Limit Of Large Separation Research Articles

Surface Casimir Densities on Branes Orthogonal to the Boundary of Anti-De Sitter Spacetime

The paper investigates the vacuum expectation value of the surface energy–momentum tensor (SEMT) for a scalar field with general curvature coupling in the geometry of two branes orthogonal to the boundary of anti-de Sitter (AdS) spacetime. For Robin boundary conditions on the branes, the SEMT is decomposed into the contributions corresponding to the self-energies of the branes and the parts induced by the presence of the second brane. The renormalization is required for the first parts only, and for the corresponding regularization the generalized zeta function method is employed. The induced SEMT is finite and is free from renormalization ambiguities. For an observer living on the brane, the corresponding equation of state is of the cosmological constant type. Depending on the boundary conditions and on the separation between the branes, the surface energy densities can be either positive or negative. The energy density induced on the brane vanishes in special cases of Dirichlet and Neumann boundary conditions on that brane. The effect of gravity on the induced SEMT is essential at separations between the branes of the order or larger than the curvature radius for AdS spacetime. In the considerably large separation limit, the decay of the SEMT, as a function of the proper separation, follows a power law for both massless and massive fields. For parallel plates in Minkowski bulk and for massive fields the fall-off of the corresponding expectation value is exponential.

Large-Separation Behavior of the Casimir–Polder Force from Real Graphene Sheet Deposited on a Dielectric Substrate

The Casimir–Polder force between atoms or nanoparticles and graphene-coated dielectric substrates is investigated in the region of large separations. Graphene coating with any value of the energy gap and chemical potential is described in the framework of the Dirac model using the formalism of the polarization tensor. It is shown that the Casimir–Polder force from a graphene-coated substrate reaches the limit of large separations at approximately 5.6 μm distance between an atom or a nanoparticle and graphene coating independently of the values of the energy gap and chemical potential. According to our results, however, the classical limit, where the Casimir–Polder force no longer depends on the Planck constant and the speed of light, may be attained at much larger separations depending on the values of the energy gap and chemical potential. In addition, we have found a simple analytic expression for the Casimir–Polder force from a graphene-coated substrate at large separations and determined the region of its applicability. It is demonstrated that the asymptotic results for the large-separation Casimir–Polder force from a graphene-coated substrate are in better agreement with the results of numerical computations for the graphene sheets with larger chemical potential and smaller energy gap. Possible applications of the obtained results in nanotechnology and bioelectronics are discussed.

Stability and asymptotic interactions of chiral magnetic skyrmions in a tilted magnetic field

Using a general framework, interaction potentials between chiral magnetic solitons in a planar system with a tilted external magnetic field are calculated analytically in the limit of large separation. The results are compared to previous numerical results for solitons with topological charge \pm 1±1. A key feature of the calculation is the interpretation of Dzyaloshinskii-Moriya interaction (DMI) as a background SO(3)SO(3) gauge field. In a tilted field, this leads to a U(1)U(1)-gauged version of the usual equation for spin excitations, leading to a distinctive oscillating interaction profile. We also obtain predictions for skyrmion stability in a tilted field which closely match numerical observations.

Solar Wind Magnetic Field Line Dispersal: Multispacecraft Analysis and Comparison with Theoretical Results

The dominance of the global over the relative, cross-field transport of magnetic field lines (MFLs), up to scales of a couple of hours in the solar wind (SW), has been predicted both theoretically and numerically, in the approximation of self-similar, single-level power spectra of magnetic fluctuations. Here the predictions for the MFL relative cross-field transport or dispersal are tested against the results of in situ data analysis, using 23 yr of field and flow measurements on board ACE and Wind. The theoretical results are confirmed/refined by nonlinear theoretical computations and corrected to include the effects of power-level variability or intermittency. Other than confirming earlier theoretical findings at the separation scales ρ between a few ×1010 cm and the large-separation limit, with a ballistic regime followed by decorrelation and transition to diffusion in the -space, the new study reveals two new supradiffusive regimes in and clock angle θ for the MFL dispersal, distinct from a drift-induced supradiffusion found earlier, and distinct from each other. The first supradiffusion, of the nonlinear computations, is a simple nonlinear effect, which cannot be recovered by data analysis at two spacecraft of fixed separation on the analysis timescale. The second supradiffusion, of the data analysis, is much stronger for ρ < few × 1010 cm than the two previous supradiffusions, and it becomes stronger at shorter separations. It follows the ballistic regime without transition through diffusion and is recovered by multiscale, theoretical estimates. It is a Lévy-type supradiffusion, due to the intermittency observed in the SW.

