Spacetimes with a thin shell offer a framework where both the dynamical stability and the thermodynamical stability of the matter comprising the shell can be consistently studied. In the present work, we consider the dynamical and thermodynamical stability of a spherical thin shell in Einstein gravity coupled to Born-Infeld electrodynamics. For our construction, we adopt the extremally charged solution of the theory, which offers a closed analytic form for the horizon location that allows for a clear derivation of the corresponding physical quantities of interest. Under this scenario, the dynamical stability conditions under radial perturbations are readily obtained in terms of an effective potential. The complete equilibrium thermodynamics for such a shell is presented. We find that, despite a non-zero pressure at the shell (unlike the extremally charged Reissner-Nordström counterpart), its entropy is solely characterized as a function of the gravitational radius. We propose a physically suitable \emph{ansätze} for the relevant equations of state in order to obtain a closed expression for the entropy density of the shell. We find that the thermodynamical stability conditions reduce to a single inequality related to exchanges of the charge at the shell, which determines the domain where both dynamical and thermodynamical stable configurations exist.

Researchers worldwide have drawn inspiration from nature to optimize network design and dynamics. Some of the wonders of the living world exhibit remarkable abilities in generating efficient and resilient spatial structures. By mimicking biological strategies, transportation infrastructures could be profoundly rethought. This paper aims to provide the basis for a biomimicry framework for addressing transportation networks. In light of examples from the literature, the relevance of such a framework for advancing research in nature-inspired networks is demonstrated, with the aim of achieving resilience and efficiency.

Two-dimensional (2D) spectroscopy combines high temporal and spectral resolution, allowing the observation of ultrafast energy transfer and the separation of homogeneous and inhomogeneous broadening. Typically, 2D spectroscopy is dominated by the lowest-order nonlinear signal for a given phase-matching configuration while signals of higher order are present but difficult to access separately. Recently, we introduced a technique to separate nonlinear orders in 2D spectroscopy by systematically varying the intensity of the pump pulses and appropriate post-processing. Here, we unravel the full potential of higher-order 2D spectroscopy by separating multiple nonlinear orders at different multi-quantum positions. As an example, we investigate a squaraine dimer. Using a theoretical model, we find excellent qualitative and quantitative agreement throughout all nonlinear orders and multi-quantum positions. Our simulations demonstrate the sensitivity and information content hidden in the higher-order spectra such as transition dipole moments and energy levels even of highly excited states. Our results pave the way for establishing higher-order spectroscopy as a unique extension of multidimensional spectroscopy, providing access to highly excited states and their properties encoded in successive orders of nonlinearity.

We study the solution of symmetric positive-definite linear systems by way of families of full- and limited-memory methods. Our contributions are threefold. We first derive new relationships between the conjugate-gradient method (CG) and quasi-Newton methods of the Broyden class that refine existing results, and clarify when those methods generate the same iterates and enjoy quadratic termination. We extend this perspective to the limited-memory BFGS (LBFGS) method. Next, we examine how DIOM, a limited-memory variant of the full orthogonalization Krylov method (FOM), is akin to LBFGS in that it provides a memory lever that is critical in practical performance. Finally, we generalize LBFGS and DIOM to the computation of trust-region steps for unconstrained, potentially nonconvex, optimization. We report numerical experience on positive-definite linear systems and unconstrained optimization problems. The results show that memory is a key algorithmic lever: LBFGS and DIOM are consistently more robust than CG and often achieve comparable accuracy with fewer Hessian-vector products. They emerge as viable alternatives to CG when high accuracy is desirable or when operations with the Hessian are at a premium. The limited-memory SR1 (LSR1) method can be competitive in full-memory form, but its limited-memory variant suffers from discarded curvature information.

We propose a new statistical estimation framework for a large family of global sensitivity analysis indices. Our approach is based on rank statistics and uses an empirical correlation coefficient recently introduced by Chatterjee [9]. We show how to apply this approach to compute not only the Cram{é}r-von-Mises indices, which are directly related to Chatterjee's notion of correlation, but also first-order Sobol indices, general metric space indices and higher-order moment indices. We establish consistency of the resulting estimators and demonstrate their numerical efficiency, especially for small sample sizes. In addition, we prove a central limit theorem for the estimators of the first-order Sobol indices.

