13,588 research outputs found
Simulation of quantum walks and fast mixing with classical processes
We compare discrete-time quantum walks on graphs to their natural classical equivalents, which we argue are lifted Markov chains (LMCs), that is, classical Markov chains with added memory. We show that LMCs can simulate the mixing behavior of any quantum walk, under a commonly satisfied invariance condition. This allows us to answer an open question on how the graph topology ultimately bounds a quantum walk's mixing performance, and that of any stochastic local evolution. The results highlight that speedups in mixing and transport phenomena are not necessarily diagnostic of quantum effects, although superdiffusive spreading is more prominent with quantum walks. The general simulating LMC construction may lead to large memory, yet we show that for the main graphs under study (i.e., lattices) this memory can be brought down to the same size employed in the quantum walks proposed in the literature
Strong coupling theory for tunneling and vibrational relaxation in driven bistable systems
A study of the dynamics of a tunneling particle in a driven bistable
potential which is moderately-to-strongly coupled to a bath is presented. Upon
restricting the system dynamics to the Hilbert space spanned by the M lowest
energy eigenstates of the bare static potential, a set of coupled non-Markovian
master equations for the diagonal elements of the reduced density matrix,
within the discrete variale representation, is derived. The resulting dynamics
is in good agreement with predictions of ab-initio real-time path integral
simulations. Numerous results, analytical as well as numerical, for the quantum
relaxation rate and for the asymptotic populations are presented. Our method is
particularly convenient to investigate the case of shallow, time-dependent
potential barriers and moderate-to-strong damping, where both a semi-classical
and a Redfield-type approach are inappropriate.Comment: 37 pages, 23 figure
Convergence of large deviation estimators
We study the convergence of statistical estimators used in the estimation of
large deviation functions describing the fluctuations of equilibrium,
nonequilibrium, and manmade stochastic systems. We give conditions for the
convergence of these estimators with sample size, based on the boundedness or
unboundedness of the quantity sampled, and discuss how statistical errors
should be defined in different parts of the convergence region. Our results
shed light on previous reports of 'phase transitions' in the statistics of free
energy estimators and establish a general framework for reliably estimating
large deviation functions from simulation and experimental data and identifying
parameter regions where this estimation converges.Comment: 13 pages, 6 figures. v2: corrections focusing the paper on large
deviations; v3: minor corrections, close to published versio
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