6,069 research outputs found
Correlated projection operator approach to non-Markovian dynamics in spin baths
The dynamics of an open quantum system is usually studied by performing a
weak-coupling and weak-correlation expansion in the system-bath interaction.
For systems exhibiting strong couplings and highly non-Markovian behavior this
approach is not justified. We apply a recently proposed correlated projection
superoperator technique to the model of a central spin coupled to a spin bath
via full Heisenberg interaction. Analytical solutions to both the
Nakajima-Zwanzig and the time-convolutionless master equation are determined
and compared with the results of the exact solution. The correlated projection
operator technique significantly improves the standard methods and can be
applied to many physical problems such as the hyperfine interaction in a
quantum dot
Integrable Floquet dynamics, generalized exclusion processes and "fused" matrix ansatz
We present a general method for constructing integrable stochastic processes,
with two-step discrete time Floquet dynamics, from the transfer matrix
formalism. The models can be interpreted as a discrete time parallel update.
The method can be applied for both periodic and open boundary conditions. We
also show how the stationary distribution can be built as a matrix product
state. As an illustration we construct a parallel discrete time dynamics
associated with the R-matrix of the SSEP and of the ASEP, and provide the
associated stationary distributions in a matrix product form. We use this
general framework to introduce new integrable generalized exclusion processes,
where a fixed number of particles is allowed on each lattice site in opposition
to the (single particle) exclusion process models. They are constructed using
the fusion procedure of R-matrices (and K-matrices for open boundary
conditions) for the SSEP and ASEP. We develop a new method, that we named
"fused" matrix ansatz, to build explicitly the stationary distribution in a
matrix product form. We use this algebraic structure to compute physical
observables such as the correlation functions and the mean particle current.Comment: 33 pages, to appear in Nuclear Physics
Preservation of Positivity by Dynamical Coarse-Graining
We compare different quantum Master equations for the time evolution of the
reduced density matrix. The widely applied secular approximation (rotating wave
approximation) applied in combination with the Born-Markov approximation
generates a Lindblad type master equation ensuring for completely positive and
stable evolution and is typically well applicable for optical baths. For phonon
baths however, the secular approximation is expected to be invalid. The usual
Markovian master equation does not generally preserve positivity of the density
matrix. As a solution we propose a coarse-graining approach with a dynamically
adapted coarse graining time scale. For some simple examples we demonstrate
that this preserves the accuracy of the integro-differential Born equation. For
large times we analytically show that the secular approximation master equation
is recovered. The method can in principle be extended to systems with a
dynamically changing system Hamiltonian, which is of special interest for
adiabatic quantum computation. We give some numerical examples for the
spin-boson model of cases where a spin system thermalizes rapidly, and other
examples where thermalization is not reached.Comment: 18 pages, 7 figures, reviewers suggestions included and tightened
presentation; accepted for publication in PR
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