Papers

We study statistical variants of the classical largest average submatrix problem. For small submatrices (where the dimension is less than linearly proportional to the original matrix), the problem is typically well understood and believed to exhibit the statistical-computational gap (SCG). However, analytical treatment of both the information-theoretic and algorithmic aspects of the linear regime remains challenging, and no mathematically rigorous results have yet arrived anywhere close to proving or disproving SCG existence in this setting. Focusing on the linear regime, we make strong progress in several key directions: 1) We develop a generic Random Duality Theory (RDT) framework to characterize largest average submatrix values. 2) Using the plain RDT variant, we obtain closed-form upper bounds as explicit functions of dimensionality proportionality parameters. 3) We demonstrate that a lifted RDT variant strictly improves upon the plain RDT within a certain linear range of submatrix dimensions. 4) For small submatrices where the dimensional proportionality constants approach zero, we prove that our results match both the replica results from [34] (obtained via one-step replica symmetry breaking) and the sublinear results from [18,45].

This study examines how the chemical-reaction timescale alters hypersonic wall-model predictions of heat and momentum transfer. A one-dimensional finite-rate-chemistry wall model for high-enthalpy air is evaluated over 3 <= Ma_e <= 25, 2 <= p_e <= 100 kPa, and a broad range of edge and wall temperatures. All forward and reverse reaction rates are multiplied by a common factor Gamma, which changes the chemical timescale while preserving the equilibrium constants and thereby connects the frozen and fast-chemistry limits within the same governing equations. Taking a 1 percent difference in wall heat flux between the frozen and finite-rate solutions as the threshold for retaining finite-rate chemistry, two quantities obtained from the frozen solution provide practical selection criteria: Da_fr = t_shear / t_ch >= 1.93 x 10^3 and T_max >= 3760 K. The wall heat flux does not generally vary monotonically with reaction rate; instead, it can decrease below both the frozen and fast-chemistry predictions before recovering at higher rates. The two limiting chemistry solutions therefore do not generally bound the finite-rate heat-flux response, and interpolation between them can be misleading. At Ma_e >= 20, the median wall-heat-flux errors of the frozen and fast-chemistry limits are 7.1 percent and 27.6 percent, respectively. Chemistry also produces substantial changes in wall heat flux and shear stress, whereas the Reynolds analogy factor responds much less because the momentum- and enthalpy-side wall-law shifts nearly cancel. These results show that finite-rate wall transfer cannot in general be inferred from its frozen and fast-chemistry limits and provide frozen-state indicators for determining when finite-rate chemistry should be retained in hypersonic wall modelling.

Blue large-amplitude pulsators (BLAPs) are rare, hot, short-period pulsating stars whose rapid oscillations provide a unique probe of stellar interiors and atmospheres. In this paper, we study two short-period BLAPs in the Galactic bulge, OGLE-BLAP-142 ($P \approx 6.6$ min) and OGLE-BLAP-148 ($P \approx 7.5$ min), by combining light curves from the OGLE, KMTNet, and DREAMS surveys, spanning 17 years with cadences ranging from minutes to hours to days. We perform Generalized Lomb-Scargle periodogram analyses of their light curves and identify, for each BLAP, three closely spaced pulsation modes separated by $\sim 1\%$. The dominant mode can switch within timescales of order a year, accompanied by a likely blueward color shift ($\sim 0.1$–$0.2$ mag). The yearly period excursions of the resolved mode families imply apparent $|\dot{P}/P|$ values of order $10^{-6}$–$10^{-4}\,\mathrm{yr^{-1}}$, large enough to mimic or exceed smooth evolutionary period changes. One mode family in OGLE-BLAP-148 shows a coherent decade-long drift at the $\sim10^{-5}\,\mathrm{yr^{-1}}$ level, but its failure to extrapolate to the earliest and latest epochs suggests a transient mode-family drift rather than secular evolution. Such close-spaced multiple pulsations and mode switching may be common among BLAPs with periods shorter than 10 min, and their physical origin remains unclear.

