Dissipation in quantum many-body systems provides a more general and experimentally realistic perspective on particle transport than closed quantum systems. In this work, we determine the maximal speed of macroscopic particle transport in dissipative bosonic systems featuring both long-range hopping and long-range interactions. By developing a generalized optimal transport theory for open quantum systems, we rigorously establish the relationship between the minimum transport time and the source-target distance, and investigate the maximal transportable distance of bosons. We demonstrate that optimal transport exhibits a fundamental distinction depending on whether the system experiences one-body loss or multi-body loss. Moreover, we present the minimal transport time and the maximal transport distance for systems with both gain and loss. We observe that even an arbitrarily small gain rate enables transport over long distances if the lattice gas is dilute. Importantly, we generally reveal that the emergence of decoherence-free subspaces facilitates the long-distance and perfect transport process. Additionally, we derive an upper bound for the probability of transporting a given number of particles during a fixed period in the presence of particle loss. Possible experimental protocols for observing our theoretical predictions are also discussed.

We experimentally optimize the frequency of flux-tunable couplers in a superconducting quantum processor to minimize the impact of spectator transmons during quantum operations (single-qubit gates, two-qubit gates and readout) on other transmons. We adapt a popular transmon-like tunable-coupling element, achieving high-fidelity, low-leakage controlled-$Z$ gates with unipolar, fast-adiabatic pulsing only on the coupler. We demonstrate the ability of the tunable coupler to null residual $ZZ$ coupling as well as exchange couplings in the one- and two-excitation manifolds. However, the nulling of these coherent interactions is not simultaneous, prompting the exploration of tradeoffs. We present experiments pinpointing spectator effects on specific quantum operations. We also study the combined effect on the three types of operations using repeated quantum parity measurements.

We develop approximations for the Riemann zeta function that enable high-precision computation within the critical strip and other vertical strips. These approximations combine the main sum of the Riemann-Siegel formula with a simple approximation of the remainder term, which involves only elementary functions and certain precomputed coefficients obtained via Gaussian quadrature. Additionally, we provide approximations for the derivative of the Riemann zeta function and present extensive numerical evidence demonstrating the accuracy of these approximations.

Open burning of plastic waste may pose a significant threat to global health by degrading air quality, but quantitative research on this problem -- crucial for policy making -- has been stunted by lack of data. Many low- and middle-income countries, where open burning is most concerning, have little to no air quality monitoring. Here, we leverage remotely sensed data products combined with spatiotemporal causal analytic techniques to evaluate the impact of large-scale plastic waste policies on air quality. Throughout, we study Indonesia before and after 2018, when China halted its import of plastic waste, resulting in diversion of this massive waste stream to other countries. We tailor cutting-edge statistical methods to this setting, estimating effects of increased plastic waste imports on fine particulate matter (PM$_{2.5}$) near waste dump sites in Indonesia as a function of proximity to ports, an induced continuous exposure. We observe strong evidence that monthly PM$_{2.5}$increased after China's ban (2018-2019) relative to expected business-as-usual (2012-2017), with increases up to 1.68 $μ$g/m$^3$ (95% CI = [0.72, 2.48]) when exposed to medium-high port proximity. Effects were more modest for very high port proximity exposure, possibly reflecting smaller increases in dumping/burning where government oversight is greater.

The $k$-Hankel transform $F_{k,1}$ (or the $(k,1)$-generalized Fourier transform) is the Dunkl analogue of the unitary inversion operator in the minimal representation of a conformal group initiated by T. Kobayashi and G. Mano. It is one of the two most significant cases in $(k,a)$-generalized Fourier transforms. We will establish a positive radial product formula for the integral kernels of $F_{k,1}$. Such a product formula is equivalent to a representation of the generalized spherical mean operator in terms of the probability measure $σ_{x,t}^{k,1}(ξ)$. We will then study the representing measure $σ_{x,t}^{k,1}(ξ)$ and analyze the support of this measure, and derive a weak Huygens's principle for the deformed wave equation in $(k,1)$-generalized Fourier analysis.

