Related papers: Exponential Dichotomies for Nonlocal Differential …
In this paper we introduce a model, the stochastic fractional delay differential equation (SFDDE), which is based on the linear stochastic delay differential equation and produces stationary processes with hyperbolically decaying…
Continuum limits are a powerful tool in the study of many-body systems, yet their validity is often unclear when long-range interactions are present. In this work, we rigorously address this issue and put forth an exact representation of…
In a nonrelativistic contact four-fermion model we show that simple regularisation prescriptions together with a definite fine-tuning of the cut-off-parameter dependence of ``bare'' quantities give the exact solutions for the two-particle…
We investigate interacting dark energy (IDE) models with phenomenological, non-linear interaction kernels $Q$, specifically $Q_{1}=3H\delta \left(\frac{\rho_{\rm dm}\rho_{\rm de}}{\rho_{\rm dm}+\rho_{\rm de}}\right)$, $Q_{2}=3H\delta…
In the Fractional Quantum Hall Effect (FQHE), in the noninteracting limit, only a fraction $\nu $ of the Lowest Landau Level (LLL) is occupied, producing a huge degeneracy. Interactions lift this degeneracy and mix in higher LL's. In the…
In this paper, ordinary and exponential dichotomies are defined in differential equations with equations with piecewise constant argument of general type. We prove the asymptotic equivalence between the bounded solutions of a linear system…
When seeking a numerical representation of a quantum-mechanical multiparticle problem it is tempting to replace a singular short-range interaction by a smooth finite-range pseudopotential. Finite basis set expansions, e.g.~in Fock space,…
We establish the Subgradient Theorem for monotone correspondences -- a monotone correspondence is equal to the subdifferential of a potential if and only if it is conservative, i.e. its integral along a closed path vanishes irrespective of…
This paper introduces significant advancements in fractional neural operators (FNOs) through the integration of adaptive hybrid kernels and stochastic multiscale analysis. We address several open problems in the existing literature by…
The exponential orthogonal polynomials encode via the theory of hyponormal operators a shade function $g$ supported by a bounded planar shape. We prove under natural regularity assumptions that these complex polynomials satisfy a three term…
We study the global dynamics of the universe within the framework of the Interacting Dark Matter (IDM) scenario. Assuming that the dark matter obeys the collisional Boltzmann equation, we can derive analytical solutions of the global…
Interacting dark energy (IDE) models, in which dark matter (DM) and dark energy (DE) exchange energy through a non-gravitational interaction, have long been proposed as candidates to address key challenges in modern cosmology. These include…
This work focuses on a class of regime-switching neutral stochastic functional differential equations (RNSFDEs) with infinite delay, in which the switching component can possess finite or countably infinite many states. To ensure the…
We establish the existence and nonlinear stability of travelling wave solutions for a class of lattice differential equations (LDEs) that includes the discrete FitzHugh-Nagumo system with alternating scale-separated diffusion coefficients.…
It was recently shown by the authors that a semilinear elliptic equation can be represented as an infinite-dimensional dynamical system in terms of boundary data on a shrinking one-parameter family of domains. The resulting system is…
This paper establishes a Freidlin-Wentzell large deviation principle for stochastic differential equations(SDEs) under locally weak monotonicity conditions and Lyapunov conditions. We illustrate the main result of the paper by showing that…
We present some recent advances in the productive and symbiotic interplay between general potential theories (subharmonic functions associated to closed subsets $\mathcal{F} \subset \mathcal{J}^2(X)$ of the 2-jets on $X \subset…
The formalism of the continuum random-phase approximation theory which treats, without ap- proximations, the continuum part of the single-particle spectrum, is extended to describe charge- exchange excitations. Our approach is…
Infinite-range interactions are known to facilitate the production of highly entangled states with applications in quantum information and metrology. However, many experimental systems have interactions that decay with distance, and the…
We investigate singular perturbation problems caused by small delays in the view of pseudo-exponential dichotomy. For a general linear non-autonomous retarded differential equation with small delay, previous works established the existence…