Lifshitz Theory Research Articles

Casimir force tuning in 2D materials: effect of rotation in phosphorene

We theoretically examine the Casimir force with Lifshitz theory for two-dimensional media: graphene and phosphorene. We calculate the Casimir force for three different configurations: (a) phosphorene-graphene, (b) phosphorene-phosphorene (with rotation), and (c) a system composed of gold and a two-dimensional material (graphene or phosphorene). According to our calculations, we have determined that systems consisting solely of two-dimensional media can reduce the magnitude of the Casimir force by half or more, in comparison to systems composed of two-dimensional material and gold. The results show that in phosphorene configurations, high frequencies play a dominant role in contributing to the Casimir force, allowing greater force magnitudes for low interlayer distances compared to systems composed of gold or graphene. Our calculations also show that, as a result of the anisotropy of the phosphorene layers, it is possible to design a mechanical modulator with only two phosphorene layers by considering a relative rotation between them by an angle θ. In this regard, the anisotropy of phosphorene and the modulation of the separation between the phosphorene layers make it possible to tune the amplitude of Casimir force. The proposed configurations could lead to the development of nanotechnology applications incorporating 2D materials into their structures.

Adhesion Energy for Nonideal Cantilever and Its Relation to Casimir–Lifshitz Forces

The method of the adhered cantilever, borrowed from microtechnology, can help in gaining fundamental knowledge about dispersion forces acting at distances of about 10 nm, which are problematic to access in the usual Casimir-type experiments. A recently presented setup measures the shape of cantilevers with high precision, which is needed for analyzing the involved forces. The first measurements reveal several nonidealities crucial for the data analysis. In this paper, a generalized formula is deduced that relates the parameters of a cantilever to the adhesion energy. The application of the formula is demonstrated using the first test result from the setup, where a silicon cantilever adhered to a substrate sputters with ruthenium. Detailed information of the roughness of interacting surfaces, which deviates significantly from the normal distribution, is emphasized. Although not crucial, the electrostatic contribution can be significant due to the slight twisting of the cantilever. The theoretical prediction of the adhesion energy is based on Lifshitz theory. Comparing theory and experiment yields a contact distance of 45 nm and an adhesion energy of 1.3 µJ/m2, resulting from the Casimir–Lifshitz forces. Significant uncertainties arise from the uncontrolled electrostatic contribution. Factors that need to be addressed to measure weak adhesion between rough surfaces are highlighted.

Monte Carlo calculations taking into account the DLP theory to study multilayer adsorption of C2H4 and CF4 on graphite

Physisorption potentials are useful for deducing the properties of adsorption systems. The adsorption behavior is a consequence of the actual potential that describes the interactions among the adsorption system. Determining the actual isotherm is a test for the correctness of a calculated adsorption potential. The physisorption interactions decrease with the film thickness, d, according to a power law as −γ/d3, where γ is the Van der Waals coefficient. In the Dzyaloshinskii, Lifshitz, and Pitaevskii (DLP) theory, γ is a function of d where γ(d) decreases with d. In the present work, the general theory of Van der Waals forces, given by DLP, is used to derive a more exact treatment of interactions among the physisorbed systems. The Monte Carlo method is used to investigate multilayer films using a lattice gas model adsorption isotherm. Critical temperatures are determined for ethylene (C2H4) and tetrafluoromethane (CF4) on graphite. These systems exhibit comparable behavior. Unlike the findings of mean field theory, our data shows that the critical temperature rises gradually as the layer number increases. On the other hand, the comparison with experimental results and measurements has shown that our calculations are more reliable and provide a better approximation in predicting film thickness. Our isotherms appear to be in better agreement with the experimental ones.

Pull-in features of nanoswitches in the Casimir regime with account of contact repulsion

The cantilever tip of a nanoswitch in close proximity to the ground plate is considered with account of electrostatic, elastic, van der Waals (Casimir), and also contact repulsive forces. The van der Waals (Casimir) and contact repulsive forces are computed for a Si cantilever and either Au or Ni ground plates using the Lifshitz theory and the method of pairwise summation with account of surface roughness. It is shown that at short separations an impact of the van der Waals (Casimir) force leads to the pull-in and collapse of a cantilever onto the ground plate if the contact repulsion is disregarded. Taking into consideration contact repulsion, the nanoswitch is demonstrated to have the stable cyclic behavior with no pull-in when switching voltage on and off.

