ag-gipp/GoUldI

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data/267.json

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{
  "definitions" : {
    "N" : [ {
      "Q28920044" : "positive integer"
    } ],
    "i" : [ {
      "Q44917388" : "index of summation",
      "Q28920044" : "positive integer"
    } ],
    "H" : [ {
      "Q660488" : "Hamiltonian"
    } ],
    "A_{i}" : [ {
      "Q845789" : "Observable"
    } ],
    "otimes" : [ {
      "Q1163016" : "tensor product"
    } ],
    "H_{S}" : [ "Hamiltonian of the quantum system", { } ],
    "H_{i}" : [ "Hamiltonian of the i-th system in the bath", { } ],
    "V_{0}" : [ "Interaction operator", {
      "Q131030" : "operator (mapping from one vector space or module to another in mathematics)"
    } ]
  },
  "constraints" : [ ],
  "math_inputtex" : "H=H_{S}+\\sum_{i=1}^{N}H_{i}+V_{0}\\otimes\\sum_{i=1}^{N}A_{i}",
  "math_inputtex_semantic" : "\\wf{Q660488}{H} = H_{S}+\\sum_{\\w{Q28920044}{i}=1}^{\\w{Q28920044}{N}}H_{i} + \\w{Q131030}{V}_{0}\\otimes\\sum_{i=1}^{N} \\w{Q845789}{A}_{i}",
  "correct_tex" : "H=H_{S}+\\sum_{i=1}^{N}H_{i}+V_{0}\\otimes\\sum_{i=1}^{N}A_{i}",
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xref=\"p1.1.m1.1.18.cmml\">A</mi>\n              <mi id=\"p1.1.m1.1.19.1\" xref=\"p1.1.m1.1.19.1.cmml\">i</mi>\n            </msub>\n          </mrow>\n        </mrow>\n      </mrow>\n    </mrow>\n    <annotation-xml encoding=\"MathML-Content\" id=\"p1.1.m1.1b\">\n      <apply id=\"p1.1.m1.1.20.cmml\" xref=\"p1.1.m1.1.20\">\n        <eq id=\"p1.1.m1.1.2.cmml\" xref=\"p1.1.m1.1.2\"/>\n        <csymbol cd=\"latexml\" id=\"p1.1.m1.1.1.cmml\" xref=\"p1.1.m1.1.1\">Q660488</csymbol>\n        <apply id=\"p1.1.m1.1.20.1.cmml\" xref=\"p1.1.m1.1.20.1\">\n          <plus id=\"p1.1.m1.1.5.cmml\" xref=\"p1.1.m1.1.5\"/>\n          <apply id=\"p1.1.m1.1.20.1.1.cmml\" xref=\"p1.1.m1.1.20.1.1\">\n            <csymbol cd=\"ambiguous\" id=\"p1.1.m1.1.20.1.1.1.cmml\" xref=\"p1.1.m1.1.20.1.1\">subscript</csymbol>\n            <csymbol cd=\"latexml\" id=\"p1.1.m1.1.3.cmml\" xref=\"p1.1.m1.1.3\">Q660488</csymbol>\n            <ci id=\"p1.1.m1.1.4.1.cmml\" xref=\"p1.1.m1.1.4.1\">𝑆</ci>\n          </apply>\n   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xref=\"p1.1.m1.1.8.1\">Q28920044</csymbol>\n            </apply>\n            <apply id=\"p1.1.m1.1.20.1.2.2.cmml\" xref=\"p1.1.m1.1.20.1.2.2\">\n              <csymbol cd=\"ambiguous\" id=\"p1.1.m1.1.20.1.2.2.1.cmml\" xref=\"p1.1.m1.1.20.1.2.2\">subscript</csymbol>\n              <csymbol cd=\"latexml\" id=\"p1.1.m1.1.9.cmml\" xref=\"p1.1.m1.1.9\">Q660488</csymbol>\n              <csymbol cd=\"latexml\" id=\"p1.1.m1.1.10.1.cmml\" xref=\"p1.1.m1.1.10.1\">Q28920044</csymbol>\n            </apply>\n          </apply>\n          <apply id=\"p1.1.m1.1.20.1.3.cmml\" xref=\"p1.1.m1.1.20.1.3\">\n            <csymbol cd=\"latexml\" id=\"p1.1.m1.1.14.cmml\" xref=\"p1.1.m1.1.14\">tensor-product</csymbol>\n            <apply id=\"p1.1.m1.1.20.1.3.1.cmml\" xref=\"p1.1.m1.1.20.1.3.1\">\n              <csymbol cd=\"ambiguous\" id=\"p1.1.m1.1.20.1.3.1.1.cmml\" xref=\"p1.1.m1.1.20.1.3.1\">subscript</csymbol>\n              <csymbol cd=\"latexml\" id=\"p1.1.m1.1.12.cmml\" xref=\"p1.1.m1.1.12\">Q131030</csymbol>\n              <cn type=\"integer\" id=\"p1.1.m1.1.13.1.cmml\" xref=\"p1.1.m1.1.13.1\">0</cn>\n            </apply>\n            <apply id=\"p1.1.m1.1.20.1.3.2.cmml\" xref=\"p1.1.m1.1.20.1.3.2\">\n              <apply id=\"p1.1.m1.1.20.1.3.2.1.cmml\" xref=\"p1.1.m1.1.20.1.3.2.1\">\n                <power  xref=\"p1.1.m1.1.20.1.3.2.1\"/>\n                <apply id=\"p1.1.m1.1.20.1.3.2.1.2.cmml\" xref=\"p1.1.m1.1.20.1.3.2.1\">\n                  <csymbol cd=\"ambiguous\" id=\"p1.1.m1.1.20.1.3.2.1.2.1.cmml\" xref=\"p1.1.m1.1.20.1.3.2.1\">subscript</csymbol>\n                  <sum id=\"p1.1.m1.1.15.cmml\" xref=\"p1.1.m1.1.15\"/>\n                  <apply id=\"p1.1.m1.1.16.1.cmml\" xref=\"p1.1.m1.1.16.1\">\n                    <eq id=\"p1.1.m1.1.16.1.2.cmml\" xref=\"p1.1.m1.1.16.1.2\"/>\n                    <csymbol cd=\"latexml\" id=\"p1.1.m1.1.16.1.1.cmml\" xref=\"p1.1.m1.1.16.1.1\">Q28920044</csymbol>\n                    <cn type=\"integer\" id=\"p1.1.m1.1.16.1.3.cmml\" xref=\"p1.1.m1.1.16.1.3\">1</cn>\n                  </apply>\n                </apply>\n                <csymbol cd=\"latexml\" id=\"p1.1.m1.1.17.1.cmml\" xref=\"p1.1.m1.1.17.1\">Q28920044</csymbol>\n              </apply>\n              <apply id=\"p1.1.m1.1.20.1.3.2.2.cmml\" xref=\"p1.1.m1.1.20.1.3.2.2\">\n                <csymbol cd=\"ambiguous\" id=\"p1.1.m1.1.20.1.3.2.2.1.cmml\" xref=\"p1.1.m1.1.20.1.3.2.2\">subscript</csymbol>\n                <csymbol cd=\"latexml\" id=\"p1.1.m1.1.18.cmml\" xref=\"p1.1.m1.1.18\">Q845789</csymbol>\n                <csymbol cd=\"latexml\" id=\"p1.1.m1.1.19.1.cmml\" xref=\"p1.1.m1.1.19.1\">Q28920044</csymbol>\n              </apply>\n            </apply>\n          </apply>\n        </apply>\n      </apply>\n    </annotation-xml>\n    <annotation encoding=\"application/x-tex\" id=\"p1.1.m1.1c\">H=H_{S}+\\sum_{i=1}^{N}H_{i}+V_{0}\\otimes\\sum_{i=1}^{N}A_{i}</annotation>\n  </semantics>\n</math>",
  "uri" : "https://arxiv.org/abs/cond-mat/0403678",
  "title" : "Physics Context 2",
  "comment" : "",
  "type" : "equation",
  "ntcir12-type" : "9",
  "formula" : "1_17.1",
  "page" : "5",
  "ntcir12-relevance" : "3"
}