Intermediate-statistics quantum bracket, coherent state, oscillator, and representation of angular momentum [su(2)] algebra

Shen, Yao; Dai, Wu-Sheng; Xie, Mi

doi:10.1103/physreva.75.042111

Cited by 34 publications

(28 citation statements)

References 32 publications

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“…On the one hand, the realization of angular momentum algebra has been of interest for a long time. Besides the well-known Schwinger representation [11] and the Holstein-Primakoff representation [2], there are many other schemes, including the realization of su (2) algebra [3,4,12,13,14], and the realization of su q (2) and su q (n) algebra [15,16]. On the other hand, the spin wave plays an important role in magnetic problems [17,18].…”

Section: Introductionmentioning

confidence: 99%

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Intermediate-statistics spin waves

Dai

Xie²

2009

J. Stat. Mech.

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In this paper, we show that spin waves, the elementary excitation of the Heisenberg magnetic system, obey a kind of intermediate statistics with a finite maximum occupation number n. We construct an operator realization for the intermediate statistics obeyed by magnons, the quantized spin waves, and then construct a corresponding intermediate-statistics realization for the angular momentum algebra in terms of the creation and annihilation operators of the magnons. In other words, instead of the Holstein–Primakoff representation, a bosonic representation subject to a constraint on the occupation number, we present an intermediate-statistics representation with no constraints. In this realization, the maximum occupation number is naturally embodied in the commutation relation of creation and annihilation operators, while the Holstein–Primakoff representation is a bosonic operator relation with an additional putting-in-by-hand restriction on the occupation number. We deduce the intermediate-statistics distribution function for magnons from the intermediate-statistics commutation relation of the creation and annihilation operators directly, which is a modified Bose–Einstein distribution. On the basis of these results, we calculate the dispersion relations for ferromagnetic and antiferromagnetic spin waves. The relations between the intermediate statistics that magnons obey and the other two important kinds of intermediate statistics, Haldane–Wu statistics and the fractional statistics of anyons, are discussed. We also compare the spectrum of the intermediate-statistics spin wave with the exact solution of the one-dimensional s = 1/2 Heisenberg model, which is obtained by the Bethe ansatz method. For ferromagnets, we take the contributions from the interaction between magnons (the quartic contribution), the next-to-nearest-neighbor interaction, and the dipolar interaction into account for comparison with the experiment.

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Section: Introductionmentioning

confidence: 99%

“…As shown in [3] and [4], the number operator of intermediate statistics in general cannot take the form of N ℓ = a † ℓ a ℓ . The realization of the number operator (11) shows that the spin deviation corresponds to a kind of intermediate statistics.…”

Section: Introductionmentioning

confidence: 99%

Intermediate-statistics spin waves

Dai

Xie²

2009

J. Stat. Mech.

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“…Let a †i k with superscript ranging from 1 to ν and subscript ranging from 1 to m represent creating the ith particle of state k (or creating a particle of energy k at position i). The relation of creation and annihilation operators follows the n-bracket [12,13]…”

Section: The Relation Between Permutation Group and Unitary Group In ...mentioning

confidence: 99%

“…Gentile statistics is a kind of intermediate statistics which is named after Gentile [11]. The maximum occupation number of Gentile statistics is a finite number n [11][12][13]. In Gentile statistics, the states are labelled by the practical occupation number, which makes it easy to research.…”

Section: Introductionmentioning

confidence: 99%

A group method solving many-body systems in intermediate statistical representation

Shen,

Zhou,

Dai

et al. 2021

Preprint

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The exact solution of the interacting many-body system is important and is difficult to solve. In this paper, we introduce a group method to solve the interacting many-body problem using the relation between the permutation group and the unitary group. We prove a group theorem first, then using the theorem, we represent the Hamiltonian of the interacting many-body system by the Casimir operators of unitary group. The eigenvalues of Casimir operators could give the exact values of energy and thus solve those problems exactly. This method maps the interacting many-body system onto an intermediate statistical representation. We give the relation between the conjugacy-class operator of permutation group and the Casimir operator of unitary group in the intermediate statistical representation, called the Gentile representation. Bose and Fermi cases are two limitations of the Gentile representation. We also discuss the representation space of symmetric and unitary group in the Gentile representation and give an example of the Heisenberg model to demonstrate this method. It is shown that this method is effective to solve interacting many-body problems.

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“…Metamaterial, made up of SRRs or molecules which consist of SRRs, e.g. extended metal atom chains, becomes a new branch of study 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 . Many new directions are developed, such as electromagnetic cloaking 38 39 40 41 42 43 , toroidal moment 44 , liquid crystal magnetic control 45 , etc.…”

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confidence: 99%

Optical properties of drug metabolites in latent fingermarks

Shen

2016

Sci Rep

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Drug metabolites usually have structures of split-ring resonators (SRRs), which might lead to negative permittivity and permeability in electromagnetic field. As a result, in the UV-vis region, the latent fingermarks images of drug addicts and non drug users are inverse. The optical properties of latent fingermarks are quite different between drug addicts and non-drug users. This is a technic superiority for crime scene investigation to distinguish them. In this paper, we calculate the permittivity and permeability of drug metabolites using tight-binding model. The latent fingermarks of smokers and non-smokers are given as an example.

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Intermediate-statistics quantum bracket, coherent state, oscillator, and representation of angular momentum [su(2)] algebra

Abstract: In this paper, we first discuss the general properties of an intermediate-statistics quantum bracket, [u, v]

Cited by 34 publications

References 32 publications

Intermediate-statistics spin waves

Intermediate-statistics spin waves

A group method solving many-body systems in intermediate statistical representation

Optical properties of drug metabolites in latent fingermarks

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