The persistent anomalies observed in $b \to s\,(\ell^+\ell^-,\,ν\barν)$ transitions continue to provide strong motivation for exploring possible extensions of the Standard Model (SM). Motivated by these discrepancies, we present a comprehensive analysis of semileptonic flavor changing neutral current processes within the Standard Model Effective Field Theory (SMEFT), encompassing both $b \to s\,(μ^+μ^-,\,ν\barν)$ and $s \to d\,(μ^+μ^-,\,ν\barν)$ transitions. We perform a combined fit to $b \to s\,(μ^+μ^-,\,ν\barν)$ observables, allowing the relevant dimension-six Wilson coefficients to be complex. We find that the four-fermion operators involving left-handed quark and lepton doublets provide the preferred description of the current $b \to s$ data, while the electroweak operator modifying the $Z$-boson couplings also plays an important role in improving the fit. We show that flavor-universal SMEFT couplings lead to strongly enhanced rare semileptonic kaon decay branching ratios, in conflict with current experimental bounds and thus motivating the implementation of Minimal Flavor Violation. In particular, we demonstrate that flavor-symmetric frameworks based on $U(3)^5$ and $U(2)^5$ naturally restore the required CKM hierarchies and bring the predicted kaon observables into agreement with present data. We further analyze the differential distributions with respect to the dineutrino invariant mass squared $q^2$, as well as the reconstructed variable $q^2_{\mathrm{rec}}$, in $B \to K^{(*)}ν\barν$ decays, demonstrating their sensitivity to different new physics operators. In addition, we investigate the impact of complex Wilson coefficients on $\mathcal{CP}$ asymmetries in $B \to K^{(*)}μ^+μ^-$ decays and find that percent-level effects can arise in specific $q^2$ regions.

Tricriticality usually requires tuning an additional thermodynamic parameter. Here we show that, in symmetric $\mathrm{A}_n\mathrm{B}_n$ star-polymer melts, the arm number $n$ itself plays this role and drives the order--disorder transition (ODT) from second order to first order. By developing a sixth-order free-energy expansion within the random phase approximation and comparing it with self-consistent field theory (SCFT) calculations, we analytically identify a tricritical arm number, $n_{\mathrm{tc}}\approx 5.4475$. For $n<n_{\mathrm{tc}}$, the lamellar ordering transition remains continuous and occurs at the spinodal point, $(χN)_{\mathrm{s}}\approx 10.495$. For $n>n_{\mathrm{tc}}$, the transition becomes first order, and $(χN)_{\mathrm{ODT}}$ shifts below $(χN)_{\mathrm{s}}$ with a quadratic dependence near the tricritical point. SCFT calculations confirm the predicted transition character and phase-boundary shift. The origin of this behavior is traced to inter-arm correlations generated by the common junction. We further show that the noninteger tricritical arm number can be effectively realized in binary mixtures of star polymers. This provides a rare analytically tractable example of architecture-induced tricriticality in a microphase-separating polymer system.

This paper introduces a framework for Chance-Constrained Optimization with Complex Variables, addressing complex linear programming for both individual and joint probabilistic constraints in the complex domain. We first analyze the 3CP model in the density-based setting under the assumption that the random parameters follow a Complex Elliptically Symmetric distribution. The framework is then extended to distributionally robust settings, which include a moment-based model where the moments are known or bounded; a support-based model, where the ambiguity set contains distributions supported on norm-bounded uncertainty sets; and a data-driven model where moments are estimated empirically. The individual constraints are transformed into a convex deterministic second-order cone problem. We employ copula theory to the joint probability constraints and derive both upper and lower approximations. Finally, we demonstrate the proposed framework on the minimum variance distortionless response beamforming problem in signal processing. We further evaluate empirical out-of-sample rates and show that the observed behavior closely matches the prescribed probabilistic guarantees.

The propagation of solar energetic particles (SEPs) through the heliosphere is primarily guided by the interplanetary magnetic field (IMF) which is embedded in the solar wind plasma. Large-scale IMF structures can drive transient variations in SEP intensities. Using Solar Orbiter observations, we identify a distinct class of SEP variations: SEP flux deflections (SFDs), which are commonly detected in SEP events and frequently recur multiple times within a single event. SFDs are characterized by a sudden change in SEP flux directions where the intensities drop in one direction and increase in another direction, without a significant net change in total flux magnitude. These deflections occur dispersionlessly across a broad energy range-from tens of keV to over 100 MeV-and exhibit steep intensity gradients. SFDs are typically associated with magnetic flux tubes with boundary features consistent with tangential discontinuities. We further show that the solar wind inside these structures exhibits distinct plasma properties, and that the SEP streaming direction within SFDs aligns closely to the flux-tube axis. These observations suggest that magnetic flux tubes are a prevalent structural element of the solar wind, and demonstrate that SEPs can serve as an effective diagnostic tool for probing the topology and dynamics of solar wind structures.