We construct turbulent gravitational wakes in asymptotically AdS$_4$ spacetimes by solving the full non-linear Einstein equations in the characteristic formulation. Specifically, we show that a localized boundary deformation acting on a boosted black brane generates a wake whose boundary dynamics exhibit the formation of coherent vortical structures that are advected downstream by the background flow. Analysing a wake propagating along the x direction, we show that it displays the characteristic self-similar scaling of classical turbulent wakes. We then identify the geometric imprint of the wake on the horizon area density, the traceless horizon extrinsic curvature, and bulk metric perturbations, finding coherent structures that extend from the asymptotic boundary to the horizon. These results provide the first study of turbulent gravitational wakes in four-dimensional asymptotically AdS spacetimes.

In seismic exploration, the propagation of seismic waves naturally gives rise to long-range dependencies in seismic data. Capturing such global correlations can significantly improve the accuracies of seismic signal processing, inversion, and interpretation. Global modeling (GM) methods have therefore emerged as an effective paradigm for seismic exploration, offering a powerful means of exploiting the intrinsic global relationships within seismic data. However, the mainstream GM approaches, particularly Transformers, incur prohibitively high computational costs for their inherent quadratic complexity, which restricts the scalability of such methods to higher-dimensional data. To achieve efficient GM for three-dimensional (3D) seismic exploration, we propose a general framework, named lightweight Mamba-based global modeling (LMGM), to establish long-range dependencies at a relatively low computational cost. Specifically, LMGM fully leverages the linear complexity of Mamba. A three-directional scanning Mamba block is designed to exploit spatial correlations along the three dimensions of 3D seismic data. Meanwhile, a dual-domain-aware block is further developed to integrate time- and frequency-domain features for enhanced feature representation. In addition, a two-stage plug-and-play nonlinear normalization strategy is proposed to enhance the adaptability of LMGM to diverse seismic records while preserving signal characteristics. We employ 3D seismic data interpolation as a representative task to comprehensively evaluate LMGM. The results demonstrate that LMGM achieves superior processing performance while substantially reducing computational cost compared with U-Net-based and Transformer-based methods. Furthermore, experiments on random noise removal demonstrate the applicability of LMGM beyond interpolation, supporting its potential as a general GM framework.

We investigate the optimal endpoint $L^2$ restriction estimates of Laplace eigenfunctions on submanifolds of codimension 2 in a smooth closed Riemannian manifold $M$. For every fixed smooth codimension-two submanifold $\Sigma$, we prove a little-o improvement $o(\lambda^{1/2}\sqrt{\log\lambda})$ on the classical estimate $O(\lambda^{1/2}\sqrt{\log\lambda})$ of Burq–Gérard–Tzvetkov and Hu. Our proof uses the Bargmann transform and Tataru's phase-space representation to reduce the problem to Stein–Street's estimate for singular Radon transforms. The three-dimensional case can be handled directly by Ricci–Stein's estimate. Moreover, we construct explicit examples to show that the little-o improvement is optimal in general. These are closely related to earlier counterexamples for endpoint Strichartz estimates by Montgomery–Smith and Carbery–Hofmann. In particular, we establish the log-free estimate $O(\lambda^{1/2})$ when $(M,g)$ and $\Sigma$ are real analytic, whereas this estimate fails in general in the smooth setting.

Interacting dark energy (IDE) models, featuring interactions between dark matter (DM) and dark energy (DE), have received significant renewed interest. However, little attention has been devoted to understanding their genuine cosmological signatures, with comparisons against $\Lambda$CDM often carried out at fixed cosmological parameters. Considering the widely studied model with energy exchange rate proportional to the DE density, we carry out a three-level sequence of comparisons, starting from the naïve fixed-parameter comparison, then compensating for shifts in $\theta_s$ and $z_{\text{eq}}$, and then removing effects due to the modified background. We show that fixing $\theta_s$ and $z_{\text{eq}}$ leads to pre-recombination evolutions of the Weyl potential, photon monopole, and baryon velocity which are nearly identical to their $\Lambda$CDM counterparts, and hence virtually indistinguishable Cosmic Microwave Background (CMB) temperature power spectra. Comparing IDE to a non-interacting $w$CDM model with the same background, we find small scale-dependent signatures in CMB lensing. We find larger differences in the matter power spectrum, reflecting the different values of $\Omega_m$ resulting from the different partition of the dark sector into DM and DE, with only percent-level differences remaining once we compare $\Omega_m^2P_m(k)$, indicating the importance of high-fidelity determinations of $\Omega_m$. Our controlled comparison strategy can be a powerful tool for a wide range of models beyond $\Lambda$CDM.

