294 research outputs found
One-dimensional many-body entangled open quantum systems with tensor network methods
We present a collection of methods to simulate entangled dynamics of open
quantum systems governed by the Lindblad equation with tensor network methods.
Tensor network methods using matrix product states have been proven very useful
to simulate many-body quantum systems and have driven many innovations in
research. Since the matrix product state design is tailored for closed
one-dimensional systems governed by the Schr\"odinger equation, the next step
for many-body quantum dynamics is the simulation of open quantum systems. We
review the three dominant approaches to the simulation of open quantum systems
via the Lindblad master equation: quantum trajectories, matrix product density
operators, and locally purified tensor networks. Selected examples guide
possible applications of the methods and serve moreover as a benchmark between
the techniques. These examples include the finite temperature states of the
transverse quantum Ising model, the dynamics of an exciton traveling under the
influence of spontaneous emission and dephasing, and a double-well potential
simulated with the Bose-Hubbard model including dephasing. We analyze which
approach is favorable leading to the conclusion that a complete set of all
three methods is most beneficial, push- ing the limits of different scenarios.
The convergence studies using analytical results for macroscopic variables and
exact diagonalization methods as comparison, show, for example, that matrix
product density operators are favorable for the exciton problem in our study.
All three methods access the same library, i.e., the software package Open
Source Matrix Product States, allowing us to have a meaningful comparison
between the approaches based on the selected examples. For example, tensor
operations are accessed from the same subroutines and with the same
optimization eliminating one possible bias in a comparison of such numerical
methods.Comment: 24 pages, 8 figures. Small extension of time evolution section and
moving quantum simulators to introduction in comparison to v
Analyzing Tag Semantics Across Collaborative Tagging Systems
The objective of our group was to exploit state-of-the-art Information Retrieval methods for finding associations and dependencies between tags, capturing and representing differences in tagging behavior and vocabulary of various folksonomies, with the overall aim to better understand the semantics of tags and the tagging process. Therefore we analyze the semantic content of tags in the Flickr and Delicious folksonomies. We find that: tag context similarity leads to meaningful results in Flickr, despite its narrow folksonomy character; the comparison of tags across Flickr and Delicious shows little semantic overlap, being tags in Flickr associated more to visual aspects rather than technological as it seems to be in Delicious; there are regions in the tag-tag space, provided with the cosine similarity metric, that are characterized by high density; the order of tags inside a post has a semantic relevance
Anomalous light propagation and continuous lasing without inversion in an open driven -system
We explore a driven three-level -system coupled to an environment with
dynamics governed by the Lindblad master equation. We perform a transformation
into superoperator space, which brings the Lindblad equation into a
Schr\"{o}dinger-like, thus allowing us to obtain an exact analytical solution
for the time-dependence of the density matrix in a closed form. We demonstrate
a regime for continuous lasing without inversion for driving with a continuous
wave laser. We show a mechanism for achieving superluminal, negative, and
vanishing light pulse group velocities and provide a range of physical
parameters for realizing these regimes experimentally
A positive tensor network approach for simulating open quantum many-body systems
Open many-body quantum systems play an important role in quantum optics and
condensed-matter physics, and capture phenomena like transport, interplay
between Hamiltonian and incoherent dynamics, and topological order generated by
dissipation. We introduce a versatile and practical method to numerically
simulate one-dimensional open quantum many-body dynamics using tensor networks.
It is based on representing mixed quantum states in a locally purified form,
which guarantees that positivity is preserved at all times. Moreover, the
approximation error is controlled with respect to the trace norm. Hence, this
scheme overcomes various obstacles of the known numerical open-system evolution
schemes. To exemplify the functioning of the approach, we study both stationary
states and transient dissipative behaviour, for various open quantum systems
ranging from few to many bodies.Comment: 13 pages, 7 figures, significant material on error bounds adde
Accounting for risk of non linear portfolios: a novel Fourier approach
The presence of non linear instruments is responsible for the emergence of
non Gaussian features in the price changes distribution of realistic
portfolios, even for Normally distributed risk factors. This is especially true
for the benchmark Delta Gamma Normal model, which in general exhibits
exponentially damped power law tails. We show how the knowledge of the model
characteristic function leads to Fourier representations for two standard risk
measures, the Value at Risk and the Expected Shortfall, and for their
sensitivities with respect to the model parameters. We detail the numerical
implementation of our formulae and we emphasizes the reliability and efficiency
of our results in comparison with Monte Carlo simulation.Comment: 10 pages, 12 figures. Final version accepted for publication on Eur.
Phys. J.
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