Flat microwave cavities can be used to experimentally simulate quantum mechanical systems. By coupling two such cavities, we study the equivalent to the symmetry breaking in quantum mechanics. As the coupling is tunable, we can measure resonance strength distributions as a function of the symmetry breaking. We analyze the data employing a qualitative model based on Random Matrix Theory (RMT) and show that the results derived from the strength distribution are consistent with those previously obtained from spectral statistics.

B. Dietz. T. Guhr H. L. Harney A. Richter

In a unifying way, the doorway mechanism explains spectral properties in a rich variety of open mesoscopic quantum systems, ranging from atoms to nuclei. A distinct state and a background of other states couple to each other which sensitively affects the strength function. The recently measured superscars in the barrier billiard provide an ideal model for an in--depth investigation of this mechanism. We introduce two new statistical observables, the full distribution of the maximum coupling coefficient to the doorway and directed spatial correlators. Using Random Matrix Theory and random plane waves, we obtain a consistent understanding of the experimental data.

S. Åberg T. Guhr M. Miski-Oglu A. Richter

We measure elastomechanical spectra for a family of thin shells. We show that these spectra can be described by a "semiclassical" trace formula comprising periodic orbits on geodesics, with the periods of these orbits consistent with those extracted from experiment. The influence of periodic orbits on spectra in the case of two-dimensional curved geometries is thereby demonstrated, where the parameter corresponding to Planck's constant in quantum systems involves the wave number and the curvature radius. We use these findings to explain the marked clustering of levels when the shell is hemispherical.

M. Avlund C. Ellegaard M. Oxborrow T. Guhr N. Sondergaard

The spectrum of the Dirac operator near zero virtuality obtained in lattice gauge simulations is known to be universally described by chiral random matrix theory. We address the question of the maximum energy for which this universality persists. For this purpose, we analyze large ensembles of complete spectra of the Euclidean Dirac operator for staggered fermions. We calculate the disconnected scalar susceptibility and the microscopic number variance for the chiral symplectic ensemble of random matrices and compare the results with lattice Dirac spectra for quenched SU(2). The crossover to a non-universal regime is clearly identified and found to scale with the square of the linear lattice size and with $f_{\pi}^2$, in agreement with theoretical expectations.

M. E. Berbenni-Bitsch M. Göckeler T. Guhr A. D. Jackson J. -Z. Ma S. Meyer A. Schäfer H. A. Weidenmüller T. Wettig T. Wilke

Random matrix theory (RMT) is a powerful statistical tool to model spectral fluctuations. In addition, RMT provides efficient means to separate different scales in spectra. Recently RMT has found application in quantum chromodynamics (QCD). In mesoscopic physics, the Thouless energy sets the universal scale for which RMT applies. We try to identify the equivalent of a Thouless energy in complete spectra of the QCD Dirac operator with staggered fermions and $SU_c(2)$ lattice gauge fields. Comparing lattice data with RMT predictions we find deviations which allow us to give an estimate for this scale.

M. E. Berbenni T. Guhr J. -Z. Ma S. Meyer T. Wilke

Recent theoretical and numerical developments show analogies between quantum chromodynamics (QCD) and disordered systems in condensed matter physics. We study the spectral fluctuations of a Dirac particle propagating in a finite four dimensional box in the presence of gauge fields. We construct a model which combines Efetov's approach to disordered systems with the principles of chiral symmetry and QCD. To this end, the gauge fields are replaced with a stochastic white noise potential, the gauge field disorder. Effective supersymmetric non-linear sigma-models are obtained. Spontaneous breaking of supersymmetry is found. We rigorously derive the equivalent of the Thouless energy in QCD. Connections to other low-energy effective theories, in particular the Nambu-Jona-Lasinio model and chiral perturbation theory, are found.

T. Guhr T. Wilke H. A. Weidenmueller

We introduce an extension of the character expansion method to the case of supergroups. This method allows us to calculate a superversion of the Leutwyler-Smilga integral which, to the best of our knowledge, has not been calculated before. We also use the method to generalize a previously calculated superversion of the Berezin-Karpelevich integral. Our character expansion method should also allow for the calculation of other supergroup integrals.

C. Lehner T. Wettig T. Guhr Y. Wei

Rectangular real $N \times (N + \nu)$ matrices $W$ with a Gaussian distribution appear very frequently in data analysis, condensed matter physics and quantum field theory. A central question concerns the correlations encoded in the spectral statistics of $WW^T$. The extreme eigenvalues of $W W^T$ are of particular interest. We explicitly compute the distribution and the gap probability of the smallest non-zero eigenvalue in this ensemble, both for arbitrary fixed $N$ and $\nu$, and in the universal large $N$ limit with $\nu$ fixed. We uncover an integrable Pfaffian structure valid for all even values of $\nu\geq 0$. This extends previous results for odd $\nu$ at infinite $N$ and recursive results for finite $N$ and for all $\nu$. Our mathematical results include the computation of expectation values of half integer powers of characteristic polynomials.

G. Akemann T. Guhr M. Kieburg R. Wegner T. Wirtz

We show that for dual-unitary kicked chains, built upon a pair of complex Hadamard matrices, correlators of strictly local, traceless operators vanish identically for sufficiently long chains. On the other hand, operators supported at pairs of adjacent chain sites, generically, exhibit nontrivial correlations along the light cone edges. In agreement with Bertini et. al. [Phys. Rev. Lett. 123, 210601 (2019)], they can be expressed through the expectation values of a transfer matrix $T$. Furthermore, we identify a remarkable family of dual-unitary models where an explicit information on the spectrum of $T$ is available. For this class of models we provide a closed analytical formula for the corresponding two-point correlators. This result, in turn, allows an evaluation of local correlators in the vicinity of the dual-unitary regime which is exemplified on the kicked Ising spin chain.

Boris Gutkin Petr Braun Maram Akila Daniel Waltner Thomas Guhr

Conformational isomers or conformers of molecules play a decisive role in chemistry and biology. However, experimental methods to investigate chemical reaction dynamics are typically not conformer-sensitive. Here, we report on a gas-phase megaelectronvolt ultrafast electron diffraction investigation of {\alpha}-phellandrene undergoing an electrocyclic ring-opening reaction. We directly image the evolution of a specific set of {\alpha}-phellandrene conformers into the product isomer predicted by the Woodward-Hoffmann rules in real space and time. Our experimental results are in quantitative agreement with nonadiabatic quantum molecular dynamics simulations, which provide unprecedented detail of how conformation influences time scale and quantum efficiency of photoinduced ring-opening reactions. Due to the prevalence of large numbers of conformers in organic chemistry, our findings impact our general understanding of reaction dynamics in chemistry and biology.

E. G. Champenois D. M. Sanchez J. Yang J. P. F. Nunes A. Attar M. Centurion R. Forbes M. Gühr K. Hegazy F. Ji S. K. Saha Y. Liu M. -F. Lin D. Luo B. Moore X. Shen M. R. Ware X. J. Wang T. J. Martínez T. J. A. Wolf