The dynamics of two spins coupled to bosonic baths at different temperatures is studied. The analytical solution for the reduced density matrix of the system in the Markovian and Post-Markovian case with exponential memory kernel is found. The dynamics and temperature dependence of spin-spin entanglement is analyzed.
The dynamics of a simple spin chain (two spins) coupled to bosonic baths at different temperatures is studied. The analytical solution for the reduced density matrix of the system is found. The dynamics and temperature dependence of spin-spin entanglement is analyzed. It is shown that the system converges to a steady state. If the energy levels of the two spins are different, the steady-state concurrence assumes its maximum at unequal bath temperatures. It is found that a difference in local energy levels can make the steady-state entanglement more stable against high temperatures.
The dynamics of simple qubit systems in a chain configuration coupled at both ends to separate bosonic baths at different temperatures is studied. An exact analytical solution of the master equation in the Born-Markov approximation for the reduced density matrix of the qubit system is constructed. The unique non-equilibrium stationary state for the long time behavior of the reduced density matrix in obtained. Dynamical and steady state properties of the concurrence between the first and the last spin are studied.
The study is focused on the thermal entanglement of spin chains. Chains consisting of two and three qubits are considered. These chains are considered open because they are coupled to bosonic baths at different temperatures. The baths represent the environment. The dynamics of these open systems are examined as are the effects of different parameters - such as bath temperature - on the entanglement of the spins. The measure of entanglement used in these cases is the concurrence. Comparisons are made between a model that assumes a strong spinspin interaction and one that assumes a weak one. In all these cases, analytical solutions for the system dynamics are presented. It is found that at large times, all systems converge to a state that depends only on bath temperature. It is also found that increases in bath temperatures diminish the entanglement between spins and that at high enough temperatures the entanglement vanishes altogether. The time and temperature dependence of the entanglement is different for the two models that are studied.
In this paper we investigate the non-Markovian dynamics of a qubit by comparing two generalized master equations with memory. In the case of a thermal bath, we derive the solution of the recently proposed post-Markovian master equation [A. Shabani and D. A. Lidar, Phys. Rev. A 71, 020101(R) (2005)] and we study the dynamics for an exponentially decaying memory kernel. We compare the solution of the post-Markovian master equation with the solution of the typical memory kernel master equation. Our results lead to a new physical interpretation of the reservoir correlation function and bring to light the limits of usability of master equations with memory for the system under consideration.
The dynamics of a central spin-1/2 in presence of a local magnetic field and a bath of N spin-1/2 particles is studied in the thermodynamic limit. The interaction between the spins is Heisenberg XY type and the bath is considered to be a perfect thermal reservoir. In this case, the evolution of the populations of the reduced density matrix is obtained for different temperatures. A Born approximation is made but not a Markov approximation resulting a non-Markovian dynamics. The measure of the entanglement between the spin and the bath is obtained by means of the von Neumann entropy. For low temperatures, results show that there are oscillations of populations and of the von Neumann entropy as measure of entanglement, indicating that the central spin becomes disentangled of the spins of the bath with characteristic time periods in which it is possible to extract or recuperate information. In the regime of high temperatures, the evolution shows a final maximum entangled state with entropy S = ln 2 as it is expected for a two level system. I