🔬 applied physics

Non-Hermitian fluctuations enable model-free particle manipulation

This paper demonstrates a model-free approach to deterministic particle manipulation in complex, dynamic environments by exploiting non-Hermitian energy dissipation and conductance matrix variations to automatically shape electromagnetic forces without requiring prior calibration of field distributions or particle properties.

Original authors: Siarhei Zavatski, Tristan Nerson, Romain Fleury, Olivier J. F. Martin

Published 2026-06-01

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CC BY 4.0

Original authors: Siarhei Zavatski, Tristan Nerson, Romain Fleury, Olivier J. F. Martin

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to move a tiny marble through a thick, murky soup using invisible hands made of electricity. Usually, to do this, you need a perfect map of the soup, a crystal-clear understanding of the marble's weight and texture, and a complex computer model to tell you exactly how to wiggle your invisible hands. If the soup changes slightly or the marble is a bit different than expected, your plan fails, and the marble gets stuck or goes the wrong way.

This paper introduces a clever new trick called Dissipation-Guided Electromagnetic Manipulation (DGEM). Instead of needing a perfect map or a detailed model of the marble, this method uses the "messiness" of the soup itself to guide the particle.

Here is how it works, broken down with simple analogies:

1. The Problem: The "Perfect Map" Trap

Traditional methods are like trying to drive a car in a foggy city using only a printed map. If the road is slightly different than the map says (maybe a new pothole or a detour), you crash. In the lab, scientists usually have to know the exact electrical properties of the particle and the liquid beforehand. If the liquid is "lossy" (meaning it absorbs energy, like a sponge soaking up water), traditional math breaks down.

2. The Solution: Listening to the "Static"

The researchers realized that instead of fighting the energy loss (the "static" or "friction" in the system), they could use it as a guide.

Think of the liquid and the particle as a giant, complex musical instrument. When you pluck a string (apply an electrical signal), the sound you hear depends on where your finger is touching the string.

Old way: You try to calculate exactly how the string should vibrate based on a theory of how strings work.
New way (DGEM): You just listen to the sound the string makes right now. If the sound changes slightly when the particle moves, that change tells you exactly where the particle is and how to push it next.

3. The "Conductance Matrix": The System's Fingerprint

The team uses a grid of tiny metal electrodes (like a keyboard with 20 keys) sitting under the liquid.

The Test: They tap the keys in a random pattern and measure how much electricity flows through the liquid. This creates a "conductance matrix"—a giant spreadsheet of numbers that acts like a fingerprint of the system at that exact moment.
The Shift: When the particle moves, it disturbs the flow of electricity, changing the fingerprint slightly.
The Magic Math: The researchers use a special mathematical tool (called a "Variational Conductance Operator") to look at how the fingerprint changed. This tool instantly solves a puzzle: "If I want to push the particle to the right, what pattern of keys should I press?"

It's like having a magic remote control that doesn't need to know what TV you are watching. You just press a button, the TV tells you what channel it's on, and the remote instantly figures out the exact sequence of buttons to change the channel to the one you want.

4. The Results: Moving Particles in the Chaos

The team tested this with tiny glass beads (20 micrometers wide) in a liquid.

One Direction: They successfully moved a bead back and forth in a straight line, even though the liquid was "lossy" and messy.
Two Directions: They moved beads in a 2D grid, steering them around corners.
The Crowd: The most impressive feat was moving one specific bead through a crowd of other moving beads. The system didn't need to track the other beads or know their shapes. It just focused on the "fingerprint" of the target bead and pushed it along, ignoring the chaos around it.

The Big Picture

The paper claims that by deliberately measuring how energy is lost (dissipated) in the system, they can create a "model-free" way to control particles. They don't need to know the particle's size, shape, or material properties in advance. They just need to measure the electrical response, do a quick calculation, and apply the right voltage pattern.

In short: Instead of trying to predict the future with a perfect model, this method listens to the system's current reality and uses that information to steer particles with high precision, even in messy, unpredictable environments.

Technical Summary: Non-Hermitian Fluctuations Enable Model-Free Particle Manipulation

Problem Statement
Contactless manipulation of microscopic matter is essential for applications ranging from circulating tumor cell isolation to microplastic removal. While electromagnetic approaches (e.g., dielectrophoresis, optical tweezers) offer versatility, they are fundamentally constrained by the need for explicit, calibrated models of the particle-field interaction. Current methods rely on either real-time numerical simulations or pre-programmed actuation signals based on prior knowledge of system parameters (such as the Clausius–Mossotti factor). This reliance limits applicability to well-characterized, static systems; even minor fluctuations in particle properties or the surrounding medium can lead to significant manipulation errors. Furthermore, existing "model-free" wavefront shaping techniques, which retrieve system information from scattering matrices, have historically been restricted to lossless (Hermitian) systems. Real-world microfluidic environments, however, are inherently dissipative due to ionic solutions and lossy media, violating the lossless assumption and rendering standard wavefront shaping ineffective for particle control.

