Papers

We investigate which dilaton gravity models can reproduce the typical two dimensional analogue black holes realized in platforms such as superconducting quantum circuits. We identify the most reasonable assumptions these models must satisfy, and determine the dilaton models for which the state-dependence of the Hawking temperature, T, can be switched on and off, a feature that is absent in four dimensional black holes. When the analogue black hole exhibits state-independent temperature, as in the cases considered here, the kinematics governing T decouples from the dynamics underlying S. Our numerical analysis reveals that the given analogue black holes do not correspond to known dilaton gravity models, limiting their usefulness for extracting theoretical insights. We then show that the logic can be easily reversed: starting from established well known dilaton models, one can derive the conditions that laboratory implementations must satisfy. This shifts the challenge from the theoretical perspective to the experimental realization.

We construct a 3D Pauli stabilizer Hamiltonian whose ground state space can encode a qubit for exponential time when coupled to a bath at non-zero temperature. Our construction recursively applies a sequence of transformations to a seed Hamiltonian that increases the memory lifetime of the encoded qubit while maintaining geometric locality in $\mathbb{R}^3$.

Solid-state processors require control layers whose errors are legible to quantum-error-correction decoders. We show that crystallographic symmetry can provide such a layer in strain-active Lambda manifolds. When the projected strain tensor and Lambda-transition operators share a multiplicity-one two-dimensional irreducible representation, symmetry fixes the linear strain interaction to a scalar dot product. Two phase-locked mechanical modes synthesize a circular strain field, enabling complex phononic Lambda-leg control without local microwave near fields. On this manifold we construct a superadiabatic echo-lune holonomic gate using Lambda-leg control and a resonant double-quantum counterdiabatic tone. Rotating-frame simulations of a nitrogen-vacancy center give 99.88% conditional average fidelity in 1.833 microseconds, or 99.40% when leakage is counted as error. A resonant gigahertz high-overtone bulk acoustic resonator analysis translates the Hamiltonian into Rabi-rate, linewidth, and envelope-tracking requirements. The bright-state structure organizes noise: A2-sector perturbations are parity-filtered into an optically distinguishable auxiliary state, whereas transverse E-sector faults are echo suppressed and retained as a decoder stress axis. The extracted channel has 0.47% erasure probability and 0.168% residual Z error. In XZZX code-capacity simulations, this biased-erasure model yields a nominal 64% fit-extrapolated data-qubit reduction relative to an unstructured Rabi baseline. Repeated-round detector-model diagnostics preserve the nominal distance-9 proxy and identify missed erasures, transverse floors, leakage/flag timing, and strong crosstalk as validation limits. Extensions to orbital Lambda systems and bright-projector phonon-bus diagnostics identify crystallographic symmetry as a principle for co-designing phononic actuation, leakage, noise bias, and quantum decoding.

We study the parafermionization of the Monster CFT with respect to its $\mathbb{Z}_{pA}$ subgroups, with $p$ an odd prime. Under certain assumptions, we show that the parafermionization is equal to a non-invertible gauging of $\mathcal{P}(p) \times \mathcal{P}(p)^\vee$, where $\mathcal{P}(p)$ is the theory of $\mathbb{Z}_p$-parafermions and $\mathcal{P}(p)^\vee$ is an appropriate dual theory, with global symmetry characterized by the centralizer of $\mathbb{Z}_{pA}$. By tracking the symmetries of $\mathcal{P}(p) \times \mathcal{P}(p)^\vee$ through the non-invertible gauging, we argue that the diagonal Monster CFT has $\mathrm{Rep}(\mathfrak{so}(3)_p) \boxtimes \mathrm{Rep}(\mathfrak{so}(3)_p)^\mathrm{op}$ symmetry, and hence that the holomorphic Monster theory has symmetry $\mathrm{Rep}(\mathfrak{so}(3)_p)$. We then compute the defect McKay-Thompson series associated to these symmetries, and prove that their invariance subgroups are $\Gamma_1(p+2)$.

