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A Complete Bibliography of Publications in the Journal of Mathematical Physics: 2015–2019

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A Complete Bibliography of Publications in the Journal of Mathematical Physics: 2015–2019 A Complete Bibliography of Publications in the Journal of Mathematical Physics: 2015{2019 Nelson H. F. Beebe University of Utah Department of Mathematics, 110 LCB 155 S 1400 E RM 233 Salt Lake City, UT 84112-0090 USA Tel: +1 801 581 5254 FAX: +1 801 581 4148 E-mail: [email protected], [email protected], [email protected] (Internet) WWW URL: http://www.math.utah.edu/~beebe/ 27 March 2021 Version 1.30 Title word cross-reference (0; ) [1593]. (1 + 1) [1439, 1347]. (1 n d) [1077]. (2 + 1) 1 ≤ 0 ≤(1) (1) [9, 63, 967, 1249]. (4 + 1) [1635]. (A1 + A1) [376]. (A2 + A1) [376]. (p; q) [1417]. 1 [1814, 461, 1916, 1940, 1173, 103, 2118, 1481, 1682, 1455, 2048, 221, 942, 1336, 252, 806, 763, 1976]. 1 + 1 [166]. 1=2 [1699]. 16 [1033]. 2 [29, 1113, 1652, 761, 508, 1188, 1537, 1682, 1770, 1909, 2095, 725, 1068, 576, 2112, 1800, 1647, 1972, 1650]. 2 + 1 [1543, 1712]. 2k + 1 [783]. 2N [1140]. 2 2 [466]. 3 [551, 1300, 993, 1916, 1103, 994, 1919, 227, 577, 836, 900, 1125, 2203,× 1908, 1188, 347, 2179, 995, 1203, 1687, 1005, 70, 377, 787, 2082, 1656, 1961, 1930, 786, 1627, 351, 758]. 3 + 1 [590]. 33 [836]. 4 [2160, 1097, 1304, 658, 661]. 5 [1136, 1356, 1519, 2215]. 6 [1483]. [N] [N] [1564, 1476]. N [884, 460, 341]. N−1 ⊗ [113]. 1 [2055, 2120]. 2 [2077, 2190, 2155, 1994]. 3 [1687]. n [2053]. q [1981]. A [1295]. A2 [27]. AdS5 [626]. α [751, 368]. α z [87]. B [501]. B( ) (j) − 1 [1251]. B(λ) [1251]. B = j2ZMd (C) [229]. B2 [946]. Bn;l= 4 [1600]. ⊗ ∗ k (1) U¯q(sl2) [1210]. β [248, 1313]. C [564, 158]. C [1516]. C2 [194, 152]. Cn 2 N−1 [808]. = 2 [1314]. 5 [1687]. CP [553]. CP [553]. D N W 1 2 [420, 438, 772, 2021, 1731, 1077, 291, 1383, 848]. D(2; 1; α) [647]. d = 3 [406]. x¨ + f(x)_x2 + g(x) = 0 [2247, 2246, 570, 13, 19]. δ [1362, 282, 1179, 512]. 3=2 D 4 [1423]. H_ [542]. E [1277]. e6;−14 [1723]. e6;−26 [850]. E8 ≤ 2 [1197, 1048, 1350]. ` (Z) [1963]. f [1749, 1736, 1737, 1847]. F (4) [1376]. G2 (1) [946]. G2 [28]. Γ [2189, 1410]. GL(2;Fq) [576]. gl(m n) [195]. gl(N) [1925]. 2 1 s ^j ^ ^ gl2 [1896]. H(3) [1883]. H S [1355]. H [1501]. C [1690]. P [1690]. T [1690]. I [1924]. K [2110, 1786,× 1850, 668, 1089, 654]. κ [897]. kx−2 + !2x2 2 2 p [1593]. l [933, 830]. L [1028, 1590, 307]. L (R) [1639]. L [1215, 498]. L1 4 n [1821]. Lp [2107]. Λ [1305]. λϕ [1445]. LR [1531]. m [840]. m(r)=1=(1 + r4) [1682]. H3 [997]. S [280]. S3 [997]. Z(d) [280]. Z=pZ [2218]. [2190]. N [rtimes] ( ; R)C [2106]. µ [67, 1497]. N [1075, 731, 890, 1313, O h sp 2N 2128, 265, 2076, 530, 895, 1050, 1531, 1018, 630, 118, 135, 1394, 1754]. n +1 [1077]. n + 2 [630]. N =(4; 4) [622]. N = 2 [978]. N =2l [102]. N 2 [1024]. N 3 [2239]. O(1) [211]. O(3) [752, 1126]. O(N)3 [2064]. osp(n 2)≥ [1725]. p ≤ j [431, 1794, 559, 149, 1191, 305, 2198, 2183, 714]. p(x) [1288]. PIV [1391]. Pn 4 [1710]. PV [1391]. PVI [1281]. PGL(2;Fq) [576]. Φ [1218, 1920, 155]. Φ2 [247]. π [442]. PZ2n [739]. Q [1157, 107, 1327, 1850, 1021, 768, 614, 1966, 294, 1901, 213]. Q(N) [1297]. q = 1 [294]. R [73, 309, 505, 462, 53, 332, 651, 671, 1696, 118, 935]. R(p; q) [1894]. R2 [512]. R3 [910, 1879, 1285, 1632, 1179]. R6 [1316]. RN 3 [742, 266, 148, 149, 1591]. R1 [1895]. r 1 [328]. rmsl2 [716]. S 2 ≥n [550, 563, 1756, 915, 1175]. S [1898]. S [108]. σ [461]. σk [1618]. sl(2) [811]. sl(2;R) [1092, 151]. SL(3; C) [1551]. sl(3;R) [708]. slN [2103]. so(3; 2) [912]. 1j2 so(3; R) [433]. so(3;R) [1092]. SO(N) [92]. Sp(1) [1208]. sp(4) [1355]. SPq [1011]. spl(2; 1) [1349]. SU(1; 1) [1605, 1770, 1849]. SU(2) [1232, 1688, 1605, 1674]. SU(3) [1291]. SU(N)P [500, 438, 531, 532]. SU(p; q) [1469]. su(r + 1) [1089]. SU2(C) [1769, 1764]. s ps + µ [382]. T [446]. τ j j 2 [2206, 1702, 1813]. [1900, 2146]. U(1) [391, 1266]. U(1) [593]. Uq(sl2) (1) × [1031]. Uq(G2 ) [2191]. Uq(osp(1 2n)) [1138]. (MjN) (MjN) (MjNj) c d Uq(sl )Uq(sl )Uq(sl ) [1722]. Uq(gl2) [716]. Uq( 2) [2052]. 4 sl Uqsl(2 1) [506]. Ur;s(osp(1 2n)) [505]. V [1695, 1700]. ' [49]. W j j d [2007, 647, 1297, 30, 502]. W1 [650]. WN [1418]. 2 [2081]. X [1540, 1068]. 2 sl Y (R)F [592]. Z [1068]. Z2 [511]. Z2 Z2 [1314]. × * [158]. *-derivations [158]. -adic [559]. -algebra [1754, 1297]. -algebras [158, 2189, 647, 30, 502]. -arm [1481]. -associated [2035]. -belts [2203]. -body [1519, 900, 995, 135, 1394, 1075, 731]. -brane [2198]. -Camassa [1497]. -categorical [29]. -categories [446]. -class [1501]. -coherent [811]. -completions [564]. -conformal [830, 102]. -corrections [368]. -coupled [840]. -d [1814, 761, 227, 1940, 1173, 103, 2095, 942, 1976, 351]. -deformed 3 [768, 1966, 1157, 1894]. -designs [1068]. -diagonal [1068]. -dimensional [993, 994, 1919, 1304, 2021, 63, 1731, 9, 967, 1077, 291, 576, 2082, 1383, 1930, 1635, 848, 1249, 661, 772]. -discretization [1277]. -divergences [1736, 1737, 1847]. -embedding [1516]. -ensembles [1313]. -entropies [1218]. -exact-solvability [2021, 108, 1383]. -expansion [563, 1175]. -fold [1033, 2128]. -forms [668, 1188]. -function [248, 2206]. -functions [1702, 1813, 438, 1410]. -Gaussians [107]. -imaginary [155]. -interaction [1362]. -interactions [512]. -invariant [593, 391, 2064]. -Kepler [1208, 211]. -Kirchhoff [1288, 1794]. -Laplacian [1798, 1417, 149, 1191, 305, 2183, 714]. -lattice [1688]. -level [1089, 118]. -local [508]. -matrices [1696, 118, 935, 671]. -matrix [73, 309, 505, 462, 332, 651, 915]. -models [461]. -modules [1725, 811]. -norm [1028]. -orthogonal [294]. -plane [1749]. -point [577, 1540]. -polynomials [1850]. -preserving [1924]. -pseudo-bosons [420]. -qubit [658]. -Racah [1901]. -R´enyi [87]. -shell [1179]. -Sobolev [1920]. -spaces [2107]. -spacetime [897]. -spectral [1327]. -spectrum [550, 1215, 1756]. -sphere [551]. -stability [307]. -state [836]. -statistical [213]. -statistics [1021]. -step [654]. -super [933]. -supercritical [1590]. -supermanifolds [739]. -symmetries [2007]. -symplectic [1050, 1531]. -theory [1786, 1850, 2110]. -tori [1097]. -twistor [1018]. -vertex [836]. -Virasoro [614]. -wave [431]. -Yamabe [1618]. 1/2 [2073]. 2018 [2238]. 3d [1811]. 48 [804, 428]. 49 [119,4,8]. 50 [1321]. 51 [63, 571]. 52 [427]. 53 [603]. 54 [1643, 426, 908, 2247, 879, 604, 2246, 1282, 570, 19]. 55 [145, 570, 301]. 56 [302, 1322, 805, 1093, 1870, 339]. 57 [878, 465, 980, 1162, 940, 641, 1966, 1412, 605]. 58 [1123, 1352, 1283, 2243, 1871]. 59 [1967, 1904, 1642, 1906, 1492, 1764, 1822, 1763, 2011]. 60 [2244, 1905, 2245]. = [170, 1789]. ABCD [435]. Abel [429]. abelian [1128, 1361, 1513, 382, 390, 2149, 1550, 1294, 525, 1266, 1570]. Ablowitz [2206, 52, 801, 1753, 1641]. Abraham [831, 595]. Absence [94, 2080, 512]. absolutely [94, 600, 980]. absorbing [2233]. absorption [387]. AC [1159]. 4 acceleration [174, 700, 447]. acceleration-dependent [700]. according [1546]. account [79]. Accumulation [987, 620]. Achieving [688]. acknowledgment [1872]. acoustic [1619]. across [990, 1889]. acting [1509]. action [1862, 268, 3, 562, 577, 1760, 1307, 2129, 1321, 1440, 4, 1076, 41, 1851]. action-angle [2129]. action-dependent [1440]. Actions [716, 1786, 1850, 413, 664, 666, 2074]. activation [2028]. adapted [490]. added [276, 1611]. Addendum [1322]. Addition [2019, 287]. additive [508, 1156, 1809, 408, 2197]. additivity [1760]. Adiabatic [722, 453, 2164, 1943]. adic [559]. Adjoint [678, 2123, 11, 1643, 870, 1841, 1260, 796, 2128]. adjointness [1038, 510, 380]. ADM [392]. admit [1306]. AdS [896, 965, 1687, 2155, 1994]. advantage [2061]. advection [303]. adversarial [2028]. affine [1327, 2055, 28, 655, 210, 1197, 527, 809, 1858, 1447, 2067, 808, 1048, 30, 502, 678]. affine-Virasoro [2055]. affinizations [1658]. AG [2077]. against [1672]. aggregate [1003]. AGT [1136, 951]. Aharonov [23, 1254]. AKNS [1710]. algebra [2101, 167, 933, 1866, 563, 1136, 2103, 1529, 949, 1836, 328, 329, 851, 2055, 577, 2049, 194, 1004, 1863, 2248, 1771, 152, 28, 1789, 702, 816, 1894, 1659, 236, 1133, 2158, 716, 1883, 2104, 614, 2106, 1962, 1297, 151, 32, 463, 887, 1689, 1754, 1030, 848, 1938, 674, 650, 2239, 564]. algebra-valued [463]. Algebraic [683, 2240, 2241, 1636, 335, 2172, 507, 1111, 1330, 1842, 1984, 857, 319, 2224, 619, 1601, 275, 115, 1851]. algebras [122, 1314, 1900, 1867, 1543, 73, 309, 677, 478, 394, 1559, 1366, 1582, 889, 1802, 1327, 852, 708, 1444, 646, 1583, 473, 