Momentum

About: Momentum is a research topic. Over the lifetime, 19070 publications have been published within this topic receiving 367167 citations. The topic is also known as: linear momentum & translational momentum.

Longitudinal Field Modes Probed by Single Molecules

Abstract: We demonstrate that a strong longitudinal, nonpropagating field is generated at the focus of a radially polarized beam mode. This field is localized in space and its energy density exceeds the energy density of the transverse field by more than a factor of 2. Single molecules with fixed absorption dipole moments are used to probe the longitudinal field. Vice versa, it is demonstrated that orientations of single molecules are efficiently mapped out in three dimensions by using a radially polarized beam as the excitation source. We also show that there is no momentum or energy transport associated with the longitudinal field.

Material Inhomogeneities in Elasticity

Abstract: Preface -- 1 Newton's concept of physical force -- 1.1. Newton's viewpoint -- 1.2. D' Alembert's viewpoint -- 1.3. Point particles and continua 7 -- 1.4. The modern point of view: duality -- 1.5. Lagrange versus Euler -- 2 Eshelby's concept of material force -- 2.1. Ideas from solid state physics -- 2.2. Peach-Koehler force -- 2.3. Force on a singularity -- 2.4. Energy-release rate -- 2.5. Pseudomomentum -- 2.6. Relationship with phonon and photon physics -- 3 Essentials of nonlinear elasticity theory -- 3.1. Material continuum in motion -- 3.2. Elastic me sures of strains -- 3.3. Compatibility of strains -- 3.4. Balance laws (Euler-Cauchy) -- 3.5. Balance laws (Piola-Kirchhoff) -- 3.6. Constitutive equations -- 3.7. Concluding remarks -- 4 Material balance laws and inhomogeneity -- 4.1. Fully material balance laws -- 4.2. Material inhomogeneity force and pseudomomentum -- 4.3. Interpretation of pseudomomentum -- 4.4. Four formulations of the balance of linear momentum -- 4.5. Other material balance laws -- 4.6. Comments -- 5 Elasticity as a field theory -- 5.1. Elements of field theory -- 5.2. Noether's theorem -- 5.3. Variational formulation (direct-motion description) -- 5.4. Variational formulation (inverse-motion description) -- 5.5. Other material balance laws -- 5.6. Canonical Hamiltonian formulation -- 5.7. Balance of total pseudomomentum -- 5.8. Nonsimple materals: second-gradient theory -- 5.9. Complementary-energy variational principle -- 5.10. Peach-Koehler force revisited -- 5.11. Concluding remarks -- 6 Geometrical aspects of elasticity theory -- 6.1. Material uniformity and inhomogeneity -- 6.2. Eshelby stress tensor -- 6.3. Covariant material balance law of momentum -- 6.4. Continuous distributions of dislocations -- 6.5. Variational formulation using two variations -- 6.6. Second-gradient theory -- 6.7. Continuous distributions of disclinations -- 6.8. Similarity to Einstein-Cartan gravitation theory -- 7 Material inhomogeneities and brittle fracture -- 7.1. The problem of fracture -- 7.2. Generalized Reynolds and Green-Gauss theorems -- 7.3. Global material force -- 7.4. J-integral in fracture -- 7.5. Dual I-integral in fracture -- 7.6. Variational inequality: fracture propagation criterion -- 7.7. Other material balance laws and related path-independent integrals -- 7.8. Remark on the dynamical case -- 8 Material forces in electromagnetoelasticity -- 8.1. Electromagnetic elastic solids -- 8.2. Reminder of electromagnetic equations -- 8.3. Material electromagnetic fields -- 8.4. Variational principles -- 8.5. Balance of pseudomomentum and material forces -- 8.6. Fracture in electroelasticity and magnetoelasticity -- 8.7. Geometrical aspects: material uniformity -- 8.8. Electric Peach-Koehler force -- 8.9. Example of application: piezoelectric ceramics -- 9 Pseudomomentum and quasi-particles -- 9.1. Pseudomomentum of photons and phonons -- 9.2. Electromagnetic pseudomomentum -- 9.3. Conservation laws in wave theory -- 9.4. Conservation laws in soliton theory -- 9.5. Sine-Gordon systems and topological solitons -- 9.6. Boussinesq crystal equation and pseudomomentum -- 9.7. Sine-Gordon-d'Alembert systems -- 9.8. Nonlinear Schrodinger and Zakharov systems -- 10 Material forces in anelastic materials -- 10.1. Internal variables and dissipation -- 10.2. Balance of pseudomomentum -- 10.3. Global material forces -- Bibliography and references -- Index .

Diabatic and adiabatic representations for atomic collision problems.

Abstract: The equations of the general Born-Oppenheimer separation into electronic and heavy-particle coordinates are re-examined, and the coupled equations that result for the heavy-particle motion are expressed in a particularly simple form. This is accomplished by introducing a generalized matrix operator for the effective momentum associated with the heavy particles; the matrix portion of this operator represents a coupling of the nuclear momentum with the electronic motion. The commutator between the momentum and potential matrices is a force matrix, which provides an alternative means of evaluating the momentum matrix. The momentum coupling has both radial and angular parts; the angular momentum coupling agrees with Thorson's expression. In the usual adiabatic molecular representation, the potential energy matrix is diagonalized, and all the coupling is thrown into the radial and angular momentum matrices. For collision problems it is often more important to diagonalize the radial momentum matrix, putting the radial off-diagonal coupling into the potential matrix; this generates a family of diabatic representations, the most important of which dissociates to unique separated atom states. This standard diabatic representations has the properties called for by Lichten, is uniquely defined even with the inclusion of configuration interaction, and leads immediately to the Landau-Zener-Stueckelberg limiting case under appropriate conditions.