Showing new listings for Monday, 10 November 2025

Cross submissions (showing 11 of 11 entries)

We report a bosonic anomaly emerging in the quantum harmonic oscillator, whose partition function is rigorously identified as the Chern character via the Grothendieck-Riemann-Roch theorem, establishing a new connection among statistical mechanics, anomaly, Atiyah-Singer index theorem and Gromov-Witten theory. We investigate how its internal energy relates to the Atiyah-Singer index theorem, showing that the partition function can be interpreted as the Chern character of "physical sheaf" over Eucildean spacetime by using Grothentic-Riemann-Roch theorem. This correspondence reveals the internal energy of oscillator as a concrete non-SUSY manifestation of the index theorem. Moreover, we show that this connection naturally leads to the emergence of a quantum anomaly. Furthermore, we arrive at Gromov-Witten theory through a more direct and physically intuitive approach. As a result, the internal energy of the quantum harmonic oscillator serves as a bridge linking two key concepts in physics -- statistical mechanics and anomalies -- with three fundamental mathematical frameworks: the Atiyah-Singer index theorem, the Grothendieck-Riemann-Roch theorem, and Gromov-Witten theory.

Lie theory is, beyond any doubt, an absolutely essential part of differential geometry. It is therefore necessary to seek its generalization to mathbb{Z}-graded geometry. In particular, it is vital to construct non-trivial and explicit examples of graded Lie groups and their corresponding graded Lie algebras.Three fundamental families of graded Lie groups are developed in this paper: the general linear group associated with any graded vector space, the graded orthogonal group associated with a graded vector space equipped with a metric, and the graded symplectic group associated with a graded vector space equipped with a symplectic form. We provide both a direct geometric construction and a functor-of-points perspective. It is shown that their corresponding Lie algebras are isomorphic to the anticipated subalgebras of the graded Lie algebra of linear endomorphisms. Isomorphisms of graded Lie groups induced by linear isomorphisms, as well as possible applications, are also discussed.

We study a class of fourth-order quasilinear degenerate parabolic equations under both time-dependent and time-independent inhomogeneous forces, modeling non-Newtonian thin-film flow over a solid surface in the "complete wetting" regime. Using regularity theory for higher-order parabolic equations and energy methods, we establish the global existence of positive weak solutions and characterize their long-time behavior.Specifically, for power-law thin-film problem with the time-dependent force f(t,x), we prove that the weak solution converges to bar{u}_0 + frac{1}{|Omega|}int_{0}^t int_{Omega} f(s,x) , {rm d}x , {rm d}s, and provide the convergence rate, where bar{u}_0 is the spatial average of the initial data. Compared with the homogeneous case in cite{JJCLKN} (Jansen et al., 2023), this result clearly demonstrates the influence of the inhomogeneous force on the convergence rate of the solution. For the time-independent force f(x), we prove that the difference between the weak solution and the linear function bar{u}_0 + frac{t}{|Omega|}int_Omega f(x), {rm d}x is uniformly bounded. For the constant force f_0, we show that in the case of shear thickening, the weak solution coincides exactly with bar{u}_0 + tf_0 in a finite time. In both shear-thinning and Newtonian cases, the weak solution approaches bar{u}_0 + tf_0 at polynomial and exponential rates, respectively. Later, for the Ellis law thin-film problem, we find that its solutions behave like those of Newtonian fluids.Finally, we conduct numerical simulations to confirm our main analytical results.

Quantum steering is a crucial quantum resource that lies intermediate between entanglement and Bell nonlocality. Gaussian channels, meanwhile, play a foundational role in diverse quantum protocols, secure communication, and related fields. In this paper, we focus on several classes of Gaussian channels associated with quantum steering: Gaussian steering-annihilating channels, Gaussian steering-breaking channels, Gaussian unsteerable channels, and maximal Gaussian unsteerable channels. We give the concepts of these channels, derive the necessary and sufficient conditions for a Gaussian channel to belong to each class, and explore the intrinsic relationships among them. Additionally, since quantifying the steering capability of Gaussian channels in continuous-variable systems requires an understanding of the structure of free superchannels, we also provide a detailed characterization of Gaussian unsteerable superchannels and maximal Gaussian unsteerable superchannels.

