a07f721563e49508afce26521f6cebc0 computation-13-00045-v2.pdf b6afc2671df1daf7ccb31a9f5cd51fbe986c3baf computation-13-00045-v2.pdf 2aa7ce597de007f80a6ee8d8925651c43d87a40fc7d913743c7e76bdcb10364a computation-13-00045-v2.pdf Title: Displacement Current in Classical and Quantum Systems Subject: It is certain that electrical properties—whether slow (sec) or fast (nsec), even optical (fsec)—are described by Maxwell’s equations, and there are terms that depend on the rate of the change of the electric and magnetic fields. In particular, Maxwell’s equation for the curl of the magnetic field contains both the steady-state conduction current and a term depending upon the temporal derivative of the electric displacement field. The latter is referred to as the displacement current and is generally believed to have been included originally by Maxwell himself, although there is evidence it was earlier considered by Kirchhoff. Maxwell’s equations and Kirchoff’s circuit laws both are important over the wide range of frequencies with which electronics traditionally deal. Additionally, the displacement current is an important contribution to these in both classical and quantum mechanics. Here, the development of the displacement current, its importance in both classical and quantum mechanics, and some applications are provided to illustrate the fundamental role that it plays in the dynamics of a wide range of systems. Keywords: current; gauge invariance; quantum dynamics; classical dynamics Author: David K. Ferry, Xavier Oriols and Robert Eisenberg Creator: LaTeX with hyperref Producer: pdfTeX-1.40.25 CreationDate: Mon Feb 10 08:16:07 2025 CET ModDate: Mon Feb 10 10:43:07 2025 CET Custom Metadata: no Metadata Stream: no Tagged: no UserProperties: no Suspects: no Form: none JavaScript: no Pages: 31 Encrypted: no Page size: 595.276 x 841.89 pts (A4) Page rot: 0 File size: 3730901 bytes Optimized: no PDF version: 1.7 name type encoding emb sub uni object ID ------------------------------------ ----------------- ---------------- --- --- --- --------- AIRHKL+VnURWPalladioL Type 1 Custom yes yes yes 10 0 FTBREK+URWPalladioL-Roma Type 1 Custom yes yes yes 16 0 FHLAKI+URWPalladioL-Bold Type 1 Custom yes yes yes 22 0 JCJZGL+URWPalladioL-Ital Type 1 Custom yes yes yes 27 0 NEKXRQ+EURM10 Type 1 Builtin yes yes yes 53 0 AURAAG+CMBSY10 Type 1 Builtin yes yes yes 58 0 QVLDRX+CMSY10 Type 1 Builtin yes yes yes 63 0 SOSTRQ+CMR10 Type 1 Builtin yes yes yes 68 0 BFQAIQ+PazoMath-Italic Type 1 Builtin yes yes yes 73 0 LSKJWS+CMEX10 Type 1 Builtin yes yes yes 81 0 DGARQE+PazoMath Type 1 Builtin yes yes yes 92 0 IHWUPK+URWPalladioL-BoldItal Type 1 Custom yes yes yes 97 0 NJJMNO+PalatinoLinotype,Bold TrueType WinAnsi yes yes no 120 0 NJJMNP+PalatinoLinotype CID TrueType Identity-H yes yes yes 123 0 NJJMOA+PalatinoLinotype TrueType WinAnsi yes yes no 129 0 NJJMOC+PalatinoLinotype,Italic TrueType WinAnsi yes yes no 132 0 NJJNEB+PalatinoLinotype TrueType MacRoman yes yes no 135 0 NJJNLP+CambriaMath CID TrueType Identity-H yes yes yes 138 0 NJJODN+TimesNewRoman CID TrueType Identity-H yes yes yes 144 0 NJJMNO+PalatinoLinotype,Bold TrueType WinAnsi yes yes no 163 0 NJJMNP+PalatinoLinotype CID TrueType Identity-H yes yes yes 166 0 NJJMOA+PalatinoLinotype TrueType WinAnsi yes yes no 172 0 NJJMOC+PalatinoLinotype,Italic TrueType WinAnsi yes yes no 175 0 NJJNEB+PalatinoLinotype TrueType MacRoman yes yes no 178 0 NJJNLP+CambriaMath CID TrueType Identity-H yes yes yes 181 0 NJJODN+TimesNewRoman CID TrueType Identity-H yes yes yes 187 