相关论文: Real chaos and complex time

In this note we continue the study of imaginary multiplicative chaos $\mu_\beta := \exp(i \beta \Gamma)$, where $\Gamma$ is a two-dimensional continuum Gaussian free field. We concentrate here on the fine-scale analytic properties of…

We study algebraic complexity classes and their complete polynomials under \emph{homogeneous linear} projections, not just under the usual affine linear projections that were originally introduced by Valiant in 1979. These reductions are…

We study complex eigenvalues of large $N\times N$ symmetric random matrices of the form ${\cal H}=\hat{H}-i\hat{\Gamma}$, where both $\hat{H}$ and $\hat{\Gamma}$ are real symmetric, $\hat{H}$ is random Gaussian and $\hat{\Gamma}$ is such…

Chaos reveals a fundamental paradox in the scientific understanding of Complex Systems. Although chaotic models may be mathematically deterministic, they are practically non-determinable due to the finite precision, which is inherent in all…

We take into account the dynamics of three types of models of rotating galaxies in polar coordinates in a rotating frame. Due to non-axisymmetric potential perturbations, the angular momentum varies with time, and the kinetic energy depends…

The final fate of the spherically symmetric collapse of a perfect fluid which follows the $\gamma$-law equation of state and adiabatic condition is investigated. Full general relativistic hydrodynamics is solved numerically using a retarded…

We present quantum graphs with remarkably regular spectral characteristics. We call them {\it regular quantum graphs}. Although regular quantum graphs are strongly chaotic in the classical limit, their quantum spectra are explicitly…

We carry out an analysis of the cosmological perturbations in general relativity for three different models which are good candidates to describe the current acceleration of the Universe. These three set-ups are described classically by…

Let $f \colon X \to X$ be a continuous map on a compact metric space $X$ and let $\alpha_f$, $\omega_f$ and $ICT_f$ denote the set of $\alpha$-limit sets, $\omega$-limit sets and nonempty closed internally chain transitive sets…

A number of random matrix ensembles permitting exact determination of their eigenvalue and eigenvector statistics maintain this property under a rank $1$ perturbation. Considered in this review are the additive rank $1$ perturbation of the…

It is shown that distributed chaos with spontaneously broken time translational symmetry (homogeneity) has a stretched exponential frequency spectrum $E(f) \propto \exp-(f/f_0)^{1/2}$. Good agreement has been established with a laboratory…

We study optimization problems that are neither approximable in polynomial time (at least with a constant factor) nor fixed parameter tractable, under widely believed complexity assumptions. Specifically, we focus on Maximum Independent…

Quantum chaotic systems are conjectured to display a spectrum whose fine-grained features (gaps and correlations) are well described by Random Matrix Theory (RMT). We propose and develop a complementary version of this conjecture: quantum…

We observe critical phenomena in spherical collapse of radiation fluid. A sequence of spacetimes $\cal{S}[\eta]$ is numerically computed, containing models ($\eta\ll 1$) that adiabatically disperse and models ($\eta\gg 1$) that form a black…

For an even integer t \geq 2, the Matchings Connecivity matrix H_t is a matrix that has rows and columns both labeled by all perfect matchings of the complete graph K_t on t vertices; an entry H_t[M_1,M_2] is 1 if M_1\cup M_2 is a…

We investigate spectral quantities of quantum graphs by expanding them as sums over pseudo orbits, sets of periodic orbits. Only a finite collection of pseudo orbits which are irreducible and where the total number of bonds is less than or…

We study the quantum coherent-tunneling between two Bose-Einstein condensates separated through an oscillating trap potential. The cases of slowly and rapidly varying in time trap potential are considered. In the case of a slowly varying…

Matter interacting classically with gravity in 3+1 dimensions usually gives rise to a continuum of degrees of freedom, so that, in any attempt to quantize the theory, ultraviolet divergences are nearly inevitable. Here, we investigate…

We introduce a complex-plane generalization of the consecutive level-spacing distribution, used to distinguish regular from chaotic quantum spectra. Our approach features the distribution of complex-valued ratios between nearest- and…

We show that the imaginary multiplicative chaos $\exp(i\beta \Gamma)$ determines the gradient of the underlying field $\Gamma$ for all log-correlated Gaussian fields with covariance of the form $-\log |x-y| + g(x,y)$ with mild regularity…