Entanglement in Lifshitz fermion theories

We study the static entanglement structure in (1+1)-dimensional free Dirac-fermion theory with Lifshitz symmetry and arbitrary integer dynamical critical exponent. This model is different from the one introduced in [Hartmann et al., SciPost Phys.11 (2021) 031] due to a proper treatment of the square Laplace operator. Dirac fermion Lifshitz theory is local as opposed to its scalar counterpart which strongly affects its entanglement structure. We show that there is quantum entanglement across arbitrary subregions in various pure (including the vacuum) and mixed states of this theory for arbitrary integer values of the dynamical critical exponent. Our numerical investigations show that quantum entanglement in this theory is tightly bounded from above. Such a bound and other physical properties of quantum entanglement are carefully explained from the correlation structure in these theories. A generalization to (2+1)-dimensions where the entanglement structure is seriously different is addressed.

Primordial dust universe in the Hořava–Lifshitz theory

In this paper, we apply quantum cosmology to investigate the early moments of a Friedmann–Lemaître–Robertson–Walker (FLRW) cosmological model, using Hořava–Lifshitz (HL) as the gravitational theory. The matter content of the model is a dust perfect fluid. We start studying the classical model. Then, we write the total Hamiltonian of the model, quantize it and find the appropriate Wheeler–DeWitt equation. In order to avoid factor ordering ambiguities, in the Wheeler–DeWitt equation, we introduce a canonical transformation. We solve that equation using the Wentzel–Kramers–Brillouin (WKB) approximation and compute the tunneling probabilities for the birth of that universe ([Formula: see text]). Since the WKB wave function depends on the dust energy and the free coupling constants coming from the HL theory, we compute the behavior of [Formula: see text] as a function of all these quantities.

Transcending Lifshitz Theory: Reliable Prediction of Adhesion Forces between Hydrocarbon Surfaces in Condensed Phases Using Molecular Contact Thermodynamics.

Lifshitz theory is widely used to calculate interfacial interaction energies and underpins established approaches to the interpretation of measurement data from experimental methods including the surface forces apparatus and the atomic force microscope. However, a significant limitation of Lifshitz theory is that it uses the bulk dielectric properties of the medium to predict the work of adhesion. Here, we demonstrate that a different approach, in which the interactions between molecules at surfaces and in the medium are described by a set of surface site interaction points (SSIPs), yields interaction free energies that are correlated better with experimentally determined values. The work of adhesion W(Lifshitz) between hydrocarbon surfaces was calculated in 260 liquids using Lifshitz theory and compared with interaction free energies ΔΔG calculated using the SSIP model. The predictions of these models diverge in significant ways. In particular, ΔΔG values for hydrocarbon surfaces are typically small and vary little, but in contrast, W(Lifshitz) values span 4 orders of magnitude. Moreover, the SSIP model yields significantly different ΔΔG values in some liquids for which Lifshitz theory predicts similar values of W(Lifshitz). These divergent predictions were tested using atomic force microscopy. Experimentally determined works of adhesion were closer to the values predicted using the SSIP model than Lifshitz theory. In mixtures of methanol and benzyl alcohol, even greater differences were found in the interaction energies calculated using the two models: the value of ΔΔG calculated using the SSIP model declines smoothly as the benzyl alcohol concentration increases, and values are well correlated with experimental data; however, W(Lifshitz) decreases to a minimum and then increases, reaching a larger value for benzyl alcohol than for methanol. We conclude that the SSIP model provides more reliable estimates of the work of adhesion than Lifshitz theory.

Non-invertible duality interfaces in field theories with exotic symmetries

In recent years, the concept of global symmetry has generalized considerably. Two dramatic examples of this generalization are the exotic symmetries that govern theories with fractons and non-invertible symmetries, which do not fuse according to a group law. Only recently has the interplay between these two been examined. In this paper, we provide further examples of the interplay in the XY plaquette model, XY cube model, 1+1 d theory with global dipole symmetry, and the 2+1 d Lifshitz theory. They are analogs of the duality symmetries in 2d CTFs and are constructed by first gauging a finite subgroup of the momentum symmetry on half of spacetime and then performing a duality transformation. We analyze the fusion rules of the symmetries and find that they are condensation defects from an analog of higher gauging exotic symmetries. We also address their dependence on the UV cutoff when relevant.