Topologically-ordered quantum states with Abelian excitations can host defects that obey effective non-Abelian statistics, in principle allowing for quantum information processing via defect braiding. These extrinsic defects (or twists) are typically studied as static features of the lattice. However, an alternative proposal considers how an underlying topologically ordered quantum substrate can be locally perturbed to create and manipulate synthetic defects \cite{you_synthetic_2013}. Unfortunately, while largely referenced, elements of this proposal were never systematically studied. Understanding the energy spectrum is particularly important in finite size and finitely perturbed systems, which are crucial for experimental realizations. In this work we announce a significant step in this direction by explicitly constructing, simplifying, and numerically studying the spectral properties of synthetic defects in a model system. First, we introduce two alternative representations of this problem in both spin and Majorana languages. In the former we describe emergent virtual symmetries which constrain and simplify the problem and in the latter we show a direct connection to Kitaev's well-known Majorana chain. We utilize these simplifications to perform numerical calculations to indicate the location of the quantum phase transition driving the emergence of the synthetic defects. We conclude by discussing key steps for future work to more clearly and completely study this phenomena.

A single-aperture, two-layer Canted-Cosine-Theta (CCT) sextupole magnet using high-temperature superconducting (HTS) ReBCO tape has been developed for the short straight sections (SSS) of FCC through the FCCee-HTS4 project. The magnet was designed, manufactured and tested under cryogenic conditions. Two HTS tapes from two manufacturers have been qualified for this specific application. Design and manufacturing details and cryogenic temperature measurements are presented. This demonstrator represents the first HTS CCT magnet ever constructed.

Large language models demonstrate remarkable ability in factual recall, yet the fundamental limits of storing and retrieving input–output associations with neural networks remain unclear. We study these limits in a minimal setting: a linear associative memory that maps $p$ input embeddings in $\mathbb{R}^d$ to their corresponding~$d$-dimensional targets via a single layer, requiring each mapped input to be well separated from all other targets. Unlike in supervised classification, this strict separation induces~$p$ constraints per association and produces strong correlations between constraints that make a direct characterisation of the storage capacity difficult. Here, we provide a precise characterisation of this capacity in the following way. We first introduce a decoupled model in which each input has its own independent set of competing outputs, and provide numerical and analytical evidence that this decoupled model is equivalent to the original model in terms of storage capacity, spectra of the learnt weights, and storage mechanism. Using tools from statistical physics, we show that the decoupled model can store up to $p_c \log p_c / d^2 = 1 / 2$ associations, and generalise the computation of $p_c$ to linear two-layer architectures. Our analysis also gives mechanistic insight into how the optimal solution improves over a naïve Hebbian learning rule: rather than boosting input-output alignments with broad fluctuations, the optimal solution raises the correct scores just above the extreme-value threshold set by the competing outputs. These findings give a sharp statistical-physics characterisation of factual storage in linear networks and provide a baseline for understanding the memory capacity of more realistic neural architectures.

We show that the entanglement entropy (EE) of one-dimensional (1d) non-interacting fermions with $U(1)$ symmetry in the presence of a disordered or quasi-periodic potential in which the occupation number is being monitored by homodyne or projection protocols is always in an area-law phase so no measurement induced phase transition (MIPT) occurs. The reason for the previously claimed MIPT in these systems was a finite size effect related to the fact that the maximum lattice size $L \simeq 500$ was of the order of the correlation length. By increasing the system size up to $L \simeq 18000$, employing Graphics Processing Units (GPUs), and performing a careful finite-size scaling analysis, we find that the critical monitoring strength is consistent with zero, so no MIPT occurs. For the disordered case, these numerical results are fully supported by an analytical calculation based on mapping the problem onto a nonlinear sigma model (NLSM) that confirms the absence of the MIPT for any monitoring or disorder strength. The effect of disorder is captured by a change of symmetry from BDI to AIII, which results in an enhanced correlation length in the weak disorder limit, and by an effective monitoring strength that increases linearly with disorder.

We develop a theory of angular-dependent magnetoresistance (ADMR) in metallic altermagnets coupled to ferromagnetic insulators and establish criteria that distinguish them from conventional compensated magnets with spin-orbit coupling. We show that, once its full set of angular dependencies is established, the spin-splitter magnetoresistance (SSMR)– recently reported in the bilayer geometry of H. Chen et al. [Adv. Mater. 37, 2507764 (2025)] – would constitute a smoking-gun signature of collinear d-wave altermagnetism in metallic systems. Although SSMR has been regarded as a close analogue of spin Hall magnetoresistance (SMR), we demonstrate that the two differ qualitatively in three key respects: SSMR depends solely on the relative orientation between the ferromagnetic magnetization and the altermagnetic Néel vector, yields a longitudinal ADMR response of opposite sign, and features a direct proportionality between longitudinal and transverse ADMR signals, absent in SMR. Building on these distinctions, we further show that the full angular dependence of the SSMR provides a practical recipe to extract the direction of the Néel vector from customary magnetoresistance measurements. These results provide a clear route to unambiguously identify altermagnets in transport.

