This paper is concerned with two-component Bose–Einstein condensates with both attractive intraspecies and interspecies interactions passing an obstacle in a plane, which can be described by the ground states of the nonlinear Schrödinger system defined in an exterior domain Ω=R2\ω, with ω⊂R2 being a bounded smooth convex domain. Under the assumption that the trapping potentials Vi(x) for i = 1, 2 attain

This note studies the non-linear fractional Schrödinger equation iu̇−(−Δ)su+(Iα*|u|p)|u|p−2u=0. In the mass super-critical and energy sub-critical regimes, the local solutions exist globally and scatter in the energy space or blow-up in finite time if the data belong to some stable sets.

Nonlocally related partial differential equation (PDE) systems can play an important role in the analysis of a given PDE system. In this paper, a new systematic method for obtaining nonlocally related PDE systems is developed. In particular, it is shown that if a PDE system admits q point symmetries whose infinitesimal generators form a q-dimensional solvable Lie algebra, then, for each resulting q-dimensional

We study a stochastic nonlinear Schrödinger system with multiplicative white noise in energy space H1. Based on deterministic and stochastic Strichartz estimates, we prove the local well-posedness of a mild solution. Then, we prove the global well-posedness in the mass subcritical case and the defocusing case. For the mass subcritical case, we also investigate the global existence when the L2 norm

The purpose of this manuscript is to establish well posedness as well as the existence of global and exponential attractor for a nonlinear Timoshenko system subject to control terms in the two equations of the system. Since the control terms act on both equations, we will not use the nonphysical relationship known as equal speeds of propagation of waves. A combination involving friction-delay and friction

In this paper, we show that it is always possible to deform a differential equation ∂xΨ(x) = L(x)Ψ(x) with L(x)∈sl2(C)(x) by introducing a small formal parameter ℏ in such a way that it satisfies the topological type properties of Bergère, Borot, and Eynard [Annales Henri Poincaré 16(12), 2713–2782 (2015)]. This is obtained by including the former differential equation in an isomonodromic system and

In this paper, we study the Cauchy problem for the generalized double dispersion equation with structural damping. The equation behaves as the usual diffusion phenomenon over the low frequency domain, while it admits a feature of regularity-loss on the high frequency part. The feature of regularity-loss leads to the weakly dissipative property of the equation. To overcome the weakly dissipative property

In this paper, we first define a generalization of the symplectic Schur functions and their vertex operator realizations. By means of the vertex operators, we obtain a series of non-linear partial differential equations of infinite order, the symplectic UC hierarchy (called the SUC hierarchy); we regard it as an extension of the symplectic KP hierarchy.

An initial-boundary value problem for the critical generalized 2D Zakharov–Kuznetsov equation posed on rectangles is considered. The existence, uniqueness, and exponential decay rate of global regular solutions for small initial data are established.

In this paper, we establish the global existence of radially symmetric strong solutions of a fluid–particle interaction system in an unbounded annular domain. Furthermore, the description for possible breakdown of regularity for the 3D problem is studied: the concentration of mass on the center.

Considering a system of equations modeling the chevron pattern dynamics, we show that the corresponding initial boundary value problem has a unique weak solution that continuously depends on initial data, and the semigroup generated by this problem in the phase space X0 ≔ L2(Ω) × L2(Ω) has a global attractor. We also provide some insight into the behavior of the system, by reducing it under special

This paper investigates the traveling wave in a nonlocal dispersal susceptible-infected-removed epidemic model with general nonlinear incidence and nonlocal delayed effects. It is shown that the existence and nonexistence of nontrivial traveling waves are fully determined by the basic reproduction number R0 and critical wave speed c*. When R0>1 and c > c*, the existence of traveling waves is obtained

We study a class of Schrödinger–Kirchhoff system involving a critical exponent. We aim to find suitable conditions to assure the existence of a positive ground state solution of Nehari–Pohoz̆aev type uε with exponential decay at infinity for ε, and uε concentrates around a global minimum point of V as ε → 0+. The nonlinear term includes the nonlinearity f(u) ∼ |u|p−1u for the well-studied case p ∈

This paper deals with a model the equatorial water waves with the Coriolis effect in the rotating fluid, which is called rotation-two-component Camassa–Holm system. The purpose of this work is to utilize the pseudo-parabolic regularization to establish the existence and uniqueness of weak solutions in a lower order Sobolev space Hs(R)×Hs−1(R) with 1

