Victor E. Ambrus

Rotating fermions inside a cylindrical boundary

We study a quantum fermion field inside a cylinder in Minkowski space-time. On the surface of the cylinder, the fermion field satisfies either spectral or MIT bag boundary conditions. We define rigidly-rotating quantum states in both cases, assuming that the radius of the cylinder is sufficiently small that the speed-of-light surface is excluded from the space-time. With this assumption, we calculate rigidly-rotating thermal expectation values of the fermion condensate, neutrino charge current and stress-energy tensor relative to the bounded vacuum state. These rigidly-rotating thermal expectation values are finite everywhere inside and on the surface of the cylinder, and their detailed properties depend on the choice of boundary conditions. We also compute the Casimir divergence of the expectation values of these quantities in the bounded vacuum state relative to the unbounded Minkowski vacuum. We find that the rate of divergence of the Casimir expectation values depends on the conditions imposed on the boundary.

Application of mixed quadrature lattice Boltzmann models for the simulation of Poiseuille flow at non-negligible values of the Knudsen number

Abstract We consider the 2D force-driven Poiseuille flow between parallel plates, on which diffuse reflection boundary conditions apply. We present a systematic procedure for the construction of the force term in lattice Boltzmann models based on mixed Cartesian quadratures, where the quadrature on each axis is selected independently. We find that, at non-negligible value of the Knudsen number, half-range quadratures outperform the full-range Gauss–Hermite quadratures for the direction perpendicular to the diffuse-reflecting plates, while the quadrature on the periodic direction along the flow is the full-range Gauss–Hermite quadrature. Our results are validated against numerical results available in the literature.

Lattice Boltzmann models based on half-range Gauss-Hermite quadratures

We discuss general features of thermal lattice Boltzmann models based on half-range Gauss quadratures, specialising to the half-range Gauss-Hermite and Gauss-Laguerre cases. The main focus of the paper is on the construction of high order half-range Hermite lattice Boltzmann (HHLB) models. The performance of the HHLB models is compared with that of Laguerre lattice Boltzmann (LLB) and full-range Hermite lattice Boltzmann (HLB) models by conducting convergence tests with respect to the quadrature order on stationary profiles of the particle number density, macroscopic velocity, temperature and heat fluxes in the two-dimensional Couette flow. The Bhatnagar-Gross-Krook (BGK) collision term is used throughout the paper. To reduce the computational costs of the numerical simulations, we use mixed lattice Boltzmann models, constructed using different quadrature methods on each Cartesian axis. For Kn ? 0.01 , the HLB models require the least number of velocities to satisfy our convergence test. When Kn ? 0.05 , the HLB models are outperformed in terms of number of velocities employed by both the LLB and the HHLB models. Moreover, we find that the HHLB models require less quadrature points than the LLB models at all tested values of Kn, which we attribute to the Maxwellian form of the weight function for the half-range Hermite polynomials.

Renormalised fermion vacuum expectation values on anti-de Sitter space–time

Abstract The Schwinger–de Witt and Hadamard methods are used to obtain renormalised vacuum expectation values for the fermion condensate, charge current and stress-energy tensor of a quantum fermion field of arbitrary mass on four-dimensional anti-de Sitter space–time. The quantum field is in the global anti-de Sitter vacuum state. The results are compared with those obtained using the Pauli–Villars and zeta-function regularisation methods, respectively.

Lattice Boltzmann models based on Gauss quadratures

The Gauss–Laguerre quadrature method is used to construct three-dimensional thermal Lattice Boltzmann models that exactly recover integrals of the equilibrium distribution function over Cartesian octants of the momentum space. We illustrate the capability of these models to exactly implement the diffuse reflection boundary conditions by considering the Couette flow at various values of the Knudsen number.

Thermal expectation values of fermions on anti-de Sitter space-time

Making use of the symmetries of anti-de Sitter space-time, we derive an analytic expression for the bispinor of parallel transport, from which we construct in closed form the vacuum Feynman Greens function of the Dirac field on this background. Using the imaginary time anti-periodicity property of the thermal Feynman Greens function, we calculate the thermal expectation values of the fermion condensate and stress-energy tensor and highlight the effect of quantum corrections as compared to relativistic kinetic theory results.

Dirac fermions on an anti-de Sitter background

Using an exact expression for the bi-spinor of parallel transport, we construct the Feynman propagator for Dirac fermions in the vacuum state on anti-de Sitter space-time. We compute the vacuum expectation value of the stress-energy tensor by removing coincidence-limit divergences using the Hadamard method. We then use the vacuum Feynman propagator to compute thermal expectation values at finite temperature. We end with a discussion of rigidly rotating thermal states.

Quadrature-based lattice Boltzmann model for relativistic flows

A quadrature-based finite-difference lattice Boltzmann model is developed that is suitable for simulating relativistic flows of massless particles. We briefly review the relativistc Boltzmann equation and present our model. The quadrature is constructed such that the stress-energy tensor is obtained as a second order moment of the distribution function. The results obtained with our model are presented for a particular instance of the Riemann problem (the Sod shock tube). We show that the model is able to accurately capture the behavior across the whole domain of relaxation times, from the hydrodynamic to the ballistic regime. The property of the model of being extendable to arbitrarily high orders is shown to be paramount for the recovery of the analytical result in the ballistic regime.

Quantum non-equilibrium effects in rigidly-rotating thermal states

Abstract Based on known analytic results, the thermal expectation value of the stress-energy tensor (SET) operator for the massless Dirac field is analysed from a hydrodynamic perspective. Key to this analysis is the Landau decomposition of the SET, with the aid of which we find terms which are not present in the ideal SET predicted by kinetic theory. Moreover, the quantum corrections become dominant in the vicinity of the speed of light surface (SOL). While rigidly-rotating thermal states cannot be constructed for the Klein–Gordon field, we perform a similar analysis at the level of quantum corrections previously reported in the literature and we show that the Landau frame is well-defined only when the system is enclosed inside a boundary located inside or on the SOL. We discuss the relevance of these results for accretion disks around rapidly-rotating pulsars.

APPLICATION OF LATTICE BOLTZMANN MODELS BASED ON LAGUERRE QUADRATURES TO FORCE-DRIVEN FLOWS OF RAREFIED GASES

The Laguerre Lattice Boltzmann (LLB) models are constructed to exactly recover integrals of the equilibrium distribution function over octants of the momentum space. In the mesoscopic formulation of the Boltzmann equation, such integrals are necessary for the implementation of diffuse reflection boundary conditions. In this paper, we consider two implementations of the force term in the LLB models, which we compare through simulations of the Poiseuille flow for values of the Knudsen number Kn varying from 0.01 through to infinity. We find an excellent agreement with the Chapman–Enskog theory at low values of Kn and with the ballistic regime at infinite Kn.