Critical eigenstates are usually identified through wave-function geometry in a chosen basis, such as participation ratios, multifractal spectra, or finite-size scaling. Here we formulate criticality instead as a dual-space Lyapunov property. We prove a Fourier exclusion principle: exponential localization in one representation is incompatible with exponential localization in its Fourier-dual representation. This turns the Liu–Xia condition, \(\gamma_x(E)=\gamma_m(E)=0\), from a phenomenological criterion into a rigorous length-scale statement: a critical state is characterized by the simultaneous absence of exponential confinement in real and momentum space. The criterion is invariant under bounded local gauge transformations of the transfer matrix and remains compatible with conventional single-space multifractal diagnostics. More importantly, it is exactly predictive. In analytically tractable quasiperiodic models, the same condition yields closed-form critical lines, an exact finite critical region with an additional critical branch, and a complex critical surface in a non-Hermitian non-self-dual spectrum. Thus the Liu–Xia condition provides not only a diagnostic of critical states, but an exact solvability principle for locating critical sets across distinct microscopic structures.

We theoretically investigate the anomalous and diode Josephson effects in planar two-dimensional Josephson junctions with arbitrarily oriented exchange fields in two ferromagnets within the barrier, and spin-orbit coupling at the superconductor/ferromagnet interfaces, where the superconducting electrodes can have $s$-wave or arbitrarily oriented $d$-wave order parameter lobes. We perform a systematic symmetry analysis of the junction Hamiltonian and identify the minimal conditions for breaking time-reversal and space-inversion symmetries, which are required for the emergence of anomalous and diode Josephson effects. We classify the junctions into three classes, with particular attention to those between $d_{x^2-y^2}$ and $d_{xy}$ oriented superconductors. Our symmetry analysis is supported by numerical calculations of the current-phase relation (CPR) obtained using a generalized Furusaki-Tsukada (F-T) approach. By tuning the directions of exchange fields in the ferromagnets, Rashba SOC at the interfaces and superconducting order parameter orientations, nonreciprocity can be enhanced by more than 40%. We further analyze the phase-dependent Andreev bound states (ABS) spectrum and their contribution to charge transport, as well as their signatures in the nonreciprocal transport characteristics. By comparing the current carried by ABS with that obtained using the F-T technique, we find that the contribution from continuum states above the gap becomes pronounced in presence of zero energy crossings in the ABS spectrum, and in junctions with $d$-wave superconducting electrodes due to the narrower superconducting gap, which may become closed. In the nonreciprocal regime, the ABS spectra show an asymmetric profile with respect to phase inversion, indicating the presence of a finite current at zero phase difference and unequal critical currents in opposite directions.

We investigate the vacuum and thermal fluctuations of a neutral massless scalar field living in Minkowski spacetime and interacting with a finite number of point-like obstacles, modelled by zero-range potentials. The system is described rigorously in terms of self-adjoint realizations of the Laplacian, under assumptions ensuring the absence of instabilities. Using the relative zeta-function technique, we determine the renormalized connected partition function and derive explicit expressions for the thermodynamic observables, characterizing both their low- and high-temperature behaviours. Furthermore, we derive of a convergent Born series expansion for the Casimir energy, which identifies multiple-scattering processes as the mechanism underlying vacuum forces. The latter decompose into pairwise contributions directed along the lines joining the obstacles, with intensities depending non-locally on the full configuration. We also present some numerical results for identical obstacles, indicating that the Casimir forces are always attractive in this context.

Hexagonal germanium polytypes have emerged as promising direct-gap semiconductors for silicon-integrated optoelectronics, yet their optical properties remain largely unexplored beyond the well-studied 2H phase. We present a comprehensive theoretical study of optical properties of hexagonal 2H-, 4H-, and 6H-Ge polytypes through ab initio calculations of quasiparticle band structures, dipole transition matrix elements, and solution of the Bethe-Salpeter equation. While all three polytypes exhibit direct band gaps of increasing size from 2H to 6H, we reveal that the fundamental optical transition in 4H-Ge is parity-forbidden due to matching band parities at the valence and conduction band edges. This selection rule results in a radiative lifetime seven orders of magnitude longer than in 2H- and 6H-Ge, severely limiting light emission capabilities. To demonstrate that the selection rule can be lifted, we introduce controlled symmetry perturbations by substituting single Ge atoms with Si in each unit cell, breaking the crystal symmetry. This perturbation increases the optical matrix elements by up to two orders of magnitude and reduces radiative lifetimes for all perturbed polytypes. We also compute absorption coefficients and frequency-dependent dielectric tensors for both light polarizations, including excitonic effects up to 5 eV, providing complete optical characterization of ideal and symmetry-perturbed hexagonal Ge systems relevant for optoelectronic applications.

