We extend the multiplicative submodularity of the principal determinants of a nonnegative definite hermitian matrix to other spectral functions. We show that if f is the primitive of a function that is operator monotone on an interval containing the spectrum of a hermitian matrix A, then the function I 7→ trf(A[I]) is supermodular, meaning that trf(A[I])+trf(A[J ]) 6 trf(A[I∪ J ]) + trf(A[I ∩ J...

New non Hermitian Hamiltonians are generated, as isospectral partners of the generalized Swanson model, viz., H− = A†A + αA2 + βA† 2, where α , β are real constants, with α 6= β, and A† and A are generalized creation and annihilation operators. It is shown that the initial Hamiltonian H−, and its partner H+, are related by pseudo supersymmetry, and they share all the eigen energies except for t...

In this work we investigate the Lp−Lq-mapping properties of resolvent associated with time-harmonic isotropic Maxwell operator. As spectral parameters close to spectrum are also covered by our analysis, obtain an Lp−Lq-type Limiting Absorption Principle for Our analysis relies on new results Helmholtz systems zero order non-Hermitian perturbations. Moreover, provide improved version Hermitian (...

We explain why the main conclusion of Bender et al, J. Phys. A 39, 1657 (2006), regarding the practical superiority of the non-Hermitian description of PT -symmetric quantum systems over their Hermitian description is not valid. Recalling the essential role played by the Hermitian description in the characterization and interpretation of the physical observables, we maintain that as far as the ...

Delocalization transition is numerically found in a non-Hermitian extension of discrete-time quantum walk on one-dimensional random medium. At the transition, an eigenvector gets delocalized and at same time corresponding energy eigenvalue (the imaginary unit times phase time-evolution operator) becomes complex. This accordance with Anderson model one dimension, called, Hatano-Nelson model. We ...

Let X be a compact manifold of dimension 2n equipped with an almost complex structure J : TX → TX, E a Hermitian vector bundle on X, and gX a Riemannian metric on X. Assume that the almost complex structure J is compatible with gX . Consider a Hermitian line bundle L over X endowed with a Hermitian connection ∇L such that its curvature R = (∇L)2 is nondegenerate. Thus, ω = i 2πR L is a symplect...

The overlap Dirac operator in lattice QCD requires the computation of the sign function of a matrix. While this matrix is usually Hermitian, it becomes non-Hermitian in the presence of a quark chemical potential. We show how the action of the sign function of a non-Hermitian matrix on an arbitrary vector can be computed efficiently on large lattices by an iterative method. A Krylov subspace app...

The spectral flow of the hermitian Dirac–Wilson operator H(m) has been used to construct a lattice version of the index of the Dirac operator. We clarify some aspects of this construction by showing the following (in 4D): When the curvature of the lattice gauge field satisfies an approximate smoothness condition, crossings of the origin by eigenvalues of H(m) can only happen when m is close to ...

in this paper we consider the solutions of linear systems of saddle point problems‎. ‎by using the spectrum of a quadratic matrix polynomial‎, ‎we study the eigenvalues of the iterative matrix of the hermitian and skew hermitian splitting method‎.

We describe all almost contact metric, almost hermitian and G 2-structures admitting a connection with totally skew-symmetric torsion tensor, and prove that there exists at most one such connection. We investigate its torsion form, its Ricci tensor, the Dirac operator and the ∇-parallel spinors. In particular, we obtain solutions of the type II string equations in dimension n = 5, 6 and 7.