Linear Transport Coefficients Research Articles

Nonlinear electrical transport phenomena as fingerprints of a topological phase transition in ZrTe5

Topological phase transitions, influenced by magnetic fields, dopants, pressure, and temperature, create Berry curvature in band structures, challenging to detect due to resolution and scattering issues in spectroscopy and transport. Here, we propose nonlinear electrical transport phenomena as fingerprints of a topological phase transition in ZrTe5 under magnetic fields. Both a nonlinear longitudinal conductivity ΔσL in a magnetic-field-aligned electric field and a third-order nonlinear Hall (transverse) conductivity Δσxy in a magnetic-field-perpendicular electric field arise below a characteristic temperature T*. The sensitivity of nonlinear transport to the band topology allows the detection of a subtle change in the band topology hidden in linear transport coefficients. Extending the previous scaling theory between linear transport coefficients (σxx and σxy), we also propose scaling relations for both linear (σxx and σxy) and nonlinear (ΔσL and Δσxy) transport coefficients. These scaling relations will help understand the interplay between the mechanisms of nonlinear transport coefficients and the influence of Berry curvature.

Internal lipid bilayer friction coefficient from equilibrium canonical simulations

A fundamental result in the theory of Brownian motion is the Einstein-Sutherland relation between mobility and diffusion constant. Any classical linear response transport coefficient obeys a similar Einstein-Helfand relation. We show in this work how to derive the interleaflet friction coefficient of lipid bilayer by means of an adequate generalisation of the Einstein relation. Special attention must be paid in practical cases to the constraints on the system center of mass position that must be enforced when coupling the system to thermostat.

To the derivation of relativistic hydrodynamic equations for a rarefied non-ideal gas system of high-energy particles in the framework of Tsallis statistics

The paper discusses the construction of non-extensive relativistic dissipative hydrodynamics of an anomalous hadronic fluid on the basis of relativistic kinetic equation, obtained earlier in the context of the Tsallis statistics, characterized by the nonextensivity parameter q, and taking into account correlation effects (by rejecting the standard hypothesis of molecular chaos) in the collision term for heavy ions. It is shown that some specific form of local thermal equilibrium quark-gluon matter is described by a generalized version of the relativistic Yüttner distribution. With the help of this distribution all thermodynamic parameters of state are defined in explicit form. Linear constitutive relations and transport coefficients such as shear viscosity, bulk viscosity and heat conductivity are derived from the linearized collision integral written in the Anderson-Witting form and evaluated using a relaxation time approximation. The designed non-extensive relativistic fluid dynamics is designed to simulate a wide range of phenomena in astrophysics, cosmology and high-energy physics.

К выводу в рамках статистики Тсаллиса релятивистских гидродинамических уравнений для разреженной неидеальной газовой системы высокоэнергетических частиц

In the paper the construction of non-extensive relativistic dissipative hydrodynamics of identical particles on the basis of the relativistic kinetic equation obtained in a q-non-extensive context of Tsallis statistics and taking into account inclusion of correlation effects (by rejecting the molecular chaos hypothesis ) into the collision term. It is shown that the local collision equilibrium is described by a generalized version of the Yuttner relativistic distribution. With the help of this distribution all thermodynamic parameters of state are defined in explicit form. Linear constitutive relations and transport coefficients such as shear viscosity, bulk viscosity and heat conductivity are derived from the linearized collision integral written in the Anderson-Witting form and evaluated using a relaxation time approximation. The designed non-extensive relativistic fluid dynamics is designed to simulate a wide range of phenomena in astrophysics, cosmology and high-energy physics

Ionic mobility driven by correlated van der Waals and electrostatic forces.

Classical theories of dielectric friction make two critical assumptions: (i) friction due to van der Waals (vdW) forces is described by hydrodynamic drag and is independent of the ionic charge and (ii) vdW and electrostatic forces are statistically independent. Both assumptions turn out to be incorrect when tested against simulations of anions and cations with varying charge magnitude dissolved in water. Both the vdW and electrostatic components of the force variance scale linearly with the ionic charge squared. The two components are strongly anticorrelated producing simple relations for the total force variance in terms of self-variances. The inverse diffusion constant scales linearly with the charge squared. Solvation asymmetry between cations and anions extends to linear transport coefficients.

