Quantum Trajectories in Nonlinear Dynamics
Summary
The study of quantum trajectories in nonlinear dynamics marries the deterministic picture of particle paths with the intrinsically probabilistic nature of quantum mechanics. Rooted in trajectory-based formulations such as Bohmian mechanics and Madelung hydrodynamics, this approach recasts the wave function into real-valued action and probability fields, generating trajectories via a quantum force derived from the quantum potential. Extending these ideas to nonlinear or dissipative systems permits a unified description of decoherence, localisation and the quantum–classical transition. In such systems, nonlinear modifications to the Schrödinger equation incorporate environmental interactions or effective self-interactions, leading to phenomena like dissipative scattering, tunnelling with feedback, and complex hydrodynamic flow in both position and momentum representations. By analysing the evolution of wave packets, scaled trajectories reveal how coherence fades into classical-like motion, while trajectory-based dwell times quantify temporal aspects of scattering processes. Practical applications span molecular tunnelling, spin-resolved transport, surface diffusion and quantum control, offering new insights into quantum measurement, decoherence mitigation and nanoscale device design. Globally, this paradigm provides an intuitive and computationally efficient framework for exploring quantum phenomena in complex environments, bridging fundamental theory with technological innovation.
Research from Nature Portfolio
No recent Nature Portfolio content available.
Quantum Trajectories in Nonlinear Dynamics publication trend
The graph below shows the total number of articles in quantum trajectories in nonlinear dynamics across all publications each year (not limited to Nature Index journals).
Technical terms
Quantum trajectory: A path determined by solving real-valued equations of motion derived from the wave function’s phase and amplitude.
Bohmian mechanics: A formulation of quantum theory in which particles follow deterministic trajectories guided by a quantum potential.
Quantum potential: A nonclassical term arising from the wave function that drives deviations from classical motion.
Decoherence: The loss of quantum coherence due to interaction with an environment or through nonlinear self-interaction.
Dwell time: The time a quantum particle spends in a specified region, computed via trajectory ensembles.
Dissipative system: A system in which energy is exchanged with an environment, often modelled by nonlinear Schrödinger equations.
Madelung representation: A hydrodynamic form of quantum mechanics expressing the wave function in terms of fluid density and velocity fields.
References
- Tunneling Quantum Dynamics in Ammonia. International Journal of Molecular Sciences (2021).
- Quantum-classical transition in dissipative systems through scaled trajectories. Journal of Physics Communications (2018).
- Quantum surface diffusion in Bohmian mechanics. Journal of Physics Communications (2018).
- Complex Quantum Hydrodynamics in Momentum Space with Broken Time-Reversal Symmetry. Symmetry (2023).
- Dwell Times, Wavepacket Dynamics, and Quantum Trajectories for Particles with Spin 1/2. Entropy (2024).
About these summaries
This Nature Research Intelligence Topic summary is created with the cited references and a large language model. We take care to ground generated text with facts, and have systems in place to gain human feedback on the overall quality of the process in line with our AI principles. We strive to create accurate and useful summaries for people unfamiliar with the research topic and that supports this goal. These pages are a beta release and will be updated as we learn how best to help people gain value from a research topic summary.
Turn complex research questions into confident strategic decisions
When you're under pressure to set direction, justify investment, or understand your competitive position, you need more than raw data — you need trusted insights you can act on.
Benchmark your performance against global peers using robust, methodologically sound analysis.
Combine quantitative metrics with qualitative expert insight to uncover strengths, gaps and emerging opportunities.
Gain tailored, decision-ready recommendations aligned to your strategic priorities.
Talk to us to learn more about our data dashboards and bespoke strategy reports.
Grow research skills, confidence and careers with training built for every stage of the research lifecycle.
Developed with Nature Portfolio journal Editors and internationally renowned experts. Discover three ways to learn:
Self-paced, online courses in convenient bite-sized units, covering key skills across scientific writing, publishing, grant writing, data analysis, and more.
Expert trainer-led workshops with hands-on exercises and real-time feedback across core research skills, delivered via interactive group sessions.
Editor-led workshops combining core principles in writing and publishing, personalised 1:1 feedback from Nature Portfolio Editors and hands-on exercises.
Explore course catalogues and workshop agendas, enquire about the options or request institutional pricing.