Freestanding GdBa2Cu3O7 (GdBCO) superconducting thin films were fabricated using a water-soluble Sr3Al2O6 (SAO) sacrificial layer in combination with thermal release tape. An amorphous Al2O3 capping layer was introduced to suppress crack formation during the lift-off process. The influence of buffer-layer design inserted between the GdBCO and SAO layers was systematically investigated with respect to structural integrity and superconducting properties after lift-off. A LaAlO3/SrTiO3 bilayer buffer was found to be essential for maintaining epitaxial growth and a superconducting transition temperature (Tc) of approximately 92 K after lift-off, comparable to that of the as-grown films. In contrast, a reversed SrTiO3/LaAlO3 bilayer and single-layer buffer structures led to a suppression of Tc, highlighting the critical role of stacking sequence. These results demonstrate that optimization of the buffer-layer design is a key factor for realizing high-quality freestanding GdBCO films while maintaining their superconducting characteristics.

We demonstrate how crystalline symmetry lowering, as for instance through strain, allows elemental superconductors such as vanadium and niobium to realize spin-singlet orbitally polarized Cooper pairs composed of electrons with identical orbital moments. Using superconducting density functional theory, we show that lowering of trigonal symmetry to $C_s$, thus keeping only a single mirror plane, activates interorbital pairing in bulk and (111) surfaces, with a pronounced surface enhancement. In a magnetic field, the resulting orbitally polarized superconducting state leads to a novel transverse magnetic response. For in–plane field orientations that break the remaining mirror symmetry, a sizable orbital magnetization emerges perpendicular to the applied field. We show that this effect is a direct consequence of equal–orbital-moment Cooper pairing, providing an experimentally accessible signature of this state. Our results establish strained elemental superconductors as a minimal material platform for superconducting orbitronics.

In our previous article [arXiv:2307.12552], we introduced local topological order (LTO) axioms for abstract quantum spin systems which allow one to access topological order via a boundary algebra construction. Using the LTO axioms, we produced a canonical pure state on the quasi-local algebra, which gives a net of von Neumann algebras associated to a poset of cones in $\mathbb{R}^n$. In this article, motivated by [arXiv:2509.23734], we introduce an axiom for LTOs which ensures Haag duality for cone-like regions using Tomita-Takesaki theory. We prove this axiom is satisfied for all known topologically ordered commuting projector models. We thus get an independent proof of Haag duality for the Levin-Wen string net models originally proved in [arXiv:2509.23734]. We also give a reflection positivity axiom for LTOs, connecting to the recent article [arXiv:2510.20662]. We again prove this axiom is satisfied for all known topologically ordered commuting projector models about some $\mathbb{Z}/2$-reflection symmetry.

We develop a Ginzburg-Landau theory for superconducting thin films under quantum confinement. Starting from the Ginzburg-Landau theory and the recently developed confinement theory of metallic thin films, explicit analytical expressions are derived for the coherence length, penetration depth, electronic mean free path, and Ginzburg-Landau parameter in confined geometries. The central result is that quantum confinement directly renormalizes the intrinsic superconducting coherence length through confinement-induced modifications of the electronic density of states and Fermi energy. This effect is absent in conventional thin-film transport theories based solely on surface scattering. As a consequence, confinement simultaneously suppresses the coherence length and enhances the penetration depth, thereby driving superconductors toward stronger type-II behavior over a broad thickness range. The interplay between quantum confinement and disorder can also produce reentrant type-I/type-II crossovers. The theory predicts a crossover regime in which confinement-induced renormalization of superconducting length scales and transport scattering become strongly intertwined. Comparison with recent penetration-depth measurements in Al thin films shows that the observed enhancement of the penetration depth originates from the interplay between confinement-induced renormalization of the coherence length and suppression of the effective mean free path by surface and disorder scattering. The results establish a direct connection between quantum confinement and superconducting electrodynamics in confined metallic films.

