Quantum Tunnelling Velocity Dynamics Advance Understanding of Fundamental Processes

Quantum tunnelling, the ability of particles to penetrate barriers they classically shouldn’t, governs processes from nuclear fusion to photosynthesis, yet the precise way particles move during this phenomenon remains a mystery. Xiao-Wen Shang, Jian-Peng Dou, and colleagues at Shanghai Jiao Tong University, along with Sen Lin from Jiangsu Normal University, now reveal a surprising dynamic, demonstrating that a tunnelling particle’s velocity continuously decreases as it traverses a barrier, potentially even approaching zero. This research challenges existing interpretations of particle behaviour within barriers, showing that the probability distribution builds gradually, unlike previously held assumptions, and establishes a clear relationship between particle velocity and barrier width. By defining velocity based on particle motion rather than current, the team resolves a long-standing paradox of vanishing velocity alongside finite particle density, offering a robust theoretical framework for future experiments probing the dynamics of quantum tunnelling.

Velocity Calculation Within Potential Barriers

This research details a comprehensive methodology for simulating particle behaviour within potential barriers, focusing specifically on calculating particle velocity inside these barriers. The study addresses a common oversight in standard quantum mechanics, which often concentrates on particle behaviour at the boundaries of barriers rather than within them. Scientists demonstrate that even when a particle’s energy is less than the barrier height, its velocity is not necessarily zero, due to the oscillatory and exponential components of its wave function. The investigation combines theoretical calculations, solving the time-independent Schrödinger equation for various energy levels, with numerical simulations using the Split-Step Fourier Method to model wave function propagation in time and space.

Researchers systematically varied barrier height, width, and initial conditions to observe their influence on the velocity profile. The core of the research lies in deriving particle velocity from the spatial derivative of the wave function’s phase. The velocity calculation is heavily dependent on the relationship between the particle’s energy and the barrier height, with oscillatory solutions emerging when energy is less than the barrier height. The study emphasizes the importance of considering barrier width, noting that semi-infinite or finite barriers with absorbing boundaries simplify calculations by eliminating reflections.

The results demonstrate that particles maintain a non-zero velocity within potential barriers, even when their energy is insufficient to overcome the barrier classically, challenging the intuitive notion that barriers halt particle motion. The velocity profile varies depending on particle energy, barrier height, and width, highlighting the complex interplay of these factors. This work presents a rigorous analysis of particle velocity within potential barriers, combining theoretical and computational approaches to advance our understanding of this fundamental quantum phenomenon.

Tunnelling Particle Velocity Relaxation Dynamics Revealed

Scientists have gained detailed insights into the dynamics of quantum tunnelling, analyzing the temporal evolution of tunnelling itself. The research pioneers a method for examining particle motion within a barrier, revealing that particle velocity continuously relaxes as it tunnels, decreasing from an initial value and potentially approaching zero under certain conditions. This work directly addresses a long-standing debate concerning the interpretation of particle velocity during tunnelling, challenging existing assumptions about its behaviour. Researchers employed the time-dependent Schrödinger equation to model the tunnelling process, allowing them to extract the time-dependent velocity and probability density within the barrier.

The team simulated a one-dimensional tunnelling event using a carefully constructed wave function pulse, characterized by a specific width and duration, and directed it towards a potential barrier. By systematically varying the particle’s energy relative to the barrier height, they simulated three distinct energy regimes. Solving the time-dependent Schrödinger equation yielded the wave function, enabling the determination of the Bohmian velocity, a key parameter for understanding particle motion. Pseudocolour images were generated to visualize the probability distribution within the barrier at a specific time, providing a clear representation of the tunnelling process.

The team focused on the moment when the midpoint of the pulse reached the barrier’s edge, providing a snapshot of the particle’s state. For energies exceeding the barrier height, the wave packet maintained forward propagation, penetrating deeply into the potential wall. This detailed analysis establishes a clear dynamical picture for the formation of tunnelling flow and provides a theoretical foundation for testing time-resolved tunnelling phenomena.

Velocity Relaxation During Quantum Tunneling

Scientists have achieved a detailed understanding of particle motion during quantum tunnelling, revealing a surprising relaxation of velocity within the potential barrier. The research demonstrates that a particle’s velocity continuously decreases as it tunnels through a classically forbidden region, potentially approaching zero in certain conditions. This finding resolves a long-standing paradox concerning the coexistence of a vanishing velocity and a finite particle density within the barrier. The team simulated the tunnelling process using the time-dependent Schrödinger equation, allowing them to extract the velocity and probability density of particles inside the barrier.

Experiments revealed that when the particle’s energy exceeds the barrier height, the wave packet maintains forward propagation, penetrating deep into the potential wall, with the velocity decreasing from approximately 5000km/s to around 2000km/s. When the particle’s energy equals the barrier height, the probability density decays within the barrier, and velocities decrease to below 250km/s. Further analysis, with the particle’s energy below the barrier height, showed the velocity approaching zero within the barrier during the pulse plateau phase, exhibiting a distinct transition over time. This indicates the tunnelling process can be divided into distinct phases: entry, stationary, and exit.

Introducing a finite particle lifetime stabilized the velocity within the barrier, demonstrating the influence of dissipation on the tunnelling dynamics. These findings establish a clear dynamical picture for the formation of tunnelling flow and provide a theoretical foundation for testing time-resolved tunnelling phenomena. The research highlights that a zero velocity can emerge within the potential barrier, a counterintuitive result that challenges conventional understanding of particle behaviour during tunnelling.

Time-Dependent Velocity During Quantum Tunnelling

This research establishes a clear dynamical picture of quantum tunnelling, resolving long-standing questions about particle behaviour within potential barriers. Scientists investigated the evolution of particle velocity during tunnelling, demonstrating that it continuously decreases as the particle enters the barrier, potentially approaching zero in certain conditions. This finding challenges conventional understandings of particle motion and clarifies the apparent paradox of a finite particle density coexisting with a vanishing velocity. The team’s analysis reveals that the velocity reduction occurs as the probability density builds up within the barrier, contrasting with previous steady-state descriptions of the process.

By examining the time-dependent wave function, they derived a relationship between particle velocity and barrier width, confirming the velocity approaches zero for sufficiently wide barriers. This work distinguishes between different methods of defining particle velocity, highlighting the importance of using the Bohmian velocity derived from the wave function, rather than inferences from probability densities. They suggest that future research could focus on experimentally verifying these dynamical predictions using time-resolved measurements of tunnelling phenomena, providing a crucial test of this theoretical framework and deepening our understanding of this fundamental quantum process.