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Chapter 1 Basic quantum electrodynamics required for the analysis of quantum antennas |
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1 | (12) |
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1 | (1) |
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1.2 The problems to be discussed |
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2 | (2) |
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1.3 EM field Lagrangian density |
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4 | (1) |
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1.4 Electric and magnetic fields in special relativity |
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4 | (1) |
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1.5 Canonical position and momentum fields in electrodynamics |
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4 | (1) |
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1.6 The matter fields in electrodynamics |
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5 | (1) |
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1.7 The Dirac bracket in electrodynamics |
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5 | (1) |
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1.8 Hamiltonian of the em field |
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6 | (1) |
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1.9 Interaction Hamiltonian between the current field and the electromagnetic field |
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7 | (1) |
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1.10 The Boson commutation relations for the creation and annihilation operator fields for the EM field in momentum-spin domain |
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8 | (1) |
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1.11 Electrodynamics in the Coulomb gauge |
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8 | (1) |
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1.12 The Dirac second quantized field |
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9 | (2) |
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1.13 The Dirac equation in an EM field, approximate solution using Perturbation theory |
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11 | (1) |
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1.14 Electromagnetically perturbed Dirac current |
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11 | (2) |
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Chapter 2 Effects of the gravitational field on a quantum antenna and some basic non-Abelian gauge theory |
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13 | (32) |
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2.1 The effect of a gravitational field on photon paths |
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13 | (1) |
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2.2 Interaction of gravitation with the photon field |
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14 | (1) |
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2.3 Quantum description of the effect of the gravitational field on the photon propagator |
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15 | (1) |
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2.4 Electrons and positrons in a mixture of the gravitational field and an EM field Quantum antennas in a background gravitational field |
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16 | (1) |
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2.5 Dirac equation in a gravitational field and a quantum white noise photon field described in the Hudson-Parthasarathy formalism |
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17 | (1) |
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2.6 Dirac-Yang-Mills current density for non-Abelian gauge theories |
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18 | (1) |
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19 | (2) |
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2.8 Harish-Chandra's discrete series representations of SL(2,R) and its application to pattern recognition under Lorentz transformations in the plane |
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21 | (1) |
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2.9 Estimating the shape of the antenna surface from the scattered EM field when an incident EM field induces a surface current density on the antenna that is determined by Pocklington's integral equation obtained by setting the tangential component of the total incident plus scattered electric field on the surface to zero |
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21 | (2) |
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2.10 Surface current density operator induced on the surface of a quantum antenna when a quantum EM field is incident on it |
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23 | (3) |
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2.11 Summary of the second quantized Dirac field |
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26 | (3) |
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2.12 Electron propagator computation |
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29 | (2) |
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2.13 Quantum mechanical tunneling of a Dirac particle through the critical radius of the Schwarzchild blackhole |
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31 | (1) |
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2.14 Supersymmetry-supersymmetric current in an antenna comprising superpartners of elementary particles |
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32 | (13) |
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Chapter 3 Conducting fluids as quantum antennas |
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45 | (26) |
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3.1 A short course in basic non-relativistic and relativistic fluid dynamics with antenna theory applications |
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45 | (9) |
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3.2 Flow of a 2-D conducting fluid |
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54 | (1) |
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3.3 Finite element method for solving the fluid dynamical equations |
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55 | (1) |
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3.4 Elimination of pressure, incompressible fluid dynamics in terms of just a single stream function vector field with vanishing divergence |
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56 | (1) |
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3.5 Fluids driven by random external force fields |
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57 | (1) |
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3.6 Relativistic fluids, tensor equations |
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58 | (1) |
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3.7 General relativistic fluids, special solutions |
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59 | (1) |
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3.8 Galactic evolution using perturbed fluid dynamics, dispersive relations. The unperturbed metric is the Roberson-Walker metric corresponding to a homogeneous and isotropic universe |
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59 | (1) |
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3.9 Magnetohydrodynamics-diffusion of the magnetic field and vorticity |
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60 | (1) |
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3.10 Galactic equation using perturbed Newtonian fluids |
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61 | (1) |
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3.11 Plotting the trajectories of fluid particles |
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61 | (1) |
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3.12 Statistical theory of fluid turbulence, equations for the velocity field moments, the Kolmogorov-Obhukov spectrum |
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62 | (1) |
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3.13 Estimating the velocity field of a fluid subject to random forcing using discrete space velocity measurements based on discretization and the Extended Kalman filter |
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63 | (1) |
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3.14 Quantum fluid dynamics. Quantization of the fluid velocity field by the introduction of an auxiliary Lagrange multiplier field |
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63 | (2) |
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3.15 Optimal control problems for fluid dynamics |
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65 | (1) |
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3.16 Hydrodynamic scaling limits for simple exclusion models |
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66 | (1) |
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3.17 Appendix: The complete fluid dynamical equations in orthogonal curvilinear coordinate systems specializing to cylindrical and spherical polar coordinates |
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67 | (4) |