The precise atomic-scale structure around Eu$^{2+}$ activators in the $\beta$-Si$_{6-z}$Al$_z$O$_z$N$_{8-z}$:Eu$^{2+}$ commercial green phosphor remains elusive. We use the first-principles $\Delta$SCF excited-state method, embedding of the interatomic force constants for supercells up to 3501 atoms, and Huang-Rhys theory to clarify this issue. Monte Carlo exploration is used to identify representative low-energy structural models spanning different levels of Al/O concentration $z$. For the lowest-energy structure at low $z$, our computed photoluminescence spectrum reproduces the experimental vibronic peaks at 6~K with excellent agreement in peak positions and intensities, validating the Eu-N$_9$ coordination model with Al, O, and Eu confined to the same crystallographic plane. Analysis of the low-energy structures reveals that the electron-phonon coupling is weak ($S \approx 2.15$) with a robust characteristic phonon signature across different Al/O arrangements, explaining the surprising persistence of resolved phonon replicas with increasing $z$. We explain the experimentally observed red-shift of emission with increasing $z$ through systematic trends in zero-phonon line energies, modest increases in Huang-Rhys factors, and larger configurational diversity at higher compositions.

We investigate two-dimensional Dirac fermions embedded in a deep-subwavelength cavity formed by high-impedance metasurfaces. We point out that, unlike conventional metallic boundaries, these metasurfaces support quasielectrostatic transverse-magnetic modes that mediate a long-range interaction between two-dimensional electrons. Combining static electronic screening with a Dyson-Schwinger analysis, we show that this engineered interaction can qualitatively alter the ground-state properties of Dirac materials. For a fermion flavor number $N_{f}$ below a critical value $N_{c}=16/\pi$, the interaction drives an excitonic insulating phase through an infinite-order quantum phase transition and spontaneously generates a mass gap. At $N_{f}>N_{c}$, the system remains gapless but enters a non-Fermi-liquid critical regime where the quasiparticle residue is singularly suppressed to zero, and the Dirac cone exhibits a nonanalytic dispersion relation. Furthermore, under a perpendicular magnetic field, the cavity fluctuations dynamically lift the zeroth Landau level degeneracy across all $N_{f}$. These results identify high-impedance metasurface cavities as promising platforms for engineering correlated Dirac matter.

Proper weight initialization prior to training has historically been one of the key factors that helped kick off the deep learning revolution. Initialization is even more crucial in "reservoir computing", where the weights of a readout layer are learned linearly while the reservoir weights are fixed and largely determine the richness, stability and memory of the resulting dynamics. In the infinite-width limit it has been shown that meaningful initializations are those sitting at an effective critical point of the randomly initialized model. The phase transition is controlled by the weight variance $g^2$ and separates an ordered phase from a chaotic one where information progressively degrades. Here we derive a simple criterion to estimate the critical $g_c$ for a broad class of recurrent architectures and we show that it closely tracks the gain at which a gated-RNN reservoir achieves peak performance on a chaotic forecasting task. Finally, we argue that our criterion can serve as a design principle for future initialization schemes.

We investigate infectious disease spreading on scale-free networks using a heterogeneous mean-field approach applied to the susceptible-infected-susceptible model, incorporating a mitigation factor. Individual heterogeneity is incorporated through a power-law distribution, while a mitigation factor accounts for behavioral responses and external effects that effectively reduce transmission from infected individuals. This mechanism, inspired by Malthus-Verhulst-type constraints, introduces a nonlinear saturation effect that encodes self-limiting dynamics in a tractable way. Analytical results are supported by stochastic simulations. We find that the mitigation factor induces a nontrivial behavior in the probability that a link points to an infected node, which develops a maximum at finite infection rates. In contrast, the overall prevalence remains a monotonically increasing function of the transmission rate. Additionally, the mitigation mechanism leads to an inversion in the dependence of epidemic observables on the degree exponent at sufficiently high transmission rates. While in the standard model smaller exponents yield higher endemic prevalence, in the modified model this trend reverses, with larger exponents producing higher prevalence and increased infection probability along network links.

