nonrel_fermion_math.h

00001 /*
00002   -------------------------------------------------------------------
00003   
00004   Copyright (C) 2006, 2007, 2008, Andrew W. Steiner
00005   
00006   This file is part of O2scl.
00007   
00008   O2scl is free software; you can redistribute it and/or modify
00009   it under the terms of the GNU General Public License as published by
00010   the Free Software Foundation; either version 3 of the License, or
00011   (at your option) any later version.
00012   
00013   O2scl is distributed in the hope that it will be useful,
00014   but WITHOUT ANY WARRANTY; without even the implied warranty of
00015   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
00016   GNU General Public License for more details.
00017   
00018   You should have received a copy of the GNU General Public License
00019   along with O2scl. If not, see <http://www.gnu.org/licenses/>.
00020 
00021   -------------------------------------------------------------------
00022 */
00023 /* math2c
00024    Destination: nonrel_fermion.cpp
00025    (* For convenience *)
00026    pi=ArcCos[-1.0]
00027    (* --------------------------------------------------------*)
00028    m=5.0
00029    mu=5.1
00030    T=0.01
00031    dist=1/(1+Exp[x^2*m/2/T-(mu-m)/T])
00032    t1=NIntegrate[x^2*m^3*dist/pi/pi,{x,0,10.0}]
00033    Reference: den1 t1
00034    t2=NIntegrate[x^4*m^4/2*dist/pi/pi,{x,0,10.0}]+t1*m
00035    Reference: ed1 t2
00036    t3=NIntegrate[-x^2*m^3/pi/pi*(dist*Log[dist]+\
00037    (1.0-dist)*Log[1.0-dist]),{x,0,10.0}]
00038    Reference: en1 t3
00039    t4=-t2+t3*T+t1*mu
00040    Reference: pr1 t4
00041    (* --------------------------------------------------------*)
00042    m=5.0
00043    mu=5.1
00044    T=0.1
00045    dist=1/(1+Exp[x^2*m/2/T-(mu-m)/T])
00046    t1=NIntegrate[x^2*m^3*dist/pi/pi,{x,0,10.0}]
00047    Reference: den2 t1
00048    t2=NIntegrate[x^4*m^4/2*dist/pi/pi,{x,0,10.0}]+t1*m
00049    Reference: ed2 t2
00050    t3=NIntegrate[-x^2*m^3/pi/pi*(dist*Log[dist]+\
00051    (1.0-dist)*Log[1.0-dist]),{x,0,10.0}]
00052    Reference: en2 t3
00053    t4=-t2+t3*T+t1*mu
00054    Reference: pr2 t4
00055    (* --------------------------------------------------------*)
00056    m=5.0
00057    mu=5.1
00058    T=1.0
00059    dist=1/(1+Exp[x^2*m/2/T-(mu-m)/T])
00060    t1=NIntegrate[x^2*m^3*dist/pi/pi,{x,0,10.0}]
00061    Reference: den3 t1
00062    t2=NIntegrate[x^4*m^4/2*dist/pi/pi,{x,0,10.0}]+t1*m
00063    Reference: ed3 t2
00064    t3=NIntegrate[-x^2*m^3/pi/pi*(dist*Log[dist]+        \
00065    (1.0-dist)*Log[1.0-dist]),{x,0,10.0}]
00066    Reference: en3 t3
00067    t4=-t2+t3*T+t1*mu
00068    Reference: pr3 t4
00069    (* --------------------------------------------------------*)
00070    m=5.0
00071    mu=6.0
00072    T=0.05
00073    dist=1/(1+Exp[x^2*m/2/T-(mu-m)/T])
00074    t1=NIntegrate[x^2*m^3*dist/pi/pi,{x,0,10.0}]
00075    Reference: den4 t1
00076    t2=NIntegrate[x^4*m^4/2*dist/pi/pi,{x,0,10.0}]+t1*m
00077    Reference: ed4 t2
00078    t3=NIntegrate[-x^2*m^3/pi/pi*(dist*Log[dist]+        \
00079    (1.0-dist)*Log[1.0-dist]),{x,0,10.0}]
00080    Reference: en4 t3
00081    t4=-t2+t3*T+t1*mu
00082    Reference: pr4 t4
00083    (* --------------------------------------------------------*)
00084    m=5.0
00085    mu=6.0
00086    T=0.1
00087    dist=1/(1+Exp[x^2*m/2/T-(mu-m)/T])
00088    t1=NIntegrate[x^2*m^3*dist/pi/pi,{x,0,10.0}]
00089    Reference: den5 t1
00090    t2=NIntegrate[x^4*m^4/2*dist/pi/pi,{x,0,10.0}]+t1*m
00091    Reference: ed5 t2
00092    t3=NIntegrate[-x^2*m^3/pi/pi*(dist*Log[dist]+        \
00093    (1.0-dist)*Log[1.0-dist]),{x,0,10.0}]
00094    Reference: en5 t3
00095    t4=-t2+t3*T+t1*mu
00096    Reference: pr5 t4
00097    (* --------------------------------------------------------*)
00098    m=5.0
00099    mu=6.0
00100    T=1.0
00101    dist=1/(1+Exp[x^2*m/2/T-(mu-m)/T])
00102    t1=NIntegrate[x^2*m^3*dist/pi/pi,{x,0,10.0}]
00103    Reference: den6 t1
00104    t2=NIntegrate[x^4*m^4/2*dist/pi/pi,{x,0,10.0}]+t1*m
00105    Reference: ed6 t2
00106    t3=NIntegrate[-x^2*m^3/pi/pi*(dist*Log[dist]+        \
00107    (1.0-dist)*Log[1.0-dist]),{x,0,10.0}]
00108    Reference: en6 t3
00109    t4=-t2+t3*T+t1*mu
00110    Reference: pr6 t4
00111 
00112 */

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