H–He collision-induced satellite in the Lyman α profile of DBA white dwarf stars

ABSTRACT The spectra of helium-dominated white dwarf stars with hydrogen in their atmosphere present a distinctive broad feature centred around 1160 Å in the blue wing of the Lyman α line. It is extremely apparent in WD 1425+540 recently observed with Hubble Space Telescope(HST) Cosmic Origins Spectrograph (COS). With new theoretical line profiles based on ab initio atomic interaction potentials we show that this feature is a signature of a collision-induced satellite due to an asymptotically forbidden transition. This quasi-molecular spectral satellite is crucial to understanding the asymmetrical shape of Lyman α seen in this and other white dwarf spectra. Our previous work predicting this absorption feature was limited by molecular potentials that were not adequate to follow the atomic interactions with spectroscopic precision to the asymptotic limit of large separation. A new set of potential energy curves and electronic dipole transition moments for the lowest electronic states of the H–He system were developed to account accurately for the behaviour of the atomic interactions at all distances, from the chemical regime within 1 Å out to where the radiating H atoms are not significantly perturbed by their neighbours. We use a general unified theory of collision-broadened atomic spectral lines to describe a rigorous treatment of hydrogen Lyman α with these potentials and present a new study of its broadening by radiative collisions of hydrogen and neutral helium. These results enable ab initio modelling of radiative transport in DBA white dwarf atmospheres.

Large-separation expansion of peak clustering in Gaussian random fields

In the peaks approach, the formation sites of observable structures in the Universe are identified as peaks in the matter density field. The statistical properties of the clustering of peaks are particularly important in this respect. In this paper, we investigate the large-separation expansion of the correlation function of peaks in Gaussian random fields. The analytic formula up to third order is derived, and the resultant expression can be evaluated by a combination of one-dimensional fast Fourier transforms, which are evaluated very fast. The analytic formula obtained perturbatively in the large-separation limit is compared with a method of Monte-Carlo integrations, and a complementarity between the two methods is demonstrated.

LeClair-Mussardo series for two-point functions in Integrable QFT

We develop a well-defined spectral representation for two-point functions in relativistic Integrable QFT in finite density situations, valid for space-like separations. The resulting integral series is based on the infinite volume, zero density form factors of the theory, and certain statistical functions related to the distribution of Bethe roots in the finite density background. Our final formulas are checked by comparing them to previous partial results obtained in a low-temperature expansion. It is also show that in the limit of large separations the new integral series factorizes into the product of two LeClair-Mussardo series for one-point functions, thereby satisfying the clustering requirement for the two-point function.

Holographic mutual information of two disjoint spheres

We study quantum corrections to holographic mutual information for two disjoint spheres at a large separation by using the operator product expansion of the twist field. In the large separation limit, the holographic mutual information is vanishing at the semiclassical order, but receive quantum corrections from the fluctuations. We show that the leading contributions from the quantum fluctuations take universal forms as suggested from the boundary CFT. We find the universal behavior for the scalar, the vector, the tensor and the fermionic fields by treating these fields as free fields propagating in the fixed background and by using the 1/n prescription. In particular, for the fields with gauge symmetries, including the massless vector boson and massless graviton, we find that the gauge parts in the propagators play an indispensable role in reading the leading order corrections to the bulk mutual information.