Massless Lifshitz field theory for arbitrary z

By using the notion of fractional derivatives, we introduce a class of massless Lifshitz scalar field theory in (1+1)-dimension with an arbitrary anisotropy index z. The Lifshitz scale invariant ground state of the theory is constructed explicitly and takes the form of Rokhsar-Kivelson (RK). We show that there is a continuous family of ground states with degeneracy parameterized by the choice of solution to the equation of motion of an auxiliary classical system. The quantum mechanical path integral establishes a 2d/1d correspondence with the equal time correlation functions of the Lifshitz scalar field theory. We study the entanglement properties of the Lifshitz theory for arbitrary z using the path integral representation. The entanglement measures are expressed in terms of certain cross ratio functions we specify, and satisfy the c-function monotonicity theorems. We also consider the holographic description of the Lifshitz theory. In order to match with the field theory result for the entanglement entropy, we propose a z-dependent radius scale for the Lifshitz background. This relation is consistent with the z-dependent scaling symmetry respected by the Lifshitz vacuum. Furthermore, the time-like entanglement entropy is determined using holography. Our result suggests that there should exist a fundamental definition of time-like entanglement other than employing analytic continuation as performed in relativistic field theory.

Substantiating the mechanisms of electronic and phonon friction in the conjugation of materials of samples (parts) by the methods of solid state physics

The article elucidates the essence of the mechanisms of electronic and phonon friction in the coupling of samples (parts) using the methods of solid state physics.
 It is shown that in the triboconjugation of samples made of metallic materials, the flow of fluctuation-electromagnetic and electron-phonon processes should be distinguished. Fluctuation-electromagnetic interactions have long-range effects, and electron-phonon interactions have short-range effects. Based on Lifshitz's fluctuation-electromagnetic theory, the force of friction in moving couplings of metal samples is substantiated, taking into account the frequency ratio in the atomic absorption spectrum and the plasma frequency. A formula for estimating the friction force was obtained, taking into account the dielectric function and the Clausius-Mossotti formula.
 The electronic friction force was estimated using the "jelly" model and the generation of electron-hole pairs in the quantum perturbation theory of solid-state physics.
 The mechanism of electronic friction was discovered based on the phenomenological theory of braking losses of slow ions in solids. The scheme of the model of the electronic friction mechanism is close to the Persson model, which connects the braking force with the electron scattering process. A refined formula for estimating the electronic friction force is proposed.
 The strength of phonon friction is justified on the basis of structural effects that can be induced by the mechanism of breaking adhesive bonds, and perturbation theory. A formula was obtained for estimating the force of phonon friction, taking into account the frequency of phonons, the inverse decay time and the function of the two-dimensional Fourier image of the force of interaction between the atoms of the conjugated surface of the triboelement.
 Cases of static and dynamic phonon friction are considered.
 Electronic and phonon frictional forces are considered at the nanolevel. The Debye low-temperature approximation and refinement of the expressions for estimating the electronic and phonon friction forces are given, taking into account the type of interatomic potential

A New Method for Calculating the Hamaker Constant Based on the Hansen Solubility Parameters for Non-Polar Liquids

A simple relationship between the Hamaker constant and the Hansen solubility parameters for non-polar liquids is derived by combining a Hamaker constant/surface tension relationship derived by Israelachvili and a Hansen solubility parameters/surface tension relationship derived by Abbott. With this relationship, one can easily estimate the Hamaker constant of non-polar liquids on the basis of the database of the Hansen solubility parameters. This is an entirely new method for calculating the Hamaker constant without recourse to data on the frequency-dependent dielectric permittivity of those substances (which are required for the rigorous Lifshitz theory) and laborious numerical calculations.

Casimir effect of a rough membrane in 2 + 1 Hořava–Lifshitz theory

We investigate the Casimir effect of a rough membrane within the framework of the Hořava–Lifshitz theory in 2+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2+1$$\\end{document} dimensions. Quantum fluctuations are induced by an anisotropic scalar field subject to Dirichlet boundary conditions. We implement a coordinate transformation to render the membrane completely flat, treating the remaining terms associated with roughness as a potential. The spectrum is obtained through perturbation theory and regularized using the ζ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\zeta $$\\end{document}-function method. We present an explicit example of a membrane with periodic border. Additionally, we consider the effect of temperature. Our findings reveal that the Casimir energy and force depend on roughness, the anisotropic scaling factor and temperature.

