On the Integrability of the Rabi Model

The exact spectrum of the Rabi hamiltonian is analytically found for arbitrary coupling strength and detuning. I present a criterion for integrability of quantum systems containing discrete degrees of freedom which shows that in this case a finite symmetry group may entail integrability, even without the presence of conserved charges beyond the hamiltonian itself. Moreover, I introduce and solve a natural generalization of the Rabi model which has no symmetries and is therefore probably the smallest non-integrable physical system.Comment: 7 pages, 4 figures, figure captions correcte

Solution of the Dicke model for N=3

The N=3 Dicke model couples three qubits to a single radiation mode via dipole interaction and constitutes the simplest quantum-optical system allowing for Greenberger-Horne-Zeilinger states. In contrast to the case N=1 (the Rabi model), it is non-integrable if the counter-rotating terms are included. The spectrum is determined analytically, employing the singularity structure of an associated differential equation. While quasi-exact eigenstates known from the Rabi model do not exist, a novel type of spectral degeneracy becomes possible which is not associated with a symmetry of the system.Comment: 10 pages, 4 figure

Spontaneous Magnetization in the Disorder dominated Phase of the Twodimensional Random Bond Ising Model

The selfconsistent approach to the 2D Ising Model with quenched random bonds is extended to the full lattice theory of four real fermions. The additional degrees of freedom, neglected in the renormalization-group theory, lead to a new phase between the ferromagnetic and the paramagnetic phase. The disorder averaged spin-spin correlation function decays exponentially with distance. The corresponding correlation length is $1/\eta^2$, where $\eta$ denotes the order parameter of the new phase introduced by Ziegler.Comment: 18 pages,plainTEX,TKM-74-9

Note on the Analytical Solution of the Rabi Model

It is shown that a recent critique (arXiv:1210.1130 and arXiv:1211.4639) concerning the analytical solution of the Rabi model is unfounded.Comment: This version contains the reply to a comment on the previous versio

Fermi's golden rule and the second law of thermodynamics

We present a Gedankenexperiment that leads to a violation of detailed balance if quantum mechanical transition probabilities are treated in the usual way by applying Fermi's "golden rule". This Gedankenexperiment introduces a collection of two-level systems that absorb and emit radiation randomly through non-reciprocal coupling to a waveguide, as realized in specific chiral quantum optical systems. The non-reciprocal coupling is modeled by a hermitean Hamiltonian and is compatible with the time-reversal invariance of unitary quantum dynamics. Surprisingly, the combination of non-reciprocity with probabilistic radiation processes entails negative entropy production. Although the considered system appears to fulfill all conditions for Markovian stochastic dynamics, such a dynamics violates the Clausius inequality, a formulation of the second law of thermodynamics. Several implications concerning the interpretation of the quantum mechanical formalism are discussed.Comment: thoroughly revised, 30.5 pages, 9 figures, published online in Foundations of Physic

Conductivity of a quasiperiodic system in two and three dimensions

A generalization of the Aubry-Andre model in two and three dimensions is introduced which allows for quasiperiodic hopping terms in addition to the quasiperiodic site potentials. This corresponds to an array of interstitial impurities within the periodic host crystal. The resulting model is exactly solvable and I compute the density of states and the ac-conductivity. There is no mobility edge as in completely disordered systems but the regular ac-conductivity and the strongly reduced Drude weight indicate a precursor of the Anderson transition as the Fermi energy goes from the center to the band edges.Comment: 4 pages,6 figures, references adde

On the Spectrum of the XXZ-chain at roots of unity

In a recent paper (cond-mat/0009279), Fabricius and McCoy studied the spectrum of the spin 1/2 XXZ-model at Delta = (q+q^{-1})/2 and q^{2N}=1 for integer N >1. They found a certain pattern of degeneracies and linked it to the sl(2)-loop symmetry present in the commensurable spin sector (N divides S^z). We show that the degeneracies are due to zero-energy, transparent excitations, the cyclic bound states. These exist both in commensurable and incommensurable sectors, indicating a symmetry, of which sl(2)-loop is a partial manifestation. Our approach treats both sectors on even footing and yields an analytical expression for the degeneracies in the case N = 3.Comment: 27 page

Predicting teachers' use of an educational system by intention, attitude and self-reported use

Acceptance studies are for organizations a means to gain insight into users’ perceptions of a (newly introduced) technology. However, the validity of an acceptance study might be limited (a) in the case where a technology can be used receptively (e.g. to download information) as well as generatively (e.g. to share knowledge); and (b) if actual use of the technology is not measured. For this study, different dimensions of actual use of an educational portal (number of logins, downloads, uploads, reactions and pageviews) of 864 teachers were collected on two occasions (T1 and T2), and linked to their responses on an acceptance questionnaire based upon scales of TAM and TPB (taken at T1). Two research questions were put forward: (1) which dimensions of actual use can be predicted by attitude, intention and self-reported use; and (2) which factors discern the uploaders from the non-uploaders. Regression analyses showed that receptive use (logging in, downloading and browsing) could be predicted by attitude, intention and self-reported use, with variance explained ranging between .13 and .16; whereas generative use (uploading and reacting on contributions of other teachers) could not be predicted (Adj. R2 between .01 and .04). Logistic regression showed that the more positive teachers’ attitudes towards the portal are and the higher their perceptions of control; the more likely they will upload information onto the portal. This study is a call for more research on the factors that influence different dimensions of actual educational technology use