Tunneling in Complex Systems

by Tomsovic, Steve

• ISBN13: 9789810234461
• ISBN10: 9810234465
• Format: Hardcover
• Copyright: 1998-08-01
• Publisher: WORLD SCIENTIFIC PUB CO INC

Summary

A compilation of six articles gathered from courses given during the spring of 1997 at the National Institute of Nuclear Physics program - Tunneling in complex systems - given to expose graduate students & postdoctoral researchers to the recent theoretical advances & experimental contexts of tunneling. DLC: Tunneling (Physics) Congresses.

Table of Contents

Preface	v
Some General Aspects of Quantum Tunneling and Coherence Application to the BEC Atomic Gases	1	(34)
A.J. Leggett
Tunnelling in Two Dimensions	35	(66)
S.C. Creagh
1. Introduction	35	(4)
2. Dynamics and the Zoology of Wavefunctions	39	(9)
2.1 Integrable and near-integrable dynamics	40	(4)
2.2 Mixed dynamics	44	(1)
2.3 Chaotic dynamics	45	(3)
3. Tunnelling in Integrable and Near-integrable Systems	48	(15)
3.1 Exactly integrable case	49	(4)
3.2 Analytic continuation of KAM tori	53	(5)
3.3 Wilkinson's formula	58	(5)
4. Chaos-assisted Tunnelling	63	(12)
4.1 Overview and statistics	63	(6)
4.2 Scattering matrix approach	69	(6)
5. Chaos and Complex Trajectories	75	(20)
5.1 A dynamical perspective	76	(8)
5.2 Complete chaos in the energy domain	84	(11)
6. Conclusion	95	(1)
References	96	(5)
Quantum Environments: Spin Baths, Oscillator Baths, and Applications to Quantum Magnetism	101	(98)
P. C. E. Stamp
1. Introduction	101	(2)
2. Effective Hamiltonians: Spin Baths and Oscillator Baths	103	(39)
2.1 Truncation to low energies	104	(3)
2.2 Spin baths and nanomagnets -- a worked example	107	(11)
2.3 Some other systems coupled to spin baths	118	(9)
2.4 Coupling to the oscillator bath	127	(15)
3. Tunneling Dynamics: Resonance, Relaxation, Decoherence	142	(29)
3.1 Generalities	142	(4)
3.2 Dynamics of the spin-boson problem	146	(6)
3.3 Other bosonic models	152	(6)
3.4 Central spin model	158	(13)
4. Quantum Nanomagnetism	171	(23)
4.1 Resonant tunneling relaxation	173	(16)
4.2 Macroscopic quantum coherence	189	(5)
References	194	(5)
Coherent Magnetic Moment Reversal in Small Particles with Nuclear Spins	199	(30)
A. Garg
1. Motivation for This Work	199	(2)
2. Introduction to Physical Problems and Models	201	(6)
2.1 Physical system	201	(3)
2.2 What to calculate; preliminary arguments	204	(3)
3. The Discrete WKB Method	207	(3)
4. Tunnel Splitting for the Hamiltonian (1)	210	(2)
5. Inclusion of Nuclear Spins	212	(11)
5.1 One-coflip splittings	212	(5)
5.2 Two co-flip splittings	217	(3)
5.3 Higher coflip processes; effective Hamiltonian	220	(3)
6. Conclusions	223	(3)
References	226	(3)
Tunneling from Super- to Normal-deformed Minima in Nuclei	229	(48)
Teng Lek Khoo
1. Introduction	229	(1)
2. Superdeformation in Nuclei	230	(10)
2.1 General properties	230	(3)
2.2 Tunneling from SD states	233	(1)
2.3 Experiments	234	(2)
2.4 Feeding of SD banks	236	(3)
2.5 Cold cascades within SD rotational bands	239	(1)
3. Decay from SD Bands: Tunneling Out of the False Vacuum	240	(22)
3.1 Physics from decay out of SD bands	240	(1)
3.2 Decay mechanisms	240	(2)
3.3 Spectra from decay out SD states	242	(6)
3.4 Spin/parity quantum numbers, energies and decay scheme of SD bands	248	(6)
3.5 Identical bands	254	(1)
3.6 Quenching of pairing with excitation energy	255	(4)
3.7 Onset of chaos with excitation energy	259	(3)
4. Some Other Examples of Tunneling in Nuclear Physics	262	(5)
4.1 Delta I = 4 bifurcation in SD bands	262	(1)
4.2 Sub-barrier fusion	263	(1)
4.3 Proton emitters	264	(3)
5. Comments on Tunneling in Nuclei	267	(1)
5.1 Analogies with other systems	268	(1)
6. Summary	268	(2)
References	270	(7)
Solitons in the Bose Condensate	277
William P. Reinhardt
1. Introduction	277	(2)
2. Preliminaries: Mean Fields, the Condensate Wave Function, and the Pseudopotential	279	(6)
3. Separation of Variables in a Box, Jacobi Solutions for the 1-dimensional NLSE	285	(8)
4. Stationary State Solutions of the NLSE and Condensate Collisions	293	(9)
5. An Elementary Introduction to Solitons	302	(21)
References	323