Papers

Non-Gaussian states are key resources for quantum technologies, making the quantification of non-Gaussianity a fundamental challenge. We introduce an energetic framework for characterizing non-Gaussianity in single-mode bosonic states by decomposing the total energy into Gaussian and non-Gaussian contributions. For pure states, we show that the non-Gaussian energy defines a bona fide measure of non-Gaussianity and establish a direct connection with the relative entropy of non- Gaussianity. As an illustration, we consider non-Gaussian states generated from coherent states with tunable amplitudes using a SNAP gate. We find that the resulting non-Gaussian energy and Wigner negativity are maximized at similar input amplitudes. For mixed states, we demonstrate that the non-Gaussian energy provides a faithful witness of non-Gaussianity. Our results uncover an energetic fine structure of non-Gaussian quantum states and offer new insights into the efficient generation and manipulation of non-Gaussian resources.

New numerical methods are proposed for the mixing entropy maximization problem in the context of Miller-Robert-Sommeria's (MRS) statistical mechanics theory of two-dimensional turbulence, particularly in the case of spherical geometry. Two of the methods are for the canonical problem; the other is for the microcanonical problem. The methods are based on the original MRS theory and thus take into account all Casimir invariants. Compared to the methods proposed in previous studies, our new methods make it easier to detect multiple statistical equilibria and to search for solutions with broken zonal symmetry. The methods are applied to a zonally symmetric initial vorticity distribution which is barotropically unstable. Two statistical equilibria are obtained, one of which has a wave-like structure with zonal wavenumber 1, and the other has a wave-like structure with zonal wavenumber 2. While the former is the maximum point of the mixing entropy, the wavenumber 2 structure of the latter is nearly the same as the structure that appears in the end state of the time integration of the vorticity equation. The new methods allow for efficient computation of statistical equilibria for initial vorticity distributions consisting of many levels of vorticity patches without losing information about all the conserved quantities. This means that the statistical equilibria can be obtained from an arbitrary initial vorticity distribution, which allows for the application of statistical mechanics to interpret a wide variety of flow patterns appearing in geophysical fluids.

Galaxy mergers are a central driver of galaxy evolution across cosmic time, and thus, quantifying their frequency is critical for constraining hierarchical models of galaxy formation. Motivated by the need to robustly quantify these fractions and their evolution, we build on our previous close-pair analysis by exploring morphological identification techniques within the Deep Extragalactic VIsible Legacy Survey (DEVILS), using the D10 (COSMOS) field, which covers an area of $1.47$ deg$^2$. While close-pairs trace the early stages of galaxy interactions, morphological methods probe more advanced phases of the merging process, including systems with disturbed structures and post-merger remnants. We present galaxy merger fractions over the redshift range $0.2 < z < 0.9$ using visual classification and automated identification based on non-parametric statistics: concentration ($C$), asymmetry ($A$), smoothness ($S$), Gini ($G$), and $M_{20}$, applied to HST/ACS imaging. To enhance the detection of subtle structural perturbations, we measure asymmetry on unsharp-masked images. We find relatively little overlap between visually and automatically identified samples, which highlights their distinct sensitivities and limitations. Moreover, galaxy merger fractions derived from morphological disturbances are consistently higher than those from close-pair counts at all redshifts. This potentially reflects how each method probes different stages of the merger process, with distinct observability timescales, as well as the fact that morphologically disturbed galaxies, at a given redshift, are typically the later-stage descendants of close-pairs from earlier epochs. This comparison allows us to examine systematic differences between identification techniques and assess how they impact the observed evolution of the galaxy merger fraction.

