Papers

Observable gravitational waves (GWs) from first-order phase transitions (FOPTs) can coexist with distinct particle physics signatures. These include same-sign dilepton plus four~jet events at colliders, such as $e^+ e^-/\mu^+\mu^- \to \ell^\pm \ell^\pm 4j$, neutrinoless double beta decay, as well as charged lepton flavor violating (cLFV) processes such as $\mu \to e \gamma$. We explore this synergy within the minimal low-scale linear seesaw model. This framework successfully reproduces neutrino oscillation data, providing a direct avenue to probe the neutrino mass ordering and Majorana nature at colliders. Crucially, the FOPT responsible for the GW background is driven by a leptophilic Higgs doublet, establishing a direct link between early-universe cosmology and terrestrial laboratory experiments.

A common approach to studying elastic localization is to pose the problem on an infinite domain, avoiding explicit treatment of the end conditions. For a finite structure, this approach raises a natural question: how long must the structure be for the infinite-domain approximation to become accurate, and how large is the resulting error? To address this question, we develop a constructive method that provides an explicit length threshold beyond which the approximation error is small and explicitly bounded. Applied to a prototypical model arising from localized buckling of a twisted rod, the method yields the threshold and error bounds analytically. The threshold is found to vary with loading, showing that whether the infinite-domain approximation is appropriate depends on both structural length and loading state. The load-dependent length threshold also clarifies the validity of weakly nonlinear analysis: the finite-domain expansion is appropriate only over a limited range near bifurcation, beyond which the infinite-domain expansion is more appropriate. The method is then applied to the fully nonlinear problem of localized bulging in cylindrical membrane tubes. Numerical evaluation of the model-dependent estimates yields a length threshold and an upper bound on the approximation error, while direct comparisons of the finite- and infinite-domain solutions support these predictions. Together, these results characterize the applicability of the infinite-domain approximation and weakly nonlinear description to elastic localization in finite structures.

Warm-blooded vertebrates accumulate approximately conserved numbers of physiological cycles over a natural lifetime: of order $10^9$ heartbeats and $10^8$–$3\times10^8$ breaths. These regularities are not exact constants, but their persistence across orders-of-magnitude variation in body mass, metabolic power, physiological frequency, and lifespan suggests that biological time is not measured by chronological duration alone. We develop the Principle of Biological Time Equivalence (PBTE), a thermodynamic framework in which lifetime cycle count is determined by the ratio between total lifetime entropy production and the entropy cost of one physiological cycle. Starting from the open-system entropy balance $\dot S=\dot e_p-\dot h_d$, we define the entropy cost per cycle as $\sigma_0=d\Sigma/dN$, where $d\Sigma$ is the entropy produced as the physiological clock advances by $dN$ cycles. For an adult homeostatic regime, this gives the cycle-count relation $N_\star=\Sigma/\langle\sigma_0\rangle$, with $\Sigma=\int_0^L \dot e_p(t)\,dt$, where $N_\star$ is the lifetime cycle count, $\Sigma$ is total lifetime entropy production, and $\langle\sigma_0\rangle$ is the lifetime-averaged entropy cost per cycle. In the homeostatic limit, $\dot e_p\simeq P/T$, so direct measurement of metabolic power $P$, body temperature $T$, and physiological frequency $f$ gives $\sigma_0\simeq P/(Tf)$. PBTE converts the empirical lifetime-cycle invariants into entropy-cost invariants. Under Kleiber metabolic scaling and quarter-power physiological-frequency scaling, the mass-specific entropy cost satisfies $\bar\sigma_0=P/(TfM)\propto M^{3/4+1/4-1}=M^0$, providing a thermodynamic interpretation of allometric mass cancellation.

