We show that networks of quantum frames of reference, in which one frame may be used to produce multiple other frames that in their turn prepare systems which may interact with one another, have counterintuitive properties that make following the exchange of conserved quantities very subtle, and raise questions about the very nature of conserved quantities. In addition, we present an alternative approach to analysing quantum reference frames that we believe will be useful in discussions related to quantum frames of reference.

Quantum communication networks require transmission of high-fidelity, uncoded qubits for applications such as entanglement distribution and quantum key distribution. However, current implementations are constrained by limited buffer capacity and qubit decoherence, which degrades qubit quality while waiting in the buffer. A key challenge arises from the stochastic nature of qubit generation, there exists a random delay (D) between the initiation of a generation request and the availability of the qubit. This induces a fundamental trade off early initiation increases buffer waiting time and hence decoherence, whereas delayed initiation leads to server idling and reduced throughput. We model this system as an admission control problem in a finite buffer queue, where the reward associated with each job is a decreasing function of its sojourn time. We derive analytical conditions under which a simple "no lag" policy where a new qubit is generated immediately upon the availability of buffer space is optimal. To address scenarios with unknown system parameters, we further develop a Bayesian learning framework that adaptively optimizes the admission policy. In addition to quantum communication systems, the proposed model is applicable to delay sensitive IoT sensing and service systems.

We prove that there is only one translation-invariant Gibbsian point process w.r.t. to a chosen interaction if any of them satisfies a certain bound related to concentration-of-measure. This concentration-of-measure bound is e.g. fulfilled if a corresponding modified logarithmic Sobolev inequality holds. In particular, for natural examples with non-uniqueness regimes, a modified logarithmic Sobolev inequality cannot be satisfied. Therefore, in these situations, the free-energy dissipation in related continuous-time birth-and-death dynamics in $\mathbb{R}^d$ is not exponentially fast.

In the context of the Scintillating Fibre (SciFi) Tracker for the LHCb Upgrade 2, radiation-induced damage in silicon photomultipliers (SiPMs) has been studied over a wide temperature range, from room temperature down to 100 K. With the LHCb detector Upgrade 1, installed during the LHC's Long Shutdown 2 (LS2) (2019-2021), the first large-scale SciFi tracker read out by multichannel silicon photomultipliers (SiPMs) was constructed, installed, and has been operated ever since. A major challenge for the SciFi tracker is the neutron radiation at the SiPMs' location. At the end of the lifetime of the Upgrade 1 detector, the expected neutron fluence for the SiPMs will reach 6e11 neq/cm^2. Cryogenic operation is being investigated to mitigate even higher radiation-induced damage for Upgrade 2, where the total neutron fluence is expected to reach 3e12 neq/cm^2. A large set of custom SiPM arrays, varying in pixel size, electric field configuration, and doping implant concentration, developed by FBK and Hamamatsu, were tested after neutron irradiation. Characterisation was performed in a dedicated cryogenic test setup, where the operating temperature was varied over a wide range. Key performance parameters such as breakdown voltage, gain, dark count rate, optical crosstalk, and afterpulsing were characterised as functions of temperature, overvoltage, and neutron fluence. The result is a precise assessment of radiation damage for state-of-the-art technology from two leading SiPM manufacturers, allowing the results to be transferred to other SiPM applications.

We study the algebraic exceptional set for surfaces (S,B) of log general type, when B has at least three irreducible components; we prove that in most cases it is finite or empty.

