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Lang Li-Jun
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What does "hard-core" mean? What is "hard-core boson" model?
Any mathmatical representations? Is that means {a,a+}=1(hard core, like fermion), while [a, a+]=1(boson)?genneth said:Hard core means that they cannot occupy the same quantum state --- like fermions, but without the exchange antisymmetry. The Hilbert space for the system can be difficult to construct by hand, however. One way to do this is to incorporate a delta-function repulsive interaction; the low energy states will then be appropriate. Incidentally, most composite bosons in condensed matter (He-4, etc.) have very large repulsive interactions at close range, which can be (to first order) renormalised into a hard core boson model.
Hard-core bosons are a type of quantum particle that obey the laws of Bose-Einstein statistics, which describe the behavior of particles with integer spin. They are also characterized by their inability to occupy the same quantum state, giving rise to the term "hard-core".
Hard-core bosons have zero size and do not interact with each other, except for through collisions. They also have integer spin and obey Bose-Einstein statistics, which means they tend to occupy the same quantum state at low temperatures.
The main difference between hard-core bosons and soft-core bosons is their ability to occupy the same quantum state. Hard-core bosons cannot occupy the same state, while soft-core bosons can. This leads to different behaviors and properties, such as the formation of Bose-Einstein condensates for soft-core bosons but not for hard-core bosons.
Some examples of hard-core bosons include atomic nuclei, mesons, and photons. These particles have integer spin and obey Bose-Einstein statistics, making them suitable examples of hard-core bosons in the real world.
Scientists are currently studying the behavior of hard-core bosons in different systems, such as in optical lattices or in low-dimensional systems. They are also exploring their potential applications in quantum computing and simulating complex quantum systems.