Linear Variable Differential Transformers (LVDTs) are widely used as high-precision, contactless displacement sensors in industrial, metrological, and scientific applications. Their performance is typically characterised only within the central linear operating region, whereas their behaviour across large displacements, where geometric and electromagnetic effects introduce significant non-linearity, remains poorly researched. In this work, we present a comprehensive analysis of the full-range response of an LVDT, spanning its entire mechanical stroke. Using a combination of custom-developed finite-element modelling pipeline and dedicated laboratory measurements, we demonstrate that the LVDT response comprises several distinct dynamical regimes. We introduce an analytically unified expression that accurately reproduces the measured response over all displacement scales, including linear and non-linear ranges, capturing the underlying physical features of the device. The model achieves high fidelity across the full range and provides closed-form first and second derivatives, enabling unambiguous displacement reconstruction, even in the non-linear regime where the voltage is multivalued. The derivative structure further clarifies the contribution of geometric coupling, noise-dominated central behaviour, and envelope decay. This study establishes, for the first time, a systematic framework for modelling, interpreting, and utilising the full-range behaviour of LVDTs. It offers guidance for systems that undergo large quasi-static excursions, overload recovery, or long-range alignment.

We introduce the Dirac Inverted Oscillator, a new exactly solvable relativistic quantum system obtained through a Hermitian modification of the generalized momentum operator in the Dirac equation. In contrast to the conventional Dirac oscillator, where the generalized momentum is intrinsically non-Hermitian while the Hamiltonian remains Hermitian, the present construction reverses these Hermiticity properties: the generalized momentum becomes Hermitian, whereas the corresponding Dirac Hamiltonian is intrinsically non-Hermitian. This inversion leads to a new class of relativistic Hamiltonians within the framework of non-Hermitian quantum mechanics. Starting from the stationary Dirac equation, we derive the corresponding second-order wave equation and establish the generalized symmetry properties of the model, including pseudo-Hermiticity and pseudo- symmetry. We then prove that the Dirac Inverted Oscillator is exactly related to the conventional Dirac oscillator through a Hermitian but non-unitary similarity transformation generated by a dilation operator. This transformation is bijective and invertible, mapping the original non-Hermitian relativistic problem onto an equivalent Hermitian Schrodinger eigenvalue problem while preserving its complete spectral structure. The transformed Hermitian problem is solved analytically, allowing the exact relativistic spectrum and the corresponding eigenfunctions of the original non-Hermitian Hamiltonian to be determined explicitly. The present work therefore establishes an exact correspondence between a non-Hermitian relativistic Dirac system and a Hermitian Schrodinger problem, providing a new exactly solvable model and illustrating the effectiveness of Hermitian non-unitary similarity transformations for constructing analytically solvable relativistic Hamiltonians beyond the conventional Hermitian framework.

Research on optical rotational manipulation leveraging the imaginary Poynting momentum (IPM) force has predominantly centered on cylindrically polarized Gaussian and annular beams. Here, we extend this framework to tightly focused cylindrically polarized structured light fields possessing closed or open arbitrary-intensity trajectories. We systematically elucidate the rotational dynamics induced by IPM in such fields, characterizing the underlying mechanical effects and trapping flexibilities. Notably, despite carrying zero net angular momentum, these fields drive microparticles into bidirectional rotation along predefined trajectories, thereby challenging conventional paradigms reliant on spin or orbital angular momentum. This IPM-mediated optical spanner offers unprecedented spatial degrees of freedom, paving the way for high-precision optical manipulation along arbitrarily tailored paths.

The discovery of superconductivity in Ruddlesden-Popper bilayer nickelates under both high pressure and ambient conditions has opened a new paradigm for exploring unconventional superconductivity. This review provides a brief survey of theoretical progress on bilayer nickelate superconductors. Drawing from the key experimental observations, we summarize essential physical ingredients including the hybridized Ni-3$d_{x^2-y^2}$ and 3$d_{z^2}$ electronic structure, orbital-dependent electronic correlation, Hund's coupling, and strong interlayer magnetic coupling. The fundamental theoretical models including the bilayer two-orbital Hubbard model and its minimal $t$-$J$ variants are introduced. Starting from the atomic-limit interlayer valence bond picture of the half-filled $d_{z^2}$ orbital, we elaborate on strong correlation interlayer pairing mechanisms based on different limiting considerations. Specific emphasis is placed on the hybridization mechanism, where the $d_{z^2}$ local singlet pairs provide the pairing energy and their hybridization with itinerant $d_{x^2-y^2}$ promotes superconducting phase coherence. We further analyze the pairing symmetry, the dependence of $T_c$ on various internal and external parameters, the nontrivial normal state properties including the Fermi liquid, non-Fermi liquid, weakly insulating and pseudogap behaviors. Effects of pressure tuning, oxygen content, and Kondo scattering induced by oxygen vacancies are also discussed. Finally, weak correlation theories based on spin fluctuations associated with Fermi surface nesting are briefly covered.

