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Imagine having a set of LEGO bricks, but with a strange rule: every time you add one, the sizes of the others change unpredictably. In quantum physics, scientists use tools called 'coherent states' to describe how particles behave. Usually, these particles follow very precise and predictable rules, much like a steady heartbeat.

However, a new study has introduced a way to 'customize' these rules using a super complex mathematical tool called the Fox H function. Thanks to this discovery, scientists can create quantum states that don't behave like classical ones. Instead of following a regular growth or decay pattern, these particles can exhibit 'anomalous' behaviors.

What does this mean in practice? It means we can better control how particles interact with each other or their surroundings. For instance, we can decide whether particles should cluster in unusual ways or distribute themselves differently. It is like discovering a new remote control to regulate the chaos of the microscopic world, opening the door to new technologies that today seem like pure science fiction!

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The research focuses on generalizing coherent states using Fox H auxiliary functions. Standard coherent states are fundamental in quantum mechanics because they minimize uncertainty according to Heisenberg's uncertainty principle. By using the Fox H function, researchers have managed to include specific cases such as Mittag-Leffler and Wright states, which offer unprecedented mathematical flexibility. A crucial aspect is the resolution of identity in Fock space through a weight function composed of the Fox H function and the Wright generalized hypergeometric function. This allows for the study of non-standard statistics: through the Mandel Q factor, it is possible to transition from super-Poissonian to sub-Poissonian distributions simply by adjusting mathematical parameters. This control is vital for quantum computing and quantum optics, where precision in excitation distribution determines the efficiency of information processes.

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Authors:
Filippo Giraldi
Date Published:
Original Article www.mdpi.com
Fact-check verified on 21/07/2026
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Creative Commons License CC BY-NC-SA 4.0

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