Random-matrix approach to transition-state theory.

To model a complex system intrinsically separated by a barrier, we use two random Hamiltonians, coupled to each other either by a tunneling matrix element or by an intermediate transition state. We study that model in the universal limit of large matrix dimension. We calculate the average probability 〈P_{ab}〉 for transition from scattering channel a coupled to the first Hamiltonian to scattering channel b coupled to the second Hamiltonian. Using only the assumption ∑_{b^{'}}T_{b^{'}}≫1 we find 〈P_{ab}〉=P_{a}T_{b}/∑_{b^{'}}T_{b^{'}}. Here P_{a} is the probability of formation of the tunneling channel or the transition state, and the T_{b^{'}} are the transmission coefficients for channels b^{'} coupled to the second Hamiltonian. That result confirms transition-state theory in its general form. For tunneling through a very thick barrier the condition ∑_{b^{'}}T_{b^{'}}≫1 is relaxed and independence of formation and decay of the tunneling process hold more generally.

Laser-nucleus reactions: population of states far above yrast and far from stability.

Nuclear reactions induced by a strong zeptosecond laser pulse are studied theoretically in the quasiadiabatic regime where the photon absorption rate is comparable to the nuclear equilibration rate. We find that multiple photon absorption leads to the formation of a compound nucleus in the so-far unexplored regime of excitation energies several hundred MeV above the yrast line. At these energies, further photon absorption is limited by neutron decay and/or induced nucleon emission. With a laser pulse of ≈ 50 zs duration, proton-rich nuclei far off the line of stability are produced.

Universal quantum graphs.

For time-reversal invariant graphs we prove the Bohigas-Giannoni-Schmit conjecture in its most general form: For graphs that are mixing in the classical limit, all spectral correlation functions coincide with those of the Gaussian orthogonal ensemble of random matrices. For open graphs, we derive the analogous identities for all S-matrix correlation functions.

Chaotic scattering on individual quantum graphs.

For chaotic scattering on quantum graphs, the semiclassical approximation is exact. We use this fact and employ supersymmetry, the color-flavor transformation, and the saddle-point approximation to calculate the exact expression for the lowest and asymptotic expressions in the Ericson regime for all higher correlation functions of the scattering matrix. Our results agree with those available from the random-matrix approach to chaotic scattering. We conjecture that our results hold universally for quantum-chaotic scattering.

Universal chaotic scattering on quantum graphs.

We calculate the S-matrix correlation function for chaotic scattering on quantum graphs and show that it agrees with that of random-matrix theory. We also calculate all higher S-matrix correlation functions in the Ericson regime. These, too, agree with random-matrix theory results as far as the latter are known. We conjecture that our results give a universal description of chaotic scattering.

Chaos in fermionic many-body systems and the metal-insulator transition.

We show that finite Fermi systems governed by a mean field and a few-body interaction generically possess spectral fluctuations of the Wigner-Dyson type and are, thus, chaotic. Our argument is based on an analogy to the metal-insulator transition. We construct a sparse random-matrix scaffolding ensemble (ScE) that mimics this transition. Our claim then follows from the fact that the generic random-matrix ensemble modeling a fermionic interacting many-body system is much less sparse than ScE.

Quantum chaotic scattering in microwave resonators.

In a frequency range where a microwave resonator simulates a chaotic quantum billiard, we have measured moduli and phases of reflection and transmission amplitudes in the regimes of both isolated and of weakly overlapping resonances and for resonators with and without time-reversal invariance. Statistical measures for S -matrix fluctuations were determined from the data and compared with extant and/or newly derived theoretical results obtained from the random-matrix approach to quantum chaotic scattering. The latter contained a small number of fit parameters. The large data sets taken made it possible to test the theoretical expressions with unprecedented accuracy. The theory is confirmed by both a goodness-of-fit-test and the agreement of predicted values for those statistical measures that were not used for the fits, with the data.

Induced violation of time-reversal invariance in the regime of weakly overlapping resonances.

We measure the complex scattering amplitudes of a flat microwave cavity (a "chaotic billiard"). Time-reversal (T) invariance is partially broken by a magnetized ferrite placed within the cavity. We extend the random-matrix approach to T violation in scattering, determine the parameters from some properties of the scattering amplitudes, and successfully predict others. Our work constitutes the most precise test of the random-matrix theoretical approach to T violation so far available.

Chaotic scattering in the regime of weakly overlapping resonances.

We measure the transmission and reflection amplitudes of microwaves in a resonator coupled to two antennas at room temperature in the regime of weakly overlapping resonances and in a frequency range of 3-16GHz . Below 10.1GHz the resonator simulates a chaotic quantum system. The distribution of the elements of the scattering matrix S is not Gaussian. The Fourier coefficients of S are used for a best fit of the autocorrelation function of S to a theoretical expression based on random-matrix theory. We find very good agreement below but not above 10.1GHz .

Induced time-reversal symmetry breaking observed in microwave billiards.

Using reciprocity, we investigate the breaking of time-reversal (T) symmetry due to a ferrite embedded in a flat microwave billiard. Transmission spectra of isolated single resonances are not sensitive to T violation, whereas those of pairs of nearly degenerate resonances do depend on the direction of time. For their theoretical description a scattering matrix model from nuclear physics is used. The T-violating matrix elements of the effective Hamiltonian for the microwave billiard with the embedded ferrite are determined experimentally as functions of the magnetization of the ferrite.

Distribution of spectral widths and preponderance of spin-0 ground states in nuclei.

We use a single j-shell model with random two-body interactions to derive closed expressions for the distribution of and the correlations between spectral widths of different spins. This task is facilitated by introducing two-body operators whose squared spectral widths sum up to the squared spectral width of the random Hamiltonian. The spin-0 width is characterized by a relatively large average value and small fluctuations, while the width of maximum spin has the largest average and the largest fluctuations. The approximate proportionality between widths and spectral radii explains the preponderance of spin-0 ground states.

Nonuniversal behavior of the k-body embedded Gaussian unitary ensemble of random matrices.

Using a novel approach, we investigate the shape of the average spectrum and the spectral fluctuations of the k-body embedded unitary ensemble in the limit of a large matrix dimension. We identify the transition point between a semicircle and a Gaussian shape. The transition also affects the spectral fluctuations which deviate from the Wigner-Dyson form and become Poissonian in the limit k<