How soliton changes time, space, and rules

If it walks like a particle and talks like a particle… then it might not be a particle. A topological soliton is a special type of wave or decay that behaves like a particle: it can move but cannot expand and disappear as expected, for example, from a ripple to the surface of a pond. In a new study published in natureResearchers from the University of Amsterdam demonstrate the unusual behavior of topological isolations in a robotic metamaterial, which could be used in the future to control how robots move, sense their environment and communicate.

Topological solitons can be found in many places and on many different length scales. For example, they take the form of folds in coiled telephone wires and large molecules such as proteins. On a completely different scale, A Black hole It can be understood as a topological soliton in the space-time structure. Solitons play an important role in biological systems, being important for protein folding and conformation – the development of cells or organs.

The unique properties of topological solitons—that they can move but always maintain their shape and cannot suddenly disappear—are particularly interesting when combined with so-called nonreciprocal interactions. “In such an interaction, factor A interacts with factor B differently from how factor B interacts with factor A,” explains Jonas Veenstra, a doctoral student at the University of Amsterdam and first author of the new publication.

“Non-reciprocal interactions are common in society and complex living systems, but have long been neglected by most physicists because they can only exist in a nonequilibrium system,” Veenstra continues. By introducing non-reciprocal interactions into materials, we hope to blur the line between materials and machines and create animated or realistic materials.

The Automated Materials Laboratory where Veenstra conducts his research specializes in design metamaterials: Artificial materials and robotic systems that interact with their environment in a programmable manner. The research team decided to study the interplay between non-reciprocal interactions and topological isolations almost two years ago, when students Anheta Sarvi and Kris Ventura Minnersen decided to continue their research project as part of the master's course “Academic Skills for Research”.

The metasomatite containing the soliton and anti-soliton lies on the boundary between the left and right oblique series sections. Each blue rod is connected to its neighbors by pink rubber bands, and there is a small motor under each rod that makes interactions between adjacent rods non-reciprocal. Credit: Jonas Feenstra/UVA

Solitons move like dominoes

The soliton host metamaterial developed by the researchers consists of a series of rotating rods linked together by flexible bands – see figure below. Each rod is mounted on a small motor that applies a small force to the rod, depending on its orientation relative to its neighbors. It is important to note that the applied force depends on the side of the neighbour, making the interactions between adjacent bars non-reciprocal. Finally, the magnets on the bars are attracted to magnets placed next to the chain so that each bar has two preferred positions, facing either left or right.

The isolates in this metamaterial are where the left and right parts of the chain meet. Complementary boundaries between right- and left-facing string segments are called anti-solitons. This is similar to the bends of old coiled telephone wire, where the rotating sections of wire meet clockwise and counterclockwise.

When the series drives are turned off, the solitons and anti-isolators can be manually driven in any direction. However, once the motors – and thus the mutual interactions – are triggered – the solitons and antisolons automatically slide along the chain. They both move in the same direction, at a constant speed through the reciprocal resistance imposed by the motors.

Feenstra: “Much research has focused on moving topological solitons by applying external forces. In the systems studied so far, solitons and anti-solitons naturally move in opposite directions. However, if you want to control the behavior of solitons, “You might want to push them in the same direction. We've found that non-reciprocal interactions do just that. Non-reciprocal forces are proportional to the spin generated by the soliton, so each soliton generates its own driving force.”

The movement of solitons is like a series of falling dominoes, each knocking down its neighbor. However, unlike dominoes, non-reciprocal interactions ensure that the “flip” can only happen in one direction. Although dominoes can only fall once, a soliton moving along the metamaterial simply prepares the chain for the anti-soliton to move in the same direction. In other words, any number of isolators and anti-isolates can move through the chain without having to be “reset”.

Motion control

Understanding the role of nonreciprocal behavior will not only help us better understand the behavior of topological solitons in living systems, but may also lead to technological advances. The mechanism that generates self-contained unidirectional isolators discovered in this study could be used to control the movement of different types of waves (called wave steering) or to provide metamaterial with a basic information-processing ability such as filtering. .

Future robots will also be able to use topological isolations for basic robotic functions such as locomotion, signaling, and sensing their surroundings. These functions will no longer be controlled from a central point, but will emerge from the sum of the robot's active parts.

In general, the domino effect of solitons in synthetic materials, which has now become an interesting laboratory observation, may soon begin to play a role in various branches of engineering and design.