Superconductivity has been demonstrated in the family of multi-layered nickelates La$_3$Ni$_2$O$_7$ and La$_4$Ni$_3$O$_{10}$. Key questions remain open regarding the low-energy electronic states that support superconductivity in these compounds. Here we take advantage of the natural polymorphism between bilayer (2222) and alternating monolayer-trilayer (1313) stacking sequences that arises in bulk La$_3$Ni$_2$O$_7$ crystals, and by employing angle-resolved photoemission spectroscopy (ARPES) we identify a universal low-energy electronic structure in this family of materials. We observe the fingerprint of a doping-dependent spin-density wave (SDW) instability -- strong and coherent enough to reconstruct the Fermi surface, both by gapping out regions of the low-energy electronic structure as well as translating the $β$ pocket by a vector $Q_{tβ}$ consistent with the results of previous neutron and x-ray scattering experiments. Using an effective tight-binding model, we simulate the spectral weight distribution observed in our ARPES dichroism experiments and establish that the low-energy electronic phenomenology is dominated by oxygen-centered planar orbitals, which evolve from the $d_{3x^2-r^2}$ and $d_{3y^2-r^2}$ symmetry characteristic of 3-spin polarons (3SP) to the familiar $d_{x^2-y^2}$ Zhang-Rice singlets (ZRS) that support high-temperature superconductivity in cuprates. By inclusion of magnetic moments on plaquettes of oxygen orbitals in our model, we show that ZRS-like states mediate the SDW. Combined with the observation that oxygen annealing is required to induce superconductivity in both thin films and bulk La$_3$Ni$_2$O$_7$, this demonstrates that the ZRS population dictates whether the ground state favors density-wave order or superconductivity -- with hole doping suppressing the former and stabilizing the latter, as in the cuprates.

The measurements of cluster abundances, gravitational lensings, redshift space distortions and peculiar velocities at lower redshifts point out to much smaller sigma_8 than its value deduced from the measurements of the CMB fluctuations assuming the standard LCDM cosmology. High redshift measurements of ALMA and JWST imply even more striking problems for LCDM. We examine and compare the sigma_8 redshift dependence calculated within the gauge invariant formalism. Because the CMB fluctuations comprise a cosmological data from the recombination era to the present, the S_8 problem of the LCDM cosmology is not a surprise from the standpoint of the Einstein-Cartan cosmology because it predicts much larger mass density and sigma_8(z) than the LCDM model at high redshifts.

Quantum key distribution (QKD) has emerged as a promising solution to protect current cryptographic systems against the threat of quantum computers. As QKD transitions from laboratories to real-world applications, its implementation under various environmental conditions has become a pressing challenge. Major obstacles to practical QKD implementation are the loss of photons in the transmission media and the presence of extreme noise, which can severely limit long-range transmission. In this paper, we investigate the impact of extreme noise on QKD system parameters, including timing jitter, rate-dependent timing shifts, changes in effective detector dead time, and rate-dependent detection efficiency. Contrary to manufacturers' specifications, which assume these parameters to be constant, we demonstrate that these parameters exhibit significant variations in extreme noise conditions. We show that changes in these parameters play a key role in determining system performance in noisy environments. To address these nonidealities, we develop a model that adapts to detector-dependent timing distortions and recovery effects. In particular, our model is independent of source parameters and can be implemented using data from the detection unit. Our results show that the model enables reliable characterization and optimization of QKD performance under strong noise.

