Dissipative Quantum Dynamics in 2D

Simulating non-Markovian quantum dissipative dynamics remains a major challenge in theoretical and computational chemistry. While traditional numerical methods such as hierarchical equations of motion are numerically exact, they suffer from prohibitive computational costs when modeling systems with complex environmental couplings or strong non-Markovian effects. To address this limitation, we propose a deep learning framework based on two-dimensional convolutional neural networks (2D-CNN) for efficiently predicting long-time quantum dissipative dynamics using only short-time trajectory data. Our approach incorporates a 1D-to-2D feature reconstruction strategy, which transforms 1D time-series data into 2D images, and a multi-timescale fusion network to resolve complex dynamical features. We validate the framework on two paradigmatic cases — dissipative relaxation in a two-level system and Rabi oscillations in a dissipative spin system — achieving prediction mean absolute errors of $10^{-3}$ and $10^{-2},$ respectively. The results highlight the effectiveness of our 2D-CNN approach in capturing long-time temporal correlations, providing a computationally efficient pathway for simulating quantum dynamics in realistic open systems.Simulating non-Markovian quantum dissipative dynamics remains a major challenge in theoretical and computational chemistry. While traditional numerical methods such as hierarchical equations of motion are numerically exact, they suffer from prohibitive computational costs when modeling systems with complex environmental couplings or strong non-Markovian effects. To address this limitation, we propose a deep learning framework based on two-dimensional convolutional neural networks (2D-CNN) for efficiently predicting long-time quantum dissipative dynamics using only short-time trajectory data. Our approach incorporates a 1D-to-2D feature reconstruction strategy, which transforms 1D time-series data into 2D images, and a multi-timescale fusion network to resolve complex dynamical features. We validate the framework on two paradigmatic cases — dissipative relaxation in a two-level system and Rabi oscillations in a dissipative spin system — achieving prediction mean absolute errors of $10^{-3}$ and $10^{-2},$ respectively. The results highlight the effectiveness of our 2D-CNN approach in capturing long-time temporal correlations, providing a computationally efficient pathway for simulating quantum dynamics in realistic open systems.

Communications in Computational ChemistryJun 1, 20250 citations

Incorporating Dissipation in Quantum Dynamics

Alberto Acevedo, Manuel Berrondo, Jean-François S. Van Huele

Bulletin of the American Physical SocietyOct 18, 20140 citations

Dissipative Dynamics of a Quantum System.

Lit-Deh Chang

Jan 1, 19850 citations

Dynamical properties of dissipative XYZ Heisenberg lattices

R. Rota, Fabrizio Minganti, Alberto Biella +1 more

We study dynamical properties of dissipative XYZ Heisenberg lattices where anisotropic spin-spin coupling competes with local incoherent spin flip processes. In particular, we explore a region of the parameter space where dissipative magnetic phase transitions for the steady state have been recently predicted by mean-field theories and exact numerical methods. We investigate the asymptotic decay rate towards the steady state both in 1D (up to the thermodynamical limit) and in finite-size 2D lattices, showing that critical dynamics does not occur in 1D, but it can emerge in 2D. We also analyze the behavior of individual homodyne quantum trajectories, which reveal the nature of the transition.We study dynamical properties of dissipative XYZ Heisenberg lattices where anisotropic spin-spin coupling competes with local incoherent spin flip processes. In particular, we explore a region of the parameter space where dissipative magnetic phase transitions for the steady state have been recently predicted by mean-field theories and exact numerical methods. We investigate the asymptotic decay rate towards the steady state both in 1D (up to the thermodynamical limit) and in finite-size 2D lattices, showing that critical dynamics does not occur in 1D, but it can emerge in 2D. We also analyze the behavior of individual homodyne quantum trajectories, which reveal the nature of the transition.

arXiv:1712.02716New Journal of PhysicsMar 15, 201849 citations

Quantum dynamics of a dissipative free particle

Claude Aslangul, No�lle Pottier, Daniel Saint-James

Physics Letters AAug 1, 19873 citations

Dynamical crossover of vortex-pair annihilation in two-dimensional quantum turbulence

Toshiaki Kanai, Chuanwei Zhang

Understanding the elementary mechanism for the dissipation of vortex energy in quantum liquids is one central issue in quantum hydrodynamics, such as quantum turbulence in systems ranging from neutron stars to atomic condensates. In a two-dimensional (2D) Bose-Einstein condensate (BEC) at zero temperature, in addition to the vortex drift-out process from the boundary, a vortex-antivortex pair can annihilate in bulk, but controversy remains on the number of vortices involved in the annihilation process. We find that a dynamic crossover exists from four-body to three-body vortex annihilation processes with time evolution in decaying 2D quantum turbulence of a boundary-less uniform quasi-2D BEC. Such a dynamical crossover depends on the initial vortex pair density and occurs when the sound waves generated in the vortex annihilation process surpass a threshold energy. As the confinement along the third direction is relaxed in a quasi-2D BEC, the threshold sound wave energy decreases due to the three-dimensional (3D) vortex line curve and reconnection, shifting the dynamical crossover to the early time. Our work reveals an elementary mechanism for the dissipation of vortex energy that may help understand exotic matter and dynamics in quantum liquids.Understanding the elementary mechanism for the dissipation of vortex energy in quantum liquids is one central issue in quantum hydrodynamics, such as quantum turbulence in systems ranging from neutron stars to atomic condensates. In a two-dimensional (2D) Bose-Einstein condensate (BEC) at zero temperature, in addition to the vortex drift-out process from the boundary, a vortex-antivortex pair can annihilate in bulk, but controversy remains on the number of vortices involved in the annihilation process. We find that a dynamic crossover exists from four-body to three-body vortex annihilation processes with time evolution in decaying 2D quantum turbulence of a boundary-less uniform quasi-2D BEC. Such a dynamical crossover depends on the initial vortex pair density and occurs when the sound waves generated in the vortex annihilation process surpass a threshold energy. As the confinement along the third direction is relaxed in a quasi-2D BEC, the threshold sound wave energy decreases due to the three-dimensional (3D) vortex line curve and reconnection, shifting the dynamical crossover to the early time. Our work reveals an elementary mechanism for the dissipation of vortex energy that may help understand exotic matter and dynamics in quantum liquids.

Physical Review AAug 11, 20252 citations

10^{-3}

and

10^{-2},

respectively. The results highlight the effectiveness of our 2D-CNN approach in capturing long-time temporal correlations, providing a computationally efficient pathway for simulating quantum dynamics in realistic open systems.