Narrow Results

In this paper, we have studied the area and mass spectrum of a Lifshitz black hole in 2+1 dimensions. This black hole is obtained for conformal gravity in 2+1 dimensions and is asymptotic to z = 0 Lifshitz spacetime. Quasinormal modes (QNM) frequencies of the conformally coupled scalar field perturbations are employed for the purpose of analyzing the area spectrum of the black hole. We have used two methods: modified Hod's conjecture and Kunsttater's method. In both methods, the area and the mass spectrum is shown to be equally spaced. We compared our results with the area spectrum of the BTZ black hole and the z = 3 black hole and made suggestions to extend this work in the future.

By engineering the boundary conditions of electromagnetic fields between material interfaces, one can dramatically change the Casimir-Lifshitz force between surfaces as a result of the modified zero-point energy density of the system. Repulsive interactions between macroscopic bodies occur when their dielectric responses obey a particular inequality, as pointed out by Dzyaloshinskii, Lifshitz, and Pitaevskii. We discuss experimental verification of this behavior as well as a description of how this can be used to develop a scheme for quantum levitation. Based on these concepts, we discuss the possible development of a new class of devices based on ultra-low static friction and the ability to sort objects based on their dielectric functions.

This introduction to Lifshitz-type field theories reviews some of its aspects in Particle Physics. Attractive features of these models are described with different examples, as the improvement of graphs convergence, the introduction of new renormalizable interactions, dynamical mass generation, asymptotic freedom, and other features related to more specific models. On the other hand, problems with the expected emergence of Lorentz symmetry in the IR are discussed, related to the different effective light cones seen by different particles when they interact.

We consider the one-loop effective potential at zero temperature in Lifshitz-type field theories with anisotropic space–time scaling, with critical exponent z = 3, including scalar, fermion and gauge fields. The fermion determinant generates a symmetry breaking term at one loop in the effective potential and a local minimum appears, for nonzero scalar field, for every value of the Yukawa coupling. Depending on the relative strength of the coupling constants for the scalar and the gauge field, we find a second symmetry breaking local minimum in the effective potential for a bigger value of the scalar field.

We review interesting results achieved in recent studies on the holographic Lifshitz field theory. The holographic Lifshitz field theory at finite temperature is described by a Lifshitz black brane geometry. The holographic renormalization together with the regularity of the background metric allows to reproduce thermodynamic quantities of the dual Lifshitz field theory where the Bekenstein–Hawking entropy appears as the renormalized thermal entropy. All results satisfy the desired black brane thermodynamics. In addition, hydrodynamic properties are further reviewed in which the holographic retarded Green functions of the current and momentum operators are studied. In a nonrelativistic Lifshitz field theory, intriguingly, there exists a massive quasinormal mode at finite temperature whose effective mass is linearly proportional to temperature. Even at zero temperature and in the nonzero momentum limit, a quasinormal mode still remains unlike the dual relativistic field theory. Finally, we account for how adding impurity modifies the electric property of the nonrelativistic Lifshitz theory.

In this work, the Dirac equation is studied in the $z=0$ Lifshitz black hole ($Z0$LBH) spacetime. The set of equations representing the Dirac equation in the Newman–Penrose (NP) formalism is decoupled into a radial set and an angular set. The separation constant is obtained with the aid of the spin weighted spheroidal harmonics. The radial set of equations, which are independent of mass, is reduced to Zerilli equations (ZEs) with their associated potentials. In the near horizon (NH) region, these equations are solved in terms of the Bessel functions of the first and second kinds arising from the fermionic perturbation on the background geometry. For computing the boxed quasinormal modes (BQNMs) instead of the ordinary quasinormal modes (QNMs), we first impose the purely ingoing wave condition at the event horizon. Then, Dirichlet boundary condition (DBC) and Newmann boundary condition (NBC) are applied in order to get the resonance conditions. For solving the resonance conditions, we follow the Hod’s iteration method. Finally, Maggiore’s method (MM) is employed to derive the entropy/area spectra of the $Z0$LBH which are shown to be equidistant.

By engineering the boundary conditions of electromagnetic fields between material interfaces, one can dramatically change the Casimir-Lifshitz force between surfaces as a result of the modified zero-point energy density of the system. Repulsive interactions between macroscopic bodies occur when their dielectric responses obey a particular inequality, as pointed out by Dzyaloshinskii, Lifshitz, and Pitaevskii. We discuss experimental verification of this behavior as well as a description of how this can be used to develop a scheme for quantum levitation. Based on these concepts, we discuss the possible development of a new class of devices based on ultra-low static friction and the ability to sort objects based on their dielectric functions.