Methodology
The authors introduce Dissipation-Guided Electromagnetic Manipulation (DGEM), a framework that extends wavefront shaping principles to quasistatic, dissipative systems. The core innovation is the utilization of non-Hermitian fluctuations—specifically, energy dissipation—as a source of information for deterministic control, rather than treating it as a hindrance.

The methodology operates through a closed-loop, four-step process:

Initialization: A target particle is displaced using a random actuation signal to establish a new equilibrium.
Response Measurement: The system measures the conductance matrix ( $G$ ) at the electrode boundaries. This matrix encodes the power dissipation of the system.
Operator Calculation: By measuring $G$ at multiple particle positions and computing spatial derivatives ( $\partial_x G, \partial_y G$ ), the authors construct a Variational Conductance (VC) operator ( $R_{\hat{e}_r}$ ). This operator is derived from a theoretical identity linking mechanical work to variations in the conductance matrix in lossy media.
Actuation: The VC operator is diagonalized. The eigenvector corresponding to the maximum or minimum eigenvalue provides the optimal voltage pattern to apply to the electrodes to generate a dielectrophoretic (DEP) force in a desired direction.

Theoretical derivation shows that in the low-frequency, conduction-dominated regime, the mechanical force can be retrieved exactly from the conductance matrix variations without prior knowledge of the particle's geometry or dielectric properties. This is achieved by mapping the physical lossy conduction problem onto an auxiliary lossless dielectric problem, where the susceptance of the auxiliary system matches the conductance of the physical system.

Key Contributions

Theoretical Framework: The paper establishes a port-based force identity for lossy, inhomogeneous media, demonstrating that mechanical information is encoded in the dissipative (conductance) response rather than the reactive (susceptance) response. This resolves the limitation of previous wavefront shaping methods that assumed lossless systems.
Model-Free Control: The DGEM approach eliminates the need for explicit models of the particle or the medium. It relies solely on measured electrical signals (conductance variations) and particle position feedback.
Experimental Demonstration: The authors validated DGEM using a microfluidic chip with 20 individually addressable planar metal electrodes. They successfully manipulated 20 µm silica microbeads in both one and two dimensions.
Robustness in Complex Environments: The system demonstrated the ability to steer a target particle through a disordered background of freely moving 5 µm particles. Remarkably, the control remained effective even as the target particle's effective shape changed due to the attachment of smaller beads, a scenario where traditional model-based algorithms would fail due to the lack of precise geometric knowledge.

Results

One-Dimensional Manipulation: A single 20 µm silica bead was translated approximately 300 µm over 40 seconds (approx. 7.5 µm/s) in a closed-loop manner. The system successfully identified the correct voltage patterns to move the particle against, with, or perpendicular to the field gradient.
Two-Dimensional and Complex Steering: The method enabled arbitrary 2D translation and routing of particles through T-junctions.
Disordered Backgrounds: In the presence of a dense population of uncontrolled particles, the target particle faithfully followed prescribed trajectories. The algorithm did not require tracking the background particles, relying instead on the aggregate change in the conductance matrix caused by the target's position.
Force Retrieval Accuracy: Numerical simulations confirmed that the force predicted by the VC operator using the conductance matrix ( $G$ ) quantitatively agreed with forces calculated via the Minkowski stress tensor. In contrast, methods relying on the susceptance matrix ( $B$ ) showed significant deviations in the lossy, low-frequency regime relevant to the experiments.

Significance
The paper claims to provide the first demonstration of model-free particle micromanipulation in dissipative media using extended electromagnetic wavefront shaping principles. By deliberately measuring and exploiting the non-Hermitian response of the system, DGEM establishes a pathway toward deterministic force control in realistic, dynamically evolving environments where wave-matter interactions cannot be fully pre-characterized.

The authors assert that this framework expands the scope of micromanipulation beyond well-defined laboratory settings to complex, real-world applications such as point-of-care diagnostics, single-cell biology, and the handling of heterogeneous mixtures (e.g., cells, extracellular vesicles, and microdroplets) without the need for system-specific tuning or prior calibration. The method is presented as a generalizable approach that could potentially extend to the nanoscale and label-free characterization of particle electromechanical properties.

1. The Problem: The "Perfect Map" Trap

2. The Solution: Listening to the "Static"

3. The "Conductance Matrix": The System's Fingerprint

4. The Results: Moving Particles in the Chaos

The Big Picture

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