Papers

We study linear gravitational perturbations and the corresponding quasinormal-mode spectra of electrically and magnetically charged black holes in the presence of higher-order corrections to the Einstein-Hilbert action. In particular, we consider a four-derivative interaction that couples the Riemann tensor to the electromagnetic field strength in the unique (Horndeski) combination that preserves second-order equations of motion. We provide a comprehensive analysis of the stability conditions. We numerically confirm the absence of exponentially growing modes throughout the physically admissible region of parameter space where the theory remains free of pathologies. We then investigate in detail the properties of the quasinormal-mode spectra and identify several distinctive features induced by the higher-order interaction.

We investigate the high-energy collision of two spinless bodies within the Self-Force Effective Field Theory (EFT), taking one of them to be massless and highly energetic, such that it generates a gravitational shockwave (GSW) background. The GSW is perturbed by the second body, either massless or massive, satisfying respectively $E_2/E_1\ll1$ or $m_2/E_1\ll1$. Although the Self-Force expansion for shockwaves is frame-dependent, we freely choose a frame in which this EFT manifests its power, obtaining results valid to all orders in Newton's constant that make the underlying resummation patterns evident. Specifically, we push the expansion to 1SF order and prove the all-order vanishing of the so-called recoil operators in light-cone gauge. We obtain the exact graviton propagator on the shockwave background, matching previous results, and use it to compute the on-shell waveform at 1SF order in momentum space, specialising to the massless-massless collision. The waveform is computed to all orders in the Post-Minkowskian, or weak-field, expansion. In the trans-Planckian regime, its resummed form is proved to yield a UV-finite angular spectrum of radiated energy.

We obtain one-point functions of the ambient Lagrangian $\mathcal{O}_{\mathcal{L}}$ in $\mathcal{N}=4$ SYM with $\frac{1}{2}$-BPS boundaries, defects and interfaces classified by Gaiotto and Witten, which include maximally supersymmetric Janus interfaces and BCFTs relevant for double holography, as well as for Janus interfaces with reduced supersymmetry. For Janus interfaces we extend recent results capturing $\langle \mathcal{O}_{\mathcal{L}}\rangle$ in certain limits to exact dependence on $N$ and $\lambda$, and confirm a non-renormalization conjecture. We also clarify recent results for Janus variants preserving less supersymmetry. For general $\frac{1}{2}$-BPS Gaiotto-Witten theories with genuine defect degrees of freedom we derive one-point functions using supersymmetric localization, confirm that the results agree with holographic predictions in the appropriate limits, and show that the one-point functions in general exhibit non-trivial coupling dependence.

In this paper, we study non-perturbative vortex partition functions of four-dimensional N=1 supersymmetric gauge theories on the space-time geometry $T^2 \times D^2$, and we propose that these partition functions offer a notion of quantum elliptic cohomology. For particular U(1)-gauge theories we calculate these partition functions explicitly by applying equivariant localization methods to Handsaw quiver varieties that realize for this particular class of U(1)-gauge theories the moduli spaces of the non-perturbative vortex sectors. The determined vortex partition functions are annihilated by difference operators, which are interpreted as Ward identities among N=(0,2) BPS surface defects. Compared to lower dimensional gauge theories with four supercharges, anomalies play an essential role for a consistent formulation of the four-dimensional partition functions. In our proposal towards a mathematical formulation of the vortex partition functions in terms of equivariant elliptic cohomology, the gauge theory anomalies relate to geometric properties of the Thom sheaves corresponding to the relevant quasimap moduli spaces. Motivated by the explicit computations we reflect on the existence of a `virtual structure sheaf' on the moduli space of quasimaps for a general mathematical theory of quantum elliptic cohomology.

Triangular loop signals appear frequently in cosmological collider models but their analytical forms remain unknown due to multiple technical challenges. Here, we determine for the first time the leading analytical cosmological collider signals generated by a massive scalar triangle loop in inflationary bispectrum and trispectrum. Combining a directional cutting rule with partial Mellin-Barnes representations, we obtain both the local and nonlocal trispectrum signals in a soft limit and derive the leading signal in the squeezed bispectrum. Remarkably, all these signals are reproduced by the corresponding bubble diagram with a single effective pinched coupling. Signals beyond leading order and cases with arbitrary internal masses, spins, and interactions can be generated within the same framework. Our approach also provides a systematic route to extracting analytical loop signals from general cosmological correlators.

