Feynman diagram. In theoretical physics, Feynman diagrams are pictorial representations of the mathematical expressions governing the behavior of subatomic particles. The scheme is named for its inventor, Nobel Prize-winning American physicist Richard Feynman, and was first introduced in 1948. The interaction of sub-atomic particles can be complex and difficult to understand intuitively, and the Feynman diagrams allow for a simple visualization of what would otherwise be a rather arcane and abstract formula. As David Kaiser writes, "since the middle of the 20th century, theoretical physicists have increasingly turned to this tool to help them undertake critical calculations", and as such "Feynman diagrams have revolutionized nearly every aspect of theoretical physics".[1] While the diagrams are applied primarily to quantum field theory, they can also be used in other fields, such as solid-state theory.
Motivation and history[edit] Alternative names[edit] Representation of physical reality[edit] where. Quantum tunnelling. Quantum tunnelling or tunneling (see spelling differences) refers to the quantum mechanical phenomenon where a particle tunnels through a barrier that it classically could not surmount. This plays an essential role in several physical phenomena, such as the nuclear fusion that occurs in main sequence stars like the Sun.[1] It has important applications to modern devices such as the tunnel diode,[2] quantum computing, and the scanning tunnelling microscope. The effect was predicted in the early 20th century and its acceptance as a general physical phenomenon came mid-century.[3] Tunnelling is often explained using the Heisenberg uncertainty principle and the wave–particle duality of matter. Pure quantum mechanical concepts are central to the phenomenon, so quantum tunnelling is one of the novel implications of quantum mechanics.
History[edit] After attending a seminar by Gamow, Max Born recognised the generality of tunnelling. Introduction to the concept[edit] The tunnelling problem[edit] or. Berezin integral. In mathematical physics, a Berezin integral, named after Felix Berezin, (or Grassmann integral, after Hermann Grassmann) is a way to define integration of elements of the exterior algebra (Hermann Grassmann 1844). It is called integral because it is used in physics as a sum over histories for fermions, an extension of the path integral. Integration on an exterior algebra[edit] Let be the exterior algebra of polynomials in anticommuting elements over the field of complex numbers. (The ordering of the generators is fixed and defines the orientation of the exterior algebra.)
Is the linear functional with the following properties: for any where means the left or the right partial derivative. Expresses the Fubini law. Is set to be ; the integral of vanishes. Is calculated in the similar way and so on. Change of Grassmann variables[edit] be odd polynomials in some antisymmetric variables . Where the left and the right derivatives coincide and are even polynomials. Berezin integral[edit] ) . , where and in. Quantum Consciousness. In: Toward a Science of Consciousness II: The 1996 Tucson Discussions and Debates Editors Stuart Hameroff, Alfred Kaszniak, Alwyn Scott MIT Press, Cambridge MA 1998 In "Brainshy: Non-neural theories of conscious experience," (this volume) Patricia Churchland considers three "non-neural" approaches to the puzzle of consciousness: 1) Chalmers' fundamental information, 2) Searle's "intrinsic" property of brain, and 3) Penrose-Hameroff quantum phenomena in microtubules.
In rejecting these ideas, Churchland flies the flag of "neuralism. " She claims that conscious experience will be totally and completely explained by the dynamical complexity of properties at the level of neurons and neural networks. As far as consciousness goes, neural network firing patterns triggered by axon-to-dendrite synaptic chemical transmissions are the fundamental correlates of consciousness.
There is no need to look elsewhere. Neurotransmitter vesicle release is probabilistic (and possibly non-computable). Microscopic Structure Of Quantum Gases Made Visible: Bose-Einste. Scientists at the Johannes Gutenberg University Mainz have, for the first time, succeeded in rendering the spatial distribution of individual atoms in a Bose-Einstein condensate visible. Bose-Einstein condensates are small, ultracold gas clouds which, due to their low temperatures, can no longer be described in terms of traditional physics but must be described using the laws of quantum mechanics.
The first Bose-Einstein condensates were generated in 1995 by Eric A. Cornell, Carl E. Wieman and Wolfgang Ketterle, who received the Nobel Prize in Physics for their work only six years later. Since then, these unique gas clouds, the coldest objects humans ever created, have become a global research object. Physicists working with Dr Herwig Ott in the study group for quantum, atomic and neutron physics (QUANTUM) at Mainz University have now developed a new tech-nology that can be used to plot the individual atoms in a Bose-Einstein condensate.
Quantum Computing Gets Boost From 'Entanglement' Of Atom Pairs. Physicists at the Commerce Department's National Institute of Standards and Technology (NIST) have taken a significant step toward transforming entanglement--an atomic-scale phenomenon described by Albert Einstein as "spooky action at a distance"--into a practical tool. They demonstrated a method for refining entangled atom pairs (a process called purification) so they can be more useful in quantum computers and communications systems, emerging technologies that exploit the unusual rules of quantum physics for pioneering applications such as "unbreakable" data encryption. The NIST work, reported in the Oct. 19, 2006, issue of Nature,* marks the first time atoms have been both entangled and subsequently purified; previously, this process had been carried out only with entangled photons (particles of light). The NIST demonstration also is the first time that scientists have been able to purify particles nondestructively.
. * R. Reichle, D.