Related papers: Quantum dynamical entropy, chaotic unitaries and c…
The development and spread of entanglement in complex quantum systems is central to exploring many-body phenomena out of equilibrium. Measuring entanglement dynamics can shed light on information scrambling and thermalisation, namely on…
Quantum circuit dynamics with local projective measurements can realize a rich spectrum of entangled states of quantum matter. Motivated by the physics of the Kitaev quantum spin liquid [1], we study quantum circuit dynamics in…
Based on the Hilbert space approach to the theory of nonlinear dynamical systems developed by the author a hypothesis is formulated concerning the "quantal" criterion for classical ordinary differential systems to exhibit chaotic behaviour.
More than 15 years ago, a new approach to quantum mechanics was suggested, in which Hermiticity of the Hamiltonian was to be replaced by invariance under a discrete symmetry, the product of parity and time-reversal symmetry, $\mathcal{PT}$.…
Intrinsic instability of trajectories characterizes chaotic dynamical systems. We report here that trajectories can exhibit a surprisingly high degree of stability, over a very long time, in a chaotic dynamical system. We provide a detailed…
We propose a scheme for data-driven parameterization of unresolved dimensions of dynamical systems based on the mathematical framework of quantum mechanics and Koopman operator theory. Given a system in which some components of the state…
We develop a unified, information theoretic interpretation of the number-phase complementarity that is applicable both to finite-dimensional (atomic) and infinite-dimensional (oscillator) systems, with number treated as a discrete Hermitian…
Consider a classically chaotic system which is described by a Hamiltonian H_0. At t=0 the Hamiltonian undergoes a sudden-change H_0 -> H. We consider the quantum-mechanical spreading of the evolving energy distribution, and argue that it…
Coarse-grained measurements offer a scalable alternative to full state tomography for characterizing complex quantum dynamics. We show that observational entropy (OE), an information-theoretic entropy defined directly from finite-resolution…
The main purpose of these lectures is to discuss briefly recent methods of calculation of statistical properties of quantum eigenvalues for chaotic systems based on semi-classical trace formulas. Under the assumption that periodic orbit…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
We show that the rate of increase of von Neumann entropy computed from the reduced density matrix of an open quantum system is an excellent indicator of the dynamical behavior of its classical hamiltonian counterpart. In decohering quantum…
We examine the conjecture that entropy production in subsystems of a given system can be used as a dynamical criterion for quantum chaos in the latter. Numerical results are presented for finite dimensional spin systems as also for the…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
The quantum dynamics of isolated systems under quench condition exhibits a variety of interesting features depending on the integrable/chaotic nature of system. We study the exact dynamics of trivially integrable system of harmonic chains…
Quantum chaos in isolated quantum systems is intimately linked to thermalization and the rapid relaxation of observables. Although the spectral properties of the chaotic phase in the tilted Bose-Hubbard model have been well characterized,…
The random matrix ensembles (RME) of quantum statistical Hamiltonian operators, {\em e.g.} Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied to following quantum statistical systems:…
We extend some results of group representation theory and von Neumann algebras to the quaternionic Hilbert space case, proving the double commutant theorem (whose quaternionic proof requires a different procedure) and extend to the…
Systems where time evolution follows a multiplicative process are ubiquitous in physics. We study a toy model for such systems where each time step is given by multiplication with an independent random $N\times N$ matrix with complex…
It is an outstanding goal to unveil the key features of quantum dynamics at eigenstate transitions. Focusing on quadratic fermionic Hamiltonians that exhibit localization transitions, we identify physical observables that exhibit…