direction of propagation of the pulse. The evolution of the electromagnetic field is classically derived on the basis of the Maxwell’s equations. The electronic system of carbon nanotubes is considered in the low-temperature approximation. Our analysis reveals the novel and unique ability of controlling the shape of propagating short optical pulses by tuning the intensity of the applied magnetic field. This effect paves the way for the possible development of innovative applications in optoelectronics.

Atomic Layer Deposition of Zinc Oxide: Diethyl Zinc Reactions and Surface Saturation from First-Principles

Zinc oxide thin films grown via atomic layer deposition have been under intense research for the past few years. Here, we present a comprehensive density functional theory study on the atomic layer deposition of zinc oxide. The adsorption of diethyl zinc and subsequent surface reactions are studied on an ideal (100) ZnO surface as well as on a stepped surface to compare ideal and nonideal surface structures. Our results show that diethyl zinc adsorbs and reacts rapidly on the surface to form monoethyl zinc. Our calculations also show that the initial ligand-exchange reactions are preferred on the planar surface over the step surface. Further reaction from monoethyl zinc to adsorbed zinc atoms has a high reaction barrier. We present two surface structures for the saturated zinc oxide surface at the end of the diethyl zinc pulse corresponding to low and high temperature approximations that are in good agreement with the experiments.

Quantum Paraelectric States in SrTiO3and KTaO3: Barrett Model, Vendik Model, and Quantum Criticality

The dielectric constants of the quantum paraelectrics SrTiO3 and KTaO3 are measured between 4 and 325 K. Their temperature dependences are analyzed on the basis of the Barrett and Vendik models. The former model deals with a ferroelectric optical mode coupled with other optical modes, whereas the latter deals with the mode coupled with acoustic modes. In addition, the latter contains a measure of the density of defects and inhomogeneity. The dielectric constants at low temperatures can be accurately described using Vendik’s formula; however, they cannot be accurately described using Barrett’s formula, even after the introduction of a measure of the density of defects and inhomogeneity. A critical quantum paraelectric region has been introduced recently between a classical region and a quantum paraelectric one. We point out that the critical region is where a low-temperature approximation is well realized for the model with the coupling between the ferroelectric and acoustic modes.

Finite temperature bosonic charge and current densities in compactified cosmic string spacetime

In this paper we study the expectation values of the induced charge and current densities for a massive bosonic field with nonzero chemical potential in the geometry of a higher dimensional compactified cosmic string with magnetic fluxes, along the string core and also enclosed by the compactified direction, in thermal equilibrium at finite temperature $T$. These densities are calculated by decomposing them into the vacuum expectation values and finite temperature contributions coming from the particles and antiparticles. The only nonzero components correspond to the charge, azimuthal and axial current densities. By using the Abel-Plana formula, we decompose the components of the densities into the part induced by the cosmic string and the one by the compactification. The charge density is an odd function of the chemical potential and even periodic function of the magnetic flux with a period equal to the quantum flux. Moreover, the azimuthal (axial) current density is an even function of the chemical potential and an odd (even) periodic function of the magnetic flux with the same period. In this paper our main concern is the thermal effect on the charge and current densities, including some limiting cases, the low and high temperature approximations. We show that in all cases the temperature enhances the induced densities.

Solitons and nonlinear waves along quantum vortex filaments under the low-temperature two-dimensional local induction approximation.

Very recent experimental work has demonstrated the existence of Kelvin waves along quantized vortex filaments in superfluid helium. The possible configurations and motions of such filaments is of great physical interest, and Svistunov previously obtained a Hamiltonian formulation for the dynamics of quantum vortex filaments in the low-temperature limit under the assumption that the vortex filament is essentially aligned along one axis, resulting in a two-dimensional (2D) problem. It is standard to approximate the dynamics of thin filaments by employing the local induction approximation (LIA), and we show that by putting the two-dimensional LIA into correspondence with the first equation in the integrable Wadati-Konno-Ichikawa-Schimizu (WKIS) hierarchy, we immediately obtain solutions to the two-dimensional LIA, such as helix, planar, and self-similar solutions. These solutions are obtained in a rather direct manner from the WKIS equation and then mapped into the 2D-LIA framework. Furthermore, the approach can be coupled to existing inverse scattering transform results from the literature in order to obtain solitary wave solutions including the analog of the Hasimoto one-soliton for the 2D-LIA. One large benefit of the approach is that the correspondence between the 2D-LIA and the WKIS allows us to systematically obtain vortex filament solutions directly in the Cartesian coordinate frame without the need to solve back from curvature and torsion. Implications of the results for the physics of experimentally studied solitary waves, Kelvin waves, and postvortex reconnection events are mentioned.