Realizable hyperuniform and nonhyperuniform particle configurations with targeted spectral functions via effective...

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Computational Physics

Background:

• Identifying realizable many-body configurations for targeted pair correlation functions (g2(r)) or structure factors (S(k)) is crucial but challenging due to infinite configuration degeneracy.
• Sufficient conditions for the realizability of structure factors are generally unknown, limiting the design of materials with specific properties.

Purpose of the Study:

• To expand theoretical knowledge on realizable pair correlation functions and structure factors in classical disordered systems, including hyperuniform varieties.
• To develop and validate a computational algorithm for constructing particle configurations with targeted pair statistics.

Main Methods:

• Introduced a theoretical formalism to draw configurations from canonical ensembles with pairwise-additive potentials corresponding to targeted structure factors.
• Devised an improved algorithm to systematically construct canonical-ensemble particle configurations with targeted pair statistics.
• Tested the algorithm using known realizable and unrealizable structure factors across dimensions, including hyperuniform and nonhyperuniform examples.

Main Results:

• The algorithm successfully constructed configurations for all tested realizable structure factors and correctly identified unrealizable ones.
• Demonstrated the algorithm's accuracy in achieving targeted structure factors for various complex systems, including hyperuniform, hyposurficial, and antihyperuniform configurations.
• Showed that nonequilibrium perfect glass structure factors can be realized by equilibrium pair interactions, leading to a conjecture about effective pair interactions.

Conclusions:

• The developed algorithm accurately identifies realizable structure factors and constructs corresponding particle configurations.
• Findings suggest that a broad range of structure factors, including those from nonequilibrium systems, can be achieved through equilibrium ensembles with effective pair interactions.
• The study advances the understanding of many-body physics and offers applications in designing materials with tunable properties via pair statistics.