We consider magnetic impurities coupled to a conduction sea via a fully isotropic ferromagnetic spin-exchange term, the strength of which depends on the conduction-electron modes involved in the scattering. In the single-impurity case we show both analytically and numerically that there exists a parameter regime in which the conventional Kondo effect develops at low temperatures, leading to a singlet ground state. In the case of a lattice of impurities, we show that this leads to a heavy Fermi liquid state that is energetically favored over magnetic ordering in a broad parameter range. We argue that these effects are analogs of Anderson-Morel superconductivity, and discuss routes to their experimental realization.

The present work aims to enhance the electrostrictive strain of the P(VDF-TrFE-CFE) terpolymer for use in adaptive optics, specifically in deformable mirror actuation. In the context of the FlexSiMirror project, these systems seek to operate under alternating electric fields of up to 50 V/um and within the kilohertz (kHz) frequency range, thereby framing the ranges of characterization considered in this study. To achieve greater strains, the incorporation of a polymeric plasticizer up to 20 vol.% and its impact on the actuation strain performance was studied. Hence, the relevance of this approach lies both in the kHz characterization of the mechanical and dielectric properties of the materials and in the utilization of a polymeric plasticizer, instead of the commonly used phthalates suitable for lower frequency ranges. In the kHz range, polymeric plasticizer addition markedly reduces the elastic modulus while limiting molecular migration, leading to more than a threefold increase of the figure of merit associated with strain (FOMstrain) and yielding 1.50% strain output under 50 V/um, 3.6 times greater than that of the unmodified terpolymer. Therefore, these findings show that modified P(VDF-TrFE-CFE) exhibits enhanced electromechanical performance in the kHz range. This advancement opens new possibilities for developing next-generation actuators intended for adaptive optics applications.

The origin of the Fanaroff--Riley Class I/II (FRI/FRII) morphological dichotomy remains uncertain. We investigate whether cluster-scale environment contributes to this distinction using a morphologically classified LoTSS DR2 catalogue at \(z<0.4\). We construct a volume-limited sample with \(L_{144}>4\times10^{24}\,\mathrm{W\,Hz^{-1}}\) and a luminosity--redshift paired sample, and cross-match them with DESI Legacy Imaging Survey galaxy clusters. A radio galaxy is associated with a cluster if \(|Δz|<0.01\), projected separation \(<2R_{500}\). In the volume-limited sample, \(48.6\%\) of FRIs and \(30.6\%\) of FRIIs are cluster-associated; in the paired sample, the corresponding fractions are \(45.6\%\) and \(32.6\%\). The difference is stronger at \(L_{144}>10^{26}\,\mathrm{W\,Hz^{-1}}\), where the fractions are \(55.6\%\) versus \(19.0\%\) in the volume-limited sample and \(50.0\%\) versus \(6.7\%\) in the paired sample. However, cluster-associated FRIs and FRIIs occupy similar environments: their radio luminosities and stellar masses show similar trends with cluster richness and \(M_{500}\), and their radial distributions both peak near \(0.5R_{500}\) and decline beyond \(R_{500}\). Most cluster-associated sources are brightest cluster galaxies (BCGs), with fractions of \(74.8\%\) for FRIs and \(61.9\%\) for FRIIs in the volume-limited sample, and \(78.1\%\) and \(65.9\%\) in the paired sample. These results show that FRIIs are less frequently found in clusters, especially at high radio luminosity, consistent with dense intracluster gas disrupting or decelerating jets and suppressing stable FRII structures. Nevertheless, once inside clusters, FRIs and FRIIs inhabit similar large-scale environments, implying that cluster-scale properties alone are unlikely to be the primary driver of the FRI/FRII dichotomy.

We study finite-dimensional spaces of rational one-forms on a projective manifold by means of their integrable locus.

