Related papers: Almost Mathieu operators with completely resonant …
We consider Schr\^odinger operators $H_\alpha$ given by equation (1.1) below. We study the asymptotic behavior of the spectral density $E(H_\alpha, \lambda)$ when $\lambda$ goes to $0$ and the $L^1\to L^\infty$ dispersive estimates…
We introduce a one-parameter generalized oscillator algebra A(k) (that covers the case of the harmonic oscillator algebra) and discuss its finite- and infinite-dimensional representations according to the sign of the parameter k. We define…
Resonances in the reflection probability amplitude r(E) can occur in energy ranges in which the reflection probability R(E)=|r(E)|^2 is 1. They occur as the phase phi(E) defined by r(E) = t*(E)/t(E) = 1e^{i 2phi(E)} undergoes a rapid change…
We prove the existence and asymptotic expansion of a large class of solutions to nonlinear Helmholtz equations of the form \begin{equation*} (\Delta - \lambda^2) u = N[u], \end{equation*} where $\Delta = -\sum_j \partial^2_j$ is the…
We have obtained the metric operator $\Theta=\exp T$ for the non-Hermitian Hamiltonian model $H=\omega(a^{\dag}a+1/2)+\alpha(a^{2}-a^{\dag^{2}})$. We have also found the intertwining operator which connects the Hamiltonian to the adjoint of…
We consider the quasi-periodic Jacobi operator $H_{x,\omega}$ in $l^2(\mathbb{Z})$ $(H_{x,\omega}\phi)(n) = -b(x+(n+1)\omega)\phi(n+1) - b(x+n\omega)\phi(n-1) + a(x+n\omega)\phi(n) = E\phi(n),\ n\in\mathbb{Z},$ where $a(x),\ b(x)$ are…
We consider continuous one-dimensional multifrequency Schr\"odinger operators, with analytic potential, and prove Anderson localization in the regime of positive Lyapunov exponent for almost all phases and almost all Diophantine…
This paper presents a novel approach to address the constrained coding challenge of generating almost-balanced sequences. While strictly balanced sequences have been well studied in the past, the problem of designing efficient algorithms…
For a fixed d-tuple $\alpha=(\alpha_1,...,\alpha_d)\in(-1,\infty)^d$, consider the product space $\mathbb{R}_+^d:=(0,\infty)^d$ equipped with Euclidean distance $\arrowvert \cdot \arrowvert$ and the measure…
We investigate the electromagnetic field concentration between two nearly-touching inclusions that possess high-contrast electric permittivities in the quasi-static regime. By using layer potential techniques and asymptotic analysis in the…
A renormalization group procedure for effective particles is applied to quantum chromodynamics of one flavor of quarks with large mass m in order to calculate light-front Hamiltonians for heavy quarkonia, H_lambda, using perturbative…
This work deals with the Landau equation for very soft and Coulomb potentials near the associated Maxwellian equilibrium. We first investigate the corresponding linearized operator and develop a method to prove stability estimates of its…
Using the Hartree-Fock plus random-phase-approximation (HF+RPA), we study the impurity effect of $\Lambda$ hyperon on the collective vibrational excitations of double-$\Lambda$ hypernuclei. To this end, we employ a Skyrme-type $\Lambda N$…
The quasiparticle time blocking approximation (QTBA) is applied to describe E1 excitations in the even-even tin isotopes. Within the model pairing correlations, two-quasiparticle (2q), and 2q*phonon configurations are included. Thus the…
For a class of discrete quasi-periodic Schroedinger operators defined by covariant re- presentations of the rotation algebra, a lower bound on phase-averaged transport in terms of the multifractal dimensions of the density of states is…
Consider a semiclassical Hamiltonian \begin{equation*} H_{V, h} := h^{2} \Delta + V - E \end{equation*} where $h > 0$ is a semiclassical parameter, $\Delta$ is the positive Laplacian on $\mathbb{R}^{d}$, $V$ is a smooth, compactly supported…
We are concerned with the study of the twin non-local inequalities featuring non-homogeneous differential operators $$\displaystyle -\Delta^2 u + \lambda\Delta u \geq (K_{\alpha, \beta} * u^p)u^q \quad\text{ in } \mathbb{R}^N (N\geq 1),$$…
We give an explicit characterization of the most general quasi-Hermitian operator H, the associated metric operators \eta_+, and \eta_+-pseudo-Hermitian operators acting in two-dimensional complex Euclidean space C^2. These operators…
To find the Hermitian phase operatorof a single-mode electromagnetic field in quantum mechanics, the Schroedinger representation is extended to a larger Hilbert space augmented by states with infinite excitation by nonstandard analysis. The…
We study the Complex Ginzburg--Landau initial value problem $\partial_t u=(1+i\alpha) \partial_x^2 u + u - (1+i\beta) u |u|^2$, $u(x,0)=u_0(x)$ for a complex field $u\in{\bf C}$, with $\alpha,\beta\in{\bf R}$. We consider the Benjamin--Feir…