A superposition of a matrix ensemble refers to the ensemble constructed from two independent copies of the original, while a decimation refers to the formation of a new ensemble by observing only every second eigenvalue. In the cases of the classical matrix ensembles with orthogonal symmetry, it is known that forming superpositions and decimations gives rise to classical matrix ensembles with u...

Let Ω be a space with probability measure μ for which the notion of symmetry is defined. Given A ⊆ Ω, let ms(A) denote the supremum of μ(B) over symmetric B ⊆ A. An r-coloring of Ω is a measurable map χ : Ω → {1, . . . , r} possibly undefined on a set of measure 0. Given an r-coloring χ, let ms(Ω;χ) = max1≤i≤r ms(χ (i)). With each space Ω we associate a Ramsey type number ms(Ω, r) = infχ ms(Ω;χ...

The three chiral generations of quarks and leptons may be generated through a spontaneous breakdown of the noncompact horizontal gauge symmetry GH which governs, together with the standard gauge symmetry SU(3)× SU(2)× U(1), the world in a vectorlike manner. In a framework of supersymmetric theory, the simplest choice GH = SU(1, 1) works quite well for this scenario in which quarks, leptons and ...

The gauge sector of the Standard Model (SM) exhibits a flavour symmetry which allows for independent unitary transformations of the fermion multiplets. In the SM the flavour symmetry is broken by the Yukawa couplings to the Higgs boson, and the resulting fermion masses and mixing angles show a pronounced hierarchy. In this work we connect the observed hierarchy to a sequence of intermediate eff...

In classical mechanics, the system of two coupled harmonic oscillators is shown to possess the symmetry of the Lorentz group O(3, 3) applicable to a six-dimensional space consisting of three space-like and three time-like coordinates, or SL(4, r) in the four-dimensional phase space consisting of two position and two momentum variables. In quantum mechanics, the symmetry is reduced to that of O(...

The autocorrelation function C ';" (('; ") = hg('; ") g(' + '; " + ")i (' and " are rescaled magnetic ux and energy) for the magnetoconductance of a ballistic chaotic quantum dot is calculated in the framework of the su-persymmetric non-linear-model. The Hamiltonian of the quantum dot is modelled by a Gaussian random matrix. The particular form of the symmetry breaking matrix is found to be rel...

We provide experimental evidence for a transition from a random-matrix ensemble with broken timereversal symmetry to an ensemble with partially broken spin-rotation symmetry. The transition from a Gaussian unitary ensemble to the ensemble in which the Zeeman degeneracy of electrons is lifted is accompanied by a factor of 2 change in 1/f noise fluctuations measured in a mesoscopic Li wire at low...

We consider the conductivity sigma of graphene with negligible intervalley scattering at half filling. We derive the effective field theory, which, for the case of a potential disorder, is a symplectic-class sigma model including a topological term with theta=pi. As a consequence, the system is at a quantum critical point with a universal value of the conductivity of the order of e(2)/h. When t...

If a HamiltonianH has an unbroken PT symmetry, then it also possesses a hidden symmetry represented by the linear operator C. The operator C commutes with both H and PT . The inner product with respect to CPT is associated with a positive norm and the quantum theory built on the associated Hilbert space is unitary. In this paper it is shown how to construct the operator C for the non-Hermitian ...

We review recent developments in strong interaction symmetries. We have tried to emphasize a simple approach starting from very well known facts such as charge independance and isotopic spin. We then present unitary symmetry after a short introduction to the language of Lie Algebras. The experimental data, on masses, multiplets, scattering cross sections are confronted with the theory. We brief...