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1.
Abstruct Quasi-set theory provides a mathematical background for dealing with coll ections of indistinguishable elementary particles.
In this paper, we show how to obtain the quantum statistics into the scope of quasi-set theory and we also discuss the Helium
atom, which represents the simplest example where indistinguishability plays an important role. One of the advantages of our
approach is that one of the most basic principles of quantum theory, namely, the Indistinguishability Postulate, does not
need to be assumed even implicitely in the axiomatic basis of quantum mechanics. 相似文献
2.
No Heading Quasi-set theory is a first-order theory without identity, which allows us to cope with non-individuals in a sense. A weaker
equivalence relation called “indistinguishability” is an extension of identity in the sense that if x is identical to y then x and y are indistinguishable, although the reciprocal is not always valid. The interesting point is that quasi-set theory provides
us with a useful mathematical background for dealing with collections of indistinguishable elementary quantum particles. In
the present paper, however, we show that even in quasi-set theory it is possible to label objects that are considered as non-individuals.
This is the first paper of a series that will be dedicated to the philosophical and physical implications of our main mathematical
result presented here.
* Permanent address: Departamento de Matemática, Universidade Federal do
Paraná, C. P. 019081, Curitiba, PR, 81531-990, Brazil. 相似文献
3.
G. Lanyi 《Foundations of Physics》2003,33(3):511-528
In 1916, Einstein rederived the blackbody radiation law of Planck that originated the idea of quantized energy one hundred years ago. For this purpose, Einstein introduced the concept of transition probability, which had a profound influence on the development of quantum theory. In this article, we adopt Einstein's assumptions with two exceptions and seek the statistical condition for the thermal equilibrium of matter without referring to the inner details of either statistical thermodynamics or quantum theory. It is shown that the conditions of thermodynamic equilibrium of electromagnetic radiation and the energy balance of thermal radiation by the matter, between any of its two energy-states, not only result in Planck's radiation law and the Bohr frequency condition, but they remarkably yield the law of the statistical thermal equilibrium of matter: the Maxwell–Boltzmann distribution. Since the transition probabilities of the modern quantum theory of radiation coincide with their definition in Einstein's theory of blackbody radiation, the presented deduction of the Maxwell–Boltzmann distribution is equally valid within the bounds of modern quantum theory. Consequently, within the framework of the fundamental assumptions, the Maxwell–Boltzmann distribution of energy-states is not only a sufficient, but a necessary condition for thermal equilibrium between the matter and radiation. 相似文献
4.
In physics, communication theory, engineering, statistics, and other areas, one of the methods of deriving distributions is the optimization of an appropriate measure of entropy under relevant constraints. In this paper, it is shown that by optimizing a measure of entropy introduced by the second author, one can derive densities of univariate, multivariate, and matrix-variate distributions in the real, as well as complex, domain. Several such scalar, multivariate, and matrix-variate distributions are derived. These include multivariate and matrix-variate Maxwell–Boltzmann and Rayleigh densities in the real and complex domains, multivariate Student-t, Cauchy, matrix-variate type-1 beta, type-2 beta, and gamma densities and their generalizations. 相似文献
5.
In this paper, a lattice Boltzmann (LB) scheme for convection diffusion on irregular lattices is presented, which is free of any interpolation or coarse graining step. The scheme is derived using the axioma that the velocity moments of the equilibrium distribution equal those of the Maxwell–Boltzmann distribution. The axioma holds for both Bravais and irregular lattices, implying a single framework for LB schemes for all lattice types. By solving benchmark problems we have shown that the scheme is indeed consistent with convection diffusion. Furthermore, we have compared the performance of the LB schemes with that of finite difference and finite element schemes. The comparison shows that the LB scheme has a similar performance as the one-step second-order Lax–Wendroff scheme: it has little numerical diffusion, but has a slight dispersion error. By changing the relaxation parameter ω the dispersion error can be balanced by a small increase of the numerical diffusion. 相似文献
6.