A master equation for strongly interacting dipoles

We consider a pair of dipoles such as Rydberg atoms for which direct electrostatic dipole–dipole interactions may be significantly larger than the coupling to transverse radiation. We derive a master equation using the Coulomb gauge, which naturally enables us to include the inter-dipole Coulomb energy within the system Hamiltonian rather than the interaction. In contrast, the standard master equation for a two-dipole system, which depends entirely on well-known gauge-invariant S-matrix elements, is usually derived using the multipolar gauge, wherein there is no explicit inter-dipole Coulomb interaction. We show using a generalised arbitrary-gauge light-matter Hamiltonian that this master equation is obtained in other gauges only if the inter-dipole Coulomb interaction is kept within the interaction Hamiltonian rather than the unperturbed part as in our derivation. Thus, our master equation depends on different S-matrix elements, which give separation-dependent corrections to the standard matrix elements describing resonant energy transfer and collective decay. The two master equations coincide in the large separation limit where static couplings are negligible. We provide an application of our master equation by finding separation-dependent corrections to the natural emission spectrum of the two-dipole system.

The large-scale correlations of multicell densities and profiles: implications for cosmic variance estimates

In order to quantify the error budget in the measured probability distribution functions of cell densities, the two-point statistics of cosmic densities in concentric spheres is investigated. Bias functions are introduced as the ratio of their two-point correlation function to the two-point correlation of the underlying dark matter distribution. They describe how cell densities are spatially correlated. They are computed here via the so-called large deviation principle in the quasi-linear regime. Their large-separation limit is presented and successfully compared to simulations for density and density slopes: this regime is shown to be rapidly reached allowing to get sub-percent precision for a wide range of densities and variances. The corresponding asymptotic limit provides an estimate of the cosmic variance of standard concentric cell statistics applied to finite surveys. More generally, no assumption on the separation is required for some specific moments of the two-point statistics, for instance when predicting the generating function of cumulants containing any powers of concentric densities in one location and one power of density at some arbitrary distance from the rest. This exact "one external leg" cumulant generating function is used in particular to probe the rate of convergence of the large-separation approximation.

Ferminoic Casimir effect between spheres

We consider the Casimir interaction between two spheres corresponding to massless Dirac fields with MIT-bag boundary conditions. Using operator approach, we derive the TGTG-formula for the Casimir interaction energy between the two spheres. A byproduct is the explicit formula for the translation matrix that relates the fermionic spherical waves in different coordinate systems. In the large separation limit, it is found that the order of the Casimir interaction energy is $L^{-5}$, where $L$ is the separation between the centers of the spheres. This order is intermediate between that of two Dirichlet spheres (of order $L^{-3}$) and two Neumann spheres (of order $L^{-7}$). In the small separation limit, we derive analytically the asymptotic expansion of the Casimir interaction energy up to the next-to-leading order term. The leading term agrees with the proximity force approximation. The result for the next-to-leading order term is compared to the corresponding results for scalar fields and electromagnetic fields.

Interaction forces among two-dimensional bright solitons and many-soliton molecules

We consider two-dimensional bright matter-wave solitons in two-dimensional Bose-Einstein condensates. From the asymptotic form of their wave function, we derive an analytic expression for the force of interaction between solitons in the large separation limit, which turns out to decay with solitons separation Δ as F(Δ)∝exp(-Δ)/√Δ. Simulating the dynamics of two solitons using the relevant Gross-Pitaevskii equation, we obtain the force of the interaction for the full range of Δ, which turns out to be of molecular type. We show that many-soliton molecules can exist as a result of such a molecular-type of interaction. These include string-shaped, ring-shaped, or regular-lattice-shaped soliton molecules. By calculating their binding energy, we investigate the stability of these structures. Contrary to one-dimensional soliton molecules, which have no binding energy, two-dimensional molecules of a lattice of solitons with alternating phases are robust and have a negative binding energy. Lattices of size larger than 2 × 2 solitons have many discrete equilibrium values of the separation between two neighboring solitons.

Casimir energy and entropy in the sphere-sphere geometry

We calculate the Casimir energy and entropy for two spheres described by the perfect metal model, plasma model, and Drude model in the large separation limit. We obtain nonmonotonic behavior of the Helmholtz free energy with separation and temperature for the perfect metal and plasma models, leading to parameter ranges with negative entropy, and also nonmonotonic behavior of the entropy with temperature and the separation between the spheres. This nonmonotonic behavior has not been found for Drude model. The appearance of this anomalous behavior of the entropy is discussed as well as its thermodynamic consequences.

