Using the near-detailed-balance distribution function obtained in our recent work, we present a set of covariant gravito-thermal transport equations (i.e. the flow of various charges as linear response to thermodynamical forces) for neutral relativistic gases in a generic stationary spacetime. All relevant tensorial transport coefficients are worked out and are presented using some particular integration functions in <math><mo>(</mo><mi>α</mi><mo>,</mo><mi>ζ</mi><mo>)</mo></math>, where <math><mi>α</mi><mo>=</mo><mo>−</mo><mi>β</mi><mi>μ</mi></math> and <math><mi>ζ</mi><mo>=</mo><mi>β</mi><mi>m</mi></math> is the relativistic coldness, with β being the inverse temperature and μ being the chemical potential. It is shown that the Onsager reciprocal relation holds in the gravito-thermal transport phenomena, and that the heat conductivity and the gravito-conductivity tensors are proportional to each other, with the coefficient of proportionality given by the product of the so-called Lorenz number with the temperature, thus proving a gravitational variant of the Wiedemann-Franz law. It is remarkable that, for strongly degenerate Fermi gases, the Lorenz number takes a universal constant value <math><mi>L</mi><mo>=</mo><msup><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>/</mo><mn>3</mn></math>, which extends the Wiedemann-Franz law into the Wiedemann-Franz-Lorenz law.

China

Xin Hao

Song Liu

Liu Zhao

Gravito-thermal transports, Onsager reciprocal relation and gravitational Wiedemann-Franz law

We have estimated the electrical and thermal conductivity of a hadron resonance gas (HRG) for a time-varying magnetic field, which is also compared with constant and zero magnetic field cases. Considering the exponential decay of electromagnetic fields with time, a kinetic theory framework can provide the microscopic expression of electrical conductivity and thermal conductivity related to baryon current in terms of relaxation and decay times. In the absence of the magnetic field, only a single timescale appears, and in the finite magnetic field case, their expressions carry two timescales—relaxation time and cyclotron time period. Estimating the conductivities for HRG matter in three cases—zero, constant, and time-varying magnetic fields, we have studied the validity of the Wiedemann–Franz law. We noticed that at a high-temperature domain, the ratio saturates at a particular value, which may be considered as Lorenz number of the hadron resonance gas. With respect to the saturation values, the deviation of the Wiedemann–Franz law has been quantified at the low-temperature domain. For the first time, the present work sketches this quantitative deviation of the Wiedemann–Franz law for hadron resonance gas at a constant and a time-varying magnetic field.

India

Kamaljeet Singh

Jayanta Dey

Raghunath Sahoo

Sabyasachi Ghosh

Effect of time-varying electromagnetic field on Wiedemann-Franz law in a hot hadronic matter

In this work, a hadron resonance gas under van der Waals interactions has been studied. Both attractive and repulsive interactions between the meson-meson and (anti)baryon-(anti)baryon have been taken into consideration. Various transport properties such as electrical conductivity (<math><msub><mi>σ</mi><mi>el</mi></msub></math>) and thermal conductivity (<math><msub><mi>κ</mi><mi>th</mi></msub></math>) have been estimated by solving the Boltzmann transport equation under the relaxation time approximation. The effect of baryochemical potential (<math><msub><mi>μ</mi><mi>B</mi></msub></math>) and temperature is also explicitly explored for the mentioned observables. Comparisons have been made with the results obtained from other existing theoretical models. We observe the violation of Wiedemann-Franz law in a hadron resonance gas at a high-temperature regime. The corresponding diffusivities have also been estimated, which can help us to understand the systems better.

Kshitish Kumar Pradhan

Dushmanta Sahu

Ronald Scaria

Conductivity, diffusivity, and violation of the Wiedemann-Franz Law in a hadron resonance gas with van der Waals interactions

