6 Wave equation in spherical polar coordinates
... This is another example of a BC (periodic in this case) quantising a separation constant. In principle m can take any integer value between −∞ and ∞. It turns out in Quantum Mechanics that m is the integer magnetic quantum number and −l ≤ m ≤ l for the z-component of angular momentum. In that contex ...
... This is another example of a BC (periodic in this case) quantising a separation constant. In principle m can take any integer value between −∞ and ∞. It turns out in Quantum Mechanics that m is the integer magnetic quantum number and −l ≤ m ≤ l for the z-component of angular momentum. In that contex ...
Localized - Current research interest: photon position
... In standard quantum mechanics a measurement is associated with an operator and collapse to one of its eigenvectors. For the position observable this requires a position operator and collapse to a localized state. The generalized theory of observables only requires a partition of the identity operato ...
... In standard quantum mechanics a measurement is associated with an operator and collapse to one of its eigenvectors. For the position observable this requires a position operator and collapse to a localized state. The generalized theory of observables only requires a partition of the identity operato ...
Path Integrals in Quantum Mechanics Dennis V. Perepelitsa
... phase, and interfere destructively with each other. Integrating over more and more such trajectories should cause their contribution to average out to zero. In this way, the classical trajectory is qualitatively important. In general, the region of coherence is related to the “classical” nature of t ...
... phase, and interfere destructively with each other. Integrating over more and more such trajectories should cause their contribution to average out to zero. In this way, the classical trajectory is qualitatively important. In general, the region of coherence is related to the “classical” nature of t ...
Quantum networking with single ions J¨ urgen Eschner
... well-defined energy, and the laser is assumed monochromatic, the only uncertainty is the duration of the scattering process. Hence the emission time distribution determines also the spectral distribution. Again, also in this case the blue photon will be Fourier-limited. It is important to emphasize ...
... well-defined energy, and the laser is assumed monochromatic, the only uncertainty is the duration of the scattering process. Hence the emission time distribution determines also the spectral distribution. Again, also in this case the blue photon will be Fourier-limited. It is important to emphasize ...
Computational Power of the Quantum Turing Automata
... Although nothing universal has been proven about the relationship between the relative speeds of quantum and classical computation, several such relativized† results have made progress that suggests the direction that future work will eventually go. The first results discovered appeared to suggest t ...
... Although nothing universal has been proven about the relationship between the relative speeds of quantum and classical computation, several such relativized† results have made progress that suggests the direction that future work will eventually go. The first results discovered appeared to suggest t ...
Topological Order and the Kitaev Model
... intrincate states that can occur in different situations and scales, for instance: plasmas, BoseEinstein condensates, quantum spin liquids or superfluids to mention a few. States of matter are, in general, classified into phases that can be connected to each other via phase transitions. This is, dif ...
... intrincate states that can occur in different situations and scales, for instance: plasmas, BoseEinstein condensates, quantum spin liquids or superfluids to mention a few. States of matter are, in general, classified into phases that can be connected to each other via phase transitions. This is, dif ...
Long Distance, Unconditional Teleportation of Atomic States V 87, N
... 1 ms). By monitoring a cavity for the fluorescence from this cycling transition, we can reliably detect whether or not a 795 nm photon has been absorbed by the atom in that cavity. If neither atom or if only one atom has absorbed such a photon, then we cycle both atoms back to their A states and sta ...
... 1 ms). By monitoring a cavity for the fluorescence from this cycling transition, we can reliably detect whether or not a 795 nm photon has been absorbed by the atom in that cavity. If neither atom or if only one atom has absorbed such a photon, then we cycle both atoms back to their A states and sta ...
Detection of Quantum Critical Points by a Probe Qubit
... superconductors [2] and fractional quantum Hall systems [3]. Related phenomena have also been experimentally observed in heavy fermion systems [4], common metals [5], and in Bose-Einstein condensates [6]. QPTs occur as a result of competing interactions and the different phases often show different ...
... superconductors [2] and fractional quantum Hall systems [3]. Related phenomena have also been experimentally observed in heavy fermion systems [4], common metals [5], and in Bose-Einstein condensates [6]. QPTs occur as a result of competing interactions and the different phases often show different ...