Correlated dynamics of inclusions in a supported membrane

The hydrodynamic theory of heterogeneous fluid membranes is extended to the case of a membrane adjacent to a solid substrate. We derive the coupling diffusion coefficients of pairs of membrane inclusions in the limit of large separation compared to the inclusion size. Two-dimensional compressive stresses in the membrane make the coupling coefficients decay asymptotically as 1/r(2) with interparticle distance r. For the common case, where the distance to the substrate is of submicrometer scale, we present expressions for the coupling between distant disklike inclusions, which are valid for arbitrary inclusion size. We calculate the effect of inclusions on the response of the membrane and the associated corrections to the coupling diffusion coefficients to leading order in the concentration of inclusions. While at short distances the response is modified as if the membrane were a two-dimensional suspension, the large-distance response is not renormalized by the inclusions.

Thermal Casimir interaction between two magnetodielectric plates

We investigate the thermal Casimir interaction between two magnetodielectric plates made of real materials. On the basis of the Lifshitz theory, it is shown that for diamagnets and for paramagnets in the broad sense (with exception of ferromagnets) the magnetic properties do not influence the magnitude of the Casimir force. For ferromagnets, taking into account the realistic dependence of magnetic permeability on frequency, we conclude that the impact of magnetic properties on the Casimir interaction arises entirely from the contribution of the zero-frequency term in the Lifshitz formula. The computations of the Casimir free energy and pressure are performed for the configurations of two plates made of ferromagnetic metals (Co and Fe), for one plate made of ferromagnetic metal and the other of nonmagnetic metal (Au), for two ferromagnetic dielectric plates (on the basis of polystyrene), and for a ferromagnetic dielectric plate near a nonmagnetic metal plate. The dielectric permittivity of metals is described using both the Drude and the plasma model approaches. It is shown that the Casimir repulsion through the vacuum gap can be realized in the configuration of a ferromagnetic dielectric plate near a nonmagnetic metal plate described by the plasma model. In all cases considered, the respective analytical results in the asymptotic limit of large separations between the plates are obtained. The impact of the magnetic phase transition through the Curie temperature on the Casimir interaction is considered. In conclusion, we propose several experiments allowing to determine whether the magnetic properties really influence the Casimir interaction and to independently verify the Drude and plasma model approaches to the thermal Casimir force.

Correlators of supersymmetric Wilson loops at weak and strong coupling

We continue our study of the correlators of a recently discovered family of BPS Wilson loops in $$ \mathcal{N} $$ = 4 supersymmetric U(N) Yang-Mills theory. We perform explicit computations at weak coupling by means of analytical and numerical methods finding agreement with the exact formula derived from localization. In particular we check the localization prediction at order g 6 for different BPS “latitude” configurations, the $$ \mathcal{N} $$ = 4 perturbative expansion reproducing the expected results within a relative error of 10−4. On the strong coupling side we present a supergravity evaluation of the 1/8 BPS correlator in the limit of large separation, taking into account the exchange of all relevant modes between the string worldsheets. While reproducing the correct geometrical dependence, we find that the associated coefficient does not match the localization result.

The open string pair-production rate enhancement by a magnetic flux

We extend the amplitude calculations of [1] to exhaust the remaining cases for which one set of Dp branes carrying a flux (electric or magnetic) is placed parallel at separation to the other set carrying also a flux but with the two fluxes sharing at most one common field-strength index. We then find that the basic structure of amplitudes remains the same when the two fluxes share at least one common index but it is more general when the two fluxes share no common index. We discuss various properties of the amplitudes such as the large separation limit, the onset of various instabilities and the open string pair production. In particular, when one flux is electric and weak and the other is magnetic and fixed, we find that the open string pair production rate is greatly enhanced by the presence of this magnetic flux when the two fluxes share no common field-strength index and this rate becomes significant when the separation is on the order of string scale.

