on line
... group law is polynomial, the product map G × G → G becomes under the correspondence an algebra homomorphism ∆ going the other way. Likewise for the rest of the Hopf algebra structure. Two examples are as follows. The “affine line” is described by the coordinate algebra k[x] (polynomials in one varia ...
... group law is polynomial, the product map G × G → G becomes under the correspondence an algebra homomorphism ∆ going the other way. Likewise for the rest of the Hopf algebra structure. Two examples are as follows. The “affine line” is described by the coordinate algebra k[x] (polynomials in one varia ...
Radiation to atom quantum mapping by collective recoil in a Bose
... In the limit of high CARL gain the teleported state on the atomic beam is given by ju0 i ¼ P u jn; N ni. This indicates that any proper n n verification of the teleportation should involve a measurement also on the condensate, e.g., a two mode tomographic method involving both the measurement of bo ...
... In the limit of high CARL gain the teleported state on the atomic beam is given by ju0 i ¼ P u jn; N ni. This indicates that any proper n n verification of the teleportation should involve a measurement also on the condensate, e.g., a two mode tomographic method involving both the measurement of bo ...
The Kabbalistic Radla and Quantum Physics
... the 1920’s 7 and, more tellingly, resolution of the EPR (Einstein-PodolskyRosen) paradox,8 which resulted from repeated experimental violation (1972-1982) of “Bell’s inequality” (1964) in favor of quantum theory. Moreover, the results of these experiments (especially that of Alain Aspect in 1982) im ...
... the 1920’s 7 and, more tellingly, resolution of the EPR (Einstein-PodolskyRosen) paradox,8 which resulted from repeated experimental violation (1972-1982) of “Bell’s inequality” (1964) in favor of quantum theory. Moreover, the results of these experiments (especially that of Alain Aspect in 1982) im ...
Quantum theory without measurement or state reduction problems
... Several experiments have demonstrated a loss of quantum behavior when a previously isolated system interacts with its environment or emits photons [26]. Of course quantum theory is widely used in modeling nonisolated objects. But more must be put into the model than QTIS. This is true even at the mo ...
... Several experiments have demonstrated a loss of quantum behavior when a previously isolated system interacts with its environment or emits photons [26]. Of course quantum theory is widely used in modeling nonisolated objects. But more must be put into the model than QTIS. This is true even at the mo ...
Zeno dynamics in quantum open systems
... there are several attempts to observe QZE in truly decaying states[14, 15]. QZE has become a focus of attention not only because it can be applied in robust quantum information processing, but also because of its foundational implications about the nature of quantum measurement[2] as well as indisti ...
... there are several attempts to observe QZE in truly decaying states[14, 15]. QZE has become a focus of attention not only because it can be applied in robust quantum information processing, but also because of its foundational implications about the nature of quantum measurement[2] as well as indisti ...
Computing with Atoms and Molecules
... superpositions of 0 and 1, denoted by α|0〉 + β|1〉, where α and β are the weights of the superposition. It this notation, |x〉 signifies a quantum state and the + sign indicates a superposition. The states |0〉 and |1〉 may represent, for example, horizontal and vertical polarization of a single photon, ...
... superpositions of 0 and 1, denoted by α|0〉 + β|1〉, where α and β are the weights of the superposition. It this notation, |x〉 signifies a quantum state and the + sign indicates a superposition. The states |0〉 and |1〉 may represent, for example, horizontal and vertical polarization of a single photon, ...
Statistical Physics (PHY831): Part 1 - The foundations Course Outline
... justification for a discrete system is provided by the principle of detailed balance. Thus, if the dynamics of a system leads to an equal probability of occupancy of all microstates at the same energy, then the system is “well mixed”, it exhibits“molecular chaos”, it is called “ergodic”, and at long ...
... justification for a discrete system is provided by the principle of detailed balance. Thus, if the dynamics of a system leads to an equal probability of occupancy of all microstates at the same energy, then the system is “well mixed”, it exhibits“molecular chaos”, it is called “ergodic”, and at long ...
Probability and the Maxwell
... N! / ∏r=1,c nr! = P, the complexion or possibility number. For N sufficiently large, we again use Stirling’s theorem, and obtain lnP ≈ NlnN – ∑r=1,c nrlnnr (noting that all the numbers nr must be sufficiently large). By assigning a maximum value to P, with the constraint that ∑r=1,c nr = N, we can o ...
... N! / ∏r=1,c nr! = P, the complexion or possibility number. For N sufficiently large, we again use Stirling’s theorem, and obtain lnP ≈ NlnN – ∑r=1,c nrlnnr (noting that all the numbers nr must be sufficiently large). By assigning a maximum value to P, with the constraint that ∑r=1,c nr = N, we can o ...