Among the crowd of dark matter candidates, light scalar and vector particles have been the focus of intense theoretical and experimental investigations over the past 15 years. However, those are always described as scalar or vector fields. Instead, we investigate their embedding as antisymmetric rank-three and rank-two tensor fields. By reconciling theoretical investigations, regarding the nature of the dualities relating the standard and tensorial descriptions and their different possible Stueckelberg gauge representations, and phenomenological examinations considering the effective interactions between tensor fields and the Standard Model, we prove these tensor fields to provide a completely distinct framework. This alternative set allows for different couplings and therefore different experimental signatures for the detection or production of dark matter at both low energy and colliders.

In this paper, we investigate the localization of various $q$-form fields on a codimension-two brane. In particular, the $0$-form scalar field, the $1$-form $U(1)$ gauge vector field, and the $2$-form Kalb-Ramond field are considered with gravitational coupling, where a coupling function $F(R)$ is introduced into the six-dimensional actions of these fields. The function $F(R)$ depends on the scalar curvature of the bulk. Within this framework, we find that the massless modes of different $q$-form fields can be localized on the thick brane for positive values of the coupling parameters $t_1$ and $t_2$. For the massive modes, the different $q$-form fields exhibit similar localization properties determined by the coupling parameter $t_2$. When $0<t_2<v^2/24$, the massive modes of these fields cannot be localized on the brane, while they may exist as the resonant modes. In the case $t_2=v^2/24$, a finite number of massive modes can be localized on the thick brane, and the number of localized modes increases with the coupling parameter $t_1$. Finally, when $t_2>v^2/24$, the effective potentials associated with the Kaluza-Klein modes of these $q$-form fields form infinitely deep potential wells, so that all massive modes can be localized on the brane. Moreover, the tachyonic massive modes can always be excluded for different $q$-form fields.

We establish a Levy interpretation of normalized forward BFKL small-$x$ evolution at leading order and fixed coupling, and exclude a probability law at fixed-order next-to-leading accuracy in the symmetric scheme. After the Marchesini-Onofri conjugation and growth subtraction, one positive step measure in closed form covers all conformal spins, on the cylinder of logarithmic transverse momentum and azimuth. The process is pure jump, and the Pomeron intercept is the relaxation rate of its first azimuthal harmonic. With $s_0=q_1q_2$ and the coupling at that argument, the negative cubic collinear pole of the truncated eigenvalue excludes a probability law at every positive coupling and rapidity. Its leading coefficient is independent of $N_c$ and $n_f$. The pole dominates the leading-order simple pole within $\sqrt{\bar\alpha/2}$ of the edge in the leading collinear approximation. Translation-preserving multiplicative conjugations cannot restore positivity. No non-negative step measure generates that truncated evolution, while a positive radial completion at zero conformal spin matches the computed order, so the obstruction is a property of the fixed-order truncation. The tested symmetric-scheme resummations also fail positivity, as shown in closed form for the pure and matched all-poles forms, except for a degenerate zero process, and by computation at the examined couplings for the full prescription. The improved finite-rapidity Green function fails at the displayed parameters under the contour assumption. A resummed kernel in another rapidity scheme has a non-negative step measure at tested couplings. An unweighted transverse walk describes the leading-order evolution with no approximation, but a probabilistic resummation of the symmetric next-to-leading kernel must establish positivity beyond perturbative matching, and whether one exists is left open.