We study the gravitational collapse of a shell, modeled as a coherent state of quantum matter. Without adding any physics beyond semiclassical gravity, we show that the universal gravitational coupling between matter and geometry induces an interaction between the shell and the negative-frequency modes present in the $|in \rangle$ vacuum state. We find that this interaction occurs unavoidably immediately after a trapping horizon forms, making it a universal feature of semiclassical gravitational collapse. The resulting transfer of energy from the collapsing matter to outgoing Hawking radiation acts as a gravitational quantum friction, opposing the formation of trapped regions while simultaneously imprinting the information carried by the collapsing matter onto the emitted quanta. We discuss the implications of this mechanism for the black hole information-loss problem and speculate about the possible endpoints of collapse, potentially preventing horizon and singularity formation.

We initiate the study of two-to-two scattering amplitudes involving two distinct scalar particles in $d = 4$ spacetime dimensions using the primal S-matrix bootstrap. We impose a $\mathbb{Z}_2 \times \mathbb{Z}_2$ global symmetry under which the two particles are the lightest ones carrying charges $(-,+)$ and $(+,-)$, guaranteeing their absolute stability and absence of triangular anomalous thresholds. For unequal masses, the presence of a pseudo-physical cut whose discontinuity is not directly constrained by physical unitarity qualitatively changes the bootstrap problem. We find several observables to be unbounded, while others obey non-trivial one-sided bounds or become bounded once another observable is fixed. In the equal-mass limit, where the pseudo-physical region disappears, two-sided bounds are recovered. As a proof of concept, we show that supplying information about the pseudo-physical discontinuity through an Omnès parametrisation also restores boundedness. Our results provide a starting point for future studies of physical processes such as pion-kaon and pion-nucleon scattering.

This paper briefly outlines a proposal for a GLSM Coulomb-branch interpretation of the quantum elliptic cohomology rings currently being developed in mathematics by Bouaziz-Huq-Kuruvilla-Lee. The proposal is modeled on the established GLSM computations of quantum cohomology and quantum K theory of Fano toric varieties, where ring relations arise as critical loci of twisted effective superpotentials. In the case of quantum elliptic cohomology, the natural generalization would be to encode ring relations in Coulomb branch computations in two-dimensional theories obtained by KK reductions from four-dimensional theories, describing OPEs of parallel surface defects, which we review. However, in some basic examples, this interpretation is obstructed by four-dimensional gauge anomalies. In such cases, we provide a classical superpotential whose critical loci generate the expected ring relations, but which is not obtained by KK reduction from four dimensions, though it shares many characteristics with such KK reductions. We describe some simple examples, and make some predictions for the case of gerbes.

The entangling power of a unitary operator acting on a bipartite Hilbert space measures the entanglement it generates from product states, averaged over the inputs. A finite-dimensional unitary has a spectral decomposition $U=\sum_{a=1}^{n}e^{i\theta_a}P_a$, where $e^{i\theta_a}$ are the eigenvalues, $P_a$ the corresponding eigen-projectors, and $n$ is the number of distinct eigenvalues. After removing an overall phase, the entangling power is a function on the $(n-1)$-torus of relative eigenphases at fixed spectral projectors. We prove that this function is stationary at all $2^{n-1}$ points on the torus where every relative phase is $0$ or $\pi$, which we define as corners. Up to an overall phase, $U$ at each corner is a generalized reflection $R=\mathbb{I}-2Q$ satisfying $R^2=\mathbb{I}$, where $Q$ is the sum of spectral projectors whose relative phase is $\pi$. At the corner the entangling power is expressed in terms of seven local-unitary invariants of $Q$. A unitary gate $U$ can be realized as a corner of some projector family if and only if $U^2\propto\mathbb{I}$, a condition satisfied by many Clifford and non-Clifford gates. We illustrate the theorem with two-qubit gates, $SU(N)$ channel decompositions, and two-site spin chains, obtaining examples of minima, maxima, and saddle points. In addition, a corner that is a saddle point on the full phase torus can appear as a local maximum or minimum along different time-evolution trajectories.