In this paper, which is a follow-up of our first paper "Normal forms for ordinary differential operators, I", we extend the theory of normal forms for non-commuting operators, and obtain as an application a commutativity criterion for operators in the Weyl algebra or, more generally, in the ring of ordinary differential operators, which we prove in the case when operators have a normal form with the restriction top line (for details see Introduction).

The linear stability of two exact stationary solutions of the parametrically driven, damped nonlinear Dirac equation is investigated. Stability is ascertained through the resolution of the eigenvalue problem, which stems from the linearization of this equation around the exact solutions. On the one hand, it is proven that one of these solutions is always unstable, which confirms previous analysis based on a variational method. On the other hand, it is shown that sufficiently large dissipation guarantees the stability of the second solution. Specifically, we determine the stability curve that separates stable and unstable regions in the parameter space. The dependence of the stability diagram on the driven frequency is also studied, and it is shown that low-frequency solitons are stable across the entire parameter space. These results have been corroborated with extensive simulations of the parametrically driven and damped nonlinear Dirac equation by employing a novel and recently proposed numerical algorithm that minimizes discretization errors.

This work unveils a novel and fundamental connection between structured light and topological field theory by showing how the natural geometrical setting for paraxial vector beams is that of a SU(2) principal bundle over mathbb{R}^{2+1}. Going beyond the usual high-order Poincaré sphere approach, we show how the nonseparable structure of polarisation and spatial modes in vector beams is naturally described by a non-Abelian Chern-Simons gauge theory. In this framework, we link the Chern-Simons charge to spin-orbit coupling, and we propose a simple way to experimentally detect the presence of non-Abelian phases through Wilson lines. This new insight on vector beams opens new possibilities for realising and probing topological quantum field theories using classical optics, as well as it lays the foundation for implementing topologically protected classical and quantum information protocols with structured light.

We introduce and analyze a nonlinear exchange dynamics for Ising spin systems with arbitrary interactions. The evolution is governed by a quadratic Boltzmann-type equation that conserves the mean magnetization. Collisions are encoded through a spin-exchange kernel chosen so that the dynamics converge to the Ising model with the prescribed interaction and mean magnetization profile determined by the initial state. We prove a general convergence theorem, valid for any interaction and any transport kernel. Moreover, we show that, for sufficiently weak interactions, the system relaxes exponentially fast to equilibrium in relative entropy, with optimal decay rate independent of the initial condition. The proof relies on establishing a strong version of the Kac program from kinetic theory. In particular, we show that the associated Kac particle system satisfies a modified logarithmic Sobolev inequality with constants uniform in the number of particles. This is achieved by adapting the method of stochastic localization to the present conservative setting.

A Poisson line process is a random set of straight lines contained in the plane, as the image of the map (x,v)mapsto (x+vt)_{tinmathbb{R}}, for each point (x,v) of a Poisson process in the space-velocity plane. By associating a step with each line of the process, a random surface called multitime walk field is obtained. The diffusive rescaling of the surface converges to the multitime Brownian motion, a classical Gaussian field also called Lévy-Chentsov field. A cut of the multitime fields with a perpendicular plane, reveals a one dimensional continuous time random walk and a Brownian motion, respectively.A hard rod is an interval contained in mathbb{R} that travels ballistically until it collides with another hard rod, at which point they interchange positions. By associating each line with the ballistic displacement of a hard rod and associating surface steps with hard rod jumps, we obtain the hydrodynamic limits of the hard rods in the Euler and diffusive scalings. The main tools are law of large numbers and central limit theorems for Poisson processes.When rod sizes are zero we have an ideal gas dynamics. We describe the relation between ideal gas and hard-rod invariant measures.