We characterize the bath resources needed to supply repeated uses of a fixed finite-dimensional quantum channel in a closed device. For each horizon $T$, one bath, one initial state and one repeated unitary are fixed before the user. Each output is returned before the next input arrives; no reset, discard, fresh ancilla or uncounted controller is available. Approximation error must vanish against arbitrary adaptive users with quantum memory and references. Writing $r=\lim \log_2(R_T)/T$ for the bath dimension rate and $s=\lim S(\omega_T)/T$ for the actual initial entropy rate, we prove that the achievable region is exactly $s\ge 0$, $r+s\ge h$ and $r-s\ge\kappa$. Here $h$ is maximum entropy exchange and $\kappa$ is a smoothed independent-reference extension cost, with the zero-error limit taken before the supremum over full-rank inputs. Its exact fixed-input form is an affine transform of the zero-leakage quantum privacy funnel. The minimum dimension rate is $(h+\kappa)/2$. The proof combines entropy converses, a bath-dimension-independent support repair, and a closed adaptive implementation of encoder-only fully quantum Slepian–Wolf recycling. All seeds, clocks, workspace and retained residues are counted. Worked examples include dephasing, pure replacement and a qubit channel with $0<\kappa<h$. No computability of $\kappa$ or efficient circuit synthesis is claimed.

We explore a class of Lorentz-violating scalar-field models where the effects of the scalar field on antimatter can be strongly enhanced compared to matter. Non-trivial differences in phenomenology arise for spectroscopy measurements depending on whether the scalar field changes slowly or rapidly on the atomic scale. We highlight opportunities for precision tests in the laboratory including dark matter searches, in particular with spectroscopy and interferometry measurements, as well as certain types of antimatter experiments.

In order to ascertain the precise atomic characteristics, it is important to incorporate a wide range of electron correlations in the computational analysis. However, it is important to note that undertaking such studies will result in substantial increases of the CSF expansions. The present publication, as well as the series of articles that have been published by G. Gaigalas, P. Rynkun, and L. Kitovienė, are dedicated to the analysis and resolution of the problem in question. In this series, a method was developed based on second-order perturbation theory to identify the most important core-valence, core, core-core, and valence-valence correlations. The method under discussion is based on a combination of the relativistic configuration interaction method and the stationary second-order Rayleigh-Schrödinger many-body perturbation theory in an irreducible tensorial form. In this study, the method is further expanded to encompass additional core-valence electron correlations of the third and fourth types. Conversely, the correlations that are not encompassed by perturbation theory are addressed in a conventional manner. This method can be used to calculate the properties of an atom or ion with any number of valence and core electrons. As an example of its application, the atomic calculations of the energy structure and lifetime for Ne II are presented.

Time-dependent coherent control can enhance excitation transport in open quantum networks, but independently controlling every inter-site coupling creates a control space of high dimension and leads to difficult optimization problems. We introduce an edge-ranking strategy based on the control-induced change in the gradient component of the time-integrated quantum probability current, which is obtained via a graph Hodge decomposition. When our strategy is applied to the seven-site Fenna-Matthews-Olson (FMO) model, the six-edge set retains $99.83\%$ of the enhancement achieved by full control, and the four-edge set retains $97.60\%$ while reducing the pulse fluence—used here as a proxy for control effort—by $41.55\%$ relative to full control. Dephasing scans and comparisons with random edge sets and random networks provide numerical support for the relevance and potential broader utility of the ranking. These results show that edge selection guided by the quantum probability current can substantially reduce the control space while preserving high transport performance with lower control effort.

Core-collapse supernovae (CCSNe) are intense sources of feebly interacting particles (FIPs), whose visible decays beyond the stellar envelope can generate distinct electromagnetic signals. We propose the circumstellar medium (CSM) surrounding the CCSNe progenitor as a new target for 511 keV line searches. FIPs escaping the stellar interior may decay into electron-positron pairs and inject positrons into the CSM, where they slow down and subsequently annihilate, giving rise to a 511 keV line as an electromagnetic precursor to the supernova shock breakout. Using dark photons as a benchmark, we calculate the time-dependent signal for CSM profiles motivated by SN 2023ixf and SN 2024ggi. For a Galactic supernova at 10 kpc, the projected reach of COSI and AMEGO extends beyond existing supernova limits over part of the MeV-scale dark-photon parameter space. The same FIP decays can simultaneously heat the CSM and sublimate circumstellar dust, producing a rapid spectral transition from infrared excess to optical or ultraviolet emission [Y. Cheng et al., Phys. Rev. Lett. 137, 111005 (2026)]. The coincident appearance of this transition and the 511 keV line would provide a distinctive correlated multiwavelength signature of FIP decays in the dense presupernova environment.

