A constructive algorithm based on the theory of spectral pairs for constructing nonuniform wavelet basis in \(L^{2}(\mathbb R)\) was considered by Gabardo and Nashed (J Funct. Anal. 158:209-241, 1998). In this setting, the associated translation set \({\Lambda } =\left \{ 0,r/N\right \}+2 \mathbb Z\) is no longer a discrete subgroup of \(\mathbb R\) but a spectrum associated with a certain one-dimensional

As discussed in Bahns et al. (2015) fundamental physical principles suggests that, close to cosmological singularities, the effective Planck length diverges, hence a “quantum point” becomes infinitely extended. We argue that, as a consequence, at the origin of times spacetime might reduce effectively to a single point and interactions disappear. This conclusion is supported by converging evidences

In 1983, Klaus studied a class of potentials with bumps and computed the essential spectrum of the associated Schrödinger operator with the help of some localisations at infinity. A key hypothesis is that the distance between two consecutive bumps tends to infinity at infinity. In this article, we introduce a new class of graphs (with patterns) that mimics this situation, in the sense that the distance

In this paper, first, we investigate the commuting property between the normal Jacobi operator \({\bar R}_{N}\) and the structure Jacobi operator Rξ for Hopf real hypersurfaces in the complex quadric Qm = SOm+ 2/SOmSO2 for \(m \geqslant 3\), which is defined by \({\bar R}_{N} R_{\xi } = R_{\xi }{\bar R}_{N}\). Moreover, a new characterization of Hopf real hypersurfaces with \(\mathfrak A\)-principal

The two-time distribution gives the limiting joint distribution of the heights at two different times of a local 1D random growth model in the curved geometry. This distribution has been computed in a specific model but is expected to be universal in the KPZ universality class. Its marginals are the GUE Tracy-Widom distribution. In this paper we study two limits of the two-time distribution. The first

Tensor field theory (TFT) focuses on quantum field theory aspects of random tensor models, a quantum-gravity-motivated generalisation of random matrix models. The TFT correlation functions have been shown to be classified by graphs that describe the geometry of the boundary states, the so-called boundary graphs. These graphs can be disconnected, although the correlation functions are themselves connected

It is shown that when dependence on the second flow of the KP hierarchy is added, the resulting semi-stationary wave function of certain points in George Wilson’s adelic Grassmannian are generating functions of the exceptional Hermite orthogonal polynomials. This surprising correspondence between different mathematical objects that were not previously known to be so closely related is interesting in

Let X be a compact Riemann surface of genus \(g \geqslant 2\), and let D ⊂ X be a fixed finite subset. Let \({\mathscr{M}}(r,d,\alpha )\) denote the moduli space of stable parabolic G-bundles (where G is a complex orthogonal or symplectic group) of rank r, degree d and weight type α over X. Hitchin, in his paper Hitchin (Duke Math. J. 54(1), 91–114, 1987) discovered that the cotangent bundle of the

In this paper, we prove the uniform-in-η estimates of the local strong solutions of the density-dependent incompressible MHD system in a bounded domain. Here η is the resistivity coefficient.

We propose a general procedure to construct noncommutative deformations of an algebraic submanifold M of \(\mathbb {R}^{n}\), specializing the procedure [G. Fiore, T. Weber, Twisted submanifolds of \(\mathbb {R}^{n}\), arXiv:2003.03854] valid for smooth submanifolds. We use the framework of twisted differential geometry of Aschieri et al. (Class. Quantum Grav. 23, 1883–1911, 2006), whereby the commutative

Let \(H:\text {dom}(H)\subseteq \mathfrak {F}\to \mathfrak {F}\) be self-adjoint and let \(A:\text {dom}(H)\to \mathfrak {F}\) (playing the role of the annihilation operator) be H-bounded. Assuming some additional hypotheses on A (so that the creation operator A∗ is a singular perturbation of H), by a twofold application of a resolvent Kreı̆n-type formula, we build self-adjoint realizations \(\widehat

