Related papers: Scale-invariant critical dynamics at eigenstate tr…

Understanding quantum phase transitions in highly excited Hamiltonian eigenstates is currently far from being complete. It is particularly important to establish tools for their characterization in time domain. Here we argue that a scaled…

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…

Recent observation for scale invariant neural avalanches in the brain have been discussed in details in the scientific literature. We point out, that these results do not necessarily imply that the properties of the underlying neural…

The emergence of quantum chaos in a system of trapped interacting bosons with externally impressed rotation is studied through spectral form factor (SFF) and power spectrum using exact diagonalization. Two distinct interaction regimes are…

We explore the concept of scaling invariance in a type of dynamical systems that undergo a transition from order (regularity) to disorder (chaos). The systems are described by a two-dimensional, nonlinear mapping that preserves the area in…

The spectral form factor (SFF) captures universal spectral fluctuations as signatures of quantum chaos, and has been instrumental in advancing multiple frontiers of physics including the studies of black holes and quantum many-body systems.…

Through a combination of rigorous analytical derivations and extensive numerical simulations, this work reports an exotic multifractal behavior, dubbed "logarithmic multifractality", in effectively infinite-dimensional systems undergoing…

We consider the most general scale invariant radial Hamiltonian allowing for anisotropic scaling between space and time. We formulate a renormalisation group analysis of this system and demonstrate the existence of a quantum phase…

We clarify novel forms of scaling functions of conductance, critical conductance distribution and localization length in a disorder-driven quantum phase transition between band insulator and Weyl semimetal phases. Quantum criticality of the…

Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…

We develop a theory of finite-time scaling for dynamic quantum criticality by considering the competition among an external time scale, an intrinsic reaction time scale and an imaginary time scale arising respectively from an external…

Scale invariance usually occurs in extended systems where correlation functions decay algebraically in space and/or time. Here we introduce a new type of scale invariance, occurring in the distribution functions of physical observables. At…

In quantum chaotic systems, the spectral form factor (SFF), defined as the Fourier transform of the two-level spectral correlation function, is known to follow random matrix theory (RMT), namely a 'ramp' followed by a 'plateau' in…

We demonstrate the existence of a universal transition from a continuous scale invariant phase to a discrete scale invariant phase for a class of one-dimensional quantum systems with anisotropic scaling symmetry between space and time.…

Scale invariance has received very little attention in physics. Nevertheless, it provides a natural conceptual foundation for a relational understanding of the universe, where absolute size loses meaning and only dimensionless ratios retain…

We use multifractal finite-size scaling to perform a high-precision numerical study of the critical properties of the Anderson localization-delocalization transition in the unitary symmetry class, considering the Anderson model including a…

To understand the finite-size-scaling properties of phases transitions in classical and quantum models in the presence of quenched disorder, it has proven to be fruitful to introduce the notion of a finite-size-pseudo-critical point in each…

Scale invariance is a hallmark of criticality in complex dynamical systems. While random external inputs or tunable stochastic interactions are typically required to produce critical behavior, it remains unclear whether scale-invariant…

Random matrix models provide a phenomenological description of a vast variety of physical phenomena. Prominent examples include the eigenvalue statistics of quantum (chaotic) systems, which are conveniently characterized using the spectral…

Due to their analytical tractability, random matrix ensembles serve as robust platforms for exploring exotic phenomena in systems that are computationally demanding. Building on a companion letter [arXiv:2312.17481], this paper investigates…