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Solvable One-Dimensional Multi-State Models for Statistical and Quantum Mechanics

  • Book
  • © 2021

Overview

Authors:
  1. Rajendran Saravanan

    1. Indian Institute of Technology Mandi, Mandi, India

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  2. Aniruddha Chakraborty

    1. Indian Institute of Technology Mandi, Mandi, India

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  • Highlights the need for studying multi-state models analytically for understanding the physics of molecular processes?
  • Presents time-domain methods to solve Smoluchowski-based reaction-diffusion systems with single-state and two-states
  • Discusses the transient features of quantum two-state models

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-xix
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  2. Theoretical Background and Motivation

    • Rajendran Saravanan, Aniruddha Chakraborty
    Pages 1-43

  3. Mathematical Methods for Solving Multi-state Smoluchowski Equations

    • Rajendran Saravanan, Aniruddha Chakraborty
    Pages 45-117

  4. Investigation of Wave Packet Dynamics Using the Presented Time-Domain Method

    • Rajendran Saravanan, Aniruddha Chakraborty
    Pages 119-153

  5. Summary and Future Scope

    • Rajendran Saravanan, Aniruddha Chakraborty
    Pages 155-156

  6. Back Matter

    Pages 157-174
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Keywords

About this book

This book highlights the need for studying multi-state models analytically for understanding the physics of molecular processes. An intuitive picture about recently solved models of statistical and quantum mechanics is drawn along with presenting the methods developed to solve them. The models are relevant in the context of molecular processes taking place in gaseous phases and condensed phases, emphasized in the introduction. Chapter 1 derives the arisal of multi-state models for molecular processes from the full Hamiltonian description. The model equations are introduced and the literature review presented in short. In Chapter 2, the time-domain methods to solve Smoluchowski-based reaction-diffusion systems with single-state and two-state descriptions are discussed. Their corresponding analytical results derive new equilibrium concepts in reversible reactions and studies the effect of system and molecular parameters in condensed-phase chemical dynamics. In Chapter 3, time-domain methods to solve quantum scattering problems are developed. Along side introducing a brand new solvable model in quantum scattering, it discusses transient features of quantum two-state models. In interest with electronic transitions, a new solvable two-state model with localized non-adiabatic coupling is also presented. The book concludes by proposing the future scope of the model, thereby inviting new research in this fundamentally important and rich applicable field.​

Authors and Affiliations

  • Indian Institute of Technology Mandi, Mandi, India

    Rajendran Saravanan, Aniruddha Chakraborty

About the authors

Dr. Rajendran Saravanan received his PhD in physics from the Indian Institute of Technology Mandi, India. His research interests include mathematical physics, theoretical chemical physics, econophysics, etc. Currently he is persuing his postdoc under Prof. Raphael D Levine at the University of Jerusalem, Israel.​


Dr. Aniruddha Chakraborty obtained his Ph.D. in physical chemistry from the Indian Institute of Science, Bangalore. Having done his postdoc from the University of Oregon, currently he is an associate professor at Indian Institute of Technology Mandi. His research interests include almost all areas of theoretical physics, mainly focused on understanding chemical physics problems.

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