The direct detection of gravitational waves (GWs) is a very significant achievement in the history of physics and has opened a new window to probe the possible deviations of physics from that of general relativity (GR). In this work, we forecast constraints on the free parameter of an $f(Q)$ gravity model that mimics a $\Lambda$CDM background at the level of cosmic expansion. We consider modified gravitational wave signals from inspiraling of compact bianry systems such as binary black holes (BBH), binary neutron stars (BNS)and black hole neutron star binary (BBHNS) systems in the context of the $f(Q)$ gravity model and perform parameter estimation for two future third-generation ground-based GW detectors, namely Einstein Telescope (ET) and Cosmic explorer (CE), respectively. Our results show that both detectors can give tight constraints on the model parameter up to a significantly high redshift. These results show the potential of future GW observations to probe the deviations of the nature of GWs from that of GR within the framework of $f(Q)$ gravity.

The spectral form factor (SFF) is a measure of energy correlations and has been widely used to identify the transition from the ergodic to the localized phase in interacting many-body quantum systems. In this work, we show that in a disordered Heisenberg spin-$\frac{1}{2}$ model, the finite temperature SFF can be used to generate a canonical phase diagram exhibiting a critical temperature $T_\mathrm{MBL}$. Using simple ideas of statistical mechanics, we obtain the critical energy density $\epsilon_\mathrm{MBL}$ dual to $T_\mathrm{MBL}$. We show that the mobility edge, numerically estimated from the spread of local perturbations and the optical conductivity, indeed coincides with $\epsilon_\mathrm{MBL}$.

We study a finite Floquet chain in which a uniform nearest-neighbor hopping coexists with a periodically rotating, SU(2)-dictated spin-assisted hopping profile. The resulting coupling is spatially inhomogeneous – weakest at the chain boundaries and strongest in the bulk – and produces a frequency-dependent Floquet-Sambe bottleneck. In the closed system, the mean inverse participation ratio (MIPR) of the Floquet eigenstates exhibits a striking nonmonotonic dependence on the driving frequency $\omega $: the states remain extended at both low and high frequencies, but become maximally localized at an intermediate frequency. We demonstrate that this localization maximum occurs at $\omega _{\mathrm{peak}}\sim \mu _{-s}=\sqrt{% 2s}$, a scale controlled by the first boundary bottleneck. To connect these spectral properties to measurable transport, we construct an open-system Floquet-Sambe Green-function inverse participation ratio from the spatial density of the injected scattering state. This open-system diagnostic recovers the same nonmonotonic localization trend as its closed-system counterpart, with the peak shifted to higher frequencies by the static bandwidth and the lead self-energy. These findings establish the driven synthetic spin chain as a directly realizable, frequency-tunable platform for coherent information storage and retrieval, rooted in the interplay of Floquet-Sambe virtual channels, boundary-controlled localization, and frequency-selective transport in emerging multi-level superconducting circuit architectures.

Strong light-matter coupling between molecules and optical or plasmonic cavity modes has emerged as a promising platform for advancing photonics, materials science, and chemistry. However, optical cavities and plasmonic resonators in particular are inherently lossy systems characterized by finite photon lifetimes. Accurate theoretical descriptions of molecular dynamics under strong coupling therefore require a proper treatment of cavity losses. In this work, we compare three theoretical approaches for modeling dissipative molecule-cavity dynamics within a realistic parameter regime: the Lindblad master equation, the stochastic Schrödinger equation, and the non-Hermitian Schrödinger equation. As an example, we consider the two lowest energy state of Na2 molecule coupled to a cavity mode and analyze the time evolution of the excited-state population and the mean photon number. Our results demonstrate that the stochastic Schrödinger equation provides an accurate and computationally efficient alternative to the Lindblad master equation, while the non-Hermitian Schrödinger approach is found to be applicable only within a limited range of conditions. Furthermore, we show that inclusion of molecular rotation leads to rotational-vibrational-photonic coupling and gives rise to pronounced nonadiabatic dynamics through light-induced conical intersections. These findings highlight the importance of both dissipation and rotational degrees of freedom for a realistic description of molecular dynamics in strongly coupled molecule-cavity systems.