Two-fluid nonlinear MHD simulations using the TM1 code demonstrate that the formation of magnetic islands at the top and bottom of the H-mode pedestal, together with the strong screening of resonant fields in the gradient region of the pedestal, can account for ELM suppression and density pump-out by n = 2 Resonant Magnetic Perturbations (RMPs) in low-collisionality DIII-D ITER Similar Shape (ISS) plasmas. Using experimentally relevant transport coefficients, neoclassical resistivity, electron collisionality, and RMP amplitudes, nonlinear MHD simulations reproduce the observed level of density reduction (density pump-out) in DIII-D due the formation of narrow magnetic islands and resulting enhanced collisional transport in the resistive foot of pedestal. For large amplitude RMPs (Br/Bt>1*10-4) simulations predict field penetration and pressure reduction at the top of the pedestal consistent with experimental observations at the onset of ELM suppression. The predicted reduction in the height and width of the pedestal by magnetic island enhanced transport provides a quantitative mechanism for the stabilization of the Peeling-Ballooning Mode (PBM). Importantly, these simulations predict strong screening of resonant fields in the steep gradient region of the pedestal due to strong ExB and diamagnetic flows. However, if the plasma resistivity is made artificially larger (~10X) than neoclassical, the simulations predict magnetic stochasticity throughout the plasma edge and the collapse of the pedestal due to the reduction in the penetration threshold with increasing resistivity. A scaling relation for resonant field penetration at the pedestal top, using several hundred nonlinear simulations, reproduces the density and ExB dependence of the ELM suppression threshold observed in DIII-D.

We propose a variational approach to principal spectral values of non-selfadjoint operator pencils $\mathcal L u=\lambda\mathcal G u$, where the weight operator $\mathcal G$ may be singular. The aim is to obtain Rayleigh-type minimax formulas for selected real spectral levels in settings where the standard selfadjoint variational theory is unavailable and positivity-based methods may not apply directly. The construction is based on the extended two-variable Rayleigh quotient \[ \mathcal R(u,v) = \frac{\langle \mathcal L u,v\rangle} {(\mathcal G u,v)_H},\] defined on admissible cone pairs. It leads to dual sup-inf and inf-sup principal levels, cone quasi-eigenvalues, and corresponding trapping and saddle-point principles. The resulting minimax formulas characterize selected real cone levels of non-selfadjoint operator pencils and identify them with principal spectral values whenever positive right-left eigenpairs exist, including cases with non-invertible operators and singular weights. We prove that these formulas are stable under finite-dimensional approximation. Thus the classical idea of approximating spectral data by finite-dimensional variational problems acquires an analogue for non-selfadjoint operator pencils in an ordered cone setting. The method also yields a posteriori spectral certificates, one-sided perturbation bounds, and approximation estimates. Elliptic examples illustrate both the scope of the method and the sharpness of the estimates.

We present an estimate of the Sivers asymmetry in back-to-back $J/\psi$-photon and $J/\psi$-jet production in electron-proton collisions in the kinematics of the upcoming Electron-Ion Collider (EIC) in a transverse momentum dependent (TMD) factorization framework, and also incorporating the TMD evolution. We use the non-relativistic Quantum Chromodynamics (NRQCD) model to study the production mechanism of $J/\psi$. The gluon induced channel dominates, and these are promising probes of the less known gluon Sivers function. We incorporate the TMD evolution in the cross section and Sivers asymmetry in the Collins-Soper-Sterman (CSS) approach and show that the asymmetry is sizable even after the evolution. Although the cross section for $J/\psi$-jet production depends on the long-distance matrix element (LDME) set chosen, the asymmetry remains largely unaffected. The asymmetry is independent of the LDME at leading order for $J/\psi$-photon production. Thus, the Sivers asymmetry in both processes is a robust probe of the gluon Sivers function.

We put forward a physical model of a relativistic Unruh-DeWitt battery moving along a general accelerated trajectory, including a linear motion and a circular motion with a reflecting boundary. The maximal amount of quantum work extraction, defined as the ergotropy, serves as a witness to Unruh effect modified by motion trajectories. It is found out that for a very low Unruh temperature, linear motion yields a high amount of ergotropy, while for a high temperature, circular motion becomes optimal for estimating the Unruh effect. For a specific acceleration, the ergotropy is the same for two different trajectories. The behavior demonstrates that, in a certain condition, one can simulate the work extraction of the accelerated battery in a linear motion by exploring the battery in circular motion. The observed ergotropy for the thermality is closely related to quantum coherence affected by spacetime vacuum fluctuations. In the presence of a reflecting boundary plane, we study different ways for the dynamics of the ergotropy. When the battery moves near the boundary, the prominent oscillation of the ergotropy will happen and exhibit some large instantaneous peaks. The interesting phenomenon results from the protection of quantum coherence for the accelerated battery in the vicinity of the boundary. Far away from the boundary, the oscillation behavior can be suppressed and the ergotropy rapidly arrives at a steady value. By contrast, the circular motion contributes to prolonging the oscillation evolution. The asymptotic amount of the ergotropy can rise progressively up to a saturation value with increasing the distance from the circular trajectory to the boundary plane. From the perspective of energy transfer, optimized quantum work extraction for the accelerated battery moving along a selected motion with a boundary plane is advantageous for probing Unruh thermality.

