283 research outputs found
Pseudo-Hermiticity and Electromagnetic Wave Propagation in Dispersive Media
Pseudo-Hermitian operators appear in the solution of Maxwell's equations for
stationary non-dispersive media with arbitrary (space-dependent) permittivity
and permeability tensors. We offer an extension of the results in this
direction to certain stationary dispersive media. In particular, we use the WKB
approximation to derive an explicit expression for the planar time-harmonic
solutions of Maxwell's equations in an inhomogeneous dispersive medium and
study the combined affect of inhomogeneity and dispersion.Comment: 8 pages, to appear in Phys. Lett.
Pseudo-Hermiticity for a Class of Nondiagonalizable Hamiltonians
We give two characterization theorems for pseudo-Hermitian (possibly
nondiagonalizable) Hamiltonians with a discrete spectrum that admit a
block-diagonalization with finite-dimensional diagonal blocks. In particular,
we prove that for such an operator H the following statements are equivalent.
1. H is pseudo-Hermitian; 2. The spectrum of H consists of real and/or
complex-conjugate pairs of eigenvalues and the geometric multiplicity and the
dimension of the diagonal blocks for the complex-conjugate eigenvalues are
identical; 3. H is Hermitian with respect to a positive-semidefinite inner
product. We further discuss the relevance of our findings for the merging of a
complex-conjugate pair of eigenvalues of diagonalizable pseudo-Hermitian
Hamiltonians in general, and the PT-symmetric Hamiltonians and the effective
Hamiltonian for a certain closed FRW minisuperspace quantum cosmological model
in particular.Comment: 17 pages, slightly revised version, to appear in J. Math. Phy
On the Dynamical Invariants and the Geometric Phases for a General Spin System in a Changing Magnetic Field
We consider a class of general spin Hamiltonians of the form
where and describe the dipole
interaction of the spins with an arbitrary time-dependent magnetic field and
the internal interaction of the spins, respectively. We show that if is
rotationally invariant, then admits the same dynamical invariant as
. A direct application of this observation is a straightforward
rederivation of the results of Yan et al [Phys. Lett. A, Vol: 251 (1999) 289
and Vol: 259 (1999) 207] on the Heisenberg spin system in a changing magnetic
field.Comment: Accepted for publication in Phys. Lett.
On the Pseudo-Hermiticity of a Class of PT-Symmetric Hamiltonians in One Dimension
For a given standard Hamiltonian H=[p-A(x)]^2/(2m)+V(x) with arbitrary
complex scalar potential V and vector potential A, with x real, we construct an
invertible antilinear operator \tau such that H is \tau-anti-pseudo-Hermitian,
i.e., H^\dagger=\tau H\tau^{-1}. We use this result to give the explicit form
of a linear Hermitian invertible operator with respect to which any standard
PT-symmetric Hamiltonian with a real degree of freedom is pseudo-Hermitian. Our
results do not make use of the assumption that H is diagonalizable or that its
spectrum is discrete.Comment: published versio
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