31,354 research outputs found
Exact solutions to the time-dependent supersymmetric muliphoton Jaynes-Cummings model and the Chiao-Wu model
By using both the Lewis-Riesenfeld invariant theory and the invariant-related
unitary transformation formulation, the present paper obtains the exact
solutions to the time-dependent supersymmetric two-level multiphoton
Jaynes-Cummings model and the Chiao-Wu model that describes the propagation of
a photon inside the optical fiber. On the basis of the fact that the two-level
multiphoton Jaynes-Cummings model possesses the supersymmetric structure, an
invariant is constructed in terms of the supersymmetric generators by working
in the sub-Hilbert-space corresponding to a particular eigenvalue of the
conserved supersymmetric generators (i.e., the time-independent invariant). By
constructing the effective Hamiltonian that describes the interaction of the
photon with the medium of the optical fiber, it is further verified that the
particular solution to the Schr\"{o}dinger equation is the eigenfunction of the
second-quantized momentum operator of photons field. This, therefore, means
that the explicit expression (rather than the hidden form that involves the
chronological product) for the time-evolution operator of wave function is
obtained by means of the invariant theories.Comment: 14 pages, Latex. This is a revised version of the published paper:
Shen J Q, Zhu H Y 2003 Ann. Phys.(Leipzig) Vol.12 p.131-14
BPS -branes in Dual to Loop Operators
In this paper, we first compute the Killing spinors of and its certain orbifolds. Based on this, two classes of -brane
solutions are found. The first class of solutions includes -branes dual to
Wilson loops in the fundamental representation as special cases. The second
class includes the candidates of the holographic description of vortex loops in
the dual field theories.Comment: v6, typoes fixed, 14 pages, no figure
Extended Bose-Hubbard model with pair tunneling: spontaneous symmetry breaking, effective ground state and fragmentation
The extended Bose-Hubbard model for a double-well potential with pair
tunneling is studied through both exact diagonalization and mean field theory
(MFT). When pair tunneling is strong enough, the ground state wavefunction
predicted by the MFT is complex and doubly degenerate while the quantum ground
state wavefunction is always real and unique. The time reversal symmetry is
spontaneously broken when the system transfers from the quantum ground state
into one of the mean field ground states upon a small perturbation. As the gap
between the lowest two levels decreases exponentially with particle number, the
required perturbation inducing the spontaneous symmetry breaking (SSB) is
infinitesimal for particle number of typical cold atom systems. The quantum
ground state is further analyzed with the Penrose-Onsager criterion, and is
found to be a fragmented condensate. The state also develops the pair
correlation and has non-vanishing pair order parameter instead of the
conventional single particle order parameter. When this model is generalized to
optical lattice, a pair superfluid can be generated. The mean field ground
state can be regarded as effective ground state in this simple model. The
detailed computation for this model enables us to offer an in-depth discussion
of the relation between SSB and effective ground state, giving a glimpse on how
nonlinearity arises in the SSB of a quantum system.Comment: 6 pages, 6 figure
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