Reply to the Comment of S. Ayik and D. Lacroix, posted as arXiv:1909.1361v1, on the recent article "Fission Dynamics of 240Pu from Saddle-to-Scission and Beyond" by Bulgac et al, published as Phys. Rev. C 100, 034615 (2019)

**mean**

**field**approach free of the difficulties in the stochastic mean field model due to S. Expand abstract.

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**field**approach free of the difficulties in the stochastic

**mean**

**field**model due to S. Ayik.

5/10 relevant

arXiv

A Finite-Volume Method for Fluctuating Dynamical Density Functional Theory

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**field**... Expand abstract.

**fields**or interaction potentials. This allows us to simulate a range of physical phenomena where thermal fluctuations play a crucial role, such as nucleation and further energy-barrier crossing transitions. A positivity-preserving algorithm for the density is derived based on a hybrid space discretization of the deterministic and the stochastic terms and different implicit and explicit time integrators. We show through numerous applications that not only our scheme is able to accurately reproduce the statistical properties (structure factor and correlations) of the physical system, but, because of the multiplicative noise, it allows us to simulate energy barrier crossing dynamics, which cannot be captured by

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**field**approaches.

4/10 relevant

arXiv

Calculation of excited states via symmetry constraints in the Variational Quantum Eigensolver

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**field**state. In the case of the CH$_2$ using $\textit{k}$-UpCCGSD, up-shifted singlet states relative to FCI are observed. Comparing the optimized cluster amplitudes between $\textit{k}$-UpCCGSD and UCCGSD, the lack of generalized double excitations in $\textit{k}$-UpCCGSD accounts for the increased energy of the first singlet state. In addition, we observe crossover between different spin states when using generalized ans\"{a}tze which can be prevented by penalty terms in the hamiltonian and qubit registers encoding multireference states. Comparison of calculations with qubit registers encoding different types of singlets (closed-shell and open-shell) suggest that conventional VQE may be able to calculate higher excited states beyond the first one for a particular set of symmetries, although with a significant loss in accuracy.

4/10 relevant

arXiv

Linear-Quadratic **Mean**-**Field** Reinforcement Learning: Convergence of
Policy Gradient Methods

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**field**linear-quadratic setting. Expand abstract.

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**field**control problems in discrete time, which can be viewed as Markov decision processes for a large number of exchangeable agents interacting in a

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**field**manner. Such problems arise, for instance when a large number of robots communicate through a central unit dispatching the optimal policy computed by minimizing the overall social cost. An approximate solution is obtained by learning the optimal policy of a generic agent interacting with the statistical distribution of the states of the other agents. We prove rigorously the convergence of exact and model-free policy gradient methods in a

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**field**linear-quadratic setting. We also provide graphical evidence of the convergence based on implementations of our algorithms.

10/10 relevant

arXiv

Nature vs. Nurture: Dynamical Evolution in Disordered Ising Ferromagnets

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**field**setting with light-tailed couplings, the disorder averages out and the limiting trajectories of the magnetization and twin overlap match those of the homogenous Curie--Weiss model. Expand abstract.

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**field**ferromagnets with light-tailed and heavy-tailed coupling distributions, as well as highly-disordered models with a variety of other geometries. In the

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**field**setting with light-tailed couplings, the disorder averages out and the limiting trajectories of the magnetization and twin overlap match those of the homogenous Curie--Weiss model. On the other hand, when the coupling distribution has heavy tails, or the geometry changes, the effect of the disorder persists in the thermodynamic limit. Nonetheless, qualitatively all such random ferromagnets share a similar time evolution for their twin overlap, wherein the two twins initially decorrelate, before either partially or fully converging back together due to the ferromagnetic drift.

4/10 relevant

arXiv

Asymptotic Analysis of the Elephant Random Walk

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**field**limit for this random walk. Expand abstract.

**mean**

**field**limit for this random walk.

4/10 relevant

arXiv

A generalized variational principle with applications to excited state
**mean** **field** theory

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**field**theory by an order of magnitude. Expand abstract.

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**field**theory, density functional theory, multi-reference theory, and quantum Monte Carlo. Like the standard variational principle, this generalized variational principle amounts to the optimization of a nonlinear function that, in the limit of an arbitrarily flexible wave function, has the desired Hamiltonian eigenstate as its global minimum. Unlike the standard variational principle, it can target excited states and select individual states in cases of degeneracy or near-degeneracy. As an initial demonstration of how this approach can be useful in practice, we employ it to improve the optimization efficiency of excited state

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**field**theory by an order of magnitude. With this improved optimization, we are able to demonstrate that the accuracy of the corresponding second-order perturbation theory rivals that of singles-and-doubles equation-of-motion coupled cluster in a substantially broader set of molecules than could be explored by our previous optimization methodology.

10/10 relevant

arXiv

Linearly-Solvable **Mean**-**Field** Approximation for Multi-Team Road Traffic
Games

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**field**approximation that a Nash equilibrium in the limit of a large population can be found by linearly solvable algorithms. Expand abstract.

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**field**approximation that a Nash equilibrium in the limit of a large population can be found by linearly solvable algorithms.

10/10 relevant

arXiv

Numerical resolution of McKean-Vlasov FBSDEs using neural networks

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**field**games and mean field control problems in high dimension. Expand abstract.

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**field**games and

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**field**control problems in high dimension. We analyze the numerical behavior of our algorithms on several examples including non linear quadratic models.

4/10 relevant

arXiv

Regularized pseudopotential for **mean**-**field** calculations

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**field**level, and we compare them with those obtained using the standard Gogny D1S finite-range effective interaction. Expand abstract.

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**field**level, and we compare them with those obtained using the standard Gogny D1S finite-range effective interaction.

10/10 relevant

arXiv