Related papers: Streamlined Krylov construction and classification…

A diagrammatic method is presented for averaging over the circular ensemble of random-matrix theory. The method is applied to phase-coherent conduction through a chaotic cavity (a ``quantum dot'') and through the interface between a normal…

Neutral atom arrays driven into Rydberg states constitute a promising approach for realizing programmable quantum systems. Enabled by strong interactions associated with Rydberg blockade, they allow for simulation of complex spin models and…

Floquet engineering is the concept of tailoring a system by a periodic drive. It has been very successful in opening new classes of Hamiltonians to the study with ultracold atoms in optical lattices, such as artificial gauge fields,…

In this paper, the mathematical framework providing a description of completely positive and trace preserving dynamics of open quantum systems is addressed. Special case of time-dependent Lindbladian governed by periodic Hamiltonian is…

We describe a simple quantum algorithm to simulate time-dependent Hamiltonian, extending the methodology of quantum signal processing. The framework achieves optimal scaling up to some factor with respect to other parameters, and nearly…

The complexity of quantum evolutions can be understood by examining their dispersion in a chosen basis. Recent research has stressed the fact that the Krylov basis is particularly adept at minimizing this dispersion [V. Balasubramanian et…

Floquet engineering, i.e. driving the system with periodic Hamiltonians, not only provides great flexibility in analog quantum simulation, but also supports phase structures of great richness. It has been proposed that Floquet systems can…

We investigate the dynamics of quantum scrambling, characterized by the out-of-time ordered correlators (OTOCs), in a non-Hermitian quantum kicked rotor subjected to quasi-periodical modulation in kicking potential. Quasi-periodic…

We give a general overview of the high-frequency regime in periodically driven systems and identify three distinct classes of driving protocols in which the infinite-frequency Floquet Hamiltonian is not equal to the time-averaged…

We uncover a dynamical entanglement transition in a monitored quantum system that is heralded by a local order parameter. Classically, chaotic systems can be stochastically controlled onto unstable periodic orbits and exhibit controlled and…

We investigate signatures of quantum chaos within Ising spin chains subjected to transverse and longitudinal fields, incorporating both local (nearest-neighbor) and non-local (long-range) couplings. While local Ising models may exhibit…

The Birkhoff Ergodic Theorem asserts under mild conditions that Birkhoff averages (i.e. time averages computed along a trajectory) converge to the space average. For sufficiently smooth systems, our small modification of numerical Birkhoff…

A wide variety of complex systems exhibit large fluctuations both in space and time that often can be attributed to the presence of some kind of critical phenomena. Under such critical scenario it is well known that the properties of the…

The generic behavior of quantum systems has long been of theoretical and practical interest. Any quantum process is represented by a sequence of quantum channels. We consider general ergodic sequences of stochastic channels with arbitrary…

We propose a Markov chain simulation method to generate simple connected random graphs with a specified degree sequence and level of clustering. The networks generated by our algorithm are random in all other respects and can thus serve as…

We propose an efficient procedure for numerically evolving the Delta Kicked Harmonic Oscillator. The method allows for longer and more accurate simulations of the system as well as a simple procedure for calculating the systems Floquet…

Statistical mechanics is founded on the assumption that all accessible configurations of a system are equally likely. This requires dynamics that explore all states over time, known as ergodic dynamics. In isolated quantum systems, however,…

The recent years have witnessed a growing interest for covariant Lyapunov vectors (CLVs) which span local intrinsic directions in the phase space of chaotic systems. Here we review the basic results of ergodic theory, with a specific…

In this work, we explore in detail, the time evolution of Krylov complexity. We demonstrate, through analytical computations, that in finite many-body systems, while ramp and plateau are two generic features of Krylov complexity, the manner…

Many scientific applications require the evaluation of the action of the matrix function over a vector and the most common methods for this task are those based on the Krylov subspace. Since the orthogonalization cost and memory requirement…