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Flow-Induced Non-Hermitian Sensing and Fundamental Capacity Budget

This paper introduces a scalable, flow-induced non-Hermitian sensing scheme in a liquid-metal thermal lattice that utilizes advective flow as a tunable synthetic imaginary gauge field to achieve highly sensitive boundary coupling detection while revealing an intrinsic trade-off between sensitivity and dynamic range.

Original authors: Ying Li, Qiang-Kai-Lai Huang, Yanxiang Wang, Pei-Chao Cao, Yuhan Zhong, Ran Ju, Dong Wang, Xiaochang Xing, Yifan Shou, Hanqi Chen, Wenduo Yu, Haoran Yan, Lianjie Li, Run Hu, Yihao Yang, Fei Gao, Rui X

Published 2026-08-19

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Ying Li, Qiang-Kai-Lai Huang, Yanxiang Wang, Pei-Chao Cao, Yuhan Zhong, Ran Ju, Dong Wang, Xiaochang Xing, Yifan Shou, Hanqi Chen, Wenduo Yu, Haoran Yan, Lianjie Li, Run Hu, Yihao Yang, Fei Gao, Rui Xi, Cheng-Wei Qiu, Hongsheng Chen

Original paper licensed under CC BY 4.0 (https://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

In the physical world, most things behave predictably when you push or pull them. If you push a swing, it moves forward; if you push it from the other side, it moves back. This symmetry is a fundamental rule for many systems, from sound waves to electrical circuits. However, there is a special class of systems where this balance is broken. In these "non-Hermitian" systems, the rules of interaction are not equal in both directions. Imagine a hallway where you can walk easily from left to right, but the path from right to left is blocked or much harder to traverse. This one-way flow creates unique behaviors, such as waves that pile up at one end of a system rather than spreading out evenly. Scientists have long been fascinated by these systems because they can be incredibly sensitive to tiny changes at their edges, making them potential candidates for ultra-precise sensors. The challenge has been building these systems. Traditionally, researchers have had to construct them using complex, bulky electronic parts that act as one-way valves, which makes the systems hard to scale up or adjust.

A team of researchers has now found a way to create these one-way effects using something much simpler and more fluid: liquid metal flowing through a series of tiny channels. Instead of using heavy electronic components, they built a lattice of small metal cavities connected by pipes. Inside these pipes, a liquid metal alloy flows from one end to the other. This flow acts as a continuous, tunable force that breaks the symmetry of the system, effectively creating the one-way behavior without needing complex electronics. By heating the metal cavities and watching how the heat travels through the flowing liquid, the researchers could observe how the system responds to changes at its boundaries. They discovered that this setup creates a phenomenon where heat waves become trapped and amplified at the very end of the chain, a behavior known as the non-Hermitian skin effect. This trapping makes the system exquisitely sensitive to anything that touches the ends of the chain.

The researchers used this setup to test how well they could detect a target object placed at the boundary of the system. They introduced thin sheets of titanium of varying thicknesses to act as the target, which changed how heat could escape or enter the system. As they increased the thickness of the titanium, they measured how much the system's natural rhythm, or frequency, shifted. They found that the system could detect these tiny changes with incredible precision. The more they increased the flow speed of the liquid metal or added more sections to the chain, the more sensitive the system became. In fact, they were able to tune the sensitivity of their sensor by a factor of twenty simply by adjusting the flow and the size of the setup. This level of control allows the system to detect extremely faint signals that would be invisible to traditional sensors.

However, the researchers also uncovered a fundamental limit to this power. While increasing the sensitivity made the system better at detecting weak signals, it also made the system much more fragile. There is a strict trade-off: the more sensitive the sensor becomes, the smaller the range of signals it can handle before it breaks down or becomes confused. They described this as a "capacity budget." If you tune the system to be hyper-sensitive to a whisper, it will be unable to hear a shout without distorting the sound. Specifically, they found that as the sensitivity grew exponentially, the maximum signal the system could measure shrank exponentially. This means that for any given task, engineers must carefully balance the need for extreme sensitivity against the need to measure a wide range of values. You cannot have both at the same time; you must choose the setting that fits the job.

