Classical Analogies in the Solution of Quantum Many-Body Problems

by Aydin Cem Keser

Overview

This book addresses problems in three main developments in modern condensed matter physics– namely topological superconductivity, many-body localization and strongly interacting condensates/superfluids–by employing fruitful analogies from classical mechanics. This strategy has led to tangible results, firstly in superconducting nanowires: the density of states, a smoking gun for the long sought Majorana zero mode is calculated effortlessly by mapping the problem to a textbook-level classical point particle problem. Secondly, in localization theory even the simplest toy models that exhibit many-body localization are mathematically cumbersome and results rely on simulations that are limited by computational power. In this book an alternative viewpoint is developed by describing many-body localization in terms of quantum rotors that have incommensurate rotation frequencies, an exactly solvable system. Finally, the fluctuations in a strongly interacting Bose condensate and superfluid, anotoriously difficult system to analyze from first principles, are shown to mimic shastic fluctuations of space-time due to quantum fields. This analogy not only allows for the computation of physical properties of the fluctuations in an elegant way, it sheds light on the nature of space-time. The book will be a valuable contribution for its unifying style that illuminates conceptually challenging developments in condensed matter physics and its use of elegant mathematical models in addition to producing new and concrete results.

Product Details

ISBN-13:	9783030004873
Publisher:	Springer International Publishing
Publication date:	11/08/2018
Series:	Springer Theses
Edition description:	1st ed. 2018
Pages:	99
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

Aydin Cem Keser received his PhD from the University of Maryland in 2017. He now holds a postdoctoral research position at the University of New South Wales, Australia.

Table of Contents

Chapter1. Introduction.- Chapter2. Long Range p-Wave Proximity Effect into a Disordered Metal.- Chapter3. Analogue Shastic Gravity in Strongly Interacting Bose-Einstein Condensates.- Chapter4. Dynamical Many-Body Localization in an Integrable Model.- Chapter5. Conclusions.