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Chapter 4 Quantum robots in motion carrying Dirac current as quantum antennas |
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71 | (6) |
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4.1 A short course in classical and quantum robotics with antenna theory applications |
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71 | (2) |
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4.2 A fluid of interacting robots |
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73 | (1) |
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4.3 Disturbance observer in a robot |
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74 | (1) |
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4.4 Robot connected to a spring mass with damping system |
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75 | (2) |
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Chapter 5 Design of quantum gates using electrons, positrons and photons, quantum information theory and quantum stochastic filtering |
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77 | (22) |
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5.1 A short course in quantum gates, quantum computation and quantum information with antenna theory applications |
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77 | (13) |
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5.2 The Baker-Campbell-Hausdor formula. A, B are n x n matrices |
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90 | (1) |
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5.3 Yang-Mills radiation field (an approximation) |
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91 | (2) |
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5.4 Belavkin filter applied to estimating the spin of an electron in an external magnetic field. We assume that the magnetic field is B0(t) ε R3 |
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93 | (6) |
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Chapter 6 Pattern classification for image fields in motion using Lorentz group representations |
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99 | (6) |
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6.1 SL(2,C), SL(2,R) and image processing |
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99 | (6) |
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Chapter 7 Optimization problems in classical and quantum stochastics and information with antenna design applications |
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105 | (16) |
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7.1 A course in optimization techniques |
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105 | (8) |
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7.2 Group theoretical techniques in optimization theory |
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113 | (6) |
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7.3 Feynman's diagrammatic approach to computation of the scattering amplitudes of electrons, positrons and photons |
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119 | (2) |
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Chapter 8 Quantum waveguides and cavity resonators |
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121 | (4) |
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121 | (4) |
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Chapter 9 Classical and quantum filtering and control based on Hudson-Parthasarathy calculus, and filter design methods |
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125 | (40) |
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9.1 Belavkin filter and Luc-Bouten control for electron spin estimation and quantum Fourier transformed state estimation when corrupted by quantum noise |
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125 | (2) |
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9.2 General Quantum filtering and control |
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127 | (1) |
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9.3 Some topics in quantum filtering theory |
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127 | (33) |
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9.4 Filter design for physical applications |
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160 | (5) |
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Chapter 10 Gravity interacting with waveguide quantum fields with filtering and control |
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165 | (12) |
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10.1 Waveguides placed in the vicinity of a strong gravitational field |
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165 | (2) |
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10.2 Some study projects regarding waveguides and cavity resonators in a gravitational field |
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167 | (2) |
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10.3 A comparison between the EKF and Wavelet based block processing algorithms for estimating transistor parameters in an amplifier drived by the Ornstein-Uhlenbeck process |
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169 | (1) |
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10.4 Computing the Haar measure on a Lie group using left invariant vector fields and left invariant one forms |
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170 | (1) |
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10.5 How background em radiation affects the expansion of the universe |
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171 | (2) |
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10.6 Stochastic BHJ equations in discrete and continuous time for stochastic optimal control based on instantaneous feedback |
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173 | (1) |
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10.7 Quantum stochastic optimal control of the HP-Schrodinger equation |
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174 | (2) |
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10.8 Bath in a superposition of coherent states interacting with a system |
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176 | (1) |
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Chapter 11 Basic triangle geometry required for understanding Riemannian geometry in Einstein's theory of gravity |
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177 | (2) |
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11.1 Problems in mathematics and physics for school students |
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177 | (1) |
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11.2 Geometry on a curved surface, study problems |
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178 | (1) |
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Chapter 12 Design of gates using Abelian and non-Abelian gauge quantum field theories with performance analysis using the Hudson-Parthasarathy quantum stochastic calculus |
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179 | (12) |
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12.1 Design of quantum gates using Feynman diagrams |
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179 | (2) |
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12.2 An optimization problem in electromagnetism |
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181 | (3) |
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12.3 Design of quantum gates using non-Abelian gauge theories |
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184 | (1) |
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12.4 Design of quantum gates using the Hudson-Parthasarathy quantum stochastic Schrodinger equation |
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185 | (1) |
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12.5 Gravitational waves in a background curved metric |
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185 | (2) |
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12.6 Topics for a short course on electromagnetic field propagation at high frequencies |
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187 | (4) |
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Chapter 13 Quantum gravity with photon interactions, cavity resonators with inhomogeneities, classical and quantum optimal control of fields |
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191 | (28) |
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13.1 Quantum control of the HP-Schrodinger equation by state feedback |
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191 | (2) |
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13.2 Some ppplications of poisson processes |
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193 | (4) |
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13.3 A problem in optimal control |
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197 | (1) |
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13.4 Interaction between photons and gravitons |
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198 | (5) |
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13.5 A version of quantum optimal control |
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203 | (5) |
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13.6 A neater formulation of the quantum optimal control problem |