In this paper, we first introduce the first-order formalism with the self-dual structure of the motion equations, also called the Bogomol’nyi and Prasad–Sommerfield (BPS) equations. We observe that BPS equations arising in the generalized Maxwell–Higgs model under specific circumstances can be transformed into a vortices–antivortices equation, which is a nonlinear elliptic equation with the exponential

In this paper, we are concerned with non-isentropic Navier–Stokes equations governing compressible viscous and heat-conductive gases. We formulate an additional regularity assumption of low frequencies in Rd(d≥3) and then establish the sharp time-weighted inequality, which allows us to get the time-decay estimates of global strong solutions in the Lp critical Besov spaces. Precisely, it is shown that

We study the general solution of the Fokker–Planck equation in d dimensions with arbitrary space and time dependent diffusion matrix and drift terms. We show how to construct the solution for arbitrary initial distributions as an asymptotic expansion for small time. This generalizes the well-known asymptotic expansion of the heat kernel for the Laplace operator on a general Riemannian manifold. We

Let X be a toric Fano manifold given by a reflexive polytope Δ and let Crit(f)⊂(C*)s be the solution scheme of the Landau–Ginzburg system associated with a Laurent polynomial fu(z)≔∑n∈Δ◦(0)∩Zsunzn∈L(Δ◦). Motivated by mirror symmetry, we construct a map E : Crit(fu) → Pic(X) and show various cases of (X, fu) for which its image Eu(X)≔E(z)|z∈Crit(fu)⊂Pic(X) is a full strongly exceptional collection of

We prove an upper bound on the free energy of a two-dimensional homogeneous Bose gas in the thermodynamic limit. We show that for a2ρ ≪ 1 and βρ ≳ 1, the free energy per unit volume differs from the one of the non-interacting system by at most 4πρ2|lna2ρ|−1(2−[1−βc/β]+2) to leading order, where a is the scattering length of the two-body interaction potential, ρ is the density, β is the inverse temperature

For a large class of physically relevant operators on a manifold with discrete group action, we prove general results on the (non-)existence of a basis of well-localized Wannier functions for their spectral subspaces. This turns out to be equivalent to the freeness of a certain Hilbert module over the group C*-algebra canonically associated with the spectral subspace. This brings into play K-theoretic

In this paper, we consider the mean field limit and non-relativistic limit of the relativistic Vlasov–Maxwell particle system to the Vlasov–Poisson equation. With the relativistic Vlasov–Maxwell particle system being a starting point, we carry out the estimates (with respect to N and c) between the characteristic equation of both the Vlasov–Maxwell particle model and the Vlasov–Poisson equation, where

A remarkable mathematical property—somehow hidden and recently rediscovered—allows obtaining the eigenvectors of a Hermitian matrix directly from their eigenvalues. This opens the possibility to get the wavefunctions from the spectrum, an elusive goal of many fields in physics. Here, the formula is assessed for simple potentials, recovering the theoretical wavefunctions within machine accuracy. A striking

We provide a proof of the first correction to the leading asymptotics of the minimal energy of pseudo-relativistic molecules in the presence of magnetic fields, the so-called “relativistic Scott correction,” when max Zkα ≤ 2/π, where Zk is the charge of the kth nucleus and α is the fine structure constant. Our theorem extends a previous result by Erdős, Fournais, and Solovej to the critical constant

In this article, we answer the following question: If the wave equation possesses bound states, but it is exactly solvable for only a single non-zero energy, can we find all bound state solutions (energy spectrum and associated wavefunctions)? To answer this question, we use the “tridiagonal representation approach” to solve the wave equation at the given energy by expanding the wavefunction in a series

We introduce a group-theoretical extension of the Dicke model, which describes an ensemble of two-level atoms interacting with a finite radiation field. The latter is described by a spin model whose main feature is that it possesses a maximum number of excitations. The approach adopted here leads to a nonlinear extension of the Dicke model that takes into account both the intensity dependent coupling

In this paper, we analyze the capacity of a general model for arbitrarily varying classical-quantum channels (AVCQCs) when the sender and the receiver use correlation as a resource. In this general model, a jammer has side information about the channel input. We determine a single letter formula for the correlation assisted capacity. As an application of our main result, we determine the correlation

We construct a parameterized family of n ⊗ n PPT (positive partial transpose) states of corank one for each n ≥ 3. With a suitable choice of parameters, we show that they are n ⊗ n PPT entangled edge states of corank one for 3 ≤ n ≤ 1000. They violate the range criterion for separability in the most extreme way. Note that corank one is the smallest possible corank for such states. The corank of the

