Uncertainty relations for a q-deformed coherent spin state

A Coherent Spin State (CSS) is defined as an eigenstate of the spin component in the direction specified by angles (θ₀,?₀). This state satisfies minimum uncertainty relation, with uncertainties equally distributed on any two orthogonal components normal to the direction of the total spin vector 〈S〉. Starting from this concept, we apply the notion of CSS to quantum groups and discuss the properties of q-deformed CSS and the associated uncertainty relations. We show that these states behave as Intelligent Spin States (ISS) on two orthogonal components normal to the direction of the mean value of the spin operator.     

Real space renormalization group approach to the two-dimensional antiferromagnetic Heisenberg model (I) – The singlet triplet gap

The low energy behaviour of the two-dimensional antiferromagnetic Heisenberg model is studied in the sector with total spins S = 0,1,2 by means of a renormalization group procedure, which generates a recursion formula for the interaction matrix Δ_S ⁽ⁿ⁺¹⁾ of 4 neighbouring “n clusters” of size 2ⁿ × 2ⁿ, n = 1,2,3,... from the corresponding quantities Δ_S ⁽ⁿ⁾. Conservation of total spin S is implemented explicitly and plays an important role. It is shown, how the ground state energies E_S ⁽ⁿ⁺¹⁾, S = 0,1,2 approach each other for increasing n, i.e. system size. The most relevant couplings in the interaction matrices are generated by the transitions 〈S’,m’;n+1|S_q ^*|S,m;n+1〉 between the ground states |S,m;n+1〉 (m = -S,...,S) on an (n+1)-cluster of size 2ⁿ⁺¹ × 2ⁿ⁺¹, mediated by the staggered spin operator S_q ^*.     

Spin frustration,charge ordering,and enhanced antiferromagnetism in TMTTF2SbF6

We theoretically investigate the effects of charge order and spin frustration on the spin ordering in TMTTF salts. Using first-principles band calculations, we find that a diagonal inter-chain transfer integral t_q1, which causes spin frustration between the inter-chain dimers in the dimer-Mott insulating state, strongly depends on the choice of anion. Within the numerical Lanczos exact diagonalization method, we show that the ferroelectric charge order changes the role of t_q1 from the spin frustration to the enhancement of the two-dimensionality in spin sector. The results indicate that t_q1 assists the cooperative behavior between charge order and antiferromagnetic state observed in TMTTF₂SbF₆.     

Verwey transition in spin polarization of field-emitted electrons from 〈1 1 0〉-oriented single crystal magnetite whisker

We measured temperature dependence of a spin polarization of field-emitted electrons from a single-crystalline magnetite (Fe₃O₄) whisker with 〈1 1 0〉 orientation. The spin polarization of emitted electrons began to increase above 130 K corresponding to the temperature of Verwey point (T_v). The increase is considered as reflection of the change of the spin state near the Fermi level due to the Verwey transition. Our experimental results support a localization of t_2g orbital electrons below the Verwey point and a model of charge ordering for magnetite.     

The correlation function of the Ising model in the MFA and their sum rule

It is shown that in the correctly performed molecular field approximation the correlation function 〈S(q) S(-q)〉 fulfills the sum rule N^-1Σ_q〈S(q) S(-q)〉 = 1. This can be proved for ferro- and antiferromagnets and the disordered phases of o-hydrogen.     

Tendencies toward nematic order in YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>6+δ</Subscript>: Uniform distortion <Emphasis Type="Italic">vs.</Emphasis> incipient charge stripes

Recent neutron scattering and transport data obtained on underdoped YBa₂Cu₃O_6+δ, with strong signatures of rotation symmetry breaking at low temperatures, point toward electron-nematic order in the charge sector. Such order may originate from a uniform distortion with d-wave symmetry or as a precursor of a uni-directional stripe phase. Here, we discuss whether the neutron scattering data can be linked to incipient charge stripes. We employ and extend a phenomenological model for collective spin and charge fluctuations and analyze the resulting spin excitation spectrum under the influence of lattice anisotropies. Our results show that the experimentally observed temperature-dependent magnetic incommensurability is compatible with a scenario of incipient stripes, the temperature dependence being due to the temperature variation of both strength and correlation length of the charge stripes. Finally, we propose further experiments to distinguish the possible theoretical scenarios.     

Dynamical susceptibility of the ising model in a transverse magnetic field

An approximate expression is obtained for the dynamical susceptibility, χ_zz(q, ω), of the spin one half, simple cubic Ising model in a transverse magnetic field, which is appropriate to the disordered state (〈S_z〉 = 0). The susceptibility along the direction of the field is shown to contain a thermal part with a relative weight proportional to the difference between the isothermal and adiabatic susceptibilities and a width determined by the thermal diffusion constant.     

