Zobrazeno 1 - 10
of 680
pro vyhledávání: '"34L05"'
Autor:
Curran, Mitchell, Marangell, Robert
We use the Maslov index to study the eigenvalue problem arising from the linearisation about a standing wave in the fourth-order cubic nonlinear Schr\"odinger equation (NLSE). Our analysis is motivated by a recent work by Bandara et. al., in which th
Externí odkaz:
http://arxiv.org/abs/2411.16903
Autor:
Davies, Bryn, Xiao, Yu
In this work, we characterise the statistics of Markov chains by constructing an associated sequence of periodic differential operators. Studying the density of states of these operators reveals the absolutely continuous invariant measure of the Mark
Externí odkaz:
http://arxiv.org/abs/2410.15829
Autor:
Parisi, Ignacio Bono, Pacharoni, Inés
In the theory of matrix-valued orthogonal polynomials, there exists a longstanding problem known as the Matrix Bochner Problem: the classification of all $N \times N$ weight matrices $W(x)$ such that the associated orthogonal polynomials are eigenfun
Externí odkaz:
http://arxiv.org/abs/2411.00798
Autor:
Lyu, Kang, Yang, Chuanfu
In this paper, we consider Schr\"odinger operators on $L^2(0,\infty)$ given by \begin{align} Hu=(H_0+V)u=-u^{\prime\prime}+V_0u+Vu=Eu,\nonumber \end{align} where $V_0$ is real, $1$-periodic and $V$ is the perturbation. It is well known that under per
Externí odkaz:
http://arxiv.org/abs/2410.09509
The purpose of this paper is to study nonnegative self-adjoint extensions associated with singular Sturm-Liouville expressions with strictly positive minimal operators. We provide a full characterization of all possible nonnegative self-adjoint exten
Externí odkaz:
http://arxiv.org/abs/2410.04647
Autor:
Bifulco, Patrizio, Kerner, Joachim
We study Schr\"odinger operators on compact finite metric graphs subject to $\delta'$-coupling conditions. Based on a novel modified local Weyl law, we derive an explicit expression for the limiting mean eigenvalue distance of two different self-adjo
Externí odkaz:
http://arxiv.org/abs/2407.21719
We study composite assemblages of dielectrics and metamaterials with respectively positive and negative material parameters. In the continuum case, for a scalar equation, such media may exhibit so-called plasmonic resonances for certain values of the
Externí odkaz:
http://arxiv.org/abs/2407.06661
Autor:
Safronov, Oleg
We consider the discrete Schr\"odinger operators with potentials whose values are read along the orbits of a shift of finite type. We study a certain subset of the collection of energies at which the Lyapunov exponent is zero and prove monotonicity o
Externí odkaz:
http://arxiv.org/abs/2407.05373
In this paper we introduce an index $\ell_c \in \mathbb{N}_0 \cup \lbrace \infty \rbrace$ which we call the `regularization index' associated to the endpoints, $c\in\{a,b\}$, of nonoscillatory Sturm-Liouville differential expressions with trace class
Externí odkaz:
http://arxiv.org/abs/2407.04847
Autor:
Freitas, Pedro, Lipovský, Jiří
We derive an expression for the spectral determinant of a second-order elliptic differential operator $\mathcal{T}$ defined on the whole real line, in terms of the Wronskians of two particular solutions of the equation $\mathcal{T} u=0$. Examples of
Externí odkaz:
http://arxiv.org/abs/2405.03469