1089, 462, 1696, 439, 762, 1542, 1541, 1882, 210, 26, 1736, 1737, 1847, 1251, 1504, 2120, 809, 112, 652, 158, 1803, 269, 895, 1110, 1741, 1470, 1299, 1662, 633, 2189, 1060, 849, 1887, 25, 649, 2067, 355, 647, 808, 1914, 1418, 30, 502, 137, 1135, 270, 1030, 421, 155, 446, 310, 153, 847, 2027]. algebro [178]. algebro-geometric [178]. Algebroid [1812]. algebroids [368, 1008]. algorithm [878, 799, 2203, 218, 1252, 1640, 1489, 554]. Algorithmic [1041, 1042]. Algorithms [438, 1922]. Alice [1690]. aligned [676, 1301]. All-order [925, 591]. Almost [1220, 1510, 1354, 827, 1528, 2241, 1221, 2114, 2200, 1501, 1634]. almost-commutative [2241, 1221]. almost-symmetries [2114]. alone [396]. along [448]. alternating [2052]. ambient [1620]. ambiguity [34]. Amp`ere [1119]. amplifier [2194, 682]. amplitude [1594, 966]. Analog [436, 1080]. analogs [2103]. analogue [357, 1226]. Analysis [1389, 724, 1765, 743, 182, 1172, 1452, 2040, 1626, 535, 759, 740, 1310, 2031, 258, 838, 700, 2130, 604, 1044, 1282, 874, 1495, 12, 1283, 1685, 163, 1527, 977, 1174, 1236, 872, 843, 1053, 1176, 2170, 15, 605, 1249].
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  • What Is Noncommutative Geometry ? How a Geometry Can Be Commutative and Why Mine Is Not
    What is Noncommutative Geometry ? How a geometry can be commutative and why mine is not Alessandro Rubin Junior Math Days 2019/20 SISSA - Scuola Internazionale Superiore di Studi Avanzati This means that the algebra C∞(M) contains enough information to codify the whole geometry of the manifold: 1. Vector fields: linear derivations of C∞(M) 2. Differential 1-forms: C∞(M)-linear forms on vector fields 3. ... Question Do we really need a manifold’s points to study it ? Do we really use the commutativity of the algebra C∞(M) to define the aforementioned objects ? Doing Geometry Without a Geometric Space Theorem Two smooth manifolds M, N are diffeomorphic if and only if their algebras of smooth functions C∞(M) and C∞(N) are isomorphic. 1/41 Question Do we really need a manifold’s points to study it ? Do we really use the commutativity of the algebra C∞(M) to define the aforementioned objects ? Doing Geometry Without a Geometric Space Theorem Two smooth manifolds M, N are diffeomorphic if and only if their algebras of smooth functions C∞(M) and C∞(N) are isomorphic. This means that the algebra C∞(M) contains enough information to codify the whole geometry of the manifold: 1. Vector fields: linear derivations of C∞(M) 2. Differential 1-forms: C∞(M)-linear forms on vector fields 3. ... 1/41 Do we really use the commutativity of the algebra C∞(M) to define the aforementioned objects ? Doing Geometry Without a Geometric Space Theorem Two smooth manifolds M, N are diffeomorphic if and only if their algebras of smooth functions C∞(M) and C∞(N) are isomorphic.
