-
Notifications
You must be signed in to change notification settings - Fork 0
/
SuzukiTrotterDecomposition_PauliMatrices.nb
2279 lines (2259 loc) · 91 KB
/
SuzukiTrotterDecomposition_PauliMatrices.nb
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
(* Content-type: application/vnd.wolfram.mathematica *)
(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)
(* CreatedBy='Mathematica 12.3' *)
(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 158, 7]
NotebookDataLength[ 92991, 2271]
NotebookOptionsPosition[ 91604, 2243]
NotebookOutlinePosition[ 91994, 2259]
CellTagsIndexPosition[ 91951, 2256]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
Notebook[{
Cell["\<\
Hamiltonian H=H1+H2, where [H1,H2]!=0 don\[CloseCurlyQuote]t commute. \
Simplest example: Pauli matrices.
For these simple \[OpenCurlyDoubleQuote]Hamiltonians\[CloseCurlyDoubleQuote], \
the error can be computed in closed-form.
First order Suzuki-Trotter decomposition leads to a \[Delta]t^2 error in the \
unitary, while second order leads to \[Delta]t^3.\
\>", "Text",
CellChangeTimes->{{3.918731960383634*^9, 3.91873197689609*^9}, {
3.918796483478034*^9,
3.9187965510154247`*^9}},ExpressionUUID->"aee3bce7-6f21-4e31-a41f-\
2960f820efc3"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{
RowBox[{"(*", " ",
RowBox[{"X", ",", " ", "Y"}], " ", "*)"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"Clear", "[",
RowBox[{
"\[Delta]t", ",", "X", ",", "Y", ",", "U1", ",", "U2", ",", "U3", ",",
" ", "diff2", ",", "diff3"}], "]"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"{",
RowBox[{"X", ",", "Y"}], "}"}], "=",
RowBox[{"{",
RowBox[{
RowBox[{"PauliMatrix", "[", "1", "]"}], ",",
RowBox[{"PauliMatrix", "[", "2", "]"}]}], "}"}]}], ";"}],
"\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"X", ".", "Y"}], "-",
RowBox[{"Y", ".", "X"}]}], ";"}], "\[IndentingNewLine]",
"\[IndentingNewLine]",
RowBox[{"(*", " ",
RowBox[{
RowBox[{"first", " ", "order", " ", "Suzuki"}], "-",
RowBox[{"Trotter", " ", "decomposition"}]}], " ", "*)"}],
"\[IndentingNewLine]",
RowBox[{
RowBox[{"U1", "=",
RowBox[{"MatrixExp", "[",
RowBox[{
RowBox[{"-", "I"}],
RowBox[{"(",
RowBox[{"X", "+", "Y"}], ")"}], "\[Delta]t"}], "]"}]}], ";"}],
"\[IndentingNewLine]",
RowBox[{
RowBox[{"U2", "=",
RowBox[{
RowBox[{"MatrixExp", "[",
RowBox[{
RowBox[{"-", "I"}],
RowBox[{"(", "X", ")"}], "\[Delta]t"}], "]"}], ".",
RowBox[{"MatrixExp", "[",
RowBox[{
RowBox[{"-", "I"}],
RowBox[{"(", "Y", ")"}], "\[Delta]t"}], "]"}]}]}], ";"}],
"\[IndentingNewLine]",
RowBox[{"diff2", "=",
RowBox[{
RowBox[{"Refine", "[",
RowBox[{
RowBox[{"Norm", "[",
RowBox[{"U1", "-", "U2"}], "]"}], ",",
RowBox[{"{",
RowBox[{"\[Delta]t", ">", "0"}], "}"}]}], "]"}], "//", "Simplify"}]}],
"\[IndentingNewLine]",
RowBox[{"LogLogPlot", "[",
RowBox[{
RowBox[{"{",
RowBox[{"diff2", ",",
RowBox[{"\[Delta]t", "^", "2"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"\[Delta]t", ",", "0.01", ",", "2"}], "}"}]}], "]"}],
"\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{"(*", " ",
RowBox[{
RowBox[{"second", " ", "order", " ", "Suzuki"}], "-",
RowBox[{"Trotter", " ", "decomposition"}]}], " ", "*)"}],
"\[IndentingNewLine]",
RowBox[{
RowBox[{"U3", "=",
RowBox[{
RowBox[{
RowBox[{"MatrixExp", "[",
RowBox[{
RowBox[{"-", "I"}],
RowBox[{"(", "X", ")"}],
RowBox[{"\[Delta]t", "/", "2"}]}], "]"}], ".",
RowBox[{"MatrixExp", "[",
RowBox[{
RowBox[{"-", "I"}],
RowBox[{"(", "Y", ")"}], "\[Delta]t"}], "]"}], ".",
RowBox[{"MatrixExp", "[",
RowBox[{
RowBox[{"-", "I"}],
RowBox[{"(", "X", ")"}],
RowBox[{"\[Delta]t", "/", "2"}]}], "]"}]}], "//", "Simplify"}]}],
";"}], "\[IndentingNewLine]",
RowBox[{"diff3", "=",
RowBox[{
RowBox[{"Refine", "[",
RowBox[{
RowBox[{"Norm", "[",
RowBox[{"U1", "-", "U3"}], "]"}], ",",
RowBox[{"{",
RowBox[{"\[Delta]t", ">", "0"}], "}"}]}], "]"}], "//", "Simplify"}]}],
"\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{"Series", "[",
RowBox[{"diff3", ",",
RowBox[{"{",
RowBox[{"\[Delta]t", ",", "0", ",", "3"}], "}"}]}], "]"}], "*)"}],
"\[IndentingNewLine]",
RowBox[{"LogLogPlot", "[",
RowBox[{
RowBox[{"{",
RowBox[{"diff3", ",",
RowBox[{
RowBox[{"(",
