Nambu-Jona Lasinio and nonlinear sigma models in condensed matter systems

Ryosuke Yoshii, Muneto Nitta

Research output: Contribution to journalReview article

Abstract

We review various connections between condensed matter systems with the Nambu-Jona- Lasinio model and nonlinear sigma models. The field theoretical description of interacting systems offers a systematic framework to describe the dynamical generation of condensates. Recent findings of a duality between the Nambu-Jona-Lasinio model and nonlinear sigma models enables us to investigate various properties underlying both theories. In this review, we mainly focus on inhomogeneous condensations in static situations. The various methods developed in the Nambu-Jona-Lasinio model reveal the inhomogeneous phase structures and also yield new inhomogeneous solutions in nonlinear sigma models owing to the duality. The recent progress on interacting systems in finite systems is also reviewed.

Original languageEnglish
Article number636
JournalSymmetry
Volume11
Issue number5
DOIs
Publication statusPublished - 2019 May 1

Fingerprint

Nonlinear sigma Model
Duality
Condensate
Condensation
Model
Phase structure
condensates
condensation
Review

Keywords

  • Condensed matter system
  • Lowdimensional system
  • Nambu-Jona-Lasinio model
  • Nonlinear σ model
  • Superconductivity
  • Superfluidity
  • Ultracold atomic gases

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Chemistry (miscellaneous)
  • Mathematics(all)
  • Physics and Astronomy (miscellaneous)

Cite this

Nambu-Jona Lasinio and nonlinear sigma models in condensed matter systems. / Yoshii, Ryosuke; Nitta, Muneto.

In: Symmetry, Vol. 11, No. 5, 636, 01.05.2019.

Research output: Contribution to journalReview article

@article{89a36e2dbe7f49a59a501b757b4fd331,
title = "Nambu-Jona Lasinio and nonlinear sigma models in condensed matter systems",
abstract = "We review various connections between condensed matter systems with the Nambu-Jona- Lasinio model and nonlinear sigma models. The field theoretical description of interacting systems offers a systematic framework to describe the dynamical generation of condensates. Recent findings of a duality between the Nambu-Jona-Lasinio model and nonlinear sigma models enables us to investigate various properties underlying both theories. In this review, we mainly focus on inhomogeneous condensations in static situations. The various methods developed in the Nambu-Jona-Lasinio model reveal the inhomogeneous phase structures and also yield new inhomogeneous solutions in nonlinear sigma models owing to the duality. The recent progress on interacting systems in finite systems is also reviewed.",
keywords = "Condensed matter system, Lowdimensional system, Nambu-Jona-Lasinio model, Nonlinear σ model, Superconductivity, Superfluidity, Ultracold atomic gases",
author = "Ryosuke Yoshii and Muneto Nitta",
year = "2019",
month = "5",
day = "1",
doi = "10.3390/sym11050636",
language = "English",
volume = "11",
journal = "Symmetry",
issn = "2073-8994",
publisher = "Multidisciplinary Digital Publishing Institute (MDPI)",
number = "5",

}

TY - JOUR

T1 - Nambu-Jona Lasinio and nonlinear sigma models in condensed matter systems

AU - Yoshii, Ryosuke

AU - Nitta, Muneto

PY - 2019/5/1

Y1 - 2019/5/1

N2 - We review various connections between condensed matter systems with the Nambu-Jona- Lasinio model and nonlinear sigma models. The field theoretical description of interacting systems offers a systematic framework to describe the dynamical generation of condensates. Recent findings of a duality between the Nambu-Jona-Lasinio model and nonlinear sigma models enables us to investigate various properties underlying both theories. In this review, we mainly focus on inhomogeneous condensations in static situations. The various methods developed in the Nambu-Jona-Lasinio model reveal the inhomogeneous phase structures and also yield new inhomogeneous solutions in nonlinear sigma models owing to the duality. The recent progress on interacting systems in finite systems is also reviewed.

AB - We review various connections between condensed matter systems with the Nambu-Jona- Lasinio model and nonlinear sigma models. The field theoretical description of interacting systems offers a systematic framework to describe the dynamical generation of condensates. Recent findings of a duality between the Nambu-Jona-Lasinio model and nonlinear sigma models enables us to investigate various properties underlying both theories. In this review, we mainly focus on inhomogeneous condensations in static situations. The various methods developed in the Nambu-Jona-Lasinio model reveal the inhomogeneous phase structures and also yield new inhomogeneous solutions in nonlinear sigma models owing to the duality. The recent progress on interacting systems in finite systems is also reviewed.

KW - Condensed matter system

KW - Lowdimensional system

KW - Nambu-Jona-Lasinio model

KW - Nonlinear σ model

KW - Superconductivity

KW - Superfluidity

KW - Ultracold atomic gases

UR - http://www.scopus.com/inward/record.url?scp=85066337530&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85066337530&partnerID=8YFLogxK

U2 - 10.3390/sym11050636

DO - 10.3390/sym11050636

M3 - Review article

VL - 11

JO - Symmetry

JF - Symmetry

SN - 2073-8994

IS - 5

M1 - 636

ER -