Reduced rank extrapolation (RRE) is an acceleration method typically used to accelerate the iterative solution of nonlinear systems of equations using a fixed-point process. In this context, the iterates are vectors generated from a fixed-point mapping function. However, when considering the iterative solution of large-scale matrix equations, the iterates are low-rank matrices generated from a fixed-point process for which, generally, the mapping function changes in each iteration. To enable acceleration of the iterative solution for these problems, we propose two novel generalizations of RRE. First, we show how to effectively compute RRE for sequences of low-rank matrices. Second, we derive a formulation of RRE that is suitable for fixed-point processes for which the mapping function changes each iteration. We demonstrate the potential of the methods on several numerical examples involving the iterative solution of large-scale Lyapunov and Riccati matrix equations.

Making use of the simple fact that all separable complex Hilbert spaces of given dimension are isomorphic, we show that there are just six basic ways to define generalized coordinate operators in Quantum Mechanics. In each case a canonically conjugate generalized momentum operator can be defined, but it may not be self-adjoint. Even in those cases we show there is always either a self-adjoint extension of the operator or a Neumark extension of the Hilbert space that produces a self-adjoint momentum operator. In one of the six cases both extensions work, thus leading to seven basic pairs of coordinate and momentum operators. We also show why there are more ways of defining basic coordinate and momentum measurements. A special role is reserved for measurements that simultaneously measure both.

In this paper, we study the phenomenon of coming down from infinity for subcritical cooperative branching processes with pairwise interactions (BPI processes) under suitable conditions. BPI processes are continuous-time Markov chains that extend classical branching models by incorporating additional mechanisms accounting for both competitive and cooperative interactions between pairs of individuals. Our main focus is on characterising the speed at which BPI processes evolve when starting from a very large initial population in the subcritical regime. In addition, we investigate their second-order fluctuations. Furthermore, our results also apply to a class of exchangeable fragmentation-coalescent processes introduced by Berestycki (2004) and several other models from population genetics.

This paper presents a heuristic for finding the optimum number of CUDA streams by using tools common to the modern AI-oriented approaches and applied to the parallel partition algorithm. A time complexity model for the GPU realization of the partition method is built. Further, a refined time complexity model for the partition algorithm being executed on multiple CUDA streams is formulated. Computational experiments for different SLAE sizes are conducted, and the optimum number of CUDA streams for each of them is found empirically. Based on the collected data a model for the sum of the times for the non-dominant GPU operations (that take part in the stream overlap) is formulated using regression analysis. A fitting non-linear model for the overhead time connected with the creation of CUDA streams is created. Statistical analysis is done for all the built models. An algorithm for finding the optimum number of CUDA streams is formulated. Using this algorithm, together with the two models mentioned above, predictions for the optimum number of CUDA streams are made. Comparing the predicted values with the actual data, the algorithm is deemed to be acceptably good.

Various methods have been introduced to measure the orbital angular momentum (OAM) of light, from fork holograms to Dove prism interferometers, from tilted lenses to triangular apertures - each with their own benefits and limitations. Here we demonstrate how simple knife-edge diffraction can be used to identify the OAM of an optical phase vortex from the formation of fork dislocations within the Fresnel diffraction pattern. For vector vortex beams without net OAM, the conventional Fresnel fringes are recovered, whereas the polarization in the geometric shadow is changed in its ellipticity. The observed diffraction patterns agree with simulations and their features can be explained by considering diffraction as an interference phenomenon. Knife-edge diffraction provides not only an instructive illustration of various properties of phase and polarization vortices, but can also serve as an ideal method for the quick determination of optical OAM, with potential applications beyond optics, where alternative detection measurement methods may be harder to realize.

In this paper, we give a generalization of the Chern-Lashof theorem for submanifolds with singularities called frontals in Euclidean space. We prove that, for an $n$-dimensional admissible compact frontal in $(n+r)$-dimensional Euclidean space $\boldsymbol{R}^{n+r}$, its total absolute curvature is greater than or equal to the sum of the Betti numbers. Furthermore, if the total absolute curvature is equal to $2$, and all singularities are of the first kind, then the image of the frontal coincides with a closed convex domain of an affine $n$-dimensional subspace of $\boldsymbol{R}^{n+r}$.