In this paper, the well-posedness is studied for the initial boundary value problem of the two-dimensional compressible ideal magnetohydrodynamic (MHD) equations in bounded perfectly conducting domains with corners. The presence of corners yields intrinsic analytic obstacles: the lack of smooth tangential vectors to the boundary prevents the use of classical anisotropic Sobolev spaces, and due to the coupling of normal derivatives near corners, one can not follow the usual way to estimate the normal derivatives of solutions from the equations. To overcome these difficulties, a new class of anisotropic Sobolev spaces H^m_*(Omega) is introduced to treat corner geometries. Within this framework, the well-posedness theory is obtained for both linear and nonlinear problems of the compressible ideal MHD equations with the impermeable and perfectly conducting boundary conditions. The associated linearized problem is studied in several steps: first one deduces the existence of weak solutions by using a duality argument in high order tangential spaces, then verifies that it is indeed a strong solution by several smoothing procedures preserving traces to get a weak-strong uniqueness result, afterwards the estimates of normal derivatives are obtained by combining the structure of MHD equations with the Helmholtz-type decomposition for both of velocity and magnetic fields.

We construct exact strong zero mode operators (ESZM) in integrable quantum circuits and the spin-1/2 XXZ chain for general open boundary conditions, which break the bulk U(1) symmetry of the time evolution operators. We show that the ESZM is localized around one of the boundaries induces infinite boundary coherence times. Finally we prove that the ESZM becomes spatially non-local under the map that relates the spin-1/2 XXZ chain to the asymmetric simple exclusion process, which suggests that it does not play a significant role in the dynamics of the latter.

Replacement submissions (showing 21 of 21 entries)

We consider the Anderson tight-binding model on mathbb{Z}^d, dgeq 2, with Gaussian noise and at low disorder lambda>0. We derive a diffusive scaling limit for the entries of the resolvent R(z) at imaginary part operatorname*{Im} zsimlambda^{2+kappa_d}, kappa_d>0, with high probability. As consequences, we establish quantum diffusion (in a time-averaged sense) for the Schrödinger propagator at the longest timescale known to date and improve the best available lower bounds on the localization length of eigenfunctions. Our results for d=2 are the first quantum diffusion results for the Anderson model on mathbb{Z}^2. The proof avoids the use of diagrammatic expansions and instead proceeds by analyzing certain self-consistent equations for R(z). This is facilitated by new estimates for |R(z)|_{ell^prightarrow ell^q} that control the recollisions.

We define two families of determinantal random spanning subgraphs of a finite connected graph, one supported by acyclic spanning subgraphs (spanning forests) with fixed number of connected components, the other by connected spanning subgraphs with fixed number of independent cycles. Each family generalizes the uniform spanning tree and the generating functions of these probability measures generalize the classical Kirchhoff and Symanzik polynomials.We call Symanzik spanning forests the elements of the acyclic spanning subgraphs family, and single out a particular determinantal mixture of these, having as kernel a normalized Laplacian on 1-forms, which we call the Laplacian spanning forest.Our proofs rely on a set of integral and real or complex (which we call geometric) multilinear identies involving cycles, coboundaries, and forests on graphs. We prove these identities using classical pieces of the algebraic topology of graphs and the exterior calculus applied to finite determinantal point processes, both of which we treat in a self-contained way.We emphasize the matroidal nature of our constructions, thereby showing how the above two families of random spanning subgraphs are dual to one another, as well as possible generalisations.

We present an algorithm for explicitly computing the categorical (Drinfeld) center of a pivotal fusion category. Our approach is based on decomposing the images of simple objects under the induction functor from the category to its center. We have implemented this algorithm in a general-purpose software frameworkthis http URLfor tensor categories that we develop within the open-source computer algebra system OSCAR. We compute explicit models for the centers in form of the tuples (X,gamma) where X is an object and gamma is a half-braiding. From these models we can compute the F-symbols and R-symbols. Using the data from the AnyonWiki, we were able to compute the center together with its F-symbols and R-symbols for all the 279 multiplicity-free fusion categories up to rank 5, and furthermore some chosen examples of rank 6, including the Haagerup subfactor (presented in a separate paper).

