Related papers: Quantum Chaos on Edge
Weakly interacting quasiparticles play a central role in the low-energy description of many phases of quantum matter. At higher energies, however, quasiparticles cease to be well-defined in generic many-body systems due to a proliferation…
We sketch the semiclassical core of a proof of the so-called Bohigas-Giannoni-Schmit conjecture: A dynamical system with full classical chaos has a quantum energy spectrum with universal fluctuations on the scale of the mean level spacing.…
We examine the dynamics of a wave packet that initially corresponds to a coherent state in the model of quantum kicked rotator. This main model of quantum chaos, which allows for a transition from regular to to chaotic behavior in the…
Quantum chaos is central to understanding quantum dynamics and is crucial for generating random quantum states, a key resource for quantum information tasks. In this work, we introduce a new class of quantum many-body dynamics, termed…
Quantum chaotic systems are often defined via the assertion that their spectral statistics coincides with, or is well approximated by, random matrix theory. In this paper we explain how the universal content of random matrix theory emerges…
Finding the ground state of strongly-interacting fermionic systems is often the prerequisite for fully understanding both quantum chemistry and condensed matter systems. The Sachdev--Ye--Kitaev (SYK) model is a representative example of…
We show that the low temperature phase of a conjugate pair of uncoupled, quantum chaotic, nonhermitian systems such as the Sachdev-Ye-Kitaev (SYK) model or the Ginibre ensemble of random matrices are dominated by replica symmetry breaking…
We investigate the spread complexity of a generic two-level subsystem of a larger system to analyze the influence of energy level statistics, comparing chaotic and integrable systems. Initially focusing on the nearest-neighbor level…
Quantum chaotic and integrable systems are known to exhibit a characteristic $1/f$ and $1/f^{2}$ noise, respectively, in the power spectrum associated to their spectral fluctuations. A recent work [R. Riser, V. A. Osipov, and E. Kanzieper,…
We introduce a notion of local level spacings and study their statistics within a random-matrix-theory approach. In the limit of infinite-dimensional random matrices, we determine universal sequences of mean local spacings and of their…
The fine grained energy spectrum of quantum chaotic systems is widely believed to be described by random matrix statistics. A basic scale in such a system is the energy range over which this behavior persists. We define the corresponding…
We study classical and quantum scattering properties in the ballistic regime of particles in two-dimensional chaotic billiards that are models of electron- or micro- waveguides. To this end we construct the purely classical counterparts of…
A short historical overview is given on the development of our knowledge of complex dynamical systems with special emphasis on ergodicity and chaos, and on the semiclassical quantization of integrable and chaotic systems. The general trace…
We investigate the dynamics of classical and quantum N-component phi^4 oscillators in the presence of an external field. In the large N limit the effective dynamics is described by two-degree-of-freedom classical Hamiltonian systems. In the…
We introduce randomness into a class of integrable models and study the spectral form factor as a diagnostic to distinguish between randomness and chaos. Spectral form factors exhibit a characteristic dip-ramp-plateau behavior in the $N>2$…
In chaotic quantum systems the spectral form factor exhibits a universal linear ramp and plateau structure with superimposed erratic oscillations. The mean signal and the statistics of the noise can be probed by the moments of the spectral…
Employing efficient diagonalization techniques, we perform a detailed quantitative study of the regular and chaotic regions in phase space in the simplest non-integrable atom-field system, the Dicke model. A close correlation between the…
Quantum-chaotic systems exhibit several universal properties, ranging from level repulsion in the energy spectrum to wavefunction delocalization. On the other hand, if wavefunctions are localized, the levels exhibit no level repulsion and…
More than four decades of research on chaos in isolated quantum systems have led to the identification of universal signatures -- such as level repulsion and eigenstate thermalization -- that serve as cornerstones in our understanding of…
We use semiclassical methods to evaluate the spectral two-point correlation function of quantum chaotic systems with discrete geometrical symmetries. The energy spectra of these systems can be divided into subspectra that are associated to…