RowBox[{
SqrtBox["5"], "/", "6"}], ")"}], " ",
RowBox[{"\[Delta]t", "^", "3"}]}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"\[Delta]t", ",", "0.01", ",", "2"}], "}"}]}],
"]"}]}]}]], "Input",
CellChangeTimes->{{3.918725953510738*^9, 3.9187260643430357`*^9}, {
3.9187261216415987`*^9, 3.91872613801195*^9}, {3.918726168358262*^9,
3.918726171241171*^9},
3.918731870175412*^9},ExpressionUUID->"5dcf4052-1d0e-412b-9bf8-\
7b9f0d215724"],
Cell[BoxData[
RowBox[{
SqrtBox["2"], " ",
SqrtBox[
RowBox[{"1", "-",
RowBox[{
SuperscriptBox[
RowBox[{"Cos", "[", "\[Delta]t", "]"}], "2"], " ",
RowBox[{"Cos", "[",
RowBox[{
SqrtBox["2"], " ", "\[Delta]t"}], "]"}]}], "-",
RowBox[{
SqrtBox["2"], " ",
RowBox[{"Cos", "[", "\[Delta]t", "]"}], " ",
RowBox[{"Sin", "[", "\[Delta]t", "]"}], " ",
RowBox[{"Sin", "[",
RowBox[{
SqrtBox["2"], " ", "\[Delta]t"}], "]"}]}]}]]}]], "Output",
CellChangeTimes->{{3.91872594367129*^9, 3.9187260661755743`*^9},
3.918726175547929*^9},
CellLabel->
"Out[166]=",ExpressionUUID->"f7e3a0d2-02f1-4202-b100-99a7217a1012"],
Cell[BoxData[
GraphicsBox[{{{}, {},
TagBox[
{RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
1.], LineBox[CompressedData["
1:eJwVzXs41PkewPFxvyZGRnKfbWzNLsI2pO18xGJWHbdDO2VJCll1ZLC2mvS4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"]]},
Annotation[#, "Charting`Private`Tag$29594#1"]& ],
TagBox[
{RGBColor[0.880722, 0.611041, 0.142051], AbsoluteThickness[1.6], Opacity[
1.], LineBox[CompressedData["
1:eJwt0H9Qk3UcwPEHBo6NH20PAZr82g684o7KvJuW2UfxkE4TtUvd1Y3IHx2X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"]]},
Annotation[#, "Charting`Private`Tag$29594#2"]& ]}, {}},
AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
Axes->{True, True},
AxesLabel->{None, None},
AxesOrigin->{-4.605170185988091, -9.2103623823857},
CoordinatesToolOptions:>{"DisplayFunction" -> ({
Exp[
Part[#, 1]],
Exp[
Part[#, 2]]}& ), "CopiedValueFunction" -> ({
Exp[
Part[#, 1]],
Exp[
Part[#, 2]]}& )},
DisplayFunction->Identity,
Frame->{{False, False}, {False, False}},
FrameLabel->{{None, None}, {None, None}},
FrameTicks->{{Quiet[
Charting`ScaledTicks[{Log, Exp}][#, #2, {6, 6}]]& ,
Charting`ScaledFrameTicks[{Log, Exp}]}, {Quiet[
Charting`ScaledTicks[{Log, Exp}][#, #2, {6, 6}]]& ,
Charting`ScaledFrameTicks[{Log, Exp}]}},
GridLines->{None, None},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
ImagePadding->All,
Method->{
"DefaultBoundaryStyle" -> Automatic,
"DefaultGraphicsInteraction" -> {
"Version" -> 1.2, "TrackMousePosition" -> {True, False},
"Effects" -> {
"Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2},
"Droplines" -> {
"freeformCursorMode" -> True,
"placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" ->
AbsolutePointSize[6], "ScalingFunctions" -> None},
PlotRange->NCache[{{-4.605170185988091,
Log[2]}, {-9.2103623823857, 1.3862941448620387`}}, {{-4.605170185988091,
0.6931471805599453}, {-9.2103623823857, 1.3862941448620387`}}],
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.05],
Scaled[0.05]}},
Ticks->FrontEndValueCache[{Quiet[
Charting`ScaledTicks[{Log, Exp}][#, #2, {6, 6}]]& , Quiet[
Charting`ScaledTicks[{Log, Exp}][#, #2, {6,
6}]]& }, {{{-4.605170185988091,
FormBox[
TagBox[
InterpretationBox[
StyleBox["\"0.01\"", ShowStringCharacters -> False], 0.01,
AutoDelete -> True], NumberForm[#, {
DirectedInfinity[1], 2}]& ], TraditionalForm], {0.01,
0.}}, {-2.995732273553991,
FormBox[
TagBox[
InterpretationBox[
StyleBox["\"0.05\"", ShowStringCharacters -> False], 0.05,
AutoDelete -> True], NumberForm[#, {
DirectedInfinity[1], 2}]& ], TraditionalForm], {0.01,
0.}}, {-2.3025850929940455`,
FormBox[
TagBox[
InterpretationBox[
StyleBox["\"0.10\"", ShowStringCharacters -> False], 0.1,
AutoDelete -> True], NumberForm[#, {
DirectedInfinity[1], 2}]& ], TraditionalForm], {0.01,
0.}}, {-0.6931471805599453,
FormBox[
TagBox[
InterpretationBox[
StyleBox["\"0.50\"", ShowStringCharacters -> False], 0.5,
AutoDelete -> True], NumberForm[#, {
DirectedInfinity[1], 2}]& ], TraditionalForm], {0.01, 0.}}, {0.,
