Biological in forma tion TWO TECHNOLOGIESHistorically, the cost of computation has been directly related to the energy used in that computation. Today's electronic wristwatch does far more computation than the Eniac did when it was built. It is not the computation itself that costs-it is the energy consumed, and the system overhead required to supply that energy and to get rid of the heat: the boxes, the connectors, the circuit boards, the power supply, the fans, all of the superstructure that makes the system work. As the technology has evolved, it has always moved in the direction of lower energy per unitcomputation. That trend took us from vacuum tubes to transisitors, and from transistors to integrated circuits. It was the force behind the transition from n-MOS to CMOS technology that happened less than ten years ago. Today, it still is pushing us down to submicron sizes in semiconductor technology.So it pays to look at just how much capability the nervous system has in computation.There is a myth that the nervous system is slow, is built out of slimy stuff, uses ions instead of electrons, and is therefore ineffective. When the Whirlwind computer was first built back at M.I.T., they made a movie about it, which was called "Faster than Thought." The Whirwind did less computation than your wristwatch does. We have evolved by a factor of about 10 million in the cost of computation since the Whirlwind. Yet we still cannot begin to do the simplest computations that can be done by the brains of insects, let alone handle the tasks routinely performed by the brains of humans. So we have finally come to the point where we can see what is difficult and what is easy. Multiplying numbers to balance a bank account is not that difficult. What is difficult is processing the poorly conditioned sensory information that comes in through the lens of an eye or through the eardrum.A typical microprocessor does about 10 million operations/s, and uses about 1 W. In round numbers, it cost us about l O -' J to do one operation, the way we do it today, on a single chip. If we go off the chip to the box level, a whole computer uses about 10-5J/operation. Awhole computer is thus about two orders of magnitude less efficient than is a single chip.Back in the late 1960's we analyzed what would limit the electronic device technology as we know it; those calculations have held up quite well to the present [I]. The standard i ntegrated-ci rcu it fabricat ion processes available today allow usto build transistorsthat have minimum dimensions of about 1 p m). By ten years from now, we will have reduced these dimensions by another factor of 10, and we will be getting close to the fundamental physical limits: if we make the devices any smaller, they will stop working. It is conceiveable that a whole new class of devices will be invented-devices that are not subject to the same limitations. But certainly the ones we have thought of up to now-including the superconducting ones-will not make our circuits more than abouttwoordersof magnitude more den...
A strictly diabatic electronic basis is defined as one for which all components of the nuclear momentum coupling vanish. We examine the possibility that such a basis may exist, and we find that, in general, it does not. The only important exception is for diatomic states of the same symmetry. We also consider some conditions for the definition of an approximately diabatic electronic basis. For molecular systems with three or more nuclei, one can obtain useful approximate diabatic basis sets if the transverse (solenoidal) part of the coupling is negligible; this may occur, for example, if the part of the coupling due to the internuclear-distance dependence of the configurational wave functions is negligible as compared to that due to the internuclear-distance dependence of the configurational coefficients. We derive a criterion showing that such approximations may be useful and accurate if the role of the coupling is important over regions of sufficiently small linear dimensions.
We show how the presence of a conical intersection in the adiabatic potential energy hypersurface can be handled by including a new vector potential in the nuclear-motion Schrödinger equation. We show how permutational symmetry of the total wave function with respect to interchange of nuclei can be enforced in the Born–Oppenheimer approximation both in the absence and the presence of conical intersections. The treatment of nuclear-motion wave functions in the presence of conical intersections and the treatment of nuclear-interchange symmetry in general both require careful consideration of the phases of the electronic and nuclear-motion wave functions, and this is discussed in detail.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.