Helical carbon coils exhibit unique three dimensional chiral architectures that can effectively interact with microwaves in the 2 to 18 GHz range. Inspired by recent experimental studies, we develop a coarse grained electrodynamic model for helical carbon coil arrays supported on quartz substrates, and examine their potential as microwave absorbers. Guided by the heuristic relation $f_{\mathrm{res}} = c / (n_{\mathrm{eff}} p)$, we compute absorption and reflection fractions for both bare helical carbon coil on substrate and helical carbon coil with anchoring layer on substrate configurations. The anchoring layer thickness is treated as a tunable parameter to improve absorption at selected frequencies. We find that the introduction of a carbon based anchoring layer of optimized thickness enhances impedance matching absorption. The parameters are chosen as representative values for demonstration purposes, and may vary within a certain range depending on preparation conditions. Our results serve to illustrate the potential of helical carbon coils as microwave absorbing devices, and to identify possible active tuning strategies. In the discussion section, we consider extensions of the present model to account for circular dichroism absorption, and examine the influence of actual interfacial reflection on microwave absorption and reflection.

Greenland iceberg discharge exhibits complex nonlinear dynamics with limited observability, challenging traditional predictive models. We present a Hybrid NARX-LLM framework that combines a nonlinear autoregressive model with exogenous inputs (NARX) and a large language model (LLM) for residual correction. We further propose a Physics-Informed Prompt (PIP) method that transforms unstructured physical knowledge into structured prompts for zero-shot in-context reasoning. The primary objective is to explore the corrective potential of this framework for modeling Greenland iceberg discharge, rather than merely optimizing predictive accuracy. The NARX component captures intrinsic temporal dependencies, while the LLM, guided by PIP, encodes glacier dynamics and environmental drivers and perceives key trend patterns to correct systematic prediction errors. This integration allows the model to reason about unmodeled factors and produce interpretable residuals, enhancing overall predictive accuracy. Applied to Greenland iceberg discharge time series, our approach addresses extreme events that are difficult to predict due to rare variations and nonstationary trends, a limitation often overlooked by traditional methods. By fusing structured time-series modeling with knowledge-driven foundation AI, the framework offers a scalable and interpretable pathway to bridge data-limited climate forecasting with physics-informed LLM reasoning. The code is available.

This paper is a specialization of a broad and complicated continuum theory [arXiv:2403.07582] to a relatively simple and useful case so that it is more reader friendly. A continuum theory of the flow of charged particles in an elastic solid is presented. It can describe the behavior of soft solid electrolytes and elastic semiconductors. It is nonlinear and is valid for large deformation and strong fields. The theory is derived from a three-continuum mixture model including a charged lattice continuum, a bound charge continuum for electric polarization, and an ideal fluid for the flow of mobile charges. The basic electromechanical laws are applied systematically to the model. The electric fields are quasistatic and are in SI units.

Spontaneous symmetry breaking (SSB) is central to modern physics but is conventionally defined only for infinite systems, raising challenges for its interpretation in finite, real-world setups. This paper argues that the key to resolving this issue lies in the underappreciated role of boundary conditions in quantum systems. Inspired by both the relational approach to symmetries and the physical mechanism behind symmetry breaking, we formulate a relational interpretation of SSB: a finite system exhibits SSB relative to a reference environment which can induce perturbations across the boundary. This eliminates the need for the thermodynamic limit, offering a more physical picture of SSB that emphasizes the observable consequences of the interactions that real-life systems inevitably have with their environment. We show how, in this relational interpretation, SSB for both lattice systems and (gauge) field theories should be understood as subtle, rather than spontaneous, symmetry breaking, still in contrast to explicit symmetry breaking. We also explain how algebraic definitions of SSB for infinite systems relate to the intuitive picture of SSB in finite systems and illustrate how asymptotic boundary conditions push the environment "to infinity". In this way, our relational interpretation of SSB provides a unified conceptual framework applicable to symmetry-breaking in systems of any size.

