Loss of Ergodicity in the Transition from Annealed to Quenched Disorder in a Finite Kinetic Ising Model

We consider a kinetic Ising model which represents a generic agent-based model for various types of socio-economic systems. We study the case of a finite (and not necessarily large) number of agents N as well as the asymptotic case when the number of agents tends to infinity. The main ingredient are individual decision thresholds which are either fixed over time (corresponding to quenched disorder in the Ising model, leading to nonlinear deterministic dynamics which are generically non-ergodic) or which may change randomly over time (corresponding to annealed disorder, leading to ergodic dynamics). We address the question how increasing the strength of annealed disorder relative to quenched disorder drives the system from non-ergodic behavior to ergodicity. Mathematically rigorous analysis provides an explicit and detailed picture for arbitrary realizations of the quenched initial thresholds, revealing an intriguing “jumpy” transition from non-ergodicity with many absorbing sets to ergodicity. For large N we find a critical strength of annealed randomness, above which the system becomes asymptotically ergodic. Our theoretical results suggests how to drive a system from an undesired socio-economic equilibrium (e.g. high level of corruption) to a desirable one (low level of corruption).     

Three Flavor Neutrino Mixing and Dark Energy Above GUT Scale

Neutrino mixing lead to a non zero contribution to the dark energy of the universe. We assume that the neutrino masses and mixing arise through physics at a scale intermediate between Planck Scale and the electroweak scale. The mechanism of neutrino mixing is a possible candidate to contribute the cosmological dark energy. Quantum gravitational (Planck scale) effects lead to an effective SU(2) _L ×U(1) invariant dimension-5 Lagrangian involving neutrino and Higgs fields, which gives rise to additional terms in neutrino mass matrix. There additional term can be considered to be perturbation of the GUT scale bi-maximal neutrino mass matrix. We assume that the gravitational interaction is flavor. In this paper, we discuss the three flavor neutrino mixing and cosmological dark energy contributes due to Planck scale effects.     

Quantum Diffusion and Eigenfunction Delocalization in a Random Band Matrix Model

We consider Hermitian and symmetric random band matrices H in d ≥ 1 dimensions. The matrix elements H _xy , indexed by \({x,y \in \Lambda \subset \mathbb{Z}^d}\), are independent, uniformly distributed random variables if \({\lvert{x-y}\rvert}\) is less than the band width W, and zero otherwise. We prove that the time evolution of a quantum particle subject to the Hamiltonian H is diffusive on time scales \({t\ll W^{d/3}}\). We also show that the localization length of the eigenvectors of H is larger than a factor W ^d/6 times the band width. All results are uniform in the size \({\lvert{\Lambda}\rvert}\) of the matrix.     

Cosmological Models with Variable <Emphasis Type="Italic">G</Emphasis> in <Emphasis Type="Italic">C</Emphasis>-Field Cosmology

Cosmological models with variable G in C-field cosmology for barotropic fluid distribution in FRW space-time are investigated. To get the deterministic model of the universe, we have assumed that G=R ⁿ where R is the scale factor and n the constant. To obtain the results in terms of cosmic time t, we have assumed n=−1. We find that for n=−1, Creation field (C) and spatial volume increase with time, G and ρ (matter density) decreases with time, the model represent accelerating universe. Thus inflationary scenario exists in the model. The model is also free from horizon. The results so obtained match with the astronomical observations.     

Blowup Criterion for Viscous Baratropic Flows with Vacuum States

We prove that the maximum norm of the deformation tensor of velocity gradients controls the possible breakdown of smooth(strong) solutions for the 3-dimensional (3D) barotropic compressible Navier-Stokes equations. More precisely, if a solution of the 3D barotropic compressible Navier-Stokes equations is initially regular and loses its regularity at some later time, then the loss of regularity implies the growth without bound of the deformation tensor as the critical time approaches. Our result is the same as Ponce’s criterion for 3-dimensional incompressible Euler equations (Ponce in Commun Math Phys 98:349–353, 1985). In addition, initial vacuum states are allowed in our cases.     

The Entanglement Properties Induced by Atoms in Two Separate Cavities Connected by an Optical Fiber

We study the entanglement evolution between two atoms, which are initially entangled with a third atom and trapped in two separated cavities coupled by an optical fiber. We also investigate the temporal evolution in the entanglement between the atom and the local cavity mode. The influence of the state-selective measurement on the atom outside the cavities and the influence of cavity-fiber coupling coefficient on the entanglement are discussed. The results show that the entanglement can be strengthened through the state-selective measurement on the atom outside the cavities. We also find that, by increasing the cavity-fiber coupling coefficient, the atom-atom entanglement is strengthened, but the atom-cavity entanglement is weakened.     

A Generalized Hadamard-Fresnel Complementary Transformation Derived by Virtue of New Coherent-Entangled State

The new coherent-entangled state |z,x;θ〉 is proposed in the two-mode Fock space, which exhibits both the properties of coherent and entangled states. The completeness relation of |z,x;θ〉 is proved by virtue of the technique of integral within an ordered product of operators. A generalized Hadamard-Fresnel complementary transformation derived by virtue of the coherent-entangled state |z,x;θ〉, which is unitary. The new unitary operator plays the role of both Hadamard transformation for ([^(a)]₁sinq-[^(a)]₂cosq)(\hat{a}_{1}\sin\theta -\hat{a}_{2}\cos\theta) and Fresnel transformation for ([^(a)]₁cosq+[^(a)]₂sinq)(\hat{a}_{1}\cos\theta +\hat{a}_{2}\sin\theta), respectively.     

On Random Field Induced Ordering in the Classical <Emphasis Type="Italic">XY</Emphasis> Model

Consider the classical XY model in a weak random external field pointing along the Y axis with strength ε. We study the behavior of this model as the range of the interaction is varied. We prove that in any dimension d≥2 and for all ε sufficiently small, there is a range L=L(ε) so that whenever the inverse temperature β is larger than some β(ε), there is strong residual ordering along the X direction.     

Neuronal expression of muskelin in the rodent central nervous system

Background  

The kelch repeat protein muskelin mediates cytoskeletal responses to the extracellular matrix protein thrombospondin 1, (TSP1), that is known to promote synaptogenesis in the central nervous system (CNS). Muskelin displays intracellular localization and affects cytoskeletal organization in adherent cells. Muskelin is expressed in adult brain and has been reported to bind the Cdk5 activator p39, which also facilitates the formation of functional synapses. Since little is known about muskelin in neuronal tissues, we here analysed the tissue distribution of muskelin in rodent brain and analysed its subcellular localization using cultured neurons from multiple life stages.