2 resultados para variational mean-field method

em Memorial University Research Repository


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In this thesis, we consider N quantum particles coupled to collective thermal quantum environments. The coupling is energy conserving and scaled in the mean field way. There is no direct interaction between the particles, they only interact via the common reservoir. It is well known that an initially disentangled state of the N particles will remain disentangled at times in the limit N -> [infinity]. In this thesis, we evaluate the η-body reduced density matrix (tracing over the reservoirs and the N - η remaining particles). We identify the main disentangled part of the reduced density matrix and obtain the first order correction term in 1/N. We show that this correction term is entangled. We also estimate the speed of convergence of the reduced density matrix as N -> [infinity]. Our model is exactly solvable and it is not based on numerical approximation.

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Geometric frustration occurs in the rare earth pyrochlores due to magnetic rare earth ions occupying the vertices of the network of corner-sharing tetrahedra. In this research, we have two parts. In the first one we study the phase transition to the magnetically ordered state at low temperature in the pyrochlore Er₂Ti₂O₇. The molecular field method was used to solve this problem. In the second part, we analyse the crystal electric field Hamiltonian for the rare earth sites. The rather large degeneracy of the angular momentum J of the rare earth ion is lifted by the crystal electric field due to the neighboring ions in the crystal. By rewriting the Stevens operators in the crystal electric field Hamiltonian ᴴCEF in terms of charge quadruple operators, we can identify unstable order parameters in ᴴCEF . These may be related to lattice instabilities in Tb₂Ti₂O₇.