0 QITBVI+MSBM10 Type 1 Builtin yes yes yes 201 0 NJJMNO+PalatinoLinotype,Bold TrueType WinAnsi yes yes no 213 0 NJJMNP+PalatinoLinotype CID TrueType Identity-H yes yes yes 216 0 NJJMOA+PalatinoLinotype TrueType WinAnsi yes yes no 222 0 NJJMOC+PalatinoLinotype,Italic TrueType WinAnsi yes yes no 225 0 NJJNEB+PalatinoLinotype TrueType MacRoman yes yes no 228 0 NJJNLP+CambriaMath CID TrueType Identity-H yes yes yes 231 0 NJJODN+TimesNewRoman CID TrueType Identity-H yes yes yes 237 0 BCDEEE+PalatinoLinotype-Bold TrueType WinAnsi yes yes no 248 0 SymbolMT CID TrueType Identity-H yes no yes 252 0 BCDFEE+PalatinoLinotype-Roman TrueType WinAnsi yes yes no 260 0 BCDGEE+PalatinoLinotype-Italic TrueType WinAnsi yes yes no 264 0 BCDHEE+PalatinoLinotype-Italic CID TrueType Identity-H yes yes yes 268 0 BCDJEE+PalatinoLinotype-Roman CID TrueType Identity-H yes yes yes 275 0 BCDKEE+CambriaMath CID TrueType Identity-H yes yes yes 282 0 TimesNewRomanPSMT CID TrueType Identity-H yes no yes 290 0 NJJMNO+PalatinoLinotype,Bold TrueType WinAnsi yes yes no 309 0 NJJMNP+PalatinoLinotype CID TrueType Identity-H yes yes yes 312 0 NJJMOA+PalatinoLinotype TrueType WinAnsi yes yes no 318 0 NJJMOC+PalatinoLinotype,Italic TrueType WinAnsi yes yes no 321 0 NJJNEB+PalatinoLinotype TrueType MacRoman yes yes no 324 0 NJJNLP+CambriaMath CID TrueType Identity-H yes yes yes 327 0 NJJODN+TimesNewRoman CID TrueType Identity-H yes yes yes 333 0 NJJMNO+PalatinoLinotype,Bold TrueType WinAnsi yes yes no 353 0 NJJMNP+PalatinoLinotype CID TrueType Identity-H yes yes yes 356 0 NJJMOA+PalatinoLinotype TrueType WinAnsi yes yes no 362 0 NJJMOC+PalatinoLinotype,Italic TrueType WinAnsi yes yes no 365 0 NJJNEB+PalatinoLinotype TrueType MacRoman yes yes no 368 0 NJJNLP+CambriaMath CID TrueType Identity-H yes yes yes 371 0 NJJMNO+PalatinoLinotype,Bold TrueType WinAnsi yes yes no 391 0 NJJMNP+PalatinoLinotype CID TrueType Identity-H yes yes yes 394 0 NJJMOA+PalatinoLinotype TrueType WinAnsi yes yes no 400 0 NJJMOC+PalatinoLinotype,Italic TrueType WinAnsi yes yes no 403 0 NJJNEB+PalatinoLinotype TrueType MacRoman yes yes no 406 0 NJJNLP+CambriaMath CID TrueType Identity-H yes yes yes 409 0 NJJODN+TimesNewRoman CID TrueType Identity-H yes yes yes 415 0 VFIWZQ+EURM7 Type 1 Builtin yes yes yes 425 0 NJJMNO+PalatinoLinotype,Bold TrueType WinAnsi yes yes no 453 0 NJJMNP+PalatinoLinotype CID TrueType Identity-H yes yes yes 456 0 NJJMOA+PalatinoLinotype TrueType WinAnsi yes yes no 462 0 NJJMOC+PalatinoLinotype,Italic TrueType WinAnsi yes yes no 465 0 NJJNEB+PalatinoLinotype TrueType MacRoman yes yes no 468 0 NJJNLP+CambriaMath CID TrueType Identity-H yes yes yes 471 0 NJJMNO+PalatinoLinotype,Bold TrueType WinAnsi yes yes no 488 0 NJJMNP+PalatinoLinotype CID TrueType Identity-H yes yes yes 491 0 NJJMOA+PalatinoLinotype TrueType WinAnsi yes yes no 497 0 NJJMOC+PalatinoLinotype,Italic TrueType WinAnsi yes yes no 500 0 NJJNEB+PalatinoLinotype TrueType MacRoman yes yes no 503 0 NJJNLP+CambriaMath CID TrueType Identity-H yes yes yes 506 0 NJJODN+TimesNewRoman CID TrueType Identity-H yes yes yes 512 0 Jhove (Rel. 1.28.0, 2023-05-18) Date: 2025-05-29 02:09:11 CEST RepresentationInformation: computation-13-00045-v2.pdf ReportingModule: PDF-hul, Rel. 1.12.4 (2023-03-16) LastModified: 2025-05-28 12:39:38 CEST Size: 3730901 Format: PDF Version: 1.7 Status: Well-Formed and valid SignatureMatches: PDF-hul MIMEtype: application/pdf PDFMetadata: Objects: 795 FreeObjects: 1 IncrementalUpdates: 0 DocumentCatalog: PageLayout: SinglePage PageMode: UseNone Outlines: