Tunneling In Complex Systems

By: Steve Tomsovic (Editor)

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Hardcover | 24 June 1998

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340 Pages

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23.5 x 16.51 x 1.91

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Quantum tunneling is an intriguing phenomenon arising in a multitude of physical contexts. New experiments in systems as wide ranging as superdeformed nuclei, Bose-Einstein condensed gases, and nanomagnetic systems are spurring theoretical studies into the fundamental nature of tunneling. In this volume, the articles include: (i) tunneling out of a metastable state, (ii) coherence between two wells in tunneling contact, (iii) the consequences of the nature of the underlying dynamics (i.e. regular motion, chaos or some mixture) in low-dimensional systems and its connection to newly identified tunneling phenomena such as chaos-assisted tunneling, (iv) nanomagnetic systems with focus on comparing environmental descriptions of nuclear spins and oscillators, (v) solitons in Bose condensates, (vi) tunneling out of the nuclear superdeformed well and its use as a probe of pairing and chaos in excited nuclear states, and (vii) problems linked to the Bose condensed phase of atomic alkali gases.These subjects and others are gathered in six pedagogical courses given during the spring of 1997 at the National Institute of Nuclear Physics program “Tunneling in complex systems”. The purpose of the courses was to give graduate students and postdoctoral researchers exposure to a sampling of such recent theoretical advances and experimental contexts of tunneling as well as a bridge for the communication gaps between researchers in the various fields concerned with tunneling.

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

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Hardcover

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