The quantum simulation of topological phases in (2+1)D quantum electrodynamics with Wilson fermions provides a promising route toward realizing topological phenomena in near-term lattice experiments. We show that the commonly used staggered-fermion discretizations in Hamiltonian gauge theories possesses an exact time-reversal symmetry, which forbids the emergence of nontrivial topological phases and has led to confusion in the existing literature. In this work, we resolve this obstacle by systematically analyzing fermion discretization effects in (2+1)D lattice Hamiltonians of fermions coupled to U(1) gauge fields that satisfy Gauss' law. We show that Wilson fermions, already in the minimal one-flavor theory, naturally enable topological regimes with nonzero Chern numbers, and that the two-flavor extension at finite chemical potential further enriches the accessible topological structure. We develop gauge-invariant diagnostics of topological response, including many-body Chern numbers and current correlators that remain robust probes at weak coupling. Finally, through extensive exact diagonalization calculations across both flavor settings, we characterize the spectrum, correlators, and topological invariants, providing a concrete foundation for near-term quantum simulations of topological phases in lattice field theories. The implications of this work for quantum simulations of lattice field theory are analyzed in a joint submission [1].

Topological superconductivity could host quasiparticles that are key candidates for fault-tolerant quantum computation due to their immunity to noise as they obey non-Abelian exchange statistics. For example, in the case of Majorana Zero Modes (MZM), braiding enables two topologically protected quantum gates. While their direct manipulation in solid-state systems remains experimentally challenging, digital emulation of MZM behavior has provided insight as well as a deeper understanding of controlling these topological quantum systems. This emulation is typically accomplished by mapping the topological and trivial phases of a Majorana system to ferromagnetic and paramagnetic Hamiltonians of a spin-glass model. This approach usually relies on adiabatic evolution of superconducting Hamiltonians, which require circuits with very large depths. In this work, we present a resource-efficient method to emulate MZM braiding in a trijunction geometry using a quantum processor. We introduce direct braiding operators which simulate the evolution more efficiently, reducing the quantum gate overhead. We then further generalize this method to emulate braiding operations in extended trijunction architectures based on Kitaev chains.

A speedup, like a time change in discrete time dynamics, is a way of moving faster through the orbits of a dynamical system. Linearly recurrence is a stronger form of minimality for subshifts, shared by e.g.\ all primitive substitution shifts and Sturmian shifts associated with rotation numbers of bounded type. We prove that the homeomorphic speedup of a linearly recurrent two-sided subshift is again linearly recurrent.

The energy levels of the ground states of the three-particle and four-particle bound states of leptons in quantum electrodynamics are calculated. For the calculation, the variational method with Gaussian basis functions is used. The hyperfine structure of the spectrum is taken into account due to the pairwise spin-spin interaction of particles.

Photonic links between disparate quantum technologies$-$such as photon sources, memories, processors, clocks, and sensors$-$are key to scaling quantum networks and realizing a versatile quantum internet for secure quantum communication, distributed quantum computing, and entanglement-enhanced metrology. In practice, each technology is most suitably implemented on a different quantum platform; the substantial spectral mismatch between them, along with scarce native telecom interfaces, thus poses a major bottleneck to achieving efficient interconnections over long distances. Here we demonstrate the first deployed two-node hybrid network that operates entirely in the telecom C-band. Our approach uses no quantum frequency conversion or external filtering; instead, we develop a neutral atom single photon source and a solid-state rare-earth quantum memory that both operate in previously unexplored telecom regimes with state-of-the-art performance. The source achieves a high single-photon purity at 46 kcps, and the memory a storage efficiency of 10.6% with high multimode capacity. We leverage the intrinsic tunability of both systems to optimize their spectral overlap and demonstrate microsecond-level storage and retrieval with a large time-bandwidth product. Moreover, we showcase real-world networking competencies such as support for multiplexing across 37 temporal modes and preservation of non-classicality over fibers of 10.6 km (metropolitan) and 49.2 km (laboratory). Our work establishes a backbone for telecom-native quantum repeater links and unlocks a path towards high-bandwidth, large-scale quantum networking.