In this paper we consider Wronskian polynomials labeled by partitions that can be factorized via the combinatorial concepts of p-cores and p-quotients. We obtain the asymptotic behavior for these polynomials when the p-quotient is fixed while the size of the p-core grows to infinity. For this purpose, we associate the p-core with its characteristic vector and let all entries of this vector simultaneously

We prove that Weyl quantization preserves constant of motion of the Harmonic Oscillator. We also prove that if f is a classical constant of motion and \(\mathfrak {Op}(f)\) is the corresponding operator, then \(\mathfrak {Op}(f)\) maps the Schwartz class into itself and it defines an essentially self-adjoint operator on \(L^{2}(\mathbb {R}^{n})\). As a consequence, we obtain detailed spectral information

The formation of singularity of strong solutions to the two-dimensional (2D) Cauchy problem of the compressible Navier-Stokes equations with variable viscosity is considered. It is shown that for the initial density allowing vacuum, the strong solution exists globally if the density is bounded from above. Some weighted estimates play a crucial role in the proof.

We consider a scalar quantum field ϕ with arbitrary polynomial self-interaction in perturbation theory. If the field variable ϕ is repaced by a global diffeomorphism ϕ(x) = ρ(x) + a1ρ2(x) + …, this field ρ obtains infinitely many additional interaction vertices. We propose a systematic way to compute connected amplitudes for theories involving vertices which are able to cancel adjacent edges. Assuming

We develop scattering theory for non-local Schrödinger operators defined by functions of the Laplacian that include its fractional power (−Δ)ρ with \(0<\rho \leqslant 1\). In particular, our function belongs to a wider class than the set of Bernstein functions. By showing the existence and non-existence of the wave operators, we clarify the threshold between the short and long-range decay conditions

This paper reformulates Li-Bland’s definition for LA-Courant algebroids, or Poisson Lie 2-algebroids, in terms of split Lie 2-algebroids and self-dual 2-representations. This definition generalises in a precise sense the characterisation of (decomposed) double Lie algebroids via matched pairs of 2-representations. We use the known geometric examples of LA-Courant algebroids in order to provide new

We construct a solution for the 1d integro-differential stationary equation derived from a finite-volume version of the mesoscopic model proposed in Giacomin and Lebowitz (J. Stat. Phys. 87(1), 37–61, 1997). This is the continuous limit of an Ising spin chain interacting at long range through Kac potentials, staying in contact at the two edges with reservoirs of fixed magnetizations. The stationary

We study spinful non-interacting electrons moving in two-dimensional materials which exhibit a spectral gap about the Fermi energy as well as time-reversal invariance. Using Fredholm theory we revisit the (known) bulk topological invariant, define a new one for the edge, and show their equivalence (the bulk-edge correspondence) via homotopy.

We propose an extended version of supersymmetric quantum mechanics which can be useful if the Hamiltonian of the physical system under investigation is not Hermitian. The method is based on the use of two, in general different, superpotentials. Bi-coherent states of the Gazeau-Klauder type are constructed and their properties are analyzed. Some examples are also discussed, including an application

We determine a counterexample to strong diamagnetism for the Laplace operator in the unit disc with a uniform magnetic field and Robin boundary condition. The example follows from the accurate asymptotics of the lowest eigenvalue when the Robin parameter tends to \(-\infty \).

The notion of Poisson quasi-Nijenhuis manifold generalizes that of Poisson-Nijenhuis manifold. The relevance of the latter in the theory of completely integrable systems is well established since the birth of the bi-Hamiltonian approach to integrability. In this note, we discuss the relevance of the notion of Poisson quasi-Nijenhuis manifold in the context of finite-dimensional integrable systems.

