广西师范大学学报：自然科学版

J＝J1＋J2时耦合与非耦合表象的变换通式

张振华, 彭景翠

Published Jan 1, 2000• 0 citations

Abstract

针对矢耦系数采用Ｒａｃａｈ表达式进行计算过于复杂，而矢耦系数表又过于零碎的问题，提出了ｊ＝ｊ１＋ｊ２时，耦合表象与非耦合表象的变换通式，并用数学归纳法予以严格证明，同时将单电子的表象变换作为特例，用此变换通式予以计算，与现有文献的结论完全相同。该变换通式简洁对称，易于使用。

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广西师范大学学报：自然科学版

J＝J1＋J2时耦合与非耦合表象的变换通式

张振华, 彭景翠

Published Jan 1, 2000• 0 citations

OpenAlex

Abstract

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Two entangled particles in threedimensional Hilbert space (per particle) are considered in an EPR-type arrangement. On each side the Kochen-Specker observables

\{J_1^2,J_2^2,J_3^2\}

and

\{\bar J_1^2, \bar J_2^2,J_3^2\}

with

[J_1^2,\bar J_1^2]\neq 0

are measured. The outcomes of measurements of

J_3^2

(via

J_1^2,J_2^2

) and

J_3^2

(via

\bar J_1^2,\bar J_2^2

) are compared. Although formally

J_3^2

is associated with the same projection operator, a strong form of quantum contextuality states that an outcome depends on the complete disposition of the measurement apparatus, in particular whether

J_1^2

\bar J_1^2

is measured alongside. It is argued that in this case it is impossible to measure contextuality directly, a necessary condition being a non-operational counterfactuality of the argument.

The surface scaling behavior of classical isotropic Heisenberg magnets is investigated by Monte Carlo methods in

d=3

dimensions for various values of the surface-to-bulk coupling ratio

{J}_{1}/J.

For

{J}_{1}/J<~1.0,

critical behavior according to the ordinary surface universality class is found. Estimates for magnetic surface exponents are presented and compared to older estimates and their theoretical counterparts. For

{J}_{1}/J>~2.0,

scaling is still valid with effective exponents which depend on

{J}_{1}/J.

The surface structure factor

{S}_{1}(p,L)

is investigated at bulk criticality as a function of the momentum transfer p parallel to the surface and the system size L. For

{J}_{1}/J<~1.0

and

{J}_{1}/J>~2.0

the full p dependence of

{S}_{1}(p,L)

can be captured by generalized shape functions to a remarkable accuracy. Profiles of the magnetization and the energy density also confirm scaling, where for

{J}_{1}/J<~1.0

the ordinary surface universality class is recovered and for

{J}_{1}/J>~2.0,

scaling with

{J}_{1}/J

dependent exponents is found. For

{J}_{1}/J=1.5

the system displays a striking crossover behavior from spurious long-range surface order to the ordinary surface universality class. For

{J}_{1}/J>~2.0

the effective scaling laws must be interpreted as nonasymptotic and the value

{J}_{1}/J=1.5

marks a crossover regime, in which the crossover from the nonasymptotic to the asymptotic (ordinary) surface scaling behavior can be resolved within numerically attainable system sizes.