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  • Equilibrium Measures and Capacities in Spectral Theory
    EQUILIBRIUM MEASURES AND CAPACITIES IN SPECTRAL THEORY BARRY SIMON∗ Abstract. This is a comprehensive review of the uses of potential theory in studying the spectral theory of orthogonal polynomials. Much of the article focuses on the Stahl–Totik theory of regular measures, especially the case of OPRL and OPUC. Links are made to the study of ergodic Schr¨odinger operators where one of our new results implies that, in complete generality, the spectral measure is supported on a set of zero Hausdorff dimension (indeed, of capacity zero) in the region of strictly positive Lyapunov exponent. There are many examples and some new conjectures and indications of new research directions. Included are appendices on potential the- ory and on Fekete–Szeg˝otheory. 1. Introduction This paper deals with applications of potential theory to spectral and inverse spectral theory, mainly to orthogonal polynomials especially on the real line (OPRL) and unit circle (OPUC). This is an area that has traditionally impacted both the orthogonal polynomial community and the spectral theory community with insufficient interrelation. The OP approach emphasizes the procedure of going from measure to recursion parameters, that is, the inverse spectral problem, while spectral theo- rists tend to start with recursion parameters and so work with direct spectral theory. Potential theory ideas in the orthogonal polynomial community go back at least to a deep 1919 paper of Faber [35] and a seminal 1924 paper of Szeg˝o[107] with critical later developments of Kalm´ar [63] and Date: August 23, 2007. 2000 Mathematics Subject Classification. Primary: 31A15, 05E35, 34L05. Sec- ondary: 31A35, 33D45, 34P05.
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  • Spectral Decimation of a Self-Similar Version of Almost Mathieu-Type Operators
    SPECTRAL DECIMATION OF A SELF-SIMILAR VERSION OF ALMOST MATHIEU-TYPE OPERATORS RADHAKRISHNAN BALU, GAMAL MOGRABY, KASSO A. OKOUDJOU, AND ALEXANDER TEPLYAEV Abstract. We introduce self-similar versions of the one-dimensional almost Mathieu operators. Our defi- nition is based on a class of self-similar Laplacians instead of the standard discrete Laplacian, and includes the classical almost Mathieu operators as a particular case. Our main result establishes that the spectra of these self-similar almost Mathieu operators can be completely described by the spectra of the corresponding self-similar Laplacians through the spectral decimation framework used in the context of spectral analysis on fractals. In addition, the self-similar structure of our model provides a natural finite graph approximation model. This approximation is not only helpful in executing the numerical simulation, but is also useful in finding the spectral decimation function via Schur complement computations of given finite-dimensional matrices. The self-similar Laplacians used in our model were considered recently by Chen and Teplyaev [23] who proved the emergence of singularly continuous spectra for specific parameters. We use this result to arrive at similar conclusions in the context of the self-similar almost Mathieu operators. Finally, we derive an explicit formula of the integrated density of states of the self-similar almost Mathieu operators as the weighted pre-images of the balanced invariant measure on a specific Julia set. Contents 1. Introduction 1 2. Self-similar Laplacians and almost Mathieu operators4 2.1. Self-similar p Laplacians on the half-integer lattice4 2.2. The self-similar almost Mathieu operators7 3.
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