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Title:
Random Matrix Theory for Quantum Many-body systems
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Abstract:
Embedded random matrix ensembles, generated by random interactions, operating in many-particle spaces apply in a generic way to isolated finite interacting systems such as nuclei, atoms, quantum dots, small metallic grains, interacting spin systems modeling quantum computing core and ultracold atoms. The simplest of these ensembles are the embedded Gaussian ensembles (EGE) of two-body interactions for spinless fermion/boson systems. It is now well understood that EGE generate paradigmatic models for many-body chaos exhibited by isolated finite interacting many-body quantum systems. In realistic applications, EGE with good quantum numbers should be studied as there are several properties of real systems that require explicit inclusion of symmetries. I will present several results for embedded ensembles with spin degree of freedom and their applications.
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