Time crystals
Author(s)
Bibliographic Information
Time crystals
（Springer series on atomic, optical, and plasma physics, 114）
Springer Nature Switzerland AG, 2020
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Note
Includes bibliographical references and index
Description and Table of Contents
Description
This book provides the first comprehensive description of time crystals which have a repeating structure in time. It introduces the fundamental concepts behind time crystals and explores the many different branches of this new research area.
The book starts with the original idea of the time crystallization in quantum systems as introduced by Wilczek and follows the development of the field up to the present day. Both spontaneous formation of crystalline structures in time and concepts of the condensed matter physics in the time domain, ranging from Anderson localization in time to many-body systems with exotic interactions, are described. The prospect of creation of novel objects by means of time engineering is also presented.
The book assumes knowledge of quantum mechanics to the graduate level. It serves as a valuable reference with pointers to future research directions for graduate students and senior scientists alike.
Table of Contents
I. Spontaneous formation of space crystals
II. Spontaneous breaking of continuous time translation symmetry
II.1 Wilczek model
II.2 Lack of time crystal formation by systems in the ground states
II.3 Excited eigenstates and time crystals formation
II.4 Superfluid phase and Josephson oscillations and their relation to time crystals
III.Discrete time crystals
III.1 Proposals of discrete time crystals
III.1.1 Formation of discrete time crystals by atoms bouncing on an oscillating mirror
III.1.2 Formation of discrete time crystals by periodically driven spin systems
III.1.3 Different proposals of discrete time crystals
III.2 Experimental realizations of discrete time crystals
IV. Spontaneous formation of quasi-crystals structures in time
V. Condensed matter physics in the time domain
V.1 Emergence of crystalline structures in time in periodically driven systems
V.2 Anderson localization in time
V.3 Topological time crystals
V.4 Quasi-crystals in time
V.5 Many-body time crystals with exotic interactions
V.6 Many-body localization induced by temporal disorder
V.7 Time crystals with properties of 2D or 3D space crystals
VI. Time engineering
VII. Time crystals in photonic materials
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