In this work, we investigate a generalized nonlinear Schrödinger equation on the quarter plane. The initial data are vanishing at infinity while the boundary data are time-periodic, of the form ae2iωt+iδ. The main purpose of this work is to consider the long-time asymptotics of the solution to the initial-boundary value problems. Furthermore, we find that the solutions of the initial-boundary value

We consider the existence of global attractor for non-Newtonian fluids near the BCS-BEC crossover in this paper. By Gronwall’s inequality, interpolar inequality and the techniques for proving regularity theory in partial differential equations, etc., we establish suitable prior estimates and obtain the global attractor for non-Newtonian fluids.

We regard the Cauchy problem for a particular Whitham–Boussinesq system modelling surface waves of an inviscid incompressible fluid layer. The system can be seen as a weak nonlocal dispersive perturbation of the shallow water system. The proof of well-posedness relies on energy estimates. However, due to the symmetry lack of the nonlinear part, in order to close the a priori estimates one has to modify

We study the motion of charged particle under a natural choice of electromagnetic field in a general class of compact homogeneous spaces. As a special case we describe the motion in homogeneous Riemannian spaces (G/H,g), where g is any deformation of a normal metric along the fibers of a homogeneous fibration \(K/H\rightarrow G/H\rightarrow G/K\).

Given N absolutely continuous probabilities \(\rho _{1}, \dotsc , \rho _{N}\) over \({\mathbb {R}}^{d}\) which have Sobolev regularity, and given a transport plan P with marginals \(\rho _{1}, \dotsc , \rho _{N}\), we provide a universal technique to approximate P with Sobolev regular transport plans with the same marginals. Moreover, we prove a sharp control of the energy and some continuity properties

We study the spectrum and dynamics of a one-dimensional discrete Dirac operator in a random potential obtained by damping an i.i.d. environment with an envelope of type n−α for α > 0. We recover all the spectral regimes previously obtained for the analogue Anderson model in a random decaying potential, namely: absolutely continuous spectrum in the super-critical region \(\alpha >\frac 12\); a transition

For a system of N bosons in one space dimension with two-body δ-interactions the Hamiltonian can be defined in terms of the usual closed semi-bounded quadratic form. We approximate this Hamiltonian in norm resolvent sense by Schrödinger operators with rescaled two-body potentials, and we estimate the rate of this convergence.

We construct P(ϕ)1-processes indexed by the full time-line, separately derived from the functional integral representations of the relativistic and non-relativistic Nelson models in quantum field theory. These two cases differ essentially by sample path regularity. Associated with these processes we define a martingale which, under an appropriate scaling, allows to obtain a central limit theorem for

We analyse a Curie-Weiss model with two disjoint groups of spins with homogeneous coupling. We show that similarly to the single-group Curie-Weiss model a bivariate law of large numbers holds for the normed sums of both groups’ spin variables. We also show central limit theorem in the high temperature regime.

In this paper, by maximal regularity estimates for the Stokes equation, we establish the local existence of solutions to the three-dimensional magnetic Bénard system with Hall, ion-slip effects and zero thermal conductivity under the condition that the initial data *.

In this article, we study the mean curvature type flow of spacelike graphical hypersurfaces in Lorentzian warped product. This flow was introduced by Guan and Li in [6]. Under mild assumptions on the warping function and the Ricci curvature of the base manifold, we obtain the longtime existence and smooth convergence to an umbilic slice for this flow in Lorentzian setting. As an application of the

We study the structure of the Mather and Aubry sets for the family of Lagrangians given by the kinetic energy associated to a Riemannian metric g on a closed manifold M. In this case the Euler-Lagrange flow is the geodesic flow of (M, g). We prove that there exists a residual subset of the set of all conformal metrics to g, such that, if \( \overline g \in G\) then the corresponding geodesic flow has

We give a direct proof for the positivity of Kirillov’s character on the convolution algebra of smooth, compactly supported functions on a connected, simply connected nilpotent Lie group G. Then we use this positivity result to construct a representation of G × G and establish a G × G-equivariant isometric isomorphism between our representation and the Hilbert–Schmidt operators on the underlying representation