The topologically twisted index of ABJM theory captures the microscopic entropy of magnetically charged supersymmetric $\mathrm{AdS}_4$ black holes. Building on the companion Letter arXiv:2608.04107, which reconstructed the finite-rank twisted superpotential at the universal twist, we determine the finite-rank index using high-precision Bethe-vacuum data, physics-informed symbolic regression, and integer relations. The Hessian, effective dilaton, and one-loop factors encode information beyond the on-shell twisted superpotential. The two observables share the same shifted rank. Within a declared finite class, we reconstruct the index constant map from the ABJM $S^3$ constant maps at levels $k$ and $k/2$, the constant map of the twisted superpotential, and elementary terms. We prove that it equals a convergent one-kernel integral for real $k>0$, resumming the large-$k$ expansion, fixing a previously numerical constant, and yielding type-IIA coefficients at arbitrary genus. We also prove that the Clausen expression in arXiv:2608.04107 equals an alternating Euler sum and an absolutely convergent integral, giving closed evaluations for two rational-argument Euler-sum families. At $k=1,2,4$, the exponentially suppressed sectors exhibit arithmetic structure. The reconstructed coefficients of the twisted superpotential obey a divisor-sum formula with a conjectural all-order Eichler-integral series associated with a weight-four Eisenstein form. The index coefficients reduce to two rational generators; one admits modular-product formulas reproducing every available coefficient and suggesting an all-order completion. Conditional on this continuation, modular transformations determine the nearest logarithmic singularity, radius of convergence, and leading coefficient growth. These results provide a finite-$N$ benchmark for quantum gravitational blocks and bulk black hole quantum entropy.

The mass ratios of the quarks and charged leptons follow a simple pattern. The logarithmic generation steps come in a two to one ratio, a note to its octave, and the ordering is mirrored between the up-down and down-lepton comparisons. The pattern, read as charge counting on a $Z_N$ clock, is realized at level four and at no level that is not a multiple of four, which motivates modular level four and the finite group $S_4$, with the generations in the triplet at $T$ charges $(3,1,0)$ and the mirror in the sign singlet. The charged-lepton mass ratios lie on a theta-dressed lattice at $0.02\%$, which sets the base $\varepsilon=0.18664$, taken as $14/75$, and the harmonic modulus $\tau=1.0685i$. Five postulates in the weight one-half theta constants, identified on the same data, reproduce the six quark masses from three lepton masses and the electroweak scale. Two more and one empirical relation for $|V_{td}|$ close the CKM matrix, giving $|V_{us}|=\sqrt{m_d/m_s}=0.2255$, $|V_{cb}|=0.04197$, $|V_{ub}|=0.003721$, and $\delta=1.138$ against the measured $1.139\pm0.023$, with no continuous parameter. The unitarity triangle follows, with apex $(0.161,0.348)$ against the measured $(0.161\pm0.010,0.347\pm0.010)$, and $J=3.11\times10^{-5}$ against $(3.09\pm0.07)\times10^{-5}$. The same structure carries the neutrinos. A single theta insertion gives $\sin\theta_{13}=\theta_2(\tau)m_2/m_3$, which holds at $0.7\sigma$ on the 207-day JUNO data, and the harmonic condition completes a normal-ordered spectrum with $m_1=0.25$~meV, $\Sigma m_\nu=0.0589$~eV, a CP-conserving phase $\delta_{CP}=\pi$, and effective Majorana masses quantized at $1.3$ to $3.9$~meV. The ultraviolet completion belongs to the magnetized torus class, with Pati–Salam the natural gauge embedding.

Higher genus Gromov-Witten invariants of Calabi-Yau threefolds are encoded in a generating function which is an asymptotic series in a formal parameter $\lambda$. Using resurgence, analytic functions in this formal parameter were uncovered. In this paper we focus on the resolved conifold and study the enumerative meaning of the strong-coupling asymptotic expansion, in powers of $ 1/\lambda $, of the resurgent analytic functions. We show that this expansion contains both a closed curve-counting contribution in dual variables and a contribution governed by relative Gromov-Witten invariants, naturally interpreted in logarithmic geometry.

