Wave zone in the Hořava–Lifshitz theory at the kinetic-conformal point in the low energy regime

We show that in the Hořava–Lifshitz theory at the kinetic-conformal point, in the low energy regime, a wave zone for asymptotically flat fields can be consistently defined. In it, the physical degrees of freedom, the transverse traceless tensorial modes, satisfy a linear wave equation. The Newtonian contributions, among which there are terms which manifestly break the relativistic invariance, are non-trivial but do not obstruct the free propagation (radiation) of the physical degrees of freedom. For an appropriate value of the couplings of the theory, the wave equation becomes the relativistic one in agreement with the propagation of the gravitational radiation in the wave zone of General Relativity. Previously to the wave zone analysis, and in general grounds, we obtain the physical Hamiltonian of the Hořava–Lifshitz theory at the kinetic-conformal point in the constrained submanifold. We determine the canonical physical degrees of freedom in a particular coordinate system. They are well defined functions of the transverse-traceless modes of the metric and coincide with them in the wave zone and also at linearized level.

Casimir Puzzle and Casimir Conundrum: Discovery and Search for Resolution

This paper provides a review of the complicated problems in Lifshitz theory describing the Casimir force between real material plates composed of metals and dielectrics, including different approaches to their resolution. For both metallic plates with perfect crystal lattices and any dielectric plates, we show that the Casimir entropy calculated in the framework of Lifshitz theory violates the Nernst heat theorem when the well-approved dielectric functions are used in computations. The respective theoretical Casimir forces are excluded by the measurement data of numerous precision experiments. In the literature, this situation has been called the Casimir puzzle and the Casimir conundrum for the cases of metallic and dielectric plates, respectively. This review presents a summary of both the main theoretical and experimental findings on this subject. Next, a discussion is provided of the main approaches proposed in the literature to bring the Lifshitz theory into agreement with the measurement data and with the laws of thermodynamics. Special attention is paid to the recently suggested spatially nonlocal Drude-like response functions, which consider the relaxation properties of conduction electrons, as does the standard Drude model, but lead to the theoretical results being in agreement with both thermodynamics and the measurement data through the alternative response to quantum fluctuations of the mass shell. Further advances and trends in this field of research are discussed.

Optical and surface energy probe of Hamaker constant in copper oxide thin films for NEMS and MEMS stiction control applications

Copper oxide films hold substantial promise as anti-stiction coatings in micro-electromechanical (MEMS) devices and with shrinking dimensions on the nanometre scale on nano electromechanical (NEMS) devices. The Hamaker constant will play a very significant role in understanding stiction and tribology in these devices. We used an approximate but sufficiently accurate form of the Lifshitz theory using the multiple oscillator model to calculate the Hamakers constant of symmetric copper oxide thin films based on experimentally obtained dielectric data in the wavelength range 190-850 nm using spectroscopic ellipsometry. We also used the Tabor–Winterton approximation (TWA) and Surface energy measurements to determine the Hamaker constant. There was better agreement in the Hamaker constant values obtained by the limited Lifshitz theory and TWA approach than with the Surface energy approach. The difference is explained through the influence of surface roughness on the surface energy using extensions of the stochastic KPZ growth model and the Family-Vicsek scaling relation and rigorous treatment of the Cassie-Baxter and Wenzel models as optimisations of a surface free energy functional linking roughness and surface tension. The dominance of the Cu2O phase in the films and of the London dispersion force on the surface of the films was previously confirmed by FTIR Cu(I)–O vibrational mode observation and XPS Cu 2p3/2 binding energy peak and its fitted satellites. The use of the limited Lifshitz theory and ellipsometry data would seem to provide a suitable best first approximation for determining the Hamaker constant of predominantly dispersive anti-stiction coatings in technologically important MEMS/NEMS devices.

Casimir and Casimir-Polder Forces in Graphene Systems: Quantum Field Theoretical Description and Thermodynamics

We review recent results on the low-temperature behaviors of the Casimir-Polder and Casimir free energy an entropy for a polarizable atom interacting with a graphene sheet and for two graphene sheets, respectively. These results are discussed in the wide context of problems arising in the Lifshitz theory of van der Waals and Casimir forces when it is applied to metallic and dielectric bodies. After a brief treatment of different approaches to theoretical description of the electromagnetic response of graphene, we concentrate on the derivation of response function in the framework of thermal quantum field theory in the Matsubara formulation using the polarization tensor in (2 + 1)-dimensional space—time. The asymptotic expressions for the Casimir-Polder and Casimir free energy and entropy at low temperature, obtained with the polarization tensor, are presented for a pristine graphene as well as for graphene sheets possessing some nonzero energy gap Δ and chemical potential μ under different relationships between the values of Δ and μ. Along with reviewing the results obtained in the literature, we present some new findings concerning the case μ≠0, Δ=0. The conclusion is made that the Lifshitz theory of the Casimir and Casimir-Polder forces in graphene systems using the quantum field theoretical description of a pristine graphene, as well as real graphene sheets with Δ>2μ or Δ<2μ, is consistent with the requirements of thermodynamics. The case of graphene with Δ=2μ≠0 leads to an entropic anomaly, but is argued to be physically unrealistic. The way to a resolution of thermodynamic problems in the Lifshitz theory based on the results obtained for graphene is discussed.

An alternative response to the off-shell quantum fluctuations: a step forward in resolution of the Casimir puzzle

The spatially nonlocal response functions are proposed which nearly coincide with the commonly used local response for electromagnetic fields and fluctuations on the mass shell, but differ significantly for the off-shell fluctuating field. It is shown that the fundamental Lifshitz theory using the suggested response functions comes to an agreement with the measurement data for the Casimir force without neglecting the dissipation of free electrons. We demonstrate that reflectances of the on-shell electromagnetic waves calculated using the nonlocal and commonly employed local responses differ only slightly. The Kramers–Kronig relations for nonlocal response functions possessing the first- and second-order poles at zero frequency are derived, i.e., the proposed response satisfies the principle of causality. An application of these results to resolution of the Casimir puzzle, which lies in the fact that the Lifshitz theory is experimentally consistent only with discarded dissipation, is discussed.

The case for a Casimir cosmology

The cosmological constant, also known as dark energy, was believed to be caused by vacuum fluctuations, but naive calculations give results in stark disagreement with fact. In the Casimir effect, vacuum fluctuations cause forces in dielectric media, which is very well described by Lifshitz theory. Recently, using the analogy between geometries and media, a cosmological constant of the correct order of magnitude was calculated with Lifshitz theory (Leonhardt 2019 Ann. Phys. ( New York ) 411 , 167973. ( doi:10.1016/j.aop.2019.167973 )). This paper discusses the empirical evidence and the ideas behind the Lifshitz theory of the cosmological constant without requiring prior knowledge of cosmology and quantum field theory. This article is part of a discussion meeting issue ‘The next generation of analogue gravity experiments’.

ℱ(P) quantum mechanics

We explore the possibility to extend the Heisenberg’s uncertainty principle to a nonlinear extension of the quantum algebra related to a functional operator of the momenta as [Formula: see text]. We show that such an extension of quantum mechanics is intimately connected to the non-commutative space-time algebra and the Lorentz symmetry deformations. We show that a large class of [Formula: see text] models can introduce superluminal modes in the quantized theories. We also show that the Hořava–Lifshitz theory is related to a large class of [Formula: see text] Quantum Mechanics.