Emergence of unitary symmetry of microcanonically truncated operators in chaotic quantum systems.

We study statistical properties of matrix elements of observables written in the energy eigenbasis and truncated to small microcanonical windows. We present numerical evidence indicating that for all few-body operators in chaotic many-body systems, truncated below a certain energy scale, collective statistical properties of matrix elements exhibit emergent unitary symmetry. Namely, we show that below a certain scale the spectra of the truncated operators exhibit universal behavior, matching our analytic predictions, which are numerically testable for system sizes beyond exact diagonalization.

Real-time broadening of bath-induced density profiles from closed-system correlation functions.

The Lindblad master equation is one of the main approaches to open quantum systems. While it has been widely applied in the context of condensed matter systems to study properties of steady states in the limit of long times, the actual route to such steady states has attracted less attention yet. Here, we investigate the nonequilibrium dynamics of spin chains with a local coupling to a single Lindblad bath and analyze the transport properties of the induced magnetization.

Eigenstate Thermalization Hypothesis and Its Deviations from Random-Matrix Theory beyond the Thermalization Time.

The eigenstate thermalization hypothesis explains the emergence of the thermodynamic equilibrium in isolated quantum many-body systems by assuming a particular structure of the observable's matrix elements in the energy eigenbasis. Schematically, it postulates that off-diagonal matrix elements are random numbers and the observables can be described by random matrix theory (RMT). To what extent a RMT description applies, more precisely at which energy scale matrix elements of physical operators become truly uncorrelated, is, however, not fully understood.

Nontrivial damping of quantum many-body dynamics.

Understanding how the dynamics of a given quantum system with many degrees of freedom is altered by the presence of a generic perturbation is a notoriously difficult question. Recent works predict that, in the overwhelming majority of cases, the unperturbed dynamics is just damped by a simple function, e.g.

Simulating Hydrodynamics on Noisy Intermediate-Scale Quantum Devices with Random Circuits.

In a recent milestone experiment, Google's processor Sycamore heralded the era of "quantum supremacy" by sampling from the output of (pseudo-)random circuits. We show that such random circuits provide tailor-made building blocks for simulating quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. Specifically, we propose an algorithm consisting of a random circuit followed by a trotterized Hamiltonian time evolution to study hydrodynamics and to extract transport coefficients in the linear response regime.

Eigenstate thermalization hypothesis beyond standard indicators: Emergence of random-matrix behavior at small frequencies.

Using numerical exact diagonalization, we study matrix elements of a local spin operator in the eigenbasis of two different nonintegrable quantum spin chains. Our emphasis is on the question to what extent local operators can be represented as random matrices and, in particular, to what extent matrix elements can be considered as uncorrelated. As a main result, we show that the eigenvalue distribution of band submatrices at a fixed energy density is a sensitive probe of the correlations between matrix elements.

Exponential damping induced by random and realistic perturbations.

Given a quantum many-body system and the expectation-value dynamics of some operator, we study how this reference dynamics is altered due to a perturbation of the system's Hamiltonian. Based on projection operator techniques, we unveil that if the perturbation exhibits a random-matrix structure in the eigenbasis of the unperturbed Hamiltonian, then this perturbation effectively leads to an exponential damping of the original dynamics. Employing a combination of dynamical quantum typicality and numerical linked cluster expansions, we demonstrate that our theoretical findings for random matrices can, in some cases, be relevant for the dynamics of realistic quantum many-body models as well.

Relaxation of dynamically prepared out-of-equilibrium initial states within and beyond linear response theory.

We consider a realistic nonequilibrium protocol, where a quantum system in thermal equilibrium is suddenly subjected to an external force. Due to this force, the system is driven out of equilibrium and the expectation values of certain observables acquire a dependence on time. Eventually, upon switching off the external force, the system unitarily evolves under its own Hamiltonian and, as a consequence, the expectation values of observables equilibrate towards specific constant long-time values.

Impact of eigenstate thermalization on the route to equilibrium.

The eigenstate thermalization hypothesis (ETH) and the theory of linear response (LRT) are celebrated cornerstones of our understanding of the physics of many-body quantum systems out of equilibrium. While the ETH provides a generic mechanism of thermalization for states arbitrarily far from equilibrium, LRT extends the successful concepts of statistical mechanics to situations close to equilibrium. In our work, we connect these cornerstones to shed light on the route to equilibrium for a class of properly prepared states.

Relation between far-from-equilibrium dynamics and equilibrium correlation functions for binary operators.

Linear response theory (LRT) is one of the main approaches to the dynamics of quantum many-body systems. However, this approach has limitations and requires, e.g.

Pull or Push? Octopuses Solve a Puzzle Problem.

Octopuses have large brains and exhibit complex behaviors, but relatively little is known about their cognitive abilities. Here we present data from a five-level learning and problem-solving experiment. Seven octopuses (Octopus vulgaris) were first trained to open an L shaped container to retrieve food (level 0).

Octopus arm movements under constrained conditions: adaptation, modification and plasticity of motor primitives.

The motor control of the eight highly flexible arms of the common octopus (Octopus vulgaris) has been the focus of several recent studies. Our study is the first to manage to introduce a physical constraint to an octopus arm and investigate the adaptability of stereotypical bend propagation in reaching movements and the pseudo-limb articulation during fetching. Subjects (N=6) were placed inside a transparent Perspex box with a hole at the center that allowed the insertion of a single arm.