Despite extensive research, the precise spin Hamiltonian of the van der Waals antiferromagnet NiPS$_3$ -- which hosts a zigzag-ordered ground state -- remains debated. While consensus has emerged on ferromagnetic nearest-neighbor ($J_1$) and antiferromagnetic third-nearest-neighbor ($J_3$) Heisenberg interactions, recent studies suggest a biquadratic ($B$) exchange term may also play a role, though its estimated magnitude varies widely. To address this controversy, we perform density functional theory calculations and extract a positive biquadratic interaction with $B/J_3 \approx 0.44$. Within the minimal $J_1$-$J_3$-$B$ model, we show that these parameters naturally stabilize zigzag ordering using minimally augmented spin-wave theory. Density-matrix renormalization group calculations further validate our extracted parameters as a reasonable description of the ground state. Although fully resolving the spin Hamiltonian of NiPS$_3$ requires further investigation, our findings provide new insights into its biquadratic interaction.

In all forms of the local Langlands program the abelian category of smooth representations of p-adic groups G in vector spaces over a field k plays a central role. Of particular interest are its finiteness properties. If the field k has characteristic zero then, by work of Bernstein, this category is most of the time locally noetherian. But if the field has characteristic p then this remains the case only for very special groups. The basic idea of this paper is that if G is an amalgam, i.e., a colimit of certain subgroups then this is reflected by Mod(G) being the limit of the corresponding categories for these subgroups. This allows to deduce finiteness properties of Mod(G) from finite properties of the categories in the limit diagram.

Stimulated Brillouin-Mandelstam scattering offers exceptional capabilities for photonic signal processing, but current platforms demand performance trade-offs between long interaction lengths, high gain, low optical losses, and practical implementation. Here, we demonstrate a novel platform based on the reversible freezing of a carbon disulfide filled liquid-core optical fiber. This approach delivers a giant in-fiber Brillouin gain of 434 W-1m-1 with a linewidth of 24 MHz, while maintaining low propagation losses in a fully spliced architecture and providing the potential for meter-scale interaction lengths. Leveraging this gain, as a proof of principle, we realize an optoacoustic memory operating at sub-nanojoule pulse energies - more than two orders of magnitude lower than state-of-the-art implementations. This power reduction is universal for Brillouin-based fiber applications in general and will enable low-power photonic signal processing and neuromorphic computing, efficient microwave photonics and sensing, as well as in-fiber quantum optomechanics-based technologies.

We present HEALFormer, a transformer-based neural network architecture for weak gravitational lensing mass mapping that reconstructs convergence maps from incomplete and noisy shear observations on the celestial sphere. The model operates directly on the Hierarchical Equal Area isoLatitude Pixelization and employs learnable mask tokens to handle arbitrary survey geometries without requiring preprocessing. Through a progressive training strategy, HEALFormer efficiently processes high-resolution maps up to Nside = 1024 and demonstrates excellent performance across diverse survey footprints including KiDS, DES, DECaLS, and Planck. The model generalizes robustly to cosmological parameters beyond its training set, producing nearly unbiased reconstructions with superior noise suppression compared to traditional Kaiser-Squires and Wiener filter methods. Remarkably, HEALFormer exceeds the theoretical phase recovery limits of linear reconstruction methods at small scales, achieving a fundamental breakthrough in weak lensing analysis. The combination of computational efficiency, reconstruction accuracy, and adaptability to varying survey configurations makes HEALFormer well-suited for current and next-generation cosmological surveys. Code is available at GitHub.

We obtain exact expressions for the quasinormal modes (QNMs) of the massive scalar, fermionic and vector perturbations around a rotating BTZ-like black hole in the Einstein-bumblebee gravity. We find that the Lorentz symmetry breaking (LSB) parameter $\ell$ leaves its imprint only on the imaginary parts of the quasinormal frequencies and the corresponding perturbation field decays more slowly for a larger $\ell$, except for the left-moving quasinormal frequencies $ω_L$ with positive mass and the right-moving ones $ω_R$ with negative mass for the fundamental modes under the vector perturbation where the imaginary parts are independent of $\ell$. We also note that, regardless of the kind of perturbations, the real parts depend only on the angular quantum number, which are the same as those in the standard BTZ black hole. Furthermore, we investigate the AdS/CFT correspondence from the QNMs and observe that the expected universal relation for the left and right conformal weights ($h_L,h_R$) of the boundary operators dual to various fields still holds even for the BTZ-like black hole in the Einstein-bumblebee gravity. These results strongly support the AdS/CFT correspondence and could help us better understand the Einstein-bumblebee gravity with the Lorentz symmetry violation.

