Pablo Rodriguez-Lopez

Effect of finite temperature and uniaxial anisotropy on the Casimir effect with three-dimensional topological insulators

In this work we study the Casimir effect with three-dimensional topological insulators including the effects of temperature and uniaxial anisotropy. We find that the reported repulsive behavior and the equilibrium point are robust features of the system, and are favored by low temperatures and the enhancement of the optical response parallel to the optical axis. The dependence of the equilibrium point with temperature and with the topological magnetoelectric polarizability characteristic of three-dimensional topological insulators is also discussed. PACS numbers:

Repulsive Casimir effect with Chern insulators

We theoretically predict that the Casimir force in vacuum between two Chern insulator plates can be repulsive (attractive) at long distances whenever the sign of the Chern numbers characterizing the two plates are opposite (equal). A unique feature of this system is that the sign of the force can be tuned simply by turning over one of the plates or alternatively by electrostatic doping. We calculate and take into account the full optical response of the plates and argue that such repulsion is a general phenomena for these systems as it relies on the quantized zero frequency Hall conductivity. We show that achieving repulsion is possible with thin films of Cr-doped (Bi,Sb)2Te3, that were recently discovered to be Chern insulators with quantized Hall conductivity.

Casimir repulsion between topological insulators in the diluted regime

The Pairwise Summation Approximation (PSA) of Casimir energy is applied to a system of two dielectrics with magnetoelectric coupling. In particular, the case of Topological Insulators (TI) is studied in detail. Depending on the the optical response of the TI, we obtain a stable equilibrium distance, atraction for all distances, or repulsion for all distances at zero temperature. This equilibrium distance disappears in the high temperature limit. These results are independent on the geometry of the TI, but are only valid in the diluted approximation.

Dynamical approach to the Casimir effect.

Casimir forces can appear between intrusions placed in different media driven by several fluctuation mechanisms, either in equilibrium or out of it. Herein, we develop a general formalism to obtain such forces from the dynamical equations of the fluctuating medium, the statistical properties of the driving noise, and the boundary conditions of the intrusions (which simulate the interaction between the intrusions and the medium). As a result, an explicit formula for the Casimir force over the intrusions is derived. This formalism contains the thermal Casimir effect as a particular limit and generalizes the study of the Casimir effect to such systems through their dynamical equations, with no appeal to their Hamiltonian, if any exists. In particular, we study the Casimir force between two infinite parallel plates with Dirichlet or Neumann boundary conditions, immersed in several media with finite correlation lengths (reaction-diffusion system, liquid crystals, and two coupled fields with non-Hermitian evolution equations). The driving Gaussian noises have vanishing or finite spatial or temporal correlation lengths; in the first case, equilibrium is reobtained and finite correlations produce nonequilibrium dynamics. The results obtained show that, generally, nonequilibrium dynamics leads to Casimir forces, whereas Casimir forces are obtained in equilibrium dynamics if the stress tensor is anisotropic.

Stochastic quantization and Casimir forces

In this paper we show how the stochastic quantization method developed by Parisi and Wu can be used to obtain Casimir forces. Both quantum and thermal fluctuations are taken into account by a Langevin equation for the field. The method allows the Casimir force to be obtained directly, derived from the stress tensor instead of the free energy. It only requires the spectral decomposition of the Laplacian operator in the given geometry. The formalism provides also an expression for the fluctuations of the force. As an application we compute the Casimir force on the plates of a finite piston of arbitrary cross-section. Fluctuations of the force are also directly obtained, and it is shown that, in the piston case, the variance of the force is twice the force squared.

Pairwise summation approximation of Casimir energy from first principles.

We obtain the pairwise summation approximation (PSA) of the Casimir energy from first principles in the soft dielectric and soft diamagnetic limit, this analysis let us find that the PSA is an asymptotic approximation of the Casimir energy valid for large distances between the objects. We also obtain the PSA for the electromagnetic coupling part of the Casimir energy, so we are able to complete the PSA limit for the first time for the complete electromagnetic field.

CASIMIR ENERGY AND ENTROPY BETWEEN PERFECT METAL SPHERES

We calculate the Casimir energy and entropy for two perfect metal spheres in the large and short separation limit. We obtain nonmonotonic behavior of the Helmholtz free energy with separation and temperature, leading to parameter ranges with negative entropy, and also nonmonotonic behavior of the entropy with temperature and with the separation between the spheres. The appearance of this anomalous behavior of the entropy is discussed as well as its thermodynamic consequences.

STOCHASTIC QUANTIZATION AND CASIMIR FORCES: PISTONS OF ARBITRARY CROSS SECTION

Recently, a method based on stochastic quantization has been proposed to compute the Casimir force and its fluctuations in arbitrary geometries. It relies on the spectral decomposition of the Laplace operator in the given geometry. Both quantum and thermal fluctuations were considered. Here we use this method to compute the Casimir force on the plates of a finite piston of arbitrary cross section. Asymptotic expressions valid at low and high temperatures, as well as short and long distances are obtained. The case of a piston with triangular cross section is analyzed in detail. The regularization of the divergent stress tensor is described.