We study here a novel application of Kim & Lee charged wormholes assuming them to be dark halo objects playing the role of lenses in the Galactic microlensing with source stars belonging to the Galactic Bulge and the Large Magellanic Cloud. First, we observe that both the backreacted scalar ($\alpha $) and electrically ($Q$) charged wormholes have the same zero ADM mass as has the background Ellis-Bronnikov wormhole having a special equation of state parameter $\gamma=-1$. In particular, we argue that, for $\alpha\neq 0$, the solution formally resembles, but can at best be sourcewise different from, that of the background wormhole. The charge ($Q\neq 0$) thus provides an extra degree of freedom that introduces a non-trivial redshift function $\Phi$ to the background, alters its throat radius to $r_{th}$, yet keeps the wormhole massless. Second, we focus on this electrically charged case and calculate the light deflection angle up to 4$^{th}$ PPN order, analyze the effect of $Q$ on the lensing observables such as the image positions, magnification, centroid and time delay of images of the source stars. Third, we analyze the probabilistic features such as optical depth and event rate estimated on the basis of the hypothesis that the wormhole lens could be bound or unbound to our Galaxy. Finally, we report an intriguing qualitative prediction that, compared to the Schwarzschild black hole, the Paczyński light curves of the electrically charged wormhole are much dimmer that also show characteristic gutters at the times the source enters and exits the Einstein ring. \textit{The gutters gradually come together as $Q$ approaches the extreme limit $r_{th}/\sqrt{2}$, at which the Einstein radius $R_{E}$ vanishes so that the source crosses it instantly.} It is speculated that re-analyzing past data on Galactic microlensing may betray the presence of charged wormholes.

We introduce a radical-fragment many-body expansion at the two-body level (MBE2) for quantum chemistry of linear alkanes. Instead of heterolytic bond cleavage with hydrogen capping atoms and electrostatic embedding like in Fragment Molecular Orbital (FMO), we perform homolytic C-C bond cleavage to produce open-shell radical fragments (CH3, CH2) treated with restricted open-shell Hartree-Fock (ROHF) in isolation. The two-body MBE2 assembly formula reconstructs total alkane energies from only four unique fragment calculations regardless of chain length, reducing the maximum qubit requirement. We benchmark this framework against five energy solvers (RHF, CCSD, VQE, ADAPT-VQE, and SQD) across 11 linear alkanes from butane (C4H10) to hexacosane (C26H54). The MBE2 decomposition achieves a 12.3x qubit reduction for C26H54 (from 368 to 30 qubits) and a 12.8x reduction in unique calculations via symmetry exploitation. MBE2-VQE and MBE2-SQD (executed on IBM quantum hardware) closely track their respective classical MBE2 references, demonstrating that fragmentation-based quantum chemistry is viable for scaling quantum solvers to large molecular systems.

Recently, a class of static spherically symmetric power law corrected Lorentz violating (LV) Schwarzschild black holes in the Kalb-Ramond model have been derived and studied in the specific range of LV parameters ($0<\lambda \leq 2,\Upsilon \geq 0$) that correspond to energy condition preserving ($\rho >0$) source. On the other hand, there exist well known black holes that do not preserve the energy conditions. In this paper, we shall therefore relax energy conditions and numerically explore the horizon patterns of the enlarged class of LSMA black holes. Four generic types of LV corrected black holes emerge, which interestingly include the analogue of the braneworld black hole ($\rho <0$) lending to $\Upsilon$ a new interpretation of "tidal charge" known as an imprint from the $5d$ bulk in the Randall-Sundrum scenario. We shall then show that Thorne's hoop conjecture, $\mathcal{H} \leq 1$, where $\mathcal{H}$ is the Hod function, consistently holds for three types and their generalizations. However, intriguingly, it turns out that, for the remaining type (viz., Schwarzschild-de Sitter and its generalizations), the hoop conjecture does not hold. It is also shown that braneworld tidal charge black holes increases the LV correction to planetary perihelion advance in contrast to the decrease due to ordinary black holes thereby providing a qualitative distinction between them.