Estimating linear mass transport coefficients in solid solutions via correlation splitting and a law of total diffusion

Directly computing linear mass transport coefficients in stochastic models entails integrating over time the equilibrium correlations between atomic displacements. Here, we show how to improve the accuracy of kinetic Monte Carlo simulations via correlation splitting and conditioning, which statistically amounts to estimating the mass transport coefficients through a law of total diffusion. We illustrate the approach with kinetic path sampling simulations of atomic diffusion in a random alloy model in which percolating solute clusters trap the mediating vacancy. There, Green functions serve to generate first-passage paths escaping the traps and to propagate the long-time dynamics. When they also serve to estimate mean-squared displacements via conditioning, colossal reductions of statistical errors are achieved.

Dielectrophoresis of Proteins in Solution.

A nonionic particle placed in the gradient of an electric field experiences the dielectrophoretic force which scales linearly with the gradient of the electric field squared. The proportionality constant is the dielectrophoretic susceptibility, that is, a linear transport coefficient. For proteins in solution, it is mostly affected by the following two parameters: the squared dipole moment and the cavity susceptibility accounting for cross-correlations of the protein dipole with the hydration shell (protein-water Kirkwood factor). Both of these parameters enter the dielectric increment of the solution which fully specifies the dielectrophoretic susceptibility. The link between these two measurable properties is proven here to hold using molecular dynamics simulations of solvated proteins. The dielectrophoretic susceptibility for proteins is in the range of 104, significantly exceeding traditional estimates limiting it to values below unity. Part of this large magnitude of the dielectrophoretic response is the cavity susceptibility of the protein-water interface, which significantly exceeds dielectric estimates. The study analyzes local fields inside the protein in terms of the reaction-field and directing-field components. We find that the local field exceeds the external field by a substantial factor described by the local field susceptibility. The electric field produced by water inside the protein is retarded by 3-4 orders of magnitude compared to the bulk.

Microscopic approach to the macrodynamics of matter with broken symmetries

A unified set of hydrodynamic equations describing condensed phases of matter with broken continuous symmetries is derived using a generalization of the statistical-mechanical approach based on the local equilibrium distribution. The dissipativeless and dissipative parts of the current densities and the entropy production are systematically deduced in this approach by expanding in powers of the gradients of the macrofields. Green–Kubo formulas are obtained for all the linear transport coefficients. The consequences of microreversibility and spatial symmetries are investigated, leading to the prediction of cross effects resulting from Onsager–Casimir reciprocal relations. Crystalline solids and liquid crystals are potential examples of application. The approach is clarifying the links between the microscopic Hamiltonian dynamics and the thermodynamic and transport properties at the macroscale.

Brownian thermal transistors and refrigerators in mesoscopic systems

Fluctuations are significant in mesoscopic systems and of particular importance in understanding quantum transport. Here, we show that fluctuations can be considered as a resource for the operations of open quantum systems as functional devices. We derive the statistics of the thermal transistor amplification factor and the cooling-by-heating refrigerator efficiency under the Gaussian fluctuation framework. Statistical properties of the stochastic thermal transistor and the cooling-by-heating efficiency are revealed in the linear-response regime. We clarify the unique role of inelastic processes on thermal transport in mesoscopic systems. We further show that elastic and inelastic processes lead to different bounds based on the linear transport coefficients by establishing a generic theoretical framework for mesoscopic heat transport, which treats electron and bosonic collective excitations in an equal-footing manner. The underlying physics are illustrated concretely using a double-quantum-dot three-terminal system, though the theory applies to more general systems.

Hydrodynamics for charge density waves and their holographic duals

We formulate a theory of dissipative hydrodynamics with spontaneously broken translations, describing charge density waves in a clean isotropic electronic crystal. We identify a novel linear transport coefficient, lattice pressure, capturing the effects of background strain and thermal expansion in a crystal. We argue that lattice pressure is a generic feature of systems with spontaneously broken translations and must be accounted for while building and interpreting holographic models. We also provide the first calculation of the coefficients of thermal and chemical expansion in a holographic electronic crystal.

Driving an electrolyte through a corrugated nanopore

We characterize the dynamics of a z - z electrolyte embedded in a varying-section channel. In the linear response regime, by means of suitable approximations, we derive the Onsager matrix associated with externally enforced gradients in electrostatic potential, chemical potential, and pressure, for both dielectric and conducting channel walls. We show here that the linear transport coefficients are particularly sensitive to the geometry and the conductive properties of the channel walls when the Debye length is comparable to the channel width. In this regime, we found that one pair of off-diagonal Onsager matrix elements increases with the corrugation of the channel transport, in contrast to all other elements which are either unaffected by or decrease with increasing corrugation. Our results have a possible impact on the design of blue-energy devices as well as on the understanding of biological ion channels through membranes.

