2 research outputs found
On the Representation Theory of Negative Spin
We construct a class of negative spin irreducible representations of the
su(2) Lie algebra. These representations are infinite-dimensional and have an
indefinite inner product. We analyze the decomposition of arbitrary products of
positive and negative representations with the help of generalized characters
and write down explicit reduction formulae for the products. From the
characters, we define effective dimensions for the negative spin
representations, find that they are fractional, and point out that the
dimensions behave consistently under multiplication and decomposition of
representations.Comment: 21 pages, no figures, Latex2
Non-equilibrium entangled steady state of two independent two-level systems
We determine and study the steady state of two independent two-level systems
weakly coupled to a stationary non-equilibrium environment. Whereas this
bipartite state is necessarily uncorrelated if the splitting energies of the
two-level systems are different from each other, it can be entangled if they
are equal. For identical two-level systems interacting with two bosonic heat
baths at different temperatures, we discuss the influence of the baths
temperatures and coupling parameters on their entanglement. Geometric
properties, such as the baths dimensionalities and the distance between the
two-level systems, are relevant. A regime is found where the steady state is a
statistical mixture of the product ground state and of the entangled singlet
state with respective weights 2/3 and 1/3