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Collaborative Research Center 910Embedding strategies for delay problems in different fields (17.05.2019)

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Embedding strategies for delay problems in different fields

Friday, 17. May 2019

Location: Technische Universität Berlin
Main building, Room H 3005
Straße des 17. Juni 135, 10623 Berlin

Guests are welcome!

Programme

Friday, 17. May 2019

 

Programme
15:00
Transfer-tensor-method and Markovian embeddings based on orthogonal polynomials
Dr. Javier Cerrillo
Technische Universität Berlin
15:25
The pseudospectral approximation method for delay differential equations
Babette de Wolff
Freie Universität Berlin
15:50
Coffee Break
16:10
Fokker-Planck description of a delayed stochastic process via Markovian embedding
Sarah A.M. Loos
Technische Universität Berlin
16:35
Non-Markovian quantum feedback in the presence of finite temperatures
Dr. Alexander Carmele
Technische Universität Berlin
17:00
Informal get-together ("Stammtisch")

Abstracts

Transfer-tensor-method and Markovian embeddings based on orthogonal polynomials
Dr. Javier Cerrillo

Comprehensive simulation methods of general open quantum systems tend to be numerically
demanding, in particular in the presence of non-Markovian effects and strong coupling to the
environment. It is generally the case that the size of the propagator or of the stochastic sample scales unfavorably with the time length of the simulation or the corresponding perturbative expansion order, and can be interpreted in terms of the exponential growth of the relevant Hilbert space. The question arises whether there are regimes where this scaling can be mitigated in some form, i.e. if an effective
propagator of a reduced size can be extracted that facilitates long-time simulations. This question was
addressed with the creation of a tool known as the transfer-tensor-method (TTM), which has been
shown to provide extraordinary acceleration of non-Markovian open quantum system simulations. This
is achieved by blackbox learning from sample exact trajectories for some short initial period
and subsequent generation of a compact multiplicative propagator for the system degrees of freedom
alone. For a learning period longer than the environment correlation time, the propagator accurately
reproduces the long time system dynamics with linear effort. TTM is a general and flexible approach
that does not depend on the form of the environment or the interaction, and has generated widespread
interest. In particular, it has been shown to be a useful tool for the reproduction of absorption and
emission spectra of atomic or molecular systems dressed with environmental vibrations and in the
context of laser cooling experiments.

 

The pseudospectral approximation method for delay differential equations
Babette de Wolff

The pseudospectral approximation method for delay equations was introduced by Breda et al. in 2005
as a method to approximate eigenvalues of delay differential equations (DDEs) by eigenvalues of a
family of ordinary differential equations (ODEs). Because of the specific structure of the family of
ODEs, it has been proposed that also the bifurcation behaviour of the DDEs is approximated by the
bifurcation behaviour of the ODEs. This would allow us to use ODE bifurcation tools to analyze the
bifurcation behaviour of delay equations.
In this talk, we will introduce the pseudospectral method and discuss its bifurcation behaviour. In
particular, we will discuss the convergence of the Lyapunov coefficient in the Hopf bifurcation.

 

Fokker-Planck description of a delayed stochastic process via Markovian embedding
Sarah A.M. Loos

A discrete time delay in the Langevin equation naturally leads to an infinite hierarchy of Fokker-Planck
(FP) equations for the n-time joint probability distribution functions [1]. Finding a probabilistic
description is hence challenging, especially for systems subject to nonlinear forces. One major issue is
that the higher members of the hierarchy contain unknown functional derivatives between noise and the
stochastic state variable.
In this talk, I will introduce a new way to derive the Fokker-Planck equation via a Markovian
embedding technique. In particular, I will discuss an extended Markovian system with auxiliary
variables which generates the same dynamics as the original (delayed) system in the limit of an
infinitely large system. This extended system can further be studied under a stochastic
thermodynamical [2] perspective, allowing to find a closed expression for the entropy production,
which is a nontrivial problem in the presence of delay.
[1] Loos & Klapp, ArXiv:1903.02322 (2019).
[2] Loos & Klapp, Sci. Rep. 9, 2491 (2019).

 

Non-Markovian quantum feedback in the presence of finite temperatures
Dr. Alexander Carmele

Feedback introduces additional non-Markovian memory and noise into open quantum system
dynamics. In this talk, a detailed discussion of non-Markovian feedback is presented in the case of
quantum coherence control for exotic pure dephasing dynamics in acoustic cavities. It is shown that
feedback allows to stabilize initial coherences in the system up to room temperature due to quantum
interference effects. Furthermore, an outlook is given how to implement non-Markovian contributions
in an augmented density matrix approach relying on real-time Feynman path integrals.

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