Ladislas Natanson and Alfred Landé versus Planck’s law, the Boltzmann-Planck-Natanson statistics and the Bose statistics

The article describes the context and content of the November 1925 correspondence – so far overlooked by historians of physics – between Władysław (Ladislas) Natanson and Alfred Landé on Planck’s law and Bose statistics, and the effects of this interaction. The article publishes for the first time the transcription of two original letters in German and their translations into English.

A Deformed Quon Algebra

The quon algebra is an approach to particle statistics in order to provide a theory in which the Pauli exclusion principle and Bose statistics are violated by a small amount. The quons are particles whose annihilation and creation operators obey the quon algebra which interpolates between fermions and bosons. In this paper we generalize these models by introducing a deformation of the quon algebra generated by a collection of operators ai,k, (i, k) ∈ ℕ* × [m], on an infinite dimensional vector space satisfying the deformed q-mutator relations {a_j}_{,l}a_{i,k}^\dagger = qa_{i,k}^\dagger{a_{j,l}} + {q^{{\beta _{k,l}}}}{\delta _{i,j}} We prove the realizability of our model by showing that, for suitable values of q, the vector space generated by the particle states obtained by applying combinations of ai,k’s and a_{i,k}^\dagger ‘s to a vacuum state |0〉 is a Hilbert space. The proof particularly needs the investigation of the new statistic cinv and representations of the colored permutation group.

The divergent histories of Bose-Einstein statistics and the forgotten achievements of Władysław Natanson (1864–1937)

This article investigates the forgotten achievements of Władysław Natanson (1864–1937) related to the creation of Bose-Einstein statistics. The introductory part of the article presents considerations regarding the methodology of history and the history of exact sciences, and then the divergent research perspectives that can be taken in the description of the history of Bose-Einstein statistics, as well as the author’s integrated approach to this issue, which eliminates the disadvantages of these divergent views. This integrated approach is then used to describe the achievements of Władysław Natanson related to the creation of Bose-Einstein statistics. These achievements are presented against the background and in the context of discussions which – relatively sporadically – took place among various groups of researchers: historians and philosophers of science, physicists, sociologists of scientific knowledge in the 20th and 21st centuries. These discussions have now been reordered here. They are followed by a presentation of the complete list of Natanson’s publications regarding the subject. Also shown is his strategy to quote reliably the bibliography with regard to the explanation of the distribution of blackbody radiation and related issues. Additionally, a list of scientists who knew Natanson’s publications has been supplemented in the article and the precursorship of Natanson’s achievements is explained. This is followed by a rebuttal of many erroneous or simplified statements about him and his achievements. The already well-known terminological conventions have been recalled: “Bose statistics” and “Bose-Einstein statistics”, as well as recently introduced: “Planck-Bose statistics” (1984), “Natanson’s statistics” (1997)”, “Natanson-Bose-Einstein statistics” (2005), “Planck-Natanson-Bose-Einstein statistics” (2011), and “Natanson statistics” (2013). New terminological conventions have been introduced: “Boltzmann-Planck-Natanson statistics” and “Boltzmann-Planck-Natanson-Bose-Einstein statistics”. A side effect of this research is a discovery that Robert K. Merton – the author of the label ‘Matthew effect’ – chose the name of the effect using erroneous premises and the effect should therefore be named after its actual discoverer. The article is accompanied by four appendixes: the first presents reflections on the methodology of historiography and historiography of exact sciences, the second – a commentary on the use of the terms: “Bose statistics”, “Bose-Einstein statistics”, “Einstein-Bose statistics” and “Planck-Bose statistics”, the third – a very important letter by Max Planck to Władysław Natanson (of 25 January 1913), and the fourth – the excerpts of two letters from Sommerfeld to Rubinowicz (of 1 October 1919 and 1 November 1919). Rozbieżne historie statystyki Bosego-Einsteina i zapomniane osiągnięcia Władysława Natansona (1864–1937) Abstrakt Artykuł bada zapomniane osiągnięcia Władysława Natansona (1864–1937) związane z powstaniem statystyki Bosego-Einsteina. W części wstępnej artykułuwskazano rozbieżne perspektywy badawcze, jakie przyjmowano w opisie historii statystyki Bosego-Einsteina, a także autorskie zintegrowane ujęcie tego zagadnienia, które eliminuje wady tych rozbieżnych perspektyw. Wspomniane zintegrowane ujęcie zastosowano następnie do opisania osiągnięć Władysława Natansona (1864–1937), związanych z powstaniem statystyki Bosego-Einsteina. Dokonania Natansona przedstawiono na tle i w kontekście dyskusji, jakie toczyły się (stosunkowo sporadycznie) wśród różnych grup badaczy: historyków i filozofów nauki, fizyków, socjologów wiedzy naukowej w XX i XXI w. Dyskusje uporządkowano oraz przedstawiono kompletną listę publikacji Natansona dotyczących omawianego zagadnienia. Wskazano także strategię rzetelnego cytowania przez Natansona bibliografii dotyczącej wyjaśnienia rozkładu promieniowania ciała doskonale czarnego i pokrewnych zagadnień; uzupełniono listę naukowców, którzy znali publikacje Natansona; skorygowano wiele błędnych lub uproszczonych stwierdzeń na temat Natansona i znaczenia jego publikacji, wyjaśniono kwestię prekursorstwa jego osiągnięć etc. Przypomniano już znane konwencje terminologiczne: „statystyka Bosego” i „statystyka Bosego-Einsteina”, jak również niedawno wprowadzone: „statystyka Plancka-Bosego” (1984), „statystyka Natansona” (1997, 2013), „statystyka Natansona-Bosego-Einsteina” (2005) oraz „statystyka Plancka-Natansona-Bosego-Einsteina” (2011). Wprowadzono nowe konwencje terminologiczne: „statystyka Boltzmanna-Plancka-Natansona” i „statystyka Boltzmanna-Plancka-Natansona-Bosego-Einsteina”. Skutkiem pobocznym tych badań jest odkrycie, iż socjolog Robert K. Merton – autor określenia „efekt św. Mateusza” – wybrał tę nazwę, posługując się błędnymi przesłankami i dlatego należy nazywać ten efekt nazwiskiem jego faktycznego odkrywcy. Do artykułu dołączone są cztery dodatki: pierwszy – przedstawia rozważania z zakresu metodologii historii i historii nauk ścisłych, drugi – komentarz dotyczący użycia terminów: „statystyka Bosego”, „statystyka Bosego-Einsteina”, „statytyska Einsteina-Bosego” oraz „statystyka Plancka-Bosego, trzeci – bardzo ważny list Maxa Plancka do Władysława Natansona z 25 stycznia 1913 r, a czwarty – fragmenty dwóch listów Sommerfelda do Rubinowicza z 1 października 1919 i 1 listopada 1919.

