17,139 research outputs found
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 , where 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
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