Related papers: Fundamental Limits to Moore's Law
An indispensable part of our lives, computing has also become essential to industries and governments. Steady improvements in computer hardware have been supported by periodic doubling of transistor densities in integrated circuits over the…
Using sum rules and a new dipole-free sum-over-states expression, we calculate the fundamental limits of the dispersion of the real and imaginary parts of all electronic nonlinear-optical susceptibilities. As such, these general results can…
Critical quantum metrology aims to harness critical properties near quantum phase transitions to enhance parameter estimation precision. However, critical slowing down inherently limits the achievable precision within a finite evolution…
The physical limits to computation have been under active scrutiny over the past decade or two, as theoretical investigations of the possible impact of quantum mechanical processes on computing have begun to make contact with realizable…
We derive Moore-type upper bounds for regular simplicial complexes and present logarithmic lower bounds on their diameter based on minimum degree.
Topological mapping of a large physical system on a graph, and its decomposition using universal measures is proposed. We find inherent limits to the potential for optimization of a given system and its approximate representations by…
This paper presents two interesting scaling laws, which relate some critical exponents in the critical behavior of spherically symmetric gravitational collapses. These scaling laws are independent of the details of gravity theory under…
The traditional formulation of the ultimate goal of physics (in the narrower sense of axiomatic theory) involves the derivation of physical laws from first principles. Though, such option doesn't make things easier since the task of the…
Quantum systems are open, continually exchanging energy and information with the surrounding environment. This interaction leads to decoherence and decay of quantum states. In complex systems, formed by many particles, decay can become…
In this paper, we present a comprehensive system for the treatment of the topic of limits--conceptually, computationally, and formally. The system addresses fundamental linguistic flaws in the standard presentation of limits, which attempts…
Many physical systems share the property of scale invariance. Most of them show ordinary power-law scaling, where quantities can be expressed as a leading power law times a scaling function which depends on scaling-invariant ratios of the…
We give an upper bound on the largest eigenvalue of a graph of given order, size, and girth.
Limit theorems of strong law of large numbers and central limit theorem types are obtained for the compositions of independent identically distributed random unitary channels.
This article describes the various experimental bounds on the variation of the fundamental constants of nature. After a discussion on the role of fundamental constants, of their definition and link with metrology, the various constraints on…
Disclosure of scaling relationship between observable quantities gives direct information about dynamics of natural phenomenon. This is the main reason why scaling plays a key role in the methodology of natural sciences. In this talk, Part…
This work describes underlying features of the universe such as fundamental constants and cosmological parameters, conservation laws, baryon and lepton asymmetries, etc. in the context of local gauge theories for fundamental forces under…
We prove upper bounds on the face numbers of simplicial complexes in terms on their girths, in analogy with the Moore bound from graph theory. Our definition of girth generalizes the usual definition for graphs.
Although the brain has long been considered a potential inspiration for future computing, Moore's Law - the scaling property that has seen revolutions in technologies ranging from supercomputers to smart phones - has largely been driven by…
Properties of local and global slope of a function and its approximate critical points sets are studied in relation to determination of the function.
We describe here, for the first time, a lower bound on the total number of fundamental constants required for a mathematical description of our physical universe to be complete. The answer is shown to be one. The formal arithmetized…