Item: Title: Introduction Destination: section.1 Item: Title: Maxwell’s Equation and Gauge Destination: section.2 Children: Item: Title: Gauge and Gauge Invariance Destination: subsection.2.1 Item: Title: Polarization and Magnetization Destination: subsection.2.2 Item: Title: Conduction and Displacement Currents Destination: subsection.2.3 Item: Title: A Simple Gauge Example: I Destination: subsection.2.4 Item: Title: A Simple Gauge Example: II Destination: subsection.2.5 Item: Title: Some Implications Destination: section.3 Children: Item: Title: Guided Waves Destination: subsection.3.1 Item: Title: Ion Channels Destination: subsection.3.2 Item: Title: High-Frequency Quantum Devices Destination: subsection.3.3 Item: Title: Displacement Current in Quantum Mechanics Destination: section.4 Children: Item: Title: Quantum Electron and Classical Light Destination: subsection.4.1 Item: Title: Quantum Matter and Quantum Light Destination: subsection.4.2 Item: Title: Displacement Current for an Ensemble of Experiments Destination: subsection.4.3 Item: Title: Displacement Current for a Single Experiment Destination: subsection.4.4 Item: Title: Computational Considerations Destination: section.5 Item: Title: Discussion Destination: section.6 Item: Title: Appendix A Destination: appendix.A. Item: Title: References Destination: appendix.B. Info: Title: Displacement Current in Classical and Quantum Systems Author: David K. Ferry, Xavier Oriols and Robert Eisenberg Subject: It is certain that electrical properties whether slow (sec) or fast (nsec), even optical (fsec) are described by Maxwell’s equations, and there are terms that depend on the rate of the change of the electric and magnetic fields. In particular, Maxwell’s equation for the curl of the magnetic field contains both the steady-state conduction current and a term depending upon the temporal derivative of the electric displacement field. The latter is referred to as the displacement current and is generally believed to have been included originally by Maxwell himself, although there is evidence it was earlier considered by Kirchhoff. Maxwell’s equations and Kirchoff’s circuit laws both are important over the wide range of frequencies with which electronics traditionally deal. Additionally, the displacement current is an important contribution to these in both classical and quantum mechanics. Here, the development of the displacement current, its importance in both classical and quantum mechanics, and some applications are provided to illustrate the fundamental role that it plays in the dynamics of a wide range of systems. Keywords: current; gauge invariance; quantum dynamics; classical dynamics Creator: LaTeX with hyperref Producer: pdfTeX-1.40.25 CreationDate: Mon Feb 10 08:16:07 CET 2025 ModDate: Mon Feb 10 10:43:07 CET 2025 ID: 0x33898b541902a48e94563efab4c4fbf2, 0x33898b541902a48e94563efab4c4fbf2 Filters: FilterPipeline: FlateDecode Fonts: Type1: Font: BaseFont: IHWUPK+URWPalladioL-BoldItal FontSubset: true FirstChar: 65 LastChar: 120 FontDescriptor: FontName: IHWUPK+URWPalladioL-BoldItal Flags: Symbolic FontBBox: -170, -300, 1073, 935 FontFile: true EncodingDictionary: Differences: true ToUnicode: true Font: BaseFont: SOSTRQ+CMR10 FontSubset: true FirstChar: 40 LastChar: 93 FontDescriptor: FontName: SOSTRQ+CMR10 Flags: Symbolic FontBBox: -40, -250, 1009, 750 FontFile: true ToUnicode: true Font: BaseFont: BFQAIQ+PazoMath-Italic FontSubset: true FirstChar: 35 LastChar: 182 FontDescriptor: FontName: BFQAIQ+PazoMath-Italic Flags: