相关论文: The $1/r^2$ Integrable system: The Universal Hamil…

We obtain exact analytic expressions for a class of functions expressed as integrals over the Haar measure of the unitary group in d dimensions. Based on these general mathematical results, we investigate generic dynamical properties of…

The complicated interactions in presence of disorder lead to a correlated randomization of states. The Hamiltonian as a result behaves like a multi-parametric random matrix with correlated elements. We show that the eigenvalue correlations…

Random matrix theory is used to represent generic loss of coherence of a fixed central system coupled to a quantum-chaotic environment, represented by a random matrix ensemble, via random interactions. We study the average density matrix…

We study numerically and analytically the quench dynamics of isolated many-body quantum systems. Using full random matrices from the Gaussian orthogonal ensemble, we obtain analytical expressions for the evolution of the survival…

We put forward a possible new interpretation and explanatory framework for quantum theory. The basic hypothesis underlying this new framework is that quantum particles are conceptual entities. More concretely, we propose that quantum…

The appearance of chaotic quantum dynamics significantly depends on the symmetry properties of the system, and in cold atomic systems many of these can be experimentally controlled. In this work, we systematically study the emergence of…

The incoherent dynamical properties of open quantum systems are generically attributed to an ongoing correlation between the system and its environment. Here, we propose a novel way to assess the nature of these system-environment…

Despite their simplicity, quantum harmonic oscillators are ubiquitous in the modeling of physical systems. They are able to capture universal properties that serve as reference for the more complex systems found in nature. In this spirit,…

The growth in the demand for precisely crafted many-body systems of spin-$1/2$ particles/qubits is due to their top-notch versatility in application-oriented quantum-enhanced protocols and the fundamental tests of quantum theory. Here we…

We study the quantum entanglement caused by unitary operators that have classical limits that can range from the near integrable to the completely chaotic. Entanglement in the eigenstates and time-evolving arbitrary states is studied…

In this review the problem of statistical description of isolated quantum systems of interacting particles is discussed. Main attention is paid to a recently developed approach which is based on chaotic properties of compound states in the…

Perturbation theory in quantum mechanics studies how quantum systems interact with their environmental perturbations. Harmonic perturbation is a rare special case of time-dependent perturbations in which exact analysis exists. Some…

How do symmetries induce natural and useful quantum structures? This question is investigated in the context of models of three interacting particles in one-dimension. Such models display a wide spectrum of possibilities for dynamical…

The emergence of macroscopic coherence in a many-body quantum system is a ubiquitous phenomenon across different physical systems and scales. This Chapter reviews key concepts characterizing such systems (correlation functions,…

We consider a mobile impurity particle injected into a one-dimensional quantum gas. The time evolution of the system strongly depends on whether the mass of the impurity and the masses of the host particles are equal or not. For equal…

We show that the most important measures of quantum chaos like frame potentials, scrambling, Loschmidt echo, and out-of-time-order correlators (OTOCs) can be described by the unified framework of the isospectral twirling, namely the Haar…

The density matrix of a non-relativistic quantum system, divided into $N$ sub-systems, is rewritten in terms of the set of all partitioned density matrices for the system. For the case where the different sub-systems are distinguishable, we…

We define one-dimensional particles with generalized exchange statistics. The exact solution of a Hubbard-type Hamiltonian constructed with such particles is achieved using the Coordinate Bethe Ansatz. The chosen deformation of the…

The spectral properties of interacting strongly chaotic systems are investigated for growing interaction strength. A very sensitive transition from Poisson statistics to that of random matrix theory is found. We introduce a new random…

Cavity quantum electrodynamics of multipartite systems is studied in depth, which consist of an arbitrary number of emitters in interaction with an arbitrary number of cavity modes. The governing model is obtained by taking the full…