In this note, we initiate a study of the finite-dimensional representation theory of a class of algebras that correspond to noncommutative deformations of compact surfaces of arbitrary genus. Low dimensional representations are investigated in detail and graph representations are used in order to understand the structure of non-zero matrix elements. In particular, for arbitrary genus greater than one

In this paper, we provide a new approach to get global well-posedness for the 3D liquid crystal system with large vertical velocity in the critical L2 framework. The novelty is that there is not one additional derivative when we treat the pressure. Furthermore, our idea can be applied to get global well-posedness for the 3D damped Euler equations with large vertical velocity, while the previous ideas

Using a left multiplication defined on a right quaternionic Hilbert space, we shall demonstrate that pure squeezed states, which are obtained by the sole action of the squeeze operator on the vacuum state, can be defined with all the desired properties on a right quaternionic Hilbert space. Further, we shall also demonstrate that squeezed states, which are obtained by the action of the squeeze operator

We prove that for every semigroup of Schwarz maps on the von Neumann algebra of all bounded linear operators on a Hilbert space which has a subinvariant faithful normal state there exists an associated semigroup of contractions on the space of Hilbert-Schmidt operators of the Hilbert space. Moreover, we show that if the original semigroup is weak∗ continuous then the associated semigroup is strongly

We consider a generic system composed of a fixed number of particles distributed over a finite number of energy levels. We make only general assumptions about system’s properties and the entropy. System’s constraints other than fixed number of particles can be included by appropriate reduction of system’s state space. For the entropy we consider three generic cases. It can have a maximum in the interior

We introduce the notion of Reeb parallel structure Jacobi operator for real hypersurfaces in the complex hyperbolic quadric \(Q^{*m}=SO^{0}_{2,m}/SO_{2} SO_{m}\), \(m \geqslant 3\), and give a classification theorem for real hypersurfaces in Q∗m, \(m \geqslant 3\), with Reeb parallel structure Jacobi operator.

We describe the main classes of non-signalling bipartite correlations in terms of states on operator system tensor products. This leads to the introduction of another new class of games, called reflexive games, which are characterised as the hardest non-local games that can be won using a given set of strategies. We provide a characterisation of their perfect strategies in terms of operator system

Cecotti and Vafa proposed in 1993 a beautiful idea how to associate spectral numbers\(\alpha _{1},...,\alpha _{n}\in \mathbb {R}\) to real upper triangular n × n matrices S with 1’s on the diagonal and eigenvalues of S− 1St in the unit sphere. Especially, \(\exp (-2\pi i\alpha _{j})\) shall be the eigenvalues of S− 1St. We tried to make their idea rigorous, but we succeeded only partially. This paper

This paper deals with the Cauchy problem of compressible magnetohydrodynamic equations in the whole space ℝ3. We show that if, in addition, the conservation law of the total mass is satisfied (i.e., ρ0 ∈ L1), then the global existence theorem with small density and L3-norm of H0 holds for any γ > 1. It is worth mentioning that the initial velocity can be arbitrarily large and the initial vacuum is

The purpose of the present paper is to analyze correlation structures of the ground states of the Schrödinger operator. We construct Griffiths inequalities for the ground state expectations by applying operator-theoretic correlation inequalities. As an example of such an application, we study the ground state properties of Schrödinger operators.

Spectral properties of random Schrödinger operators are encoded in the average of products of Greens functions. For probability distributions with enough finite moments, the supersymmetric approach offers a useful dual representation. Here we use supersymmetric polar coordinates to derive a dual representation that holds for general distributions. We apply this result to study the density of states

We consider the stochastic higher spin six vertex (SHS6V) model introduced by Corwin and Petrov (Commun. Math. Phys., 343(2), 651–700 2016) with general integer spin parameters I, J. Starting from near stationary initial condition, we prove that the SHS6V model converges to the Kardar-Parisi-Zhang (KPZ) equation under weakly asymmetric scaling. This generalizes the result in Corwin et al. (2018, Theorem

In this paper we consider fourth order differential operators on semi-axis with Robin type boundary condition at zero. Using the commutation method we obtain sharp Lieb-Thirring inequalities for the negative eigenvalues of double multiplicity.

