相关论文: A route from maximal chaoticity to integrability

The study of chaos and complexity in non-Hermitian quantum systems poses significant challenges due to the emergence of complex eigenvalues in their spectra. Recently, the singular value decomposition (SVD) method was proposed to address…

The route to chaos and phase dynamics in a rotating shallow-water model were rigorously examined using a five-mode Galerkin truncated system with complex variables. This system is valuable for investigating how large/meso-scales destabilize…

We apply a notion of quantum complexity, called "Krylov complexity", to study the evolution of systems from integrability to chaos. For this purpose we investigate the integrable XXZ spin chain, enriched with an integrability breaking…

We propose an extension of the Sachdev-Ye-Kitaev (SYK) model that exhibits a quantum phase transition from the previously identified non-Fermi liquid fixed point to a Fermi liquid like state, while still allowing an exact solution in a…

A remarkable feature of chaos in many-body quantum systems is the existence of a bound on the quantum Lyapunov exponent. An important question is to understand what is special about maximally chaotic systems which saturate this bound. Here…

The multiscaling properties of the mixed Obukhov-Novikov shell model of turbulence are investigated numerically and compared with those of the complex GOY model, mostly studied in the recent years. Two types of generic singular fluctuations…

Quantum entanglement and quantum magic are two distinct fundamental resources that enable quantum systems to exhibit complex phenomena beyond the capabilities of classical computer simulations. While quantum entanglement has been…

Nonperturbative formulation of the Sachdev-Ye-Kitaev (SYK) model is discussed. The partition function of the model can be represented as a functional integral over the Grassmann variables in Euclidean time which is well defined but it…

We consider a recent proposal for a physical realization of the Sachdev-Ye-Kitaev (SYK) model in the zeroth-Landau-level sector of an irregularly-shaped graphene flake. We study in detail charge transport signatures of the unique non-Fermi…

{}From Feynman's path integral, we derive quasi-classical quantization rules in supersymmetric quantum mechanics (SUSY-QM). First, we derive a SUSY counterpart of Gutzwiller's formula, from which we obtain the quantization rule of Comtet,…

The goal of this note is to explore the behavior of effective action in the SYK model with general continuous global symmetries. A global symmetry will decompose the whole Hamiltonian of a many-body system to several single charge sectors.…

Time-independent Hamiltonian flows are viewed as geodesic flows in a curved manifold, so that the onset of chaos hinges on properties of the curvature two-form entering into the Jacobi equation. Attention focuses on ensembles of orbit…

The Family-Vicsek scaling is a fundamental framework for understanding surface growth in non-equilibrium classical systems, providing a universal description of temporal surface roughness evolution. While universal scaling laws are well…

This paper considers a type of generalized large $q$ SYK models which include multi-body interactions between Majorana fermions. We derive an effective action in the limit of large $N$ and large $q$ (with ${~q^2\over N} $ small), and find a…

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…

Complex quantum systems -- composed of many, interacting particles -- are intrinsically difficult to model. When a quantum many-body system is subject to disorder, it can undergo transitions to regimes with varying non-ergodic and localized…

We use superspace methods to study an SYK-like model with $\mathcal N=2$ supersymmetry in one dimension, and an analog of this model in two dimensions. We find the four-point function as an expansion in the basis of eigenfunctions of the…

The supersymmetry invariant integrable structure of two-dimensional superconformal field theory is considered. The classical limit of the corresponding infinite family of integrals of motion (IM) coincide with the family of IM of SUSY N=1…

The robustness of the universality class concept of the chaotic transition was investigated by analytically obtaining its critical exponent for a wide class of maps. In particular, we extended the existing one-dimensional chaotic maps,…

Strongly correlated metals comprise an enduring puzzle at the heart of condensed matter physics. Commonly a highly renormalized heavy Fermi liquid occurs below a small coherence scale, while at higher temperatures a broad incoherent regime…