To prove this concept, the team built a physical model using molybdenum cavities and photosensitive resin pipes, connecting them with a liquid metal alloy made of gallium, indium, and tin. They heated the cavities using small electronic elements and used an infrared camera to watch the temperature change over time. By analyzing the temperature data, they could reconstruct the system's internal behavior and see how it reacted to the titanium sheets. Their experiments confirmed that the system worked exactly as their theory predicted. They observed that the system could be reconfigured on demand; by changing the number of cavities or the speed of the liquid flow, they could shift the sensor's performance to suit different needs. For example, they could set it up to detect very weak thermal connections with high precision, or adjust it to measure stronger connections over a wider range.

This work represents a significant step forward in how we build sensors. By replacing rigid, hardware-heavy components with a flowing fluid, the researchers have created a system that is both adaptable and efficient. The ability to tune the non-reciprocal behavior simply by changing the flow rate offers a new way to explore the physics of open systems. It suggests that in the future, we might see sensors made from flowing liquids that can be reprogrammed for different tasks without changing a single wire. The discovery of the capacity budget also provides a clear guide for engineers: it tells them exactly how much sensitivity they can gain before they sacrifice the ability to measure larger signals. This clarity helps in designing better tools for thermal management and detection, moving beyond the limitations of traditional, fixed designs. The study confirms that while the laws of physics impose limits, understanding those limits allows us to build smarter, more flexible systems that work with the flow of energy rather than fighting against it.

Technical Summary: Flow-Induced Non-Hermitian Sensing and Fundamental Capacity Budget

Problem Statement
Non-Hermitian physics offers a framework for controlling open systems, enabling phenomena such as exceptional points (EPs) and the non-Hermitian skin effect (NHSE) for high-sensitivity sensing. However, existing implementations of non-reciprocal coupling—the central route to these phenomena—rely heavily on hardware-intensive, discrete active components (e.g., amplifiers or external processors). This component-level architecture results in spatially discrete and localized non-reciprocity, which constrains scalable integration and complicates the systematic tuning of parameters (such as non-reciprocal strength and system size) required to explore dynamic non-Hermitian responses. There is a need for a platform that achieves spatially continuous, tunable non-reciprocity without discrete active elements to facilitate the exploration of non-Hermitian dynamics in diffusive media.

Methodology
The authors propose and experimentally realize a reconfigurable liquid-metal thermal lattice that utilizes advective flow to generate a synthetic imaginary gauge field. The methodology involves three primary components:

Physical Platform: A modular thermal lattice consisting of $N$ identical unit cells (cavities) connected by liquid-metal minichannels. Advective flow through these channels acts as a spatially continuous, tunable synthetic imaginary gauge field ( $\mathcal{A}$ ), creating distributed non-reciprocity without discrete active components. The system is reconfigurable, allowing for on-demand adjustment of the lattice size ( $N$ ) and flow rate (non-reciprocal strength).
Compact Thermal-Circuit Modeling: To analyze the continuum thermo-hydrodynamics, the authors developed a compact thermal-circuit method. This approach maps the continuum system onto a discrete non-Hermitian tight-binding Hamiltonian. By approximating effective thermophysical parameters via thermal circuits and applying the first law of thermodynamics, they derived a nodal Kirchhoff equation featuring a surrogate coupling diode. This model quantitatively captures the non-reciprocal coupling strengths ( $h_+$ and $h_-$ ), which scale exponentially with the flow velocity.
Sensing Protocol and Data Processing: The sensing scheme exploits the boundary sensitivity associated with the NHSE. A target boundary coupling ( $\tau$ ) is introduced (simulated by titanium sheets of varying thickness), and the system's response is measured via the frequency shift of the $N/2$ -th eigenmode. The experimental setup uses thermoelectric elements to sequentially excite cavities and infrared thermography to record transient temperature trajectories. A data-processing pipeline employing Locally Weighted Scatterplot Smoothing (LOWESS) is used to reconstruct the eigenvalue spectrum from noisy experimental data, ensuring robustness against fluctuations.

