The nuclear shell model as a testing ground for many-body quantum chaos

Nuclear structure, random interactions and mesoscopic physics

“…With the interaction strength artificially increased beyond its realistic value, one can reach the GOE limit uniformly in excitation energy [24,10]. It is important that for the realistic, and therefore consistent with the mean field, interaction strength information entropy I α is a smooth monotonously increasing to the middle of the spectrum function of excitation energy E α .…”

“…Considering the dependence on the interaction strength, the chaotic statistics of nearest level spacings and the so-called ∆ 3 statistics of level number fluctuations emerge when the interparticle interactions are turned on with their strength still much weaker than the realistic value. This happens without any randomness in the Hamiltonian, in spite of correlations due to the two-body character of the forces and the fact that the realistic distributions of the many-body matrix elements are generically close to exponential rather than Gaussian [10]. The mechanism of spectral chaotization is provided by multiple avoided crossings of levels inside a fixed symmetry class.…”

“…The degree of complexity of an eigenstate |α with respect to the reference basis |k can be quantified with the help of Shannon information entropy [22,23,10]. If the eigenfunction is given by the normalized superposition…”

“…It is important that for the realistic, and therefore consistent with the mean field, interaction strength information entropy I α is a smooth monotonously increasing to the middle of the spectrum function of excitation energy E α . This allows one to treat information entropy as a thermodynamic variable and build up the corresponding temperature scale [24,10,11] avoiding any reference to a heat bath or Gibbs ensemble. Thus, one can consider thermodynamics of a closed mesoscopic system based on typical properties of individual quantum states.…”

“…From a more general theoretical viewpoint related to many-body quantum chaos [9,10,11], we deal with closed mesoscopic systems that generically display chaotization of motion due to intrinsic interactions. In the absence of a heat bath and external disorder, the interactions play the role of a randomizing or thermalizing factor.…”