Pretrained diffusion models provide powerful learned priors, but in scientific sampling the target distribution often depends on physical context that is not fully represented by one generative model. We introduce Generative Gibbs for Physics-Aware Sampling (GG-PA), a training-free framework that formulates the composition of learned partial priors and explicit physical context as inference over a joint target distribution in an augmented state space. We derive a Gibbs sampler for this joint target, show that it is asymptotically exact as the diffusion time approaches zero, and prove that in settings with quadratic interactions it remains exact at finite diffusion times. We further introduce replica exchange over diffusion time to accelerate mixing. Experiments on a double-well system, a $\phi^4$ lattice model, and atomistic peptide systems show that GG-PA recovers context-induced distribution shifts and emergent collective behavior in interacting systems using partial priors without retraining. These results demonstrate GG-PA as a practical approach for combining pretrained generative priors with explicit physical context.

Thermochemical energy storage (TCES) in oxide perovskites relies on reversible oxygen vacancy formation, and computational high-throughput screening of candidate materials has predominantly used the single oxygen vacancy formation energy (OVFE) as the key descriptor. We demonstrate that the OVFE is insufficient for screening cubic CaMnO3 perovskites, because the stoichiometric compound is not the minimum energy reference state; vacancies are inherently present at operating temperatures. Materials with negative single OVFEs are routinely excluded from screening datasets as unsuitable, but this reflects a mischoice of reference state rather than a genuine materials limitation, and risks discarding promising TCES candidates. We address this by computing OVFEs as a function of vacancy concentration using ab initio density functional theory, establishing the equilibrium vacancy concentration as the correct reference point. OVFE curves referenced to this minimum align with experimentally measured reduction enthalpies, providing a framework directly comparable to experiments. We further show that A-site and B-site doping modify the vacancy formation landscape through distinct mechanisms. A-site dopants act primarily through strain relaxation and symmetry breaking, while B-site dopants reshape the local redox environment and introduce strong configurational dependence. Finally, we develop a thermodynamic model incorporating configurational entropy that accurately predicts equilibrium oxygen stoichiometry as a function of temperature and oxygen partial pressure and reveals that selective reduction of Mn4+ versus B-site dopant ions can tune the onset temperature for vacancy formation. These results establish a screening framework for perovskite TCES materials and provide practical guidance for extending high-throughput workflows beyond the single-vacancy paradigm.

We explore how the thermodynamic properties and dynamics of a self-interstitial prismatic dislocation loop are affected by microscopic-scale variations in its geometric configuration, an aspect that rarely received attention in literature. We develop a machine-learning (ML) model to predict the formation energy of an arbitrary geometrically complex configuration of a self-interstitial atom dislocation loop. Trained on atomistic simulation data, the ML model achieves high predictive accuracy across a broad range of configurations, with a typical error in the 1% range. From the ML model, we evaluate the density of configurational microstates as a function of loop's formation energy and derive analytical expressions valid in tractable limiting cases. Using statistical mechanics, we derive the configurational free energy, the average energy, and the thermodynamic entropy of a dislocation loop as a function of temperature. We also simulate the dynamics of self-climb of dislocation loops with various geometries and evaluate their diffusion coefficients and effective activation energy for diffusion. Analysis shows that there is a single universal parameter describing the morphological irregularity of the loop configuration in its ground state. This parameter determines the thermodynamic properties of a loop as well as its dynamics, and simulations illustrate how the properties and mobility of a configurationally complex loop vary as functions of the irregularity parameter.

We introduce a technique that enables Neural-ODEs to approximate arbitrary velocity fields with a priori planted fixed-points. Specifically, a recipe is given to explicitly accommodate for a finite collection of points in the reference multi-dimensional space of the Neural-ODE where the velocity field is exactly equal to zero. In this way, the gradient-based training is rigorously constrained inside the prescribed hypothesis class while leaving the expressive power of the Neural-ODE unaltered. We rigorously prove the universality of the Neural-ODE under any local constraints in the velocity field and give a computationally convenient way of imposing the fixed points. Our method is then tested on two paradigmatic physical models.

Altermagnets are a novel class of magnetic systems characterized by their momentum-dependent spin splitting without net magnetization. In this work, we extend established Euclidean tight-binding models of altermagnets to regular hyperbolic lattices in two spatial dimensions defined on a discretized Poincaré disk. Using hyperbolic crystallography and Abelian hyperbolic band theory, we show that the inclusion of next-nearest neighbor hopping is sufficient to induce spin splitting in minimal tight-binding models of bipartite hyperbolic lattices. While certain families and special cases of hyperbolic lattices remain antiferromagnetic, we identify an entire family and a special case that generically permit spin splitting in this framework. Hence, altermagnetism is inherent to certain hyperbolic lattices. Since Abelian hyperbolic band theory yields a momentum space that is at least four-dimensional, we classify the leading spin-splitting harmonics using four-dimensional atomic orbitals. As an outlook, we apply non-Abelian hyperbolic band theory to the $\{10,5\}$ lattice. Although its Abelian spectrum is spin degenerate, two selected higher-genus supercells exhibit spin splitting. This finding suggests, that spin degeneracy does not necessarily persist within all translation representation sectors.

