Related papers: Location of eigenvalues of three-dimensional non-s…

. We study the statistical properties of the eigenvalues of non-Hermitian operators assoicated with the dissipative complex systems. By considering the Gaussian ensembles of such operators, a hierarchical relation between the correlators is…

In this paper we will prove new extrinsic upper bounds for the eigenvalues of the Dirac operator on an isometrically immersed surface $M^2 \hookrightarrow {\Bbb R}^3$ as well as intrinsic bounds for 2-dimensional compact manifolds of genus…

We consider a non-self-adjoint third order operator on the interval $[0,2]$ with real 1-periodic coefficients and three-point Dirichlet conditions at the points 0, 1 and 2. The eigenvalues of this operator consist an auxiliary spectrum for…

Discussed are $\pm m$ modes and $\pm m$ resonances of Dirac operators with vector potentials $H_{\!A}= \alpha \cdot (D - A(x)) + m \beta$. Asymptotic limits of $\pm m$ modes at infinity are derived when $|A(x)| \le C<x>^{-\rho}$, $\rho >…

A recently proposed approach for avoiding the ultraviolet divergence of Hamiltonians with particle creation is based on interior-boundary conditions (IBCs). The approach works well in the non-relativistic case, that is, for the Laplacian…

At nonzero density the eigenvalues of the Dirac operator move into the complex plane, while its singular values remain real and nonnegative. In QCD-like theories, the singular-value spectrum carries information on the diquark (or pionic)…

We show that the spectrum of the Dirac operator in complex Langevin simulations of QCD at non-zero chemical potential must behave in a way which is radically different from the one in simulations with ordinary non-complexified gauge fields:…

The paper concerns a problem of Dirac fermion doublet in the external monopole potential arisen out of embedding the Abelian monopole solution in the non-Abe- lian scheme. In this particular case, the Hamiltonian is invariant under some…

For a class of non-selfadjoint h-pseudodifferential operators in dimension 2, we determine all eigenvalues in an h-independent domain in the complex plane and show that they are given by a Bohr-Sommerfeld quantization condition. No complete…

In this work, we develop the method of multipliers for electromagnetic Dirac operators and establish sufficient conditions on the magnetic and electric fields that guarantee the absence of point spectrum. In the massless case, our approach…

Motivated by the problems of analytic hypoellipticity, we show that a special family of compact non self-adjoint operators has a non-zero eigenvalue. We recover old results by Christ,Hanges, Himonas, Pham-The-Lai and Robert proved by using…

Using the well known approach developed in the papers of B. Davies and his co-authors we obtain inequalities for the location of possible complex eigenvalues of non-selfadjoint functional difference operators. When studying the sharpness of…

We consider discrete one-dimensional Schr\"odinger operators with Sturmian potentials. For a full-measure set of rotation numbers including the Fibonacci case we prove absence of eigenvalues for all elements in the hull.

Assume that the compact Riemannian spin manifold $(M^n,g)$ admits a $G$-structure with characteristic connection $\nabla$ and parallel characteristic torsion ($\nabla T=0$), and consider the Dirac operator $D^{1/3}$ corresponding to the…

We consider the 3-dimensional Stark operator perturbed by a complex-valued potential. We obtain an estimate for the number of eigenvalues of this operator as well as for the sum of imaginary parts of eigenvalues situated in the upper…

A third order self-adjoint differential operator with periodic boundary conditions and an one-dimensional perturbation has been considered. For this operator, we first show that the spectrum consists of simple eigenvalues and finitely many…

We study the eigenvalue problem for the $g-$Laplacian operator in fractional order Orlicz-Sobolev spaces, where $g=G'$ and neither $G$ nor its conjugated function satisfy the $\Delta_2$ condition. Our main result is the existence of a…

Random Schroedinger operators with imaginary vector potentials are studied in dimension one. These operators are non-Hermitian and their spectra lie in the complex plane. We consider the eigenvalue problem on finite intervals of length n…

In this paper we study absence of embedded eigenvalues for Schr\"odinger operators on non-compact connected Riemannian manifolds. A principal example is given by a manifold with an end (possibly more than one) in which geodesic coordinates…

By developing the method of multipliers, we establish sufficient conditions on the magnetic field and the complex, matrix-valued electric potential, which guarantee that the corresponding system of Schr\"odinger operators has no point…