A possible coupling mechanism between magnetism and dielectric properties in EuTiO3

The dielectric constant of an incipient ferroelectric EuTiO₃ exhibits a sharp decrease at about 5.5K, at which the antiferromagnetic ordering of the Eu spins simultaneously appears. This fact indicates the existence of a coupling between the magnetism and dielectric properties of EuTiO₃. We propose a possible coupling mechanism between the magnetic and electrical subsystems as -g\dsum_l \dsum_〈i,j〉q²_l\vec S_i·\vec S_j. In the framework of soft-mode theory, we have obtained analytically a dielectric constant expression related to the spin correlation of nearest neighbours of Eu ions.     

Is KNO scaling proved or postulated?

Assuming Feynman's scaling law, Koba, Nielson and Olesen had shown that as s → ∞, (i) 〈n^q〉/〈n〉^q → d_q where d_q is independent of s and $\text{(ii)}\text{σ}{}_{\mathrm{n}}\text{(s)/σ}{}^{\mathrm{(s)}}{}_{\mathrm{<mtext>incl</mtext>}}\text{→ (}\text{1}\text{〈n〉)}\text{Ψ(n/〈n〉)}$. The derivation of the latter result is, however, not rigorous and it does not follow, as a necessary consequence, from the scaling law.     

Spinpolarisation von Feldemissionselektronen aus einkristallinem Wolfram

Field-emitted electrons from tungsten tips extracted in magnetic fields of 3–25 kG at 80 K show spin polarization. The observed polarization is always found to be parallel to the external magnetic field for the polycrystalline and oriented tips (〈100〉, 〈110〉 and 〈111〉) investigated. The maximum values of polarization obtained with these monocrystalline emitters range betweenP _max=11–13 percent.     

Optical Tomography for Single- and Two-Mode Squeezed Chaotic Fields

Different from the previous methods of obtaining optical tomography of quantum states, in this paper we use the Radon transform between the single- (two-)mode Wigner operator and the pure-state density operator |q〉 _{f,g f,g} 〈q| (|η,τ ₁,τ ₂〉〈η,τ ₁,τ ₂|) to analytically obtain optical tomograms for single- (two-)mode squeezed chaotic fields, where the states |q〉 _f,g (|η,τ ₁,τ ₂〉) refer to the newly introduced intermediate coordinate-momentum (entangled) states. More interestingly, we find that the tomograms of squeezed chaotic fields and those of coherent states are related by a integration. Thus, we establish a new convenient approach of obtaining tomograms for quantum states.     

Solutions for the T = 0 quantum spin glass transition in a metallic model with spin-charge coupling

We solve several low temperature problems of an infinite range metallic spin glass model. A compensation problem of T 0 divergencies is solved for the free energy which helped to extract the quantum critical behaviour of the spin glass order parameters as a function of δJ = J – J_c (T = 0). The critical value J_c(T = 0) = 3/16p_F^?1 of the frustrated spin coupling J, which separates spin glass from nonmagnetic (spin liquid) phase, is determined exactly in the static saddle point solution for a semielliptic metallic band model in terms of the density of states at the Fermi level. In addition to the replica-overlap order parameter 〈Q^ab〉, a ≠ b, the diagonal 〈Q^aa〉 is confirmed as order parameter by the result 〈Q^aa〉 _SP ～ (δJ)^β, β = 1, and its susceptibility χ^aaaa ～(-δJ)^?γ with γ = 1/2 at T = 0. The value for γ agrees with the one for the transverse field Ising spin glass. The low γ decay of 〈Q^aa〉, ～ T is obtained exactly in the whole quantum disordered phase including the critical value.     

Consistent MFA correlation functions of Ising models for all temperatures

A correct calculation of the Ising model correlation function C(q) = 〈(S(q) ? 〈S(q)〉) (S(-q) ? 〈S(-q)〉)〉 in the MFA results in

$\text{C(q)=}\text{〈S}{}^2\text{〉?〈〉}{}^2\text{1?(〈S}{}^2\text{〉?〈S〉}{}^2\text{βJ(q}\text{1}\text{N}\text{∑}\text{q}\text{1}\text{1?〈S〉}{}^2\text{βJ(q)}{}^{\mathrm{?1}}\text{C(q) fulfills the exact sum rule N}{}^{-1}\text{Σ}{}_{\mathrm{q}}\text{C(q) = 〈S}{}^2\text{〉 ? 〈S〉}{}^2$

. Previous literature supposed a violation of this sum rule to be a characteristic disadvantage of this approximation.     