From the study of the high order freeness of random matrices, it is known that the order r cumulant of the trace of a polynomial of N-dimensional GUE/GOE is of order N^{2-r} if r is fixed. In this work, we extend the study along three directions. First, we also consider generally distributed Wigner matrices with subexponential entries. Second, we include the deterministic matrices into discussion and consider arbitrary polynomials in random matrices and deterministic matrices. Third, more importantly, we consider the ultra high order cumulants in the sense that r is arbitrary, i.e., could be N dependent. Our main results are the upper bounds of the ultra high order cumulants, for which not only the N-dependence but also the r-dependence become significant. These results are then used to derive three types of quantitative CLT for the trace of any given self-adjoint polynomial in these random matrix variables: a CLT with a Cramér type correction, a Berry-Esseen bound, and a concentration inequality which captures both the Gaussian tail in the small deviation regime and M-dependent tail in the large deviation regime, where M is the degree of the polynomial. In contrast to the second order freeness which implies the CLT for linear eigenvalue statistics of polynomials in random matrices, our study on the ultra high order cumulants leads to the quantitative versions of the CLT.

We classify simple differential Lie and Jordan (super)coalgebras of finite rank. In particular, we provide an explicit description of the Lie supercoalgebras associated with the operator product expansion (OPE) of the n=2,3,4 superconformal Lie algebras and the exceptional Lie conformal superalgebra CK_6

In field theory, one can consider a variety of states. Within the framework of factorization algebras, one typically works with the natural augmentation state langle-rangle_{rm aug}. In physics, however, other states arise naturally, such as the compactification state langle-rangle_{rm cptf} or the Schwartz state langle-rangle_{rm Sch}, defined by imposing Schwartz boundary conditions. At first sight, the relation among these three states is not obvious.This paper gives a definition of the compactification state in factorization algebras and provides a method for handling infrared divergences in the massless theory. We then prove that the three states are equivalent in both the massive and massless cases.

One of the most unconventional features of topological phases of matter is the emergence of quasiparticles with exotic statistics, such as non-Abelian anyons in two dimensional systems. Recently, a different type of exotic particle statistics that is consistently defined in any dimension, called R-parastatistics, is also shown to be possible in a special family of topological phases. However, the physical significance of emergent parastatistics still remains elusive. Here we demonstrate a distinctive physical consequence of parastatistics by proposing a challenge game that can only be won using physical systems hosting paraparticles, as passing the challenge requires the two participating players to secretly communicate in an indirect way by exploiting the nontrivial exchange statistics of the quasiparticles. The winning strategy using emergent paraparticles is robust against noise, as well as the most relevant class of eavesdropping via local measurements. This provides both an operational definition and an experimental identity test for paraparticles, alongside a potential application in secret communication.

In this paper, we consider the magnetic anomaly detection problem which aims to find hidden ferromagnetic masses by estimating the weak perturbation they induce on local Earth's magnetic field. We consider classical detection schemes that rely on signals recorded on a moving sensor, and modeling of the source as a function of unknown parameters. As the usual spherical harmonic decomposition of the anomaly has to be truncated in practice, we study the signal vector subspaces induced by each multipole of the decomposition, proving they are not in direct sum, and discussing the impact it has on the choice of the truncation order. Further, to ease the detection strategy based on generalized likelihood ratio test, we rely on orthogonal polynomials theory to derive an analytical set of orthonormal functions (multipolar orthonormal basis functions) that spans the space of the noise-free measured signal. Finally, based on the subspace structure of the multipole vector spaces, we study the impact of the truncation order on the detection performance, beyond the issue of potential surparametrization, and the behaviour of the information criteria used to choose this order.

