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Modern technology has brought novel types of wealth. In contrast to hard cash, digital currency does not have a physical form. It exists in electronic forms only. To date, it has not been clear what impacts its ongoing growth will have, if any, on wealth distribution. Here, we propose to identify all forms of contemporary wealth into two classes: ‘distinguishable’ or ‘identical’. Traditional tangible moneys are all distinguishable. Financial assets and cryptocurrencies, such as bank deposits and Bitcoin, are boson-like, while non-fungible tokens are fermion-like. We derived their ownership-based distributions in a unified manner. Each class follows essentially the Poisson or the geometric distribution. We contrast their distinct features such as Gini coefficients. Furthermore, aggregating different kinds of wealth corresponds to a weighted convolution where the number of banks matters and Bitcoin follows Bose–Einstein distribution. Our proposal opens a new avenue to understand the deepened inequality in modern economy, which is based on the statistical physics property of wealth rather than the individual ability of owners. We call for verifications with real data.

Two new flavor quantum numbers D and U for down and up quarks, respectively, are introduced, and then quark quantum number H is proposed as the sum of the flavor quantum numbers of quarks. Moreover, lepton quark-like quantum number HL and finally fermion quantum number F are brought forward. Old and new additive quantum numbers are conserved at three different levels in weak interaction, and F builds up a clear relationship to the electric charge of fermions.

A quantum game is described making use of coins embodied as entangled Fermions in a potential energy well. It is shown that the odds are affected by the Pauli Exclusion Principle. They depend on the elevation in the energy well where the coins are selected, ranging from being a certainty of winning at the bottom of the well to being near classical at the top. These odds differ markedly from those in a classical game in which they are independent of elevation. The thermodynamics counterpart of the quantum game is discussed. It is shown that the temperature of a Maxwellian gas column in a potential energy gradient is independent of elevation. However, the temperature of a Fermion gas is shown to drop with elevation. The game and the gas column utilize the same components. When Fermions are used, a shifting of odds is produced in the game and a shifting of kinetic energy is produced in the thermodynamic experiment, leading to a spontaneous temperature gradient.

ABSTRACT:The level structure of 125Te by considering 124Te as a core for positive parity low-lying states has been investigated. Spectroscopic factor for both pick-up and stripping reactions were deduced according to the Interacting Boson-Fermion Model(IBFM) and compared with experimental results. Considering 126Te as a core gives best description to the 125Te nucleus.

In recent work, the authors used canonical lowering and raising operators to define Appell systems on Clifford algebras of arbitrary signature. Appell systems can be interpreted as polynomial solutions of generalized heat equations, and in probability theory they have been used to obtain non-central limit theorems. The natural grade-decomposition of a Clifford algebra of arbitrary signature lends it a natural Appell system decomposition. In the current work, canonical raising and lowering operators defined on a Clifford algebra of arbitrary signature are used to define chains and cochains of vector spaces underlying the Clifford algebra, to compute the associated homology and cohomology groups, and to derive long exact sequences of underlying vector spaces. The vector spaces appearing in the chains and cochains correspond to the Appell system decomposition of the Clifford algebra. Using Mathematica, kernels of lowering operators ∇ and raising operators R are explicitly computed, giving solutions to equations ∇x = 0 and Rx = 0. Connections with quantum probability and graphical interpretations of the lowering and raising operators are discussed.En recientes trabajos, los autores usaron operadores canónicos de bajada y de elevación para definir sistemas de Appell sobre algebras de Clifford de signo arbitrario. Los sistemas de Appell pueden ser interpretados como soluciones polinomiales de ecuaciones del calor generalizadas, y en teoría de probabilidades estos han sido usados para obtener teoremas de límite no central. La natural malla-descomposición para una algebra de Clifford de signo arbitrario presta una descomposición natural del sistema de Appel. En este trabajo, operadores canónicos de elevación y de bajada definidos sobre una algebra de Clifford de signo arbitrario son usados para definir cadenas y cocadenas de espacios vectoriales de llegada de algebras de Clifford; para calcular los grupos de homología y cohomología asociados; y para obtener el tamaño de las sucesiones exactas de los espacios vectoriales de llegada. Los espacios vectoriales que aparecen en las cadenas y cocadenas corresponden a la descomposición de sistemas de Appell de la algebra de Clifford. Usando MATHEMATICA, son calculados expíıcitamente los núcleos de operadores de bajada ∇ y de operadores de elevación R dando soluciones para las ecuaciones ∇x = 0 y Rx = 0. Son discutidas conecciones con probabilidad cuantica y interpretaciones graficas para los operadores de bajada y de elevación.

We give an exposition of iterant algebra, a generalization of matrix algebra that is motivated by the structure of measurement for discrete processes. We show how Clifford algebras and matrix algebras arise naturally from iterants, and we then use this point of view to discuss the Schrödinger and Dirac equations, Majorana Fermions, representations of the braid group and the framed braids in relation to the structure of the Standard Model for physics.

We show that both fermionic and bosonic uniform d -dimensional lattices can be reduced to a set of independent one-dimensional chains. This reduction leads to the expression for ballistic energy fluxes in uniform fermionic and bosonic lattices. By the use of the Jordan–Wigner transformation we can extend our analysis to spin lattices, proving the coexistence of both ballistic and non-ballistic subspaces in any dimension and for any system size. We then relate the nature of transport to the number of excitations in the homogeneous spin lattice, indicating that a single excitation always propagates ballistically and that the non-ballistic behaviour of uniform spin lattices is a consequence of the interaction between different excitations.

On the basis of a microscopic model of self-consistent field, the thermodynamics of the many-particle Fermi system at finite temperatures with account of three-body interactions is built and the quasiparticle equations of motion are obtained. It is shown that the delta-like three-body interaction gives no contribution into the self-consistent field, and the description of three-body forces requires their nonlocality to be taken into account. The spatially uniform system is considered in detail, and on the basis of the developed microscopic approach general formulas are derived for the fermion's effective mass and the system's equation of state with account of contribution from three-body forces. The effective mass and pressure are numerically calculated for the potential of "semi-transparent sphere" type at zero temperature. Expansions of the effective mass and pressure in powers of density are obtained. It is shown that, with account of only pair forces, the interaction of repulsive character reduces the quasiparticle effective mass relative to the mass of a free particle, and the attractive interaction raises the effective mass. The question of thermodynamic stability of the Fermi system is considered and the three-body repulsive interaction is shown to extend the region of stability of the system with the interparticle pair attraction. The quasiparticle energy spectrum is calculated with account of three-body forces.

We obtain a positive probability distribution or Q -function for an arbitrary fermionic many-body system. This is different to previous Q -function proposals, which were either restricted to a subspace of the overall Hilbert space, or used Grassmann methods that do not give probabilities. The fermionic Q -function obtained here is constructed using normally ordered Gaussian operators, which include both non-interacting thermal density matrices and BCS states. We prove that the Q -function exists for any density matrix, is real and positive, and has moments that correspond to Fermi operator moments. It is defined on a finite symmetric phase-space equivalent to the space of real, antisymmetric matrices. This has the natural SO (2 M ) symmetry expected for Majorana fermion operators. We show that there is a physical interpretation of the Q -function: it is the relative probability for observing a given Gaussian density matrix. The distribution has a uniform probability across the space at infinite temperature, while for pure states it has a maximum value on the phase-space boundary. The advantage of probabilistic representations is that they can be used for computational sampling without a sign problem.