Attractors are effective low-dimensional structures, defined in a chosen set of observables, that trajectories from different initial states approach; hydrodynamic attractors are those on which the late-time evolution is governed by hydrodynamic constitutive relations. Motivated by nuclear collisions and ultracold atomic gases, this chapter distinguishes attractorization (the loss of sensitivity to some directions in the space of initial states) from hydrodynamization (the onset of validity of hydrodynamic constitutive relations). Using mainly conformal, boost-invariant Bjorken flow, we compare Müller-Israel-Stewart-type theories, kinetic theory, holography, and classical Yang-Mills fields. Forward attraction, produced by the decay of non-hydrodynamic modes, is distinguished from pullback attraction, which can select a unique regular solution, and from expansion-driven attraction, which can suppress initial-state sensitivity before microscopic relaxation, with or without a subsequent fluid regime. Divergent gradient expansions and their transseries completions, the state-space picture, and adiabatic hydrodynamization provide complementary descriptions. Applications to nuclear collisions include particle production, transverse energy and flow, the initialization of and linear response around attracting backgrounds, jet quenching, and attractor-informed modifications of hydrodynamic models. For ultracold Fermi gases, we review theoretical proposals for bulk-channel attractors under scattering-length drives and distinguish them from recent measurements of short-time contact and momentum-distribution dynamics.

We derive the two-loop anomalous dimension relevant for the resummation of subleading non-global and, for the first time, also clustering logarithms within the framework of effective field theory. Special emphasis is put on the choice of the renormalization scheme. We show that the modified minimal subtraction scheme is problematic since it requires extra dimensions to set up the parton shower to perform the resummation. We discuss a set of modified dipole subtraction schemes which are free from this complication and can be used to obtain a frame-independent result for the renormalization-group evolution. We implement the leading-color limit of our result in the Marzili framework and numerically verify the scheme independence for gap-between-jets cross sections.

We investigate three flavor neutrino phenomena in an effective holonomy corrected Schwarzschild geometry. We derive the weak-deflection angle through second post-Minkowskian order, obtain the semiclassical phases along radial and nonradial trajectories, and formulate the two-image flavor probability by including magnifications, Fermat phases, and wave packet overlap. The cross path phase acquires a logarithmic holonomy contribution and can retain information about the absolute neutrino mass scale. We also characterize flavor mode correlations and trajectory-flavor entanglement through the balance among path predictability, interference visibility, and I-concurrence. Neutrino-antineutrino annihilation outside an effective neutrinosphere is examined, with holonomy entering the integrated power through the radial proper volume measure. For a solar mass lens and $10\,\mathrm{MeV}$ neutrinos, the numerical results show displaced oscillation fringes and a geometry dependent redistribution among the electron, muon, and tau channels. The electron-neutrino trajectory-flavor concurrence reaches approximately $0.23$, with an entropy near $0.10$ bit, while remaining weakly sensitive to the mass ordering in the selected configuration. By contrast, the annihilation power increases monotonically, reaching an increase of approximately $39.3\%$ relative to Schwarzschild spacetime (for a particular configuration, i.e., $\lambda=2$ and $M/R_{\nu}=1/3$). Furthermore, at fixed source parameters and $M/R_\nu=1/3$, an assumed maximum excess of $10\%$ in the integrated annihilation power relative to Schwarzschild yields the conditional bounds $a/(2M)\leq0.2879$ and $|\lambda|\leq0.6358$.

We study the existence of supersymmetric M5-brane instantons in asymptotically AdS$_4 \times S^7/\mathbf{Z}_k$ geometries of M-theory, dual to the ABJM theory. The supersymmetric embeddings of these instantons are determined by the M5-brane $\kappa$-symmetry, which forces them to localise to the equivariant fixed points in the asymptotically AdS$_4$ geometry, and wrap $(S^3\times S^3)/\mathbf{Z}_k $. At the quantum level we find that the one-loop partition function of these instantons vanishes, suggesting that the bulk partition function is instead to be expanded in terms of supergravity modes and M2-brane instantons, in line with known results for the $S^3$ partition function of the dual ABJM theory.

In the context of the atomic classification of 5d SCFTs building blocks with non-simply laced global symmetries are lacking. In this work we fill this gap by introducing a new class of 5d UV fixed points (the 5d SCFT "fixtures"). Physically, 5d SCFTs fixtures are the result of a Higgs branch RG flow, realized geometrically by M-theory on singular threefolds which we identify explicitly. In particular, this enables the construction of 5d conformal matter SCFTs with non-simply laced flavor symmetry. Along the way, we discuss their circle reduction in relation to 4d theories of class-S type.