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208 | (2) |
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13.7 Calculating the approximate shift in the oscillation frequency of a cavity resonator having arbitrary cross section when the medium has a small inhomogeneity |
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210 | (5) |
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13.8 Optimal control for partial dierential equations |
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215 | (4) |
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Chapter 14 Quantization of cavity fields with in homogeneous media, field dependent media parameters from Boltzmann-Vlasov equations for a plasma, quantum Boltzmann equation for quantum radiation pattern computation, optimal control of classical fields, applications classical nonlinear filtering |
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219 | (32) |
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14.1 Computing the shift in the characteristic frequencies of oscillation in a cavity resonator due to gravitational effects and the effect of non-uniformity in the medium |
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219 | (2) |
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14.2 Quantization of the field in a cavity resonator having non-uniform permittivity and permeability |
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221 | (1) |
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14.3 Problems in transmission lines and waveguides |
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222 | (1) |
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14.4 Problems in optimization theory |
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223 | (1) |
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14.5 Another approach to quantization of wave-modes in a cavity resonator having non-uniform medium based on the scalar wave equation |
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224 | (4) |
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14.6 Derivation of the general structure of the field dependent permittivity and permeability of a plasma |
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228 | (1) |
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14.7 Other approaches to calculating the permittivity and permeability of a plasma via the use of Boltzmann's kinetic transport equation |
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229 | (2) |
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14.8 Derivation of the permittivity and permeability functions using quantum statistics |
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231 | (1) |
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14.9 Approximate discrete time nonlinear filtering for non-Gaussian process and measurement noise |
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231 | (3) |
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14.10 Quantum theory of many body systems with application to current computation in a Fermi liquid |
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234 | (3) |
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14.11 Optimal control of gravitational, matter and em fields |
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237 | (2) |
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14.12 Calculating the modes in a cylindrical cavity resonator with a partition in the middle |
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239 | (1) |
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14.13 Summary of the algorithm for nonlinear filtering in discrete time applied to fan rotation angle estimation |
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240 | (3) |
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14.14 Classical filtering theory applied to Levy process and Gaussian measurement noise. Developing the EKF for such problems |
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243 | (3) |
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14.15 Quantum Boltzmann equation for calculating the radiation fields produced by a plasma |
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246 | (5) |
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Chapter 15 Classical and quantum drone design |
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251 | (4) |
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15.1 Project proposal on drone design for the removal of pests in a farm |
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251 | (1) |
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15.2 Quantum drones based on Dirac's relativistic wave equation |
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252 | (3) |
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Chapter 16 Current in a quantum antenna |
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255 | (6) |
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16.1 Hartree-Fock equations for obtaining the approximate current density produced by a system of interacting electrons |
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255 | (2) |
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16.2 Controlling the current produced by a single quantum charged particle quantum antenna |
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257 | (4) |
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Chapter 17 Photons in a gravitational field with gate design applications and image processing in electromagnetics |
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261 | (28) |
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17.1 Some remarks on quantum blackhole physics |
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261 | (2) |
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17.2 EM field pattern produced by a rotated and translated antenna with noise deblurring |
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263 | (2) |
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17.3 Estimation of the 3-D rotation and translation vector of an antenna from electromagnetic field measurements |
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265 | (1) |
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17.4 Mackey's theory of induced representations applied to estimating the Poincare group element from image pairs |
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266 | (6) |
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17.5 Effect of electromagnetic radiation on the expanding universe |
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272 | (2) |
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17.6 Photons inside a cavity |
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274 | (2) |
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17.7 Justication of the Hartree-Fock Hamiltonian using second order quantum mechanical perturbation theory |
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276 | (1) |
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17.8 Tetrad formulation of the Einstein-Maxwell field equations |
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277 | (3) |
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17.9 Optimal quantum gate design in the presence of an electromagnetic field propagating in the Kerr metric |
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280 | (6) |
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17.10 Maxwell's equations in the Kerr metric in the tetrad formalism |
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286 | (3) |
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Chapter 18 Quantum fluid antennas interacting with media |
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289 | (15) |
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18.1 Quantum MHD antenna in a quantum gravitational field |
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289 | (1) |
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18.2 Applications of scattering theory to quantum antennas |
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290 | (2) |
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18.3 Wave function of a quantum field with applications to writing down the Schrodinger equation for the expanding universe |
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292 | (2) |
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18.4 Simple exclusion process and antenna theory |
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294 | (1) |
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18.5 MHD and quantum antenna theory |
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295 | (2) |
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18.6 Approximate Hamiltonian formulation of the diffusion equation with applications to quantum antenna theory |
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297 | (1) |
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18.7 Derivation of the damped wave equation for the electromagnetic field in a conducting media in quantum mechanics using the Lindblad formalism |
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298 | (4) |
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18.8 Boson-Fermion unication in quantum stochastic calculus |
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302 | (2) |
| References |
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