Related papers: Numerical search for a fundamental theory
Grover's algorithm relies on the superposition and interference of quantum mechanics, which is more efficient than classical computing in specific tasks such as searching an unsorted database. Due to the high complexity of quantum…
Due to M\"{u}ller's theorem, the Kolmogorov complexity of a string was shown to be equal to its quantum Kolmogorov complexity. Thus there are no benefits to using quantum mechanics to compress classical information. The quantitative amount…
An uncomplicated and easily handling prescription that converts the task of checking the unitarity of massive, topologically massive, models into a straightforward algebraic exercise, is developed. The algorithm is used to test the…
Cosmic Probes of Fundamental Physics take two primary forms: Very high energy particles (cosmic rays, neutrinos, and gamma rays) and gravitational waves. Already today, these probes give access to fundamental physics not available by any…
In an attempt to progress towards proving the conjecture the numerical range W (A) is a 2--spectral set for the matrix A, we propose a study of various constants. We review some partial results, many problems are still open. We describe our…
Depth is a complexity measure for natural systems of the kind studied in statistical physics and is defined in terms of computational complexity. Depth quantifies the length of the shortest parallel computation required to construct a…
The values of the fundamental constants such as $\mu = m_P/m_e$, the proton to electron mass ratio and $\alpha$, the fine structure constant, are sensitive to the product $\sqrt{\zeta_x^2(w+1)}$ where $\zeta_x$ is a coupling constant…
We discuss several ways of illustrating fundamental concepts in statistical and thermal physics by considering various models and algorithms. We emphasize the importance of replacing students' incomplete mental images by models that are…
A common statistical task lies in showing asymptotic normality of certain statistics. In many of these situations, classical textbook results on weak convergence theory suffice for the problem at hand. However, there are quite some…
Following the successful prediction of an exact value for the fine structure constant later confirmed to differ numerically from the centre value of the latest experimental recommended CODATA range by 10^{-12}, further analysis and…
Algorithmic approach is based on the assumption that any quantum evolution of many particle system can be simulated on a classical computer with the polynomial time and memory cost. Algorithms play the central role here but not the…
Taking the view that computation is after all physical, we argue that physics, particularly quantum physics, could help extend the notion of computability. Here, we list the important and unique features of quantum mechanics and then…
We outline a program with the potential to solve both the cosmological constant and quantum gravity problems within a single, comprehensive framework, one that is formulated entirely in four spacetime dimensions. The program is based on an…
We search a simplest and minimal way to determine whether a given quantum system is entangled or separable. For this end, we propose binary correlation measurements in which restricted knowledge of only zero or non-zero correlations is…
Probabilistic algorithms are applied to prove theorems about the finite general linear and unitary groups which are typically proved by techniques such as character theory and Moebius inversion. Among the theorems studied are Steinberg's…
For a real or complex one-dimensional map satisfying a weak hyperbolicity assumption, we study the existence and statistical properties of physical measures, with respect to geometric reference measures. We also study geometric properties…
We explore the effects of a positive cosmological constant on astrophysical and cosmological configurations described by a polytropic equation of state. We derive the conditions for equilibrium and stability of such configurations and…
Physical systems, characterized by an ensemble of interacting elementary constituents, can be represented and studied by different algebras of observables or operators. For example, a fully polarized electronic system can be investigated by…
A brief overview is given on precision determinations of values of the fundamental physical constants and the search for their variation with time by means of precision spectroscopy in the optical domain.
Mathematical inequalities, combined with atomic-physics sum rules, enable one to derive lower and upper bounds for the Rosseland and/or Planck mean opacities. The resulting constraints must be satisfied, either for pure elements or…