This study investigates the simultaneous use of multiple metadata schemas at research data repositories. The analysis covers how eight disciplinary research data repositories from the geosciences and social sciences use disciplinary metadata schemas and the DataCite Metadata Schema, and how two metadata records describing the same dataset compare. The results show that DataCite metadata records could be improved considerably by optimizing schema crosswalks. However, the parallel use of disciplinary and multidisciplinary metadata records is complex. For example, discipline has a significant effect on the completeness of DataCite metadata. A temporal analysis also highlights that metadata workflows are diverse, and in some cases, suboptimal crosswalks are likely not the sole cause of incomplete DataCite metadata. Comparing the disciplinary metadata schemas and the DataCite Metadata Schema on a structural level reveals that most differences between schemas are the result of different approaches to modelling statements about datasets, not the lack of opportunity to express them. The element sets of both disciplinary metadata schemas and the DataCite Metadata Schema could be extended to describe datasets in more detail. These observations demonstrate that disciplinary and multidisciplinary metadata schemas serve distinct purposes. Disciplinary repositories should take full advantage of the opportunities both options provide.

The astrophysical $S$-factor for the proton-proton fusion is calculated in the low-energy regime for a variety of nuclear interactions and consistent nuclear currents, derived within chiral effective field theory. We estimate, for the first time, the theoretical uncertainty on the $S$-factor due to the truncation of the chiral expansion of the currents using a Bayesian analysis. In order to reach an accuracy at the percent level in the calculation, the electromagnetic potential includes contributions beyond the leading Coulomb interaction, such as two-photon exchange and vacuum polarization. The initial proton-proton state is expanded in partial waves and only the ${}^1S_0$ contribution is included, as it is known that the other partial-waves effects are negligible. The low-energy constant entering the contact term in the weak axial current operator is calibrated to reproduce the Gamow-Teller matrix element in Tritium $β$-decay. The value $S(0)$ is found to be $S(0)=(4.068 \pm 0.025)\times 10^{-25} \: \text{MeV}\: \text{b}$.

In this work, we derive the bipartite density matrix for the $e^{+}e^{-} \rightarrow J/ψ\rightarrow Λ(pπ^{-}) \barΛ(\bar{p}π^{+})$ process at BESIII. We evaluate the impact of mass corrections and memory effects (within Markovian and non-Markovian regimes) on quantum correlations even beyond entanglement. The dependence of these quantum properties on the scattering angle $φ$ is analyzed, with a particular focus on the impact of mass corrections. By comparing massless and mass-corrected scenarios, we demonstrate that the inclusion of mass effects enhances the maximum violation of the Bell inequality. While the qualitative temporal behavior remains unchanged, mass corrections quantitatively modify the angular distribution and introduce additional extrema at $φ=0$ and $φ=π$, thereby strengthening non-local correlations without altering their fundamental dynamical origin. An examination of the hierarchy of quantum correlations in baryon-antibaryon systems yields partial confirmation: $\text{Bell Nonlocality} \subset \text{Steering} \subset \text{Entanglement} \subset \text{Discord}$. Additionally, our results show that classical correlations serve to mitigate the decoherence and the decay of quantum correlations. This interplay between classical and quantum correlations suggests practical applications in quantum information and provides a robust framework for investigating baryon-antibaryon interactions.