Symbolic FontBBox: -70, -277, 902, 733 FontFile: true ToUnicode: true Font: BaseFont: QITBVI+MSBM10 FontSubset: true FirstChar: 125 LastChar: 125 FontDescriptor: FontName: QITBVI+MSBM10 Flags: Symbolic FontBBox: -55, -420, 2343, 920 FontFile: true ToUnicode: true Font: BaseFont: VFIWZQ+EURM7 FontSubset: true FirstChar: 26 LastChar: 26 FontDescriptor: FontName: VFIWZQ+EURM7 Flags: Symbolic FontBBox: -5, -243, 1229, 720 FontFile: true ToUnicode: true Font: BaseFont: AIRHKL+VnURWPalladioL FontSubset: true FirstChar: 160 LastChar: 225 FontDescriptor: FontName: AIRHKL+VnURWPalladioL Flags: Symbolic FontBBox: -166, -283, 1021, 943 FontFile: true EncodingDictionary: Differences: true ToUnicode: true Font: BaseFont: FTBREK+URWPalladioL-Roma FontSubset: true FirstChar: 2 LastChar: 246 FontDescriptor: FontName: FTBREK+URWPalladioL-Roma Flags: Symbolic FontBBox: -166, -283, 1021, 943 FontFile: true EncodingDictionary: Differences: true ToUnicode: true Font: BaseFont: LSKJWS+CMEX10 FontSubset: true FirstChar: 0 LastChar: 114 FontDescriptor: FontName: LSKJWS+CMEX10 Flags: Symbolic FontBBox: -24, -2960, 1454, 772 FontFile: true ToUnicode: true Font: BaseFont: NEKXRQ+EURM10 FontSubset: true FirstChar: 14 LastChar: 34 FontDescriptor: FontName: NEKXRQ+EURM10 Flags: Symbolic FontBBox: -32, -243, 1060, 720 FontFile: true ToUnicode: true Font: BaseFont: FHLAKI+URWPalladioL-Bold FontSubset: true FirstChar: 3 LastChar: 121 FontDescriptor: FontName: FHLAKI+URWPalladioL-Bold Flags: Symbolic FontBBox: -152, -301, 1000, 935 FontFile: true EncodingDictionary: Differences: true ToUnicode: true Font: BaseFont: AURAAG+CMBSY10 FontSubset: true FirstChar: 114 LastChar: 114 FontDescriptor: FontName: AURAAG+CMBSY10 Flags: Symbolic FontBBox: -26, -940, 1332, 825 FontFile: true ToUnicode: true Font: BaseFont: JCJZGL+URWPalladioL-Ital FontSubset: true FirstChar: 44 LastChar: 122 FontDescriptor: FontName: JCJZGL+URWPalladioL-Ital Flags: Symbolic FontBBox: -170, -305, 1010, 941 FontFile: true EncodingDictionary: Differences: true ToUnicode: true Font: BaseFont: DGARQE+PazoMath FontSubset: true FirstChar: 68 LastChar: 229 FontDescriptor: FontName: DGARQE+PazoMath Flags: Symbolic FontBBox: -40, -283, 878, 946 FontFile: true ToUnicode: true Font: BaseFont: QVLDRX+CMSY10 FontSubset: true FirstChar: 0 LastChar: 114 FontDescriptor: FontName: QVLDRX+CMSY10 Flags: Symbolic FontBBox: -29, -960, 1116, 775 FontFile: true ToUnicode: true Pages: Page: Sequence: 1 Annotations: Annotation: Subtype: Link Rect: 34, 177, 152, 186 Annotation: Subtype: Link Rect: 34, 165, 103, 174 Annotation: Subtype: Link Rect: 36, 75, 152, 84 Annotation: Subtype: Link Rect: 34, 63, 89, 72 Annotation: Subtype: Link Rect: 34, 773, 165, 809 Annotation: Subtype: Link Rect: 515, 773, 560, 809 Annotation: Subtype: Link Rect: 115, 684, 126, 698 Annotation: Subtype: Link Rect: 196, 684, 208, 698 Annotation: Subtype: Link Rect: 327, 684, 338, 698 Annotation: Subtype: Link Rect: 305, 262, 312, 271 ActionDest: 534 Annotation: Subtype: Link Rect: 212, 192, 219, 201 ActionDest: 534 Annotation: Subtype: Link Rect: 538, 66, 545, 76 ActionDest: 534 Annotation: Subtype: Link Rect: 390, 27, 560, 37 Annotation: Subtype: Link Rect: 34, 308, 87, 327 Page: Sequence: 2 Annotations: Annotation: Subtype: Link Rect: 260, 731, 267, 740 ActionDest: 534 Annotation: Subtype: Link Rect: 267, 730, 274, 740 ActionDest: 534 Annotation: Subtype: Link Rect: 553, 630, 560, 642 ActionDest: 381 Annotation: Subtype: Link Rect: 374, 603, 381, 615 ActionDest: 522 Annotation: Subtype: Link Rect: 291, 