Now, consider a scenario involving a dynamic CMOS logic circuit where all the CMOS transistors have zero shunt capacitance (and hence infinite impedance paths at suitable junctions to ground). There is no location to store the charge in the alleged precharge interval and therefore also no source for the pull down transistor network to sink the charge from a storage device in the evaluation interval. With no capacitances in this network, how would a dynamic CMOS logic circuit work? While this is a fairly simple example of the absence of parasitic capacitance leading to what the idealists might regard as a paradox, there are several other examples in electromagnetic theory where capacitances and even inductances are unavoidable and in fact predicted by theory, e.g. in transmission lines, interconnects, ground bounces, etc. The moral is not to treat the word 'parasitic' in parasitic elements too literally, and reconcile with their existence by appealing to complete or at least refined device physics models.
Saturday, August 23, 2008
Parasitic Capacitance...is it really parasitic?
Now, consider a scenario involving a dynamic CMOS logic circuit where all the CMOS transistors have zero shunt capacitance (and hence infinite impedance paths at suitable junctions to ground). There is no location to store the charge in the alleged precharge interval and therefore also no source for the pull down transistor network to sink the charge from a storage device in the evaluation interval. With no capacitances in this network, how would a dynamic CMOS logic circuit work? While this is a fairly simple example of the absence of parasitic capacitance leading to what the idealists might regard as a paradox, there are several other examples in electromagnetic theory where capacitances and even inductances are unavoidable and in fact predicted by theory, e.g. in transmission lines, interconnects, ground bounces, etc. The moral is not to treat the word 'parasitic' in parasitic elements too literally, and reconcile with their existence by appealing to complete or at least refined device physics models.
Saturday, January 19, 2008
125 Big Questions In Science
Sunday, December 16, 2007
Quantum Computing
Authors: Steven Duplij (Kharkov National University), Illia Shapoval (NSC Kharkov Institute of Physics and Technology)
(Submitted on 7 Dec 2007)
Abstract: Basic concepts of quantum theory of information, principles of quantum calculations and the possibility of creation on this basis unique on calculation power and functioning principle device, named quantum computer, are briefly reviewed. The main blocks of quantum logic, schemes of implementation of quantum calculations, as well as some known today effective quantum algorithms, called to realize advantages of quantum calculations upon classical, are concerned. Among them special place is taken by Shor's algorithm of number factorization, Grover's algorithm of unsorted database search and, finally, the most promising in application methods of quantum phenomena simulation, particularly quantum chaos. The most perspective methods of experimental realization of quantum computer, namely nuclear-magnetic resonance and trapped ions realizations, are discussed. Phenomena of decoherence, its influence on quantum computer stability and methods of quantum error correction are described.
Thursday, March 8, 2007
Visualizing representations of U(1), SU(2), SU(3)
I had a fun discovery in February. I was working on software to visualize quaternions at quaternions.sf.net. The idea is that one generates a large number of quaternions somehow, and then sorts those quaternions by their time. One can then decide to plot those quaternions in a 10 second universe at 10 frames/second, or 100 frames total. Depending on the time, it will determine what frame a quaternion is drawn.
Where the quaternion is drawn is determined by the x, y, and z. Generate the 100 frames, use some tools from ImageMagick, and out comes a gif animation that can be viewed on the web. The frames can be drawn with ImageMagick (kind of flat), GnuPlot (kind of like a physics paper), or POVRay, a great 3D image creator, the clear winner.
Space and time reversal
Yellow is input, from txyz=(-5, -5, -5, -5) to (0, 0, 0, 0).
Blue is a spatial reversal, from txyz=(-5, 5, 5, 5) to (0, 0, 0, 0)
Green is a time reversal, from txyz=(5, -5, -5, -5) to (0, 0, 0, 0)
up/down | ||
near/far | left/right | that is |
I could have written the code is anything, but I want my stuff to last. The only user interface that has lasted 30 years is the command line, so I decided to use that approach: small programs that play with quaternions, and can pipe their results into other programs that can do a math operation on quaternions. I've got about 40 such programs, like q_add, q_sin, etc. A Perl program called q_graph can takes streams of quaternions and make the animations in one step. The process for number crunching is fast, but making animation is not.
Back to the physics. I decide to generate important groups, such as SU(2), which can be generated from the expression exp(q-q*). Take a thousand randomly generated quaternions, stick it in that expression, and plot.
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near/far | left/right | that is |
The image is kind of interesting. Time is almost always greater than zero. It does fill up space smoothly. The Lie algebra su(2) has 3 degrees of freedom, but a quaternion has 4. How to get the 4th? Why not q/|q| exp(q-q*)? Notice that because I am using the same darn quaternion throughout, this particular bit of quaternion multiplication is Abelian because q/|q| exp(q-q*) = exp(q-q*) q/|q|. 3 degrees of freedom go into exp(q-q*), leaving 1 for q/|q|, meaning q/|q| happens to be a representation of U(1)! So take a new 1000 random quaternions, plug into q/|q| exp(q-q*), and see U(1)xSU(2), electroweak symmetry. This is more like a 4D sphere, but is has a real for negative time.
So how does one fill up uniformly a unit volume of spacetime using quaternions? I took the conjugate of one U(1)xSU(2) times a different quaternion, q* q'. Why should this create a different group? Quaternion multiplication as Hamilton practiced it is associative. I call a product that tosses a conjugate in the middle a "Euclidean product". The Euclidean product is not associative, since (a)*bc != (ab)*c. The norms are the same, but the results point in a different direction. The norm of (q/|q| exp(q-q*))* q'/|q'| exp(q'-q'*) is one, and there are 8 independent numbers that go into the system, just like the Lie algebra su(3).
up/down | ||
near/far | left/right | that is |
A longer page with a few more examples is over here: standard model . Based on the algebra, and even more importantly, these analytic animations, we now have a reason for the symmetries that appear in the standard model: it is about having the ability to describe smoothly any possible way of generating events in spacetime using quaternions. If you want to know how to bring in gravity, image 2 of these sphere, with slightly different sizes. The group Diff(M) will help smoothly describe the changes in those sizes by taking small continous steps with a changing metric.
doug
Wednesday, January 3, 2007
test
EDIT: This is from our good friend Tim John, who has done (quite a) few good deeds this new year...starting by taking this page more seriously ;-).
Sunday, December 24, 2006
Testing LaTeX
PS--Thanks to Tom for the encouragement [;)].
Saturday, December 23, 2006
quant-ph/0609163
quant-ph/0609163
Authors: H. Nikolic
Comments: 28 two-column pages, pedagogic review
Subj-class: Quantum Physics; Physics Education
A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of "myths", that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.