Revised Formulation of Fick's, Fourier's, and Newton's Laws for Spatially Varying Linear Transport Coefficients.

We argue that for situations involving spatially varying linear transport coefficients (diffusivities, thermal conductivities, and viscosities), the original Fick’s, Fourier’s, and Newton’s law equations should be modified to place the diffusivity, thermal conductivity, and viscosity inside the derivative operator, that is, in one-dimensional rectilinear situations, , , and . We present simple derivations of these formulas in which diffusive mass transfer, conductive heat transfer, and molecular momentum transfer processes are described using lattice random walk models. We also present simple examples demonstrating how these modifications affect calculations.

Temperature-dependent resistivity and anomalous Hall effect in NiMnSb from first principles

We present implementation of the alloy analogy model within fully relativistic density-functional theory with the coherent potential approximation for a treatment of nonzero temperatures. We calculate contributions of phonons and magnetic and chemical disorder to the temperature-dependent resistivity, anomalous Hall conductivity (AHC), and spin-resolved conductivity in ferromagnetic half-Heusler NiMnSb. Our electrical transport calculations with combined scattering effects agree well with experimental literature for Ni-rich NiMnSb with 1--2% Ni impurities on Mn sublattice. The calculated AHC is dominated by the Fermi surface term in the Kubo-Bastin formula. Moreover, the AHC as a function of longitudinal conductivity consists of two linear parts in the Ni-rich alloy, while it is nonmonotonic for Mn impurities. We obtain the spin polarization of the electrical current $P>90%$ at room temperature and we show that $P$ may be tuned by chemical composition. The presented results demonstrate the applicability of an efficient first-principles scheme to calculate temperature dependence of linear transport coefficients in multisublattice bulk magnetic alloys.

Diffusion in Deterministic Interacting Lattice Systems.

We study reversible deterministic dynamics of classical charged particles on a lattice with hard-core interaction. It is rigorously shown that the system exhibits three types of transport phenomena, ranging from ballistic, through diffusive to insulating. By obtaining an exact expressions for the current time-autocorrelation function we are able to calculate the linear response transport coefficients, such as the diffusion constant and the Drude weight. Additionally, we calculate the long-time charge profile after an inhomogeneous quench and obtain diffusive profilewith the Green-Kubo diffusion constant. Exact analytical results are corroborated by MonteCarlo simulations.

Anomalous transport from holography: part II

This is a second study of chiral anomaly-induced transport within a holographic model consisting of anomalous U(1)_Vtimes U(1)_A Maxwell theory in Schwarzschild–AdS_5 spacetime. In the first part, chiral magnetic/separation effects (CME/CSE) are considered in the presence of a static spatially inhomogeneous external magnetic field. Gradient corrections to CME/CSE are analytically evaluated up to third order in the derivative expansion. Some of the third order gradient corrections lead to an anomaly-induced negative B^2-correction to the diffusion constant. We also find modifications to the chiral magnetic wave nonlinear in B. In the second part, we focus on the experimentally interesting case of the axial chemical potential being induced dynamically by a constant magnetic and time-dependent electric fields. Constitutive relations for the vector/axial currents are computed employing two different approximations: (a) derivative expansion (up to third order) but fully nonlinear in the external fields, and (b) weak electric field limit but resuming all orders in the derivative expansion. A non-vanishing nonlinear axial current (CSE) is found in the first case. The dependence on magnetic field and frequency of linear transport coefficient functions is explored in the second.

First-principles calculation of the thermoelectric figure of merit for [2,2]paracyclophane-based single-molecule junctions

Here we present a theoretical study of the thermoelectric transport through {[}2,2{]}para\-cyclo\-phane-based single-molecule junctions. Combining electronic and vibrational structures, obtained from density functional theory (DFT), with nonequilibrium Green's function techniques, allows us to treat both electronic and phononic transport properties at a first-principles level. For the electronic part, we include an approximate self-energy correction, based on the DFT+$\Sigma$ approach. This enables us to make a reliable prediction of all linear response transport coefficients entering the thermoelectric figure of merit $ZT$. Paracyclophane derivatives offer a great flexibility in tuning their chemical properties by attaching different functional groups. We show that, for the specific molecule, the functional groups mainly influence the thermopower, allowing to tune its sign and absolute value. We predict that the functionalization of the bare paracyclophane leads to a largely enhanced electronic contribution $Z_{\mathrm{el}}T$ to the figure of merit. Nevertheless, the high phononic contribution to the thermal conductance strongly suppresses $ZT$. Our work demonstrates the importance to include the phonon thermal conductance for any realistic estimate of the $ZT$ for off-resonant molecular transport junctions. In addition, it shows the possibility of a chemical tuning of the thermoelectric properties for a series of available molecules, leading to equally performing hole- and electron-conducting junctions based on the same molecular framework.