304, 298, 313 ActionDest: 534 Page: Sequence: 3 Annotations: Annotation: Subtype: Link Rect: 549, 745, 556, 754 ActionDest: 534 Annotation: Subtype: Link Rect: 235, 717, 242, 726 ActionDest: 534 Annotation: Subtype: Link Rect: 328, 605, 335, 614 ActionDest: 534 Page: Sequence: 4 Annotations: Annotation: Subtype: Link Rect: 507, 137, 514, 146 ActionDest: 534 Page: Sequence: 5 Annotations: Annotation: Subtype: Link Rect: 333, 675, 340, 684 ActionDest: 534 Page: Sequence: 6 Annotations: Annotation: Subtype: Link Rect: 248, 563, 255, 572 ActionDest: 534 Annotation: Subtype: Link Rect: 256, 563, 267, 572 ActionDest: 534 Annotation: Subtype: Link Rect: 548, 533, 558, 545 ActionDest: 528 Page: Sequence: 7 Annotations: Annotation: Subtype: Link Rect: 494, 703, 506, 712 ActionDest: 534 Annotation: Subtype: Link Rect: 522, 689, 534, 698 ActionDest: 534 Annotation: Subtype: Link Rect: 529, 647, 541, 656 ActionDest: 534 Annotation: Subtype: Link Rect: 420, 455, 432, 464 ActionDest: 534 Annotation: Subtype: Link Rect: 252, 230, 259, 242 ActionDest: 108 Page: Sequence: 8 Page: Sequence: 9 Annotations: Annotation: Subtype: Link Rect: 467, 419, 474, 431 ActionDest: 151 Page: Sequence: 10 Annotations: Annotation: Subtype: Link Rect: 396, 500, 408, 509 ActionDest: 534 Annotation: Subtype: Link Rect: 464, 440, 476, 449 ActionDest: 534 Annotation: Subtype: Link Rect: 477, 440, 489, 449 ActionDest: 534 Annotation: Subtype: Link Rect: 195, 326, 202, 338 ActionDest: 151 Annotation: Subtype: Link Rect: 457, 229, 464, 241 ActionDest: 197 Annotation: Subtype: Link Rect: 247, 131, 254, 143 ActionDest: 151 Annotation: Subtype: Link Rect: 274, 131, 281, 143 ActionDest: 197 Annotation: Subtype: Link Rect: 269, 117, 276, 129 ActionDest: 197 Annotation: Subtype: Link Rect: 553, 89, 560, 101 ActionDest: 151 Page: Sequence: 11 Annotations: Annotation: Subtype: Link Rect: 348, 510, 360, 519 ActionDest: 534 Annotation: Subtype: Link Rect: 400, 229, 412, 238 ActionDest: 534 Page: Sequence: 12 Annotations: Annotation: Subtype: Link Rect: 527, 305, 534, 317 ActionDest: 299 Page: Sequence: 13 Annotations: Annotation: Subtype: Link Rect: 402, 745, 414, 754 ActionDest: 534 Annotation: Subtype: Link Rect: 430, 632, 442, 641 ActionDest: 534 Annotation: Subtype: Link Rect: 240, 576, 252, 585 ActionDest: 534 Annotation: Subtype: Link Rect: 384, 576, 396, 585 ActionDest: 534 Annotation: Subtype: Link Rect: 211, 549, 223, 558 ActionDest: 537 Annotation: Subtype: Link Rect: 266, 521, 278, 530 ActionDest: 537 Annotation: Subtype: Link Rect: 448, 507, 460, 516 ActionDest: 537 Annotation: Subtype: Link Rect: 212, 355, 224, 364 ActionDest: 537 Annotation: Subtype: Link Rect: 232, 243, 244, 252 ActionDest: 537 Annotation: Subtype: Link Rect: 500, 160, 512, 169 ActionDest: 537 Page: Sequence: 14 Annotations: Annotation: Subtype: Link Rect: 285, 730, 297, 740 ActionDest: 537 Annotation: Subtype: Link Rect: 298, 730, 310, 740 ActionDest: 537 Annotation: Subtype: Link Rect: 478, 703, 490, 712 ActionDest: 537 Annotation: Subtype: Link Rect: 444, 644, 451, 656 ActionDest: 343 Annotation: Subtype: Link Rect: 455, 647, 467, 656 ActionDest: 537 Annotation: Subtype: Link Rect: 432, 433, 443, 441 ActionDest: 537 Annotation: Subtype: Link Rect: 520, 384, 532, 393 ActionDest: 537 Annotation: Subtype: Link Rect: 272, 231, 284, 240 ActionDest: 537 Page: Sequence: 15 Annotations: Annotation: Subtype: Link Rect: 367, 508, 379, 517 ActionDest: 537 Annotation: Subtype: Link Rect: 380, 508, 392, 517 ActionDest: 537 Annotation: Subtype: Link Rect: 304, 396, 