This is a concise and compact introduction to a framework for spacetime, gravity, and fundamental physics based on the IKKT matrix model, focusing on conceptual and structural aspects. The approach rests on nontrivial vacua or matrix backgrounds, which serve as 3+1-dimensional noncommutative spacetime. We discuss a specific class of backgrounds describing expanding homogeneous and isotropic FLRW spacetime, which provide a solution of the one-loop effective action with finitely many dof per volume. Perturbations of the background give rise to fields propagating on spacetime governed by a weakly-coupled gauge theory, as well as a nonstandard description of (quantum) gravity leading to some IR modifications. Maximal supersymmetry of the model is essential to ensure effective locality.

In our previous work [C. Lorcé et al., Phys. Lett. B 868 (2025) 139792], we investigated the 2D spatial distributions of transverse total angular momentum, including orbital angular momentum and intrinsic spin, relative to the canonical center (or center of spin). In the present work, we extend this analysis in two directions. First, we study the corresponding transverse boost distributions relative to the canonical center. Second, since the definition of generalized angular momentum density depends crucially on the choice of pivot, we analyze how the spatial distributions of transverse total angular momentum and boost are modified when they are defined relative to different relativistic centers, viz.~the relativistic centers of mass, energy, and spin. Considering spin-1/2 targets, we derive the corresponding 2D spatial distributions in the transverse plane, and further investigate how the spatial patterns evolve under longitudinal Lorentz boosts. Additionally, we provide the corresponding light-front distributions in the transverse plane, establishing a clear connection between the instant-form and light-front descriptions of transverse angular momentum and boost.

Representing multi-loop scattering amplitudes as linear combinations of multivalued transcendental functions with process-dependent rational coefficients has long been understood to be advantageous. In general, these transcendental functions satisfy a system of differential equations with coupled homogeneous blocks. When these coupled blocks can be removed through algebraic basis transformations, the relation between the rational and algebraic bases is universal and minimal. Here, we ask whether an analogous universal and minimal relation exists when decoupling requires transformations involving complete elliptic integrals. We elaborate on the method proposed in ref. arXiv:2504.20897, in which we suggested that a basis constructed using an elliptic generalization of leading singularities may provide an answer to this question. We extend this analysis to the off-diagonal blocks of the rational differential equations satisfied by the bases obtained through this construction. We find that the $\epsilon$ dependence of these blocks can be organized into a universal structure that is preserved under the decoupling transformation used to express the solutions in terms of iterated integrals.

We analyze the covariant phase space of Klusoň's canonical Carroll non-BPS D$_p$-brane actions. The Carroll limit is formulated as a contraction of the canonical phase space: the canonical one-form is invariant under the scaling of conjugate pairs, while the leading Hamiltonian constraint differs between the electric-like and magnetic-like sectors. This difference controls the weak closure of the electric-like constraint algebra and the stronger closure of the magnetic-like Hamiltonian brackets. We separate the generic non-BPS sector, which carries $D-1$ local phase-space degrees of freedom, from the tachyon-vacuum sector, which carries $D-2$ only after imposing second-class background conditions. We also identify the rank condition for the generic electric-like sector and its strengthening in the vacuum sector. Finally, we show that the Carroll–Weyl $\chi$ transformation, the matter-sector analogue of the null-string Carroll–Weyl symmetry, preserves the symplectic form and admits a charge, but is obstructed by the constraints and cannot be promoted to a first-class gauge generator except in a highly restricted global vacuum sector. The obstruction is algebraic in $\chi$, so no restriction of its spacetime profile can remove it. This contrasts with null string theory, where a restricted $\chi$-symmetry can be completed to an additional first-class constraint.