We investigate the emergence of generalized Schwarzian dynamics from a bulk-first BF perspective. Starting from two-dimensional BF gravity, we analyze the associated boundary phase space and its Drinfeld-Sokolov reductions. For the sl(2,R) theory, we recover the ordinary Schwarzian action as the reduced boundary dynamics arising from a particular sector of the BF asymptotic phase space. We then extend this construction to sl(3,R), where the reduced dynamics is governed by the second and third Wilczynski invariants, providing a natural higher-rank generalization of the Schwarzian derivative. In this framework, generalized Schwarzian dynamics emerges directly from flat BF connections and their companion forms rather than being introduced as an independent boundary theory. We further relate the resulting projective invariants to Casimir charges, monodromy data, and generalized Schwarzian thermodynamics, including monodromy spectra and semiclassical thermodynamics. In particular, constant projective invariants determine the corresponding Casimir sectors and monodromy data, which in turn organize the thermodynamic structure of the theory. Our results provide a unified bulk-first description of Schwarzian and generalized Schwarzian dynamics and reveal a direct link between BF gravity, asymptotic symmetry reductions, projective geometry, and boundary thermodynamics.

High-energy photons from GRB 221009A provide a powerful opportunity to probe axion-like particles (ALPs) through photon-ALP oscillations in cosmic magnetic fields. We revisit the ALP constraints implied by the LHAASO observation of this burst, with particular emphasis on the magnetic-field environments encountered along the line of sight. We include the host-galaxy, intergalactic, and Milky-Way magnetic fields and assess their respective impacts on the photon survival probability and on the exclusion limits in the ALP mass-coupling plane. We show that the constraints are only mildly affected by the choice of host-galaxy and Galactic magnetic-field models, but can change significantly once the intergalactic magnetic field is varied. Its field strength, coherence scale, and stochastic properties can all leave visible imprints on the derived exclusion contours, and in some cases generate pronounced oscillatory features. This demonstrates that the intergalactic magnetic field constitutes the dominant astrophysical uncertainty in extracting ALP limits from GRB 221009A. Our analysis highlights the importance of realistic propagation modeling in future gamma-ray searches for ALPs.

Negative-pion and neutral-pion mesonic decays of the hypernucleus $ _\Lambda ^5$He are investigated within two-body and three-body relativistic kinematics in the rest-frame of the hypernucleus. 4-momentum conservation fully constrains the two-body decay, giving rise to a monochromatic pion momentum that is determined through the Newton-Raphson root-finding algorithm. In the case of three-body decay, where 4-momentum conservation is insufficient, the final-state momenta are parametrised by variables whose variations account for all kinematically allowed momenta. A Monte Carlo sampling method is then employed to generate 50 000 decay events per channel that simultaneously satisfy both energy and momentum conservation. The resulting pion momentum distributions exhibit clear peaks at 103.0 MeV/c for neutral pion decay and 97.3 MeV/c for negative pion decay. In addition, only 0.27% of neutral pion decay events and 0.03% of negative pion decay events produce nucleons with momenta exceeding the Fermi momentum of $ ^4$He, and are therefore allowed by the Pauli exclusion principle.

We further investigate the 3d gauged linear sigma model (GLSM)/~quantum K-theory correspondence for partial flag manifolds $X \equiv {\rm Fl}(\boldsymbol{k};n)$. This is a 3d uplift of the 2d GLSM/quantum cohomology correspondence with the 3d theory compactified on $\mathbb{R}^2\times S^1_\beta$. Recently, a set of half-BPS line operators, called Schubert line defects, were constructed that correspond to the Schubert classes in the K-theory ring of $X$. Utilizing algebro-geometric algorithms, we compute $2$-point and $3$-point correlation functions of these line operators in the 3d A-model regime of the theory. These are interpreted as genus-$0$ K-theoretic Gromov–Witten invariants, and they produce the K-theoretic Littlewood–Richardson coefficients of the quantum K-theory ring of $X$. We show how this works explicitly in examples, going beyond the existing results in the literature. Taking the small $\beta$ limit, we apply these techniques to the resulting 2d GLSM. We explicitly compute the quantum cohomology ring relations of $X$ for some cases and match with existing results in the literature in examples.

