Related papers: Spatial Correlations in Chaotic Eigenfunctions
An initially homogeneous freely evolving fluid of inelastic hard spheres develops inhomogeneities in the flow field (vortices) and in the density field (clusters), driven by unstable fluctuations. Their spatial correlations, as measured in…
We show that, in the semiclassical limit and whenever the elements of the Hamiltonian matrix are random enough, the eigenvectors of strongly chaotic time-independent systems in ordered bases can on average be exponentially localized across…
We show how a recently introduced statistics [Patil et al, Phys. Rev. Lett. 81 5878 (2001)] provides a direct relationship between dimension and predictability in spatiotemporal chaotic systems. Regions of low dimension are identified as…
Shannon entropies of one- and two-electron atomic structure factors in the position and momentum representations are used to examine the behavior of the off-diagonal elements of density matrices with respect to the uncertainty principle and…
Using the random matrix description of open quantum chaotic systems we calculate in closed form the universal autocorrelation function and the probability distribution of the total photodissociation cross section in the regime of quantum…
The scattering matrix approach is employed to determine a joint probability density function of reflection eigenvalues for chaotic cavities coupled to the outside world through both ballistic and tunnel point contacts. Derived under…
The apparent randomness of chaotic eigenstates in interacting quantum systems hides subtle correlations dynamically imposed by their finite energy per particle. These correlations are revealed when Berrys approach for chaotic eigenfunctions…
Quantum chaos is linked to Brownian diffusion of the underlying quantum energy level-spacing sequences. The level-spacings viewed as functions of their order execute random walks which imply uncorrelated random increments of the…
This paper uses the assumptions of ergodicity and a microcanonical distribution to compute estimates of the largest Lyapunov exponents in lower-dimensional Hamiltonian systems. That the resulting estimates are in reasonable agreement with…
In a previous Letter [Phys. Rev. Lett. 77, 4158 (1996)], a new correlation measure was introduced that sensitively probes phase space localization properties of eigenstates. It is based on a system's response to varying an external…
Using the supersymmetry technique, we calculate the joint distribution of local densities of electron wavefunctions in two coupled disordered or chaotic quantum billiards. We find novel spatial correlations that are absent in a single…
We define auto- and cross-correlation functions capable to capture dynamical characteristics induced by local phase space structures in a general dynamical system. These correlation functions are calculated in the Standard Map for a range…
A chain of coupled chaotic elements with different time scales is studied. In contrast with the adiabatic approximation, we find correlations between faster and slower elements when the differences in the time scales of the elements lie…
We consider stochastically quantized self-interacting scalar fields as suitable models to generate dark energy in the universe. Second quantization effects lead to new and unexpected phenomena is the self interaction strength is strong. The…
The Quantum Ergodic Conjecture equates the Wigner function for a typical eigenstate of a classically chaotic Hamiltonian with a delta-function on the energy shell. This ensures the evaluation of classical ergodic expectations of simple…
We discuss a modification to Random Matrix Theory eigenstate statistics, that systematically takes into account the non-universal short-time behavior of chaotic systems. The method avoids diagonalization of the Hamiltonian, instead…
We discuss a general and efficient approach for "bootstrapping" short-time correlation data in chaotic or complex quantum systems to obtain information about long-time dynamics and stationary properties, such as the local density of states.…
We show that "dry" active nematics, e.g. collections of shaken elongated granular particles, exhibit large-scale spatiotemporal chaos made of interacting dense, ordered, band-like structures in a parameter region including the linear onset…
Quantum mechanics requires that identical particles are treated as indistinguishable. This requirement leads to correlations in the fluctuating properties of a system. Theoretical predictions are made for an experiment on a multi-lead…
Spatial correlation functions provide a glimpse into the quantum correlations within a quantum system. Ions in a linear trap collectively form a nonuniform, discretized background on which a scalar field of phonons propagates. Trapped ions…