1,994 research outputs found
A Graph Theoretic Method for Determining Generating Sets of Prime Ideals in Quantum Matrices
We take a graph theoretic approach to the problem of finding generators for
those prime ideals of which are
invariant under the torus action (. Launois
\cite{launois3} has shown that the generators consist of certain quantum minors
of the matrix of canonical generators of
and in \cite{launois2} gives an
algorithm to find them. In this paper we modify a classic result of
Lindstr\"{o}m \cite{lind} and Gessel-Viennot~\cite{gv} to show that a quantum
minor is in the generating set for a particular ideal if and only if we can
find a particular set of vertex-disjoint directed paths in an associated
directed graph.Comment: 29 pages, 9 figure
Optically bistable driven-dissipative Bose-Hubbard dimer: Gutzwiller approaches and entanglement
We theoretically examine the driven-dissipative Bose-Hubbard dimer in the
optical bistable regime. Various approximation schemes based on a Gutzwiller
mean field decoupling are applied and compared. Depending on the system
parameters we show that a decoupling with respect to the real space or to the
reciprocal space can be more accurate. The Gutzwiller decoupling is applied
both at the level of the density matrix and for the wavefunction during a
quantum trajectory simulation. The latter is shown to be a more accurate
approximation. A Gaussian approximation for the non-homogeneous anti-bonding
mode is also explored. We also show that entanglement in this system is
witnessed by squeezing in reciprocal space
Critical dynamical properties of a first-order dissipative phase transition
We theoretically investigate the critical properties of a single
driven-dissipative nonlinear photon mode. In a well-defined thermodynamical
limit of large excitation numbers, the exact quantum solution describes a
first-order phase transition in the regime where semiclassical theory predicts
optical bistability. We study the behavior of the complex spectral gap
associated with the Liouvillian superoperator of the corresponding master
equation. We show that in this limit the Liouvillian gap vanishes exponentially
and that the bimodality of the photon Wigner function disappears. The
connection between the considered thermodynamical limit of large photon numbers
for the single-mode cavity and the thermodynamical limit of many cavities for a
driven-dissipative Bose-Hubbard system is discussed.Comment: revised version accepted for publication in PR
On the robustness of strongly correlated multi-photon states in frustrated driven-dissipative cavity lattices
We present a theoretical study on the robustness of multi-photon states in a
frustrated lattice of coupled nonlinear optical cavities, which are described
by a driven-dissipative Bose-Hubbard model. In particular, we focus here on a
Lieb lattice with two elementary cells and periodic boundary conditions. Due to
the geometric frustration of the lattice, the non-equilibrium steady state can
exhibit dark sites with low photon density and strong correlations, ascribable
to the population of multi-photon modes. We explore the sensitivity of such
strong correlations on the random inhomogeneity of the lattice parameters. We
show that the correlations are more sensitive to the inhomogeneity of the
cavity frequencies than to the random fluctuations of the hopping strength.Comment: Accepted for publication on EPJ-Special Topics "Quantum gases and
quantum coherence": 10 pages, 5 figure
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