We study the splitting dynamics of multiply quantized vortices with winding numbers $n=5,6,7$ and $8$ in a two-dimensional holographic superfluid at finite temperature, by combining linear perturbation analysis of quasinormal modes with fully nonlinear real-time numerical simulations. Three new physical phenomena are revealed. First, the number of unstable modes no longer strictly follows the $2n-3$ formula as $n$ increases. For the vortex with $n=8$, the unstable mode with $p=2(n-1)$ is absent throughout the entire temperature range, so that only $2n-4$ unstable modes exist. Second, the transition of the dominant unstable mode with increasing temperature exhibits new characteristics. For vortices with $n\le 6$, the dominant mode changes sequentially as $p=2,3,\dots,n$, whereas for $n\ge 7$ jump-like transitions occur-for instance, for $n=7$ the dominant mode jumps from $p=2$ to $p=4$ at $T=0.325T_c$ and then directly to $p=7$ at $T=0.359T_c$, and for $n=8$ it jumps directly from $p=2$ to $p=8$ at $T=0.302T_c$. Third, a single splitting pattern of high-winding-number vortices can contain multiple sub-splitting patterns with distinct topological structures, as exemplified by the $l=4$ pattern of the $n=8$ vortex, which exhibits three sub-patterns at low, intermediate and high temperatures. The nonlinear simulations confirm the predictions of the linear stability analysis, and the implications of our results for cold-atom experiments are discussed.

We investigate a geometric mechanism for mass generation in a codimension-two hedgehog braneworld. A massless particle propagating in the bulk acquires an effective four-dimensional mass through its motion along the compact angular extra dimension, yielding a dynamically determined Kaluza-Klein spectrum after canonical quantization. While the bosonic sector exhibits no radial confinement, extending the analysis to N = 1, 2 spinning-particle models shows that the spin-curvature coupling modifies the effective potential and introduces a level-dependent localization pattern for the Kaluza-Klein modes. The results establish a particle-mechanics realization of geometric mass generation in flux-supported codimension-two braneworlds and highlight the interplay between bulk geometry, spin, and the effective four-dimensional mass spectrum.

We propose that the 3d symplectic Chern-Simons theory $USp(2n)$ at level $k=n+\frac12+\ell$ with a single chiral multiplet in the fundamental representation is dual, for every pair of positive integers $(n,\ell)$, to the Abelian rank-$0$ theory $\mathcal{T}_{\ell,n}$ of Creutzig, Garner and Kim. The fundamental is pseudo-real, so the level is half-integral, there is no non-Abelian flavor symmetry, and the supersymmetry is enhanced to $\mathcal{N}=4$. Both sides have vanishing Higgs and Coulomb branches. We match the counting of supersymmetric vacua under real mass deformations for all $(n,\ell)$, and the supersymmetric indices in a number of cases. We then study in detail the case $\ell=1$, the minimal $USp(2n)$ Chern-Simons theory at level $n+\frac32$, whose dual is a $U(1)^{n}$ theory with a tadpole level matrix and a bare monopole superpotential.

We revisit gravitational decoherence of matter superpositions using the leading soft sector of the graviton $S$-matrix. Starting from Weinberg's soft theorem and the overlap of coherent radiation states, we derive, for branch configurations with the same total four-momentum, a gauge-invariant, nonnegative leading-soft decoherence exponent and evaluate the polarization sum and angular integrals exactly at this order. In the vacuum, coherence between branches with distinguishable soft radiation vanishes as the infrared cutoff is removed. The leading nonrelativistic term is purely quadrupolar as a consequence of energy–momentum conservation. We extend the analysis to single- and two-mode squeezed graviton states, including the two-mode case motivated by inflation. Squeezing can enhance or suppress decoherence depending on the relative phase, while phase averaging gives an enhancement governed by the graviton occupation. For a phase-averaged relic background with an approximately flat energy-density spectrum over the relevant soft frequency band, the sharp-cutoff identification of the infrared scale with the inverse observation time gives a contribution that grows with the gravitational-wave energy density and with the fourth power of the observation time. These results connect soft-graviton scattering, infrared quantum information, and decoherence in nonvacuum gravitational backgrounds.

We characterize several quantum resources carried by the spins of the $\tau^{+}\tau^{-}$ pair produced in $e^{+}e^{-}$ annihilation. At the Belle-II energy, $\sqrt{s}=10.579\,\mathrm{GeV}$, Bell nonlocality, steerability, entanglement of formation, and coherence are governed by the production angle and are largest for transverse emission, $\vartheta=\pi/2$. Their common kinematic origin is exposed by expressing the spin state as a velocity and angle-dependent mixture of a separable contribution and a maximally entangled component. Within the physical production domain, this representation connects the weakly correlated threshold state at $\sqrt{s}=2m_{\tau}$ to the Bell-state limit approached at ultrarelativistic energies. We then propagate the two-spin state through a phenomenological correlated-dephasing channel to determine how environmental memory and inter-channel classical correlations affect the available resources. Memory effects generate collapses and revivals that are absent from the monotonic Markovian evolution. The analysis therefore separates the kinematic mechanism that creates the spin correlations from the noise properties that control their subsequent survival.