In this paper, which is a follow-up of our first paper "Normal forms for ordinary differential operators, I", we extend the explicit parametrisation of torsion free rank one sheaves on projective irreducible curves with vanishing cohomology groups obtained earlier to analogous parametrisation of torsion free sheaves of arbitrary rank with vanishing cohomology groups on projective irreducible curves.As an illustration of our theorem we calculate one explicit example of such parametrisation, namely for rank two sheaves on a Weierstrass cubic curve.

We develop a unified theoretical framework for neural architectures whose internal representations evolve as stationary states of dissipative Schrödinger-type dynamics on learned latent graphs. Each layer is defined by a fixed-point Schrödinger-type equation depending on a weighted Laplacian encoding latent geometry and a convex local potential. We prove existence, uniqueness, and smooth dependence of equilibria, and show that the dynamics are equivalent under the Bloch map to norm-preserving Landau--Lifshitz flows. Training over graph weights and topology is formulated as stochastic optimization on a stratified moduli space of graphs equipped with a natural Kähler--Hessian metric, ensuring convergence and differentiability across strata. We derive generalization bounds -- PAC-Bayes, stability, and Rademacher complexity -- in terms of geometric quantities such as edge count, maximal degree, and Gromov--Hausdorff distortion, establishing that sparsity and geometric regularity control capacity. Feed-forward composition of stationary layers is proven equivalent to a single global stationary diffusion on a supra-graph; backpropagation is its adjoint stationary system. Finally, directed and vector-valued extensions are represented as sheaf Laplacians with unitary connections, unifying scalar graph, directed, and sheaf-based architectures. The resulting model class provides a compact, geometrically interpretable, and analytically tractable foundation for learning latent graph geometry via fixed-point Schrödinger-type activations.

We develop foundations for a relational approach to quantum field theory (RQFT) based on the operational quantum reference frames (QRFs) framework considered in a relativistic setting. Unlike other efforts in combining QFT with QRFs, we use the latter to provide novel mathematical and conceptual foundations for the former. We focus on scalar fields in Minkowski spacetime and discuss the emergence of relational local (bounded) observables and (pointwise) fields from the consideration of Poincaré-covariant (quantum) frame observables defined over the space of (classical) inertial reference frames. We recover a relational notion of Poincaré covariance, with transformations on the system directly linked to the state preparations of the QRF. We introduce and analyse various causality conditions, and construct an explicit example of a covariant scalar relational quantum field which is causal relative to operationally meaningful preparations of a relativistic QRF. The theory makes direct contact with established foundational approaches to QFT: we demonstrate that the vacuum expectation values derived within our framework reproduce many of the essential properties of Wightman functions, carry out a detailed comparison of the proposed formalism with Wightman QFT with the frame smearing functions describing the QRF's localisation uncertainty playing the role of the Wightmanian test functions, and show how the properties of algebras generated by relational local observables suitably extend the core axioms of Algebraic QFT. We finish with an extensive outlook describing a number of further research directions. This work is an early step in revisiting the mathematical foundations of QFT from a relational and operational perspective.

There is a growing mechanics literature concerning the macroscopic properties of mechanism-based mechanical metamaterials. This amounts mathematically to a homogenization problem involving nonlinear elasticity. A key goal is to identify the "soft modes" of the metamaterial. We achieve this goal using methods from homogenization for some specific 2D examples -- including discrete models of the Rotating Squares metamaterial and the Kagome metamaterial -- whose soft modes are compressive conformal maps. The innovation behind this achievement is a new technique for bounding the effective energy from below, which takes advantage of the metamaterial's structure and symmetry.