The Chemical Reaction Networks (CRN) interpreted through the differential semantics, even when restricted to elementary reactions with mass action law kinetics, form a Turing-complete language. This means that any computable real function can thus be programmed, and in fact compiled, in an abstract CRN that will compute it with an arbitrarily high precision. In this computational framework, the information carriers are the molecular concentrations, the required precision is given as input, and the output concentration is guaranteed to satisfy the required precision. On the other hand, one can be interested in estimating the derivative of an unknown input signal or in reading the concentration value of an input molecular species. By nature, such problems can only be approximated with a finite precision. Hence, the computation framework proposed previously cannot be applied and we need to design and analyze custom CRNs to perform these tasks. In this paper, we present an analog-dyadic converter CRN which takes as input one molecular concentration (in [0, 1] but not necessarily computable), and produces as output a sequence of ''on'' and ''off'' spikes corresponding to some extent to the sequence of bits in the dyadic representation of the input concentration. We provide a detailed analysis of the source of errors and their behavior when varying the reactions rate constants. We conclude by sketching a possible design for a reader module that takes as input an arbitrary concentration and a desired precision and outputs a dyadic encoding approximating the value of the concentration with the desired precision. We leave as an open question to prove the correctness of our construction.

The communication complexity of a voting rule is the worst-case number of bits that n voters must transmit to a central authority under the most efficient elicitation protocol in an election with m candidates. We study the communication complexity of Instant-Runoff Voting (IRV). Conitzer and Sandholm [2005] established an upper bound of O(n (log m)${}^2$), but did not provide a matching lower bound beyond $Ω$(n log m). We resolve this open problem by raising the lower bound to $Ω$(n (log m)${}^2$) using the fooling set technique, thereby showing that the communication complexity of IRV is $Θ$(n (log m)${}^2$). We further show that this complexity drops to $Θ$(n log m) under the single-peakedness restriction, and that both the IRV-Average variant and Single Transferable Vote (STV), the multiwinner extension of IRV, have the same asymptotic communication complexity as IRV.

We study the limit CM rate of single-winner voting rules under Impartial Culture, defined as the probability that a preference profile is coalitionally manipulable in the limit of large electorates. For m = 3 candidates, Lepelley and Valognes [1999] derived a closed-form expression for Plurality with Runoff, or equivalently Instant-Runoff Voting (IRV), and showed that its limit CM rate is strictly below 1. This is remarkable because Kim and Roush [1996] established a limit of 1 for several major rules, including Maximin and all positional scoring rules except Veto. In this paper, we generalize the result of Lepelley and Valognes to any number of candidates m $\ge$ 4. We show that Plurality with Runoff has a limit CM rate equal to 1 for all m $\ge$ 4, whereas IRV retains a limit CM rate strictly below 1. To this end, we rely on the notion of Super Condorcet Winner, recently introduced by Durand [2025], which yields an upper bound on the CM rate of IRV. We prove that this bound is asymptotically tight and compute the probability that a Super Condorcet Winner exists, thereby obtaining the exact limit CM rate of IRV.

We suggest a model of Fermi Bubbles (FBs) in the Galactic halo of the altitude about 7-8 kpc, which is seen in non-thermal microwave and gamma-ray ranges. It was assumed that this emission is generated by relativistic electrons of cosmic rays whose origin is still under debate. It has been assumed that the FB shell is generated in the halo by the release of energy, generated by the routine capture of stars at the central black hole of the Galactic Centre (GC). In this case cosmic ray electrons (CR) in the shells of the FBs of sufficiently high energies are generated by the standard shock acceleration. However, one of the problems of this model is that the Mach number of the FB shock is not high enough to generate the observed non-thermal radiation from the halo. We propose an alternative model of stochastic CR acceleration by Rayleigh-Taylor (RT) instabilities in the shell of the FB at the late stages of the evolution of the shell in the halo. Unlike the shock model of CR acceleration, the RT model of in-situ acceleration in the FBs does not require strong shock fronts. In our model, we derived the spectrum of RT instabilities and estimate the spectra of kinetic equations for MHD-fluctuations needed for acceleration of CRs. We assessed the time of CR electron acceleration up to TeV energies that needed to interpret the observed data of gamma-ray and microwave emission from the envelope of FBs.