We construct a power series representation of certain functional integrals involving Grassmann variables that appear in Euclidean fermionic quantum field theory on a finite lattice in dimensions greater than or equal to 2. Our expansion has a local structure, is clean, and provides an easy alternative to the decoupling expansion and Mayer-type cluster expansions in any analysis. As an example, we show

In flat spacetime, two inequivalent vacuum states that arise rather naturally are the Rindler vacuum |R〉 and the Minkowski vacuum |M〉. We discuss several aspects of the Rindler vacuum, concentrating on the propagator and Schwinger (heat) kernel defined using |R〉, both in the Lorentzian and Euclidean sectors. We start by exploring an intriguing result due to Candelas and Raine [J. Math. Phys. 17, 2101

In this paper, we prove a reducibility result for a linear Schrödinger equation with a time quasi-periodic perturbation on T. In contrast with previous reducibility results of the Schrödinger equation, the assumption of the small amplitude of the time quasi-periodic perturbation is replaced by fast oscillating.

In this paper, we prove an infinite dimensional Kolmogorov-Arnold-Moser theorem. As an application, it is shown that there are many small-amplitude linearly-stable quasi-periodic solutions for higher dimensional wave equations with a real Fourier multiplier, which are under nonlocal and forced perturbations with a special structure in space and short range property.

From a three-dimensional boundary value problem for the time harmonic classical Maxwell equations, we derive the dispersion relation for a surface wave, the edge plasmon-polariton (EP), which is localized near and propagates along the straight edge of a planar, semi-infinite sheet with a spatially homogeneous, scalar conductivity. The sheet lies in a uniform and isotropic medium and serves as a model

This work is devoted to a class of Langevin equations involving strong damping and fast Markov switching. Modeling using continuous dynamics and discrete events together with their interactions much enlarged the applicability of Langevin equations in a random environment. Strong damping and fast switching are characterized by the use of multiple small parameters, resulting in singularly perturbed systems

Motivated by the realization of the Yang–Baxter equation of 2D integrable models in the 4D gauge theory of Costello–Witten–Yamazaki (CWY), we study the embedding of integrable 2D Toda field models inside this construction. This is done by using the Lax formulation of 2D integrable systems and by thinking of the standard Lax pair L± in terms of components of CWY gauge connection, propagating along particular

In this paper, q-deformed pseudo-fuzzy Dirac and chirality operators on the q-deformed pseudo-fuzzy EAdS2, using the pseudo-generalization of the quantum pseudo-fuzzy Ginsparg–Wilson algebra, have been constructed. Gauged q-deformed pseudo-fuzzy Dirac and chirality operators have also been constructed. In the limit case q → 1, it will be shown that these operators will become Dirac and chirality operators

A quantum mechanical model that realizes the Z2×Z2-graded generalization of the one-dimensional supertranslation algebra is proposed. This model shares some features with the well-known Witten model and is related to parasupersymmetric quantum mechanics, though the model is not directly equivalent to either of these. The purpose of this paper is to show that novel “higher gradings” are possible in

We present classical groups SL⋆(2) and SU⋆(2) as well as classical Lie algebra sl2⋆(C) associated with a new associative multiplication on 2 × 2 matrices. The idea of the new multiplication is generalized to the action of a 2 × 2 square matrix on a 2 × 1 column one. The coordinate Hopf algebra O(SLq⋆(2)) is introduced as a q-generalization of Hopf algebra O(SL⋆(2)), and it is shown that the coordinate

Berezin integration of functions of anticommuting Grassmann variables is usually seen as a formal operation, sometimes even defined via differentiation. Using the formalism of geometric algebra and geometric calculus in which the Grassmann numbers are endowed with a second associative product coming from a Clifford algebra structure, we show how Berezin integrals can be realized in the high dimensional

New families of non-parity-time-symmetric complex potentials with all-real spectra are derived by the supersymmetry method and the pseudo-Hermiticity method. With the supersymmetry method, we find families of non-parity-time-symmetric complex partner potentials, which share the same spectrum as base potentials with known real spectra, such as the (complex) Wadati potentials. Different from previous

We define an extension of operator-valued positive definite functions from the real or complex setting to topological algebras and describe their associated reproducing kernel spaces. The case of entire functions is of special interest, and we give a precise meaning to some power series expansions of analytic functions that appears in many algebras.