Двумерные триплетные магнитоэкситоны и магнетофермионный конденсат в GaAs/AlGaAs гетероструктурах

A fundamentally new collective state, namely, the magnetofermionic condensate, is discovered during photoexcitation of a sufficiently dense gas of long-lived triplet cyclotron magnetoexcitons in a twodimensional Hall insulator with a high electron mobility, a filling factor of ν = 2, and temperatures of T < 1 K. The condensed phase coherently interacts with an external electromagnetic field, exhibits superradiant properties in the recombination of correlated condensate electrons with heavy holes in the valence band, and spreads nondissipatively in the layer of a two-dimensional electron gas to macroscopical large distances, transferring an integer spin. The observed effects are explained in terms of a coherent condensate in a nonequilibrium system of two-dimensional fermions with a fully quantized energy spectrum, in which a degenerate ensemble of long-lived triplet magnetoexcitons obeying the Bose statistics is present.

Thermalization in Many-Particle Quantum Walks

Many-particle quantum walks of particles obeying Bose statistics, moving on graphs of various topologies are introduced. A single coin tossing commands the conditional shift operation over the whole graph. Vertex particle densities, mean values of phase space variables, second order spatial correlations and counting statistics are evaluated and simulated. The evidence of universal dynamics is presented.

RELATIONS BETWEEN INTERMEDIATE STATISTICS AND QUANTUM STATISTICS

We provide the relations among intermediate, Bose and Fermi statistics through a simplified quantum dot model. We show that the high-temperature (near-classical) behavior of the intermediate statistics is like the Bose statistics: We develop the virial expansion of the intermediate statistics, and find that the first n (maximum occupation number on a single state) expansion coefficients are the same as the corresponding Bose virial coefficients. We also show that under low-temperature (near-quantum) conditions, the n-intermediate statistics on a single state behaves more like the Fermi statistics on an n-degenerate state.

TWO-PHOTON DECAY OF Z′ AS A PROBE OF BOSE SYMMETRY VIOLATION AT THE CERN LHC

The question if the Bose statistics is broken at the TeV scale is discussed. The decay of a new heavy spin-1 gauge boson Z′ into two photons, Z′ → γγ, is forbidden by the Bose statistics among other general principles of quantum field theory (Landau–Yang theorem). We point out that the search for this decay can be effectively used to probe the Bose symmetry violation at the CERN LHC.