Symmetry Breaking and Defects

Kibble, T. W. B.

doi:10.1007/978-94-007-1029-0_1

Cited by 26 publications

(27 citation statements)

References 55 publications

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“…The nematic liquid crystals (LCs) are convenient model systems for the study of defects and can be useful even for the "cosmology in laboratory" experiments [6][7][8][9]. Long-range orientational order in nematic LCs is usually described by the director field ) ( ) ( r n r n r r − = representing the average spatial orientation of the LC molecules [1].…”

Section: Introductionmentioning

confidence: 99%

Optical Trapping, Manipulation, and 3D Imaging of Disclinations in Liquid Crystals and Measurement of their Line Tension

Smalyukh

Senyuk

Shiyanovskii

et al. 2006

Molecular Crystals and Liquid Crystals

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We demonstrate optical trapping and manipulation of defects and transparent microspheres in nematic liquid crystals (LCs). The three-dimensional director fields and positions of the particles are visualized using the Fluorescence Confocal Polarizing Microscopy. We show that the disclinations of both half-integer and integer strengths can be manipulated by either using optically trapped colloidal particles or directly by tightly-focused laser beams. We employ this effect to measure the line tensions of disclinations; the measured line tension is in a good agreement with theoretical predictions. The laser trapping of colloidal particles and defects opens new possibilities for the fundamental studies of LCs.

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Section: Introductionmentioning

confidence: 99%

Optical Trapping, Manipulation, and 3D Imaging of Disclinations in Liquid Crystals and Measurement of their Line Tension

Smalyukh

Senyuk

Shiyanovskii

et al. 2006

Molecular Crystals and Liquid Crystals

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“…One of us then pointed out [2] that analogues of cosmological phase transitions can be studied in the laboratory. In such experiments the equilibrium critical scalings predict various aspects of the non-equilibrium dynamics of symmetry breaking, including the density of residual topological defects [2,3].These ideas led to the Kibble-Zurek mechanism (KZM), a theory of defect formation that uses the critical scalings of the relaxation time and of the healing length to deduce size (ξ) of domains that choose the same "broken symmetry vacuum" [3,4]. When the broken symmetry phase permits their existence, KZM predicts defects will appear with density of about one defect unit (e.g., one monopole or aξ-sized section of a string) perξ-sized domain.…”

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confidence: 99%

Dynamics of a Quantum Phase Transition

2005

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We present two approaches to the dynamics of a quench-induced phase transition in the quantum Ising model. One follows the standard treatement of thermodynamic second order phase transitions but applies it to the quantum phase transitions. The other approach is quantum, and uses LandauZener formula for transition probabilities in avoided level crossings. We show that predictions of the two approaches of how the density of defects scales with the quench rate are compatible, and discuss the ensuing insights into the dynamics of quantum phase transitions.PACS numbers: 03. 05.70.Fh, 73.43.Nq, 75.10.Jm Studies of phase transitions traditionally focussed on equilibrium scalings of various properties near the critical point. The first major exception was an attempt to model the physics of the early Universe: Kibble [1] noted that cosmological phase transitions in a variety of field theoretic models lead to formation of topological defects (such as monopoles or cosmic strings) which may have observable consequences. One of us then pointed out [2] that analogues of cosmological phase transitions can be studied in the laboratory. In such experiments the equilibrium critical scalings predict various aspects of the non-equilibrium dynamics of symmetry breaking, including the density of residual topological defects [2,3].These ideas led to the Kibble-Zurek mechanism (KZM), a theory of defect formation that uses the critical scalings of the relaxation time and of the healing length to deduce size (ξ) of domains that choose the same "broken symmetry vacuum" [3,4]. When the broken symmetry phase permits their existence, KZM predicts defects will appear with density of about one defect unit (e.g., one monopole or aξ-sized section of a string) perξ-sized domain. This KZM prediction has been tested, extended and refined with the help of numerical simulations [5,6], and verified in a variety of increasingly sophisticated and reliable experiments in liquid crystals [7,8], superfluids [9, 10, 11], superconductors [12, 13, 14], and other systems [15].A majority of the experimental data agree with KZM. One notable exception is the case of superfluid 4He, where initial reports of KZM vortices being detected [9] were retracted [10] after it turned out that stirring had inadvertently induced vorticity. In view of various uncertainties, it is still not clear whether 4He experiments are at odds with the numerics-assisted KZM predictions. Regardless, KZM provides a theory of the dynamics of second order phase transitions ranging from low temperature Bose-Einstein condensation to grand unification scales encountered in particle physics and cosmology.In this paper we consider a barely explored problem: the dynamics of quantum phase transitions. Quantum many-body systems (e.g., Bose gases) can undergo thermodynamic phase transformation (such as Bose-Einstein condensation that follows evaporative cooling). KZM theory, developed to deal with thermodynamic phase transitions, applies in this case directly, even though the dynamics of Bose cond...

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“…The number of kinks, therefore, depends on the quenching speed, and tends to zero when t → ∞. The form of the dependence of the number of kinks on the quenching speed is predicted by the so called Kibble-Zureck mechanism [16,17], that predicts a dependence of the form ν ∝ t −1/2 . The same dependence has been observed for systems of different nature that also present a quantum phase transition (see for instance [18] and references therein).…”

Section: Quantum Quenchingmentioning

confidence: 99%

Compressed simulation of thermal and excited states of the one-dimensionalXYmodel

Boyajian

Kraus

2015

Phys. Rev. A

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Since several years the preparation and manipulation of a small number of quantum systems in a controlled and coherent way is feasible in many experiments. In fact, these experiments are nowadays commonly used for quantum simulation and quantum computation. As recently shown, such a system can, however, also be utilized to simulate specific behaviors of exponentially larger systems. That is, certain quantum computations can be performed by an exponentially smaller quantum computer. This compressed quantum computation can be employed to observe for instance the quantum phase transition of the 1D XY-model using very few qubits. We extend here this notion to simulate the behavior of thermal as well as excited states of the 1D XY-model. In particular, we consider the 1D XY-model of a spin chain of n qubits and derive a quantum circuit processing only log(n) qubits which simulates the original system. We demonstrate how the behavior of thermal as well as any eigenstate of the system can be efficiently simulated in this compressed fashion and present a quantum circuit on log(n) qubits to measure the magnetization, the number of kinks, and correlations occurring in the thermal as well as any excited state of the original systems. Moreover we derive compressed circuits to study time evolutions.

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Symmetry Breaking and Defects

Cited by 26 publications

References 55 publications

Optical Trapping, Manipulation, and 3D Imaging of Disclinations in Liquid Crystals and Measurement of their Line Tension

Optical Trapping, Manipulation, and 3D Imaging of Disclinations in Liquid Crystals and Measurement of their Line Tension

Dynamics of a Quantum Phase Transition

Compressed simulation of thermal and excited states of the one-dimensionalXYmodel

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