The usual action integral of classical electrodynamics is derived starting from Lanczos’s electrodynamics – a pure field theory in which charged particles are identified with singularities of the homogeneous Maxwell’s equations interpreted as a generalization of the Cauchy–Riemann regularity conditions from complex to biquaternion functions of four complex variables. It is shown that contrary to the usual theory based on the inhomogeneous Maxwell’s equations, in which charged particles are identified with the sources, there is no divergence in the self-interaction so that the mass is finite, and that the only approximations made in the derivation are the usual conditions required for the internal consistency of classical electrodynamics. Moreover, it is found that the radius of the boundary surface enclosing a singularity interpreted as an electron is on the same order as that of the hypothetical “bag” confining the quarks in a hadron, so that Lanczos’s electrodynamics is engaging the reconsideration of many fundamental concepts related to the nature of elementary particles. 相似文献
7.
G. Domenech F. Holik L. Kniznik D. Krause 《International Journal of Theoretical Physics》2010,49(12):3085-3091
Our aim in this paper is to show an example of the formalism we have developed to avoid the label-tensor-product-vector-space-formalism
of quantum mechanics when dealing with indistinguishable quanta. States in this new vector space, that we call the Q-space,
refer only to occupation numbers and permutation operators act as the identity operator on them, reflecting in the formalism
the unobservability of permutations, a goal of quasi-set theory. 相似文献
8.
In previous research, we showed that ‘texts that tell a story’ exhibit a statistical structure that is not Maxwell–Boltzmann but Bose–Einstein. Our explanation is that this is due to the presence of ‘indistinguishability’ in human language as a result of the same words in different parts of the story being indistinguishable from one another, in much the same way that ’indistinguishability’ occurs in quantum mechanics, also there leading to the presence of Bose–Einstein rather than Maxwell–Boltzmann as a statistical structure. In the current article, we set out to provide an explanation for this Bose–Einstein statistics in human language. We show that it is the presence of ‘meaning’ in ‘texts that tell a story’ that gives rise to the lack of independence characteristic of Bose–Einstein, and provides conclusive evidence that ‘words can be considered the quanta of human language’, structurally similar to how ‘photons are the quanta of electromagnetic radiation’. Using several studies on entanglement from our Brussels research group, we also show, by introducing the von Neumann entropy for human language, that it is also the presence of ‘meaning’ in texts that makes the entropy of a total text smaller relative to the entropy of the words composing it. We explain how the new insights in this article fit in with the research domain called ‘quantum cognition’, where quantum probability models and quantum vector spaces are used in human cognition, and are also relevant to the use of quantum structures in information retrieval and natural language processing, and how they introduce ‘quantization’ and ‘Bose–Einstein statistics’ as relevant quantum effects there. Inspired by the conceptuality interpretation of quantum mechanics, and relying on the new insights, we put forward hypotheses about the nature of physical reality. In doing so, we note how this new type of decrease in entropy, and its explanation, may be important for the development of quantum thermodynamics. We likewise note how it can also give rise to an original explanatory picture of the nature of physical reality on the surface of planet Earth, in which human culture emerges as a reinforcing continuation of life. 相似文献
9.
A. López-Ortega 《General Relativity and Gravitation》2005,37(1):167-190
Some properties of the Hawking radiation emitted by the family of black holes of the Einstein–Maxwell–Dilaton with cosmologicalconstant theory in three dimensions found by Chan and Mann are studiedusing the complex paths method and the Damour–Ruffini method. Theexact values of the quasinormal frequencies of the massless Diracfield propagating on a particular black hole of this family arecalculated. Taking as a basis the results obtained for the values ofthe quasinormal frequencies the instability of some modes isdiscussed. The extension of these results to the black holes of theEinstein–Maxwell–Dilaton theory in four dimensions is studied in theappendix. 相似文献
10.
D. Ioffe 《Journal of statistical physics》2002,106(1-2):375-384
Using the renormalization methods we show that the symmetry breaking in the quantum Widom–Rowlison model of particles obeying Boltzmann statistics occurs at any value of the inverse temperature >0 once the activity of the particles is sufficiently large. 相似文献
11.
