Lectures on the Geometry of Quantization
... Ĥ. As soon as we wish to “quantize” a more complicated energy function, such as (1 + q 2 )p2 , we run in to the problem that the operators q̂ and p̂ do not commute with one another, so that we are forced to choose between (1 + q̂ 2 )p̂2 and p̂2 (1 + q̂ 2 ), among a number of other possibilities. Th ...
... Ĥ. As soon as we wish to “quantize” a more complicated energy function, such as (1 + q 2 )p2 , we run in to the problem that the operators q̂ and p̂ do not commute with one another, so that we are forced to choose between (1 + q̂ 2 )p̂2 and p̂2 (1 + q̂ 2 ), among a number of other possibilities. Th ...
Quasiclassical and semiclassical calculations on reactions with oriented molecules cos β
... why a hexapole eld is needed to select symmetric top molecules in a certain rotational state and what the demands are for a hexapole apparatus. In the experimental setup a molecular beam is made by expanding CH3 X through a nozzle with a diameter of 110 m. This nozzle can be viewed as a point sour ...
... why a hexapole eld is needed to select symmetric top molecules in a certain rotational state and what the demands are for a hexapole apparatus. In the experimental setup a molecular beam is made by expanding CH3 X through a nozzle with a diameter of 110 m. This nozzle can be viewed as a point sour ...
On disorder effects in topological insulators and semimetals
... width, indicating edge state transport. Indeed, each of the two edges of the quantum well sample is expected to harbor an edge dispersion as in Figure 1.1 with a single ballistic transport channel propagating in each direction. Further, it was ...
... width, indicating edge state transport. Indeed, each of the two edges of the quantum well sample is expected to harbor an edge dispersion as in Figure 1.1 with a single ballistic transport channel propagating in each direction. Further, it was ...
Stability and Mobility of Localized and Extended Excitations in Nonlinear Schr¨
... waveguides. The inversion of stability of stationary solutions occurs also in the two-dimensional array, but in this setting it fails to give good mobility of localized excitations. The reason for this is also explained. In a two-dimensional lattice a discrete breather can have the form of a vortex. ...
... waveguides. The inversion of stability of stationary solutions occurs also in the two-dimensional array, but in this setting it fails to give good mobility of localized excitations. The reason for this is also explained. In a two-dimensional lattice a discrete breather can have the form of a vortex. ...
Light-Matter Interaction: Conversion of Optical Energy and
... front facet of the mirror travels forward and gives rise to elastic vibrations through the entire thickness of the mirror and its substrate.2,3 Similarly, the passage of a light pulse through a transparent dielectric slab sets in motion elastic waves of mechanical vibration, which mediate the exchan ...
... front facet of the mirror travels forward and gives rise to elastic vibrations through the entire thickness of the mirror and its substrate.2,3 Similarly, the passage of a light pulse through a transparent dielectric slab sets in motion elastic waves of mechanical vibration, which mediate the exchan ...
Establishing Quantum Monte Carlo and Hybrid Density Functional
... require a solution of the fundamental many-electron Schrödinger equation. Since an exact solution of Schrödinger’s equation is intractable, several numerical methods have been developed to obtain approximate solutions. Currently, the two most successful methods are density functional theory (DFT) ...
... require a solution of the fundamental many-electron Schrödinger equation. Since an exact solution of Schrödinger’s equation is intractable, several numerical methods have been developed to obtain approximate solutions. Currently, the two most successful methods are density functional theory (DFT) ...
Spin-Orbital Order Modified by Orbital Dilution in Transition Metal
... We investigate the changes in spin and orbital patterns induced by magnetic transition metal ions without an orbital degree of freedom doped in a strongly correlated insulator with spin-orbital order. In this context we study the 3d ion substitution in 4d transition metal oxides in the case of 3d3 d ...
... We investigate the changes in spin and orbital patterns induced by magnetic transition metal ions without an orbital degree of freedom doped in a strongly correlated insulator with spin-orbital order. In this context we study the 3d ion substitution in 4d transition metal oxides in the case of 3d3 d ...
Controlling electron quantum dot qubits by spin
... Especially the spin degree of freedom in quantum dots has attracted attention for two reasons. First, the electron spin provides a natural quantum two level system, suitable for encoding the information bit. Second, the spin is less coupled to the environment than are electron orbital degrees of fre ...
... Especially the spin degree of freedom in quantum dots has attracted attention for two reasons. First, the electron spin provides a natural quantum two level system, suitable for encoding the information bit. Second, the spin is less coupled to the environment than are electron orbital degrees of fre ...
Quantum Techniques for Stochastic Mechanics
... networks. First, the ‘deficiency zero theorem’ gives conditions for the existence of equilibria in the approximation where the number of molecules of each kind is treated as varying continuously in a deterministic way. Our proof uses tools borrowed from quantum mechanics, including a stochastic anal ...
... networks. First, the ‘deficiency zero theorem’ gives conditions for the existence of equilibria in the approximation where the number of molecules of each kind is treated as varying continuously in a deterministic way. Our proof uses tools borrowed from quantum mechanics, including a stochastic anal ...
Chapter 1. Some experimental facts
... If ν was to become much higher than UV it would become first X-rays and then gamma rays. The walls of the enclosure would be permeable to such radiation. Also the temperature of the wall would have to be much higher and the enclosure would melt and vaporize. From relativity we know that a particle o ...
... If ν was to become much higher than UV it would become first X-rays and then gamma rays. The walls of the enclosure would be permeable to such radiation. Also the temperature of the wall would have to be much higher and the enclosure would melt and vaporize. From relativity we know that a particle o ...
Classification of topological quantum matter with
... states give rise to a quantized transverse Hall conductivity. These edge states arise due to a nontrivial wave function topology, that can be measured in terms of a quantized topological invariant, i.e., the Chern or TKNN number (Kohmoto, 1985; Thouless et al., 1982). This invariant, which is propor ...
... states give rise to a quantized transverse Hall conductivity. These edge states arise due to a nontrivial wave function topology, that can be measured in terms of a quantized topological invariant, i.e., the Chern or TKNN number (Kohmoto, 1985; Thouless et al., 1982). This invariant, which is propor ...
Interacting Fermionic Atoms in Optical Lattices
... In contrast to a real solid, the strengths of all potentials can be controlled by varying the laser intensities. By the use of Feshba resonances it in addition became possible to freely tune the interactions between the atoms, something that is impossible to aieve in a real solid, where one has to ...
... In contrast to a real solid, the strengths of all potentials can be controlled by varying the laser intensities. By the use of Feshba resonances it in addition became possible to freely tune the interactions between the atoms, something that is impossible to aieve in a real solid, where one has to ...