We establish a Cramér-type moderate deviation theorem for double-index permutation statistics (DIPS). To the best of our knowledge, previous results only provided Berry-Esseen type bounds for DIPS, which cannot yield moderate deviation results and are insufficient to capture the optimal convergence rates for some relatively sparse DIPS. Our result overcome these limitations: it not only recover the optimal convergence rates for classical DIPS, such as the Mann-Whitney-Wilcoxon statistic, but also extend to sparse statistics, including the number of descents in permutations and Chatterjee's rank correlation coefficient, for which previous approaches do not apply. To prove this result, we establish a Cramér-type moderate deviation of normal approximation for bounded exchangeable pairs. Compared with existing results, our theorem requires more easily verifiable conditions.

A measurement is presented of dijet angular distributions in proton-proton collisions at $\sqrt{s}$ = 13 TeV, using data collected with the CMS detector at the CERN LHC and corresponding to an integrated luminosity of 138 fb$^{-1}$. For the first time, the dijet angular distributions, corrected for detector effects, are compared with the predictions of perturbative quantum chromodynamics at next-to-next-to-leading order, including next-to-leading-order electroweak corrections. While data are generally found to be in agreement with predictions, a small difference in shape of the normalized distributions is seen for dijet masses ranging from 2.4 to 4.8 TeV and above 6 TeV. The distributions are used to search for proposed signatures of quark compositeness, extra spatial dimensions, quantum black holes, dark-matter mediators, axion-like particles, and anomalous gluon couplings. The most stringent limits to date are set for most of these scenarios. Quark contact interactions are excluded at 95% confidence level (CL) up to a scale of 17 (37) TeV for destructive (constructive) interference in a benchmark scenario, valid to next-to-leading order in quantum chromodynamics, and in which only left-handed quarks participate. The coupling of axion-like particles to the gluon, $c_{\text{g}}/f_{\text{a}}$, is constrained to be lower than 0.42 TeV$^{-1}$ at 95% CL. The anomalous triple-gluon coupling, $C_{\text{G}}/Λ^2$, in a standard model effective field theory is constrained to be lower than 0.0076 TeV$^{-2}$ at 95% CL.

Buoyancy-driven convection in porous media governs heat and mass transport in a wide range of natural and engineered systems, from groundwater aquifers and geothermal reservoirs to carbon storage in geological formations and flows through planetary interiors. Yet the transient regime, in which fingering flows emerge and transport is strongly enhanced, is still described largely through empirical scaling laws, limiting predictive capability across conditions. Here we show that transient porous buoyancy-driven mixing obeys exact time-dependent balances that couple transport, flow intensity, and scalar dissipation. These balances remain accurate when restricted to the actively mixing layer, revealing that the essential dynamics are localized within a finite region. Leveraging these results, we derive a minimal one-parameter closure for the mean scalar field. The theory we propose predicts self-similar mean profiles, universal second-order statistics, and a linear transport law without case-by-case tuning. Direct numerical simulations up to spatial resolution of $2048\times2048\times16384$ points validate these predictions. Our results place transient porous mixing on a predictive footing, showing how macroscopic transport laws emerge from exact balances and self-similar dynamics, and provide a general framework for buoyancy-driven transport in porous media.

In this paper, we study the homogeneous components of the Chern--Schwartz--MacPherson (CSM) classes of Schubert cells. We prove that, under suitable conditions, each such component is represented by an irreducible subvariety. In particular, our result extends Huh's result \cite{Huh} by relaxing the regularity assumption on log resolutions. As a consequence, the conclusion holds for all cominuscule Schubert cells of classical type and for a large family of exceptional cases. We also obtain analogous results for certain Schubert varieties in symplectic Grassmannians and flag varieties.

