Related papers: Dry Ten Martini problem for non self-dual extended…
Motivated by recent progress on non-Hermitian topological band theories, we study the energy spectrum of a generic two-band non-Hermitian Hamiltonian. We prove rigorously that the complex energy spectrum of such a non-Hermitian Hamiltonian…
The paper considers parabolic equations in non-divergent form with discontinuous coefficients at higher derivatives. Their investigation is most complicated because, in general, in the case of discontinuous coefficients, the uniqueness of a…
We present a new duality theory for non-convex variational problems, under possibly mixed Dirichlet and Neumann boundary conditions. The dual problem reads nicely as a linear programming problem, and our main result states that there is no…
It is shown that a one-dimensional damped wave equation with an odd time derivative nonlinearity exhibits small amplitude bifurcating time periodic solutions, when the bifurcation parameter is the linear damping coefficient is positive and…
Based on a thorough numerical analysis of the spectrum of Harper's operator, which describes, e.g., an electron on a two-dimensional lattice subjected to a magnetic field perpendicular to the lattice plane, we make the following conjecture:…
An extended Anderson model, including screening channels (non-hybridizing, but interacting with the local orbit), is studied within the Anderson-Yuval approach, originally devised for the single-channel Kondo problem. By comparing the…
This paper explores multiple closely related themes: bounding the complexity of Diophantine equations over the integers and developing mathematical proofs in parallel with formal theorem provers. Hilbert's Tenth Problem (H10) asks about the…
This paper is a continuation of the work on the spectral problem of Harper operator using algebraic geometry. We continue to discuss the local monodromy of algebraic Fermi curves based on Picard-Lefschetz formula. The density of states over…
In this paper we deal with two dimensional cubic Dirac equations appearing as effective model in gapped honeycomb structures. We give a formal derivation starting from cubic Schr\"odinger equations and prove the existence of standing waves…
We study dissipative translationally invariant free-fermionic theories with quadratic Liouvillians. Using a Lie-algebraic approach, we solve the Lindblad equation and find the density matrix at all times for arbitrary time dependence of the…
In this paper we discuss a general problem on metrical Diophantine approximation associated with a system of linear forms. The main result is a zero-one law that extends one-dimensional results of Cassels and Gallagher. The paper contains a…
We suggest that KAM theory could be extended for certain infinite-dimensional systems with purely discrete linear spectrum. We provide empirical arguments for the existence of square summable infinite-dimensional invariant tori in the…
This paper investigates the spectral properties of Jacobi matrices with limit-periodic coefficients. We show that for a residual set of such matrices, the spectrum is a Cantor set of zero Lebesgue measure, and the spectral measures are…
In the context of Hilbert's tenth problem, an outstanding open case is that of complex entire functions in one variable. A negative solution is known for polynomials (by Denef) and for exponential polynomials of finite order (by Chompitaki,…
Any form of dark matter which was in thermal equilibrium with the Standard Model in the early Universe must have some annihilation mechanism in order to avoid overclosure. In general, such models are now constrained by the negative…
We extend the theory of viscosity solutions to treat scalar-valued doubly-nonlinear evolution equations. Such equations arise naturally in many mechanical models including a dry friction. After providing a suitable definition for…
We consider extended CMV matrices with analytic quasi-periodic Verblunsky coefficients with Diophantine frequency vector in the perturbatively small coupling constant regime and prove the analyticity of the tongue boundaries. As a…
We employ weakly nonlinear theory to derive an amplitude equation for the conserved-Hopf instability, i.e., a generic large-scale oscillatory instability for systems with two conservation laws. The resulting equation represents in the…
Examples of scalar conserved currents are presented for trigonometric, hyperbolic and elliptic versions of the Hubbard model with non-nearest neighbour variable range hopping. They support for the first time the hypothesis about the…
We address the problem of constructing the non-associative version of the Dynkin form of the Baker-Campbell-Hausdorff formula; that is, expressing $\log (\exp (x)\exp(y))$, where $x$ and $y$ are non-associative variables, in terms of the…