Computing dynamical expectation values typically relies on approximations optimized for the state or observable separately, without accounting for how their errors combine in the final expression. This work explores an alternative approach in which each approximation is guided by both the state and the observable, accounting for how they jointly determine the target expectation value. This idea is implemented through a sweep algorithm with coupled loss functions for forward state and backward observable updates. Exact error relations provide an analytical rationale for how the proposed losses can improve the accuracy. Numerical tests on 30-qubit random circuits show errors two to three orders of magnitude smaller than those of variational state compression at equal bond dimensions. These results motivate further exploration of joint state and observable approximation for dynamical expectation value estimation.

We investigate the purity dynamics of a quantum system coupled to a continuous-variable pointer through a von Neumann-type interaction Hamiltonian of the form $\hat H_{\mathrm{int}}=g\,\hat H\otimes\hat p$. For an initially Gaussian pointer state, the interaction generates energy-dependent conditional translations whose mutual overlaps are determined explicitly by the populated spectral separations of the system Hamiltonian. After tracing out the pointer degrees of freedom, we obtain the reduced density operator and derive an exact analytical expression for the time-dependent purity. Using this expression, we establish two-sided purity bounds governed by the minimum and maximum nonzero energy gaps on the populated spectral support. These bounds provide a state-dependent spectral characterization of the loss of purity and become exact for two-level systems. We further show that the short-time decrease of purity is controlled by the Hamiltonian variance of the initial state, with $\mathcal P''(0)=-(g^2/\sigma^2) \operatorname{Var}_{\psi_S}(\hat H)$. In addition, an explicit sufficient timescale is derived for the purity to approach its asymptotic value within a prescribed tolerance, revealing the scaling $t_{\varepsilon}\propto\sigma/(|g|\Delta_{\min})$. Finally, the general results are illustrated for an equally weighted $N$-level system with an equally spaced spectrum, for which the asymptotic purity is $1/N$. The analysis clarifies the distinct roles of spectral separation, energy variance, coupling strength, and pointer width in Hamiltonian-conditioned purity loss.

The method based on the second-order perturbation theory to identify the most important configuration state functions of the various correlations is extended to include valence-valence correlations, which are described by the three-particle Feynman diagram. The extension presented in this work complements the core-valence, core, core-core, and valence-valence correlations which were developed in a series of previous papers by G. Gaigalas, P. Rynkun and L. Kitovienė. Whereas these valence-valence correlations are described by the three-particle Feynman diagram, additional developments to calculate the spin-angular parts of this diagram have been made to the program library librang of the Grasp. As an example of the application of the developed method, the atomic calculations of the energy structure for the Se III are presented. In the present work, this method was also used to select the most significant configuration state functions and to use this basis to solve the self-consistent field equations.

Multi-messenger astronomy (MMA), the joint study of cosmic sources through gravitational waves (GWs), electromagnetic (EM) radiation, neutrinos, and cosmic rays, is rapidly reshaping time-domain astrophysics. Realizing the promise of MMA will require coordinating heterogeneous observing resources and automating the chain from alert to analysis to follow-up. RADAR (Radio Afterglow Detection and AI-driven Response) is a federated, privacy-enhancing framework for the radio follow-up of GW events, previously validated on GW170817. Here, we extend it along three axes. First, we benchmark three large language models (LLMs; GPT-5.5, Claude-Opus-4.7, and Gemini-3.5-Flash) against the GW170817 radio light curve dataset. GPT-5.5 attains the highest event-level $F_1$ score, the harmonic mean of precision and recall, at $0.893 \pm 0.010$, and the highest GCN-level recall, $0.794 \pm 0.013$, improving on previous GPT-4.1 results by 16% and 10%, respectively, while Claude-Opus-4.7 achieves the highest precision, $0.978 \pm 0.014$. Second, we introduce concurrent likelihood evaluation, which speeds up the MCMC computation by a factor of $40\times$ over our previous results. Third, we present an LLM-driven scheme that converts natural-language observing requests into submission-ready scheduling blocks for the Karl G. Jansky Very Large Array. Together, these developments advance RADAR toward a scalable, largely autonomous system for GW radio follow up.