We study one of the simplest integrable two-dimensional quantum field theories with a boundary: N free non-compact scalars in the bulk, constrained non-linearly on the boundary to lie on an (N-1)-sphere of radius 1/sqrt{g}. The N=1 case reduces to the single-channel Kondo problem, for N=2 the model describes dissipative Coulomb charging in quantum dots, and larger N is analogous to higher-spin impurity or multi-channel scenarios. Adding a boundary magnetic field -- a linear boundary coupling to the scalars -- enriches the model's structure while preserving integrability. Lukyanov and Zamolodchikov (2004) conjectured an expansion for the boundary free energy on the infinite half-cylinder in powers of the magnetic field. Using large-N saddle-point techniques, we confirm their conjecture to next-to-leading order in 1/N. Renormalization of the subleading solution turns out to be highly instructive, and we connect it to the RG running of g studied by Giombi and Khanchandani (2020).

We prove integrated local energy decay for solutions of the damped wave equation with time-dependent damping satisfying an appropriate generalization of the geometric control condition on asymptotically flat, stationary space-times. We first obtain a high frequency estimate, which we prove via a positive commutator estimate using an escape function explicitly constructed in terms of the damping around individual space-time trajectories. We combine the high frequency estimate with low and medium frequency results for the undamped problem, then we handle the damping term as a perturbation to obtain local energy decay.

Let (mathcal{A},mathrm{tr}) be a von Neumann algebra with a faithful, normal trace mathrm{tr}:mathcal{A}rightarrowmathbb{C}. For each ainmathcal{A}, define [ S(lambda,varepsilon)=mathrm{tr}[log((a-lambda)^{ast}(a-lambda )+varepsilon)],quadlambdainmathbb{C},~varepsilon>0, ] so that the limit as varepsilonrightarrow0^{+} of S is the log potential of the Brown measure of a. Suppose that for a fixed lambdainmathbb{C}, the function [ varepsilonmapstofrac{partial S}{partialvarepsilon}(lambda ,varepsilon)=mathrm{tr}[((a-lambda)^{ast}(a-lambda)+varepsilon )^{-1}] ] admits a real analytic extension to a neighborhood of 0 in mathbb{R}. Then we will show that lambda is outside the spectrum of a.We will apply this result to several examples involving circular and elliptic elements, as well as free multiplicative Brownian motions. In most cases, we will show that the spectrum of the relevant element a coincides with the support of its Brown measure.

We show that the requirement that the trace of the stress-energy tensor of matter must vanish if invariance under Weyl rescalings is a symmetry of a given gravitational theory is not universal. This requirement holds wherever the masses of timelike fields are constant parameters that are not transformed by Weyl rescalings, or if the energy density of perfect fluids transforms as rhorightarrowOmega^{-3}rho. In contrast, if the masses of timelike fields are point-dependent quantities transforming under the Weyl rescalings as mrightarrowOmega^{-1}m, and the energy density of perfect fluids transforms as rhorightarrowOmega^{-4}rho, the Weyl symmetry does not require the vanishing of the trace of the matter SET. This result is demonstrated in two different ways. In consequence, any matter fields, regardless of whether the trace of their stress-energy tensor vanishes or not, can be coupled to gravity. The phenomenological consequences of the novel result are drawn.

We show that a family of secret communication challenge games naturally define a hierarchy of emergent quasiparticle statistics in three-dimensional (3D) topological phases. The winning strategies exploit a special class of the recently proposed R-paraparticles to allow nonlocal secret communication between the two participating players. We first give a high-level, axiomatic description of emergent R-paraparticles, and show that any physical system hosting such particles admits a winning strategy. We then analyze the games using the categorical description of topological phases (where point-like excitations in 3D are described by symmetric fusion categories), and show that only R-paraparticles can win the 3D challenge in a noise-robust way, and the winning strategy is essentially unique. This analysis associates emergent R-paraparticles to deconfined gauge theories based on an exotic class of finite groups. Thus, even though this special class of R-paraparticles are fermions or bosons under the categorical classification, their exchange statistics can still have nontrivial physical consequences in the presence of appropriate defects, and the R-paraparticle language offers a more convenient description of the winning strategies. Finally, while a subclass of non-Abelian anyons can win the game in 2D, we introduce twisted variants that exclude anyons, thereby singling out R-paraparticles in 2D as well. Our results establish the secret communication challenge as a versatile diagnostic for both identifying and classifying exotic exchange statistics in topological quantum matter.