A flat-top transmon pulse with cosine ramps has exact spectral zeros at half-integer values of ramp duration times anharmonicity, (\tau|\alpha|=n+1/2), which predict endpoint-leakage minima in the weak-drive regime. For any self-similar one-scale envelope (\Omega(t)=\Omega_0 f(t/\sigma)), the non-adiabaticity parameter is exactly degenerate with pulse area, (\eta_ref\theta=C_shape); an independent ramp timescale (\tau) is therefore required. The Fourier amplitude of the resulting envelope at the anharmonicity vanishes at (\tau|\alpha|=n+1/2) through destructive interference between the rising and falling edges, independently of plateau length and total pulse duration. Dynamically, the endpoint-leakage amplitude is perturbatively determined by the Fourier component of the envelope weighted by the instantaneous excited-state amplitude. This weighting removes a second, plateau-derived family of envelope zeros not followed by the dynamics. Four-level Duffing simulations using parameters representative of IBM Heron r2 devices collapse the minima onto the half-integer sequence for six pulse durations from 50 to 100 ns, with an RMS deviation of 0.034 in (\tau|\alpha|). For four durations resolved on a finer grid, first-order population weighting reduces the positional deviation from 0.0234 to 0.0096. The competing plateau condition does not collapse the data. The residual weak-drive displacement from the half-integers is captured by the population-weighted correction.

We derive the exact evolution equation for the probability density function of particle displacements generated by arbitrary Gaussian velocity processes, when neither Markovianity and nor stationarity are assumed. Starting from the characteristic function of the density of the position, we construct a systematic hierarchy of equations based on Wick's theorem, in which the dynamics is governed by sums of geometrically connected Wick contractions. This approach yields a closed non-Markovian diffusion equation that generalizes the Fokker-Planck description and preserves Gaussianity only in the infinite-order limit.

High-entropy alloys (HEAs) are known for superb combination of performance attributes, making them ideal for advanced applications, e.g., nuclear engineering. The concept of cobalt-free HEAs aims to mitigate concerns about cobalt's radioactivity, however, predicting their phase formation remains challenging due to their complex compositions. In this work, we integrate six semiempirical parameters, i.e., mixing entropy ({\Delta}Smix), mixing enthalpy ({\Delta}Hmix), atomic size difference ({\delta}), valence electron concentration (VEC), d-orbital energy level (Md), and the {\Omega} parameter, along with machine learning (ML) to predict the body-centered cubic phase stability in Co free HEAs. To address the limitations of experimental data, generative adversarial networks were used to augment the dataset, thus improving the accuracy of the Gaussian process classification model used for phase prediction. After dimensionality reduction to five principal components, the model achieved an accuracy of 84%, with {\Delta}Hmix and {\delta} identified as the key descriptors influencing phase formation. This approach highlights the synergy of ML and data augmentation in accelerating the design of HEAs for advanced applications.

We investigate the vortex lattices of harmonically confined quasi-two-dimensional tilted rotational dipolar Bose-Einstein condensates. By employing an extended Gross-Pitaevskii equation for a rotating condensate, we reveal the structural transformation of vortices from square to triangular lattices as the tilt of dipolar bosons relative to the polarization axis approaches a critical angle. When the tilt of the magnetic dipoles surpasses the magic angle, the condensate elongates diagonally and becomes devoid of vortices. Moreover, we include the Lee-Huang-Yang correction, which enables the formation of vortices in the elongated condensate. Additionally, when dipoles are oriented perpendicular to the polarization axis, the Lee-Huang-Yang correction results in the fragmentation of condensates under strong rotation. The quench dynamics of the rotational frequency demonstrate the development of vortex lattices; however, with a strong rotational quench, the condensate remains free of vortices. Our numerical analysis highlights the beyond mean-field effects of the rotational properties of anisotropic dipolar bosons, which can be observed in current dipolar quantum gas experiments.