Two‐State Quantum Asymptotics

Hans Primas

Ranjith Kumar R, S Rahul, Surya Narayan +1 more

We present results for asymptotic freedom like behavior for the topological state of the helical spin liquid system with finite proximity induced superconducting gap. We derive two different quantum Berezinskii-Kosterlitz-Thouless (BKT) equations for the two different limit of this model Hamiltonian. The common quantum phase for these two quantum BKT transitions is the helical Luttinger liquid phase where there is no evidence of asymptotic freedom. There is no evidence of superconductor-insulator transition for this asymptotic freedom study. We observe the evidance of asymptotic freedom for the two model Hamiltonian, but the character of the asymptotic phases are different. We also observe that the Luttinger liquid parameter plays a significant role to determine the asymptotic freedom but the chemical potential has no effect on it.

Michael Berry

Аурелиан Исар

In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we solve in the asymptotic long-time regime the master equation for two independent harmonic oscillators interacting with an environment. We give a description of the continuous-variable asymptotic entanglement in terms of the covariance matrix of the considered subsystem for an arbitrary Gaussian input state. Using Peres–Simon necessary and sufficient condition for separability of two-mode Gaussian states, we show that for certain classes of environments the initial state evolves asymptotically to an entangled equilibrium bipartite state, while for other values of the coefficients describing the environment, the asymptotic state is separable. We calculate also the logarithmic negativity characterizing the degree of entanglement of the asymptotic state.

Laurent Bruneau, Alain Joye, Marco Merkli

AURELIAN ISAR

In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we solve in the asymptotic long-time regime the master equation for two independent harmonic oscillators interacting with an environment. We give a description of the continuous-variable asymptotic entanglement in terms of the covariance matrix of the considered subsystem for an arbitrary Gaussian input state. Using Peres--Simon necessary and sufficient condition for separability of two-mode Gaussian states, we show that for certain classes of environments the initial state evolves asymptotically to an entangled equilibrium bipartite state, while for other values of the coefficients describing the environment, the asymptotic state is separable. We calculate also the logarithmic negativity characterizing the degree of entanglement of the asymptotic state.