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  "authors": [
    {
      "affiliations": [
        {
          "country": "Japan", 
          "value": "Nishina Center, , RIKEN, Wako 351-0198, , Japan"
        }
      ], 
      "surname": "Hidaka", 
      "email": "hidaka@riken.jp", 
      "full_name": "Hidaka, Yoshimasa", 
      "given_names": "Yoshimasa"
    }, 
    {
      "affiliations": [
        {
          "country": "China", 
          "value": "Department of Physics, Zhejiang University, , Hangzhou 310027, , China"
        }
      ], 
      "surname": "Minami", 
      "email": "hidaka@riken.jp", 
      "full_name": "Minami, Yuki", 
      "given_names": "Yuki"
    }
  ], 
  "titles": [
    {
      "source": "OUP", 
      "title": "Spontaneous symmetry breaking and Nambu\u2013Goldstone modes in open classical and quantum systems"
    }
  ], 
  "dois": [
    {
      "value": "10.1093/ptep/ptaa005"
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  "publication_info": [
    {
      "journal_title": "Progress of Theoretical and Experimental Physics", 
      "material": "article", 
      "journal_volume": "2020", 
      "artid": "033A01", 
      "year": 2020, 
      "journal_issue": "3"
    }
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    "submission_number": "89cc36f2616411ebbd0e02163e01809a"
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  "page_nr": [
    30
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    {
      "url": "http://creativecommons.org/licenses/by/4.0/", 
      "license": "CC-BY-4.0"
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  "copyright": [
    {
      "statement": "\u00a9 The Author(s) 2020. Published by Oxford University Press on behalf of the Physical Society of Japan.", 
      "year": "2020"
    }
  ], 
  "control_number": "59717", 
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      "primary": "Progress of Theoretical and Experimental Physics"
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    {
      "categories": [
        "hep-th", 
        "cond-mat.mes-hall", 
        "cond-mat.quant-gas", 
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  "abstracts": [
    {
      "source": "OUP", 
      "value": "Abstract We discuss spontaneous symmetry breaking of open classical and quantum systems. When a continuous symmetry is spontaneously broken in an open system, a gapless excitation mode appears corresponding to the Nambu\u2013Goldstone mode. Unlike isolated systems, the gapless mode is not always a propagation mode, but it is a diffusion one. Using the Ward\u2013Takahashi identity and the effective action formalism, we establish the Nambu\u2013Goldstone theorem in open systems, and derive the low-energy coefficients that determine the dispersion relation of Nambu\u2013Goldstone modes. Using these coefficients, we classify the Nambu\u2013Goldstone modes into four types: type-A propagation, type-A diffusion, type-B propagation, and type-B diffusion modes."
    }
  ], 
  "imprints": [
    {
      "date": "2020-03-26", 
      "publisher": "OUP"
    }
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}