Related papers: The Hubbard chain: Lieb-Wu equations and norm of t…
The optimized single-particle wave functions contained in the parameters of the Hubbard model (t and U) were determined for an infinite atomic chain. In effect, the electronic properties of the chain as a function of interatomic distance R…
The method used earlier for analysis of correlated nanoscopic systems is extended to infinite (periodic) s-band like systems described by the Hubbard model and its extensions. The optimized single-particle wave functions contained in the…
The nonlinear wave equation $u_{tt}-c(u)(c(u)u_x)_x=0$ determines a flow of conservative solutions taking values in the space $H^1(\mathbb{R})$. However, this flow is not continuous w.r.t. the natural $H^1$ distance. Aim of this paper is to…
This is a historical note. Bethe Ansatz solvable models are considered, for example XXZ Heisenberg anti-ferromagnet and Bose gas with delta interaction. Periodic boundary conditions lead to Bethe equation. The square of the norm of Bethe…
We find a novel phenomenon in the solution to the Wheeler-DeWitt equation by solving numerically the equation assuming $O(4)$-symmetry and imposing the Hartle-Hawking wave function as a boundary condition. In the slow-roll limit, as…
We test the validity of Isaacson's formula which states that high frequency and low amplitude gravitational waves behave as a radiation fluid on average. For this purpose, we numerically construct a solution of the vacuum Einstein equations…
For an arbitrary solution to the KdV hierarchy, the generating series of logarithmic derivatives of the tau-function of the solution can be expressed by the basic matrix resolvent via algebraic manipulations. Based on this we develop in…
Isochronous waveform solutions of homogeneous Li\'enard equations are obtained by a modification of the nonlinear factorization method of Rosu and Cornejo-P\'erez. The scheme is based on the assumption that the intermediate function $\Phi$…
A canonical structure compatible with the action of the Lorentz group can be obtained considering the energy and time as conjugate variables of an extended phase space. Scalar probability waves, describing free relativistic particles, are…
Given a continuous Hamiltonian $H : (x,p,u) \mapsto H(x,p,u)$ defined on $ T^*M \times \mathbb R $, where $M$ is a closed connected manifold, we study viscosity solutions, $u_\lambda : M\to \mathbb R$, of discounted equations: $ H(x, d_x…
With the ionic Hubbard model (IHM) in mind, we construct a non-trivial generalization of the Bethe ansatz (BA) wave function which naturally generalizes the Lieb-Wu wave function with an ionic parameter $\Delta$, and reduces to Lieb-Wu…
We consider the defocusing nonlinear wave equations (NLW) on the two-dimensional torus. In particular, we construct invariant Gibbs measures for the renormalized so-called Wick ordered NLW. We then prove weak universality of the Wick…
We identify the norm of the semigroup generated by the non-self-adjoint harmonic oscillator acting on $L^2(\Bbb{R})$, for all complex times where it is bounded. We relate this problem to embeddings between Gaussian-weighted spaces of…
The problem of classical particle in linear potential is studied by using the formalism of Hilbert space and tomographic probability distribution. The Liouville equation for this problem is solved by finding the density matrix satisfying…
In our previous works, a relationship between Hermite's two approximation problems and Schlesinger transformations of linear differential equations has been clarified. In this paper, we study tau-functions associated with holonomic…
We study the nonlinear wave equation (NLW) on the two-dimensional torus $\mathbb T^2$ with Gaussian random initial data on $H^s(\mathbb T^2) \times H^{s-1}(\mathbb T^2)$, $s < 0$, distributed according to the base Gaussian free field $\mu$…
We derive a closed formula for the determinant of the Hankel matrix whose entries are given by sums of negative powers of the zeros of the regular Coulomb wave function. This new identity applied together with results of Grommer and…
This paper is concerned with the existence and the regularity of global solutions to the linear wave equation associated with two-point type boundary conditions. We also investigate the decay properties of the global solutions to this…
As a first result we prove higher order Schauder estimates for solutions to singular/degenerate elliptic equations of type: \[ -\mathrm{div}\left(\rho^aA\nabla w\right)=\rho^af+\mathrm{div}\left(\rho^aF\right) \quad\textrm{in}\; \Omega \]…
Wave propagation in curved tubular domains is considered. A general version of Webster's equation is derived from the scattering passive wave equation. More precisely, it is shown that planar averages of a sufficiently smooth solution of…