316, 405 ActionDest: 537 Annotation: Subtype: Link Rect: 316, 396, 328, 405 ActionDest: 537 Annotation: Subtype: Link Rect: 308, 285, 320, 294 ActionDest: 537 Annotation: Subtype: Link Rect: 453, 146, 465, 155 ActionDest: 537 Annotation: Subtype: Link Rect: 466, 146, 478, 155 ActionDest: 537 Annotation: Subtype: Link Rect: 224, 76, 236, 85 ActionDest: 534 Annotation: Subtype: Link Rect: 236, 76, 248, 85 ActionDest: 537 Annotation: Subtype: Link Rect: 249, 76, 261, 85 ActionDest: 537 Page: Sequence: 16 Annotations: Annotation: Subtype: Link Rect: 213, 756, 220, 768 ActionDest: 381 Annotation: Subtype: Link Rect: 441, 728, 447, 740 ActionDest: 381 Annotation: Subtype: Link Rect: 389, 647, 401, 656 ActionDest: 537 Annotation: Subtype: Link Rect: 299, 378, 310, 387 ActionDest: 537 Annotation: Subtype: Link Rect: 533, 341, 545, 350 ActionDest: 537 Annotation: Subtype: Link Rect: 439, 327, 450, 336 ActionDest: 537 Annotation: Subtype: Link Rect: 544, 299, 556, 308 ActionDest: 537 Annotation: Subtype: Link Rect: 369, 257, 381, 266 ActionDest: 537 Annotation: Subtype: Link Rect: 253, 229, 265, 238 ActionDest: 537 Page: Sequence: 17 Annotations: Annotation: Subtype: Link Rect: 470, 714, 477, 726 ActionDest: 50 Annotation: Subtype: Link Rect: 244, 579, 256, 588 ActionDest: 537 Annotation: Subtype: Link Rect: 257, 579, 269, 588 ActionDest: 537 Annotation: Subtype: Link Rect: 428, 264, 440, 273 ActionDest: 537 Annotation: Subtype: Link Rect: 440, 264, 452, 273 ActionDest: 537 Page: Sequence: 18 Annotations: Annotation: Subtype: Link Rect: 473, 322, 485, 332 ActionDest: 537 Annotation: Subtype: Link Rect: 394, 225, 406, 234 ActionDest: 537 Annotation: Subtype: Link Rect: 407, 225, 419, 234 ActionDest: 537 Annotation: Subtype: Link Rect: 419, 225, 431, 234 ActionDest: 537 Page: Sequence: 19 Annotations: Annotation: Subtype: Link Rect: 370, 715, 382, 724 ActionDest: 537 Annotation: Subtype: Link Rect: 516, 302, 528, 311 ActionDest: 537 Page: Sequence: 20 Annotations: Annotation: Subtype: Link Rect: 242, 700, 254, 709 ActionDest: 537 Annotation: Subtype: Link Rect: 254, 700, 266, 709 ActionDest: 537 Annotation: Subtype: Link Rect: 267, 700, 279, 709 ActionDest: 537 Annotation: Subtype: Link Rect: 319, 542, 330, 551 ActionDest: 537 Annotation: Subtype: Link Rect: 331, 542, 343, 551 ActionDest: 537 Annotation: Subtype: Link Rect: 359, 500, 371, 509 ActionDest: 537 Annotation: Subtype: Link Rect: 372, 500, 384, 509 ActionDest: 537 Annotation: Subtype: Link Rect: 225, 472, 237, 481 ActionDest: 537 Annotation: Subtype: Link Rect: 237, 472, 249, 481 ActionDest: 537 Annotation: Subtype: Link Rect: 250, 472, 262, 481 ActionDest: 537 Annotation: Subtype: Link Rect: 458, 371, 470, 380 ActionDest: 537 Annotation: Subtype: Link Rect: 366, 329, 378, 338 ActionDest: 537 Annotation: Subtype: Link Rect: 291, 315, 303, 324 ActionDest: 537 Page: Sequence: 21 Annotations: Annotation: Subtype: Link Rect: 356, 744, 368, 754 ActionDest: 537 Annotation: Subtype: Link Rect: 368, 745, 380, 754 ActionDest: 537 Annotation: Subtype: Link Rect: 379, 290, 391, 299 ActionDest: 537 Annotation: Subtype: Link Rect: 391, 290, 403, 299 ActionDest: 537 Annotation: Subtype: Link Rect: 349, 262, 361, 271 ActionDest: 537 Annotation: Subtype: Link Rect: 488, 262, 500, 271 ActionDest: 537 Annotation: Subtype: Link Rect: 311, 248, 323, 257 ActionDest: 537 Annotation: Subtype: Link Rect: 360, 150, 372, 159 ActionDest: 537 Annotation: Subtype: Link Rect: 352, 134, 359, 146 ActionDest: 443 Annotation: Subtype: Link Rect: 551, 134, 558, 146 