16,261 research outputs found

### Mathematical Structure of Rabi Oscillations in the Strong Coupling Regime

In this paper we generalize the Jaynes--Cummings Hamiltonian by making use of
some operators based on Lie algebras su(1,1) and su(2), and study a
mathematical structure of Rabi floppings of these models in the strong coupling
regime. We show that Rabi frequencies are given by matrix elements of
generalized coherent operators (quant--ph/0202081) under the rotating--wave
approximation.
In the first half we make a general review of coherent operators and
generalized coherent ones based on Lie algebras su(1,1) and su(2). In the
latter half we carry out a detailed examination of Frasca (quant--ph/0111134)
and generalize his method, and moreover present some related problems.
We also apply our results to the construction of controlled unitary gates in
Quantum Computation. Lastly we make a brief comment on application to Holonomic
Quantum Computation.Comment: Latex file, 24 pages. I added a new section (Quantum Computation), so
this paper became self-contained in a certain sens

### Note on Coherent States and Adiabatic Connections, Curvatures

We give a possible generalization to the example in the paper of Zanardi and
Rasetti (quant-ph/9904011). For this generalized one explicit forms of
adiabatic connection, curvature and etc. are given.Comment: Latex file, 12 page

### Flow Representation of the Bose-Hubbard Hamiltonian : General Case

In this paper the explicit flow representation to the Bose-Hubbard
Hamiltonian is given in the general case. This representation may be useful in
creating cat states for the system of atoms trapped in the optical ring.Comment: Latex ; 8 pages ; 1 figure ; minor change

### More on the Isomorphism $SU(2)\otimes SU(2)\cong SO(4)$

In this paper we revisit the isomorphism $SU(2)\otimes SU(2)\cong SO(4)$ to
apply to some subjects in Quantum Computation and Mathematical Physics.
The unitary matrix $Q$ by Makhlin giving the isomorphism as an adjoint action
is studied and generalized from a different point of view. Some problems are
also presented.
In particular, the homogeneous manifold $SU(2n)/SO(2n)$ which characterizes
entanglements in the case of $n=2$ is studied, and a clear-cut calculation of
the universal Yang-Mills action in (hep-th/0602204) is given for the abelian
case.Comment: Latex ; 19 pages ; 5 figures ; minor changes. To appear in
International Journal of Geometric Methods in Modern Physics (vol.4, no.3

### General Solution of the Quantum Damped Harmonic Oscillator

In this paper the general solution of the quantum damped harmonic oscillator
is given.Comment: Latex ; 10 pages ; no figure ; typos corrected. The quantum damped
harmonic oscillator is solved completel

### Coherent states, Path integral, and Semiclassical approximation

Using the generalized coherent states we argue that the path integral
formulae for $SU(2)$ and $SU(1,1)$ (in the discrete series) are WKB exact,if
the starting point is expressed as the trace of $e^{-iT\hat H}$ with $\hat H$
being given by a linear combination of generators. In our case,WKB
approximation is achieved by taking a large ``spin'' limit: $J,K\rightarrow
\infty$. The result is obtained directly by knowing that the each coefficient
vanishes under the $J^{-1}$($K^{-1}$) expansion and is examined by another
method to be legitimated. We also point out that the discretized form of path
integral is indispensable, in other words, the continuum path integral
expression leads us to a wrong result. Therefore a great care must be taken
when some geometrical action would be adopted, even if it is so beautiful, as
the starting ingredient of path integral.Comment: latex 33 pages and 2 figures(uuencoded postscript file),
KYUSHU-HET-19 We have corrected the proof of the WKB-exactness in the section

### Shell structures in oxygen isotopes described with modern nucleon-nucleon interactions

Shell structures in the N\simeq Z nucleus ^{17}O and the neutron-rich oxygen
isotopes ^{23}O and ^{25}O are microscopically described by calculating
single-particle energies with modern nucleon-nucleon interactions within the
framework of the unitary-model-operator approach. It is found that the effect
of three-body cluster terms on the single-particle energy is more important in
^{23}O and ^{25}O than ^{17}O.Comment: 5 pages, 1 figure, Talk at the International Symposium on "A New Era
of Nuclear Structure Physics (NENS03)", 19-22 Nov. 2003, Niigata, Japa

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