Approximation to the quantum planar rotor coupled to a finite temperature bath

Abstract

An approximation to the description of the dynamics of a quantum planar rotor coupled to a finite temperature bath is derived by considering a microscopic model of interaction based on an angular momentum exchange with two different environments coupled independently to the positive and negative angular momentum spectrum. A non-Lindblad master equation is derived for this microscopic model by using the Born-Markov approximation in the weak coupling limit. We show that under this approximation the rotor dynamics presents the correct damping behavior of the motion and the thermal state reached by the rotor is in the form of Boltzmann distribution. The case of the quantum rotor in an external uniform field and the quantum kicked rotor are briefly discussed as exemplification.

Emergence of stationary entanglement in a dissipative kicked linear chain of three qubits

“…It has been shown for the kicked oscillator and the kicked rotor that at the quasi stationary regime they follow the Fourier's law where the average energy of the systems and the dissipated energy to the environment per period of the kick are directly proportional to each other, seee.g. [3,4]. In our case, we have found the same linear relation as it can be seen at the right figure of figure 1 for decreasing periods of the kick and different angles of rotation ranging from zero to p…”

“…In [25] a derivation of a master equation for a linear chain of three nuclear spins system with second neighbor Ising interaction has been done and also similar lines of derivation of a master equation has been done for the quantum planar rotor in [4]. In both cases, the energy spectrum of the system has a non-equidistant spectrum and are coupled to the environment through creation and annihilation operators producing…”

“…Quantum kicked systems in contact with a thermal reservoir are systems subject to these two types of mechanisms. In this sense, there has been some recent developments concerning the thermodynamical properties of non-equilibrium stationary states or 'quasi steady states' reached by these systems [3,4] where, the non-equilibrium dynamics are introduced with the help of time-dependent periodic deltakicked potentials [5][6][7] and the freedom of choosing strong or weak interactions with the kicks and with the environment, has opened up new interesting features on the the emergent thermodynamical properties of the quasi stationary states reached by the system.…”

“…Additionally, features of the quantum kicked systems such as resonances or anti-resonances [5][6][7][8], disappear. Contrary to the kicked harmonic oscillator or the kicked rotator [3,4], the linear chain of qubits is a finite dimensional system and one cannot indefinitely populate states by the application of repeated kicks. This characteristic makes the quasi-steady states to present interesting features such as stationary entanglement between qubits.…”