Related papers: Universal Relation between Spectral and Wavefuncti…
The asymptotic behaviour near phase transitions can be suitably characterized by the scaling of $\Delta s/Q^2$ with $\epsilon=1-T/T_c$, where $\Delta s$ is the excess entropy and $Q$ is the order parameter. As $\Delta s$ is obtained by…
As part of the quest to uncover universal features of quantum dynamics, we study catastrophes that form in simple many-body wave functions after a quench, focusing on two-mode systems that include the two-site Bose Hubbard model, and under…
Two zero-range-interacting atoms in a circular, transversely harmonic waveguide are used as a test-bench for a quantitative description of the crossover between integrability and chaos in a quantum system with no selection rules. For such…
An energy eigenfunction in a classically chaotic system is known to have spatial correlations which (in the limit of small $\hbar$) are governed by a microcanonical distribution in the classical phase space. This result is valid, however,…
We investigate universal features of measurement-and-feedback control of quantum chaotic dynamics by examining the quantum Arnold cat map, a paradigmatic model of quantum chaos. Inspired by probabilistic control of classical chaos, our…
We experimentally study the critical properties of the non-equilibrium solid-liquid-like transition that takes place in vibrated granular matter. The critical dynamics is characterized by the coupling of the density field with the…
According to the quantum chaos paradigm, the nature of a system's classical dynamics, whether integrable or chaotic, is universally reflected in the fluctuations of its quantum spectrum. However, since many-body spectra in the mean field…
Chaotic evolutions exhibit exponential sensitivity to initial conditions. This suggests that even very small perturbations resulting from weak coupling of a quantum chaotic environment to the position of a system whose state is a non-local…
The explicit analytical expression for the distribution function of parametric derivatives of energy levels ("level velocities") with respect to a random change of scattering potential is derived for the chaotic quantum systems belonging to…
A general formulation of translationally invariant, parametrically correlated random matrix ensembles, is used to classify universality in correlation functions. Surprisingly, the range of possible physical systems is bounded, and can be…
The decoherence phenomenon arising from an environmental monitoring of the state of a quantum system, as opposed to monitoring of a preferred observable, is worked out in detail using two equivalent formulations, namely, repeated…
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…
Quantum chaotic systems with one-dimensional spectra follow spectral correlations of orthogonal (OE), unitary (UE), or symplectic ensembles (SE) of random matrices depending on their invariance under time reversal and rotation. In this…
We study a new statistics of wave functions in several chaotic and disordered systems: the random matrix model, band random matrix model, the Lipkin model, chaotic quantum billiard and the 1D tight-binding model. Both numerical and…
We study the $n$-level spectral correlation functions of classically chaotic quantum systems without time-reversal symmetry. According to Bohigas, Giannoni and Schmit's universality conjecture, it is expected that the correlation functions…
Generic and significant regularities are shown to occur in the quasienergy spectra of the generalized quantum kicked particle for arbitrary quasimomentum, a quantity most relevant in atom-optics experimental realizations of this…
Quantum phase transitions reflect singular changes taking place in a many-body ground state, however, computing and analyzing large-scale critical wave functions constitutes a formidable challenge. New physical insights into the sub-Ohmic…
We investigate dissipative dynamical systems under the influence of an external driving with two or more frequencies. Our main quantities of interest are long-time averages of expectation values which turn out to exhibit universal features.…
Second-order phase transitions are characterised by critical scaling and universality. The singular behaviour of thermodynamic quantities at the transition, in particular, is determined by critical exponents of the universality class of the…
Universality, encompassing critical exponents, scaling functions, and dimensionless quantities, is fundamental to phase transition theory. In finite systems, universal behaviors are also expected to emerge at the pseudocritical point.…