NGC 5408 X-1 is one of the best studied ultraluminous X-ray sources (ULXs) and is surrounded by a photoionized nebula. Previous optical spectroscopy established the presence of strong Balmer, [O III], and He II $\lambda4686$ emission from the nebula, but the powering engine remains uncertain. In this work, we present new integral-field observations of NGC 5408 X-1, supplemented by archival long-slit spectroscopy and Hubble Space Telescope (HST) imaging, and confirm the presence of a composite nebula, with a small He III region centered on the ULX and a large, shell-like H II region. We also confirm that the broad He II emission is point-like and most likely associated with the ULX binary system. Photoionization simulations with Cloudy show that the ULX spectral energy distribution (SED), with a total luminosity of $2.4 \times 10^{40}\ {\rm erg\ s^{-1}}$ obtained by fitting the optical/UV/X-ray data, overpredicts both the luminosity and size of the He III region. Instead, adopting the same SED shape with a reduced luminosity of $1.0 \times 10^{39}\ {\rm erg\ s^{-1}}$ together with a blackbody of temperature $30000\ {\rm K}$ and luminosity $1.3 \times 10^{39}\ {\rm erg\ s^{-1}}$ successfully reproduces both the He III and H II regions in terms of their luminosities and sizes. Such a dual-component ionizing spectrum is consistent with HST measurements of the ULX in the optical and UV, while being a factor of 24 lower than the inferred isotropic X-ray luminosity. This implies that the EUV and X-ray emission from the ULX may be mildly beamed toward our line of sight, consistent with the picture of supercritical accretion.

Artificial neural networks (NNs) and machine learning (ML) algorithms are poorly understood from a theoretical perspective, which makes it difficult to fully realize their potential and overcome their weaknesses. For instance, ML algorithms train NN weights by moving them along a low-dimensional subspace of their allowed values, but this implicitly low-dimensional learning structure is not properly exploited to improve training because its nature is not well understood. Moreover, trained NNs are easily confused by pervasive adversarial attacks whose theoretical underpinnings are still unclear. This thesis aims to improve our theoretical understanding of NNs and ML, with a particular focus on adversarial attacks and implicitly low-dimensional learning. For this purpose, we use mathematical tools from statistical mechanics to study different types of NNs and ways in which they can fit the data. In particular, we study two classes of models that fit the data with various degrees of learning and memorization: dense associative memory (DAM) and restricted Boltzmann machines (RBM). In the process, we investigate connections between different versions of these models that are useful to make analytical investigations more efficient.

Strong periodic driving of cavity-quantum electrodynamics (QED) in the ultrastrong-coupling regime creates nonequilibrium states whose dissipation is governed by Floquet quasienergies rather than undriven dressed resonances. However, modeling such a regime is a significant theoretical challenge, including a number of subtle problems such as the need to ensure gauge invariance for truncated matter-cavity systems with time-dependent driving. To fill this theoretical gap, we introduce a nonsecular Floquet generalized master equation framework for strongly driven open cavity-QED systems, formulated in the dressed basis of the quantum Rabi model and applicable to structured reservoirs without rotating-wave approximations. Our theory can thus model Floquet-driven dynamics in open ultrastrong-coupling cavity-QED, and demonstrates a wide range of quantum state control. Using strong optical pumping and parametric mechanical modulation, we compute long-time populations, fluorescence spectra, and the Floquet-Liouville eigenspectra, resolving observable resonances into hybridized quasienergy channels and decay rates. By systematically comparing with conventional time-independent dressed-basis generalized master equations, we show that static approaches only reproduce steady-state populations in restricted excitation regimes, and fail for frequency-resolved observables and break down under appropriate Floquet engineering, surprisingly, even for spectrally flat baths. Structured environments, such as Lorentzian-Ohmic reservoirs, further amplify these discrepancies through sideband-selective decay. Our results demonstrate that dissipation in driven ultrastrong cavity-QED is intrinsically quasienergy resolved and we establish Floquet-dissipative theory as an accurate and powerful framework for predicting spectra, controlling decay pathways, and engineering nonequilibrium quantum states and reservoirs.