In this paper, we establish the non-abelian Hodge correspondence over compact Kähler spaces with Kawamata log terminal (klt) singularities as well as over their regular loci, thereby extending the result of Greb-Kebekus-Peternell-Taji for projective klt varieties to the context of compact Kähler klt spaces. The proof relies on two key ingredients: first, we establish an equivalence over the regular loci-via harmonic bundles-between polystable Higgs bundles with vanishing orbifold Chern numbers and semi-simple flat bundles; second, we prove a descent theorem for semistable Higgs bundles with vanishing Chern classes along resolutions of singularities. As an application of our framework, we obtain a quasi-uniformization theorem for projective klt varieties with big canonical divisor that satisfy the orbifold Miyaoka-Yau equality.

We investigate the free, massless Dirac equation $Dψ= 0$ on a higher-dimensional manifold $M_4 \times K$ equipped with a submersion metric. These background metrics generalize the Kaluza ansatz. They encode 4D massive gauge fields and Higgs-like scalars, alongside the usual 4D metric and massless gauge fields. We show that the dimensional reduction of the Dirac equation on these backgrounds naturally violates CP symmetry in four dimensions. This provides a new geometric path to constructing models with intrinsic CP violation. In this framework, massive gauge fields can break CP for three different reasons: $i)$ a misalignment between the mass eigenspinors and the spinors in the representation basis; $ii)$ a new non-minimal term coupling 4D fermions to massive gauge fields; $iii)$ the presence of a non-abelian Pauli term. All this derives from the higher-dimensional Dirac equation. Technically, the paper uses the language of spin geometry and Riemannian submersions. Along the way, it develops detailed geometric descriptions of several constructions. It finds that the gauge representations are always anomaly-free, discusses fermion generations, and introduces a new Lie derivative of spinors along non-Killing vector fields induced by actions of compact groups.

Recent studies have shown that fractional calculus is an effective alternative mathematical tool in various scientific fields. However, some investigations indicate that results established in differential and integral calculus do not necessarily hold true in fractional calculus. In this work we will compare various methods presented in the literature to improve the Gradient Descent Method, in terms of convergence of the method, convergence to the extreme point, and convergence rate. In general, these methods that generalize the gradient descent algorithm by replacing the gradient with a fractional-order operator are inefficient in achieving convergence to the extremum point of the objective function. To avoid these difficulties, we proposed to choose the Fractional Continuous Time algorithm to generalize the gradient method. In this approach, the convergence of the method to the extreme point of the function is guaranteed by introducing the fractional order in the time derivative, rather than in of the gradient. In this case, the issue of finding the extreme point is resolved, while the issue of stability at the equilibrium point remains. Fractional Continuous Time method converges to extreme point of cost function when fractional-order is between 0 and 1. The simulations shown in this work suggests that a similar result can be found when $1 \leq α\leq 2$. { This paper highlights the main advantages and disadvantages of generalizations of the gradient method using fractional derivatives, aiming to optimize convergence in complex problems. Some chemical problems, with n=11 and 24 optimization parameters, are employed as means of evaluating the efficacy of the propose algorithms. In general, previous studies are restricted to mathematical questions and simple illustrative examples.

This paper concerns the large-time behavior of perturbations around a time-periodic solution to the Navier-Stokes-Fourier system in the three-dimensional whole space. The time-periodic solution exists when a given external force is small enough. We derive the time-decay estimate of the perturbation under the assumption that an initial perturbation is sufficiently small. The time-space integral estimate for the linearized semigroup around the constant state in the Besov spaces is effectively applied in the proof.