Correlators of supersymmetric Wilson-loops, protected operators and matrix models in 𝒩 = 4 SYM

We study the correlators of a recently discovered family of BPS Wilson loops in = 4 supersymmetric U(N) Yang-Mills theory. When the contours lie on a two-sphere in the space-time, we propose a closed expression that is valid for all values of the coupling constant g and for any rank N, by exploiting the suspected relation with two-dimensional gauge theories. We check this formula perturbatively at order (g4) for two latitude Wilson loops and we show that, in the limit where one of the loops shrinks to a point, logarithmic corrections in the shrinking radius are absent at (g6). This last result strongly supports the validity of our general expression and suggests the existence of a peculiar protected local operator arising in the OPE of the Wilson loop. At strong coupling we compare our result to the string dual of the = 4 SYM correlator in the limit of large separation, presenting some preliminary evidence for the agreement.

A slightly corrected Greenwood and Williamson model predicts asymptotic linearity between contact area and load

The author presents a very simple and slightly corrected version of the well-known Greenwood and Williamson (GW) model which closely follows the predictions of more complicated and computationally expensive theory such as the Bush, Gibson and Thomas (BGT) theory [Bush, A.W., Gibson, R.D., Thomas, T.R., 1975. Wear 35, 87]. This new model (which I call GW modified in the following) still treats the asperities of the rough surface as spherical cups, but, this time, the curvature of spheres is not constant and instead depends on the asperity height. The GW modified theory is, in particular, able to predict, in the limiting case of large separations, the same asymptotic linearity between contact area and load as in the BGT theory. This, in turn, proves that the BGT asymptotic linear area–load relation is not a consequence of having taken into account that the contact between the asperities is actually elliptic and, therefore, of having included the spread of asperity curvature at a given height (which incidentally makes the treatment very complicated), but a consequence of having included only the influence of asperity heights on the curvature distribution of the summits. I also give a simple explanation for why the GW modified model and the BGT theory follow exactly the same asymptotic behavior. Indeed, I show that the surface summits can be treated as perfectly spherical cups (all those at the same height having the same radius of curvature) as their height is increased to very large values. In fact, in the asymptotic limit of large separation, the mean curvature of summits is shown to increase proportionally to the summit height, whereas the difference of the two principal curvatures approaches a finite constant value. The consequence of this is that the Hertzian contact between the approaching elastic (initially flat) half-space and the summits exactly resemble that between an elastic half-space and a sphere.

Effect of Methoxy Substituents on the Structural and Electronic Properties of Fluorinated Cyclobutenes: A Study of Hexafluorocyclobutene and Its Vinyl Methoxy Derivatives by XRD and Periodic DFT Calculations

The effect of the methoxy substituent on the structure, crystal packing, and electrostatic properties of hexafluorocyclobutene (C(4)F(6)) was investigated in the solid-state with DFT-B3LYP calculations. Full geometry optimizations were done for the parent compound and its two vinyl methoxy derivatives C(4)F(5)OCH(3) and C(4)F(4)(OCH(3))(2), starting from the structures obtained by single-crystal X-ray diffraction at low temperature. A full topological analysis, followed by the calculation of several electrostatic properties, was performed on the periodic electron density using the quantum theory of atoms in molecules. Eventually, the cohesive energies of the three crystals were estimated. In the cyclobutene plane, the methoxy substitution yields a significant electronic rearrangement involving the pi-electrons. The solid-state (periodic) results agree with those obtained by gas-phase calculations on C(4)F(6) and its derivatives at a comparable level of theory. It was found that the substitution of one or two vinylic fluorine atoms with the OCH(3) group considerably influences the molecular dipole moment, which undergoes an enhancement in both the solid and the gas phase as large as 200% and 235% for C(4)F(5)OCH(3) and C(4)F(4)(OCH(3))(2), respectively, with respect to that calculated for C(4)F(6). The charge rearrangement due to the substituents provides a significant electrostatic contribution to the lattice energy, and in turn it can be related to the change in the observed crystal packing on going from C(4)F(6) (space group P2(1)/c) to both of its derivatives (space group P1). It is also shown that the dispersion energy significantly contributes to the lattice stability in all three compounds. Since the DFT calculations, in the limit of large separations, entirely miss the dispersion term, this was estimated by applying a recently proposed dampening function to the semiempirical atom-atom C(6) R(-6) potentials in the mainframe of Spackman's energy decomposition scheme for Mulliken multipoles.