Lindblad formulation

The DM equation for the Lindblad formulation follows along lines similar to the ones mentioned for propagation of the quantum-classical DOp without dissipation. It starts with an expansion of operators in the p-region in terms of a basis set of functions and a discretization of quasiclassical variables in the p-phase space, and leads to a matrix equation which can be written as... 

The stochastic mean-field [20] (SMF) method simultaneously resolves the following two major issues with NA MD. First, decoherence effects within the quantum subsystem that take place due to its interaction with an environment are included. Second, decoherence naturally leads to the asymptotic branching of NA trajectories. That is, the implementation of the decoherence effect in the SMF approach automatically resolves the branching problem. By extending the ordinary quantum-classical MF approximation, the SMF approach accounts for the quantum features of the environment in the Lindblad formulation. The Lindblad formulation is exact for a bath of harmonic oscillators and is an approximation for other types of solvents. While the quantum nature of the environment is treated by SMF within an approximation, its classical properties are included exactly by classical MD with a true Hamiltonian. 

Tsilou ET, Thompson D, Lindblad AS, Reed GF, Rubin B, Gahl W, Thoene J, Del Monte M, Schneider JA, Granet DB, Kaiser-Kupfer MI. A multicentre randomised double masked clinical trial of a new formulation of topical cysteamine for the treatment of corneal cystine crystals in cystinosis. Br J Ophthalmol 2003 87(1) 28-31. 

We have also outlined a treatment of systems showing dissipative dynamies. These ean be treated with a natural extension of the formulation shown here. The density operator equation differs in a signifieant way when dissipation is present, because it eontains terms whieh are not derived from a Hamiltonian, and must be written as rates involving superoperators. We have shown here one such situation, with the Lindblad form of the dissipation rate, and other forms can be treated equally well with the present eombination of a PWT and a quasielassieal approximation in phase spaee. 

Atrial muscle The first detailed model of the excitation-contraction coupling mechanism in heart cells was constructed by Hilgemann and Noble [1987] and a single cell model was completed by Earm and Noble [1990]. A similarly detailed model of rabbit atrial cells was constructed by Lindblad et al. [1996] and modified to fit data from human atrial cells by Nygren et al. [1998]. Another model of human atrial cells based on the ventricular ceU model of Luo and Rudy [1994] but with improved calcium handling equations was formulated by Courtemanche et al. [1998]. The main differences between the Nygren and... 

The three-pulse EOM-PMA can be formulated not only in terms of density matrices and master equations but also in terms of wavefunctions and Schrodinger equations [29]. The EOM-PMA can therefore be straightforwardly incorporated into computer programs which provide the time evolution of the density matrix or the wavefunction of material systems. Besides the multilevel Redlield theory, the EOM-PMA can be combined with the Lindblad master equation [49], the surrogate Hamiltonian approach [49], the stochastic Liouville equation [18], the quantum Fokker-Planck equation [18], and the density matrix [50] or the wavefunction [14] multiconfigurational time-dependent Hartree (MCTDH) methods. When using the... 

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