The calculation of the two-neutrino double-beta decay (DBD) rates has so far relied on approximations that decouple the nuclear structure from the emitted lepton kinematics. To ensure a more rigorous treatment, we propose an approach which incorporates the full interdependence between nuclear structure and lepton kinematics within a unified formula and performs calculations without resorting to these approximations. Deviations of the decay rates and electron spectra from the traditional methods, such as closure, non-closure, and Taylor expansion approximations, are presented and discussed for the isotopes $^{82}$Se and $^{136}$Xe. Our approach gives a more realistic description of the DBD process and paves the way for further theoretical and experimental investigations into the correlated nuclear structure interplay with emitted lepton kinematics contributing to the dynamics of the process. Extensions of this framework to other isotopes and to neutrinoless double-beta decay are currently underway.

Accurately modeling structural relaxation in incommensurate systems is intrinsically challenging due to the absence of global translational symmetry. In this work, we develop a variational quantum framework for structural relaxation in incommensurate Schrödinger models, where displacement fields are formulated on the configuration space and the electronic Hamiltonian is represented in reciprocal space. This yields well-defined relaxed energy, local density of states, and forces through thermodynamic limits. We propose an anisotropic scattering-channel approximation, and prove exponential convergence of the approximate equilibria. Numerical experiments are performed to support the analysis and show that the model captures domain-wall formation and its impact on the electronic spectrum.

Delegated quantum computing is likely to become the primary means for most people to access quantum computers in the future. However, these hardware inevitably operate beyond clients' control, raising concerns about potentially untrusted servers. A fundamental question thus arises – how can clients verify that the server is genuinely performing quantum computations? Here, we demonstrate that a class of remote-controlled quantum computing (RCQC) models presents the nonclassical behavior verified in a semi-device-independent way. To achieve this, with slight modifications, these models can be described by the prepare-and-measure scenario. By verifying the violations of dimension witnesses, classical causal models can be ruled out, thereby showing nonclassicality of the RCQC model. Remarkably, in the prepare-and-measure scenario, this class of RCQC models happens to exhibit reversed temporal order in quantum information processing. We also explicitly confirm the nonclassical behaviors of a specific 1-U-M RCQC model belonging to this class as an example. This work bridges the fundamental quantum theory with the practical task of quantum computing.

We give an introduction to research associated with the generalised probabilistic theories framework, also known as the convex framework. States are real vectors representing lists of probabilities of measurement outcomes. Convex combinations of the vectors represent probabilistic combinations of different state preparations. Transformations are real matrices. Measurement outcomes are represented by functionals of the states, inner products of the state with a real vector, whose values are the probability of the measurement outcome in question. The framework generalises quantum theory. We describe the operational meaning of the framework, and how the concepts can be defined in terms of cones of states and measurement outcome vectors. We describe how the classical and quantum probability theories are represented in the framework. We describe Bell non-locality and the theory with super-quantum non-locality known as box world. We discuss generalised Hamiltonian mechanics in the discrete case and in continuous phase space, including the role of negativity of the phase space density in contextuality and tunnelling.

We prove small-data global stability of the Minkowski solution to Einstein's equations in a centre-normalised outgoing null-geodesic gauge. Our scheme involves first using the $r^p$-estimates of Dafermos-Rodnianski to control certain components of the Weyl tensor which satisfy a decoupled tensorial wave equation. Having established this control, all remaining geometric quantities are controlled by transport equations, taking initial conditions at a regular central axis. This method establishes global stability for initial data which decay only weakly to flat space and can establish additional asymptotic control when the data are assumed to have more structure.