Space faces significant sustainability issues including orbital congestion and debris accumulation. The continued growth of space operations, accelerated by advancements such as reusable launch systems, further intensifies these pressures. Current mitigation strategies, such as deorbiting spacecraft or transferring them to graveyard orbits, remain inherently linear. This "take-make-waste" approach is environmentally unsustainable and economically inefficient. On Earth, similar challenges have driven the development of the circular economy (CE), which aims to eliminate waste and pollution, circulate resources at their highest value, and decouple economic growth from finite resource consumption. While these objectives have been extensively studied across terrestrial sectors, their application to the space domain remains largely unexplored. In particular, the concept of a circular space economy (CSE) remains constrained by narratives centered on reuse, recycling, and in-orbit servicing, lacking a structured definition, consistent terminology, and a clearly defined, comprehensive scope. This lack complicates the systematic integration of circularity into mission design, policy frameworks, and space system architectures. After a detailed analysis of established CE definitions and CSE definition proposals, this work conceptualizes the CSE and introduces a structured definition for the first time. It analyzes Earth-space distinctions, clarifies the relationship between space sustainability and the CSE, establishes the 10R Space Framework to narrow, slow, and close resource loops, and distinguishes three operational environments: (I) the CE in space, (II) the CE of the terrestrial (space) sector, and (III) the CE of celestial bodies beyond Earth. Ultimately, this work enables a shared understanding and aims to strengthen the concept's recognition in the space sustainability debate.

Building on prior FAST targeted and blind SETI campaigns toward 33 exoplanet systems, we introduce a wavelet-integrated search pipeline for narrowband technosignature candidates in radio dynamic spectra. At its core, the pipeline uses a Multi-Scale Wavelet Net (MSWNet) to produce an interpretable multi-resolution representation, followed by a lightweight parameter estimator for endpoint localization. Rather than relying solely on hard-threshold drift searches, the pipeline reframes narrowband detection as wavelet-guided feature extraction followed by endpoint regression, morphology-aware filtering, raw-data S/N validation, and multi-beam anticoincidence veto. Applied to real FAST data, the pipeline recovers representative events from prior analyses and produces a compact set of veto-ready candidates for downstream inspection. The resulting workflow preserves interpretability, low regression complexity, and auditable threshold control, making it readily transferable to other radio surveys and large-scale technosignature searches.

Fault-Tolerant Quantum Computation (FTQC) permits parallel execution of mutually commuting Pauli Product Rotations (PPRs), but per-qubit access point/port limits (e.g. two X and two Z edges on the surface code) force commuting groups that exceed the budget to be split, inflating circuit depth. We propose two heuristics for reducing this hardware-limited depth: 1. clique reshuffling, which permutes commuting products and re-forms port-constrained groups, and 2. generator restructuring, which rewrites each group as an equivalent generating set with reduced per-qubit port pressure. On QASMBench circuits compiled to PPRs, we combine the two heuristics and observe an average hardware-limited depth reduction of $10-20\%$ over a non-reordering baseline, with up to $50\%$ reduction. These observed gains scale with the per-qubit port budget and saturate near $20$ ports, suggesting these heuristics remain relevant as hardware exposes more access points.

For a graph $G$, the spectral radius of $G$ is the largest eigenvalue of its adjacency matrix. A connected factor of $G$ is a connected spanning subgraph of $G$. For example, a spanning tree of $G$ is a 1-connected factor of $G$. Let $G$ be a graph of order $n$ with minimum degree $δ\geq6$, where $n\geq3δ$. In this paper, we give a sharp spectral radius condition for $G$ to contain $k$ edge-disjoint 2-connected factors and $\left\lfloor\frac{δ-4k}{2}\right\rfloor$ edge-disjoint spanning trees, where $1\leq k\leq\left\lfloor\fracδ{4}\right\rfloor$ is an integer.

We study the dynamical properties of composition operators acting on Banach spaces of measurable functions. In particular, we study in some detail the composition operators induced by odometers, which allows us to give a variety of new examples and counter-examples. We also get general statements about supercyclicity and frequent hypercyclicity of composition operators on $L\_p$-spaces.

The paper introduces unbounded antilinear operators on Hilbert spaces and develops their fundamental theory. In particular, we establish a closed range theorem, a polar decomposition theorem, and the convexity of the numerical range for antilinear operators. Furthermore, we present several new results on antilinear normal operators and provide necessary and sufficient conditions for the existence of a minimal antilinear normal extension of an antilinear subnormal operator. We further develop a comprehensive characterization of antilinear block operator matrices with purely antilinear entries, establishing necessary and sufficient criteria for their closability through the framework of Schur and quadratic complements.

The Floquet-Magnus expansion is a widely used tool to derive effective descriptions of time-periodic quantum systems by approximating their dynamics with a time-independent Hamiltonian. However, its standard formulation is, strictly speaking, restricted to bounded Hamiltonians. In this work, we extend its definition and analysis to a broad class of time-periodic unbounded Hamiltonians. Our approach is based on an a priori distinct nonperturbative framework for the construction of effective Hamiltonians, which we show to reproduce the Floquet-Magnus expansion. A particular strength of our framework is that it allows us to prove that the resulting effective dynamics approximates the original time evolution propagators to arbitrary order in the high-frequency limit without requiring convergence of the Floquet-Magnus expansion, a condition that is already highly restrictive even in the bounded setting. We illustrate the scope of the method on representative models: the quantum Rabi Hamiltonian in the interaction picture, and the periodically driven quantum harmonic oscillator.

