Related papers: Semi-classical Analysis and Pseudospectra

We study the trace class perturbations of the half-line, discrete Laplacian and obtain a new bound for the perturbation determinant of the corresponding non-self-adjoint Jacobi operator. Based on this bound, we obtain the Lieb--Thirring…

The semi-classical study of a 1-dimensional Schr\"odinger operator near a non-degenerate maximum of the potential has lead Colin de Verdi\`ere and Parisse to prove a microlocal normal form theorem for any 1-dimensional pseudo-differential…

Bifurcations of classical orbits introduce divergences into semiclassical spectra which have to be smoothed with the help of uniform approximations. We develop a technique to extract individual energy levels from semiclassical spectra…

Let A(x) be a holomorphic family of bounded self-adjoint operators on a separable Hilbert space H and let A(x)_n be the orthogonal compressions of A(x) to the span of first n elements of an orthonormal basis of H. The problem considered…

We introduce the new concepts of pseu\-do numerical range for operator functions and families of sesquilinear forms as well as the pseu\-do block numerical range for $n \times n$ operator matrix functions. While these notions are new even…

We derive analytic expressions for the wavefunctions and energy levels in the semiclassical approximation for perturbed integrable systems. We find that some eigenstates of such systems are substantially different from any of the…

We study a semiclassical inverse spectral problem based on a spectral asymptotics result of arXiv:math/0502032, which applies to small non-selfadjoint perturbations of selfadjoint $h$-pseudodifferential operators in dimension 2. The…

We study descendants of inhomogeneous vertex models with boundary reflections when the spin-spin scattering is assumed to be quasi--classical. This corresponds to consider certain power expansion of the boundary-Yang-Baxter equation (or…

In this study, we are concerned with spectral problems of second-order vector dynamic equations with two-point boundary value conditions and mixed derivatives, where the matrix-valued coefficient of the leading term may be singular, and the…

We establish the various properties as well as diverse relations of the ascent and descent spectra for bounded linear operators. We specially focus on the theory of subspectrum. Furthermore, we construct a new concept of convergence for…

The paper deals with the semi-Dirac operator in a half-space arising in the description of quasiparticles in quantum mechanics as well as in semi-metals materials and related structures. It completely shows the self-adjointness, computes…

We prove local convergence results for the spectra and pseudospectra of sequences of linear operators acting in different Hilbert spaces and converging in generalised strong resolvent sense to an operator with possibly non-empty essential…

The problem of approximating the discrete spectra of families of self-adjoint operators that are merely strongly continuous is addressed. It is well-known that the spectrum need not vary continuously (as a set) under strong perturbations.…

In this short paper we discuss the precise relationship between the semiclassical and standard pseudodifferential algebras and explore implications such as for large spectral parameter elliptic estimates, even in the case of…

Depending on the behaviour of the complex-valued electromagnetic potential in the neighbourhood of infinity, pseudomodes of one-dimensional Dirac operators corresponding to large pseudoeigenvalues are constructed. This is a first systematic…

We define a class of discrete operators acting on infinite, finite or periodic sequences mimicking the standard properties of pseudo-differential operators. In particular we can define the notion of order and regularity, and we recover the…

The semiclassical limit of the derivative nonlinear Schrodinger equation with periodic initial conditions is studied analytically and numerically. The spectrum of the associated scattering problem for a certain class of initial conditions,…

We investigate the spectral analysis of a class of pseudo-differential operators in one dimension. Under symmetry assumptions, we prove an asymptotic formula for the splitting of the first two eigenvalues. This article is a first example of…

We establish the convergence of pseudospectra in Hausdorff distance for closed operators acting in different Hilbert spaces and converging in the generalised norm resolvent sense. As an assumption, we exclude the case that the limiting…

We construct an abstract pseudodifferential calculus with operator-valued symbol, adapted to the treatment of Coulomb-type interactions, and we apply it to study the quantum evolution of molecules in the Born-Oppenheimer approximation, in…