Researchers have explored the mechanism behind the emerging property of recently discovered exotic disordered state of matter, known as “hyperuniformity”.

Hyperuniformity is a property of certain heterogeneous media in which density fluctuations in the long-wavelength range decay to zero. Hyperuniform disordered materials have been observed in a variety of settings, such as in quasicrystals, large-scale structures of universe, soft and biological emulsions and colloids, etc. 

Mass, energy, and charge transport are ubiquitous in nature and manifest themselves in a variety of ways, including cloud formation, heat and electrical conduction through materials, traffic flow, avalanches in granular media, the formation of river networks and mountain ranges, and the self-assembly of droplets in cells, etc.

For simplicity, first consider traffic flow in a city. In city traffic, you can think of cars and buses as tiny “particles” in a system, analogous to electrons moving in a material that can behave as a conductor or an insulator. Likewise, the passage of water vapour from the ocean to form clouds, as well as the way rivers develop intricate networks for effective water transfer, are quite similar.

Similarly, just as traffic rules help maintain the road in order, natural systems adhere to certain norms governed by symmetries and conservation principles (e.g., those concerning energy, mass, electrical charge and momentum, among others). These rules often lead to simple and possibly universal behaviors in a wide range of systems.

For example, if you place a thermometer in water stored in a “thermos flask”, the reading will be the same regardless of where you keep it. That is, the temperature is uniform throughout, and nothing appears to change over a (reasonably) long period of time. It is as if time stands still! In the physical sciences, this type of system is known as an equilibrium one, where the concepts of time-translational and time-reversal symmetries apply. These ideas were developed by pioneer scientists who worked on thermodynamics like Sadi Carnot, James Clerk Maxwell, Rudolf Clausius, Ludwig Boltzmann, and Willard Gibbs.

According to the time reversal symmetry principle, one can theoretically 'rewind' the events in such a system - such as the collisions of water molecules in our thermos flask - and watch everything happen in reverse, just like playing a movie backwards.

However, to obtain hyperuniformity in a disordered system, the time reversal symmetry should be broken. Researchers have been exploring the results of breaking the time-reversal symmetry under conditions like application of an external force in the presence of an additional conservation law.

Scientists from S. N. Bose National Centre for Basic Sciences (SNBNCBS), an autonomous institute of Department of Science and Technology demonstrated that, while perturbations in density (say, generated spontaneously) diffuse like heat energy diffusing through a material, these perturbations are quite unlikely to occur in the first place as particle mobility is highly constrained due to an additional conservation law.

This mechanism responsible for the suppressed fluctuations in the hyperuniform systems explains the emerging properties of a recently discovered exotic disordered state of matter, known as “hyperuniformity”.

One of the most striking characteristics of such a state is that mass fluctuations are greatly suppressed as the system size grows. Indeed, it is strikingly opposite to what typically happens at the critical point of liquids (such as the water-vapour critical point-- point where (and beyond which) the distinction between “water” and “vapour” disappears) or which mass fluctuations diverge, causing “critical opalascence” (a light-scattering phenomenon, where the system looks milky white and darkish brown upon reflection and transmission of the light, respectively).

A hyperuniform matter near criticality, on the other hand, is one that falls somewhere between a perfect crystal, an amorphous solid and a liquid: The researchers have quantified this state of matter by examining what are perhaps the simplest interacting-particle systems - the driven diffusive systems.

The findings published in the journal Physical Review E shed light on the dynamical origin of “hyperuniformity” -- the precise way the constituents of a hyperuniform matter dynamically organize themselves into such a state, providing a fresh perspective on the general theoretical understanding of the problem. 

Hyperuniform materials have distinctive characteristics that could have technological or biological applications, and the mechanism of hyperuniformity could be used to control various physiological functions in cells, and energy-efficient photonic devices (such as photonic band-gap materials) that could be used for optical data transmission and communications.

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