FormBox["1", TraditionalForm], {0.01, 0.}}, {-5.298317366548036,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-5.115995809754082,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-4.961845129926823,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-4.8283137373023015`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-4.710530701645918,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-3.912023005428146,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-3.506557897319982,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-3.2188758248682006`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-2.8134107167600364`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-2.659260036932778,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-2.5257286443082556`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-2.4079456086518722`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-1.6094379124341003`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-1.2039728043259361`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-0.916290731874155,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-0.5108256237659907,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-0.35667494393873245`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-0.2231435513142097,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-0.10536051565782628`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
0.6931471805599453,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
1.0986122886681098`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
1.3862943611198906`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
1.6094379124341003`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
1.791759469228055,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
1.9459101490553132`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
2.0794415416798357`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
2.1972245773362196`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
2.302585092994046,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
2.3978952727983707`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
2.4849066497880004`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
2.5649493574615367`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
2.6390573296152584`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
2.70805020110221,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
2.772588722239781,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}}, {{-9.210340371976182,
FormBox[
TemplateBox[{"10",
RowBox[{"-", "4"}]}, "Superscript", SyntaxForm -> SuperscriptBox],
TraditionalForm], {0.01, 0.}}, {-6.907755278982137,
FormBox["0.001`", TraditionalForm], {0.01, 0.}}, {-4.605170185988091,
FormBox[
TagBox[
InterpretationBox[
StyleBox["\"0.010\"", ShowStringCharacters -> False], 0.01,
AutoDelete -> True], NumberForm[#, {
DirectedInfinity[1], 3}]& ], TraditionalForm], {0.01,
0.}}, {-2.3025850929940455`,
FormBox[
TagBox[
InterpretationBox[
StyleBox["\"0.100\"", ShowStringCharacters -> False], 0.1,
AutoDelete -> True], NumberForm[#, {
DirectedInfinity[1], 3}]& ], TraditionalForm], {0.01, 0.}}, {0.,
FormBox["1", TraditionalForm], {0.01, 0.}}, {-11.512925464970229`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-10.819778284410283`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-10.41431317630212,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-10.126631103850338`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-9.903487552536127,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-9.721165995742174,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-9.567015315914915,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-9.433483923290392,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-9.315700887634009,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-8.517193191416238,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-8.111728083308073,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-7.824046010856292,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-7.600902459542082,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-7.418580902748128,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-7.