The polar magnetic field polarity reversal is a key signature of solar cycle evolution, and precise determination of its timing is crucial for dynamo theory validation and solar cycle prediction. We investigate the polar polarity reversal of solar cycle 25 using the vector magnetic field data from the spectropolarimeter on board the Hinode satellite. We constructed polar top-down composite maps from Hinode-view magnetograms. These maps show the year-to-year polar polarity variations, with the northern polar region gradually changing from positive to negative and the southern polar region exhibiting the reverse behavior. The polarity reversals of the northern and southern polar caps (above 70 deg latitude) likely occurred in November 2024 and October 2024, respectively. The northern polarity reversal lagged the northern hemispheric sunspot number maximum by approximately 19 months, while the southern reversal possibly coincided with the southern maximum. Moreover, polarity reversal times calculated at 5 deg latitude intervals above 70 deg reveal a trend of earlier reversal in lower latitudes consistent with that of solar cycle 24. These results offer observational references for modeling polar polarity reversal in solar cycles.

Biofilms are spatially structured microbial communities whose architecture, chemistry, mechanics, and cellular states evolve over time. Bulk assays and two-dimensional projections remain useful, but cannot alone resolve how these properties vary with depth or change during growth, treatment, dispersal, and regrowth. Imaging provides complementary routes to three-dimensional measurement: fluorescence microscopy supplies molecular, taxonomic, and functional specificity; optical coherence tomography resolves mesoscale architecture and dynamics; quantitative phase imaging and holotomography report refractive index and biomass-related changes; Raman methods provide chemical and metabolic contrast; and Brillouin microscopy probes mechanical response. We compare these modalities using four independent descriptors-contrast provenance, live volumetric capability, perturbation, and demonstrated biofilm use-and connect their signals to quantitative biological readouts. No single modality simultaneously maximizes spatial coverage, resolution, acquisition speed, molecular specificity, and low perturbation. Implementations from any contrast class can serve as a longitudinal backbone when perturbation is empirically controlled at the relevant spatial and temporal scale, while molecularly specific measurements remain indispensable for identifying species, molecules, and functional states. We therefore frame four-dimensional biofilm measurement as a validated measurement architecture that integrates a low-perturbation volumetric backbone with spatially registered, molecularly specific measurements acquired continuously or at predefined validation points. Achieving this integration will require compatible cultivation formats, controlled imaging dose, shared quantitative parameters, and robust cross-modality registration.

We study the transport characteristics of an extended version of the Su-Schrieffer-Heeger (SSH) model with next-nearest-neighbor (NNN) interactions and non-Hermitian onsite energies. We observed that transport in such a system is significantly modified by the NNN interaction and the non-Hermitian terms. The transmission coefficient exhibits oscillatory behavior as the strength of the NNN interaction varies in a fixed-length chain. Moreover, the transmission coefficient also shows oscillation with system size for a fixed strength of the NNN interaction. We find that novel oscillatory behavior of the transmission coefficient, arising form the NNN interaction, is a unique feature of such a model and has not been reported previously. The presence of the non-Hermitian terms also enhances/reduces the transmission coefficient depending on the values of the other system parameters like intra-, inter- and NNN hopping. It appears from our study that both the NNN interaction and the non-Hermiticity introduce significant changes in the transport properties of the extended SSH chain, which are not observed in the standard Hermitian nearest-neighbour variant of the SSH model.