Topological corner states in two-dimensional second-order topological insulators (SOTIs) are localized in real space. We numerically demonstrate that such localized topological corner states can mediate Andreev reflection when coupled to a superconducting lead. We consider a transport setup based on a two-dimensional honeycomb lattice, consisting of a normal lead, a central SOTI region, and a superconducting lead. The central SOTI region is described by the modified Kane–Mele model with an in-plane Zeeman field and hosts topological corner states in a diamond-shaped flake. Although the central region is insulating, the local density of states shows that incident electrons can turn the localized corner state into an extended scattering state, which forms a resonant tunneling channel to the superconducting lead. This process leads to a perfect Andreev reflection peak near zero energy. Away from this resonance, antiresonance dips appear in the Andreev reflection spectrum, and their positions can be tuned by the Zeeman field strength. We show that the suppression of Andreev reflection is caused by quantum interference and the imbalance between electron and hole dwell times in the central region. These results demonstrate that topological corner states can provide a resonant tunneling path to the superconducting interface and mediate Andreev reflection in second-order topological systems.

We study quantum speedups of derivative pricing for stochastic partial differential equation (SPDE) models through their backward doubly stochastic differential equation (BDSDE) representations. We develop conditional and nested quantum-accelerated multilevel Monte Carlo (QA-MLMC) methods for estimating the resulting conditional and nested expectations, improving the sampling complexity of classical Monte Carlo methods from $\widetilde{O}(\epsilon^{-2})$ to $\widetilde{O}(\epsilon^{-1})$ within additive error $\epsilon$. We apply the framework to derivative pricing and sensitivity analysis, providing quantum-accelerated estimators for prices as well as first-order and second-order Greeks, likelihood-ratio and Malliavin-weight representations for Greeks, and Heston-type stochastic-volatility models. To enable efficient multilevel coupling, we construct a family of Forward–Backward Taylor discretization schemes for the stochastic integrals arising in the BDSDE representations and establish global strong-error order one convergence for pricing and Greek estimators. Numerical experiments showcase our schemes for first-order and second-order Greeks can reach the required orders for the full quadratic quantum speedups.

We define log conifold transitions for Fano threefold pairs of index two and study their deformation theory. Relying on the recent solution to the relative Clemens conjectures in this setting, we construct rational curves with normal bundle $\OO(-1)\oplus \OO(-1)$ by blowing up anchored points on the boundary divisor. Contracting these curves yields a singular space with ordinary double points. We prove that local smoothings of the nodes can be lifted to global first-order deformations, and that the global deformation theory of both the log resolution space and the singular log pair is unconditionally unobstructed. Crucially, the geometry of the boundary del Pezzo surface guarantees this unobstructedness. Furthermore, unlike the classical Calabi-Yau case, the underlying Fano geometry forces the vanishing of global topological balancing conditions, allowing local first-order smoothings of the nodes to be lifted independently. As applications, we construct new non-Kähler threefolds via smoothings, we analyze the effective geometry of the smoothed threefolds by determining their Picard groups and proving the persistence of free curves. Finally, we study the Hodge theory of these non-Kähler threefolds.

Motivated by the increasing efforts to understand the covariant structure of physical models associated with General Relativity using different kinds of geometric frameworks, in this article we analyze the four-dimensional Palatini-Cartan model for gravity, which is a well-known generalization of General Relativity, from the perspective of various geometric-covariant formalisms for classical field theory. At the Lagrangian level, we do not only recover the correct field equations of the theory, which are equivalent to the torsion-free condition and the Einstein equations, but we also study the gauge symmetries of the model in order to construct the Lagrangian momentum map associated with the action of the gauge symmetry group on the configuration space of the system and, consequently, its corresponding Noether currents. Within the multisymplectic approach, we analyze the action of the gauge symmetry group on the multi-momenta phase space of the model, and we also introduce the induced momentum map that allows us to recover the admissible Cauchy data of the system. Further, we also apply the algorithm to treat singular systems within the polysymplectic framework, in which, in order to obtain the correct field equations of the model, we introduce a non-trivial Dirac-Poisson bracket characterized by the generalized Moore-Penrose inverse of the matrix induced by the second class constraints of the system. Finally, using the multisymplectic framework as a starting point, we perform the space plus time decomposition of the system to recover the instantaneous Lagrangian and the extended Hamiltonian of the theory, as well as the gauge structure that characterize the Palatini-Cartan model for gravity within the instantaneous Dirac-Hamiltonian formalism.

