Superfluid States of Matter  book cover
1st Edition

Superfluid States of Matter

ISBN 9781439802755
Published April 15, 2015 by CRC Press
583 Pages 98 B/W Illustrations

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Book Description

Covers the State of the Art in Superfluidity and Superconductivity

Superfluid States of Matter addresses the phenomenon of superfluidity/superconductivity through an emergent, topologically protected constant of motion and covers topics developed over the past 20 years. The approach is based on the idea of separating universal classical-field superfluid properties of matter from the underlying system’s “quanta.” The text begins by deriving the general physical principles behind superfluidity/superconductivity within the classical-field framework and provides a deep understanding of all key aspects in terms of the dynamics and statistics of a classical-field system.

It proceeds by explaining how this framework emerges in realistic quantum systems, with examples that include liquid helium, high-temperature superconductors, ultra-cold atomic bosons and fermions, and nuclear matter. The book also offers several powerful modern approaches to the subject, such as functional and path integrals.

Comprised of 15 chapters, this text:

  • Establishes the fundamental macroscopic properties of superfluids and superconductors within the paradigm of the classical matter field
  • Deals with a single-component neutral matter field
  • Considers fundamentals and properties of superconductors
  • Describes new physics of superfluidity and superconductivity that arises in multicomponent systems
  • Presents the quantum-field perspective on the conditions under which classical-field description is relevant in bosonic and fermionic systems
  • Introduces the path integral formalism
  • Shows how Feynman path integrals can be efficiently simulated with the worm algorithm
  • Explains why nonsuperfluid (insulating) ground states of regular and disordered bosons occur under appropriate conditions
  • Explores superfluid solids (supersolids)
  • Discusses the rich dynamics of vortices and various aspects of superfluid turbulence at T →0
  • Provides account of BCS theory for the weakly interacting Fermi gas
  • Highlights and analyzes the most crucial developments that has led to the current understanding of superfluidity and superconductivity
  • Reviews the variety of superfluid and superconducting systems available today in nature and the laboratory, as well as the states that experimental realization is currently actively pursuing

Table of Contents

I Superfluidity from a Classical-Field Perspective

Neutral Matter Field

Classical Hamiltonian Formalism

Basic Dynamic and Static Properties

Matter Field Under Rotation

Superfluidity at Finite Temperatures and Hydrodynamics

Equilibrium Statistics of a Superfluid

Basics of Superfluid Hydrodynamics, Thermomechanical Effects, Hydrodynamic Hamiltonian and Action


Superfluid Phase Transition

XY Universality Class

High-Temperature Expansion for the XY Model

J-Current Models

Dual Descriptions of Normal and Superfluid Phases

High-Temperature Expansion for the |ψ|Model


Berezinskii–Kosterlitz–Thouless Phase Transition

Statistics of Vortices at Large Scales

Kosterlitz–Thouless Renormalization-Group Theory


II Superconducting and Multicomponent Systems

Charged Matter Fields

U(1) Gauge Theory

U(1) Mean-Field Gauge Theories, London and Ginzburg–LandauModels

Type-1 and Type-2 Superconductors

Vortices in a Superconductor

Upper and Lower Critical Magnetic Fields (Hc1 and Hc2)

Critical Coupling κ = 1: Bogomolny Bound and Equations

Summary of the Magnetic Response and Vortex Liquid

Magneto-Rotational Isomorphism

Superconducting Phase Transition


Multicomponent Superconductors and Superfluids, and Superconducting and Metallic Superfluids

Mixtures of Superfluids and Entrainment Effect

Multicomponent Superconductors

Fractional Vortices

Superfluid Sector of Liquid Metallic Hydrogen–Type System

Rotational Response of a Charged Sector in the Multicomponent Superconductor and Violation of the London Law

Violation of London Electrodynamics

Skyrmion and Hopfion Topological Defects

Magnetic Responses and Type-1.5 Superconductivity

Effects of Intercomponent Interactions in Multiband Systems

Composite U(1) Order and Coflow/Counterflow Superfluidity


III Quantum-Mechanical Aspects: Macrodynamics

Quantum-Field Perspective

Coherent States, Operator of Phase

Harmonic Hydrodynamic Hamiltonian

Superfluid Thermodynamics at Low Temperature

Density Matrix

Functional Integral Representation for Bosonic Fields

Classical-Field Limit: Gross Pitaevskii Equation

Superfluidity and Compressibility: The XY Model Paradox

Connectivity of the Ground-State Wavefunction

Popov Hydrodynamic Action

Long-Range Asymptotics of Off-Diagonal Correlators

Cooper Pair Problem

Where Does the Coulomb Repulsion Go?

