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A<sc>bstract</sc> Ab-initio simulations of multiple heavy quarks propagating in a Quark-Gluon Plasma are computationally difficult to perform due to the large dimension of the space of density matrices. This work develops machine learning algorithms to overcome this difficulty by approximating exact quantum states with neural network parametrisations, specifically Neural Density Operators. As a proof of principle demonstration in a QCD-like theory, the approach is applied to solve the Lindblad master equation in the 1 + 1d lattice Schwinger Model as an open quantum system. Neural Density Operators enable the study of in-medium dynamics on large lattice volumes, where multiple-string interactions and their effects on string-breaking and recombination phenomena can be studied. Thermal properties of the system at equilibrium can also be probed with these methods by variationally constructing the steady state of the Lindblad master equation. Scaling of this approach with system size is studied, and numerical demonstrations on up to 32 spatial lattice sites and with up to 3 interacting strings are performed.
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On the Dynamics of Interacting Agents on an Ising Lattice
A system of multiple agents is considered which at random times change their discrete states on an Ising lattice as a results of their internal interactions and possibly some external control. For certain applications such as directed self-assembly of charged particles, the stochastic dynamics of such interacting agents is represented by a master equation, or equivalently, by a continuous-time Markov chain. The dimension of this master equation is typically large and numerically intractable, since it grows combinatorially with the lattice size. This paper presents two alternative models at significantly lower complexity growing polynomially with the size of Ising lattice. These models describe the interactive dynamics of the agents by two different classes of coupled stochastic differential equations driven by doubly stochastic Poisson processes (Cox processes).
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- Award ID(s):
- 1941944
- PAR ID:
- 10398925
- Date Published:
- Journal Name:
- 2022 American Control Conference (ACC)
- Page Range / eLocation ID:
- 2837 to 2842
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.23919/ACC53348.2022.9867475