264430222920869,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-7.1308988302963465`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-7.013115794639964,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-6.214608098422191,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-5.809142990314028,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-5.521460917862246,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-5.298317366548036,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-5.115995809754082,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-4.961845129926823,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-4.8283137373023015`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-4.710530701645918,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-3.912023005428146,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-3.506557897319982,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-3.2188758248682006`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-2.995732273553991,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-2.8134107167600364`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-2.659260036932778,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-2.5257286443082556`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-2.4079456086518722`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-1.6094379124341003`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-1.2039728043259361`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-0.916290731874155,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-0.6931471805599453,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-0.5108256237659907,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-0.35667494393873245`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-0.2231435513142097,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-0.10536051565782628`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
0.6931471805599453,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
1.0986122886681098`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
1.3862943611198906`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
1.6094379124341003`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
1.791759469228055,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
1.9459101490553132`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
2.0794415416798357`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
2.1972245773362196`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
2.302585092994046,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
2.995732273553991,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
3.4011973816621555`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}}}]]], "Output",
CellChangeTimes->{{3.91872594367129*^9, 3.9187260661755743`*^9},
3.918726175631693*^9},
CellLabel->
"Out[167]=",ExpressionUUID->"577d1677-caae-445e-86d8-466bb20ce13f"],
Cell[BoxData[
SqrtBox[
RowBox[{"2", "-",
RowBox[{"2", " ",
SuperscriptBox[
RowBox[{"Cos", "[", "\[Delta]t", "]"}], "2"], " ",
RowBox[{"Cos", "[",
RowBox[{
SqrtBox["2"], " ", "\[Delta]t"}], "]"}]}], "-",
FractionBox[
RowBox[{
SuperscriptBox[
RowBox[{"Csc", "[",
FractionBox["\[Delta]t", "2"], "]"}], "2"], " ",
SuperscriptBox[
RowBox[{"Sin", "[", "\[Delta]t", "]"}], "3"], " ",
RowBox[{"Sin", "[",
RowBox[{
SqrtBox["2"], " ", "\[Delta]t"}], "]"}]}],
SqrtBox["2"]]}]]], "Output",
CellChangeTimes->{{3.91872594367129*^9, 3.9187260661755743`*^9},
3.918726177469057*^9},
CellLabel->
"Out[169]=",ExpressionUUID->"6f7f6de2-d432-4e3a-8c16-dc5e70fcce3a"],
Cell[BoxData[
GraphicsBox[{{{}, {},
TagBox[
{RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
1.], LineBox[CompressedData["
1:eJwB4QQe+yFib1JlAgAAAE0AAAACAAAACbFztLFrEsBXxJjTE5stwJbf1rkH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"]]},
Annotation[#, "Charting`Private`Tag$30117#1"]& ],
TagBox[
{RGBColor[0.880722, 0.611041, 0.142051], AbsoluteThickness[1.6], Opacity[
1.], LineBox[CompressedData["
1:eJwVxX040wkcAPB5Z8zZilQkbwmtkh7kqi96pBLRqVwdt0jPrrfFVl1nctLJ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"]]},