We show that using strongly coupled dual-core waveguides for supercontinuum generation shifts the wavelength of the high-frequency dispersive waves towards shorter wavelengths, as compared to generation in a single-core waveguide having the same core dimensions. In a demonstration experiment, we launch ultrashort infrared pump pulses at 1-$μ$m wavelength (285-THz frequency) into silicon nitride waveguides, where soliton formation and fission leads to generation of dispersive waves in the visible range. Efficient input coupling and controlled excitation of the fundamental supermodes of the dual-core waveguide is provided with adiabatic tapers and a dual-prong input structure. For the dual-core waveguide, the short-wavelength dispersive wave is located at 540~nm (green, 555~THz), which is blue-shifted by 80~nm (70~THz) compared to that of the single-core waveguide. Simultaneously, the dual-core waveguide generates broadband radiation spanning from the blue into the UV range, reaching to below 350~nm (above 855~THz), with typically a spectral density 25~dB below that of the dispersive wave. The broadband component can be addressed to third harmonic generation and is not observed in single-core supercontinuum generation. Numerical modeling shows good agreement with experimental measurements. The demonstrated dual-core approach and dedicated input coupling appear to hold promise also for other waveguide structures, independent of specific materials or core dimensions, by providing shorter wavelengths than with the respective single-core waveguide.

The dynamics of a cycloidal spin structure driven by an AC magnetic field is theoretically studied in the weak-field limit. A specific model Hamiltonian describing the cycloidal spin structure in a ferromagnetic thin film is constructed, and its dynamics is analyzed using the collective-coordinate approach within the Lagrangian formalism. We demonstrate that the cycloidal spin structure exhibits a unidirectional gliding motion under an AC magnetic field, and an expression for the average velocity is derived as a function of the magnitude, the direction, and the frequency of the AC magnetic field. We compare our theoretical predictions with the results of micromagnetic simulations and identify two resonance frequencies determined by the eigenenergies of the excitation modes. Furthermore, evaluating spin motive forces induced by the dynamics reveals a substantial DC voltage, which may be exploited in energy-harvesting devices utilizing ambient electromagnetic radiation.

We study finite dimensional quantum systems with arbitrary collapse events, establishing, under no-information-erasure conditions, a structural no-go for operational irreversibility along single branches of the collapse dynamics. More precisely, we prove that, for every physically admissible selector of the collapse dynamics, there exists a topologically closed, forward-invariant subset of the projective state space on which any two states can be connected with arbitrarily fine Fubini-Study precision and arbitrarily small integrated energetic cost. This shows that the preservation of information along a realized branch of outcomes guarantees islands of quasi-reversibility, while genuine irreversibility requires additional ingredients such as non-compactness or information erasure. KEYWORDS: Quantum collapse dynamics; Quasi-reversibility; Chain-recurrence; Information non-erasure.

We consider an ${\cal N}=1$ nonrenormalizable supersymmetric gauge theory with the superpotential quartic in the chiral matter superfields. With the help of the Slavnov's higher covariant derivative regularization it is demonstrated that (in the lowest nontrivial order) the leading power divergent quantum correction to the gauge coupling constant is given by an integral of double total derivatives with respect to the loop momenta. The result obtained after calculating this integral turned out to be proportional to the corresponding quantum correction to the kinetic term of the matter superfields. More exactly, in the considered approximation the quadratically divergent contributions to the gauge coupling and to the kinetic term of the chiral matter superfields are related by an equation analogous to the exact NSVZ $β$-function for the renormalizable case.