In a dataset of 423 patients who had had radical prostatectomy for localised prostate cancer we estimated the apparent Shannon information (ASI) about time to biochemical recurrence in various subsets of the available pre-op variables using a Bayesian Gamma-power-mixture survival regression model. In all the subsets examined the ASI was positive with posterior probability greater than 0.975 . Using only age and results of pre-operative blood tests (PSA and biomarkers) we achieved 0.232 (0.180 to 0.290) nats ASI (0.335 (0.260 to 0.419) bits) (posterior mean and equitailed 95% posterior confidence intervals). This is more than double the mean posterior ASI previously achieved on the same dataset by a subset of the current authors using a log-skew-Student-mixture model, and is greater than that previous value with posterior probability greater than 0.99 . Additionally using pre- or post-operative Gleason grades, operative findings, clinical stage, and presence or absence of extraprostatic extension or seminal vesicle invasion did not increase the ASI extracted. However removing the blood-based biomarkers and replacing them with either pre-operative Gleason grades or findings available from MRI scanning greatly reduced the available ASI to respectively 0.077 (0.038 to 0.120) and 0.088 (0.045 to 0.132) nats (both less than the values using blood-based biomarkers with posterior probability greater than 0.995). A greedy approach to selection of the best biomarkers gave TGFbeta1, VCAM1, IL6sR, and uPA in descending order of importance from those examined.

Momentum twistors for scattering amplitudes in particle physics are lines in three-space. We develop Landau analysis for Feynman integrals in this setting. The resulting discriminants and resultants are identified with Hurwitz and Chow forms of incidence varieties in products of Grassmannians. We study their degrees and factorizations, and the kinematic regimes in which the fibers of the Landau map are rational or real. Identifying this map with the amplituhedron map on positroid varieties, and the associated recursions with promotion maps, yields a geometric mechanism for the emergence of positivity and cluster structures in planar N=4 super Yang-Mills theory.

The Pareto sum of two-dimensional point sets $P$ and $Q$ in $\mathbb{R}^2$ is defined as the skyline of the points in their Minkowski sum. The problem of efficiently computing the Pareto sum arises frequently in bi-criteria optimization algorithms. Prior work establishes that computing the Pareto sum of sets $P$ and $Q$ of size $n$ suffers from conditional lower bounds that rule out strongly subquadratic $O(n^{2-ε})$-time algorithms, even when the output size is $Θ(n)$. Naturally, we ask: How efficiently can we \emph{approximate} Pareto sums, both in theory and practice? Can we beat the near-quadratic-time state of the art for exact algorithms? On the theoretical side, we formulate a notion of additively approximate Pareto sets and show that computing an approximate Pareto set is \emph{fine-grained equivalent} to Bounded Monotone Min-Plus Convolution. Leveraging a remarkable $\tilde{O}(n^{1.5})$-time algorithm for the latter problem (Chi, Duan, Xie, Zhang; STOC '22), we thus obtain a strongly subquadratic (and conditionally optimal) approximation algorithm for computing Pareto sums. On the practical side, we engineer different algorithmic approaches for approximating Pareto sets on realistic instances. Our implementations enable a granular trade-off between approximation quality and running time/output size compared to the state of the art for exact algorithms established in (Funke, Hespe, Sanders, Storandt, Truschel; Algorithmica '25). Perhaps surprisingly, the (theoretical) connection to Bounded Monotone Min-Plus Convolution remains beneficial even for our implementations: in particular, we implement a simplified, yet still subquadratic version of an algorithm due to Chi, Duan, Xie and Zhang, which on some sufficiently large instances outperforms the competing quadratic-time approaches.

In this article, we study the mixed Steklov--Neumann eigenvalue problem on doubly connected domains. First, we show that among all doubly connected domains in $\mathbb{R}^n$ of the form $B_{R_2}\setminus \overline{B_{R_1}}$, where $B_{R_1}$ and $B_{R_2}$ are open balls of fixed radii satisfying $\overline{B_{R_1}} \subset B_{R_2}$, the first non-zero Steklov--Neumann eigenvalue attains its maximal value when the balls are concentric. Next, we establish bounds for the first non-zero Steklov--Neumann eigenvalue on a doubly connected star-shaped domain contained in a hypersurface equipped with a revolution-type metric. We also derive the asymptotic behavior of the first non-zero Steklov--Neumann eigenvalue on a bounded domain with a spherical hole in $\mathbb{R}^n$ as the radius of the hole approaches zero. Finally, we study the number of nodal domains of the eigenfunction corresponding to the first non zero Steklov--Neumann eigenvalue on a bounded domain in $\mathbb{R}^n$ having a spherical hole.

