Universal S -matrix correlations for complex scattering of wave packets in noninteracting many-body systems: Theory, simulation, and experiment

Abstract

We present an in-depth study of the universal correlations of scattering-matrix entries required in the framework of nonstationary many-body scattering of noninteracting indistinguishable particles where the incoming states are localized wave packets. Contrary to the stationary case, the emergence of universal signatures of chaotic dynamics in dynamical observables manifests itself in the emergence of universal correlations of the scattering matrix at different energies. We use a semiclassical theory based on interfering paths, numerical wave function based simulations, and numerical averaging over random-matrix ensembles to calculate such correlations and compare with experimental measurements in microwave graphs, finding excellent agreement. Our calculations show that the universality of the correlators survives the extreme limit of few open channels relevant for electron quantum optics, albeit at the price of dealing with large-cancellation effects requiring the computation of a large class of semiclassical diagrams.

Semiclassical roots of universality in many-body quantum chaos

“…Various subsequent theoretical works have extended semiclassical quantum transport theory on the basis of encounter calculus or related approaches. These include the semiclassical calculation of higher-order corrections to the classical conductance of ballistic cavities [122], shot noise in chaotic conductors [123][124][125][126][127][128], weak antilocalization in spin-orbit coupled semiconductor cavities [129][130][131], higher transport moments and correlators [60,127,[132][133][134][135], Wigner-Smith time delay [133,[136][137][138][139], role of tunnel barriers [140][141][142][143], and extensions to the ac-conductance [144].…”

Semiclassical roots of universality in many-body quantum chaos

“…Various subsequent theoretical works have extended semiclassical quantum transport theory on the basis of encounter calculus or related approaches. These include the semiclassical calculation of higher-order corrections to the classical conductance of ballistic cavities [120], shot noise in chaotic conductors [121,122,123,124,125,126], weak antilocalization in spin-orbit coupled semiconductor cavities [127,128,129], higher transport moments and correlators [59,125,130,131,132], Wigner-Smith time delay [133,134,130,135], role of tunnel barriers [136,137], and extensions to the ac-conductance [138].…”

Semiclassical approach to $S$ matrix energy correlations and time delay in chaotic systems

“…This will be equal to M for ǫ = 0, but in general a widely fluctuating function of E. Averaging within a local energy window produces a well behaved funcion of ǫ. Such energy correlations have traditionally been studied by modelling the Hamiltonian of the system as a random hermitian matrix coupled to scattering channels [3][4][5][6][7][8][9].…”