Galactic cosmic rays (CRs) are thought to be accelerated by diffusive shock acceleration in supernova remnants (SNRs), but observations of SNRs aged ~100-1000 yr suggest maximum CR energies below the PeV level. Recently, Inoue et al. (2021) showed with kinetic-MHD simulations that CRs can be accelerated to ~3 PeV when a blast wave shock propagates through dense circumstellar material (CSM) within tens of days after explosion. Such CSM can be produced by a red-supergiant (RSG) wind with an observationally motivated mass-loss rate of ~10^-3 Ms/yr. 100 TeV gamma-rays from neutral pion decay can test PeV CR acceleration. However, hadronic gamma-rays from very young SNRs can be significantly attenuated by supernova photospheric photons and the cosmic background radiation. Using the CR distribution functions and CSM density profiles from Inoue et al. (2021), we calculate time-dependent gamma-ray fluxes from Type II-P SNe, including both attenuation processes. We find that photospheric photons attenuate the intrinsic 1-100 TeV gamma-ray flux by about one order of magnitude. For the dense CSM case with dot{M}_RSG ~ 10^-3 Ms/yr and an outer CSM radius of ~ 3x10^15 cm, CTA can detect 100 TeV gamma-rays with a 50 h observation out to ~ 4 Mpc (this is reduced to 3 Mpc if the spatial extent of the CSM is shrunk to 2x10^15 cm). These results suggest that early 100 TeV observations of nearby Type II-P SNe can probe PeV CR acceleration in sufficiently dense and extended CSM.

Can quantum entanglement continue to grow even after the entanglement entropies of subsystems have saturated? We address this question using genuine multi-entropy, which probes multi-partite entanglement structure beyond bipartite entanglement. In a two-sided BTZ black hole, this quantity grows linearly with time after every subsystem entropy of a fixed tripartition has saturated, extending the interval in which entanglement detects Einstein-Rosen bridge growth. The result refines the ER=EPR relation by identifying multi-partite structure invisible to ordinary entanglement entropies. Some spin-chain models and the spatially partitioned Sachdev-Ye-Kitaev (SYK) model exhibit distinct transients, while the late-time plateau values in holography, the SYK model, and Haar-random states share a universal behaviour.

We establish unbounded two-use Holevo additivity gaps in finite dimensions. For each sufficiently large fixed integer $K$ and all sufficiently large $n$, we construct channels $T_n$ with output dimension $K^n$, input dimension $\exp(\Theta_K(n^2))$, and \[ \chi(T_n^{\otimes2})-2\chi(T_n) \ge n\left[\frac{\log_2K}{K}-2\log_2(1+9/K)\right]-O(1/n). \] The gap is linear in output qubits, with an explicit quadratic input-qubit cost and an explicit threshold on $n$. We also obtain channels whose single-use Holevo quantity tends to zero while their two-use Holevo information, and hence classical capacity, diverges. The channels arise from structured tensor products of the complementary mixed-unitary channels used in Collins's free-probabilistic proof. We establish minimum-output-entropy gaps by combining Collins–Youn's product-group Haagerup inequality with Bordenave–Collins's quantitative strong-convergence estimates. We also provide a Lean certificate for our proofs.