We construct the Standard Model gauge group using the exceptional Jordan algebra $\mathfrak{h}_3(\mathbb{O})$ and its automorphism group $\text{F}_4$. The group $\text{F}_4$ acts on pairs of Jordan subalgebras $X \subset B \subset \mathfrak{h}_3(\mathbb{O})$ with $X \cong \mathfrak{h}_2(\mathbb{C})$ and $B \cong \mathfrak{h}_3(\mathbb{C})$, and for any such pair the stabilizer of $X$ intersected with the identity component of the stabilizer of $B$ is isomorphic to the Standard Model gauge group. Since $\mathfrak{h}_2(\mathbb{C})$ is the Jordan algebra of observables of a qubit and $\mathfrak{h}_3(\mathbb{C})$ is the Jordan algebra of observables of a qutrit, we could say $\mathfrak{h}_3(\mathbb{O})$ is the Jordan algebra of observables of an 'octonionic qutrit'. In this language our result says roughly that the Standard Model gauge group is the group of symmetries of an octonionic qutrit that restrict to act as unitary operators on an ordinary qutrit and, within that, a qubit.

We investigate the exact transience time of the Facilitated Exclusion Process (FEP) on the one-dimensional torus with $N$ sites. The FEP exhibits an active/inactive phase transition at critical density $1/2$, such that in the subcritical density regime $(0,1/2)$, it becomes frozen after a finite time period – the transience time or freezing time. We first show that for the FEP starting from a Bernoulli product measure of marginal density $\rho \in (0,1/2)$, the transience time has exactly the scale of $\Theta(\log^3 N)$. Secondly, we prove that in the near-critical case $\rho \simeq 1/2 - N^{-\alpha}$ for $\alpha \in (0,1)$, the transience time is polynomial and has a scale of $N^{1 \wedge (2\alpha)}$. The key idea is to estimate the typical size of locally supercritical intervals of the initial distribution, which has order $\log N$ in the subcritical case and $N^{1 \wedge (2\alpha)}$ in the near-critical case. In the subcritical case this is enough, whereas in the near-critical case we need additional dynamical decorrelation inequalities to apply this static result to estimate the freezing time.

Reservoir models offer a hardware-efficient learning paradigm for noisy intermediate-scale quantum devices by exploiting untrained quantum dynamics as a fixed feature map and restricting optimization to a simple classical readout layer. We propose a quantum extreme learning machine implemented using gaussian boson sampling and an encoding strategy that achieves high classification accuracy while reducing optical resource requirements. Classical inputs are jointly encoded in the squeezing parameters and in the interferometer unitary, enabling sampling-based, highly nonlinear feature maps while leveraging large-scale GBS output statistics, which are conjectured to be classically intractable. We systematically compare multiple families of quantum features accessible in the same setup and find that photon-number sampling probabilities provide the best performance, consistent with their higher effective feature dimensionality. Finally, we benchmark against classical nonlinear baselines and analyse robustness under noisy scenarios, showing competitive performance with fewer trainable parameters and indicating practical promise for near-term photonic implementations.

We study pseudo entropy $\mathcal{S}$, a recent generalization of entanglement entropy, for scalar cosmological perturbations in de Sitter space with sound speed $0.024 \leq c_s \leq 1$, and in expanding and contracting FLRW backgrounds with varying equation-of-state parameter $w$. In de Sitter space, $\mathrm{Re}(\mathcal{S})$ grows after horizon exit while $c_s$ controls its onset and saturates at late times. A similar saturation occurs in expanding-accelerating and contracting-decelerating backgrounds. In contrast, expanding-decelerating and contracting-accelerating backgrounds show large early-time $\mathrm{Re}(\mathcal{S})$ followed by oscillations after horizon re-entry. This happens because while the squeezing freezes, the squeezing angle doesn't. Unlike entanglement entropy, pseudo entropy possesses an imaginary part, $\mathrm{Im}(\mathcal{S})$, as well, which can encode the relative phase. $\mathrm{Im}(\mathcal{S})$ decays to zero in de Sitter and expanding-accelerating cases, but forms dense sub-Hubble oscillation bands in expanding-decelerating and contracting-accelerating backgrounds. Compared with entanglement entropy, Krylov complexity, and Nielsen circuit complexity, pseudo entropy captures otherwise hidden phase information; in the unsaturated regime, its slope is $\sqrt{2}$ times that of Nielsen complexity. Unlike circuit complexity, whose saturation bound is $w$-independent, pseudo entropy is sensitive to $w$ during the transition regime, making it a finer information theoretic diagnostic of cosmological dynamics.

