相关论文: Concentration of OTOC and Lieb-Robinson velocity i…
We study the finite-temperature scrambling behavior of a quantum system described by a Hamiltonian chosen from a random matrix ensemble. This effectively (0+1)-dimensional model admits an exact calculation of various ensemble-averaged…
We generalize the Lieb-Robinson theorem to systems whose Hamiltonian is the sum of local operators whose commutators are bounded.
We present exact results for the classical version of the Out-of-Time-Order Commutator (OTOC) for a family of power-law models consisting of $N$ particles in one dimension and confined by an external harmonic potential. These particles are…
We generalize to multi-commutators the usual Lieb-Robinson bounds for commutators. In the spirit of constructive QFT, this is done so as to allow the use of combinatorics of minimally connected graphs (tree expansions) in order to estimate…
The out of time order correlator (OTOC) serves as a powerful tool for investigating quantum information spreading and chaos in complex systems. We present a method employing non-equilibrium dynamical mean-field theory (DMFT) and coherent…
Let $A$ and $B$ be local operators in Hamiltonian quantum systems with $N $ degrees of freedom and finite-dimensional Hilbert space. We prove that the commutator norm $\lVert [A(t),B]\rVert$ is upper bounded by a topological combinatorial…
Out-of-time order correlators (OTOCs) are crucial tools for studying quantum chaos as they show distinct scrambling behavior for chaotic Hamiltonians. We calculate OTOC and analyze the quantum information scrambling in atom-field and…
Thermalization of chaotic quantum many-body systems under unitary time evolution is related to the growth in complexity of initially simple Heisenberg operators. Operator growth is a manifestation of information scrambling and can be…
We investigate the typicality of the growth behavior of the out-of-time-ordered commutator (OTOC) in the many-body localized (MBL) quantum spin chains across random disorder realizations. In the MBL phase of the Heisenberg XXZ chain, we…
We study out-of-time-ordered correlators (OTOC) in hard-core boson models with short-range and long-range hopping and compare the results to the OTOC in the Luttinger liquid model. For the density operator, a related `commutator function'…
The Lieb-Robinson theorem states that locality is approximately preserved in the dynamics of quantum lattice systems. Whenever one has finite-dimensional constituents, observables evolving in time under a local Hamiltonian will essentially…
We study equilibration of an isolated quantum system by mapping it onto a network of classical oscillators in Hilbert space. By choosing a suitable basis for this mapping, the degree of locality of the quantum system reflects in the…
A matrix model of an asymptotically free theory with a bound state is solved using a perturbative similarity renormalization group for hamiltonians. An effective hamiltonian with a small width, calculated including the first three terms in…
OTOC has been used to characterize the information scrambling in quantum systems. Recent studies showed that local conserved quantities play a crucial role in governing the relaxation dynamics of OTOC in non-integrable systems. In…
We propose new Lieb-Robinson bounds (bounds on the speed of propagation of information in quantum systems) with an explicit dependence on the interaction strengths of the Hamiltonian. For systems with more than two interactions it is found…
Lieb Robinson bounds quantify the maximal speed of information spreading in nonrelativistic quantum systems. We discuss the relation of Lieb Robinson bounds to out of time order correlators, which correspond to different norms of…
We consider the time evolution of the out-of-time-ordered correlator (OTOC) of two general observables $A$ and $B$ in a mean field chaotic quantum system described by a random Wigner matrix as its Hamiltonian. We rigorously identify three…
We consider a closed macroscopic quantum system in a pure state $\psi_t$ evolving unitarily and take for granted that different macro states correspond to mutually orthogonal subspaces $\mathcal{H}_\nu$ (macro spaces) of Hilbert space, each…
We study a system of a quantum particle interacting with a singular time-dependent uniformly rotating potential in 2 and 3 dimensions: in particular we consider an interaction with support on a point (rotating point interaction) and on a…
We establish Lieb-Thirring type inequalities for non self-adjoint relatively compact perturbations of certain operators of mathematical physics. We apply our results to quantum Hamiltonians of Schr{\"o}dinger and Pauli with constant…