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Abstract Numerical techniques to efficiently model out-of-equilibrium dynamics in interacting quantum many-body systems are key for advancing our capability to harness and understand complex quantum matter. Here we propose a new numerical approach which we refer to as generalized discrete truncated Wigner approximation (GDTWA). It is based on a discrete semi-classical phase space sampling and allows to investigate quantum dynamics in lattice spin systems with arbitraryS ≥ 1/2. We show that the GDTWA can accurately simulate dynamics of large ensembles in arbitrary dimensions. We apply it forS > 1/2 spin-models with dipolar long-range interactions, a scenario arising in recent experiments with magnetic atoms. We show that the method can capture beyond mean-field effects, not only at short times, but it also can correctly reproduce long time quantum-thermalization dynamics. We benchmark the method with exact diagonalization in small systems, with perturbation theory for short times, and with analytical predictions made for models which feature quantum-thermalization at long times. We apply our method to study dynamics in largeS > 1/2 spin-models and compute experimentally accessible observables such as Zeeman level populations, contrast of spin coherence, spin squeezing, and entanglement quantified by single-spin Renyi entropies. We reveal that largeSsystems can feature larger entanglement than correspondingS = 1/2 systems. Our analyses demonstrate that the GDTWA can be a powerful tool for modeling complex spin dynamics in regimes where other state-of-the art numerical methods fail.
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Quantum‐classical path integral evaluation of reaction rates with a near‐equilibrium flux formulation
Abstract Quantum‐classical formulations of reactive flux correlation functions require the partial Weyl–Wigner transform of the thermalized flux operator, whose numerical evaluation is unstable because of phase cancelation. In a recent paper, we introduced a non‐equilibrium formulation which eliminates the need for construction of this distribution and which gives the reaction rate along with the time evolution of the reactant population. In this work, we describe a near‐equilibrium formulation of the reactive flux, which accounts for important thermal correlations between the quantum system and its environment while avoiding the numerical instabilities of the full Weyl–Wigner transform. By minimizing early‐time transients, the near‐equilibrium formulation leads to an earlier onset of the plateau regime, allowing determination of the reaction rate from short‐time dynamics. In combination with the quantum‐classical path integral methodology, the near‐equilibrium formulation offers an accurate and efficient approach for determining reaction rate constants in condensed phase environments. The near‐equilibrium formulation may also be combined with a variety of approximate quantum‐classical propagation methods.
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- PAR ID:
- 10452972
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- International Journal of Quantum Chemistry
- Volume:
- 121
- Issue:
- 10
- ISSN:
- 0020-7608
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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