Understanding the mechanisms by which complex correlations emerge through the dynamics of quantum many-body systems remains a fundamental challenge in modern physics. To address this, quench dynamics starting from nonthermal states have been extensively studied, leading to significant progress. In this paper, we propose a novel quench protocol, termed the "crosscap quench", to investigate how highly structured thermal pure states relax into typical ones. We begin by analyzing conformal field theories (CFTs) and derive universal features in the time evolution of the entanglement entropy. Furthermore, leveraging the AdS/CFT correspondence, we study holographic CFTs, providing an analytically tractable example in chaotic CFTs. Finally, we validate these findings through numerical simulations in both nonintegrable and integrable quantum spin systems.

High temperatures are typically thought to increase disorder. Here we examine this idea in Quantum Field Theory in 2+1 dimensions. For this sake we explore a novel class of tractable models, consisting of nearly-mean-field scalars interacting with critical scalars. We identify UV-complete, local, unitary models in this class and show that symmetry breaking $\mathbb{Z}_2 \to \emptyset$ occurs at any temperature in some regions of the phase diagram. This phenomenon, previously observed in models with fractional dimensions, or in the strict planar limits, or with non-local interactions, is now exhibited in a local, unitary 2+1 dimensional model with a finite number of fields.

The formal sharp-interface asymptotics in a degenerate Cahn-Hilliard model for viscoelastic phase separation with cross-diffusive coupling to a bulk stress variable are shown to lead to non-local lower-order counterparts of the classical surface diffusion flow. The diffuse-interface model is a variant of the Zhou-Zhang-E model and has an Onsager gradient-flow structure with a rank-deficient mobility matrix reflecting the ODE character of stress relaxation. In the case of constant coupling, we find that the evolution of the zero level set of the order parameter approximates the so-called intermediate surface diffusion flow. For non-constant coupling functions monotonically connecting the two phases, our asymptotic analysis leads to a new family of third-order evolution laws with associated propagation operators behaving, at leading order, like the square root of the minus Laplace-Beltrami operator. In this case, the normal velocity of the moving sharp interface arises as the Lagrange multiplier in a constrained elliptic equation, which is at the core of our derivation. The constrained elliptic problem can be solved rigorously by a variational argument, and is shown to encode the gradient structure of the effective geometric evolution law. The asymptotics are presented for deep quench, an intermediate free boundary problem based on the double-obstacle potential.

We prove that any lower unitriangular and totally nonnegative matrix gives rise to a family of polynomials with only real zeros. This has consequences for problems in several areas of mathematics. We use it to develop a general theory for chain enumeration in posets and zeros of chain polynomials. The results obtained extend and unify results of the first author, Brenti, Welker and Athanasiadis. In the process we define a notion of $h$-vectors for a large class of posets which generalize the notions of $h$-vectors associated to simplicial and cubical complexes. A consequence of our methods is a characterization of the convex hull of all characteristic polynomials of hyperplane arrangements of fixed dimension and over a fixed finite field. This may be seen as a refinement of the Critical Problem of Crapo and Rota. We also use the methods developed to answer an open problem posed by Forgács and Tran on the real-rootedness of polynomials arising from certain bivariate rational functions.

We compute the Cox ring of an embedded variety $X \subseteq Z$ within a Mori dream space, under the assumption that the pullback map induces an isomorphism at the level of divisor class groups. We show that the Cox ring of $X$ is the intersection of finitely many localizations of a quotient image of the Cox ring of $Z$. As a consequence, we provide an algorithm that terminates if and only if the Cox ring of $X$ is finitely generated, thereby generalizing previous works on the subject. We apply these results to compute the Cox ring of hypersurfaces in smooth projective toric varieties.