BCS–BEC Crossover


Path Integral Representation

Lattice Path Integrals

Lattice Gauge Field and the Winding Number Formula

Continuous-Space Path Integrals

Nonclassical Moment of Inertia Formula

Green’s Function, Density Matrix, and Superfluidity

General Aspects of Path Integral Monte Carlo

Worm Algorithm


Supersolids and Insulators

Supersolid State from the Classical-Field Perspective

Supersolid State from the Quantum-Particle Perspective

Existence of Insulators

Mott Insulators

Superfluidity and Disorder

Theorem of Inclusions

Superfluidity in Disordered Lattice Models

Superfluidity of Crystalline Defects


Dynamics of Vortices and Phonons: Turbulence

Basic Relations of Vortex Dynamics

Kelvin Waves

Vortex–Phonon Interaction

Superfluid Turbulence


IV Weakly Interacting Gases

Green’s Functions and Feynman’s Diagrams

Matsubara Representation

Diagrammatic Technique for Normal Bosonic Systems

Thermodynamics of Weakly Interacting Bose Gas, BCS Theory

Main Results

Beliaev’s Diagrammatic Technique

Thermodynamic Functions in the Quasicondensate Region

Expansion Parameters: Estimates for Higher-Order Terms

Long-Range Off-Diagonal Correlations

Normal Region

Fluctuation Region

Weakly Interacting Fermi Gas


Kinetics of Bose–Einstein Condensation

Weakly Turbulent State of a Degenerate Bose Gas

Kinetic Equation in the Weak-Turbulence Regime

Self-Similar Analysis of Kinetic Equation

Strongly Nonequilibrium Bose–Einstein Condensation


Historical Overview: Nature and Laboratory

Historical Overview

Liquid Helium, Superconductivity, Einstein’s Classica Matter Field

Lambda Point, Abnormal Heat Transport, Superfluidity

Theories Enter, London, Tisza, Landau, and Bogoliubov

Off-Diagonal Long-Range Order, Vorticity

Quantization, Quantum-Statistical Insights

Meissner–Ochsenfeld Effect, London Phenomenology

Magnetic Flux Quantization

Ginzburg–Landau Phenomenology, Shubnikov Phase/Abrikosov Lattice

BCS Theory

Advent of Field-Theoretical Methods

Josephson Effect, The Phase, Popov Hydrodynamic Action

Superfluid Phase Transition

Multicomponent Order Parameters/Effective Theories

Related Developments

BEC in Ultracold Gases


Superfluid States in Nature and the Laboratory



Dilute Trapped Ultracold Gases

Resonant Fermions: From Ultracold Atoms to Neutron Stars

Electronic Superconductors

Superconductivity of Nucleons: Finite Nuclei, Neutron Stars, and Liquid Metallic Hydrogen

Color Superconductivity of Quarks

Stable, Metastable, and Unstable Elementary Excitations

Superfluid States in Optical-Lattice Emulators



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Boris Vladimirovich Svistunov received his MSc in physics in 1983 from Moscow Engineering Physics Institute, Moscow, Russia. In 1990, he received his PhD in theoretical physics from Kurchatov Institute (Moscow), where he worked from 1986 to 2003 (and is still affiliated with). In 2003, he joined the Physics Department of the University of Massachusetts, Amherst.

