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Nova Science Publishers eBooks

Trends in boson research

A. V. Ling

Published Jan 1, 2006• 6 citations
OpenAlex

Abstract

Preface. Vortex Matter in Atomic Bose-Einstein Condesates The Gross-Pitaevskii Equations and Beyond for Imhomogenous Condensed Bosons Bosonisation, Soliton-Particle Duality and Mandelstam-Halpern Operators Study of Anomalous Quartic Gauge Couplings at Gamma Colliders Higgs Pair-Production at Next Generation Linear e+eI Colliders Implicit Anyon or Single Particle Boson Mechanism of HTCS and Pseudogap Regime Remarks on Self-Consistent Models of a Particle Gauge Symmetry and its Implications for the Schwinger-Dyson Equations Index.

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Simulation of single and many particle gauge theories with ultracold atomic gases

Matthew Edmonds

The study of systems formed from ultracold atomic gases has emerged to become one of the most active research fields within the condensed matter landscape. These highly controllable macroscopic systems amalgamate ideas from many sub disciplines of physics, including the study of low temperatures, quantum optics and quantum information theory as well as the seemingly disparate field of high energy physics. The central concept of this thesis is gauge theories as applied to systems of bosonic atoms, which at temperatures close to absolute zero form Bose-Einstein condensates. To simulate the mathematical structure of a gauge theory, the geometric (Berry) phase formalism is adopted. This is in turn accomplished by considering the adiabatic following of the eigenstates of the light-matter coupling for an ensemble of atoms forming a Bose-Einstein condensate. These concepts are then applied to show how one can generate a spin-orbit coupling in a one-dimensional condensate, which additionally features a random mass term that allows us to study the physics of Anderson localization in an intriguing “quasi” relativistic regime. One of the features of light induced gauge potentials is that they are static; in the sense that there is no feedback between the light-matter interaction and the matter field. In the second part of this thesis it is demonstrated how such a feedback mechanism can be induced by the appropriate modification of the light-matter interaction. The consequences this has for the condensate are then described at the mean-field level, including the expected experimental signatures of the resulting ‘interacting’ gauge theory, in terms of the expansion of the condensate and also the structure of the solitons of this nonlinear system. Finally, this nonlinear model is applied to a double well system, from which the associated Bose-Hubbard model is derived and analysed; and the nonlinear Josephson problem studied.

•Jan 1, 2013•0 citations

Field Theories in Condensed Matter Physics

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Preface Introduction Quantum Many Particle Physics Critical Phenomena Phase Transitions and Critical Phenomena Topological Defects Introduction to Bosonization Quantum Hall Effect Low-Dimensional Quantum Spin Systems

Texts and readings in physical sciences•Jan 1, 2001•60 citations

Vortex lines attached to dark solitons in Bose-Einstein condensates and boson-vortex duality in 3+1 dimensions

Antonio Muñoz Mateo, Xiaoquan Yu, Jun Nian

We demonstrate the existence of stationary states composed of vortex lines attached to planar dark solitons in scalar Bose-Einstein condensates. Dynamically stable states of this type are found at low values of the chemical potential in channeled condensates, where the long-wavelength instability of dark solitons is prevented. In oblate, harmonic traps, U-shaped vortex lines attached by both ends to a single planar soliton are shown to be long-lived states. Our results are reported for parameters typical of current experiments, and open up a way to explore the interplay of different topological structures. These configurations provide Dirichlet boundary conditions for vortex lines and thereby mimic open strings attached to D-branes in string theory. We show that these similarities can be formally established by mapping the Gross-Pitaevskii theory into a dual effective string theory for open strings via a boson-vortex duality in 3+1 dimensions. Combining a one-form gauge field living on the soliton plane which couples to the end points of vortex lines and a two-form gauge field which couples to vortex lines, we obtain a gauge-invariant dual action of open vortex lines with their end points attached to dark solitons.

arXiv:1606.02776•Physical Review A•Dec 19, 2016•9 citations

Boson Systems: Bose–Einstein Condensation and Superfluidity

Michael El-Batanouny

Treats the Bose-Einstein condensation, and explains superfluidity from the Bogoliubov and Ginzburg-Landau perspectives. It also describes the concept of spontaneous symmetry breaking and Goldstone modes.

