13,256 research outputs found
On the 2-mode and -photon quantum Rabi models
By mapping the Hamiltonians of the two-mode and 2-photon Rabi models to
differential operators in suitable Hilbert spaces of entire functions, we prove
that the two models possess entire and normalizable wavefunctions in the
Bargmann-Hilbert spaces only if the frequency and coupling strength
satisfy certain constraints. This is in sharp contrast to the quantum Rabi
model for which entire wavefunctions always exist. For model parameters
fulfilling the aforesaid constraints we determine transcendental equations
whose roots give the regular energy eigenvalues of the models. Furthermore, we
show that for the -photon Rabi model does not possess
wavefunctions which are elements of the Bargmann-Hilbert space for all
non-trivial model parameters. This implies that the case is not
diagonalizable, unlike its RWA cousin, the -photon Jaynes-Cummings model
which can be completely diagonalized for all .Comment: LaTex 15 pages. Version to appear in Reviews in Mathematical Physic
Super Coherent States, Boson-Fermion Realizations and Representations of Superalgebras
Super coherent states are useful in the explicit construction of
representations of superalgebras and quantum superalgebras. In this
contribution, we describe how they are used to construct (quantum)
boson-fermion realizations and representations of (quantum) superalgebras. We
work through a few examples: and its quantum version
, in the non-standard and standard bases and
in the non-standard basis. We obtain free boson-fermion realizations
of these superalgebras. Applying the boson-fermion realizations, we explicitly
construct their finite-dimensional representations. Our results are expected to
be useful in the study of current superalgebras and their corresponding
conformal field theories.Comment: LaTex 20 pages. Invited contribution for the volume "Trends in Field
Theory Research" by Nova Science Publishers Inc., New York, 2004. Accepted
for publication in the volum
Hidden -algebraic structure in Rabi model and its 2-photon and two-mode generalizations
It is shown that the (driven) quantum Rabi model and its 2-photon and 2-mode
generalizations possess a hidden -algebraic structure which explains the
origin of the quasi-exact solvability of these models. It manifests the first
appearance of a hidden algebraic structure in quantum spin-boson systems
without symmetry.Comment: LaTex 14 pages. Version to appear in Annals of Physic
Exact polynomial solutions of second order differential equations and their applications
We find all polynomials such that the differential equation
where are polynomials of degree at most 4, 3, 2 respectively, has polynomial
solutions of degree with distinct roots .
We derive a set of algebraic equations which determine these roots. We also
find all polynomials which give polynomial solutions to the differential
equation when the coefficients of X(z) and Y(z) are algebraically dependent. As
applications to our general results, we obtain the exact (closed-form)
solutions of the Schr\"odinger type differential equations describing: 1) Two
Coulombically repelling electrons on a sphere; 2) Schr\"odinger equation from
kink stability analysis of -type field theory; 3) Static perturbations
for the non-extremal Reissner-Nordstr\"om solution; 4) Planar Dirac electron in
Coulomb and magnetic fields; and 5) O(N) invariant decatic anharmonic
oscillator.Comment: LaTex 25 page
Unions Improve Chinese Workers' Welfare - Results from 1,268 Firms
Based on a survey of 1,268 firms in 12 Chinese cities, this paper empirically studies the effects of unions on three aspects of workers welfare, namely, hourly wages, monthly working hours, and pension coverage. Our baseline results show that unionization increases hourly wage rates by 5.6%, reduces monthly working hours by 1.4%, and raises pension coverage by 12.3%. Taking the endogeneity of unionization into consideration, our 3SLS estimation finds larger effects. These results are robust in the subsample of domestic private enterprises where unions are less common than in other types of firms. Further econometric analysis has established two channels for unions to improve workers welfare, one by encouraging collective wage contracts, and the other by encouraging written contracts.Unionization, Chinese firms
- …