2008/04/01 by Marco Merkli, M. Merkli, G. P. Berman +2 · 26 citations
Mathematics · Physics and Astronomy · #Condensed matter physics #Coupling (piping) #Density matrix #Diagonal #Exchange interaction #Matrix (chemical analysis) #Physics #Quantum #Quantum and electron transport phenomena #Quantum decoherence #Quantum mechanics #Quantum optics and atomic interactions #Spectroscopy and Quantum Chemical Studies #Spin (aerodynamics) #Spins #Statistical physics #Thermalisation #math-ph #math.MP #msc:81V99 #msc:82C10 #quant-ph
paper · pdf · doi:10.1016/j.aop.2008.07.004
published in Annals of Physics 323(12), 3091-3112 (Elsevier BV)
arxiv created 2008/04/01 · openalex publication_date 2008/08/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We analyze the dynamics of N interacting spins (quantum register) collectively coupled to a thermal environment. Each spin experiences the same environment interaction, consisting of an energy conserving and an energy exchange part. We find the decay rates of the reduced density matrix elements in the energy basis. We show that if the spins do not interact among each other, then the fastest decay rates of off-diagonal matrix elements induced by the energy conserving interaction is of order N2, while that one induced by the energy exchange interaction is of the order N only. Moreover, the diagonal matrix elements approach their limiting values at a rate independent of N. For a general spin system the decay rates depend in a rather complicated (but explicit) way on the size N and the interaction between the spins. Our method is based on a dynamical quantum resonance theory valid for small, fixed values of the couplings. We do not make Markov-, Born- or weak coupling (van Hove) approximations.