Experimental progress in the miniaturization of electronic devices has made routinely available in the laboratory small electronic systems, on the micrometre or sub-micrometre scale, which at low temperature are sufficiently well isolated from their environment to be considered as fully coherent. Some of their most important properties are dominated by the interaction between electrons. Understanding their behaviour therefore requires a description of the interplay between interference effects and interactions. The goal of this review is to address this relatively broad issue and more specifically to address it from the perspective of the quantum chaos community. I will therefore present some of the concepts developed in the field of quantum chaos which may be applied to the study of many-body effects in mesoscopic and nanoscopic systems. Their implementation is illustrated in a few examples of experimental relevance such as persistent currents, mesoscopic fluctuations of Kondo properties or Coulomb blockade. I will furthermore try to bring out, from the various physical illustrations, some of the specific advantages on more general grounds of the quantum chaos based approach.
Experimental progress in the miniaturization of electronic devices has made routinely available in the laboratory small electronic systems, on the micrometre or sub-micrometre scale, which at low temperature are sufficiently well isolated from their environment to be considered as fully coherent. Some of their most important properties are dominated by the interaction between electrons. Understanding their behaviour therefore requires a description of the interplay between interference effects and interactions. The goal of this review is to address this relatively broad issue and more specifically to address it from the perspective of the quantum chaos community. I will therefore present some of the concepts developed in the field of quantum chaos which may be applied to the study of many-body effects in mesoscopic and nanoscopic systems. Their implementation is illustrated in a few examples of experimental relevance such as persistent currents, mesoscopic fluctuations of Kondo properties or Coulomb blockade. I will furthermore try to bring out, from the various physical illustrations, some of the specific advantages on more general grounds of the quantum chaos based approach.
Both classical and quantum principles coexist in the mesoscopic world, something between the microscopic and the macroscopic worlds.More precisely, mesoscopic physics studies how the "coherence", which governs the wave property and especially the interference effect of matter, disappear gradually as the scale increases from the microscopic to the macroscopic scale.Another important issue in mesoscopic physics is many-body effects, which originate from the interaction among electrons.Many-body effects are a fundamental issue in all modern physics, but mesoscopic physics is particularly well adopted for their study because mesoscopic systems allow for tunability of various parameters, which is not possible in bulk systems.Further, the interplay between coherence and many-body effects leads to rich physical phe-
The field of chaos in many-body quantum systems has a long history, going back to Wigner's simple models for heavy nuclei. Quantum chaos is being investigated in a broad variety of experimental platforms such as heavy nuclei, driven (few-electron) atoms, ultracold quantum gases, and photonic or microwave realizations. Quantum chaos plays a new and important role in many branches of physics, from condensed matter problems of many-body localization, including thermalization studies in closed and open quantum systems, and the question of dynamical stability relevant for quantum information and quantum simulation. This Special Issue and its related book address theories and experiments, methods from classical chaos, semiclassics, and random matrix theory, as well as many-body condensed matter physics. It is dedicated to Prof. Shmuel Fishman, who was one of the major representatives of the field over almost four decades, who passed away in 2019.
Direct experimental access to some of the most intriguing quantum phenomena is not granted due to the lack of precise control of the relevant parameters in their naturally intricate environment. Their simulation on conventional computers is impossible, since quantum behaviour arising with superposition states or entanglement is not efficiently translatable into the classical language. However, one could gain deeper insight into complex quantum dynamics by experimentally simulating the quantum behaviour of interest in another quantum system, where the relevant parameters and interactions can be controlled and robust effects detected sufficiently well. Systems of trapped ions provide unique control of both the internal (electronic) and external (motional) degrees of freedom. The mutual Coulomb interaction between the ions allows for large interaction strengths at comparatively large mutual ion distances enabling individual control and readout. Systems of trapped ions therefore exhibit a prominent system in several physical disciplines, for example, quantum information processing or metrology. Here, we will give an overview of different trapping techniques of ions as well as implementations for coherent manipulation of their quantum states and discuss the related theoretical basics. We then report on the experimental and theoretical progress in simulating quantum many-body physics with trapped ions and present current approaches for scaling up to more ions and more-dimensional systems.
The present collection of papers is devoted to a rather new and very controversial topic, the so-called “quantum chaos”. Some researchers see nothing essentially new at all in this phenomenon (apart from a number of various examples and models), and they have good reason to believe so. Indeed, the problems in this field all belong to the traditional, “old-fashion”, and rather “simple” quantum mechanics of finite-dimensional systems with a given interaction and no quantized fields. Nevertheless, many, including ourselves, consider quantum chaos to be a new discovery, though in an old field, of a great importance for fundamental physics. To understand this, the phenomenon of quantum chaos should be put into its proper perspective in recent developments in physics. The central point of this perspective is the conception of dynamical chaos (also a rather new topic) in classical mechanics (for a good review see, e.g., Refs.[l-3]). Thus before discussing the current understanding of quantum chaos we need briefly to describe classical dynamical chaos
Many-body quantum chaos results from interparticle interactions in mesoscopic systems at sufficiently high level density. A short review shows that, going beyond generic properties of local spectral statistics, the ideas of many-body quantum chaos serve as a rich source of new theoretical approaches, computational and experimental tools. Chosen examples include the enhancement of weak perturbations, thermalization in finite systems, exponential convergence of large Hamiltonian matrices and correlations between the states of different symmetry.
Quantum many-body chaos is described as a practical (theoretical, experimental, and computational) instrument in physics of mesoscopic systems of interacting particles.Using mainly nuclear physics applications, it is shown that interactions of constituents create stationary states of high complexity with respect to the nean-field basis with observable properties smoothly changing along the spectrum.Both local Gaussian orthogonal ensemble type features and the global evolution along the spectrum are used to understand the many-body physics and define thermodynamic properties of isolated mesoscopic objects.Among the examples discussed, especially interesting is a chaotic enhancement of weak perturbations illustrated by a large parity violation in neutron resonances on heavy nuclei.Artificially introduced chaotic elements are used to explore the nuclear landscape and predict phase transformations.