7,802 research outputs found
The equilibrium states of open quantum systems in the strong coupling regime
In this work we investigate the late-time stationary states of open quantum
systems coupled to a thermal reservoir in the strong coupling regime. In
general such systems do not necessarily relax to a Boltzmann distribution if
the coupling to the thermal reservoir is non-vanishing or equivalently if the
relaxation timescales are finite. Using a variety of non-equilibrium formalisms
valid for non-Markovian processes, we show that starting from a product state
of the closed system = system + environment, with the environment in its
thermal state, the open system which results from coarse graining the
environment will evolve towards an equilibrium state at late-times. This state
can be expressed as the reduced state of the closed system thermal state at the
temperature of the environment. For a linear (harmonic) system and environment,
which is exactly solvable, we are able to show in a rigorous way that all
multi-time correlations of the open system evolve towards those of the closed
system thermal state. Multi-time correlations are especially relevant in the
non-Markovian regime, since they cannot be generated by the dynamics of the
single-time correlations. For more general systems, which cannot be exactly
solved, we are able to provide a general proof that all single-time
correlations of the open system evolve to those of the closed system thermal
state, to first order in the relaxation rates. For the special case of a
zero-temperature reservoir, we are able to explicitly construct the reduced
closed system thermal state in terms of the environmental correlations.Comment: 20 pages, 2 figure
Estimating Local Function Complexity via Mixture of Gaussian Processes
Real world data often exhibit inhomogeneity, e.g., the noise level, the
sampling distribution or the complexity of the target function may change over
the input space. In this paper, we try to isolate local function complexity in
a practical, robust way. This is achieved by first estimating the locally
optimal kernel bandwidth as a functional relationship. Specifically, we propose
Spatially Adaptive Bandwidth Estimation in Regression (SABER), which employs
the mixture of experts consisting of multinomial kernel logistic regression as
a gate and Gaussian process regression models as experts. Using the locally
optimal kernel bandwidths, we deduce an estimate to the local function
complexity by drawing parallels to the theory of locally linear smoothing. We
demonstrate the usefulness of local function complexity for model
interpretation and active learning in quantum chemistry experiments and fluid
dynamics simulations.Comment: 19 pages, 16 figure
Machine Learning, Quantum Mechanics, and Chemical Compound Space
We review recent studies dealing with the generation of machine learning
models of molecular and solid properties. The models are trained and validated
using standard quantum chemistry results obtained for organic molecules and
materials selected from chemical space at random
Big-Data-Driven Materials Science and its FAIR Data Infrastructure
This chapter addresses the forth paradigm of materials research -- big-data
driven materials science. Its concepts and state-of-the-art are described, and
its challenges and chances are discussed. For furthering the field, Open Data
and an all-embracing sharing, an efficient data infrastructure, and the rich
ecosystem of computer codes used in the community are of critical importance.
For shaping this forth paradigm and contributing to the development or
discovery of improved and novel materials, data must be what is now called FAIR
-- Findable, Accessible, Interoperable and Re-purposable/Re-usable. This sets
the stage for advances of methods from artificial intelligence that operate on
large data sets to find trends and patterns that cannot be obtained from
individual calculations and not even directly from high-throughput studies.
Recent progress is reviewed and demonstrated, and the chapter is concluded by a
forward-looking perspective, addressing important not yet solved challenges.Comment: submitted to the Handbook of Materials Modeling (eds. S. Yip and W.
Andreoni), Springer 2018/201
Goldstone Theorem in the Gaussian Functional Approximation to the Scalar Theory
We verify the Goldstone theorem in the Gaussian functional approximation to
the theory with internal O(2) symmetry. We do so by reformulating
the Gaussian approximation in terms of Schwinger-Dyson equations from which an
explicit demonstration of the Goldstone theorem follows directly.Comment: 11 page
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