Annotation[#, "Charting`Private`Tag$30117#2"]& ]}, {}},
AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
Axes->{True, True},
AxesLabel->{None, None},
AxesOrigin->{-4.605170185988091, -14.802885639570531`},
CoordinatesToolOptions:>{"DisplayFunction" -> ({
Exp[
Part[#, 1]],
Exp[
Part[#, 2]]}& ), "CopiedValueFunction" -> ({
Exp[
Part[#, 1]],
Exp[
Part[#, 2]]}& )},
DisplayFunction->Identity,
Frame->{{False, False}, {False, False}},
FrameLabel->{{None, None}, {None, None}},
FrameTicks->{{Quiet[
Charting`ScaledTicks[{Log, Exp}][#, #2, {6, 6}]]& ,
Charting`ScaledFrameTicks[{Log, Exp}]}, {Quiet[
Charting`ScaledTicks[{Log, Exp}][#, #2, {6, 6}]]& ,
Charting`ScaledFrameTicks[{Log, Exp}]}},
GridLines->{None, None},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
ImagePadding->All,
Method->{
"DefaultBoundaryStyle" -> Automatic,
"DefaultGraphicsInteraction" -> {
"Version" -> 1.2, "TrackMousePosition" -> {True, False},
"Effects" -> {
"Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2},
"Droplines" -> {
"freeformCursorMode" -> True,
"placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" ->
AbsolutePointSize[6], "ScalingFunctions" -> None},
PlotRange->NCache[{{-4.605170185988091,
Log[2]}, {-14.802885639570531`,
1.0924007042820536`}}, {{-4.605170185988091,
0.6931471805599453}, {-14.802885639570531`, 1.0924007042820536`}}],
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.05],
Scaled[0.05]}},
Ticks->FrontEndValueCache[{Quiet[
Charting`ScaledTicks[{Log, Exp}][#, #2, {6, 6}]]& , Quiet[
Charting`ScaledTicks[{Log, Exp}][#, #2, {6,
6}]]& }, {{{-4.605170185988091,
FormBox[
TagBox[
InterpretationBox[
StyleBox["\"0.01\"", ShowStringCharacters -> False], 0.01,
AutoDelete -> True], NumberForm[#, {
DirectedInfinity[1], 2}]& ], TraditionalForm], {0.01,
0.}}, {-2.995732273553991,
FormBox[
TagBox[
InterpretationBox[
StyleBox["\"0.05\"", ShowStringCharacters -> False], 0.05,
AutoDelete -> True], NumberForm[#, {
DirectedInfinity[1], 2}]& ], TraditionalForm], {0.01,
0.}}, {-2.3025850929940455`,
FormBox[
TagBox[
InterpretationBox[
StyleBox["\"0.10\"", ShowStringCharacters -> False], 0.1,
AutoDelete -> True], NumberForm[#, {
DirectedInfinity[1], 2}]& ], TraditionalForm], {0.01,
0.}}, {-0.6931471805599453,
FormBox[
TagBox[
InterpretationBox[
StyleBox["\"0.50\"", ShowStringCharacters -> False], 0.5,
AutoDelete -> True], NumberForm[#, {
DirectedInfinity[1], 2}]& ], TraditionalForm], {0.01, 0.}}, {0.,
FormBox["1", TraditionalForm], {0.01, 0.}}, {-5.298317366548036,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-5.115995809754082,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-4.961845129926823,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-4.8283137373023015`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-4.710530701645918,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-3.912023005428146,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-3.506557897319982,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-3.2188758248682006`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-2.8134107167600364`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-2.659260036932778,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-2.5257286443082556`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-2.4079456086518722`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-1.6094379124341003`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-1.2039728043259361`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-0.916290731874155,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-0.5108256237659907,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-0.35667494393873245`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-0.2231435513142097,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-0.10536051565782628`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
0.6931471805599453,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
1.0986122886681098`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
1.3862943611198906`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
