No Arabic abstract
General acceptance of a mathematical proposition $P$ as a theorem requires convincing evidence that a proof of $P$ exists. But what constitutes convincing evidence? I will argue that, given the types of evidence that are currently accepted as convincing, it is inconsistent to deny similar acceptance to the evidence provided for the existence of proofs by certain randomized computations.
This paper describes in basic terms what a Thin Group is, as well as its uses in various subjects.
Quantum simulators are devices that actively use quantum effects to answer questions about model systems and, through them, real systems. Here we expand on this definition by answering several fundamental questions about the nature and use of quantum simulators. Our answers address two important areas. First, the difference between an operation termed simulation and another termed computation. This distinction is related to the purpose of an operation, as well as our confidence in and expectation of its accuracy. Second, the threshold between quantum and classical simulations. Throughout, we provide a perspective on the achievements and directions of the field of quantum simulation.
We consider idealized parton shower event generators that treat parton spin and color exactly, leaving aside the choice of practical approximations for spin and color. We investigate how the structure of such a parton shower generator is related to the structure of QCD. We argue that a parton shower with splitting functions proportional to $alpha_s$ can be viewed not just as a model, but as the lowest order approximation to a shower that is defined at any perturbative order. To support this argument, we present a formulation for a parton shower at order $alpha_s ^k$ for any $k$. Since some of the input functions needed are specified by their properties but not calculated, this formulation does not provide a useful recipe for an order $alpha_s ^k$ parton shower algorithm. However, in this formulation we see how the operators that generate the shower are related to operators that specify the infrared singularities of QCD.
We discuss a generalization of logic puzzles in which truth-tellers and liars are allowed to deviate from their pattern in case of one particular question: Are you guilty?
This paper aims at providing a global perspective on electromagnetic nonreciprocity and clarifying confusions that arose in the recent developments of the field. It provides a general definition of nonreciprocity and classifies nonreciprocal systems according to their linear time-invariant (LTI), linear time-variant (LTV) or nonlinear nonreciprocal natures. The theory of nonlinear systems is established on the foundation of the concepts of time reversal, time-reversal symmetry, time-reversal symmetry breaking and related Onsager- Casimir relations. Special attention is given to LTI systems, as the most common nonreciprocal systems, for which a generalized form of the Lorentz reciprocity theorem is derived. The delicate issue of loss in nonreciprocal systems is demystified and the so-called thermodynamics paradox is resolved from energy conservation considerations. The fundamental characteristics and applications of LTI, LTV and nonlinear nonreciprocal systems are overviewed with the help of pedagogical examples. Finally, asymmetric structures with fallacious nonreciprocal appearances are debunked.