Electron-phonon coupling in atoms and molecules adsorbed at metal surfaces gives rise to finite vibrational linewidths in infrared or electron energy loss spectra. When it is the dominant contribution to the vibrational lifetime, it manifests itself in the form of a Fano line shape. Here, we report the linewidths of vibrational modes of chemisorbed hydrogen on the (100) and (110) surfaces of molybdenum and tungsten calculated from first-order time-dependent perturbation theory. For those modes with a Fano line shape, our results are in good agreement with the experiment. We further observe that the coupling strength between vibrations and electrons depends on the nature of the mode: for Lorentzian-shaped peaks, the experimental linewidths are always larger than those predicted based on pure electron-phonon coupling. The calculated linewidths exhibit a strong coverage dependence, decreasing towards higher coverages. This finding has important implications for nonadiabatic energy dissipation in hydrogen dynamics at metal surfaces. While electron-hole pair excitation is the dominant energy-transfer mechanism between hydrogen and pristine metal surfaces, other channels for energy dissipation, such as adsorbate-adsorbate interactions, may become more significant on metal surfaces densely covered with hydrogen.

The works presented in this habilitation concern the algorithmics of polynomials. This is a central topic in computer algebra, with numerous applications both within and outside the field - cryptography, error-correcting codes, etc. For many problems, extremely efficient algorithms have been developed since the 1960s. Here, we are interested in how this efficiency is affected when space constraints are introduced. The first part focuses on the time-space complexity of fundamental polynomial computations - multiplication, division, interpolation, ... While naive algorithms typically have constant space complexity, fast algorithms generally require linear space. We develop algorithms that are both time- and space-efficient. This leads us to discuss and refine definitions of space complexity for function computation. In the second part, the space constraints are put on the inputs and outputs. Algorithms for polynomials assume in general a dense representation for the polynomials, that is storing the full list of coefficients. In contrast, we work with sparse polynomials, in which most coefficients vanish. In particular, we describe the first quasi-linear algorithm for sparse interpolation, which plays a role analogous to the Fast Fourier Transform in the sparse settings. We also explore computationally hard problems concerning divisibility and factorization of sparse polynomials.

This paper presents a novel modeling approach for unsteady aircraft airflow, leveraging the Lorenz attractor framework. The proposed model is based on the force distribution exerted by a lift-generating wing on the surrounding fluid. It distinguishes between turbulent and nominal components of the force distribution, with the nominal force distribution modeled to peak at the wing and decay linearly into the free stream. This separation allows the turbulent component to be represented by a transport equation that is influenced by flight conditions, specifically dynamic pressure and angle of attack. Consequently, the Navier-Stokes equations, along with the turbulence transport equation, can be transformed into a reduced-order model characterized by three scalar ordinary differential equations - similar to the Lorenz attractor. This resulting system effectively captures chaotic behavior, facilitating the exploration of complex dynamics without the computational demands of solving the full Navier-Stokes equations. A simulation trade study is conducted that models wing rock phenomena at high angles of attack, demonstrating the effectiveness of the proposed approach in capturing the intricate dynamics of unsteady aircraft aerodynamics.

This paper presents a systematic approach for designing robust linear proportional-integral (PI) servo-controllers that effectively manage control input and output constraints in flight control systems. The control design leverages the Nagumo Theorem and the Comparison Lemma to prove constraint satisfaction, while employing min-norm optimal controllers in a manner akin to Control Barrier Functions. This results in a continuous piecewise-linear state feedback policy that maintains the analyzability of the closed-loop system through the principles of linear systems theory. Additionally, we derive multi-input multi-output (MIMO) robustness margins, demonstrating that our approach enables robust tracking of external commands even in the presence of operational constraints. Moreover, the proposed control design offers a systematic approach for anti-windup protection. Through flight control trade studies, we illustrate the applicability of the proposed framework to real-world safety-critical aircraft control scenarios. Notably, MIMO margin analysis with active constraints reveals that our method preserves gain and phase margins comparable to those of the unconstrained case, in contrast to controllers that rely on hard saturation heuristics, which suffer significant performance degradation under active constraints. Simulation results using a nonlinear six-degree-of-freedom rigid body aircraft model further validate the effectiveness of our method in achieving constraint satisfaction, robustness, and effective anti-windup protection.