One-dimensional bosonic systems, such as helium confined to nanopores, exhibit Luttinger liquid behavior characterized by density waves as collective excitations. We investigate the impact of a scattering potential on a low dimensional quantum liquid. We consider a microscopic model of $^4$He inside a perturbed nanopore with a localized constriction, and employ quantum Monte Carlo simulations to analyze the density of the core within an effective low-energy framework. Our results reveal the emergence of Friedel oscillations in a bosonic quantum liquid without a Fermi surface. Furthermore, we utilize the Luttinger liquid model to predict experimentally observable signatures of this pinning phenomena in elastic scattering and via the temperature and pressure dependence of mass transport through the deformed nanopore.

This paper presents a generalised symbolic algorithm for solving systems of linear algebraic equations with multi-diagonal coefficient matrices. The algorithm is given in a pseudocode. A theorem which gives the condition for correctness of the algorithm is formulated and proven. Formula for the complexity of the multi-diagonal numerical algorithm is obtained.

We establish the existence of infinitely many synchronized solutions for a class of critical Hamiltonian elliptic systems with Hartree-type nonlocal interactions.

Monolayer semiconductors, given their thickness at the atomic scale, present unique electrostatic environments due to the sharp interfaces between the semiconductor film and surrounding materials. These interfaces significantly impact both the quasiparticle band structure and the electrostatic interactions between charge carriers. Akey area of interest in these materials is the behavior of bound electron-hole pairs (excitons) within the ultra-thin layer, which plays a crucial role in its optoelectronic properties. In this work, we investigate the feasibility of generating potential traps that completely confine excitons in the thin semiconductor by engineering the surrounding dielectric environment. By evaluating the simultaneous effects on bandgap renormalization and modifications to the strength of the electron-hole Coulomb-interaction, both associated to the modulation of the screening by the materials sandwiching the monolayer, we anticipate the existence of low-energy regions in which the localization of the exciton center of mass may be achieved. Our results suggest that for certain dielectric configurations, it is possible to generate complete discretization of exciton eigenenergies in the order of tens of meV. Such quantization of energy levels of two-dimensional excitons could be harnessed for applications in new-generation optoelectronic devices, which are necessary for the advancement of technologies like quantum computing and quantum communication.

We prove a flat torus theorem for quadric complexes. In particular, we show that if a non-cyclic free abelian group $G$ acts metrically properly on a quadric complex $X$, then $G \cong \mathbb{Z}^2$ and $X$ contains a $G$-invariant isometric copy of the regular square tiling of the plane. Along the way, we also give a complete proof of the fact that any closed surface subgroup in the fundamental group of a combinatorial 2-complex is represented by a combinatorial map from a cellulation of the surface that is locally injective away from vertices.

A universality conjecture of Farmer and Rhoades [Trans. Amer. Math. Soc., 357(9):3789--3811, 2005] and Farmer [Adv. Math., 411:Paper No. 108781, 14, 2022] asserts that, under some natural conditions, the roots of an entire function should become perfectly spaced in the limit of repeated differentiation. This conjecture is known as Cosine Universality. We establish this conjecture for a class of even entire functions with only real roots which are real on the real line. Along the way, we establish a number of additional universality results for Jensen polynomials of entire functions, including the Hermite Universality conjecture of Farmer [Adv. Math., 411:Paper No. 108781, 14, 2022]. Our proofs are based on finite free probability theory. We establish finite free probability analogs of the law of large numbers, central limit theorem, and Poisson limit theorem for sequences of deterministic polynomials under repeated differentiation, under optimal moment conditions, which are of independent interest.

In this article we consider the surplus process of an insurance company within the Cramer-Lundberg framework. We study the optimal reinsurance strategy and dividend distribution of an insurance company under proportional reinsurance, in which capital injections are allowed. Our aim is to find a general dynamic reinsurance strategy that maximises the expected discounted cumulative dividends until the time of passage below a given level, called ruin. These policies consist in stopping at the first time when the size of the overshoot below 0 exceeds a certain limit a, and only pay dividends when the reserve reaches an upper barrier b. Using analytical methods, we identify the value function as a particular solution to the associated Hamilton Jacobi Bellman equation. This approach leads to an exhaustive and explicit characterisation of optimal policy. The proportional reinsurance is given via comprehensive structure equations. Furthermore we give some examples illustrating the applicability of this method for proportional reinsurance treaties.