Cambridge University Press eBooks•Mar 6, 2020•0 citations

Two-dimensional nonlinear vector states in Bose-Einstein condensates

A. I. Yakimenko, Yu. Zaliznyak, Volodymyr M. Lashkin

Two-dimensional (2D) vector matter waves in the form of soliton-vortex and vortex-vortex pairs are investigated for the case of attractive intracomponent interaction in two-component Bose-Einstein condensates. Both attractive and repulsive intercomponent interactions are considered. By means of a linear stability analysis we show that soliton-vortex pairs can be stable in some regions of parameters while vortex-vortex pairs turn out to be always unstable. The results are confirmed by direct numerical simulations of the 2D coupled Gross-Pitaevskii equations.

arXiv:0901.1041•Physical Review A•Apr 28, 2009•20 citations

DYNAMICS OF INTERACTING BOSONS: A COMPACT REVIEW

Marcin Napiórkowski

The success of Gross--Pitevskii and Bogoliubov theories in the description of large systems of interacting bosons led to a substantial effort into rigorously deriving these effective theories. In this work we shall review the related existing literature in the context of dynamics of large bosonic systems.

arXiv:2101.04594•Lecture notes series, Institute For Mathematical Sciences•Feb 26, 2023•5 citations
Preface. Vortex Matter in Atomic Bose-Einstein Condesates The Gross-Pitaevskii Equations and Beyond for Imhomogenous Condensed Bosons Bosonisation, Soliton-Particle Duality and Mandelstam-Halpern Operators Study of Anomalous Quartic Gauge Couplings at Gamma Colliders Higgs Pair-Production at Next Generation Linear e+eI Colliders Implicit Anyon or Single Particle Boson Mechanism of HTCS and Pseudogap Regime Remarks on Self-Consistent Models of a Particle Gauge Symmetry and its Implications for the Schwinger-Dyson Equations Index.
The study of systems formed from ultracold atomic gases has emerged to become one of the most active research fields within the condensed matter landscape. These highly controllable macroscopic systems amalgamate ideas from many sub disciplines of physics, including the study of low temperatures, quantum optics and quantum information theory as well as the seemingly disparate field of high energy physics. The central concept of this thesis is gauge theories as applied to systems of bosonic atoms, which at temperatures close to absolute zero form Bose-Einstein condensates. To simulate the mathematical structure of a gauge theory, the geometric (Berry) phase formalism is adopted. This is in turn accomplished by considering the adiabatic following of the eigenstates of the light-matter coupling for an ensemble of atoms forming a Bose-Einstein condensate. These concepts are then applied to show how one can generate a spin-orbit coupling in a one-dimensional condensate, which additionally features a random mass term that allows us to study the physics of Anderson localization in an intriguing “quasi” relativistic regime. One of the features of light induced gauge potentials is that they are static; in the sense that there is no feedback between the light-matter interaction and the matter field. In the second part of this thesis it is demonstrated how such a feedback mechanism can be induced by the appropriate modification of the light-matter interaction. The consequences this has for the condensate are then described at the mean-field level, including the expected experimental signatures of the resulting ‘interacting’ gauge theory, in terms of the expansion of the condensate and also the structure of the solitons of this nonlinear system. Finally, this nonlinear model is applied to a double well system, from which the associated Bose-Hubbard model is derived and analysed; and the nonlinear Josephson problem studied.
We demonstrate the existence of stationary states composed of vortex lines attached to planar dark solitons in scalar Bose-Einstein condensates. Dynamically stable states of this type are found at low values of the chemical potential in channeled condensates, where the long-wavelength instability of dark solitons is prevented. In oblate, harmonic traps, U-shaped vortex lines attached by both ends to a single planar soliton are shown to be long-lived states. Our results are reported for parameters typical of current experiments, and open up a way to explore the interplay of different topological structures. These configurations provide Dirichlet boundary conditions for vortex lines and thereby mimic open strings attached to D-branes in string theory. We show that these similarities can be formally established by mapping the Gross-Pitaevskii theory into a dual effective string theory for open strings via a boson-vortex duality in 3+1 dimensions. Combining a one-form gauge field living on the soliton plane which couples to the end points of vortex lines and a two-form gauge field which couples to vortex lines, we obtain a gauge-invariant dual action of open vortex lines with their end points attached to dark solitons.
Two-dimensional (2D) vector matter waves in the form of soliton-vortex and vortex-vortex pairs are investigated for the case of attractive intracomponent interaction in two-component Bose-Einstein condensates. Both attractive and repulsive intercomponent interactions are considered. By means of a linear stability analysis we show that soliton-vortex pairs can be stable in some regions of parameters while vortex-vortex pairs turn out to be always unstable. The results are confirmed by direct numerical simulations of the 2D coupled Gross-Pitaevskii equations.