Two-dimensional higher-order topological insulators (HOTIs), characterized by distinctive one-dimensional edge states and zero-dimensional corner states, provide an ideal platform for developing higher-order topological lasers. In this work, we systematically investigate the two-dimensional Benalcazar-Bernevig-Hughes (BBH) model, which hosts quantized quadrupole moments and topologically protected corner and edge states. By confining the lasing mode to selected topological corner or edge states under controlled gain, we demonstrate that the stable light excitation achieved after long-time evolution is predominantly determined by the topological properties of the model Hamiltonian. To characterize the system's topological features, we introduce several diagnostic ratios: the corner decay ratio $\tau_{1}$ and edge-to-corner ratio $\tau_{2}$ quantify the localization degree and spatial extent of corner states, respectively, while the inter-corner transfer ratio $\chi$ measures the intensity transfer efficiency mediated by coherent edge-state dynamics. The abrupt changes in $\tau_{1}$ and $\tau_{2}$ as functions of the hopping parameter $\gamma/\lambda$ directly reveal topological phase transitions, providing a comprehensive toolkit for extracting topological signatures from the system's dynamical evolution. Additionally, modulating the lattice site parity enables flexible tuning of corner state localization positions, offering insights for device engineering. Our calculations reveal that achieving bistability between corner states and edge states is relatively challenging.

We present a physical computing paradigm that harnesses the intrinsic nonlinear dynamics of rare earth doped core shell nanoparticles as a computational substrate. By directly exploiting cross relaxation and energy transfer upconversion processes, the system realizes a state dependent transfer function whose effective decay rate evolves with the instantaneous Er3+ population, which mathematically analogous to gating and attention mechanisms in recurrent neural networks. The three spectrally resolved emission channels inherently span disparate timescales, endowing the reservoir with native multitimescale feature extraction without auxiliary engineering. Under the reservoir computing framework, the coupled three channel system achieves a total memory capacity exceeding fourfold that of a single ion reservoir; capacity decomposition further reveals that the nonzero cross memory capacity is a direct signature of many body Tm3+@Er3+ coupling. On the Mackey Glass and Santa Fe chaotic benchmarks, the system attains normalized mean squared errors of 1.2x10-3 and 2.1x10-2, respectively, with only 125 virtual nodes. These results establish rare earth nanoparticles as a compelling platform for compact and hardware integrable neuromorphic computing, and introduce "inward evolution", the deliberate exploitation of intra material quantum dynamics, as a generalizable design principle for next generation physical computing systems.

The coexistence of gain and loss in parity-time symmetric bilayer meta-gratings enables the transformation of bound states in the continuum into a ring of lasing threshold modes. Under lasing state, gain saturation drives the contraction of this mode ring into a single discrete lasing point. Additionally incident weak optical field with frequency and incident angle nearly matched to the lasing mode can obtain amplification accompanied by prominent Goos-H$\ddot{a}$nchen shifts. Specifically, active meta-grating with lasing mode at the $\Gamma$ point induce sizable Goos-H$\ddot{a}$nchen shifts. In contrast, active meta-grating with lasing mode off the $\Gamma$ point induce large Goos-H$\ddot{a}$nchen shifts that are proportional to the quality factor of the effective resonant modes under lasing state. In finite meta-grating, finite-size effects exert distinct influences on the lasing state as well as the Goos-H$\ddot{a}$nchen shifts of the additionally incident optical field: the lasing characteristics and Goos-H$\ddot{a}$nchen shifts of $\Gamma$-point lasing modes remain nearly unaffected, whereas those of off-$\Gamma$ lasing modes are significantly modulated by finite-size perturbations.