Transport with ultracold atoms at constant density

We investigate the transport through a few-level quantum system described by a Markovian master equation with temperature- and particle-density-dependent chemical potentials. From the corresponding Onsager relations we extract linear response transport coefficients in analogy to the electronic conductance, thermal conductance, and thermopower. Considering ideal Fermi and Bose gas reservoirs, we observe steady-state currents against the thermal bias as a result of the nonlinearities introduced by the constraint of a constant particle density in the reservoirs. Most importantly, we find signatures of the onset of Bose-Einstein condensation in the transport coefficients.

Electrokinetic and hydrodynamic properties of charged-particles systems

Dynamic processes in dispersions of charged spherical particles are of importance both in fundamental science, and in technical and bio-medical applications. There exists a large variety of charged-particles systems, ranging from nanometer-sized electrolyte ions to micron-sized charge-stabilized colloids. We review recent advances in theoretical methods for the calculation of linear transport coefficients in concentrated particulate systems, with the focus on hydrodynamic interactions and electrokinetic effects. Considered transport properties are the dispersion viscosity, self- and collective diffusion coefficients, sedimentation coefficients, and electrophoretic mobilities and conductivities of ionic particle species in an external electric field. Advances by our group are also discussed, including a novel mode-coupling-theory method for conduction-diffusion and viscoelastic properties of strong electrolyte solutions. Furthermore, results are presented for dispersions of solvent-permeable particles, and particles with non-zero hydrodynamic surface slip. The concentration-dependent swelling of ionic microgels is discussed, as well as a far-reaching dynamic scaling behavior relating colloidal long- to short-time dynamics.

Nonlinear closure relations theory for transport processes in nonequilibrium systems

A decade ago, a macroscopic theory for closure relations has been proposed for systems out of Onsager's region. This theory is referred to as the thermodynamic field theory (TFT). The aim of this work was to determine the nonlinear flux-force relations that respect the thermodynamic theorems for systems far from equilibrium. We propose a formulation of the TFT where one of the basic restrictions, namely, the closed-form solution for the skew-symmetric piece of the transport coefficients, has been removed. In addition, the general covariance principle is replaced by the De Donder-Prigogine thermodynamic covariance principle (TCP). The introduction of TCP requires the application of an appropriate mathematical formalism, which is referred to as the entropy-covariant formalism. By geometrical arguments, we prove the validity of the Glansdorff-Prigogine universal criterion of evolution. A new set of closure equations determining the nonlinear corrections to the linear ("Onsager") transport coefficients is also derived. The geometry of the thermodynamic space is non-Riemannian. However, it tends to be Riemannian for high values of the entropy production. In this limit, we recover the transport equations found by the old theory. Applications of our approach to transport in magnetically confined plasmas, materials submitted to temperature, and electric potential gradients or to unimolecular triangular chemical reactions can be found at references cited herein. Transport processes in tokamak plasmas are of particular interest. In this case, even in the absence of turbulence, the state of the plasma remains close to (but, it is not in) a state of local equilibrium. This prevents the transport relations from being linear.

An analysis of the far-field response to external forcing of a suspension in the Stokes flow in a parallel-wall channel

The leading-order far-field scattered flow produced by a particle in a parallel-wall channel under creeping-flow conditions has a form of the parabolic velocity field driven by a two-dimensional dipolar pressure distribution. We show that in a system of hydrodynamically interacting particles, the pressure dipoles contribute to the macroscopic suspension flow in a similar way as the induced electric dipoles contribute to the electrostatic displacement field. Using this result we derive macroscopic equations governing suspension transport under the action of a lateral force, a lateral torque, or a macroscopic pressure gradient in the channel. The matrix of linear transport coefficients in the constitutive relations linking the external forcing to the particle and fluid fluxes satisfies the Onsager reciprocal relation. The transport coefficients are evaluated for square and hexagonal periodic arrays of fixed and freely suspended particles, and a simple approximation in a Clausius–Mossotti form is proposed for the channel permeability coefficient. We also find explicit expressions for evaluating the periodic Green’s functions for the Stokes flow between two parallel walls.