In \cite{grku1}, Greither and Kurihara proved a theorem about the commutativity of projective limits and Fitting ideals for modules over the classical equivariant Iwasawa algebra $Λ_G=\mathbb{Z}_p[G][[T]]$, where $G$ is a finite, abelian group and $\Bbb Z_p$ is the ring of $p$--adic integers, for some prime $p$. In this paper, we generalize their result first to the Noetherian Iwasawa algebras $\mathcal O[[T_1, T_2, \dots, T_n]]$ and, most importantly, to non-Noetherian algebras $\mathcal O[[T_1, T_2, \dots, T_n, \dots]]$ of countably many generators, with more general rings of coefficients $\mathcal O$. The latter generalization is motivated by the recent work of Bley--Popescu on the Geometric Equivariant Iwasawa Conjecture for function fields, as well as by the emerging Iwasawa theory of Taelman class--modules associated to Drinfeld modules, where the Iwasawa algebras are not Noetherian, of the type described above. A sample application of our results to non--Noetherian geometric Iwasawa theory is given in Appendix B. Further number theoretic applications will be given in an upcoming paper.

Many current quantum error-correcting codes that achieve full fault tolerance suffer from having low ratios of logical to physical qubits and significant overhead. This makes them difficult to implement on current noisy intermediate-scale quantum (NISQ) computers and results in the inability to perform quantum algorithms at useful scales with near-term quantum processors. As a result, calculations are generally done without encoding. We propose a middle ground between these two approaches: constructions in the $[[n,n-2,2]]$ quantum error-detecting code that can detect any error from a single faulty gate by measuring the stabilizer generators of the code and additional ancillas at the end of the computation. This achieves weak fault tolerance. As we show, this yields a significant improvement over no error correction for small computations with low enough physical error probabilities and requires much less overhead than codes that achieve full fault tolerance. We give constructions for a set of gates that achieve universal quantum computation in this error-detecting code, while satisfying weak fault tolerance up to analog imprecision on the physical rotation gate.

We study a nonlocal Cahn-Hilliard model for a multicomponent mixture with cross-diffusion effects and degenerate mobility. The nonlocality is described by means of a symmetric singular kernel. We define a notion of weak solution adapted to possible degeneracies and prove, as our first main result, its global-in-time existence. The proof relies on an application of the formal gradient flow structure of the system (to overcome the lack of a-priori estimates), combined with an extension of the boundedness-by-entropy method, in turn involving a careful analysis of an auxiliary variational problem. This allows to obtain solutions to an approximate, time-discrete system. Letting the time step size go to zero, we recover the desired nonlocal weak solution where, due to their low regularity, the Cahn-Hilliard terms require a special treatment. Finally, we prove convergence of solutions for this class of nonlocal Cahn-Hilliard equations to their local counterparts.

A quasi-one-dimensional Bose-Einstein condensate loaded into a quasi-periodic potential created by two sub-lattices of comparable amplitudes and incommensurate periods is considered. Although the conventional tight-binding approximation is not applicable in this setting, the description can still be reduced to a discrete model that accounts for the modes below the mobility edge. In the respective discrete lattice, where no linear hopping exists, solutions and their dynamics are governed solely by nonlinear interactions. Families of nonlinear modes, including those with no linear limit, are described with a special focus on dimers, which correspond to breather solutions of the Gross-Pitaevskii equation with a quasi-periodic potential. The breathers are found to be stable for negative scattering lengths. Localization and stable propagation of breathers are also observed for positive scattering lengths at relatively weak and moderate nonlinearities.