Egor Sergeevich Babaev received his MSc in physics in 1996 from St. Petersburg State Polytechnical University and A. F. Ioffe Physical Technical Institute, St. Petersburg, Russia. In 2001, he received his PhD in theoretical physics from Uppsala University (Sweden). In 2007, after several years as a postdoctoral research associate at Cornell University, he joined the faculty of the Physics Department of the University of Massachusetts, Amherst. He is currently a faculty member at the Royal Institute of Technology, Sweden.

Nikolay Victorovich Prokof’ev received his MSc in physics in 1982 from Moscow Engineering Physics Institute, Moscow, Russia. In 1987, he received his PhD in theoretical physics from Kurchatov Institute (Moscow), where he worked from 1984 to 1999. In 1999, he joined the Physics Department of the University of Massachusetts, Amherst.


"This book offers a modern treatment of the subject that provides conceptual insight as well as technical details. … The book reviews the variety of superfluid and superconducting systems available today in nature and the laboratory, as well as the states that experimental realization is currently actively pursuing. … a valuable resource on the subject for a wide range of readers from beginning graduate students to established scholars."
Zentralblatt MATH 1317

"This book presents this field in an attractive way, emphasizing deep unifying concepts of symmetry and topology while maintaining firm connection to concrete physical realities."
—Frank Wilczek, Nobel Laureate in Physics (2004) and Herbert Feshbach Professor of Physics, Massachusetts Institute of Technology

"This fascinating book contains a lucid, useful, and up-to-date guide to understanding the burgeoning field of superfluid states of quantum matter. It instantly becomes the ultimate resource on the subject for a wide range of readers from beginning graduate students to established scholars."
—Professor Victor Galitski, Joint Quantum Institute, University of Maryland

"The authors develop the concepts of superfluidity in a well-organized modern view and include some of its most fascinating applications at the forefronts of interdisciplinary research, from novel electronic superconductors to cold atomic gases and quark matter. I expect this will become a celebrated book that students and researchers in our field have been waiting for."
—W. Vincent Liu, Professor of Physics, University of Pittsburgh

"This book is a timely and valuable addition to the study of superfluidity since it emphasizes the classical-field aspects and relies on Feynman path integrals. The authors are well-recognized authorities in this area."
—Professor Alexander Fetter, Stanford University

"This book on superfluidity and superconductivity is unique and comprehensive. It reflects the broad expertise of the authors who have made important contributions to our understanding of many different physical systems. I found it refreshing that the material is presented from a modern perspective in a unifying way."
—Wolfgang Ketterle, Nobel Laureate in Physics 2001 and John D. MacArthur Professor of Physics, Massachusetts Institute of Technology

"… a modern treatment of the subject that provides conceptual insight as well as technical details. … It is rare that a textbook can cover such a wide range of topics without losing too much technical detail. The textbook promises to be a must-read for graduate students in strongly correlated quantum fluids."
—Dr. Derek Lee, Department of Physics, Imperial College London

"This book fills a real gap by placing all the ‘folklore’ describing superfluid systems in terms of classical fields within a coherent theoretical framework and using this as the conceptual foundation upon which subsequent (particularly quantum) developments are developed. The authors’ scholarship and enthusiasm for the subject are evident throughout, and to their credit, they take time to develop and explain important concepts as they arise."
—Simon A. Gardiner, Professor and Head of Section in the Centre for Atomic and Molecular Physics, Durham University

"This is a very timely and welcome addition to the literature on superfluidity. Its starting point in hydrodynamics makes this book unique. The authors manage to lead the reader from the basics to the state of the art."
—Carsten Timm, Professor of Condensed Matter Theory, Technische Universität Dresden

"This is an excellent book in the field of strongly interacting systems written by authors who have made exceptional contributions to practically every topic. It combines an innovative approach with rigorous self-contained analytics and a powerful numerical scheme … The coverage of topics—from the foundations exposed in a new light to novel composite superfluids and supersolids—is exhaustive and creative."
—Anatoly Kuklov, Associate Professor of Engineering Science and Physics, College of Staten Island, The City University of New York

"The authors are scientists of international distinction, and their book is written with impressive assurance and authority…. a tour de force on theories of superfluidity" –Contemporary Physics (May 2016)