Quantum Tunneling in Complex Systems

In the last two decades remarkable progress has been made in understanding and describing tunneling processes in complex systems in terms of classical trajectories. This book introduces recent concepts and achievements with particular emphasis on a dynamical formulation and relations to specific systems in mesoscopic, molecular, atomic and nuclear physics. Advanced imaginary time techniques, e.g. for decay rates and tunnel splittings, are discussed in the first part. The second part covers current developments for wave-packet tunneling in real-time, and the third part describes thermodynamical and nonequilibrium approaches for barrier transmission in dissipative systems.

• Fluctuation phenomena and noise
• Helium-Atom-Streuung
• Quantum rate theory
• REM
• Reaction dynamics
• STEM
• Semiclassical theory
• Semiclassical tunneling
• Tunneling in complex systems

From the reviews:

"This book is a must for anyone who wants to understand quantum tunneling in depth. … Starting from the old Wentzel-Kramers-Brillouin analysis, the author rapidly moves to semiclassical initial value representations … and periodic orbit theories emanating from Gutzwiller’s famous work, which are used extensively to bridge the gap between classical and quantum mechanics. … Experimental examples are dispersed throughout the book. Special attention is given to fission and fusion, macroscopic quantum tunneling in Josephson junctions, tunneling in Bose condensates and the tunneling of magnetization." (Eli Pollak, Mathematical Reviews, Issue 2008 a)

"Ankerhold’s book is a broad compendium of the techniques that have been developed, mostly in the last few decades, for handling the many, many natural phenomena in which tunneling plays a vital role. … In summary, this volume is an excellent source of information on the important area of quantum tunneling. … For anyone wanting to enter the field or find topics worthy of further investigation, this will be the place to start." (L. S. Schulman, SIAM Review, Vol. 50 (1), 2008)

"The book provides a modern survey on semiclassical methods to describe tunneling phenomena for both individual wave packets and ensembles described by density matrices. It is well written and includes discussions of physical examples … . The author has the merit of a clear and effective presentation of arguments, where both ideas behind mathematical tools and physical meaning of results are elucidated. The monograph can be appreciated by expert and less expert readers, and can be suggested as a basic reference for tunneling processes." (Giulio Landolfi, Zentralblatt MATH, Vol. 1133 (11), 2008)

• Physikalisches Institut, Universität Freiburg, Freiburg, Germany

  Joachim Ankerhold

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