Post-Newtonian gravitational and scalar waves in scalar-Gauss-Bonnet gravity

Gravitational waves emitted by black hole binary inspiral and mergers enable unprecedented strong-field tests of gravity, requiring accurate theoretical modelling of the expected signals in extensions of General Relativity. In this paper we model the gravitational wave emission of inspiralling binaries in scalar Gauss-Bonnet gravity theories. Going beyond the weak-coupling approximation, we derive the gravitational waveform to relative first post-Newtonian order beyond the quadrupole approximation and calculate new contributions from nonlinear curvature terms. We also compute the scalar waveform to relative 0.5PN order beyond the leading -0.5PN order terms. We quantify the effect of these terms and provide ready-to-implement gravitational wave and scalar waveforms as well as the Fourier domain phase for quasi-circular binaries. We also perform a parameter space study, which indicates that the values of black hole scalar charges play a crucial role in the detectability of deviation from General Relativity. We also compare the scalar waveforms to numerical relativity simulations to assess the impact of the relativistic corrections to the scalar radiation. Our results provide important foundations for future precision tests of gravity.

An Extended Solution to the Equations Describing a 3-Conductor Transmission Line

The full derivation of the generalized and extended solution to the equations describing threeconductor Transmission line is given in this paper; the brief results are presented in a previous paper. The Considerations proceed from the c. Paul formulation of lossless transmission lines terminated by linear loads. In contrast to c. Paul, the conjoint interaction between the two lines is considered here and the influence of the Receptor line is not neglected, that is the weak-coupling approximation is not applied. In result, an extended and Generalized mathematical model compared the original model of c. Paul is obtained. In particular, a mixed Problem for the hyperbolic system describing the three-conductor transmission line is formulated. It is shown That the formulated mixed problem is equivalent to an initial value problem for a functional system on the Boundary of hyperbolic system’s domain with voltages and currents as the unknown functions in this system Are the lines’. The system of functional equations can be resolved by a fixed-point method that enables us to Find an approximated but explicit solution. The method elaborated in this paper might be applied also for linear As well as nonlinear boundary conditions.

Energy Conservation and the Correlation Quasi-Temperature in Open Quantum Dynamics

The master equation for an open quantum system is derived in the weak-coupling approximation when the additional dynamical variable—the mean interaction energy—is included into the generic relevant statistical operator. This master equation is nonlocal in time and involves the “quasi-temperature”, which is a non- equilibrium state parameter conjugated thermodynamically to the mean interaction energy of the composite system. The evolution equation for the quasi-temperature is derived using the energy conservation law. Thus long-living dynamical correlations, which are associated with this conservation law and play an important role in transition to the Markovian regime and subsequent equilibration of the system, are properly taken into account.

Boundary conditions, gauge fixing ambiguities and exact expectation values in U(1) lattice gauge theory

We analyze the interplay between gauge fixing and boundary conditions in two-dimensional U(1) lattice gauge theory. We show on the basis of a general argument that periodic boundary conditions result in an ill-defined weak coupling approximation but that the approximation can be made well-defined if the boundaries are fixed to zero. We confirm this result in the particular case of the Feynman gauge. We show that the zero momentum mode divergence in the propagator that appears in the Feynman gauge vanishes when the weak coupling approximation is well-defined. In addition we obtain exact results (for arbitrary coupling), including finite size corrections, for the partition function and for general one-point and two-point functions in the axial gauge under both periodic and zero boundary conditions and confirm these results numerically. The dependence of these objects on both lattice size and coupling constant is investigated using specific examples. These exact results may provide insight into similar gauge fixing issues in more complex models.

Competition of Superconductivity and Charge Density Waves in Cuprates: Recent Evidence and Interpretation

Explicit and implicit experimental evidence for charge density wave (CDW) presence in high-Tcsuperconducting oxides is analyzed. The theory of CDW superconductors is presented. It is shown that the observed pseudogaps and dip-hump structures in tunnel and photoemission spectra are manifestations of the same CDW gapping of the quasiparticle density of states. Huge pseudogaps are transformed into modest dip-hump structures at low temperatures,T, when the electron spectrum superconducting gapping dominates. Heat capacity jumps at the superconducting critical temperature and the paramagnetic limit are calculated for CDW superconductors. For a certain range of parameters, the CDW state in ad-wave superconductor becomes reentrant withT, the main control quantity being a portion of dielectrcally gapped Fermi surface. It is shown that in the weak-coupling approximation, the ratio between the superconducting gap at zero temperatureΔ(T=0)andTchas the Bardeen-Cooper-Schrieffer value fors-wave Cooper pairing and exceeds the corresponding value ford-wave pairing of CDW superconductors. Thus, large experimentally found values2Δ(T=0)/Tc≈5÷8are easily reproduced with reasonable input parameter values of the model. The conclusion is made that CDWs play a significant role in cuprate superconductivity.

ACCOUNTING FOR THE FINITENESS OF THE HIGGS–BOSON MASS IN THE 3D GEORGI–GLASHOW MODEL

(2 + 1)-dimensional Georgi–Glashow model is explored in the regime when the Higgs boson is not infinitely heavy, but its mass is of the same order of magnitude as the mass of the W-boson. In the weak-coupling limit, the Debye mass of the dual photon and the expression for the monopole potential are found. The cumulant expansion applied to the average over the Higgs field is checked to be convergent for the known data on the monopole fugacity. These results are further generalized to the SU (N)-case. In particular, it is found that the requirement of convergence of the cumulant expansion establishes a certain upper bound on the number of colors. This bound, expressed in terms of the parameter of the weak-coupling approximation, allows the number of colors to be large enough. Finally, the string tension and the coupling constant of the so-called rigidity term of the confining string are found at arbitrary number of colors.

Orbitals observed by Electron Momentum Spectroscopy

Numerical representations of Dyson orbitals can be extracted from the experimental data of electron momentum spectroscopy (EMS). These orbitals are solutions of the quasiparticle equation for the target electronic system. They closely obey the weak-coupling approximation. This defines a normalized Dyson orbital in terms of the sum of EMS cross sections for an orbital manifold of ion states whose momentum profiles have the same shape. Normalized Dyson orbitals are closely related to the orbitals of density functional theory. They are realistic in the sense that they give an independent-particle approximation to the target structure that reproduces experimental data, including molecular data obtained from experiments independent of EMS.