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Journal of Physics A Mathematical and General

On the removability of Berry's phase

G. Giavarini, E. Gozzi, Daniel Rohrlich, William D. Thacker

Published Sep 7, 1989• 27 citations
Publisher

Abstract

The authors present a thorough analysis of the removability of the Berry phase. They show that for any system they can, by properly restricting the parameter space turn the geometrical phase into an extra shift of the dynamical one. However, this extra shift in the dynamical phase retains its truly geometrical character. The removability is thus only apparent and the geometrical phase can still be measured in interference experiments, as indeed has already been done several times.

DOI
10.1088/0305-4470/22/17/017

Related papers

The q-deformed generalized harmonic oscillator and Berry's phase

A. Boudine, N. Mebarki, K. Benhizia

A generalized q-deformed harmonic oscillator system is studied on a unit circle and the corresponding Berry's phase is calculated explicitly as a function of the time dependent Hamiltonian parameters. It turns out that this geometric phase is complex proving the shifting of a part of the dynamical phase first advocated in Giavarini and al paper on the so called removability of the Berry's phase.

AIP conference proceedings•Jan 1, 2012•1 citation

GEOMETRIC PHASE SHIFTS IN DISSIPATIVE CLASSICAL SYSTEMS

Thomas B. Kepler

The reanalysis of the adiabatic theorem initiated by Berry and leading to the discovery of the unexpectedly elegant geometric phase shift, has been broadened in scope by many authors; most recently, to dissipative classical dynamical systems. I review this work with an emphasis on the fundamental characteristics underlying all instantiations of geometric phase shifts.

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The Geometric Phase in Quantum Systems

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The discovery of the geometric phase is one of the most interesting and intriguing findings of the last few decades. It led to a deeper understanding of the concept of phase in quantum mechanics and motivated a surge of interest in fundamental quantum mechanical issues, disclosing unexpected applications in very diverse fields of physics. Although the key ideas underlying the existence of a purely geometrical phase had already been proposed in 1956 by Pancharatnam, it was Michael Berry who revived this issue 30 years later. The clarity of Berry's seminal paper, in 1984, was extraordinary. Research on the topic flourished at such a pace that it became difficult for non-experts to follow the many different theoretical ideas and experimental proposals which ensued. Diverse concepts in independent areas of mathematics, physics and chemistry were being applied, for what was (and can still be considered) a nascent arena for theory, experiments and technology. Although collections of papers by different authors appeared in the literature, sometimes with ample introductions, surprisingly, to the best of my knowledge, no specific and exhaustive book has ever been written on this subject. The Geometric Phase in Quantum Systems is the first thorough book on geometric phases and fills an important gap in the physical literature. Other books on the subject will undoubtedly follow. But it will take a fairly long time before other authors can cover that same variety of concepts in such a comprehensive manner. The book is enjoyable. The choice of topics presented is well balanced and appropriate. The appendices are well written, understandable and exhaustive - three rare qualities. I also find it praiseworthy that the authors decided to explicitly carry out most of the calculations, avoiding, as much as possible, the use of the joke `after a straightforward calculation, one finds...' This was one of the sentences I used to dislike most during my undergraduate studies. A student is inexperienced in such matters and needs to look at details. This book is addressed to graduate physics and chemistry students and was written thinking of students. However, I would recommend it also to young and mature physicists, even those who are already `into' the subject. It is a comprehensive work, jointly written by five researchers. After a simple introduction to the subject, the book gradually provides deeper concepts, more advanced theory and finally an interesting introduction and explanation of recent experiments. For its multidisciplinary features, this work could not have been written by one single author. The collaborative effort is undoubtedly one of its most interesting qualities. I would definitely recommend it to anyone who wants to learn more on the geometric phase, a topic that is both beautiful and intruiguing.

