Related Experiment Video
Updated: Jun 18, 2026
06:44
Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
Published on: September 23, 2025
Delocalization and spreading in a nonlinear Stark ladder.
Dmitry O Krimer1, Ramaz Khomeriki, Sergej Flach
1Max-Planck Institute for the Physics of Complex Systems, Nöthnitzer Str 38, 01187 Dresden, Germany.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2009
Summary
Nonlinearity disrupts wave packet localization in Stark ladders, leading to transient trapping or immediate subdiffusion. Dynamics depend on nonlinearity strength and dc bias, impacting short and long-term behavior.
Area of Science:
- Condensed matter physics
- Quantum dynamics
- Nonlinear systems
Background:
- In nonlinear Stark ladders, normal modes are typically localized, resulting in an equidistant eigenvalue spectrum and Bloch oscillations.
- Nonlinearity introduces frequency shifts and mode-mode interactions, disrupting this localization.
Purpose of the Study:
- To investigate the impact of nonlinearity on wave packet evolution in a Stark ladder.
- To characterize the dynamics across different nonlinearity strengths and dc bias variations.
Main Methods:
- Numerical simulation of wave packet propagation in a nonlinear Stark ladder model.
- Analysis of localization, spreading, and oscillatory behaviors under varying nonlinear parameters.
Main Results:
- For strong nonlinearity: transient single-site trapping followed by explosive spreading and subdiffusion.
- For moderate nonlinearity: immediate subdiffusion.
- For weak nonlinearity: transient linear Stark localization followed by subdiffusion.
- Stability intervals observed for single-mode excitations with weak nonlinearity, dependent on dc bias.
Conclusions:
- Nonlinearity fundamentally alters wave packet dynamics in Stark ladders, transitioning from localized Bloch oscillations to various forms of delocalization.
- The observed dynamics are highly sensitive to the strength of nonlinearity and external dc bias, offering tunable control over quantum transport.
Related Concept Videos
01:26Linear Approximation in Frequency Domain
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
01:12Bewley Lattice Diagram
The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.
01:07Ladder Diagrams: Complexation Equilibria
Ladder diagrams are useful for evaluating equilibria involving metal-ligand complexes. The vertical scale of the ladder diagram represents the concentration of unreacted or free ligand, pL. The horizontal lines on the scale depict the log of stepwise formation constants for metal-ligand complexes and indicate the dominant species in all the regions.
The formation constant, K1, for the formation of Cd(NH3)2+ complex from cadmium and ammonia is 3.55 × 102. Log K1 (i.e. pNH3) is 2.55, and...
The formation constant, K1, for the formation of Cd(NH3)2+ complex from cadmium and ammonia is 3.55 × 102. Log K1 (i.e. pNH3) is 2.55, and...
01:25Deactivation Processes: Jablonski Diagram
Luminescence, the emission of light by a substance that has absorbed energy, is a process that involves the interaction of molecules with light. The energy-level diagram, or Jablonski diagram, is a graphical representation of these interactions, illustrating the various states and transitions a molecule can undergo. In a typical Jablonski diagram, the lowest horizontal line represents the ground-state energy of the molecule, which is usually a singlet state. This state represents the energies...
01:02¹H NMR: Interpreting Distorted and Overlapping Signals
Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...
01:21Linear Approximation in Time Domain
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...