Vector Calculus - New Age International
... Since dR/du is itself a vector depending on u, if its derivative with respect to u exists, then it is denoted by d2R/du2. Similarly, higher order derivatives may be defined. If r = xi + yj + zk, is the position vector of a moving particle P (x, y, z) in space, then, dr = dx i + dy j + dz k ...
... Since dR/du is itself a vector depending on u, if its derivative with respect to u exists, then it is denoted by d2R/du2. Similarly, higher order derivatives may be defined. If r = xi + yj + zk, is the position vector of a moving particle P (x, y, z) in space, then, dr = dx i + dy j + dz k ...
Quantum Interference between Single Photons from a Single Atom
... With the photon as the interconnect, the implementation may require the different physical systems to produce indistinguishable photons which is an important element in linear optics based quantum computation [10]. Yet, different physical systems produce single photons that are usually not indisting ...
... With the photon as the interconnect, the implementation may require the different physical systems to produce indistinguishable photons which is an important element in linear optics based quantum computation [10]. Yet, different physical systems produce single photons that are usually not indisting ...
Quantum Mechanics
... where we have introduced the Canonical Variables , the Characteristic Length and , the Characteristic Momentum. (Note, that ...
... where we have introduced the Canonical Variables , the Characteristic Length and , the Characteristic Momentum. (Note, that ...
Optical properties of cylindrical nanowires
... variance of the electromagnetic (EM) field within the wire, which justifies considering the response of the nanowire to the incident light in the dipole limit. For increasing wire radius, however, the wave behavior of the EM field cannot simply be neglected any more. Therefore, it is one of the main ...
... variance of the electromagnetic (EM) field within the wire, which justifies considering the response of the nanowire to the incident light in the dipole limit. For increasing wire radius, however, the wave behavior of the EM field cannot simply be neglected any more. Therefore, it is one of the main ...
Chapter 1 Principles of Probability
... sequence SECRET will occur by chance? The S could be in any one of the 6 positions with equal likelihood. The probability that it is in position 1 is (1/6). Given that S is in the first position, we have 2 E 0 s which could occur in any of the remaining 5 positions. The probability that one of them ...
... sequence SECRET will occur by chance? The S could be in any one of the 6 positions with equal likelihood. The probability that it is in position 1 is (1/6). Given that S is in the first position, we have 2 E 0 s which could occur in any of the remaining 5 positions. The probability that one of them ...
AUTOMATIC QUANTUM COMPUTER PROGRAMMING A Genetic
... algorithms require an amount of time proportional to where is the number of digits in the number to be factored. In contrast, Shor’s quantum algorithm (Beckman et al., 1996; Shor, 1998) requires time proportional to only This is an exponential savings, assuming that the known classical factoring alg ...
... algorithms require an amount of time proportional to where is the number of digits in the number to be factored. In contrast, Shor’s quantum algorithm (Beckman et al., 1996; Shor, 1998) requires time proportional to only This is an exponential savings, assuming that the known classical factoring alg ...
Topological quantum computation
... sign change is induced by the interaction as the particles pass one another. More generally, the exchange could modify the wavefunction by a multiplicative phase eiθ that could take values other than +1 or −1, but we could account for this phase change by describing the particles as either bosons or ...
... sign change is induced by the interaction as the particles pass one another. More generally, the exchange could modify the wavefunction by a multiplicative phase eiθ that could take values other than +1 or −1, but we could account for this phase change by describing the particles as either bosons or ...
New Class of Quantum Error-Correcting Codes for a Bosonic Mode
... the qubit lifetime, and then return it to the qubit prior to verification via process tomography [35]. Remarkably, it is also now possible to make quantum nondemolition measurements of photon number parity [39], which can be used to greatly simplify the measurement of Wigner functions [32,38,39]. Su ...
... the qubit lifetime, and then return it to the qubit prior to verification via process tomography [35]. Remarkably, it is also now possible to make quantum nondemolition measurements of photon number parity [39], which can be used to greatly simplify the measurement of Wigner functions [32,38,39]. Su ...
Optimum topology of quasi-one dimensional nonlinear optical
... the energies may fall between fixed boundaries that superscale with state number, so-called root boundaries. We also note that all nonrelativistic single and many particle Hamiltonians studied to date have spectra and states that generate nonlinearities that are at most 70% of the maximum for β. For ...
... the energies may fall between fixed boundaries that superscale with state number, so-called root boundaries. We also note that all nonrelativistic single and many particle Hamiltonians studied to date have spectra and states that generate nonlinearities that are at most 70% of the maximum for β. For ...
An attractive critical point from weak antilocalization on fractals
... Summary. We presented analytical arguments for validity of the scaling hypothesis on fractals, and showed that the competition between the positive quantum corrections to conductance and the diffusive conductance scaling can lead to the occurrence of an additional attractive critical point. By tunin ...
... Summary. We presented analytical arguments for validity of the scaling hypothesis on fractals, and showed that the competition between the positive quantum corrections to conductance and the diffusive conductance scaling can lead to the occurrence of an additional attractive critical point. By tunin ...
Physics at the FQMT`04 conference
... is needed to understand behaviour of small ‘‘mesoscopic’’ systems. Since during measurements, systems can be very far from equilibrium we have to understand ‘‘arrow of time’’ problems, the emergence of non-equilibrium in these systems. To develop methods for the description of ‘‘mesoscopic’’ systems ...
... is needed to understand behaviour of small ‘‘mesoscopic’’ systems. Since during measurements, systems can be very far from equilibrium we have to understand ‘‘arrow of time’’ problems, the emergence of non-equilibrium in these systems. To develop methods for the description of ‘‘mesoscopic’’ systems ...
sums, differences and products of vectors
... classified mathematically as either scalars or vectors. Values of scalar quantities are single numbers, sizes, and this includes such quantities as temperature, work, distance, speed, musical pitch, and electric charge. Values of vector quantities have both size and direction, and this includes such ...
... classified mathematically as either scalars or vectors. Values of scalar quantities are single numbers, sizes, and this includes such quantities as temperature, work, distance, speed, musical pitch, and electric charge. Values of vector quantities have both size and direction, and this includes such ...
Quantum Optics VII Conference Program
... University of Innsbruck, Institute for Experimental Physics In this talk, the basic tool box of the Innsbruck quantum information processor based on a string of trapped Ca+ ions will be reviewed. For quantum information science, the toolbox operations are used to encode one logical qubit in entangle ...
... University of Innsbruck, Institute for Experimental Physics In this talk, the basic tool box of the Innsbruck quantum information processor based on a string of trapped Ca+ ions will be reviewed. For quantum information science, the toolbox operations are used to encode one logical qubit in entangle ...
Probability amplitude
In quantum mechanics, a probability amplitude is a complex number used in describing the behaviour of systems. The modulus squared of this quantity represents a probability or probability density.Probability amplitudes provide a relationship between the wave function (or, more generally, of a quantum state vector) of a system and the results of observations of that system, a link first proposed by Max Born. Interpretation of values of a wave function as the probability amplitude is a pillar of the Copenhagen interpretation of quantum mechanics. In fact, the properties of the space of wave functions were being used to make physical predictions (such as emissions from atoms being at certain discrete energies) before any physical interpretation of a particular function was offered. Born was awarded half of the 1954 Nobel Prize in Physics for this understanding (see #References), and the probability thus calculated is sometimes called the ""Born probability"". These probabilistic concepts, namely the probability density and quantum measurements, were vigorously contested at the time by the original physicists working on the theory, such as Schrödinger and Einstein. It is the source of the mysterious consequences and philosophical difficulties in the interpretations of quantum mechanics—topics that continue to be debated even today.