Some time ago, we published the full count of degrees of freedom in the linearised weak gravity limit of arbitrary New GR models. We did it by considering the linear weak gravity equations and presented a thorough analysis with no ambiguity left. A bit later, we generalised it to linear cosmological perturbations and discussed the strong coupling issues that appear already at this level. Recently, there were claims that some dynamical modes had been missed in our work. However, the authors of the new claims did not look at the equations of motion and analysed the quadratic Lagrangian densities instead. In this paper, I take one of the most elementary cases, namely the vector modes in New GR of Type 3, and show what was their mistake that had led them to claiming that those were dynamical.
Coherent superposition of states in V-like three-level nuclei interacting with X-ray lasers has been investigated theoretically. In this study, it is assumed that an accelerated nuclear beam interacts with a pairs of coincident pulses. Also the maximum effective intensity of the laser pulses is adjusted so that the resonance condition is established, and the average area of the Rabi frequency is equal to 2 π in each pulse. Therefore, the effect of spontaneous emission caused by population of the excited state in this scheme is negligible. For numerical study ^223Ra nuclei is selected and it is shown that the superposition of states in V-like three-level nuclei can be made with a good fidelity. Furthermore, it was demonstrated that in V-like systems with more than two excited states, coherence generation can be achieved with very high fidelity using the Morris–Shore transformation technique.
We examine how a quantized harmonic field induces noncommuting response observables for an oscillator initialized with classical position and momentum data. The observables act on the field Hilbert space and inherit their operator structure from its initial quadratures. Exact field elimination, formulated through unilateral Laplace transforms, retains all preparation terms and yields a retarded equation with reversible memory. The field-quadrature transfer determines a time-dependent commutator and a Schrödinger–Robertson uncertainty bound. At resonance, an explicit analytical bound identifies an interval spanning five bare oscillator periods during which the commutator remains within 0.62
The modified Zakharov–Kuznetsov (mZK) equation governs weakly nonlinear ion-acoustic and dust-acoustic waves in a magnetized plasma whose quadratic nonlinearity is suppressed by the background composition. Writing B and C for its parallel and transverse dispersion coefficients, we show that in the obliquely propagating sector ζ =x+my , where m=tanθ measures the obliqueness of the wave normal, the anisotropic mZK equation collapses exactly onto the focusing modified Korteweg–de Vries equation. The two dispersion coefficients enter only through the single effective dispersion D=B+Cm^2 , and the magnetic field only through C/B=1+Ω^-2 , with Ω the ion-cyclotron frequency normalized to the ion plasma frequency. This places the inverse-scattering apparatus at our disposal. We construct the 2× 2 Ablowitz–Kaup–Newell–Segur Lax pair, verify the zero-curvature condition, and establish the analyticity and symmetry properties of the Jost solutions. A matrix Riemann–Hilbert problem is posed on the real spectral axis, its jump matrix derived explicitly and its solution shown to be unique by a vanishing lemma. In the reflectionless case the problem reduces to a finite algebraic system and the N -soliton family is written through a single complex τ -function. Purely imaginary eigenvalues give oblique line solitons, conjugate pairs give breathers, and the coalescence of a conjugate pair gives a degenerate double-pole structure whose peak transiently doubles the soliton amplitude. At fixed amplitude, obliqueness and weak magnetization broaden a structure as √(D) while leaving its front speed unchanged.
We examine the consistency requirements for static, spherically symmetric black holes in the Horndeski subclass G_2=η X+2Λ , G_4=(16π G)^-1+βϕ ^2 , and G_3=G_5=0 . A scalar field linear in time is compatible with a static metric in some shift-symmetric theories, but that construction cannot be transferred automatically to a coupling with explicit scalar dependence. Requiring the full metric equations to hold at every time forces a Ricci-flat metric when β q^2 0 ; the stated asymptotically flat scalar boundary conditions then conflict with a nonzero q for η 0 and Λ =0 . We correct the variational equations and horizon boundary conditions, formulate radial and non-radial null-convergence diagnostics, and distinguish a test-scalar wave equation from a coupled gravitational stability calculation. We also derive the photon-sphere and innermost stable circular orbit diagnostics and explain why percent-level geometric differences alone do not establish detectability. The previously reported hairy branch, mode frequencies, and shadow and orbital shifts require recalculation and are not used to claim existence, linear stability, or observational distinguishability.