General Relativity (GR) is widely regarded as a paradigmatic example of a background independent theory, a feature often taken to mark a decisive conceptual advance over its Newtonian and special relativistic predecessors. Yet the notion of background independence admits multiple formalizations, and its precise physical and philosophical significance remains contested. This chapter offers a systematic analysis of the strategies that have been proposed to capture background independence in classical spacetime physics. The discussion then turns to a central open question: whether, and in what sense, a successor theory of GR – such as a theory of quantum gravity – should be expected to inherit GR's background independence. Drawing on contemporary debates and a range of case studies, the chapter argues that background independence is best understood as a diagnostic and comparative tool rather than as a necessary physical requirement. The resulting perspective highlights both the conceptual virtues and the interpretive costs of eliminating background structures, and helps to explain why background independence remains an open problem in contemporary foundational research.

We present an SE(3)-invariant transformer for 3D-molecule generation, the Atomic Design Transformer (ADT). ADT places atoms one at a time, autoregressively. The SE(3) invariance is achieved by tokenization: each new atom's position is encoded in a local coordinate frame of a previously placed atom. The network is a plain causal transformer. For evaluation, we introduce xTB-Validated Rate (XVR), which checks whether the molecular topology is preserved after xTB GFN2 geometry relaxation. On QM9, ADT is competitive with state-of-the-art baselines. For GEOM-Drugs, we present a quantitative benchmark of scaffold-conditional 3D generation, evaluating seven scaffolds (benzene, pyridine, pyrimidine, pyrazine, furan, thiophene, cyclohexane) on the 30-atom-truncated ground-state GEOM-Drugs dataset. XVR ranges from 11.1% (pyrazine) to 29.7% (benzene), all from a single trained model. The generated molecules are chemically diverse, and generation is fast by virtue of the plain causal-transformer backbone. Application to the 50-atom-truncated GEOM-Drugs dataset yields lower XVR while the per-bond and per-angle quality is retained. These results position ADT as a practical proposer for in silico molecular design.

The coherent control of atomic wave packets in multiple momentum dimensions is a central challenge in Raman atom optics and a key requirement for multidimensional atom interferometry. In this paper, a momentum-basis theoretical framework is developed for two-dimensional Raman interactions. We formulate the atom-laser interaction for two-dimensional Raman beams and obtain the effective two-level ground-state Hamiltonian after adiabatic elimination of the excited states. The resulted Hamiltonian is constructed on the reachable momentum-state lattice and includes AC Stark shifts, intra-dimensional Raman couplings, and cross-dimensional Raman coupling terms, thereby describing multidimensional Raman dynamics beyond a simple superposition of independent single-dimensional models. The framework is used to analyze the principles and operating conditions of two-dimensional atom interferometry. Cross-dimensional Raman coupling and sequential reverse Raman transitions are identified as the main mechanisms that redistribute atoms into non-target momentum states and reduce the contrast of atomic interferometer fringe. Experimentally, Ramsey fringes are observed in a cold-atom fountain interferometer, with a contrast of $14.8\%$ at an interrogation time of $T=10~{\rm ms}$, in good agreement with the theoretical calculation. The conditions required for velocity-sensitive multidimensional atom interferometry are further clarified, including detuning control, velocity-class selection, and suppression of undesired inter-dimensional transitions. This work provides a theoretical and experimental basis for multidimensional Raman atom interferometry.

Time series forecasting largely benefits from combining the strengths of different models, especially using a scheme where a model corrects another model by capturing supplementary patterns from forecasting errors. Concurrently, quantum models are providing a means to augment the classical capacity, including in time series forecasting, by acting alongside classical models in hybrid architectures. In this work, we propose the first forecasting system based on error correction that jointly uses quantum and classical models. Here, quantum models first extract patterns by exploring quantum phenomena, and classical models capture the remaining patterns from the quantum errors. Compared to classical single models and classical-classical hybrid models based on error correction, the complementary capacity that emerges from this quantum-classical system provided the best results in most of the addressed problems. Therefore, this work paves the way to introduce quantum models in established hybridization schemes for time series forecasting.