Ginzburg Landau Theory Of Condensates

A primer on Ginzberg-Landau Theory considering common and topological excitations including their thermodynamics and dynamical phenomena.

This textbook series has been designed for final year undergraduate and first year graduate students, providing an overview of the entire field showing how specialized topics are part of the wider whole, and including references to current areas of literature and research.

This volume provides readers with a broad collection of theoretical, computational, and experimental methods to quantitatively study the properties of phase-separate biomolecular condensates in diverse systems. The chapters in this book cover topics such as theoretical and computational methods; methods for in vitro characterization of biomolecular condensates; and techniques that enable in-cell characterization of biomolecular condensates. Written in the highly successful Methods in Molecular Biology series format, chapters include introduction to their respective topics, lists of the necessary materials and reagents, step-by-step, readily reproducible laboratory protocols, and expert tips on troubleshooting and avoiding known pitfalls. Comprehensive and thorough, Phase-Separated Biomolecular Condensates: Methods and Protocols is a valuable resource that helps researchers learn and use established methods to study both biophysical properties and biological functions of biomolecular condensates.

The Ginzburg-Landau equation us a mathematical model of superconductors has become an extremely useful tool in many areas of physics where vortices carrying a topological charge appear. The remarkable progress in the mathematical understanding of this equation involves a combined use of mathematical tools from many branches of mathematics. The Ginzburg-Landau model has been an amazing source of new problems and new ideas in analysis, geometry and topology. This collection will meet the urgent needs of the specialists, scholars and graduate students working in this area or related areas.

Covering general theoretical concepts and the research to date, this book demonstrates that Bose-Einstein condensation is a truly universal phenomenon.

This book reports on the latest developments in the field of Superfluidity, one of the most fundamental, interesting, and important problems in physics, with applications ranging from metals, helium liquids, photons in cavities, excitons in semiconductors, to the interior of neutron stars and the present state of the Universe as a whole.

In a homogeneous two-dimensional system at non-zero temperature, although there can be no ordering of infinite range, an ordered superfluid phase is expected to occur for a Bose liquid. Theory predicts that, in this phase, the correlation function decays with distance as a power law, and quantum vortices are bound to antivortices to form molecular-like pairs. We study the relevance of this theory to microcavity exciton polaritons. These are two-dimensional bosonic quasiparticles formed as a superposition of a microcavity photon and a semiconductor quantum well exciton, and have been shown to condense at high enough densities. Because of the short lifetime, equilibrium is not established, but we instead probe the steady state of the system, in which particles are continuously injected from a pumping reservoir. We employ a Michelson interferometer setup to measure the first order spatial correlation function of such a condensate. The gaussian form of the short-distance decay allows us to define an effective thermal de Broglie wavelength, although the system is not in thermal equilibrium. The long-distance decay is measured to be a power law with an exponent in the range 0.9-1.2, larger than is possible in equilibrium. Our non-equilibrium theory suggests that this can be attributed to laser pumping noise. We also present our observation of a single vortex-antivortex pair in a condensate of the appropriate size. Pairs are generated due to pumping noise, and are formed sequentially at the same point due to the inhomogeneous pumping spot profile. They are revealed in the time-integrated phase maps acquired using Michelson interferometry. Our results suggest that vortex-antivortex pairs can be created in a two-dimensional condensate without rotation or stirring. The observed correlated motion of a vortex and antivortex imply that vortex-antivortex pairs do not dissociate, which is consistent with the measured power law decay of the spatial correlation function. These two experiments uniquely describe the condensate phase fluctuations and provide stringent tests to theories of nonequilibrium condensation. They also highlight the exciton polariton condensate as a very well characterized system showing mesoscopic coherence and deepen our understanding of fundamental two-dimensional bosonic physics. Progress in this field is expected to lead towards long-sought applications such as quantum simulation or low-threshold laser sources.