Wave-sea ice interactions shape the transition zone between open ocean and pack ice in the polar regions. Most theoretical paradigms, implemented in coupled wave-sea ice models, predict exponential decay of the wave energy but some recent observations deviate from this behaviour. Expanding on a framework based on wave energy dissipation due to ice-water drag, we account for drifting sea ice to derive an improved model for wave energy attenuation. Analytical solutions replicate the observed non-exponential wave energy decay and the spatial evolution of the effective attenuation rate in Antarctic sea ice.

We report on the development of a large-volume, wide field-of-view time projection chamber (TPC) for X-ray polarimetry, featuring a triple-GEM amplification stage and optical readout. Originally developed within the CYGNO program for directional dark matter searches, the system employs a scientific CMOS (sCMOS) camera and a photomultiplier tube (PMT) to collect secondary scintillation light produced during charge amplification. A prototype with a cylindrical active volume (radius 3.7 cm, height 5 cm) was tested at the INAF--IAPS calibration facility (Rome, Tor Vergata) to assess sensitivity to low-energy electron directionality. We fully reconstruct electrons in the 10-60 keV range, obtain angular resolutions as good as 15°, and infer modulation factors up to 0.9. These first results demonstrate robust photoelectron tracking at tens of keV with strong modulation, indicating that photoelectric-effect polarimetry can be extended to higher energies. This capability is promising for rapid transients (GRBs, solar flares) and would broaden the astrophysical reach of X-ray polarimetry.

We demonstrate a fully integrable and reconfigurable platform for controlling quantum emission by harnessing chiral exceptional bound states in the continuum (BICs) as a higher-order non-Hermitian singularity. Our architecture employs dual-microring resonators evanescently coupled to two waveguides, supporting symmetry-protected BICs. By integrating {a waveguide-coupled reflector} coupled with one resonator as a unidirectional feedback, a pair of orthogonal BICs gets transformed into a single, {chiral quasi-BIC} residing on an exceptional surface. The phase terms in external coupling and inter-modal coupling serve as two independent tuning knobs, enabling unprecedented dynamic control over the spontaneous emission dynamics of individual quantum emitters, including the Purcell enhancement and the emission lineshape. The efficiency in reconfiguring the output intensity gets promoted by more than a factor of two compared to alternative schemes, offering a promising path toward high-speed quantum optical switches and active lifetime control in integrated quantum photonic circuits.

This paper presents conservative probabilistic bounds for the spectrum of the admittance matrix and classical linear power flow models under uncertain network parameters; for example, probabilistic line contingencies. Our proposed approach imports tools from probability theory, such as concentration inequalities for random matrices. This provides a theoretical framework for understanding error bounds of common approximations of the AC power flow equations under parameter uncertainty, including the DC and LinDistFlow approximations. Additionally, we show that the upper bounds scale as functions of nodal criticality. This network-theoretic quantity captures how uncertainty concentrates at critical nodes for use in contingency analysis. We validate these bounds on IEEE test networks, demonstrating that they correctly capture the scaling behavior of spectral perturbations up to conservative constants.

In this paper, we will be studying the parameter space for the quantum multiplication for hypertoric varieties. The operation of quantum multiplication for hypertoric varieties has an explicit formulation which is given by McBreen and Shenfeld. In particular, this multiplication depends on a parameter which lives in the complement of a toric arrangement. Following a paper of deConcini and Gaiffi, I will define a compactification of this parameter space and show how the quantum multiplication can be extended to this compactification.

We present the first direct comparison between gate-based quantum computing (GQC) and adiabatic quantum computing (AQC) paradigms for solving the AC power flow (PF) equations. The PF problem is reformulated as a combinatorial optimization problem. For the GQC approach, the Quantum Approximate Optimization Algorithm (QAOA) is employed, while for the AQC approach, the problem is formulated as an Ising model. Numerical experiments on a 4-bus test system evaluate solution accuracy and computational performance. Results obtained using QAOA are benchmarked against those produced by D-Wave's Advantage system and Fujitsu's latest-generation Digital Annealer, implemented through the Quantum-Inspired Integrated Optimization (QIIO) software. The findings provide quantitative insights into the performance trade-offs, scalability, and practical viability of GQC and AQC paradigms for PF analysis, highlighting the potential of quantum optimization algorithms to address the computational challenges associated with the operation of modern electricity grids in the fault-tolerant era.

