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We introduce a log-gas model that is a generalization of a random matrix ensemble with an additional interaction, whose strength depends on a parameter $gamma$. The equilibrium density is computed by numerically solving the Riemann-Hilbert problem associated with the ensemble. The effect of the additional parameter $gamma$ associated with the two-body interaction can be understood in terms of an effective $gamma$-dependent single-particle confining potential.
We consider several limiting cases of the joint probability distribution for a random matrix ensemble with an additional interaction term controlled by an exponent $gamma$ (called the $gamma$-ensembles). The effective potential, which is essentially
The geometry of multi-parameter families of quantum states is important in numerous contexts, including adiabatic or nonadiabatic quantum dynamics, quantum quenches, and the characterization of quantum critical points. Here, we discuss the Hilbert-sp
We study analytically and numerically the dynamics of the generalized Rosenzweig-Porter model, which is known to possess three distinct phases: ergodic, multifractal and localized phases. Our focus is on the survival probability $R(t)$, the probabili
Theory of Random Matrix Ensembles have proven to be a useful tool in the study of the statistical distribution of energy or transmission levels of a wide variety of physical systems. We give an overview of certain q-generalizations of the Random Matr
We study a unitary matrix model of the Gross-Witten-Wadia type, extended with the addition of characteristic polynomial insertions. The model interpolates between solvable unitary matrix models and is the unitary counterpart of a deformed Cauchy ense