1,045 research outputs found
Time evolution of non-Hermitian Hamiltonian systems
We provide time-evolution operators, gauge transformations and a perturbative
treatment for non-Hermitian Hamiltonian systems, which are explicitly
time-dependent. We determine various new equivalence pairs for Hermitian and
non-Hermitian Hamiltonians, which are therefore pseudo-Hermitian and in
addition in some cases also invariant under PT-symmetry. In particular, for the
harmonic oscillator perturbed by a cubic non-Hermitian term, we evaluate
explicitly various transition amplitudes, for the situation when these systems
are exposed to a monochromatic linearly polarized electric field.Comment: 25 pages Latex, 1 eps figure, references adde
Non-Hermitian Hamiltonians with real eigenvalues coupled to electric fields: from the time-independent to the time dependent quantum mechanical formulation
We provide a reviewlike introduction into the quantum mechanical formalism
related to non-Hermitian Hamiltonian systems with real eigenvalues. Starting
with the time-independent framework we explain how to determine an appropriate
domain of a non-Hermitian Hamiltonian and pay particular attention to the role
played by PT-symmetry and pseudo-Hermiticity. We discuss the time-evolution of
such systems having in particular the question in mind of how to couple
consistently an electric field to pseudo-Hermitian Hamiltonians. We illustrate
the general formalism with three explicit examples: i) the generalized Swanson
Hamiltonians, which constitute non-Hermitian extensions of anharmonic
oscillators, ii) the spiked harmonic oscillator, which exhibits explicit
supersymmetry and iii) the -x^4-potential, which serves as a toy model for the
quantum field theoretical phi^4-theory.Comment: 14 pages, 3 figures, to appear in Laser Physics, minor typos
correcte
A spin chain model with non-Hermitian interaction: the Ising quantum spin chain in an imaginary field
We investigate a lattice version of the Yang-Lee model which is characterized by a non-Hermitian quantum spin chain Hamiltonian. We propose a new way to implement PT-symmetry on the lattice, which serves to guarantee the reality of the spectrum in certain regions of values of the coupling constants. In that region of unbroken PT-symmetry we construct a Dyson map, a metric operator and find the Hermitian counterpart of the Hamiltonian for small values of the number of sites, both exactly and perturbatively. Besides the standard perturbation theory about the Hermitian part of the Hamiltonian, we also carry out an expansion in the second coupling constant of the model. Our constructions turns out to be unique with the sole assumption that the Dyson map is Hermitian. Finally we compute the magnetization of the chain in the z and x direction
PT-symmetric deformations of Calogero models
We demonstrate that Coxeter groups allow for complex PT-symmetric deformations across the boundaries of all Weyl chambers. We compute the explicit deformations for the A2 and G2-Coxeter group and apply these constructions to Calogero–Moser–Sutherland models invariant under the extended Coxeter groups. The eigenspectra for the deformed models are real and contain the spectra of the undeformed case as subsystems
Resonant enhancements of high-order harmonic generation
Solving the one-dimensional time-dependent Schr\"odinger equation for simple
model potentials, we investigate resonance-enhanced high-order harmonic
generation, with emphasis on the physical mechanism of the enhancement. By
truncating a long-range potential, we investigate the significance of the
long-range tail, the Rydberg series, and the existence of highly excited states
for the enhancements in question. We conclude that the channel closings typical
of a short-range or zero-range potential are capable of generating essentially
the same effects.Comment: 7 pages revtex, 4 figures (ps files
Application of Pseudo-Hermitian Quantum Mechanics to a Complex Scattering Potential with Point Interactions
We present a generalization of the perturbative construction of the metric
operator for non-Hermitian Hamiltonians with more than one perturbation
parameter. We use this method to study the non-Hermitian scattering
Hamiltonian: H=p^2/2m+\zeta_-\delta(x+a)+\zeta_+\delta(x-a), where \zeta_\pm
and a are respectively complex and real parameters and \delta(x) is the Dirac
delta function. For regions in the space of coupling constants \zeta_\pm where
H is quasi-Hermitian and there are no complex bound states or spectral
singularities, we construct a (positive-definite) metric operator \eta and the
corresponding equivalent Hermitian Hamiltonian h. \eta turns out to be a
(perturbatively) bounded operator for the cases that the imaginary part of the
coupling constants have opposite sign, \Im(\zeta_+) = -\Im(\zeta_-). This in
particular contains the PT-symmetric case: \zeta_+ = \zeta_-^*. We also
calculate the energy expectation values for certain Gaussian wave packets to
study the nonlocal nature of \rh or equivalently the non-Hermitian nature of
\rH. We show that these physical quantities are not directly sensitive to the
presence of PT-symmetry.Comment: 22 pages, 4 figure
Histopatologia da interação Musa spp. x Fusarium oxysporum f. sp. Cubense.
O mal-do-Panamá causado pelo fungo Fusarium oxysporum f. sp. cubense (Foc) é uma das doenças mais destrutivas da bananeira e é considerada a mais importante em termos de prejuízo econômico para a cultura (1). Este fitopatógeno habita o solo e sobrevive na forma de clamidósporos sem o contato com o hospedeiro por muitos anos, sendo o uso de cultivares resistentes, o método mais eficaz de controle da doença (1)
Perturbation theory of PT-symmetric Hamiltonians
In the framework of perturbation theory the reality of the perturbed
eigenvalues of a class of \PTsymmetric Hamiltonians is proved using stability
techniques. We apply this method to \PTsymmetric unperturbed Hamiltonians
perturbed by \PTsymmetric additional interactions
- …