Entropic Test of Quantum Contextuality
... new graph theoretical method to construct joint probability distributions is presented and it is proven that for sets of measurements whose corresponding graphs do not contain cycles (i.e., there are no subsets of measurements that cyclic-commute) there always exists a joint probability distribution ...
... new graph theoretical method to construct joint probability distributions is presented and it is proven that for sets of measurements whose corresponding graphs do not contain cycles (i.e., there are no subsets of measurements that cyclic-commute) there always exists a joint probability distribution ...
Quantum entanglement, topological order, and tensor category theory
... Two gapped states, |Ψ(0)� and |Ψ(1)� (or more precisely, two ground state subspaces), are in the same phase iff they are related ...
... Two gapped states, |Ψ(0)� and |Ψ(1)� (or more precisely, two ground state subspaces), are in the same phase iff they are related ...
On the speed of fluctuations around
... principles of statistical mechanics [1]–[8]. Underlying this progress is the realization that quantum mechanics allows individual quantum states to exhibit statistical properties and that ensemble or time averages are not needed to obtain a mixed equilibrium state for the system under consideration. ...
... principles of statistical mechanics [1]–[8]. Underlying this progress is the realization that quantum mechanics allows individual quantum states to exhibit statistical properties and that ensemble or time averages are not needed to obtain a mixed equilibrium state for the system under consideration. ...
Lamb shift in radical-ion pairs produces a singlet
... the calculation, as its contribution is the simple unitary evolution dρ/dt = −i[Hm , ρ]. In [2] the magnetic Hamiltonian was treated as part of the perturbation, again leading to the same result of the ordinary unitary evolution. This is because Hm effects the state evolution to first order in dt, and ...
... the calculation, as its contribution is the simple unitary evolution dρ/dt = −i[Hm , ρ]. In [2] the magnetic Hamiltonian was treated as part of the perturbation, again leading to the same result of the ordinary unitary evolution. This is because Hm effects the state evolution to first order in dt, and ...
on the fine structure of spacetime
... the points of M and the full group of symmetries of the action S is the semi-direct product of the two groups (in the same way, the Poincaré group which is the invariance group of special relativity, is the semi-direct product of the group of translations by the group of Lorentz transformations). I ...
... the points of M and the full group of symmetries of the action S is the semi-direct product of the two groups (in the same way, the Poincaré group which is the invariance group of special relativity, is the semi-direct product of the group of translations by the group of Lorentz transformations). I ...
Chapter 9 Angular Momentum Quantum Mechanical Angular
... Notice like the nonsense operators hardness and color, none of the angular momentum component operators commute and none of the eigenvectors correspond. Also comparable, L2 is proportional to the identity operator, except in three dimensions. We can do something similar to the “hardness, color” case ...
... Notice like the nonsense operators hardness and color, none of the angular momentum component operators commute and none of the eigenvectors correspond. Also comparable, L2 is proportional to the identity operator, except in three dimensions. We can do something similar to the “hardness, color” case ...
Computational advantage from quantum
... first proposed in [2] that such a constraint can be relaxed: one can consider situations where the wires, and thus the order between gates, can be controlled by some extra variable. This is natural if one thinks of the circuit’s wires as quantum systems that can be in superposition. Such “superposit ...
... first proposed in [2] that such a constraint can be relaxed: one can consider situations where the wires, and thus the order between gates, can be controlled by some extra variable. This is natural if one thinks of the circuit’s wires as quantum systems that can be in superposition. Such “superposit ...
Seeing a single photon without destroying it
... in cavity quantum electrodynamics15, where the strength of the interaction between an atom and a photon can overwhelm all dissipative couplings to the environment. Here we report a cavity quantum electrodynamics experiment in which we detect a single photon non-destructively. We use atomic interfero ...
... in cavity quantum electrodynamics15, where the strength of the interaction between an atom and a photon can overwhelm all dissipative couplings to the environment. Here we report a cavity quantum electrodynamics experiment in which we detect a single photon non-destructively. We use atomic interfero ...