1,431 research outputs found
Approximating open quantum system dynamics in a controlled and efficient way: A microscopic approach to decoherence
We demonstrate that the dynamics of an open quantum system can be calculated
efficiently and with predefined error, provided a basis exists in which the
system-environment interactions are local and hence obey the Lieb-Robinson
bound. We show that this assumption can generally be made. Defining a dynamical
renormalization group transformation, we obtain an effective Hamiltonian for
the full system plus environment that comprises only those environmental
degrees of freedom that are within the effective light cone of the system. The
reduced system dynamics can therefore be simulated with a computational effort
that scales at most polynomially in the interaction time and the size of the
effective light cone. Our results hold for generic environments consisting of
either discrete or continuous degrees of freedom
Classes of random walks on temporal networks with competing timescales
Random walks find applications in many areas of science and are the heart of
essential network analytic tools. When defined on temporal networks, even basic
random walk models may exhibit a rich spectrum of behaviours, due to the
co-existence of different timescales in the system. Here, we introduce random
walks on general stochastic temporal networks allowing for lasting
interactions, with up to three competing timescales. We then compare the mean
resting time and stationary state of different models. We also discuss the
accuracy of the mathematical analysis depending on the random walk model and
the structure of the underlying network, and pay particular attention to the
emergence of non-Markovian behaviour, even when all dynamical entities are
governed by memoryless distributions.Comment: 16 pages, 5 figure
Universally Optimal Noisy Quantum Walks on Complex Networks
Transport properties play a crucial role in several fields of science, as
biology, chemistry, sociology, information science, and physics. The behavior
of many dynamical processes running over complex networks is known to be
closely related to the geometry of the underlying topology, but this connection
becomes even harder to understand when quantum effects come into play. Here, we
exploit the Kossakoski-Lindblad formalism of quantum stochastic walks to
investigate the capability to quickly and robustly transmit energy (or
information) between two distant points in very large complex structures,
remarkably assisted by external noise and quantum features as coherence. An
optimal mixing of classical and quantum transport is, very surprisingly, quite
universal for a large class of complex networks. This widespread behaviour
turns out to be also extremely robust with respect to geometry changes. These
results might pave the way for designing optimal bio-inspired geometries of
efficient transport nanostructures that can be used for solar energy and also
quantum information and communication technologies.Comment: 17 pages, 12 figure
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