Related papers: Complexity in some Physical Systems
For quantum many-body systems in one dimension, computational complexity theory reveals that the evaluation of ground-state energy remains elusive on quantum computers, contrasting the existence of a classical algorithm for temperatures…
The normalized multiplicity moments and their relation with soft and hard processes in relativistic heavy ion collisions are analyzed in a general two-component model. It is found that, the strong fluctuations in binary collision number N_c…
We survey classical and recent developments in numerical linear algebra, focusing on two issues: computational complexity, or arithmetic costs, and numerical stability, or performance under roundoff error. We present a brief account of the…
Recently it has been argued that entropy can be a direct measure of complexity, where the smaller value of entropy indicates lower system complexity, while its larger value indicates higher system complexity. We dispute this view and…
We study a class of functional problems reducible to computing $f^{(n)}(x)$ for inputs $n$ and $x$, where $f$ is a polynomial-time bijection. As we prove, the definition is robust against variations in the type of reduction used in its…
We investigate the notion of complexity for finitely presented groups and the related notion of complexity for three-dimensional manifolds. We give two-sided estimates on the complexity of all the Milnor groups (the finite groups with free…
The determination of supersymmetric parameters at the LHC in favorable as well as difficult scenarios is presented. If discovered and measured at the LHC and the ILC, supersymmetry may provide a link between collider physics and cosmology.
A kind of doubly special relativity theory proposed by J. Magueijo and L. Smolin [Phys. Rev. Lett. 88, 190403 (2002)] is analysed. It is shown that this theory leads to serious physical difficulties in interpretation of kinematical…
A laser model is formulated in terms of quantum harmonic oscillators. Emitters in the low lasing states are usual harmonic oscillators, and emitters in the upper states are inverted harmonic oscillators. Diffusion coefficients, consistent…
Scientists have demonstrated that quantum computing has presented novel approaches to address computational challenges, each varying in complexity. Adapting problem-solving strategies is crucial to harness the full potential of quantum…
I present a brief review of the existing models for particle multiplicity evaluation in heavy ion collisions which are at our disposal in the form of Monte Carlo simulators. Models are classified according to the physical mechanisms with…
A general condition determining the optimal performance of a complex system has not yet been found and the possibility of its existence is unknown. To contribute in this direction, an optimization algorithm as a complex system is presented.…
We study the complexity of deterministic and probabilistic inversions of partial computable functions on the reals.
An accurate assessment of a model's complexity is crucial for topics such as interpretation, generalization, and model selection. However, most existing complexity measures either rely on heuristic assumptions or are computationally…
Recently the adaption problem of Information-Based Complexity (IBC) for linear problems in the randomized setting was solved in Heinrich (J. Complexity 82, 2024, 101821). Several papers treating further aspects of this problem followed.…
A new equation for describing physical systems with radiation is obtained in this paper. Examples of such systems can be found in plasma physics, accelerator physics (synchrotron radiation) and astrophysics (gravitational waves). The new…
We define the complexity of a continuous-time linear system to be the minimum number of bits required to describe its forward increments to a desired level of fidelity, and compute this quantity using the rate distortion function of a…
Methods for the reduction of the complexity of computational problems are presented, as well as their connections to renormalization, scaling, and irreversible statistical mechanics. Several statistically stationary cases are analyzed; for…
It is well-known that in fluid dynamics an alternative to customary direct solution methods (based on the discretization of the fluid fields) is provided by so-called \emph{particle simulation methods}. Particle simulation methods rely…
In the first part of this paper, we present a unified framework for analyzing the algorithmic complexity of any optimization problem, whether it be continuous or discrete in nature. This helps to formalize notions like "input", "size" and…