Stochastic Processes in Classical and Quantum Physics and Engineering

Cover
Half Title
Title Page
Copyright Page
Preface
Brief Contents
Table of Contents
1. Stability Theory of Nonlinear Systems Based on Taylor Approximations of the Nonlinearity
1.1 Stochastic Perturbation of Nonlinear Dynamical Systems: Linearized Analysis
1.2 Large Deviation Analysis of the Stability Problem
1.3 LDP for Yang-Mills Gauge Fields and LDP for the Quantized Metric Tensor of Spacetime
1.4 String in Background Fields
2. String Theory and Large Deviations
2.1 Evaluating Quantum String Amplitudes Using Functional Integration
2.2 LDP for Poisson Fields
2.3 LDP for Strings Perturbed by Mixture of Gaussian and Poisson Noise
3. Ordinary, Partial and Stochastic Differential Equation Models for Biological Systems, Quantum Gravity, Hawking Radiation,
Quantum Fluids, Statistical Signal Processing,
Group Representations, Large Deviations in Statistical Physics
3.1 A lecture on Biological Aspects of Virus Attacking the Immune System
3.2 More on Quantum Gravity
3.3 Large Deviation Properties of Virus Combat with Antibodies
3.4 Large Deviations Problems in Quantum Fluid Dynamics
3.5 Lecture Schedule for Statistical Signal Processing
3.6 Basic Concepts in Group Theory and Group Representation Theory
3.7 Some Remarks on Quantum Gravity Using the ADM Action
3.8 Diffusion Exit Problem
3.9 Large Deviations for the Boltzmann Kinetic Transport Equation
3.10 Orbital Integrals for SL(2,R) with Applications to Statistical Image Processing
3.11 Loop Quantum Gravity (LQG)
3.12 Group Representations in Relativistic Image Processing
3.13 Approximate Solution to the Wave Equation in the Vicinity of the Event Horizon of a Schwarchild Black-hole
3.14 More on Group Theoretic Image Processing
3.15 A Problem in Quantum Information Theory
3.16 Hawking Radiation
4. Research Topics on Representations
4.1 Remarks on Induced Representations and Haar Integrals
4.2 On the Dynamics of Breathing in the Presence of a Mask
4.3 Plancherel Formula for SL(2,R)
4.4 Some Applications of the Plancherel Formula for a Lie Group to Image Processing
5. Some Problems in Quantum Information Theory
5.1 Quantum Information Theory and Quantum Blackhole Physics
5.2 Harmonic Analysis on the Schwarz Space of G = SL(2,R)
5.3 Monotonicity of Quantum Entropy Under Pinching
6. Lectures on Statistical Signal Processing
6.1 Large Deviation Analysis of the RLS Algorithm
6.2 Problem Suggested
6.3 Fidelity Between Two Quantum States
6.4 Stinespring’s Representation of a TPCP Map, i.e, of a Quantum Operation
6.5 RLS Lattice Algorithm, Statistical Performance Analysis
6.6 Approximate Computation of the Matrix Elements of the Principal and Discrete Series for G = SL(2,R)
6.7 Proof of the Converse Part of the Cq Coding Theorem
6.8 Proof of the Direct part of the Cq Coding Theorem
6.9 Induced Representations
6.10 Estimating Non-uniform Transmission Line Parameters and Line Voltage and Current Using the Extended Kalman Filter
6.11 Multipole Expansion of the Magnetic Field Produced by a Time Varying Current Distribution
7. Some Aspects of Stochastic Processes
7.1 Problem Suggested by Prof. Dhananjay
7.2 Converse of the Shannon Coding Theorem
8. Problems in Electromagnetics and Gravitation
9. Some More Aspects of Quantum Information Theory
9.1 An Expression for State Detection Error
9.2 Operator Convex Functions and Operator Monotone Functions
9.3 A Selection of Matrix Inequalities
9.4 Matrix Holder Inequality
10. Lecture Plan for Statistical Signal Processing
10.1 End-Semester Exam, Duration: Four Hours, Pattern Recognition
10.2 Quantum Stein’s Theorem
10.3 Question Paper, Short Test, Statistical Signal Processing
10.4 Question Paper on Statistical Signal Processing, Long Test
10.5 Quantum Neural Networks for Estimating EEG pdf from Speech pdf Based on Schrodinger’s Equation
10.6 Statistical Signal Processing
10.7 Monotonocity of Quantum Relative Renyi Entropy
11. My Commentary on the Ashtavakra Gita
12 LDP-UKF Based Controller
13. Abstracts for a Book on Quantum Signal Processing Using Quantum Field Theory
14. Quantum Neural Networks and Learning Using Mixed State Dynamics for Open Quantum Systems
15. Quantum Gate Design, Magnet Motion, Quantum Filtering, Wigner Distributions
15.1 Designing a Quantum Gate Using QED with a Control c-number Four Potential
15.2 On the Motion of a Magnet Through a Pipe with a Coil Under Gravity and the Reaction Force Exerted by the Induced Current
Through the Coil on the Magnet
15.3 Quantum Filtering Theory Applied to Quantum Field Theory for Tracking a Given Probability Density Function
15.4 Lecture on the Role of Statistical Signal Processing in General Relativity and Quantum Mechanics
15.5 Problems in Classical and Quantum Stochastic Calculus
15.6 Some Remarks on the Equilibrium Fokker-Planck Equation for the Gibbs Distribution
15.7 Wigner-distributions in Quantum Mechanics
15.8 Motion of An Element having Both an Electric and a Magnetic Dipole Moment in an External Electromagnetic Field Plus a Coil
16. Large Deviations for Markov Chains, Quantum Master Equation, Wigner Distribution for the Belavkin Filter
16.1 Large Deviation Rate Function for the Empirical Distribution of a Markov Chain
16.2 Quantum Master Equation in General Relativity
16.3 Belavkin Filter for the Wigner Distirbution Function
17. String and Field Theory with Large Deviations, Stochastic Algorithm Convergence
17.1 String Theoretic Corrections to Field Theories
17.2 Large Deviations Problems in String Theory
17.3 Convergence Analysis of the LMS Algorithm
17.4 String Interacting with Scalar Field, Gauge Field and a Gravitational Field