In this article we derive the reflectionless solutions of the 2 + 2 matrix NLS equation with vanishing boundary conditions and four different symmetries by using the matrix triplet method of representing the Marchenko integral kernel in separated form. Apart from using the Marchenko method, these solutions are also verified by direct substitution in the 2 + 2 NLS equation.

It is well-known that a spacetime with its causal relation is a partially ordered set (poset for short). If it is globally hyperbolic, then it is a bicontinuous poset whose the interval topology is the manifold topology. In this work, we will state a new condition on a poset, which is called DS-FI cluster point condition and we show that when a causally simple spacetime \({\mathscr{M}}\) as a poset

In this paper we focus on the large time behaviour of momentum support for a Novikov type equation. It is shown that the momentum support can be large enough as time evolves if the initial data which is compactly supported keeps its sign.

We describe a construction of generalized Maxwell theories – higher analogues of abelian gauge theories – in the factorization algebra formalism of Costello and Gwilliam, allowing for analysis of the structure of local observables. We describe the phenomenon of abelian duality for local observables in these theories as a form of Fourier duality, relating observables in theories with dual abelian gauge

We study a general class of systems of interacting particles that randomly interact to form new or different particles. In addition to the distribution of particles we consider the fluxes, defined as the rescaled number of jumps of each type that take place in a time interval. We prove a dynamic large deviations principle for the fluxes under general assumptions that include mass-action chemical kinetics

Systems of Dyson–Schwinger equation represent the equations of motion in quantum field theory. In this paper, we follow the combinatorial approach and consider Dyson–Schwinger equations as fixed point equations that determine the perturbation series by usage of graph insertion operators. We discuss their properties under the renormalization flow, prove that fixed points are scheme independent, and

We consider a symmetric random walk on the ν-dimensional lattice, whose exit probability from the origin is modified by an antisymmetric perturbation and prove the local central limit theorem for this process. A short-range correction to diffusive behaviour appears in any dimension along with a long-range correction in the one-dimensional case.

As a generalization of the integrable extended Toda hierarchy and a reduction of the extended multicomponent Toda hierarchy, from the point of a commutative subalgebra of \(gl(2,\mathbb {C})\), we construct a strongly coupled extended Toda hierarchy(SCETH) which will be proved to possess a Virasoro type additional symmetry by acting on its tau-function. Further we give the multi-fold Darboux transformations

In this study, we consider a quantum waveguide with random boundary conditions . Precisely we consider Laplace operator restricted to a two dimensional straight strip of width d. We consider Dirchilet boundary condition on y = 0, while on y = d we consider mixed, Dirchilet and Neumann boundary condition in a random way. We prove that the integrated density of states of the relevant operator exhibits

We provide sufficient conditions for the existence of a pair of symmetric periodic solutions in the Maxwell-Bloch differential equations modeling laser systems. These periodic solutions come from a zero-Hopf bifurcation studied using recent results in averaging theory.

We consider a product of 2 × 2 random matrices which appears in the physics literature in the analysis of some 1D disordered models. These matrices depend on a parameter 𝜖 > 0 and on a positive random variable Z. Derrida and Hilhorst (J. Phys. 16(12), 2641, 1983, § 3) conjecture that the corresponding characteristic exponent has a regular expansion with respect to 𝜖 up to — and not further — an order

The main result of this paper is a sharp upper bound on the first positive eigenvalue of Dirac operators in two dimensional simply connected C3-domains with infinite mass boundary conditions. This bound is given in terms of a conformal variation, explicit geometric quantities and of the first eigenvalue for the disk. Its proof relies on the min-max principle applied to the squares of these Dirac operators