1.6094379124341003`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
1.791759469228055,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
1.9459101490553132`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
2.0794415416798357`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
2.1972245773362196`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
2.302585092994046,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
2.3978952727983707`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
2.4849066497880004`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
2.5649493574615367`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
2.6390573296152584`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
2.70805020110221,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
2.772588722239781,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}}, {{-13.815510557964274`,
FormBox[
TemplateBox[{"10",
RowBox[{"-", "6"}]}, "Superscript", SyntaxForm -> SuperscriptBox],
TraditionalForm], {0.01, 0.}}, {-11.512925464970229`,
FormBox[
TemplateBox[{"10",
RowBox[{"-", "5"}]}, "Superscript", SyntaxForm -> SuperscriptBox],
TraditionalForm], {0.01, 0.}}, {-9.210340371976182,
FormBox[
TemplateBox[{"10",
RowBox[{"-", "4"}]}, "Superscript", SyntaxForm -> SuperscriptBox],
TraditionalForm], {0.01, 0.}}, {-6.907755278982137,
FormBox["0.001`", TraditionalForm], {0.01, 0.}}, {-4.605170185988091,
FormBox[
TagBox[
InterpretationBox[
StyleBox["\"0.010\"", ShowStringCharacters -> False], 0.01,
AutoDelete -> True], NumberForm[#, {
DirectedInfinity[1], 3}]& ], TraditionalForm], {0.01,
0.}}, {-2.3025850929940455`,
FormBox[
TagBox[
InterpretationBox[
StyleBox["\"0.100\"", ShowStringCharacters -> False], 0.1,
AutoDelete -> True], NumberForm[#, {
DirectedInfinity[1], 3}]& ], TraditionalForm], {0.01, 0.}}, {0.,
FormBox["1", TraditionalForm], {0.01, 0.}}, {-16.11809565095832,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-15.424948470398375`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-15.01948336229021,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-14.73180128983843,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-14.508657738524219`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-14.326336181730264`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-14.172185501903007`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-14.038654109278484`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-13.9208710736221,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-13.122363377404328`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-12.716898269296165`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-12.429216196844383`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-12.206072645530174`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-12.02375108873622,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-11.86960040890896,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-11.736069016284437`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-11.618285980628055`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-10.819778284410283`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-10.41431317630212,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-10.126631103850338`,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-9.903487552536127,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-9.721165995742174,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-9.567015315914915,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-9.433483923290392,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-9.315700887634009,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-8.517193191416238,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-8.111728083308073,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-7.824046010856292,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-7.600902459542082,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-7.418580902748128,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,
0.}}, {-7.264430222920869,
FormBox[
TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005,