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Birkhäuser Boston eBooks

Adiabatic Phases in Quantum Mechanics

Dariusz Chruściński, Andrzej Jamiołkowski

Published Jan 1, 2004• 0 citations
Publisher

Abstract

The notion of adiabaticity has played important role in the history of physics. Roughly speaking, it lies on the border of statics and dynamics, taking into account dynamical effects but in the limit of infinitely slow changes. That is, the system is no longer static but its evolution is “infinitely slow.” A typical situation where one applies adiabatic ideas is when a physical system may be divided into two subsystems with completely different time scales: a so-called slow subsystem and fast subsystem . These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

DOI
10.1007/978-0-8176-8176-0_2

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Abstract This book is an introduction to explicitly time-dependent physics. We describe the theory of the dynamic regime that we refer to as “quasi-adiabatic”. It pertains to time-dependent evolution that, while slow, is not genuinely adiabatic. It is rich in effects that can be understood even in quantum systems with complex many-body interactions. Examples from research in quantum computing, phase transitions, Bose-Enstein condensates, and quantum control will be used to illustrate these effects. Prerequisites include undergraduate introductory courses in quantum and classical mechanics, as well as complex analysis. Our book aims to fill the gap in the literature by providing an accessible, for early graduate and advanced undergraduate students, introduction to both geometric phases and nonadiabatic transitions at a level sufficient to consider numerous applications.

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The notion of adiabaticity has played important role in the history of physics. Roughly speaking, it lies on the border of statics and dynamics, taking into account dynamical effects but in the limit of infinitely slow changes. That is, the system is no longer static but its evolution is “infinitely slow.” A typical situation where one applies adiabatic ideas is when a physical system may be divided into two subsystems with completely different time scales: a so-called slow subsystem and fast subsystem . These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Many body physics is concerned with macroscopic systems consisting of a very large number of microscopic particles (N ≈ 10 20 ). In this case the direct dynamical treatment of the complete system is impossible. A quite useful and frequently applied approximation consists in the neglection of terms which are relatively small as the volume of the systems tends to infinity, the particle density remaining constant. For the concise theoretical description of the typical many body phenomena such as phase transitions and spontaneous symmetry breakdown the use of the thermodynamical limit is even necessary, since no existing theory for the finite systems shows these effects. As a general rule one can say that a quantum system behaves like a thermodynamical system only in the infinite-volume limit. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Epistemic accounts of quantum states such as quantum Bayesianism and the Rule Perspective are formulated in terms of notions such as ‘agent’, ‘epistemic situation’, and ‘state assignment’, which are neither themselves fundamental physical notions nor in any evident way reducible to such notions. In the present section I discuss an objection to the employment of such ‘ anthropocentric notions’ (as I will call them), which claims that they are far too vague and too imprecise to be used in foundational accounts. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Abstract This book is an introduction to explicitly time-dependent physics. We describe the theory of the dynamic regime that we refer to as “quasi-adiabatic”. It pertains to time-dependent evolution that, while slow, is not genuinely adiabatic. It is rich in effects that can be understood even in quantum systems with complex many-body interactions. Examples from research in quantum computing, phase transitions, Bose-Enstein condensates, and quantum control will be used to illustrate these effects. Prerequisites include undergraduate introductory courses in quantum and classical mechanics, as well as complex analysis. Our book aims to fill the gap in the literature by providing an accessible, for early graduate and advanced undergraduate students, introduction to both geometric phases and nonadiabatic transitions at a level sufficient to consider numerous applications.