相关论文: Space-Time Complexity in Hamiltonian Dynamics

Time-dependent potentials are common in galactic systems that undergo significant evolution, interactions, or encounters with other galaxies, or when there are dynamic processes like star formation and merging events. Recent studies show…

Many useful concepts for a quantum theory of scattering and decay (like Lippmann-Schwinger kets, purely outgoing boundary conditions, exponentially decaying Gamow vectors, causality) are not well defined in the mathematical frame set by the…

We analyze the equilibrium statistical mechanics of canonical, non-canonical and non-Hamiltonian equations of motion by throwing light into the peculiar geometric structure of phase space. Some fundamental issues regarding time translation…

We study Hamiltonian flows in a real separable Hilbert space endowed with a symplectic structure. Measures on the Hilbert space that are invariant with respect to the flows of completely integrable Hamiltonian systems are investigated.…

In this paper a new formulation of quantum dynamics of totally constrained systems is developed, in which physical quantities representing time are included as observables. In this formulation the hamiltonian constraints are imposed on a…

Spread complexity uses the distribution of support of a time-evolving state in the Krylov basis to quantify dispersal across accessible dimensions of a Hilbert space. Here, we describe how variations in initial conditions, the Hamiltonian,…

There is no single universally accepted definition of "Complexity". There are several perspectives on complexity and what constitutes complex behaviour or complex systems, as opposed to regular, predictable behaviour and simple systems. In…

The dynamical instability of rough hard-disk fluids in two dimensions is characterized through the Lyapunov spectrum and the Kolmogorov-Sinai entropy, $h_{KS}$, for a wide range of densities and moments of inertia $I$. For small $I$ the…

Reminiscent of physical phase transitions separatrices divide the phase space of dynamical systems with multiple equilibria into regions of distinct flow behavior and asymptotics. We introduce complex time in order to study corresponding…

We study operator complexity on various time scales with emphasis on those much larger than the scrambling period. We use, for systems with a large but finite number of degrees of freedom, the notion of K-complexity employed in…

We introduce the notion of a real form of a Hamiltonian dynamical system in analogy with the notion of real forms for simple Lie algebras. This is done by restricting the complexified initial dynamical system to the fixed point set of a…

Measuring the complexity of high-dimensional data in physical systems becomes a critical factor in determining the information and quality of the systems. However, traditional metrics, such as Lyapunov exponent, fractal dimension, and…

The dynamics by iteration of a function on a compact metric space, sometimes called a cascade, can be extended to the dynamics of a closed relation on such a space. Here we apply this relation dynamics to study semiflows (and their relation…

The Liouville theorem is a fundamental concept in understanding the properties of systems that adhere to Hamilton's equations. However, the traditional notion of the theorem may not always apply. Specifically, when the entropy gradient in…

Integrability in string/field theories is known to emerge when considering dynamics in the moduli space of physical theories. This implies that one has to look at the dynamics with respect to unusual time variables like coupling constants…

We consider the number of Bowen sets which are necessary to cover a large measure subset of the phase space. This introduce some complexity indicator characterizing different kind of (weakly) chaotic dynamics. Since in many systems its…

A new functional for the entropy that is asymptotically correct both in the high and low density limits is proposed. The new form is [ S=S^{(id)}+S^{(ln)}+S^{(r)}+S^{(c)} ] where the new term S^{(c)} depends on the p-bodies density…

Chaos and complexity entail an entropic and computational obstruction to describing a system, and thus are intrinsically difficult to characterize. In this paper, we consider time evolution by Gaussian Unitary Ensemble (GUE) Hamiltonians…

Information entropy is applied to the analysis of time series generated by dynamical systems. Complexity of a temporal or spatio-temporal signal is defined as the difference between the sum of entropies of the local linear regions of the…

We review in detail the Hamiltonian dynamics for constrained systems. Emphasis is put on the total Hamiltonian system rather than on the extended Hamiltonian system. We provide a systematic analysis of (global and local) symmetries in total…