Intermediate temperature of supercritical water enhances the dispersion of cohesive particles

Supercritical water gasification represents a promising technology for the clean conversion of coal to hydrogen, so that it is expected to replace the traditional use of coal by burning. However, the flocculation of cohesive coal particles significantly reduces the contact area between particles and supercritical water, which limits the chemical reaction that produces hydrogen. Based on Lifshitz theory, we propose a cellular flow model for numerically reproducing the flocculation of cohesive particles in supercritical fluid turbulence. Cohesion, lubrication, and direct contact forces between particles are fully accounted for, so that the model allows us to conduct a detailed analysis of the translation, rotation, growth, and breakage of flocs in supercritical fluid turbulence. The results show a transient flocculation phase of cohesive particles characterized by an increasing average floc size, followed by a statistically steady equilibrium phase. Increasing the density ratio between particles and supercritical water significantly accelerates the flocculation of dispersed cohesive particles. Higher temperature of the fluid yields faster flocculation and larger flocs when the temperature is below the critical value of 660 K. Upon raising the temperature above 660 K, the flocculation rate and floc size first decrease, and then increase again, yielding an optimal temperature around 750 K where the primary particles are most effectively dispersed by the supercritical water turbulence.

The Casimir Force between Two Graphene Sheets: 2D Fresnel Reflection Coefficients, Contributions of Different Polarizations, and the Role of Evanescent Waves

We consider the Casimir pressure between two graphene sheets and contributions to it determined by evanescent and propagating waves with different polarizations. For this purpose, the derivation of the 2-dimensional (2D) Fresnel reflection coefficients on a graphene sheet is presented in terms of the transverse and longitudinal dielectric permittivities of graphene with due account of the spatial dispersion. The explicit expressions for both dielectric permittivities as the functions of the 2D wave vector, frequency, and temperature are written along the real frequency axis in the regions of propagating and evanescent waves and at the pure imaginary Matsubara frequencies using the polarization tensor of graphene. It is shown that in the application region of the Dirac model nearly the total value of the Casimir pressure between two graphene sheets is determined by the electromagnetic field with transverse magnetic (TM) polarization. By using the Lifshitz formula written along the real frequency axis, the contributions of the TM-polarized propagating and evanescent waves into the total pressure are determined. By confronting these results with the analogous results found for plates made of real metals, the way for bringing the Lifshitz theory using the realistic response functions in agreement with measurements of the Casimir force between metallic test bodies is pointed out.

Reflected entropy and Markov gap in Lifshitz theories

We study the reflected entropy in (1+1)-dimensional Lifshitz field theory whose groundstate is described by a quantum mechanical model. Starting from tripartite Lifshitz groundstates, both critical and gapped, we derive explicit formulas for the Rényi reflected entropies reduced to two adjacent or disjoint intervals, directly in the continuum. We show that the reflected entropy in Lifshitz theory does not satisfy monotonicity, in contrast to what is observed for free relativistic fields. We analytically compute the full reflected entanglement spectrum for two disjoint intervals, finding a discrete set of eigenvalues which is that of a thermal density matrix. Furthermore, we investigate the Markov gap, defined as the difference between reflected entropy and mutual information, and find it to be universal and nonvanishing, signaling irreducible tripartite entanglement in Lifshitz groundstates. We also obtain analytical results for the reflected entropies and the Markov gap in 2 + 1 dimensions. Finally, as a byproduct of our results on reflected entropy, we provide exact formulas for two other entanglement-related quantities, namely the computable cross-norm negativity and the operator entanglement entropy.

Flow of shear response functions in hyperscaling violating Lifshitz theories

We study the flow equations of the shear response functions for hyperscaling violating Lifshitz (hvLif) theories, with Lifshitz and hyperscaling violating exponents z and theta . Adapting the membrane paradigm approach of analysing response functions as developed by Iqbal and Liu, we focus specifically on the shear gravitational modes which now are coupled to the perturbations of the background gauge field. Restricting to the zero momenta sector, we make further simplistic assumptions regarding the hydrodynamic expansion of the perturbations. Analysing the flow equations shows that the shear viscosity at leading order saturates the Kovtun–Son–Starinets (KSS) bound of frac{1}{4pi }. When z=d_i-theta , (d_i being the number of spatial dimension in the dual field theory) the first-order correction to shear viscosity exhibits logarithmic scaling, signalling the emergence of a scale in the UV regime for this class of hvLif theories. We further show that the response function associated to the gauge field perturbations diverge near the boundary when z>d_i+2-theta . This provides a holographic understanding of the origin of such a constraint and further vindicates results obtained in previous works that were obtained through near horizon and quasinormal mode analysis.