This work provides a complete analytical characterization of the transfer- matrix structure associated with the finite Kronig-Penney model consisting of one-dimensional arrays of Dirac delta potentials recently introduced by Figueroa et al. (2025). Although their study identified the emergence of specific transfer-matrix entries and related combinatorial coefficients, a rig- orous derivation of the corresponding closed-form expressions has not yet been established. By expressing the N th power of the unit-cell transfer ma- trix in terms of Chebyshev polynomials of the second kind, we obtain explicit closed-form representations for the global transmission and reflection ampli- tudes. The proposed formulation reveals a previously unrecognized structural correspondence between multiple quantum scattering processes, discrete con- volutional patterns, and hypercomplex combinatorial structures.

We investigate the Casimir effect of a complex scalar field on a two-dimensional sphere threaded by a fixed Wu–Yang magnetic monopole at the center. In this background the charged scalar field is a section of a nontrivial complex line bundle over $S^2$, reflecting the monopole's nontrivial topology. We solve the Klein–Gordon equation analytically and compute the Casimir energy using a generalized Abel–Plana formula for multivalued functions. We find that the monopole can reverse the sign of the Casimir pressure, turning an attractive force into a repulsive one when the monopole strength is sufficiently large. This behavior persists across a broad range of curvature couplings and suggests that Wu–Yang monopoles may provide a source of repulsive vacuum stress, with possible implications for gravitational and cosmological settings.

We construct the Bogomol'nyi equations for Abelian gauge–Higgs vortices in which the Maxwell gauge sector is replaced by Kruglov nonlinear electrodynamics, a power-law family that interpolates between Maxwell theory, Born–Infeld electrodynamics, and exponential electrodynamics, characterized by a dimensionless exponent $\sigma$. Using the stressless method, we derive a pair of first-order equations directly from the vanishing of the spatial stress tensor, without assuming the Higgs potential a priori. For generic $\sigma$, the gauge and Higgs sectors are coupled through an implicit algebraic relation. We therefore introduce a constitutive map $\Phi(Y;\sigma)$ and analyze its monotonicity and range to determine the conditions for a smooth admissible Bogomol'nyi branch. For $\sigma>1/2$, the constitutive map is strictly monotonic and unbounded, whereas for $0<\sigma<1/2$ it possesses a finite maximum; the marginal case $\sigma=1/2$ is bounded. These properties yield explicit bounds on the nonlinear parameter $\beta$ for the latter cases. We further obtain closed-form constitutive relations, BPS potentials, and gauge-field equations for six representative values of $\sigma$, spanning linear, quadratic, and cubic algebraic structures. The corresponding vortex profiles are then computed numerically. The resulting BPS string tension is purely topological, $\mu_{\rm BPS}=2\pi n$, independent of both $\sigma$ and $\beta$.

The symmetry content of static spherical $f(R)$ gravity is reconsidered for the pure quadratic model. We first derive the radial action without prematurely eliminating the equation carried by the radial metric variable. The Schwarzschild-type gauge may then be imposed while retaining its associated gravitational constraint. For the resulting system, radial translations and one combined scaling are exact off-shell Noether symmetries. The scaling charge reduces, on the constraint surface, to a conserved radial flux of the scalar curvature. The same flux follows independently from the trace of the four-dimensional field equations. Noether invariance, the strong point-Mei criterion, and Lie invariance of the Euler–Lagrange system are examined separately. Within the full polynomial point ansatz of total degree at most two, the Lie algebra contains precisely three independent generators. The flux also separates the solution space into a nonzero constant-curvature Einstein sector, a degenerate scalar-flat sector, and a dynamical-curvature sector. In particular, the scalar-flat sector permits a Reissner–Nordström-form metric, although its inverse-square coefficient has no electromagnetic meaning in the absence of a Maxwell field.