For complete table with all irreducible simple subalgebras of su(N) [N up to 2^15] download ancillary file; v2: further results on spin chains with limited local control, minor corrections, and updated references; v3: minor amendments in Sec. 10.6, Appendix C more reader-friendly (see C.3, C.4), electronic supplement list corrected in 2 cases (dim=560, 4928) out of 32768 instances
General dynamic properties like controllability and simulability of spin systems, fermionic and bosonic systems are investigated in terms of symmetry. Symmetries may be due to the interaction topology or due to the structure and representation of the system and control Hamiltonians. In either case, they obviously entail constants of motion. Conversely, the absence of symmetry implies irreducibility and provides a convenient necessary condition for full controllability much easier to assess than the well-established Lie-algebra rank condition. We give a complete lattice of irreducible simple subalgebras of su(2^n) for up to n=15 qubits. It complements the symmetry condition by allowing for easy tests solving homogeneous linear equations to filter irreducible unitary representations of other candidate algebras of classical type as well as of exceptional types. --- The lattice of irreducible simple subalgebras given also determines mutual simulability of dynamic systems of spin or fermionic or bosonic nature. We illustrate how controlled quadratic fermionic (and bosonic) systems can be simulated by spin systems and in certain cases also vice versa.
A proof-of-principle experiment on the spontaneous symmetry breaking machine and numerical estimation of its performance on the $K_{2000}$ benchmark problem
Measure of irregularity for Dirac, Schwinger, Wu-Yang's bases in the Abelian monopole theory and affecting of the gauge symmetry principle by allowance of singularity in physics
A Matter of Principle: The Principles of Quantum Theory, Dirac's Equation, and Quantum Information
本文讨论基本原理在理论物理中的作用，特别是量子理论。相对论的基本原理也将在量子电动力学和量子场论中发挥作用，特别是狄拉克的工作，特别是狄拉克从相对论原理和量子理论推导出的电子相对论方程，是本文的主要焦点。然而，我也将考虑海森堡对量子力学的推导，正是他启发了狄拉克。我认为海森堡和狄拉克的工作都是由他们对量子理论基本原理的坚持和信心所指导的。文章的最后一部分讨论了G. M. d 'ariano和他的同事关于量子信息理论的原理，它将量子理论及其原理扩展到一个新的方向。这一扩展使他们能够仅仅从这些原理中推导出狄拉克方程，而不使用相对性原理。
Equal-spin and opposite-spin density-density correlations in the BCS-BEC crossover: Gauge Symmetry, Pauli Exclusion Principle, Wick's Theorem and Experiments
Rhineland-Palatinate Technical University Kaiserslautern-Landau（莱茵兰-普法尔茨凯泽斯劳滕-兰道理工大学）；Georgia Institute of Technology（佐治亚理工学院）