Transformation from metallic electron charge density to electron momentum

Electron momentum densities (EMD) in Al, V, Cr and Cu metals have been estimated from the metallic electron charge densities by applying the procedure of Burkhardt, Konya and Coulson and March. The procedure has provided spherically averaged EMD from which corresponding Compton profiles, J(q) and 〈pⁿ〉 expectation values have been computed. These theoretical results show satisfactory agreement with the experimental data for Al, V, Cr and Cu.     

Spin-fluctuation gating in the c-axis non-Drude conductivity of the high Tc cuprates

An ideal antiferromagnetic (AF) ordering of the spins of the CuO layers of an underdoped cuprate prevents the low energy tunneling of the charge carriers between the layers. In order to obtain a non-vanishing c-axis conductivity (σ_c), we invoke ground state fluctuations of the spin system. These provide a frequency-dependent gating effect by changing the direction of the AF order parameter within one layer relative to that in a neighboring layer, thereby permitting some tunneling. The calculated σ_c compares favorably with experimental data in a) being small and b) having a weak frequency dependence of distinctly non-Drude form.     

Magnetic circular dichroism of [Co/Pd] and [CoB/Pd] multilayered films

Magnetic circular dichroism (MCD) and X-ray absorption spectra (XAS) at the Co L_2,3-edge of [Co/Pd]₂₀ and [CoB/Pd]₂₀ multilayered films, which were fabricated at 260 °C with different magnetic layer thicknesses (δ), have been measured. The lineshapes of XAS–MCD show that the electronic state of Co 3d of the films hardly changes even when sputtered at higher temperatures. The expectation values of orbital and spin angular momentum (〈L_z〉 and 〈S_z〉) are estimated using the sum rule, and it is found that 〈L_z〉/〈S_z〉 in δ<0.5 nm is larger than that in δ>0.5 nm.     

Mass asymmetry dependence of angular distribution in237Np(α29 and 44 MeV,f): single particle effect

Angular distributions of fission products have been measured as a function of mass asymmetry in the odd-Z ²³⁷Np(α_{29 and 44 MeV},f) system using a recoil-catcher technique and off-line gamma spectrometry. Higher angular anisotropies were observed for the asymmetric mode products compared to the symmetric mode products at both energies. Average anisotropies for individual modes are lower than those for neighbouring even-even fissioning nucleus²⁴²Pu due to odd-nucleon spin effect. Present data have been analysed according to the transition state model assuming two modes of fission with characteristic saddle-shapes, barriers and multichance fission probabilities. It is seen that angular distributions for the symmetric and asymmetric modes are decided at and well past the corresponding saddle points respectively. Odd-nucleon spin contribution (〈k ²〉) to the tilting mode variance have been deduced. For (²⁴¹)Am fission, 〈k ²〉 values for the asymmetric and symmetric modes are ≤ 14 and > 14 ?² respectively. The 〈k ²〉 value averaged over several nuclei from preactinide (²⁰¹Ti) to actinide (²⁴⁸Cf) is 11.5 ± 4.2 ?². Average 〈k ²〉 value is in close agreement with the theoretical estimate.     

一种新型的两态叠加多模叠加态光场的广义非线性等阶N次方Y压缩

本文根据量子力学中的线性叠加原理,构造了由多模(即q模)相干态的相反态|{-Z_j}〉_q及多模虚相干态的相反态|{-iZ_j}〉_q这两者的线性叠加所组成的一种新型的两态叠加多模叠加态光场|ψ_msc⁽²⁾〉_q.利用新近建立的多模辐射场的广义非线性等阶高阶压缩理论,研究了态|ψ_msc⁽²⁾〉_q的广义非线性等阶N次方Y压缩特性.结果发现,1)当压缩阶数N=2P且P=2m(m=1,2,3,…,…)时,态|ψ_msc⁽²⁾〉_q恒处于N-Y最小测不准态;2)当N=2P且P=2m’+1(m’=0,1,2,…,…)时,如果各模的初始相位φ_j、态间的初始相位差与各单模相干态光场的平均光子数之和∑_j=1^qR_j²即[(θ_pq^(R)-θ_nq^(I))-∑_j=1^qR_j²]满足一定的量子化条件,态|ψ_msc⁽²⁾〉_q可呈现周期性变化的、任意阶的等阶N次方Y压缩效应;3)当N为奇数时,态|ψ_msc⁽²⁾〉_q在一定条件下恒处于N-Y测不准态;4)态|ψ_msc⁽²⁾〉_q与文献21中的态|ψ⁽²⁾〉_q出现部分压缩简并现象,从而更进一步表明压缩简并现象的存在是有某种客观内在联系的.