Casimir–Polder Force on Atoms or Nanoparticles from Gapped and Doped Graphene: Asymptotic Behavior at Large Separations

The Casimir–Polder force acting on atoms and nanoparticles spaced at large separations from real graphene sheets possessing some energy gaps and chemical potentials is investigated in the framework of the Lifshitz theory. The reflection coefficients expressed via the polarization tensor of graphene, found based on the first principles of thermal quantum field theory, are used. It is shown that for graphene the separation distances, starting from which the zero-frequency term of the Lifshitz formula contributes more than 99% of the total Casimir–Polder force, are less than the standard thermal length. According to our results, however, the classical limit for graphene, where the force becomes independent of the Planck constant, may be reached at much larger separations than the limit of the large separations determined by the zero-frequency term of the Lifshitz formula, depending on the values of the energy gap and chemical potential. The analytic asymptotic expressions for the zero-frequency term of the Lifshitz formula at large separations are derived. These asymptotic expressions agree up to 1% with the results of numerical computations starting from some separation distances that increase with increasing energy gaps and decrease with increasing chemical potentials. The possible applications of the obtained results are discussed.

Impact of Mass-Gap on the Dispersion Interaction of Nanoparticles with Graphene out of Thermal Equilibrium

We consider the nonequilibrium dispersion force acting on nanoparticles on the source side of a gapped graphene sheet. Nanoparticles are kept at the environmental temperature, whereas the graphene sheet may be either cooler or hotter than the environment. Calculation of the dispersion force as a function of separation at different values of the mass-gap parameter is performed using the generalization of the fundamental Lifshitz theory to out-of-thermal-equilibrium conditions. The response of the gapped graphene to quantum and thermal fluctuations in the electromagnetic field is described by the polarization tensor in (2+1)-dimensional space–time in the framework of the Dirac model. The explicit expressions for the components of this tensor in the area of evanescent waves are presented. The nontrivial impact of the mass-gap parameter of graphene on the nonequilibrium dispersion force, as compared to the equilibrium one, is determined. It is shown that, unlike the case of pristine graphene, the nonequilibrium force preserves an attractive character. The possibilities of using the obtained results in the design of micro- and nanodevices, incorporating nanoparticles and graphene sheets for their functionality, is discussed.

A Wheeler–DeWitt Quantum Approach to the Branch-Cut Gravitation with Ordering Parameters

In this contribution to the Festschrift for Prof. Remo Ruffini, we investigate a formulation of quantum gravity using the Hořava–Lifshitz theory of gravity, which is General Relativity augmented by counter-terms to render the theory regularized. We are then led to the Wheeler–DeWitt (WDW) equation combined with the classical concepts of the branch-cut gravitation, which contemplates as a new scenario for the origin of the Universe, a smooth transition region between the contraction and expansion phases. Through the introduction of an energy-dependent effective potential, which describes the space-time curvature associated with the embedding geometry and its coupling with the cosmological constant and matter fields, solutions of the WDW equation for the wave function of the Universe are obtained. The Lagrangian density is quantized through the standard procedure of raising the Hamiltonian, the helix-like complex scale factor of branched gravitation as well as the corresponding conjugate momentum to the category of quantum operators. Ambiguities in the ordering of the quantum operators are overcome with the introduction of a set of ordering factors α, whose values are restricted, to make contact with similar approaches, to the integers α=[0,1,2], allowing this way a broader class of solutions for the wave function of the Universe. In addition to a branched universe filled with underlying background vacuum energy, primordial matter and radiation, in order to connect with standard model calculations, we additionally supplement this formulation with baryon matter, dark matter and quintessence contributions. Finally, the boundary conditions for the wave function of the Universe are imposed by assuming the Bekenstein criterion. Our results indicate the consistency of a topological quantum leap, or alternatively a quantum tunneling, for the transition region of the early Universe in contrast to the classic branched cosmology view of a smooth transition.

Fluctuation-induced dispersion forces on thin DNA films.

In this work, the calculation of Casimir forces across thin DNA films is carried out based on the Lifshitz theory. The variations of Casimir forces due to the DNA thicknesses, volume fractions of containing water, covering media, and substrates are investigated. For a DNA film suspended in air or water, the Casimir force is attractive, and its magnitude increases with decreasing thickness of DNA films and the water volume fraction. For DNA films deposited on a dielectric (silica) substrate, the Casimir force is attractive for the air environment. However, the Casimir force shows unusual features in a water environment. Under specific conditions, switching sign of the Casimir force from attractive to repulsive can be achieved by increasing the DNA-film thickness. Finally, the Casimir force for DNA films deposited on a metallic substrate is investigated. The Casimir force is dominated by the repulsive interactions at a small DNA-film thickness for both the air and water environments. In a water environment, the Casimir force turns out to be attractive for a large DNA-film thickness, and a stable Casimir equilibrium can be found. The influences of electrolyte screening on the Casimir pressure of DNA films are also discussed at the end. In addition to the adhesion stability, our finding could be applicable to the problems of condensation and decondensation of DNA, due to fluctuation-induced dispersion forces.