Low Energy Collision Physics : Applications to Cold Atoms.

Format:

Book

Author/Creator:

Deb, Bimalendu.

Series:

IOP Ebooks Series

Language:

English

Physical Description:

1 online resource (225 pages)

Edition:

1st ed.

Place of Publication:

Bristol : Institute of Physics Publishing, 2023.

Summary:

A book with a balanced approach to pedagogic and research frontiers in cold atomic collisions and related topics.

Contents:

Intro

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This book, consisting of eight chapters, presents basics of low energy collision physics and their applications to cold atoms. The purpose is to bridge the gap between undergraduate or graduate teaching in scattering theory and research frontiers in cold atomic and molecular sciences.&lt

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The first chapter begins with an introduction to collision phenomena in general, highlighting the distinction between low versus high energy, classical versus quantum

Acknowledgments

Author biography

Bimalendu Deb

Chapter Introduction

1.1 Classical concept of collisions

1.2 Useful terminologies and mathematical preliminaries

Differential and total scattering cross sections

Elastic, inelastic, and reactive collisions

Two-particle collisions: the center-of-mass frame

1.3 Some basics about quantum collisions

Quantum states and wave packets

Scattering channels

Scattering matrices and matrix elements

1.3.1 Lippmann-Schwinger equation

Optical theorem

Exercise

References

Chapter Single-channel scattering

2.1 Potential scattering in 3D

Asymptotic boundary conditions

Born approximation

Generalized optical theorem

2.2 Partial-wave expansion

Partial-wave tˆ-matrix element

Partial-wave Sˆ-matrix element

Phase shift

2.3 Partial-wave Green's function

2.4 Wigner threshold laws

Derivation of the Wigner threshold laws

Scattering length

Effective range expansion

2.5 Scattering by a short-range potential

Rectangular well and barrier

Rigid sphere

Zero-range potentials

2.6 Classical theory of collisions

2.7 Coulomb scattering

2.7.1 Classical expression for σ(θ)

2.7.2 Quantum mechanical expression for σ(θ).

2.8 High vs low-energy and classical vs quantum collisions

Chapter Multichannel scattering

3.1 Two-particle scattering with spin

In the absence of any external field

In the presence of an external field

3.2 Formal theory of multichannel scattering

3.2.1 Case (i): all channels are open

3.2.2 Case (iii): some channels are open, others are closed

3.2.3 Multichannel scattering cross section

Chapter Resonances and bound states

4.1 Energy dependence of phase shift near a resonance

4.2 Resonances, bound states, and analyticity of S-matrix elements

4.3 Resonances and bound states for a rectangular potential well

Zero-energy resonances

4.4 Shape resonances

4.5 Feshbach resonances

4.5.1 Two-channel model

4.6 Fano resonances

4.6.1 Fano state

4.6.2 Doubly dressed Fano state: quantum interference

4.6.3 Two coupled bound states, only one of which is coupled to a continuum

4.7 Bound state in a continuum

4.8 Resonant mean-field interaction

Chapter Cold atomic collisions

5.1 Atomic hyperfine interactions

5.2 Atom-atom potentials

5.2.1 Born-Oppenheimer approximation

5.2.2 Long-range molecular potentials

5.2.3 Fundamentals of symmetry concepts in diatomic molecules

5.3 Collisions between cold atoms

5.4 Collisions in a magnetic field

5.4.1 Magnetic Feshsbach resonance

5.4.2 Outline of the advancement in MFR

5.5 Collisions in a laser field

5.5.1 Optical Feshbach resonances

5.5.2 Theory of OFR

5.5.3 PA Hamiltonian

5.5.4 T-matrix element

5.6 Collisions in both magnetic and laser fields

5.6.1 Magneto-optical Fano-Feshbach resonance

5.7 Higher partial-wave Feshbach resonances

5.8 Collisions in a static electric field

5.8.1 Scattering between a pair of homonuclear atoms.

5.8.2 Scattering between a pair of heteronuclear atoms

5.9 Ion-atom collisions at low energy

5.10 Bound state in a continuum of cold atoms

Chapter Association spectroscopy

6.1 Photoassociation

6.1.1 Single-photon photoassociation

6.1.2 Raman photoassociation: the creation of ground-state molecules

6.1.3 A brief overview of photoassociation spectroscopy and its applications

6.2 Magneto- and magneto-optical association: Feshbach molecules

6.3 Efimov trimers

References and further reading

Chapter Collisions in low dimensions

7.1 Scattering in two dimensions

7.1.1 Theory

7.1.2 Two-dimensional zero-range potential

7.1.3 Coulomb scattering in 2D

7.2 Scattering in one dimension

7.2.1 One-dimensional zero-range potential

7.3 Cold atoms in low dimensions

Chapter Numerical methods

8.1 Numerov-Cooley algorithm

8.2 Scattering-state calculations

8.3 Green's function calculation

8.4 Bound state calculation by the Numerov method

8.5 Discrete variable representation method

8.6 Quantum defect theoretic method

Chapter

Chapter.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

0-7503-4609-4