The void probability function (VPF) is the likelihood of finding no tracers (galaxies or dark-matter haloes) within a given volume and is sensitive to the large-scale matter distribution. We investigate the VPF of dark matter haloes and galaxies using the Quijote N-body simulations across a range of cosmological models, including $\Lambda$CDM and several extensions. We examine its dependence on cosmology, redshift, halo mass, morphology, and sample dilution, and compare the results with theoretical predictions from the geometric hierarchical (GH) and negative binomial (NB) models. We find that the halo VPF is sensitive to cosmology and halo mass and follows the GH model at $z=0$, with $\Lambda$CDM showing the smallest deviation and the massive-neutrino cosmology the largest. At higher redshift and stronger sample dilution, the VPF departs from the GH model and approaches the NB model. The dependence on halo mass varies with cosmology, with low-mass haloes showing the largest deviations in $\Lambda$CDM, while intermediate- and high-mass haloes show stronger deviations in the modified-gravity scenario. In redshift space, the VPF shifts toward the NB model, with primordial non-Gaussianity producing the largest deviations. For galaxies, the VPF depends on morphology and cosmology, with ellipticals following the GH model and spirals following the NB model. We also find that cosmic variance introduces non-negligible scatter in the VPF measurements. Overall, these results suggest that the VPF could be useful as a computationally efficient probe to distinguish extensions of the standard $\Lambda$CDM model in upcoming large-volume galaxy surveys.

We develop a geometric framework in which classical thermodynamics is reformulated as a Hamiltonian dynamical system. An explicit canonical mapping $(q,p,t,H)\leftrightarrow(V,-P,S,-T)$ identifies Maxwell's relations as the characteristic equations of the thermodynamic Poincaré–Cartan one-form, in direct parallel with Hamilton's equations of motion. Treating thermodynamic potentials as action functionals, a variational principle recovers both the Maxwell relations and the thermodynamic constraints (adiabaticity, isothermality) as conserved first integrals. For adiabatic processes in an ideal gas, this yields explicit second-order ordinary differential equations for $V(T)$ and $P(T)$, each governed by a temperature-dependent Lagrangian. Assembling the component Lagrangians into a multi-parameter Lagrangian 1-form $\mathcal{L}$, we prove that the closure condition $d\mathcal{L}=0$ holds on the solution manifold, establishing that path-independence of thermodynamic state functions is a geometric consequence of multi-time integrability rather than an independent postulate.

We give a direct proof of the Burke property for the stationary O'Connell-Yor polymer using Stein's method. Building on a free energy identity developed in joint work with Firas Rassoul-Agha, Xiao Shen, and Guangqu Zheng, we establish a multilevel extension that yields a joint Gaussian-Gamma Stein identity, from which the full Burke property follows. The proof is based on a Gaussian integration-by-parts framework developed in that work. Passing to zero temperature gives the corresponding result for stationary point-to-line Brownian last-passage percolation.

Heisenberg originally envisioned the error-disturbance relation under the premise that the state after measurement must remain consistent with the Kennard-Robertson uncertainty relation. This implies that the measurement error must be formulated via a posterior observable $\hat{x}_t$, rather than a prior observable $\hat{x}_0$, because the posterior measurement error determines the post-measurement uncertainty of the electron. Building upon the preliminary conceptual foundation reported in arXiv:1504.03779, this paper presents a rigorous derivation of the error-disturbance principle formulated from the unitary transformation equations of observables. Each readout $X$ of a posterior probe observable $\hat{X}_t$ completes a single measurement event, producing a specific conditional object state. The Kennard-Robertson uncertainty relation must hold for these states. Specifically, we show that the uncertainty relation between the error $\epsilon_{X}(\hat{x}_t)$ and the disturbance $\eta_{X}(\hat{p}_0)$ holds strictly at the level of individual measurements, characterized by the specific readout $X$. We also verify that conventional error-disturbance relations, where the errors are evaluated by averaging over the unconditioned state, hold true. Our results provide a refined theoretical basis for understanding the fundamental trade-off in individual measurement outcomes.

