NMR für einen antiferromagnetischen Spin-Dimer

© Jürgen Schnack, 10. 5. 2004

Pakete laden

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Energie-Eigenwerte

E0 = {-3/2, 1/2, 1/2, 1/2}

magnetische Quantenzahlen

M = {0, 1, 0, -1}

(Subscript[s, z])(1)- Matrixelemente

SZ=(({{0, 0, (1/2), 0}, {0, (1/2), 0, 0}, {(1/2), 0, 0, 0}, {0, 0, 0, -(1/2)}}));

\(TraditionalForm\`\(s\^+\)(1)\)- Matrixelemente

SP=(({{0, 0, 0, (1/(Sqrt[2]))}, {-(1/(Sqrt[2])), 0, (1/(Sqrt[2])), 0}, {0, 0, 0, (1/(Sqrt[2]))}, {0, 0, 0, 0}}));

\(TraditionalForm\`\(s\^-\)(1)\)- Matrixelemente

SM = Transpose[SP];

aufgeweichte δ-Funktion

δ[ϵ_, x_] = 
        (1/π)*(ϵ/((x^2) + (ϵ^2)));
Plot[{δ[0.05, x], δ[0.1, x], δ[0.5, 
            x]}, {x, -2, 
          2}, 
PlotStyle -> {Red, Green, Blue}, 
        TextStyle -> {FontFamily -> Helvetica, 
            FontSize -> 18}];

Zustandssumme

Z[T_, B_] = 
      Sum[(E^(-((E0[[m]] + M[[m]]*B)/T))), {m, 1, 
          4}]

Korrelationsfunktionen

CA - (Subscript[s, z])-(Subscript[s, z])

CA[T_, B_] = 
      Sum[(E^(-((E0[[m]] + M[[m]]*B)/T)))*
            SZ[[m, n]]*
            SZ[[n, m]]*
δ[
              0.1, (E0[[m]] + M[[m]]*B) - (E0[[n]] + 
                    M[[n]]*B)], 
{m, 1, 4}, {n, 1, 
            4}]/Z[T, B]

Plot[{CA[0.1, B], CA[0.5, B], CA[1.0, B], CA[2.0, B]}, {B, 0.0, 
          3}, 
PlotStyle -> {Red, Green, Blue, 
            Orange}, 
        TextStyle -> {FontFamily -> Helvetica, 
            FontSize -> 18}];

Plot[{CA[T, 0], CA[T, 1], CA[T, 2], CA[T, 3]}, {T, 0.1, 
          2}, 
PlotStyle -> {Red, Green, Blue, 
            Orange}, 
        TextStyle -> {FontFamily -> Helvetica, 
            FontSize -> 18}];

CB - \(TraditionalForm\`\(\(s\^+\)\(-\)\)\)\(TraditionalForm\`\(s\^-\)\)

CB[T_, B_] = 
      Sum[(E^(-((E0[[m]] + M[[m]]*B)/T)))*
            SP[[m, n]]*
            SM[[n, m]]*
δ[
              0.1, (E0[[m]] + M[[m]]*B) - (E0[[n]] + 
                    M[[n]]*B)], 
{m, 1, 4}, {n, 1, 
            4}]/Z[T, B]

Plot[{CB[0.1, B], CB[0.5, B], CB[1.0, B], CB[2.0, B]}, {B, 0.0, 
          3}, 
PlotStyle -> {Red, Green, Blue, 
            Orange}, 
        TextStyle -> {FontFamily -> Helvetica, 
            FontSize -> 18}];

Plot[{CB[T, 0], CB[T, 1], CB[T, 2], CB[T, 3]}, {T, 0.1, 
          2}, 
PlotStyle -> {Red, Green, Blue, 
            Orange}, 
        TextStyle -> {FontFamily -> Helvetica, 
            FontSize -> 18}];

CC - \(TraditionalForm\`\(\(s\^-\)\(-\)\)\)\(TraditionalForm\`\(s\^+\)\)

CC[T_, B_] = 
      Sum[(E^(-((E0[[m]] + M[[m]]*B)/T)))*
            SM[[m, n]]*
            SP[[n, m]]*
δ[
              0.1, (E0[[m]] + M[[m]]*B) - (E0[[n]] + 
                    M[[n]]*B)], 
{m, 1, 4}, {n, 1, 
            4}]/Z[T, B]

Plot[{CC[0.1, B], CC[0.5, B], CC[1.0, B], CC[2.0, B]}, {B, 0.0, 
          3}, 
PlotStyle -> {Red, Green, Blue, 
            Orange}, 
        TextStyle -> {FontFamily -> Helvetica, 
            FontSize -> 18}];

Plot[{CC[T, 0], CC[T, 1], CC[T, 2], CC[T, 3]}, {T, 0.1, 
          2}, 
PlotStyle -> {Red, Green, Blue, 
            Orange}, 
        TextStyle -> {FontFamily -> Helvetica, 
            FontSize -> 18}];