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BL
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| Record Number
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859245
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| Main Entry
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Puebla, Ricardo
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| Title & Author
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Equilibrium and nonequilibrium aspects of phase transitions in quantum physics /\ Ricardo Puebla.
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| Publication Statement
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Cham, Switzerland :: Springer,, [2018]
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| Series Statement
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Springer theses,
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| Page. NO
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1 online resource
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| ISBN
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3030006522
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: 3030006530
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: 3030006549
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: 9783030006525
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: 9783030006532
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: 9783030006549
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9783030006525
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| Bibliographies/Indexes
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Includes bibliographical references.
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| Contents
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Intro; Supervisor's Foreword; Abstract; List of PublicationsParts of this thesis are based on or have been taken from material first published in the following peer-reviewed journals or as preprint (arXiv) versions:Fokker-Planck formalism approach to Kibble-Zurek scaling laws and nonequilibrium dynamics R. Puebla, R. Nigmatullin, T.E. Mehlstäubler, and M.B. Plenio Phys. Rev. B 95, 134104 (2017) arXiv:1702.02099Probing the dynamics of a superradiant quantum phase transition with a single trapped ion R. Puebla, M.-J. Hwang, J. Casanov; Acknowledgements; Cooperations and Funding; Contents.
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1 Introduction1.1 Continuous Phase Transitions; 1.1.1 Critical Exponents; 1.1.2 Finite-Size Scaling Hypothesis; 1.1.3 Universality; 1.2 Ising Model; 1.2.1 Mean-Field Theory; 1.2.2 Exact Solutions: Outline; 1.2.3 Transverse-Field Quantum Ising Model; 1.3 Nonequilibrium Dynamics and the Kibble-Zurek Mechanism; 1.4 Structure and Contents; References; 2 Structural Phase Transitions; 2.1 Ginzburg-Landau Theory; 2.1.1 Nonequilibrium Dynamics; 2.1.2 Overdamped Regime: Smoluchowski Equation; 2.1.3 General and Underdamped Regime: Kramers Equation; 2.2 Coulomb Crystal in Ion Traps.
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2.2.1 Ginzburg-Landau Map2.2.2 Defect Formation and Kibble-Zurek Scaling; 2.3 Conclusion and Outlook; References; 3 Quantum Rabi Model: Equilibrium; 3.1 Quantum Rabi Model; 3.2 Superradiant Quantum Phase Transition; 3.2.1 Low-Energy Effective Hamiltonians; 3.2.2 Signatures of the Quantum Phase Transition; 3.2.3 Finite-Frequency Scaling; 3.2.4 Universality Class; 3.3 Excited-State Quantum Phase Transition; 3.3.1 Semiclassical Approach; 3.3.2 Signatures of the ESQPT; 3.4 Conclusion and Outlook; References; 4 Quantum Rabi Model: Nonequilibrium.
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4.1 Nonequilibrium Dynamics and Kibble-Zurek Scaling Laws4.1.1 Infinite Limit: Kibble-Zurek Physics; 4.1.2 Nonlinear Protocols; 4.1.3 Thermal States; 4.1.4 Sudden Quenches; 4.2 Finite-Frequency Case: Breakdown of KZ Scaling; 4.2.1 Nonequilibrium Finite-Frequency Scaling Functions; 4.2.2 Universality Class; 4.3 Conclusion and Outlook; References; 5 Superradiant QPT with a Single Trapped Ion; 5.1 Proposed Trapped-Ion Experiment; 5.1.1 Trapped-Ion Platform and QRM; 5.1.2 Protocol and Trapped-Ion Simulations; 5.1.3 Standing-Wave Configuration; 5.1.4 Effects of Noise.
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5.2 Continuous Dynamical Decoupling5.2.1 Basic Operating Principle; 5.2.2 Trapped-Ion Setup and Continuous Dynamical Decoupling; 5.2.3 Concatenated Continuous Dynamical Decoupling; 5.3 Conclusion and Outlook; References; 6 Quantum Kibble-Zurek Mechanism; 6.1 Long-Range Transverse Field Ising Model; 6.1.1 Experimental Realization; 6.1.2 Ground-State Properties; 6.1.3 Nonequilibrium Dynamics and Scaling Laws; 6.2 Conclusion and Outlook; References; 7 Concluding Remarks and Outlook; References; Appendix A Survey on Stochastic Processes; A.1 Brownian Motion and Langevin Equation.
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| Abstract
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In this book, the equilibrium and nonequilibrium properties of continuous phase transitions are studied in various systems, with a special emphasis on understanding how well-established universal traits at equilibrium may be extended into the dynamic realm, going beyond the paradigmatic Kibble-Zurek mechanism of defect formation. This book reports on the existence of a quantum phase transition in a system comprising just a single spin and a bosonic mode (the quantum Rabi model). Though critical phenomena are inherent to many-body physics, the author demonstrates that this small and ostensibly simple system allows us to explore the rich phenomenology of phase transitions, both in- and out-of-equilibrium. Moreover, the universal traits of this quantum phase transition may be realized in a single trapped-ion experiment, thus avoiding the need to scale up the number of constituents. In this system, the phase transition takes place in a suitable limit of system parameters rather than in the conventional thermodynamic limit - a novel notion that the author and his collaborators have dubbed the finite-component system phase transition. As such, the results gathered in this book will open promising new avenues in our understanding and exploration of quantum critical phenomena.
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| Subject
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Equilibrium.
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Phase transformations (Statistical physics)
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Atomic molecular physics.
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Condensed matter physics (liquid state solid state physics)
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Equilibrium.
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Phase transformations (Statistical physics)
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Quantum physics (quantum mechanics quantum field theory)
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SCIENCE-- Energy.
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SCIENCE-- Mechanics-- General.
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SCIENCE-- Physics-- General.
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Statistical physics.
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| Dewey Classification
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530.474
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| LC Classification
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QC175.16.P5
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