40,773 research outputs found
Certifying isolated singular points and their multiplicity structure
This paper presents two new constructions related to singular solutions of
polynomial systems. The first is a new deflation method for an isolated
singular root. This construc-tion uses a single linear differential form
defined from the Jacobian matrix of the input, and defines the deflated system
by applying this differential form to the original system. The advantages of
this new deflation is that it does not introduce new variables and the increase
in the number of equations is linear instead of the quadratic increase of
previous methods. The second construction gives the coefficients of the
so-called inverse system or dual basis, which defines the multiplicity
structure at the singular root. We present a system of equations in the
original variables plus a relatively small number of new vari-ables. We show
that the roots of this new system include the original singular root but now
with multiplicity one, and the new variables uniquely determine the
multiplicity structure. Both constructions are "exact", meaning that they
permit one to treat all conjugate roots simultaneously and can be used in
certification procedures for singular roots and their multiplicity structure
with respect to an exact rational polynomial system
Combined effect of frustration and dimerization in ferrimagnetic chains and square lattice
Within the zero-temperature linear spin-wave theory we have investigated the
effect of frustration and dimerization of a Heisenberg system with alternating
spins and on one- and two-dimensional lattices. The combined
effect most visibly appears in the elementary excitation spectra. In contrast
to the ground state energy that decreases with dimerization and increases with
frustration, the excitation energies are shown to be suppressed in energy by
both dimerization and frustration. The threshold value of frustration that
signals a transition from a classical ferrimagnetic state to a spiral state,
decreases with dimerization, showing that dimerization further helps in the
phase transition. The correlation length and sublattice magnetization decrease
with both dimerization and frustration indicating the destruction of the
long-range classical ferrimagnetic. The linear spin wave theory shows that in
the case of a square lattice, dimerization initially opposes the
frustration-led transition to a spiral magnetic state, but then higher
magnitudes of lattice deformation facilitate the transition. It also shows that
the transition to spiral state is inhibited in a square lattice beyond a
certain value of dimerization.Comment: 8 pages, latex, 12 postscript figure
Single photon absorption by a single quantum emitter
We show that a three-level lambda quantum emitter with equal spontaneous
emission rates on both optically active transitions can absorb an incident
light field with a probability approaching unity, provided that the focused
light profile matches that of the emitter dipole emission pattern. Even with
realistic focusing geometries, our results could find applications in
long-distance entanglement of spin qubits.Comment: 4 pages, 4 figure
Nuclear Spin-Lattice Relaxation in One-Dimensional Heisenberg Ferrimagnets: Three-Magnon versus Raman Processes
Nuclear spin-lattice relaxation in one-dimensional Heisenberg ferrimagnets is
studied by means of a modified spin-wave theory. We consider the second-order
process, where a nuclear spin flip induces virtual spin waves which are then
scattered thermally via the four-magnon exchange interaction, as well as the
first-order process, where a nuclear spin directly interacts with spin waves
via the hyperfine interaction. We point out a possibility of the three-magnon
relaxation process predominating over the Raman one and suggest model
experiments.Comment: to be published in J. Phys. Soc. Jpn. 73, No. 6 (2004
Dissipation-induced pure Gaussian state
This paper provides some necessary and sufficient conditions for a
generalMarkovian Gaussian master equation to have a unique pure steady state.
The conditions are described by simple matrix equations; thus the so-called
environment engineering problem for pure-Gaussian-state preparation can be
straightforwardly dealt with in the linear algebraic framework. In fact, based
on one of those conditions, for an arbitrary given pure Gaussian state,we
obtain a complete parametrization of the Gaussian master equation having that
state as a unique steady state; this leads to a systematic procedure for
engineering a desired dissipative system.We demonstrate some examples including
Gaussian cluster states.Comment: 8 page
Modified spin-wave theory of nuclear magnetic relaxation in one-dimensional quantum ferrimagnets: Three-magnon versus Raman processes
Nuclear spin-lattice relaxation in one-dimensional Heisenberg ferrimagnets is
studied by means of a modified spin-wave theory. Calculating beyond the
first-order mechanism, where a nuclear spin directly interacts with spin waves
through the hyperfine coupling, we demonstrate that the
exchange-scattering-enhanced three-magnon nuclear relaxation may generally
predominate over the Raman one with increasing temperature and decreasing
field. Recent proton spin-lattice relaxation-time (T_1_) measurements on the
ferrimagnetic chain compound NiCu(C_7_H_6_N_2_O_6_)(H_2_O)_3_2H_2_O suggest
that the major contribution to 1/T_1_ be made by the three-magnon scattering.Comment: 8 pages, 5 figure
- …