Biomolecular condensates organize biochemical processes by spatially concentrating molecules while allowing for dynamic exchange with their surroundings. However, transport across their interface can be strongly attenuated, leading to enhanced retention and preferential internal mixing. Two key mechanisms have been proposed to describe this behavior: biased interfacial reflectivity, which compares how strongly particles are reflected at the interface when attempting to enter or leave the condensate, and interfacial resistance, which sets the kinetic rate at which particles can cross the interface. Quantifying these parameters experimentally has remained challenging. Here, we present a theoretical and experimental framework to address this issue, extending our previously developed half-FRAP approach. We solve the spherical diffusion problem with a semipermeable interface by spectral decomposition. By evaluating the information content of the integrated recovery curves, we show that they encode sufficient information to recover interfacial parameters over extended regions of parameter space. Applying our framework to tunable coacervates composed of poly-lysine and hyaluronic acid, we find that their interfaces exhibit strongly biased reflectivity and substantial resistance, both driving preferential internal mixing. These parameters depend on salt concentration, linking interfacial transport to intermolecular interaction strength and position in the phase diagram. Our results establish a quantitative connection between interfacial properties and condensate dynamics, revealing how their interplay gives rise to distinct transport regimes.

Strong solar activity is often accompanied by a variety of radio bursts. These bursts are valuable diagnostics of coronal and heliospheric processes and also have potential applications in space weather monitoring and forecasting. However, space weather applications require low-latency, high-sensitivity radio burst recording and reporting capabilities, which have remained limited. In this work, we present the development of a near-realtime radio burst recording and reporting system using the Owens Valley Radio Observatory Long Wavelength Array. The system directly clips data from a realtime buffer and streams them as a live radio dynamic spectrogram. These spectrograms are then processed by a deep-learning-based burst identification module for type III radio bursts. The identifier is based on a YOLO (You Only Look Once) architecture and is trained on synthetic type III radio bursts generated using a physics-based model to achieve accurate and robust detection. This system enables continuous realtime radio spectrum streaming and automatic reporting of type III radio bursts within approximately 10 seconds of their occurrence.

Phase transitions between crystalline solids occur either through the nucleation and growth mechanism, a process that is slow and destructive or through the diffusion-less and order preserving Martensitic route. In both organic and inorganic materials, Martensitic transformations are known to occur only between phases with crystalline symmetry. We demonstrate here that for canonical discotic organic semiconductor HAT6, the transition between the liquid crystalline columnar hexagonal phase (ColH) and the crystalline solid can occur through a mechanism that exhibits the hallmarks of Martensitic transformations: orientational correlations between parent and daughter phases, structural reversibility, and ultrafast kinetics. To access Martensitic-like solidification, the ColH phase of HAT6 is biaxially aligned in lithographically defined microchannels and crystallization is induced on deep supercooling. The transition mechanism is studied using a combination of polarized optical microscopy and X-ray scattering. At the largest accessible supercooling, the ColH - Crystal phase transition occurs at speeds of ~100 micrometer/s, a value that is seven orders of magnitude greater than the theoretical prediction for growth from isotropic melts. Our work suggests that Martensitic-like transformations can occur even between liquid crystals and crystals and are therefore more general than previously believed. Further, our work demonstrates that Martensitic-like transformations of anchored liquid crystals can be used to grow biaxially aligned crystals of organic molecules over arbitrarily long distances. As lattice alignment over large areas is desirable for devices like field-effect transistors and as several high-performance molecular semiconductors exhibit a ColH phase, our results hold general significance for organic electronics.