ActionDest: 443 Page: Sequence: 22 Annotations: Annotation: Subtype: Link Rect: 197, 754, 204, 768 ActionDest: 443 Annotation: Subtype: Link Rect: 254, 698, 261, 713 ActionDest: 443 Annotation: Subtype: Link Rect: 434, 698, 441, 713 ActionDest: 443 Annotation: Subtype: Link Rect: 544, 703, 556, 712 ActionDest: 537 Annotation: Subtype: Link Rect: 482, 188, 494, 197 ActionDest: 537 Page: Sequence: 23 Annotations: Annotation: Subtype: Link Rect: 227, 553, 241, 565 ActionDest: 422 Annotation: Subtype: Link Rect: 278, 511, 285, 523 ActionDest: 478 Annotation: Subtype: Link Rect: 393, 497, 400, 510 ActionDest: 443 Annotation: Subtype: Link Rect: 552, 241, 559, 255 ActionDest: 108 Annotation: Subtype: Link Rect: 401, 190, 408, 202 ActionDest: 108 Annotation: Subtype: Link Rect: 450, 100, 465, 112 ActionDest: 422 Page: Sequence: 24 Annotations: Annotation: Subtype: Link Rect: 531, 728, 543, 737 ActionDest: 537 Annotation: Subtype: Link Rect: 544, 728, 556, 737 ActionDest: 537 Annotation: Subtype: Link Rect: 345, 510, 357, 519 ActionDest: 537 Annotation: Subtype: Link Rect: 358, 510, 370, 519 ActionDest: 537 Annotation: Subtype: Link Rect: 251, 381, 263, 390 ActionDest: 537 Annotation: Subtype: Link Rect: 264, 381, 276, 390 ActionDest: 537 Annotation: Subtype: Link Rect: 301, 364, 308, 376 ActionDest: 443 Annotation: Subtype: Link Rect: 472, 226, 486, 238 ActionDest: 422 Annotation: Subtype: Link Rect: 368, 212, 375, 224 ActionDest: 478 Annotation: Subtype: Link Rect: 546, 198, 554, 212 ActionDest: 478 Annotation: Subtype: Link Rect: 411, 185, 418, 197 ActionDest: 478 Annotation: Subtype: Link Rect: 229, 115, 236, 127 ActionDest: 478 Annotation: Subtype: Link Rect: 239, 101, 246, 113 ActionDest: 478 Annotation: Subtype: Link Rect: 477, 87, 484, 99 ActionDest: 478 Page: Sequence: 25 Annotations: Annotation: Subtype: Link Rect: 208, 756, 215, 768 ActionDest: 478 Annotation: Subtype: Link Rect: 358, 576, 370, 585 ActionDest: 537 Annotation: Subtype: Link Rect: 544, 548, 556, 558 ActionDest: 537 Annotation: Subtype: Link Rect: 382, 479, 394, 488 ActionDest: 540 Annotation: Subtype: Link Rect: 371, 451, 383, 460 ActionDest: 540 Annotation: Subtype: Link Rect: 383, 451, 395, 460 ActionDest: 540 Annotation: Subtype: Link Rect: 207, 381, 219, 390 ActionDest: 537 Annotation: Subtype: Link Rect: 212, 353, 224, 363 ActionDest: 537 Annotation: Subtype: Link Rect: 224, 353, 236, 363 ActionDest: 537 Annotation: Subtype: Link Rect: 237, 353, 249, 363 ActionDest: 537 Annotation: Subtype: Link Rect: 249, 353, 261, 363 ActionDest: 540 Annotation: Subtype: Link Rect: 219, 340, 231, 349 ActionDest: 537 Annotation: Subtype: Link Rect: 232, 340, 243, 349 ActionDest: 537 Annotation: Subtype: Link Rect: 244, 340, 256, 349 ActionDest: 537 Annotation: Subtype: Link Rect: 482, 284, 494, 293 ActionDest: 537 Annotation: Subtype: Link Rect: 386, 242, 398, 251 ActionDest: 540 Annotation: Subtype: Link Rect: 446, 228, 458, 237 ActionDest: 537 Page: Sequence: 26 Annotations: Annotation: Subtype: Link Rect: 384, 689, 396, 698 ActionDest: 540 Annotation: Subtype: Link Rect: 346, 661, 358, 670 ActionDest: 540 Annotation: Subtype: Link Rect: 529, 633, 541, 642 ActionDest: 534 Annotation: Subtype: Link Rect: 473, 603, 480, 615 ActionDest: 343 Annotation: Subtype: Link Rect: 249, 549, 261, 559 ActionDest: 540 Annotation: Subtype: Link Rect: 466, 536, 478, 545 ActionDest: 534 Annotation: Subtype: Link Rect: 479, 536, 490, 545 ActionDest: 540 Annotation: Subtype: Link Rect: 371, 480, 383, 489 ActionDest: 540 Annotation: Subtype: Link