Sensing via a mechanical frequency shift is a powerful measurement tool, and, therefore, understanding and mitigating frequency noise affecting mechanical resonators is imperative. Thermomechanical noise fundamentally limits mechanical frequency stability, and its impact can be reduced with increased coherent amplitude of mechanical motion. However, large enough actuation places the resonator in the nonlinear (Duffing) regime, where conversion of amplitude noise (AM) into frequency noise (FM) can worsen sensor performance. Here, we present an experimentally straightforward method to evade this amplitude tradeoff in micromechanical sensors. Combining knowledge of the Duffing coefficients with readily available amplitude measurements, we avoid AM-FM conversion. Our approach uses dual-mechanical-mode operation on a tensioned thin-film resonator to set a baseline thermomechanically-limited stability by eliminating correlated single-mode frequency drifts. Thus, we cleanly observe AM-FM conversion at high drive, and reduce it using our method. The resulting high-stability operation beyond the linear regime contrasts long-standing perspectives in the field.

Iron molybdate (Fe$_2$(MoO$_4$)$_3$) is a widely used commercial catalyst for oxidative dehydrogenation. Recently, the possibility that bulk oxygen atoms participate in catalytic reactions has been proposed based on the experimentally observed significant reduction in Raman intensity during the catalytic process, which implies the formation of oxygen defects. In this work, we performed density functional theory (DFT) calculations to elucidate the microscopic mechanism of the experimentally observed Raman intensity variation. Our phonon analysis reveals that oxygen-dominated vibrational modes, with a small contribution from Mo, occur near 782cm$^{-1}$-- the same frequency region where the Raman intensity reduction was measured. To make the calculations computationally feasible for this large system, we introduced an effective frozen-phonon approach to mimic defect effects into the Raman intensity. Our results suggest that oxygen vibrations are primarily responsible for the decrease in the calculated Raman intensity. Moreover, structural relaxation of Fe$_2$(MoO$_4$)$_3$ containing an oxygen vacancy indicates that oxygen diffusion from the bulk to the surface may occur very rapidly, such that the local symmetry remains effectively unchanged. This interpretation is in line with the absence of measurable peak shifts or broadening in the experimental Raman spectra.

Recent studies have shown that a secondary potential barrier, forming a potential well outside the event horizon, can destabilize the Quasinormal Mode (QNM) spectrum of black holes. We find that spectral instability may persist even after the potential well vanishes, giving rise to a distinct family of spectrally unstable QNMs that differ from the spectrally stable modes localized near the potential peak and associated with the photon sphere. Nevertheless, time-domain simulations reveal that early-time ringdown waveforms remain dominated by stable modes, while unstable modes have only a subdominant contribution. These results highlight the robustness of black hole spectroscopy, as the observable ringdown signal is primarily governed by the most stable QNMs.

We revisit the nonlinear lattice design approach for the National Synchrotron Light Source II (NSLS-II) storage ring. By suppressing chaos, we identify alternative sextupole configurations to the original design, which relied on the conventional strategy of simultaneously minimizing Resonance Driving Terms (RDT) and Amplitude-Dependent Detuning (ADD). These alternatives achieve comparable performance while requiring fewer sextupoles. A detailed comparison of two representative solutions is presented and supported by experimental validation. Our results show that the dynamic aperture correlates more strongly with global chaos than with individual RDTs, and that the importance of minimizing ADD may have been overstated in earlier design strategies.

