Time evolution of non-Hermitian quantum systems and generalized master equations

We inquire into the time evolution of quantum systems associated with pseudo-or quasi-Hermitian Hamiltonians. We obtain, in the pseudo-Hermitian case, a generalized Liouville-von Neumann equation for closed systems. We show that quantum systems with quasi-Hermitian Hamiltonians admit the proper interpretation in terms of open quantum system and derive a generalized Lindblad-Kossakowski equation. Finally, we extend such formalism to the study of decaying systems. Partially supported by PRIN “Sintesi”.     

Pauli-Fierz Hamiltonians defined as quadratic forms

We study Pauli-Fierz Hamiltonians-self-adjoint operators describing a small quantum system interacting with a bosonic field. Using quadratic form techniques, we extend the results of Dereziński-Gérard and Gérard about the self-adjointness, the location of the essential spectrum and the existence of a ground state to a large class of Pauli-Fierz Hamiltonians.     

Absence of absolutely continuous spectrum of Floquet operators

The spectrum of the Floquet operator associated with time-periodic perturbations of discrete Hamiltonians is considered. If the gap between successive eigenvalues _j of the unperturbed Hamiltonian grows as _j - _j-1 j and the multiplicity of _j grows asj with >0 asj tends to infinity, then the corresponding Floquet operator possesses no absolutely continuous spectrum provided the perturbation is smooth enough.     

Non-convergent perturbation theory and misleading inferences about parameter relationships: The case of superexchange

We discuss the well-known three-centre cation–anion–cation model for superexchange in insulating transition-metal compounds using limiting expansions for the Anderson–Hubbard model. We find that due to the interfering energy scales in the model, a limiting expression for the superexchange J$J$ for the idealized Mott–Hubbard (M–H) case t?U?Δ$t?U?\Delta$ cannot be formally defined. We further show that the decomposition of the superexchange into range-dependent components is formally invalid. The well-known t⁴$t^4$ superexchange expression, obtained from path-dependent series expansions, is not unique to these systems as it can also be obtained with many other different expansions, in which either the d$d$–p$p$ energy difference Δ$\Delta$ or the d$d$-electron correlation U$U$ can actually be small. Particularly for milder relationships between the parameters, i.e.  t?U?Δ$t?U?\Delta$, the reverse from the usual form of the series expansions can yield better agreement with the exact results. This implies that the fitting of experimental data to the simple expressions derived from path-dependent series expansions can lead to qualitatively incorrect relationships between the parameters, fictitiously within the M–H regime.     

Bound-State Solutions of the Klein-Gordon Equation for the Generalized <Emphasis Type="Italic">PT</Emphasis>-Symmetric Hulthén Potential

The one-dimensional Klein-Gordon equation is solved for the PT-symmetric generalized Hulthén potential in the scalar coupling scheme. The relativistic bound-state energy spectrum and the corresponding wave functions are obtained by using the Nikiforov-Uvarov method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type. PACS numbers: 03.65.Fd, 03.65.Ge     

Electron paramagnetic resonance parameters and local structure for Gd3+ in KY3F10

The electron paramagnetic resonance parameters, zero-field splittings (ZFSs) b₂⁰, b₄⁰, b₄⁴, b₆⁰, b₆⁴ and the g factors for Gd³⁺ on the tetragonal Y³⁺ site in KY₃F₁₀ are theoretically studied from the superposition model for the ZFSs and the approximation formula for the g factor containing the admixture of the ground ⁸S_7/2 and the excited ⁶L_7/2 (L=P, D, F, G) states via the spin-orbit coupling interactions, respectively. By analysing the above ZFSs, the local structure information for the impurity Gd³⁺ is obtained, i.e., the impurity-ligand bonding angles related to the four-fold (C₄) axis for the impurity Gd³⁺ center are found to be about 0.6° larger than those for the host Y³⁺ site in KY₃F₁₀. The calculated ZFSs based on the above angular distortion as well as the g factors are in reasonable agreement with the observed values. The present studies on the ZFSs and the local structure would be helpful to understand the optical and magnetic properties of this material with Gd dopants.      

Mössbauer Study of Thin Iron Film Beryllization

Beryllium coating of the iron foil is made by means of magnetron sputtering. Mössbauer studies are performed by means of two registration techniques: conversion electron Mössbauer spectroscopy (CEMS) and the γ-ray technique in absorption geometry. Performed investigations confirm the original thermodynamic approach to creation of thermally stable multi-layer materials.

     

Remarks on pseudo-Hermitian matrices and their exceptional points

We highlight some features of pseudo-Hermitian matrices admitting exceptional points. Starting from these general considerations we discuss a fermionic time-reversal violating pseudo-Hermitian Hamiltonian which breaks diagonalizability for some critical parameter values. Partially supported by PRIN “Sintesi”. Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22, 2005.     

Similarity Transformations of Hermitian Hamiltonians and Pseudo-Hermitian Coupling Between Two Electromagnetic Modes

Pseudo-Hermitian Hamiltonians and pseudo-Hermitian coupling between two electromagnetic modes are analyzed by using similarity transformations of Hermitian Hamiltonians or of Hermitian operators, including a special metric and biorthogonal relations replacing the usual orthogonal relations used in quantum mechanics. The coupling between two electromagnetic (em) modes including certain decay and amplification processes is related to a coupling matrix G which has parity-time (PT) symmetry and which obeys the pseudo-Hermiticity condition ηGη⁻¹ = G ^† where η is a metric. The linear equations representing the pseudo-Hermitian coupling between the two em modes are diagonalized, in the interaction picture, by introducing ‘dressed’ αˉ and β~ operators which have real or pure imaginary eigenfrequencies. The commutation-relations (CR) for the α~ and β~ operators and for the two-mode operators ā and b~, in the interaction picture and under the condition of real eigenfrequencies are obtained by the use of the pseudo-Hermiticity property of the G matrix. These CR for real eigenfrequencies, are preserved in time without any Langevin noise terms.