Wormlike micellar fluids exhibit complex rheological behavior driven by the continuous breakage and recombination of self-assembled micellar networks. Existing two-species models provide a coarse binary representation of the micellar population, limiting their ability to resolve intermediate structural states and broad relaxation spectra. To address this limitation, we develop a three-species cascade breakage model consisting of gel-network, long chains, and short chains. By introducing an intermediate micellar state, the model links the rapid relaxation of short fragments to the slow recovery of the gel-network within a unified kinetic framework. This additional structural pathway gives rise to a three-mode viscoelastic response, improves the high-frequency description of the dynamic moduli, and produces a non-monotone constitutive curve that evolves into a stress plateau with coexisting shear bands in Couette flow. This cascade mechanism also governs the transient response, including stress overshoot, hysteresis, and multistep relaxation after shear cessation. Overall, the proposed three-species model provides a physically interpretable framework for worm-like micellar shear banding, capturing the connection between cascade microstructural evolution, broad relaxation dynamics, and macroscopic flow localization.

Hong-Ou-Mandel interference is one of the clearest signatures of quantum behaviour: two identical photons meeting at a beam splitter always leave together. Here we demonstrate that this symmetry can be broken. Using a programmable integrated photonic processor, we interfere imbalanced two-photon states on a variable beam splitter and show that the output state of quantum interference can be continuously tuned, reaching the extreme case where destructive interference suppresses bunching at one output port. The asymmetry creates a forbidden bunching channel: photons may exit together at one port or separately at both ports, but cannot emerge together at the other port.

We prove that logarithmic capacity convergence for phase-union spectra of quasi-periodic Schrödinger operators in the zero Lyapunov exponent regime is robust, requiring only continuity of the potential. Let $S^+(p/q)$ denote the union, over the phase, of the spectra at rational frequency $p/q$. We show that if the Lyapunov exponent vanishes on the spectrum $\Sigma(\alpha)$ at an irrational frequency $\alpha$, then for every sequence $p_n/q_n\to\alpha$, the logarithmic capacities $Cap(S^+(p_n/q_n))\longrightarrow Cap(\Sigma(\alpha)).$ We also prove convergence of the corresponding harmonic measures. As a consequence, the equilibrium measures of $S^+(p_n/q_n)$ converge in the weak$^*$ topology to the density of states measure of the quasi-periodic Schrödinger operator. We extend these results to multi-frequency Schrödinger operators and prove analogous convergence theorems, for logarithmic capacity, harmonic measure, and equilibrium measure, for ergodic Schrödinger operators in a general setting where the almost sure spectrum is approximated in the Hausdorff metric by union spectra of periodic operators. This abstract formulation applies, in particular, to uniformly almost periodic potentials along sequences of almost periods. We also provide counterexamples when the limiting frequency is rational.

We introduce an explicit construction of the non-diagonal and diagonal Wigner distributions for the homogeneous but anisotropic Taub and Kantowski-Sachs cosmological models within the framework of phase space deformation quantization. Conventional canonical quantization of these models via the Wheeler-DeWitt equation is inherently plagued by factor ordering ambiguities. To circumvent these issues, we employ the totally symmetric Weyl quantization map and the Moyal star product. By means of a canonical separation of the Hamiltonian constraint, we are able to resolve the formal convergence problems typically associated with the star product. Furthermore, to establish a rigorous connection with conventional quantum cosmology, we calculate the standard wave functions directly from the diagonal Wigner distributions, recovering the exact physical states in terms of modified Bessel functions in both cases.

Ge2Sb2SexTe5-x (GSST) alloys represent an emerging class of phase-change materials for integrated photonics. However, the microscopic origins underlying their superior performance compared to the parent compound Ge2Sb2Te5 remain elusive. By using atomic simulations, this work elucidates that the thermal stability and low optical loss of GSST are fundamentally governed by the formation of an in-layer compound-like structure with SeTe2 or Se2Te stoichiometry depending on the Se content, contrasting to the previously believed pure-element-layered model where Se and Te atoms occupy separate layers inside GSST. The newly identified compound-layered structures maintaining stability at temperature above 370 K, yield an enlarged bandgap, weakened antibonding character, and more importantly, a moderate refractive index as well as decreased extinction coefficient which align better with the experiment compared to the previously believed model. The present findings not only help bridge the long-standing theory-experiment gap regarding the optical properties of GSST by redefining its atomic structure, but also establish local chemical ordering as a critical materials design principle for high-performance photonics.