Breaking the Symmetry of a Circular System of Coupled Harmonic Oscillators

First we compute the natural frequencies of vibration of four identical particles coupled by ideal, massless harmonic springs. The four particles are constrained to move on a fixed circle. The initial computations are simplified by a transformation to symmetry coordinates. Then the symmetry of the vibrating system is broken by changing the mass of a single particle by a very small amount. We observe the effect of applying the symmetry transformation to the now slightly nonsymmetric system. We compute the new frequencies and compare them with the frequencies of the original symmetric system of oscillators. Results of similar calculations for 2,3,5, and 6particles are given

Loop-string-hadron formulation of an SU(3) gauge theory with dynamical quarks

Towards the goal of quantum computing for lattice quantum chromodynamics, we present a loop-string-hadron (LSH) framework in 1+1 dimensions for describing the dynamics of SU(3) gauge fields coupled to staggered fermions. This novel framework was previously developed for an SU(2) lattice gauge theory in $d\leq3$ spatial dimensions and its advantages for classical and quantum algorithms have thus far been demonstrated in $d=1$. The LSH approach uses gauge invariant degrees of freedoms such as loop segments, string ends, and on-site hadrons, it is free of all nonabelian gauge redundancy, and it is described by a Hamiltonian containing only local interactions. In this work, the SU(3) LSH framework is systematically derived from the reformulation of Hamiltonian lattice gauge theory in terms of irreducible Schwinger bosons, including the addition of staggered quarks. Furthermore, the superselection rules governing the LSH dynamics are identified directly from the form of the Hamiltonian. The SU(3) LSH Hamiltonian with open boundary conditions has been numerically confirmed to agree with the completely gauge-fixed Hamiltonian, which contains long-range interactions and does not generalize to either periodic boundary conditions or to $d>1$.Comment: 35 pages plus references, 5 figures. v2 includes typo corrections, trivial adjustments to text sectioning, and added reference

Four Anharmonic Oscillators on a Circle

Four identical, uniformly separated particles interconnected by ideal anharmonic springs are constrained to move on a fixed, frictionless circular track. The Lagrangian for the system is written and then transformed by matrix operations suggested by the symmetry of the arrangement of springs and particles. The equations of motion derived from the transformed Lagrangian yield four natural frequencies of motion

Breaking the symmetry of a circular system of coupled harmonic oscillators

First we compute the natural frequencies of vibration of four identical particles coupled by ideal, massless harmonic springs. The four particles are constrained to move on a fixed circle. The initial computations are simplified by a transformation to symmetry coordinates. Then the symmetry of the vibrating system is broken by changing the mass of a single particle by a very small amount. We observe the effect of applying the symmetry transformation to the now slightly nonsymmetric system. We compute the new frequencies and compare them with the frequencies of the original symmetric system of oscillators. Results of similar calculations for 2,3,5, and 6 particles are given

SU(N) Coherent States and Irreducible Schwinger Bosons

We exploit the SU(N) irreducible Schwinger boson to construct SU(N) coherent states. This construction of SU(N) coherent state is analogous to the construction of the simplest Heisenberg-Weyl coherent states. The coherent states belonging to irreducible representations of SU(N) are labeled by the eigenvalues of the $(N-1)$ SU(N) Casimir operators and are characterized by $(N-1)$ complex orthonormal vectors describing the SU(N) group manifold.Comment: 12 pages, 3 figure

Prepotential formulation of SU(3) lattice gauge theory

The SU(3) lattice gauge theory is reformulated in terms of SU(3) prepotential harmonic oscillators. This reformulation has enlarged $SU(3)\otimes U(1) \otimes U(1)$ gauge invariance under which the prepotential operators transform like matter fields. The Hilbert space of SU(3) lattice gauge theory is shown to be equivalent to the Hilbert space of the prepotential formulation satisfying certain color invariant Sp(2,R) constraints. The SU(3) irreducible prepotential operators which solve these Sp(2,R) constraints are used to construct SU(3) gauge invariant Hilbert spaces at every lattice site in terms of SU(3) gauge invariant vertex operators. The electric fields and the link operators are reconstructed in terms of these SU(3) irreducible prepotential operators. We show that all the SU(3) Mandelstam constraints become local and take very simple form within this approach. We also discuss the construction of all possible linearly independent SU(3) loop states which solve the Mandelstam constraints. The techniques can be easily generalized to SU(N).Comment: 25 pages, 10 figures, LaTeX, Minor modifications done. Version to appear in J. Phys. A: Mathematical and General, 43 (2010

Phosphocaveolin-1 is a mechanotransducer that induces caveola biogenesis via Egr1 transcriptional regulation

Caveolin-1 (Cav1) is an essential component of caveolae whose Src kinase-dependent phosphorylation on tyrosine 14 (Y14) is associated with regulation of focal adhesion dynamics. However, the relationship between these disparate functions remains to be elucidated. Caveola biogenesis requires expression of both Cav1 and cavin-1, but Cav1Y14 phosphorylation is dispensable. In this paper, we show that Cav1 tyrosine phosphorylation induces caveola biogenesis via actin-dependent mechanotransduction and inactivation of the Egr1 (early growth response-1) transcription factor, relieving inhibition of endogenous Cav1 and cavin-1 genes. Cav1 phosphorylation reduces Egr1 binding to Cav1 and cavin-1 promoters and stimulates their activity. In MDA-231 breast carcinoma cells that express elevated levels of Cav1 and caveolae, Egr1 regulated Cav1, and cavin-1 promoter activity was dependent on actin, Cav1, Src, and Rho-associated kinase as well as downstream protein kinase C (PKC) signaling. pCav1 is therefore a mechanotransducer that acts via PKC to relieve Egr1 transcriptional inhibition of Cav1 and cavin-1, defining a novel feedback regulatory loop to regulate caveola biogenesis