Journal of Physics A Mathematical and General•Nov 26, 2003•27 citations

Comment on ``Experimental Separation of Geometric and Dynamical Phases Using Neutron Interferometry"

Rajendra Bhandari

We analyse a recently reported neutron interference experiment to measure a geometric phase and attempt to bring out the inadequacy of the ``phase modulo 2π" approach to the geometric phase. A modified neutron interferometer experiment to observe 2nπphase changes of topological origin resulting from closed circuits around singularities in the parameter space of the experiment is proposed.

arXiv:quant-ph/0103134•Mar 24, 2001•1 citation

Berry's phase and orbital angular momentum

Paolo Martelli, Annalaura Fasiello, Mario Martinelli

In 1984 Berry showed that a quantum system evolving in a cyclic and adiabatic way acquires in addition to the dynamic phase also a phase which of geometric nature, depending on the path on the parameter space [1]. This geometric phase, also named Berry's phase, can be generalized to non-adiabatic situations [2] and presents some classical analogues, as in the case of the motion of a Foucault pendulum [3].

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 1, 2017•2 citations

GEOMETRIC METHODS AND THE GAUGE STRUCTURE OF BERRY'S PHASE

Bernard Francis Bednarz

The use of geometric methods to obtain the connection associated with Berry's phase is discussed. Failures and successes in past attempts at using only geometry are presented. It is argued that this approach is most useful for Hamiltonians rotated on the parameter space.

International Journal of Modern Physics A•Oct 10, 1989•2 citations
The authors present a thorough analysis of the removability of the Berry phase. They show that for any system they can, by properly restricting the parameter space turn the geometrical phase into an extra shift of the dynamical one. However, this extra shift in the dynamical phase retains its truly geometrical character. The removability is thus only apparent and the geometrical phase can still be measured in interference experiments, as indeed has already been done several times.
The discovery of the geometric phase is one of the most interesting and intriguing findings of the last few decades. It led to a deeper understanding of the concept of phase in quantum mechanics and motivated a surge of interest in fundamental quantum mechanical issues, disclosing unexpected applications in very diverse fields of physics. Although the key ideas underlying the existence of a purely geometrical phase had already been proposed in 1956 by Pancharatnam, it was Michael Berry who revived this issue 30 years later. The clarity of Berry's seminal paper, in 1984, was extraordinary. Research on the topic flourished at such a pace that it became difficult for non-experts to follow the many different theoretical ideas and experimental proposals which ensued. Diverse concepts in independent areas of mathematics, physics and chemistry were being applied, for what was (and can still be considered) a nascent arena for theory, experiments and technology. Although collections of papers by different authors appeared in the literature, sometimes with ample introductions, surprisingly, to the best of my knowledge, no specific and exhaustive book has ever been written on this subject. The Geometric Phase in Quantum Systems is the first thorough book on geometric phases and fills an important gap in the physical literature. Other books on the subject will undoubtedly follow. But it will take a fairly long time before other authors can cover that same variety of concepts in such a comprehensive manner. The book is enjoyable. The choice of topics presented is well balanced and appropriate. The appendices are well written, understandable and exhaustive - three rare qualities. I also find it praiseworthy that the authors decided to explicitly carry out most of the calculations, avoiding, as much as possible, the use of the joke `after a straightforward calculation, one finds...' This was one of the sentences I used to dislike most during my undergraduate studies. A student is inexperienced in such matters and needs to look at details. This book is addressed to graduate physics and chemistry students and was written thinking of students. However, I would recommend it also to young and mature physicists, even those who are already `into' the subject. It is a comprehensive work, jointly written by five researchers. After a simple introduction to the subject, the book gradually provides deeper concepts, more advanced theory and finally an interesting introduction and explanation of recent experiments. For its multidisciplinary features, this work could not have been written by one single author. The collaborative effort is undoubtedly one of its most interesting qualities. I would definitely recommend it to anyone who wants to learn more on the geometric phase, a topic that is both beautiful and intruiguing.