Caffarelli's contraction theorem and the analogous Laplacian result in [arXiv:2411.12109, arXiv:2501.11382] are two examples of how log-Hessian bounds on probability densities yield estimates on the derivative of the corresponding Brenier map with optimal dimensional dependence. The main goal of this paper is to extend such phenomenon to a broader class of convex estimates such as norms.

Accurate pressure measurements in micrometric channels are essential for a wide range of microfluidic applications. Existing approaches rely on a variety of sensing mechanisms, but generally require the integration of additional probes or sensing elements during or after chip fabrication. Here, we introduce a pressure sensing approach based on quantitative phase imaging of the deformation of compliant microfluidic channels. We demonstrate real-time measurements of channel deformation over a large field of view with high sensitivity, without the need for embedded components or modifications of the microfluidic device.

Given a pseudo-free self-similar action of a countable group $G$ on a countable directed graph $E$ with amenable stabilizers of the vertices, we identify the exact conditions under which these stabilizers do not contribute to the ideal structure of the corresponding Exel-Pardo algebra $\mathcal{O}_{G,E}$. Under these conditions, we give a complete description of the primitive ideal space of $\mathcal{O}_{G,E}$ in graph-theoretic terms. Our results apply in particular to certain crossed products $\mathcal{O}_E\rtimes G$, where $G$ acts on $E$ by graph automorphisms. When $G$ is trivial, this recovers Hong-Szymanski's description of the ideal structure of the Cuntz-Krieger algebras $\mathcal{O}_E$. Similar results are then obtained for self-similar actions of groups on row-finite higher rank graphs without sources. In order to obtain these results we formalize the notion of a graded groupoid with essentially central isotropy, which generalizes essentially principal groupoids and groupoids injectively graded by abelian groups. Under the amenability and second countability assumptions, we describe the primitive ideal spaces of the corresponding C$^*$-algebras as topological spaces.

Mixed-precision methods combine low and high precision arithmetics to exploit low precision computational speed and high precision accuracy. Large ODE systems that contain many heterogeneous interactions lead to a high computational cost that could be tackled with mixed-precision solvers. We tested mixedprecision versions of the Bogacki-Shampine 3(2) Runge-Kutta pair over three benchmark systems: coupled linear oscillators, the Kuramoto model and a circadian clock model. Our study is performed in a way that can be adapted to any finite-precision format, software architecture and numerical scheme. We found that mixed-precision solvers can preserve most of the high-precision solver accuracy under a wide range of solver tolerances. Moreover, mixed-precision solver accuracy improves with system size, reaching levels equivalent to high-precision solvers in small system size. We also observed that mixed-precision arithmetic does not impact the number of evaluation in a way that balances the benefit of fast operations in low precision. Taken together, these results show that mixed-precision methods can offer significant computational speed-up at little or no loss of accuracy in large coupled ODE systems.

When studying non-Hermitian electronic systems, an obvious question is how various non-Hermitian effects affect measurable quantities like the conductance. Here, we show that uniformly dissipative circuits can exhibit nonreciprocal conductance, meaning that the two nonlocal conductances are different. We describe how this happens through a difference in transmission times between left-moving and right-moving electrons. We consider a specific case of a dissipative Rashba nanowire with a skewed magnetic field, and show how this difference in transmission times comes about through interference inside the circuit, and how this is modified as the dissipation strength changes.

Classical and quantum optical communication has gained popularity and momentum in recent years, with growing investment and innovation in quantum technologies. However, the main teaching method in the education of quantum mechanics include mathematically intensive derivations or abstract analogies for the complex systems. We propose a "poor man's" spatial light modulator experiment that is an engaging and interactive learning aid for teaching quantum mechanics and optical orbital angular momentum. Fork diffraction gratings were created on photographic slide film by outsourcing to an external company, and so the gratings were easy and cheap to produce. A simple setup with a fork diffraction grating and a laser pointer successfully produces vortex beams that possess orbital angular momentum, allowing for orbital angular momentum to be easily observed and investigated in a teaching environment. How the tools can be used effectively to enhance learning is discussed, either as a demonstration or as an investigative scientific learning environment activity.