Feasibility-preserving mixer Hamiltonians offer an attractive alternative to penalty encodings for constrained quantum optimization, yet how enforcing constraints alters the state space reachable by the Quantum Approximate Optimization Algorithm (QAOA) remains largely unexplored. We address this question within the context of the Maximum Independent Set (MIS) problem. Alongside the standard controlled bit-flip mixer, we analyze the alternative $\mathit{Flip\text{-}or\text{-}Stay}$ mixer, whose restriction to the feasible subspace $W_{\mathcal{F}}$ corresponds precisely to the shifted negative Laplacian of the independent-set reconfiguration graph. Although both mixers induce identical transitions between independent sets, the diagonal modification changes the spectral structure and can substantially enlarge the set of reachable quantum states. For every connected input graph with at least two vertices, we prove that independently parameterized local controls associated with either mixer generate the full unitary Lie algebra on the feasible subspace. Standard QAOA exhibits a more nuanced algebraic structure. We prove that the dynamical Lie algebra associated with MIS-QAOA employing the conventional mixer embeds into its Flip-or-Stay counterpart. Furthermore, we construct an infinite family of graphs for which the corresponding vacuum-state dynamical group orbits exhibit strictly distinct dimensions, establishing a qualitative expressivity separation between the two architectures. For either mixer, we show that standard QAOA initialized in the empty set can prepare a state supported entirely on maximum independent sets at finite depth. For the free architectures, we also derive an exact loss-variance formula in the unitary-design limit, expressed through the number of feasible independent sets and the variance of their cardinalities.

We study the Loschmidt echo in a system of N non-interacting spinless lattice fermions released from a double-domain-wall initial state. In the large-N limit, the return probability is characterized by a large-deviation rate function known as the dynamical free energy. The Loschmidt echo is dominated by a complex instanton configuration, and the dynamical free energy develops a logarithmic singularity at the dynamical quantum phase transition. We obtain analytical results in the short-time and long-time regimes and support them with numerical computations. We show that the transition can be understood as a topological change of the dominant instanton configuration, analogous to the emergence of a cut in random matrix theory. We further show that post-selection can drive the system through two successive DQPTs, associated with successive topological changes of the dominant instanton configuration in complex time.

We propose a new source of neutrino decoherence arising from stochastic gravitational lensing by unresolved mass substructure. Unlike traditional models that treat the lensing potential as smooth and deterministic, we decompose the lensing potential into a smooth component and a stochastic population of compact clumps. The substructure induced fluctuations of the lensing potential generate stochastic corrections to the neutrino time delay, thereby producing random relative phases between different neutrino mass eigenstates. Averaging over the clump ensemble converts these phase fluctuations into an effective dampening of flavour coherence. This framework connects stochastic gravitational lensing with neutrino phenomenology and offers a novel route to probe dark matter substructure through astrophysical neutrino flavour transitions.

We develop a Dirichlet-form framework for relaxation and steady-state entropy production in preconditioned Langevin stochastic partial differential equations. In infinite dimensions, the usual Fokker–Planck calculations based on ambient Lebesgue densities and the corresponding probability-current densities are generally unavailable. For the detailed-balance class, a quasi-regular symmetric Dirichlet form on the Gibbs state space yields an exact de Bruijn entropy-dissipation formula for regular densities and an integrated inequality for arbitrary finite-entropy initial laws. Self-adjointness gives detailed balance and stationary path reversal, while a coordinate-martingale criterion identifies the associated process with the prescribed SPDE. For the one-dimensional $\Phi^4_1$ and convex Allen–Cahn-type Gibbs dynamics, we combine the established strong well-posedness theory with direct verification of the logarithmic derivatives, form closure, quasi-regularity and form–SPDE correspondence, and obtain relative-entropy decay bounds with exponents $2$ and $2(1-\lambda/m)$, respectively, with $m>\lambda$ in the latter case. Away from detailed balance, bounded skew-adjoint linear forcing preserves a Gaussian invariant law without requiring commutation between the forcing and covariance. We identify the antisymmetric action on cylinder observables and its Cameron–Martin current and prove that the squared current energy equals the steady-state entropy-production rate defined by forward–reverse path-space relative entropy per unit time, as well as the monotone limit of the Galerkin rates. Under commutation, we additionally obtain an explicit transient Onsager decomposition after a mass quench. Exclusion processes and Gaussian rotors provide finite-state and Gaussian benchmarks.