Over the past 50 years, spin glass models have generated a broad range of literature in mathematics, physics, and computer science. There has been much progress in characterizing and proving the limiting free energy of various models, stemming from the original formulas of Parisi. Comparatively less is known about the more detailed topic of free energy fluctuations. This paper concerns a family of models in which there has been considerable progress on fluctuations, namely the Sherrington-Kirkpatrick (SK) and spherical Sherrington-Kirkpatrick (SSK) models, along with their multi-species analogs. We present a survey of the literature on free energy fluctuations in these 2-spin models, discussing results from different temperature regimes, with and without an external field, including results on phase transitions.

This thesis addresses three problems arising in type II string theory compactified on a Calabi-Yau manifold. In the first one we study the hypermultiplet moduli space (HM), by working on its twistor space. Using data derived via mirror symmetry and S-duality, we compute NS5-instanton corrections to the HM metric in the one-instanton approximation.These corrections are weighted by D4-D2-D0 BPS indices, which coincide with rank 0 Donaldson-Thomas invariants and count the (signed) number of BPS black hole microstates. These invariants exhibit wall-crossing behavior and induce a Riemann-Hilbert problem. This problem can describe many setups, including the D-instanton corrected twistor space of the HM in type II string theory and is of independent mathematical interest. We consider a quantum deformation of the RH problem, induced by the refined BPS indices. Using a formulation of the problem in terms of a non-commutative Moyal star product, we provide a perturbative solution to it. From the adjoint form of this solution, we identify a generating function for coordinates on the still mysterious quantum analog of the twistor space.Finally, we study the modular properties of the D4-D2-D0 BPS indices, more precisely of their generating functions. It was previously argued, using S-duality, that the generating functions are higher depth mock modular forms. Moreover, they satisfy a modular completion equation, which fixes their shadow in terms of other (lower rank) generating functions. We start by bringing about a significant simplification to these equations and recovering subtle contributions that were overlooked. Then, we provide (a recipe for) solutions to these modular completion equations, up to all the holomorphic modular ambiguities that need to be fixed independently. For this, we use indefinite generalized theta series and Jacobi-like forms to write the solutions.

We consider interacting paraparticle chains with a constant R-matrix where the Hamiltonian sums over the internal degrees (flavors) of the paraparticles. For such flavor-blind Hamiltonians we show a general factorization of the Hilbert space into occupation and flavor parts with the Hamiltonian acting non-trivially only on the former. For open boundaries, the spectrum therefore coincides with that of the occupation Hamiltonian H_{rm occ} with the flavor part merely adding degeneracies. For periodic boundaries, a cyclic reordering of the flavors leads to a separation of H_{rm occ} into flux sectors at fixed particle number, thus making the parastatistics directly observable in the energy spectrum. For important exemplary cases, H_{rm occ} reduces to the XXZ chain with flux allowing for an exact solution. In the gapless regime, this solution shows flux-shifted c=1 conformal towers in the low-energy spectrum and a temperature-dependent chemical potential in the bulk thermodynamics.

In this article, we construct and analyse a renormalisation group (RG) map for the weakly coupled n-component |varphi|^4 model under periodic boundary conditions in dimension d ge 4. Both short-range and long-range interactions with upper critical dimension four are considered. This extends and refines the RG map constructed by Bauerschmidt, Brydges and Slade for the short-range model at d=4. This extension opens the door to establishing the exact decay rate of correlation functions of all of the models discussed. Furthermore, incorporating a large-field decay estimate and comparing with the finite-size scaling results of Michta, Park, and Slade, our analysis provides strong evidence for the emergence of a plateau in systems of finite volume with periodic boundary conditions.