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We present an extensive numerical study of spectral statistics and eigenfunctions of quantized triangular billiards. We compute two million consecutive eigenvalues for six representative cases of triangular billiards, three with generic angles with irrational ratios with π, whose classical dynamics is presumably mixing, and three with exactly one angle rational with π, which are presumably only weakly mixing or even nonergodic in case of right triangles. We find excellent agreement of short- and long-range spectral statistics with the Gaussian orthogonal ensemble of random matrix theory for the most irrational generic triangle, while the other cases show small but significant deviations which are attributed either to a scarring or superscarring mechanism. This result, which extends the quantum chaos conjecture to systems with dynamical mixing in the absence of hard (Lyapunov) chaos, has been corroborated by analyzing distributions of phase-space localization measures of eigenstates and inspecting the structure of characteristic typical and atypical eigenfunctions.

We discuss the connection between the out-of-time-ordered correlator and the number of harmonics of the phase-space Wigner distribution function. In particular, we show that both quantities grow exponentially for chaotic dynamics, with a rate determined by the largest Lyapunov exponent of the underlying classical dynamics, and algebraically—linearly or quadratically—for integrable dynamics. It is then possible to use such quantities to detect in the time domain the integrability-to-chaos crossover in many-body quantum systems.

We provide analytical and numerical evidence that Onsager reciprocal relations remain valid for systems with broken time-reversal symmetry as is typically the case when a generic magnetic field is present. Our results show that the Onsager reciprocal relations are much more general than previously assumed. Hence, the fundamental constraints they impose on heat to work conversion remain valid also with broken time-reversal symmetry. In particular, the possibility of an engine operating at the Carnot efficiency with finite power is ruled out on purely thermodynamic grounds.