If the universe follows a specific design, then a central question is which cost function is optimized by the observed forces. This is the problem of inverse optimal control, or inverse reinforcement learning, in which a reward function is inferred from the dynamics of the observed system. We first establish the {\em least cost principle}, whereby the laws of motion can be derived from minimization of a time-discounted integral of the acceleration cost minus a state-dependent reward function. After determining the functional form of the acceleration cost from basic principles, we infer the reward function from the laws of motion governing classical gravitation and Coulomb forces. The inferred reward function is high when pairs of particles have high relative velocities and when their relative motion is orthogonal to their distance vectors. All in all, our work suggests that relative motion and quasi-circular orbits are the dynamical and static features optimized by central forces in nature.

Using Parker Solar Probe measurements of the solar wind, we demonstrate that $β_{\parallel}$ is the main driver that determines which instabilities limit proton temperature anisotropy. At radial distances from 10 to 30 solar radii, $β_{\parallel}<1$ drives electromagnetic ion-cyclotron and parallel firehose instabilities, in contrast to the situation at 1 astronomical unit, where, due to most $β_{\parallel}>1$, mirror and oblique firehose modes are dominant instead. Furthermore, we show that the temperature anisotropy radially evolves following the semi-empirical anti-correlation $T_\perp/T_\parallel\simβ_\parallel^{-0.55}$, consistent with observations at larger distances from the Sun.

Text-guided diffusion models have advanced image editing by enabling intuitive control through language. However, despite their strong capabilities, we surprisingly find that SOTA methods struggle with simple, everyday transformations such as rain or blur. We attribute this limitation to weak and inconsistent textual supervision during training, which leads to poor alignment between language and vision. Existing solutions often rely on extra finetuning or stronger text conditioning, but suffer from high data and computational requirements. We argue that diffusion-based editing capabilities aren't lost but merely hidden from text. The door to cost-efficient visual editing remains open, and the key lies in a vision-centric paradigm that perceives and reasons about visual change as humans do, beyond words. Inspired by this, we introduce Visual Diffusion Conditioning (VDC), a training-free framework that learns conditioning signals directly from visual examples for precise, language-free image editing. Given a paired example -one image with and one without the target effect- VDC derives a visual condition that captures the transformation and steers generation through a novel condition-steering mechanism. An accompanying inversion-correction step mitigates reconstruction errors during DDIM inversion, preserving fine detail and realism. Across diverse tasks, VDC outperforms both training-free and fully fine-tuned text-based editing methods. The code and models are open-sourced at https://omaralezaby.github.io/vdc/

In semiconductor nanostructures, optical excitation typically creates bound electron-hole states, such as excitons, trions, and larger complexes. Their relative motion is described by the Wannier equation, which is valid only for spatially extended motion in the Coulomb-dominated, weak-confinement limit. Other small nanostructures, such as quantum dots, are in the confinement-dominated strong confinement regime, where the wavefunction factorizes into independent electron and hole parts. Nanoplatelets are in between the two regimes and require solving an unfactorized higher-dimensional Schrödinger equation, which is computationally expensive. This work demonstrates how tensor networks can partially overcome this problem, using CdSe nanoplatelets as an example. The method is also applicable to related two-dimensional systems. As a demonstration, we calculate the excitonic and trionic ground states, as well as several excited states, for nanoplatelets of varying sizes, including their energies and oscillator strengths. More importantly, overall strategies for using tensor networks in real space for systems under intermediate confinement have been developed.

It is shown that the nonselfadjoint (and non-normal) linear ordinary differential operators of a certain class are spectral operators of scalar type in the sense of Dunford and Bade. Operators of this kind appear in physical problems such as the scattering of spin waves by magnetic solitons.

In this short note we observe that the gamma factor defined by Gelfand and Kazhdan coincides with the Rankin-Selberg root number defined by Jacquet, Piatetskii-Shapiro and Shalika.