Our aim in this paper is to take quite seriously Heinz Post’s claim that the non-individuality and the indiscernibility of
quantum objects should be introduced right at the start, and not made a posteriori by introducing symmetry conditions. Using a different mathematical framework, namely, quasi-set
theory, we avoid working within a label-tensor-product-vector-space-formalism, to use Redhead and Teller’s words, and get
a more intuitive way of dealing with the formalism of quantum mechanics, although the underlying logic should be modified.
We build a vector space with inner product, the Q-space, using the non-classical part of quasi-set theory, to deal with indistinguishable
elements. Vectors in Q-space refer only to occupation numbers and permutation operators act as the identity operator on them,
reflecting in the formalism the fact of unobservability of permutations. Thus, this paper can be regarded as a tentative to
follow and enlarge Heinsenberg’s suggestion that new phenomena require the formation of a new “closed” (that is, axiomatic)
theory, coping also with the physical theory’s underlying logic and mathematics.
G. Domenech is a fellow of the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina.
D. Krause is a fellow of the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brazil. 相似文献
12.
13.
The restricted primitive model is an electrically neutral, classical model consisting of hard spheres charged either +q or –q. We show that, by appropriately selecting the diameter of the hard spheres, the pressure when q=0 can be made equal to that for a fluid of Maxwell–Boltzmann point ions and an ideal Fermi gas of electrons. We compare the series expansion of these classical and quantum systems and find that, except for intermediate de Broglie density and moderate to strong electrical interaction strength, the restricted primitive model gives a reasonable representation of the pressure of the corresponding quantum system. Much of the current interest, however, has been focused on the above, excepted region. 相似文献
14.
The general relativistic kinetic theory is applied to calculate corrections to the distribution arising from Coulomb collisions of particles in the field of a planar gravitational wave. These corrections are used in corrections to the energy-momentum tensor and in deriving the collisional-damping decrements for gravitational waves for a Boltzmann plasma and for a plasma with degenerate electrons. The largest contribution to the damping decrement in a Boltzmann plasma comes from the ions colliding with the electrons; the decrement increases as T–1/2. In a plasma with degenerate electrons, the decrement decreases linearly as the temperature falls and tends to zero at zero temperature.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 85–89, October, 1982.We wish to thank G. G. Ivanov for participation in discussion of the paper. 相似文献
15.
L.D. Pietanza G. Colonna S. Longo M. Capitelli 《Applied Physics A: Materials Science & Processing》2004,79(4-6):1047-1050
A theoretical investigation of the electron and phonon time-dependent distributions in an Ag film subjected to a femtosecond laser pulse has been carried out. A system of two coupled time-dependent Boltzmann equations, describing electron and phonon dynamics, has been numerically solved. In the electron Boltzmann equation, electron–electron and electron–phonon collision integrals are considered together with a source term for laser perturbation. In the phonon Boltzmann equation, only electron–phonon collisions are considered, neglecting laser perturbation and phonon–phonon collisions. Screening of the interactions has been accounted for in both the electron–electron and the electron–phonon collisions. The results show the simultaneous electron and phonon time-dependent distributions from the initial non-equilibrium behaviour up to the establishment of a new final equilibrium condition. PACS 72.10.-d; 71.10.Ca; 63.20.Kr 相似文献
16.
L.M. Varela J. Carrete R. Muoz-Sol J.R. Rodríguez J. Gallego 《Physics letters. A》2007,370(5-6):405-412
Classical mean-field Poisson–Boltzmann theory of ionic solutions is revisited in the theoretical framework of nonextensive Tsallis statistics. The nonextensive equivalent of Poisson–Boltzmann equation is formulated revisiting the statistical mechanics of liquids and the Debye–Hückel framework is shown to be valid for highly diluted solutions even under circumstances where nonextensive thermostatistics must be applied. The lowest order corrections associated to nonadditive effects are identified for both symmetric and asymmetric electrolytes and the behavior of the average electrostatic potential in a homogeneous system is analytically and numerically analyzed for various values of the complexity measurement nonextensive parameter q. 相似文献
17.