Rect: 251, 452, 263, 461 ActionDest: 540 Annotation: Subtype: Link Rect: 408, 396, 420, 405 ActionDest: 540 Annotation: Subtype: Link Rect: 221, 382, 228, 392 ActionDest: 381 Annotation: Subtype: Link Rect: 421, 368, 433, 377 ActionDest: 537 Annotation: Subtype: Link Rect: 434, 368, 446, 377 ActionDest: 537 Annotation: Subtype: Link Rect: 463, 313, 475, 322 ActionDest: 537 Annotation: Subtype: Link Rect: 475, 313, 487, 322 ActionDest: 537 Annotation: Subtype: Link Rect: 488, 313, 500, 322 ActionDest: 537 Annotation: Subtype: Link Rect: 378, 254, 385, 266 ActionDest: 443 Annotation: Subtype: Link Rect: 340, 159, 352, 169 ActionDest: 537 Annotation: Subtype: Link Rect: 353, 159, 365, 169 ActionDest: 537 Page: Sequence: 27 Annotations: Annotation: Subtype: Link Rect: 440, 352, 450, 364 ActionDest: 528 Page: Sequence: 28 Page: Sequence: 29 Annotations: Annotation: Subtype: Link Rect: 407, 335, 445, 346 Annotation: Subtype: Link Rect: 478, 310, 515, 321 Annotation: Subtype: Link Rect: 329, 297, 367, 308 Annotation: Subtype: Link Rect: 501, 284, 539, 295 Annotation: Subtype: Link Rect: 340, 259, 377, 270 Annotation: Subtype: Link Rect: 95, 234, 133, 244 Annotation: Subtype: Link Rect: 139, 234, 175, 244 Annotation: Subtype: Link Rect: 118, 209, 155, 219 Annotation: Subtype: Link Rect: 424, 169, 461, 180 Annotation: Subtype: Link Rect: 330, 144, 367, 155 Annotation: Subtype: Link Rect: 499, 106, 537, 117 Annotation: Subtype: Link Rect: 477, 80, 515, 91 Page: Sequence: 30 Annotations: Annotation: Subtype: Link Rect: 520, 756, 557, 767 Annotation: Subtype: Link Rect: 276, 718, 314, 729 Annotation: Subtype: Link Rect: 260, 679, 297, 690 Annotation: Subtype: Link Rect: 468, 628, 505, 639 Annotation: Subtype: Link Rect: 512, 628, 548, 639 Annotation: Subtype: Link Rect: 456, 603, 494, 614 Annotation: Subtype: Link Rect: 500, 603, 536, 614 Annotation: Subtype: Link Rect: 170, 578, 208, 588 Annotation: Subtype: Link Rect: 214, 578, 250, 588 Annotation: Subtype: Link Rect: 435, 565, 473, 576 Annotation: Subtype: Link Rect: 95, 540, 133, 550 Annotation: Subtype: Link Rect: 416, 526, 454, 537 Annotation: Subtype: Link Rect: 187, 501, 225, 512 Annotation: Subtype: Link Rect: 131, 476, 168, 486 Annotation: Subtype: Link Rect: 292, 450, 330, 461 Annotation: Subtype: Link Rect: 465, 437, 503, 448 Annotation: Subtype: Link Rect: 330, 411, 367, 422 Annotation: Subtype: Link Rect: 428, 386, 465, 397 Annotation: Subtype: Link Rect: 308, 360, 346, 371 Annotation: Subtype: Link Rect: 91, 336, 128, 346 Annotation: Subtype: Link Rect: 511, 296, 548, 307 Annotation: Subtype: Link Rect: 452, 220, 489, 231 Annotation: Subtype: Link Rect: 209, 194, 247, 205 Annotation: Subtype: Link Rect: 135, 170, 173, 180 Annotation: Subtype: Link Rect: 169, 131, 207, 141 Annotation: Subtype: Link Rect: 95, 80, 133, 90 Page: Sequence: 31 Annotations: Annotation: Subtype: Link Rect: 59, 706, 96, 716 Annotation: Subtype: Link Rect: 249, 679, 287, 690 Annotation: Subtype: Link Rect: 232, 654, 270, 665 Annotation: Subtype: Link Rect: 276, 654, 312, 665 Annotation: Subtype: Link Rect: 342, 628, 379, 639 Annotation: Subtype: Link Rect: 345, 577, 382, 588 Annotation: Subtype: Link Rect: 388, 577, 424, 588 Annotation: Subtype: Link Rect: 176, 514, 213, 524 Annotation: Subtype: Link Rect: 514, 488, 552, 499 Checksum: 4564197e Type: CRC32 Checksum: a07f721563e49508afce26521f6cebc0 Type: MD5 Checksum: b6afc2671df1daf7ccb31a9f5cd51fbe986c3baf Type: SHA-1 Checksum: 2aa7ce597de007f80a6ee8d8925651c43d87a40fc7d913743c7e76bdcb10364a Type: SHA-256