عنوان

Equilibrium and nonequilibrium aspects of phase transitions in quantum physics /

3030006522

3030006530

3030006549

9783030006525

9783030006532

9783030006549

9783030006525

Equilibrium and nonequilibrium aspects of phase transitions in quantum physics /

[Book]

Ricardo Puebla.

Cham, Switzerland :

Springer,

[2018]

1 online resource

Springer theses,

2190-5061

Includes bibliographical references.

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.

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.

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.

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.

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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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.

Springer Nature

com.springer.onix.9783030006532

9783030006525

9783030006549

Equilibrium.

Phase transformations (Statistical physics)

Atomic & molecular physics.

Condensed matter physics (liquid state & solid state physics)

Equilibrium.

Phase transformations (Statistical physics)

Quantum physics (quantum mechanics & quantum field theory)

SCIENCE-- Energy.

SCIENCE-- Mechanics-- General.

SCIENCE-- Physics-- General.

Statistical physics.

PHFC

PHFC

SCI-- 024000

SCI-- 041000

SCI-- 055000

Puebla, Ricardo

20200823072035.0

pn

[Book]

Y