We examine the problem of the trend to equilibrium for a relativistic gas which may follow Fermi–Dirac, Bose–Einsten, classical Boltzmann statistics. We use the relativistic version of the quasiclassical Boltzmann equation for fermions and bosons, the Uehling–Uhlenbeck equation. 相似文献
18.
J.N. Fuchs M. Holzmann F. Laloë 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,25(4):463-478
The purpose of this article is to discuss cluster expansions in dense quantum systems, as well as their interconnection with
exchange cycles. We show in general how the Ursell operators of order l≥ 3 contribute to an exponential which corresponds to a mean-field energy involving the second operator U2, instead of the potential itself as usual - in other words, the mean-field correction is expressed in terms of a modification
of a local Boltzmann equilibrium. In a first part, we consider classical statistical mechanics and recall the relation between
the reducible part of the classical cluster integrals and the mean-field; we introduce an alternative method to obtain the
linear density contribution to the mean-field, which is based on the notion of tree-diagrams and provides a preview of the
subsequent quantum calculations. We then proceed to study quantum particles with Boltzmann statistics (distinguishable particles)
and show that each Ursell operator Un with n≥ 3 contains a “tree-reducible part”, which groups naturally with U2 through a linear chain of binary interactions; this part contributes to the associated mean-field experienced by particles
in the fluid. The irreducible part, on the other hand, corresponds to the effects associated with three (or more) particles
interacting all together at the same time. We then show that the same algebra holds in the case of Fermi or Bose particles,
and discuss physically the role of the exchange cycles, combined with interactions. Bose condensed systems are not considered
at this stage. The similarities and differences between Boltzmann and quantum statistics are illustrated by this approach,
in contrast with field theoretical or Green's functions methods, which do not allow a separate study of the role of quantum
statistics and dynamics.
Received 18 October 2001 相似文献
19.
Robert M. Strain 《Communications in Mathematical Physics》2006,268(2):543-567
The Vlasov–Maxwell–Boltzmann system is one of the most fundamental models to describe the dynamics of dilute charged particles,
where particles interact via collisions and through their self-consistent electromagnetic field. We prove existence of global
in time classical solutions to the Cauchy problem near Maxwellians. 相似文献
20.
One of the fundamental open questions in plasma physics is the role of non-thermal particles distributions in poorly collisional plasma environments, a system that is commonly found throughout the Universe, e.g., the solar wind and the Earth’s magnetosphere correspond to natural plasma physics laboratories in which turbulent phenomena can be studied. Our study perspective is born from the method of Horizontal Visibility Graph (HVG) that has been developed in the last years to analyze time series avoiding the tedium and the high computational cost that other methods offer. Here, we build a complex network based on directed HVG technique applied to magnetic field fluctuations time series obtained from Particle In Cell (PIC) simulations of a magnetized collisionless plasma to distinguish the degree distributions and calculate the Kullback–Leibler Divergence (KLD) as a measure of relative entropy of data sets produced by processes that are not in equilibrium. First, we analyze the connectivity probability distribution for the undirected version of HVG finding how the Kappa distribution for low values of tends to be an uncorrelated time series, while the Maxwell–Boltzmann distribution shows a correlated stochastic processes behavior. Subsequently, we investigate the degree of temporary irreversibility of magnetic fluctuations that are self-generated by the plasma, comparing the case of a thermal plasma (described by a Maxwell–Botzmann velocity distribution function) with non-thermal Kappa distributions. We have shown that the KLD associated to the HVG is able to distinguish the level of reversibility that is associated to the thermal equilibrium in the plasma, because the dissipative degree of the system increases as the value of parameter decreases and the distribution function departs from the Maxwell–Boltzmann equilibrium. 相似文献