We develop an approach to study the entanglement in two coupled harmonic oscillators. We start by introducing an unitary transformation to end up with the solutions of the energy spectrum. These are used to construct the corresponding coherent states through the standard way. To evaluate the degree of the entanglement between the obtained states, we calculate the purity function in terms of the coherent and number states, separately. The result is yielded two parameters dependance of the purity, which can be controlled easily. Interesting results are derived by fixing the mixing angle of such transformation as π 2 . We compare our results with already published work and point out the relevance of these findings to a systematic formulation of the entanglement effect in two coupled harmonic oscillators.
We develop an approach in solving exactly the problem of three-body oscillators including general quadratic interactions in the coordinates for arbitrary masses and couplings. We introduce a unitary transformation of three independent angles to end up with a diagonalized Hamiltonian. Using the representation theory of the group SU (3), we explicitly determine the solutions of the energy spectrum. Considering the ground state together with reduced density matrix, we derive the corresponding purity function that is giving rise to minimal and maximal entanglement under suitable conditions. The cases of realizing one variable among three is discussed and know results in literature are recovered.
We study the dynamics and redistribution of entanglement and coherence in three time-dependent coupled harmonic oscillators. We resolve the Schrödinger equation by using time-dependent Euler rotation together with a linear quench model to obtain the state of vacuum solution. Such state can be translated to the phase space picture to determine the Wigner distribution. We show that its Gaussian matrix [Formula: see text] can be used to directly cast the covariance matrix [Formula: see text]. To quantify the mixedness and entanglement of the state, one uses respectively linear and von Neumann entropies for three cases: fully symmetric, bi-symmetric and fully nonsymmetric. Then we determine the coherence, tripartite entanglement and local uncertainties and derive their dynamics. We show that the dynamics of all quantum information quantities are driven by the Ermakov modes. Finally, we use an homodyne detection to redistribute both resources of entanglement and coherence.
We consider the thermal aspect of a system composed of two coupled harmonic oscillators and study the corresponding purity. We initially consider a situation where the system is brought to a canonical thermal equilibrium with a heat-bath at temperature T. We adopt the path integral approach and introduce the evolution operator to calculate the density matrix and subsequently the reduced matrix density. It is used to explicitly determine the purity in terms of different physical quantities and therefore study some limiting cases related to temperature as well as other parameters. Different numerical results are reported and discussed in terms of the involved parameters of our system.
We consider Pauli-Dirac fermion submitted to an inhomogeneous magnetic field. It is showed that the propagator of the neutral Dirac particle with an anomalous magnetic moment in an external linear magnetic field is the causal Green function S c (x b , x a ) of the Pauli-Dirac equation.The corresponding Green function is calculated via path integral method in global projection, giving rise to the exact eigenspinors expressions. The neutral particle creation probability corresponding to our system is analyzed, which is obtained as function of the introduced field B ′ and the additional spin magnetic moment µ.
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