Key Contributions

Flow-Induced Non-Hermitian Sensing: The establishment of a sensing scheme where advective flow generates a tunable synthetic imaginary gauge field, enabling distributed non-reciprocity in a thermal system.
Compact Modeling of Continuum Systems: The development of a method to map continuum thermo-hydrodynamics onto a discrete non-Hermitian Hamiltonian, validating the thermal NHSE through analytical and finite-element comparisons.
Universal Dual Scaling Law: The discovery and experimental validation of a fundamental trade-off in NHSE-based boundary-coupling sensing. The authors demonstrate that the exponential enhancement of sensitivity ( $S$ ) is intrinsically linked to an exponential reduction in the dynamic range ( $\tilde{\tau}_{max}$ ).
Fundamental Capacity Budget: The derivation of a "capacity budget" equation ( $S \times \tilde{\tau}_{max} \approx \text{constant}$ ), which defines an intrinsic limit for non-Hermitian boundary-coupling sensing. This budget indicates that gains in sensitivity are necessarily penalized by a commensurate loss in dynamic range.
Reconfigurable Platform: An experimental demonstration of a modular platform capable of navigating this trade-off by tuning both the lattice size ( $N$ ) and the flow rate ( $v$ ).

Results

Spectral Validation: Analytical open boundary condition (OBC) spectra derived from the compact model showed strong agreement with finite-element simulations. The system exhibited the characteristic spatial localization of eigenstates toward the final cavity, confirming the flow-induced NHSE.
Sensitivity and Dynamic Range: The system demonstrated a 20-fold tunable range in sensitivity (from 0.14 to 2.77) and a more than fourfold change in dynamic range (0.3 to over 1.2 mrad s $^{-1}$ ) by varying $N$ and $v$ .
Scaling Law Verification: Experimental data confirmed the dual scaling law. High-sensitivity configurations (large $N$ , high $v$ ) exhibited rapid spectral coalescence (degeneracy), limiting their dynamic range. Conversely, lower-sensitivity configurations maintained an extended dynamic range.
Robustness: The study mapped the $\epsilon$ -pseudospectra, showing that configurations with lower amplification gain possessed higher tolerance to external noise, further supporting the necessity of task-specific parameter selection.
Generalizability: The dual scaling law was validated not only in the thermal lattice but also theoretically in a non-Hermitian Su–Schrieffer–Heeger (SSH) lattice, suggesting the capacity budget is a universal feature of NHSE-based boundary-coupling sensing.

Significance and Claims
The paper claims to expand thermal non-Hermitian physics from the observation of intrinsic diffusive dynamics to the active response to external perturbations. By linking advective heat transport with non-Hermitian spectral theory, the work establishes a streamlined paradigm for breaking reciprocity that avoids the structural rigidity of discrete active components.

The authors emphasize that their findings provide a "system-level route" for thermal coupling detection, offering an alternative to traditional local heating and probing methods that often lack systematic architectural frameworks. Crucially, the paper posits that the identified "capacity budget" is a fundamental constraint: any strategy seeking to amplify sensitivity via NHSE must accept a corresponding reduction in dynamic range. Therefore, the significance of the work lies not only in demonstrating high sensitivity but in providing a reconfigurable framework that allows researchers to systematically optimize the balance between sensitivity and dynamic range for specific sensing tasks. The platform serves as a testbed for studying continuous non-reciprocity in systems where discrete active modulation is difficult to implement, potentially enabling adaptive thermal devices and heat-management strategies with tunable spectral responses.

Technical Summary: Flow-Induced Non-Hermitian Sensing and Fundamental Capacity Budget

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