Hospitals face challenges in long-term intensive care unit (ICU) capacity planning under uncertain demand. Admission rates fluctuate over time, and LOS distributions vary with patient heterogeneity, hospital location, case mix, and clinical practice. Common approaches rely on steady-state queueing models or heuristic rules with fixed parameters, which often fail to capture real occupancy dynamics. The widely used 85% occupancy rule, for example, recommends keeping average utilization below this level to preserve responsiveness, yet it is grounded in stationary assumptions and may lack resilience in time-varying systems. Our analysis shows that even when long-run utilization targets are satisfied, daily occupancy often exceeds 100% capacity. We propose a data-driven framework to estimate ICU bed occupancy using an $M_t/G_t/\infty$ queueing model with time-varying arrival rates and empirically fitted LOS distributions. The approach combines statistical decomposition and parametric fitting to capture temporal patterns in admissions and LOS, and is applied to multi-year data from neonatal ICUs (NICUs) in Calgary. We evaluate capacity scenarios including average-based thresholds and Poisson-based surge estimates. Results show that static heuristics are inadequate under fluctuating demand and underscore the importance of modeling LOS variability when estimating bed needs. Although the case study focuses on NICUs, the framework has potential applicability to other ICU settings and provides interpretable, data-informed support for systems facing rising demand and constrained capacity.

Calculating the laser-induced transition probability by using the fluence distribution that neglects interference effects (e.g., by employing ray-tracing methods) can lead to an overestimation of this probability, as it underestimates saturation effects. In this paper, we investigate how interference effects in the multi-pass cell, used to enhance the laser fluence, affect the laser-induced transition probability between hyperfine levels in muonic hydrogen, a bound system of a negative muon and a proton. To avoid complications related to the exact knowledge of the intra-cavity field, we develop a simple model that estimates the maximal possible interference effects for given laser and multi-pass cell parameters, thereby providing an upper bound for the resulting decrease in transition probability relative to the case where these effects are neglected. A numerical evaluation of this upper bound for muonic hydrogen shows that, under our experimental conditions, such effects can be safely neglected. Nonetheless, the methodology presented here could be applied to estimate the impact of interference effects on the laser-induced transition probability in other experiments involving coherent light in multi-pass systems.

The macroscopic model for a neutron star (NS) as a perfect liquid drop at the equilibrium is extended to rotating systems by incorporating the linear perturbation expansion over a small frequency $ω$ near the Schwarzschild gravitational metric within the effective-surface (ES) approach. The NS angular momentum $I$ and moment of inertia (MI) for a slow stationary azimuthal rotation around the symmetry axis is calculated by using the Kerr metric approach in the Boyer-Lindquist and Hogan coordinates for the perfect liquid-drop model of NSs. The off-diagonal metric element is derived analytically from equations of the General Relativity Theory (GRT) and is compared with Boyer-Lindquist and Hogan expressions. The gradient surface terms of the macroscopic NS energy density $\mathcal{E}(ρ)$ [Equation of State] are taken into account along with the volume ones at the leading order of the leptodermic parameter $a/R \ll 1$, where $a$ is the ES crust thickness and $R$ is the NS effective radius. The macroscopic NS angular momentum $I$ at small frequencies $ω$, up to quadratic terms, are specified for calculations of the adiabatic moments of inertia (MI), $Θ= d I/ d ω$. The analytical NS MI expressions, $Θ=\tildeΘ/(1-\mathcal{T}_{tφ})$, has been obtained in terms of the statistically averaged MI, $\tildeΘ$, and its time and azimuthal-angle $t,φ$ correlation, $\mathcal{T}_{tφ}$, as sums of the volume and surface components. The MI $Θ$ is changed significantly as function of the effective radius $R$ because of a strong gravity. We found the additional constraint for the NS radius to smaller accessible ranges due mainly to the $t,φ$ correlations and surface contributions. The adiabaticity condition is carried out for many neutron stars with a strong gravity.