In this paper, we give a description of the spectral analysis of the Schrödinger operator L(q) with the potential q(x) = 4 cos2 x + 4iV sin 2x for all V > 1/2. First, we consider the Bloch eigenvalues and spectrum of L(q). Then, we investigate spectral singularities and essential spectral singularities (ESS). We prove that there exists a sequence V2 < V3 < ⋯ such that the operator L(q) has no ESS and

Stochastic Schrödinger equations are a special type of stochastic evolution equations in complex Hilbert spaces, which arise in the study of open quantum systems. Quantum Bernoulli noises refer to annihilation and creation operators acting on Bernoulli functionals, which satisfy a canonical anti-commutation relation in equal time. In this paper, we investigate a linear stochastic Schrödinger equation

We build two-dimensional quantum field theories on spin surfaces starting from theories on oriented surfaces with networks of topological defect lines and junctions. The construction uses a combinatorial description of the spin structure in terms of a triangulation equipped with extra data. The amplitude for the spin surfaces is defined to be the amplitude for the underlying oriented surface equipped

In this comment, we show that the eigenvalues of a quartic anharmonic oscillator obtained recently by means of the asymptotic iteration method may not be as accurate as the authors claim them to be.

If a measurement is made on one half of a bipartite system, then, conditioned on the outcome, the other half has a new reduced state. If these reduced states defy classical explanation-that is, if shared randomness cannot produce these reduced states for all possible measurements-the bipartite state is said to be steerable. Determining which states are steerable is a challenging problem even for low

In this paper, we study the compressible viscoelastic flows in three-dimensional whole space. Under the assumption of small initial data, we establish the unique global solution by the energy method. Furthermore, we obtain the time decay rates of the higher-order spatial derivatives of the solution if the initial data belong to L1(ℝ3) additionally.

In this paper, we are concerned with a class of Schrödinger-Poisson systems with the asymptotically linear or asymptotically 3-linear nonlinearity. Under some suitable assumptions on V, K, a, and f, we prove the existence, nonexistence, and asymptotic behavior of solutions via variational methods. In particular, the potential V is allowed to be sign-changing for the asymptotically linear case.

Tensor generalizations of affine vector fields called symmetric and antisymmetric affine tensor fields are discussed as symmetry of spacetimes. We review the properties of the symmetric ones, which have been studied in earlier works, and investigate the properties of the antisymmetric ones, which are the main theme in this paper. It is shown that antisymmetric affine tensor fields are closely related

In this paper, we study the following linearly coupled system [Formula: see text], where ε > 0 is a small parameter, Pi (x) are positive potentials, and λij = λji > 0 (i ≠ j) are coupling constants for i, j = 1, …, N. We investigate the effect of potentials to the structure of the solutions. More precisely, we construct multi-spikes solutions concentrating near the local maximum point [Formula: see

We prove results about the Hölder continuity of the spectral measures of the extended CMV matrix, given power law bounds of the solution of the eigenvalue equation. We thus arrive at a unitary analogue of the results of Damanik, Killip, and Lenz ["Uniform spectral properties of one-dimensional quasicrystals, III. α-continuity," Commun. Math. Phys.55, 191-204 (2000)] about the spectral measure of the

Let (H, S, α) be a monoidal Hom-Hopf algebra and [Formula: see text] the Hom-Yetter-Drinfeld category over (H, α). Then in this paper, we first find sufficient and necessary conditions for [Formula: see text] to be symmetric and pseudosymmetric, respectively. Second, we study the u-condition in [Formula: see text] and show that the Hom-Yetter-Drinfeld module (H, adjoint, Δ, α) (resp., (H, m, coadjoint

[This corrects the article on p. 022302 in vol. 49.].

Biological systems are often subject to external noise from signal stimuli and environmental perturbations, as well as noises in the intracellular signal transduction pathway. Can different stochastic fluctuations interact to give rise to new emerging behaviors? How can a system reduce noise effects while still being capable of detecting changes in the input signal? Here, we study analytically and

The multiscale approach to N-body systems is generalized to address the broad continuum of long time and length scales associated with collective behaviors. A technique is developed based on the concept of an uncountable set of time variables and of order parameters (OPs) specifying major features of the system. We adopt this perspective as a natural extension of the commonly used discrete set of time

The alpha-stable distributions introduced by Lévy play an important role in probabilistic theoretical studies and their various applications, e.g., in statistical physics, life sciences, and economics. In the present paper we study sequences of long-range dependent random variables whose distributions have asymptotic power-law decay, and which are called (q,alpha)-stable distributions. These sequences