We investigate the spectral fluctuations and electronic transport properties of chaotic mesoscopic cavities using Kwant, an open source Python programming language based package. Discretized chaotic billiard systems are used to model these mesoscopic cavities. For the spectral fluctuations, we study the ratio of consecutive eigenvalue spacings, and for the transport properties, we focus on Landauer conductance and shot noise power. We generate an ensemble of scattering matrices in Kwant, with desired number of open channels in the leads attached to the cavity. The results obtained from Kwant simulations, performed without or with magnetic field, are compared with the corresponding random matrix theory predictions for orthogonally and unitarily invariant ensembles. These two cases apply to the scenarios of preserved and broken time-reversal symmetry, respectively. In addition, we explore the orthogonal to unitary crossover statistics by varying the magnetic field and examine its relationship with the random matrix transition parameter.

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We consider a class of systems where N identical particles with positions q1, ..., qN and momenta p1, ..., pN are enclosed in a box of size L, and exhibit the scaling U(Lr1, ..., LrN ) = α(L) U(r1, ..., rN ) for the associated potential energy function U(q1, ..., qN ). For these systems, we propose an efficient implementation of the Wang-Landau algorithm for evaluating thermodynamic observables involving energy and volume fluctuations in the microcanonical description, and temperature and volume fluctuations in the canonical description. This requires performing the Wang-Landau simulation in a scaled box of unit size and evaluating the density of states corresponding to the potential energy part only. To demonstrate the efficacy of our approach, as example systems, we consider Padmanabhan's binary star model and an ideal gas trapped in a harmonic potential within the box. arXiv:1810.11623v2 [cond-mat.stat-mech]