On the partial trace over collective spin-degrees of freedom

Abstract

We derive analytical properties for the degeneracy $\nu (N,j)$ occurring in the decomposition $\underset{j}{\overset{\frac{N}{2}}{⨁}}\nu (N,j){\mathbb{C}}^{2j+1}$ of the state space ${\mathbb{C}}^{2\otimes N}$. We also investigate the dynamics of two qubits coupled via Ising interactions to separate spin baths, and we study the thermodynamic limit.

14 pages, 6 figures, minor typographical errors fixed

References in corpus (4)

• Efficiency of energy transfer in a light-harvesting system under quantum coherence
• Non-Markovian reduced dynamics and entanglement evolution of two coupled spins in a quantum spin environment
• Time evolution and decoherence of a spin-1/2 particle coupled to a spin bath in thermal equilibrium
• Quantum Critical Dynamics of A Qubit Coupled to An Isotropic Lipkin-Meshkov-Glick Bath

Cited by in corpus (5)

• Exactly solvable model for the dynamics of two spin-1/2 particles embedded in separate spin star environments
• A nontrivial bosonic representation of large spin systems at high temperatures
• Aspects of the decoherence in high spin environments: Breakdown of the mean-field approximation
• Decay rates and decoherence of an interstitial two-level spin impurity in a ferromagnetic lattice
• Random spin distributions and the diffusion equation