171 research outputs found
A Second-Order Distributed Trotter-Suzuki Solver with a Hybrid Kernel
The Trotter-Suzuki approximation leads to an efficient algorithm for solving
the time-dependent Schr\"odinger equation. Using existing highly optimized CPU
and GPU kernels, we developed a distributed version of the algorithm that runs
efficiently on a cluster. Our implementation also improves single node
performance, and is able to use multiple GPUs within a node. The scaling is
close to linear using the CPU kernels, whereas the efficiency of GPU kernels
improve with larger matrices. We also introduce a hybrid kernel that
simultaneously uses multicore CPUs and GPUs in a distributed system. This
kernel is shown to be efficient when the matrix size would not fit in the GPU
memory. Larger quantum systems scale especially well with a high number nodes.
The code is available under an open source license.Comment: 11 pages, 10 figure
Towards integrated urban simulations
More than half of the world population lives in urban areas.
Urbanites are estimated to grow up to 68% of the population
by 2050 [1]. This rapid growth requires new contributions from
researchers and policy-makers to the development of the future
city. Again, understanding how the city will grow is a crucial
step in guiding this process towards the best outcome.
Cities are highly complex systems that traditional urban dynamic
simulations cannot grasp in their totality, if solved only
in a lightly coupled way. In addition, a model is useful only if
it can be used in the planning and management practice [2]. It’s
true that, driven by the urge to improve their models, different
sectors are developing multi-layered integrated simulations.
Nevertheless, a wider scope of considering the city in its
holistic behaviour is missing. Indeed, management, social, and
technical barriers restrain the adoption of integrated models,
such as ‘model complexity, user friendliness, administrative
fragmentation and communication’ [3]
Universal decoherence induced by an environmental quantum phase transition
Decoherence induced by coupling a system with an environment may display
universal features. Here we demostrate that when the coupling to the system
drives a quantum phase transition in the environment, the temporal decay of
quantum coherences in the system is Gaussian with a width independent of the
system-environment coupling strength. The existence of this effect opens the
way for a new type of quantum simulation algorithm, where a single qubit is
used to detect a quantum phase transition. We discuss possible implementations
of such algorithm and we relate our results to available data on universal
decoherence in NMR echo experiments
Gaussian Decoherence and Gaussian Echo from Spin Environments
We examine an exactly solvable model of decoherence -- a spin-system
interacting with a collection of environment spins. We show that in this simple
model (introduced some time ago to illustrate environment--induced
superselection) generic assumptions about the coupling strengths lead to a
universal (Gaussian) suppression of coherence between pointer states. We
explore the regime of validity of this result and discuss its relation to
spectral features of the environment. We also consider its relevance to the
experiments on the so-called Loschmidt echo (which measures, in effect, the
fidelity between the initial and time-reversed or "echo" signal). In
particular, we show that for partial reversals (e.g., when of only a part of
the total Hamiltonian changes sign) fidelity will exhibit a Gaussian dependence
on the time of reversal. In such cases echo may become independent of the
details of the reversal procedure or the specifics of the coupling to the
environment. This puzzling behavior was observed in several NMR experiments.
Natural candidates for such two environments (one of which is easily reversed,
while the other is ``irreversible'') are suggested for the experiment involving
ferrocene.Comment: Improved text and figures, to appear in the special issue of Acta
Physica Polonica B celebrating the 100th anniversary of Smoluchowski's
equation and his paper explaining Brownian motion (in
http://th-www.if.uj.edu.pl/acta/vol38/pdf/v38p1685.pdf
Dynamical Origin of Decoherence in Clasically Chaotic Systems
The decay of the overlap between a wave packet evolved with a Hamiltonian H
and the same state evolved with H}+ serves as a measure of the
decoherence time . Recent experimental and analytical evidence on
classically chaotic systems suggest that, under certain conditions,
depends on H but not on . By solving numerically a
Hamiltonian model we find evidence of that property provided that the system
shows a Wigner-Dyson spectrum (which defines quantum chaos) and the
perturbation exceeds a crytical value defined by the parametric correlations of
the spectra.Comment: Typos corrected, published versio
Sensitivity to perturbations in a quantum chaotic billiard
The Loschmidt echo (LE) measures the ability of a system to return to the
initial state after a forward quantum evolution followed by a backward
perturbed one. It has been conjectured that the echo of a classically chaotic
system decays exponentially, with a decay rate given by the minimum between the
width of the local density of states and the Lyapunov exponent. As the
perturbation strength is increased one obtains a cross-over between both
regimes. These predictions are based on situations where the Fermi Golden Rule
(FGR) is valid. By considering a paradigmatic fully chaotic system, the
Bunimovich stadium billiard, with a perturbation in a regime for which the FGR
manifestly does not work, we find a cross over from to Lyapunov decay.
We find that, challenging the analytic interpretation, these conjetures are
valid even beyond the expected range.Comment: Significantly revised version. To appear in Physical Review E Rapid
Communication
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