In this paper we study the Wiedemann-Franz laws for transport in 2+1 dimensions, and the action of Sl(2, ℤ) on this transport, for theories with an AdS/CMT dual. We find that Sl(2, ℤ) restricts the RG-like flow of conductivities and that the Wiedemann-Franz law is   <math> <mover> <mi>L</mi> <mo>¯</mo> </mover> <mo>=</mo> <mover> <mi>κ</mi> <mo>¯</mo> </mover> <mo>/</mo> <mfenced> <mi>Tσ</mi> </mfenced> <mo>=</mo> <msubsup> <mi>cg</mi> <mn>4</mn> <mn>2</mn> </msubsup> <mi>π</mi> <mo>/</mo> <mn>3</mn> </math>  $$ \overline{L}=\overline{\kappa}/\left( T\sigma \right)={cg}_4^2\uppi /3 $$ , from the weakly coupled gravity dual. In a self-dual theory this value is also the value of L = κ/(Tσ) in the weakly coupled field theory description. Using the formalism of a 0+1 dimensional effective action for both generalized SY K  q  models and the AdS 4 gravity dual, we calculate the transport coefficients and show how they can be matched at large q. We construct a generalization of this effective action that is invariant under Sl(2, ℤ) and can describe vortex conduction and integer quantum Hall effect.

Brazil

Russia

Dmitry Melnikov

Horatiu Nastase

Wiedemann-Franz laws and Sl(2, ℤ) duality in AdS/CMT holographic duals and one-dimensional effective actions for them

We introduce an algebro-geometrically motived integration-by-parts (IBP) re- duction method for multi-loop and multi-scale Feynman integrals, using a framework for massively parallel computations in computer algebra. This framework combines the com- puter algebra system Singular with the workflow management system GPI-Space, which are being developed at the TU Kaiserslautern and the Fraunhofer Institute for Industrial Mathematics (ITWM), respectively. In our approach, the IBP relations are first trimmed by modern tools from computational algebraic geometry and then solved by sparse linear algebra and our new interpolation method. Modelled in terms of Petri nets, these steps are efficiently automatized and automatically parallelized by GPI-Space. We demonstrate the potential of our method at the nontrivial example of reducing two-loop five-point non- planar double-pentagon integrals. We also use GPI-Space to convert the basis of IBP reductions, and discuss the possible simplification of master-integral coefficients in a uni- formly transcendental basis.

Germany

Dominik Bendle

Janko Böhm

Wolfram Decker

Sweden

Alessandro Georgoudis

Franz-Josef Pfreundt

Mirko Rahn

Pascal Wasser

Yang Zhang

Integration-by-parts reductions of Feynman integrals using Singular and GPI-Space

Transport coefficients serve as important probes in characterizing the QCD matter created in high-energy heavy-ion collisions. Thermal and electrical conductivities as transport coefficients have special significance in studying the time evolution of the created matter. We have adopted a color string percolation approach for the estimation of thermal conductivity (<math><mi>κ</mi></math>), electrical conductivity (<math><msub><mi>σ</mi><mrow><mi>el</mi></mrow></msub></math>), and their ratio, which is popularly known as the Wiedemann-Franz law in condensed matter physics. The ratio <math><mrow><mi>κ</mi><mo>/</mo><msub><mrow><mi>σ</mi></mrow><mrow><mi>el</mi></mrow></msub><mi>T</mi></mrow></math>, which is also known as the Lorenz number (<math><mi>L</mi></math>), is studied as a function of temperature and is compared with various theoretical calculations. We observe that the thermal conductivity for a hot QCD medium is almost temperature independent in the present formalism and matches with the results obtained in an ideal equation of state for quark-gluon plasma with a fixed coupling constant (<math><msub><mi>α</mi><mi>s</mi></msub></math>). The obtained Lorenz number is compared with the Stefan-Boltzmann limit for an ideal gas. We observe that a hot QCD medium with color degrees of freedom behaves like a free electron gas.

Pragati Sahoo

Swatantra Kumar Tiwari

Wiedemann-Franz law for hot QCD matter in a color string percolation scenario

We studied a QED analog of the Franz-Keldysh effect, and the interplay between the nonperturbative (the Schwinger mechanism) and the perturbative particle production mechanism from the vacuum in the presence of a strong slow field superimposed by a weak field. We found that the Franz-Keldysh effect significantly affects the particle production: (i) the perturbative particle production occurs even below the threshold energy; (ii) the perturbative production becomes the most efficient just above the threshold energy; and (iii) an oscillating behavior appears in the production number above the threshold energy. These nontrivial changes are suppressed only weakly by powers of the critical field strength of QED. A relation to the dynamically assisted Schwinger mechanism and implications to experiments are also discussed.

Hidetoshi Taya

Franz-Keldysh effect in strong-field QED