Maxwell’s equations for electrodynamics of dispersive and absorptive (passive) media are written in the form of the Schrödinger equation with a non-Hermitian Hamiltonian. The Lanczos time-propagation scheme is modified to include non-Hermitian Hamiltonians and used, in combination with the Fourier pseudospectral method, to solve the initial-value problem. The time-domain algorithm developed is ...

An iterative scheme is set up for solving the loop equation of the hermitian one-matrix model with a multi-cut structure. Explicit results are presented for genus one for an arbitrary but finite number of cuts. Due to the complicated form of the boundary conditions, the loop correlators now contain elliptic integrals. This demonstrates the existence of new universality classes for the hermitian...

Suppose M is an n-dimensional Kähler manifold and L is an ample line bundle over M . Let the Kähler form of M be ωg and the Hermitian metric of L be H. We assume that ωg is the curvature of H, that is, ωg = Ric(H). The Kähler metric of ωg is called a polarized Kähler metric on M . Using H and ωg, for any positive integer m, H 0(M,Lm) becomes a Hermitian inner product space. We use the following...

We present an adaptive multigrid solver for application to the non-Hermitian Wilson-Dirac system of QCD. The key components leading to the success of our proposed algorithm are the use of an adaptive projection onto coarse grids that preserves the near null space of the system matrix together with a simplified form of the correction based on the so-called γ5-Hermitian symmetry of the Dirac oper...

On an even-dimensional real submanifold of a Hermitian manifold, making use of the fundamental 2-form of the ambient manifold, we define a function. In this paper, we investigate the function in detail in some special submanifold.

Random matrix ensembles with orthogonal and unitary symmetry correspond to the cases of real symmetric and Hermitian random matrices respectively. We show that the probability density function for the corresponding spacings between consecutive eigenvalues can be written exactly in the Wigner surmise type form a(s)e−b(s) for a simply related to a Painlevé transcendent and b its anti-derivative. ...

We study asymptotics of orthogonal polynomial measures of the form |HN |2dγ where HN are real or complex Hermite polynomials with respect to the Gaussian measure γ. By means of differential equations on Laplace transforms, interpolation between the (real) arcsine law and the (complex) uniform distribution on the circle is emphasized. Suitable averages by an independent uniform law give rise to ...

A family of spherical non-Hermitian potentials of the form V (r, θ, φ) = V (r) + f (θ) e/r (where r, V (r) , f (θ) ∈ R, e ∈ C) is studied. With f (θ) = 1/ sin θ, it is shown that the corresponding non-Hermitian Hamiltonians admit some “new” PφTφ−symmetry. It is observed that whilst such PφTφ−symmetric Hamiltonians just copy the eigenvalues of V (r) , the corresponding wavefunctions would rather...

The joint numerical range of three hermitian matrices of order three is a convex and compact subset W ⊂ R which is an image of the unit sphere S ⊂ C under the hermitian form defined by the three matrices. We label classes of the analyzed set W by pairs of numbers counting the exposed faces of dimension one and two. Generically, W belongs to the class of ovals. Assuming dim(W ) = 3, the faces of...

A fermionic analogue of the Hodge star operation is shown to have an explicit operator representation in models with fermions, in spacetimes of any dimension. This operator realizes a conjugation (pairing) not used explicitly in field-theory, and induces a metric in the space of wave-function(al)s just as in exterior calculus. If made real (Hermitian), this induced metric turns out to be identi...