Introduction

Czischek, Stefanie

doi:10.1007/978-3-030-52715-0_1

Cited by 1 publication

(2 citation statements)

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“…The latter is because the A matrix has a dimension of (N + M + N × M ) × (N + M + N × M ), and is constructed only once for each time step in Euler's method, whereas it is evaluated four times in the RK4 process. For more details of the ANN approach, see [1,27].…”

Section: Artificial Neural Network: Rbm Machinementioning

confidence: 99%

“…Along with that, strong quantum correlations or entanglement growth makes quantum dynamics more intriguing. Developing numerical approaches capturing quantum correlations have been one of the main focus in the recent past [1], and lead to the development of various numerical techniques based on tensor network states and phase-space methods. The former includes, for instance, density-matrix renormalization group (DMRG) (for both ground states and dynamics) [2][3][4][5][6][7] in which the Hilbert space is truncated to states with significant probabilities, thereby leading to a polynomial growth in Hilbert space with system size.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Analyzing Rydberg excitation Dynamics in an atomic chain via discrete truncated Wigner approximation and artificial neural networks

Naik¹,

Varna²,

Li³

et al. 2021

Preprint

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We analyze the excitation dynamics numerically in a one-dimensional Rydberg atomic chain, using the methods of discrete truncated Wigner approximation (dTWA) and artificial neural networks (ANN), for both van der Waals and dipolar interactions. In particular, we look at how the number of excitations dynamically grows or evolves in the system for an initial state where all atoms are in their electronic ground state. Further, we calculate the maximum number of excitations attained at any instant and the average number of excitations. For a small system size of ten atoms, we compare the results from dTWA and ANN with that of exact numerical calculations of the Schrödinger equation. The collapse and revival dynamics in the number of Rydberg excitations are also characterized in detail. Though we find good agreement at shorter periods, both dTWA and ANN failed to capture the dynamics accurately at longer times. By increasing the number of hidden units, the accuracy of ANN has improved but suffered by numerical instabilities, especially for large interaction strengths. Finally, we look at the dynamics of a large system size of two-hundred atoms using dTWA.

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Section: Artificial Neural Network: Rbm Machinementioning

confidence: 99%