Quantum localized modes in capacitively coupled Josephson junctions

We consider the quantum dynamics of excitations in a system of two capacitively coupled Josephson junctions. Quantum breather states are found in the middle of the energy spectrum of the confined nonescaping states of the system. They are characterized by a strong excitation of one junction. These states perform slow tunneling motion from one junction to the other, while keeping their coherent nature. The tunneling time sensitively depends on the initial excitation energy. By using an external bias as a control parameter, the tunneling time can be varied with respect to the escape time and the experimentally limited coherence time. Thus one can control the flow of quantum excitations between the two junctions.Comment: 5 pages, 3 figures. Improved version, title was slightly changed. Accepted in Europhysics Letters (http://www.iop.org/EJ/journal/EPL

Quantum breathers in capacitively coupled Josephson junctions: Correlations, number conservation, and entanglement

We consider the classical and quantum dynamics of excitations in a system of two capacitively coupled Josephson junctions. In the classical case the equations of motion admit discrete breather solutions, which are time periodic and localized predominantly on one of the junctions. In the quantum case breather states are found in the central part of the energy spectrum of the confined nonescaping states of the system. We perform a systematic analysis of their tunneling frequency, site correlations, fluctuations of the number of quanta, and entanglement. Quantum breather states show strong site correlation of quanta and are characterized by a strong excitation of quanta on one junction which perform slow coherent tunneling motion from one junction to the other. They suppress fluctuations of the total number of excited quanta. Quantum breather states are the least entangled states among the group of eigenstates in the same range of the energy spectrum. We describe how quantum breather excitations could be experimentally observed by employing the already developed techniques for quantum information processing using Josephson junctions.Comment: 10 pages, 9 figures. Improved version with further discussions. Accepted in Physical Review

Flux emergence in a magnetized convection zone

We study the influence of a dynamo magnetic field on the buoyant rise and emergence of twisted magnetic flux-ropes, and their influence on the global external magnetic field. We ran 3D MHD numerical simulations using the ASH code and analysed the dynamical evolution of such buoyant flux-ropes from the bottom of the convection zone until the post-emergence phases. The global nature of this model represents very crudely and inaccurately the local dynamics of the buoyant rise, but allows to study the influence of global effects such as self-consistently generated differential rotation, meridional circulation and Coriolis forces. Although motivated by the solar context, this model cannot be thought of as a realistic model of the rise of magnetic structures and their emergence in the Sun where the local dynamics are completely different. The properties of initial phases of the buoyant rise in good agreement with previous studies. However, the effects of the interaction of the background dynamo field become increase as the flux-ropes evolve. During the buoyant rise across the CZ, the flux-rope's magnetic field strength and scales as $rho^a$, with $a\lesssim 1$. An increase of velocity, density and current precedes flux emergence at all longitudes. The geometry, latitude and relative orientation of the flux-ropes with respect to the background magnetic field influences the rise speeds, zonal flow amplitudes (which develop within the flux-ropes) and the corresponding surface signatures. This influences the morphology, duration and amplitude of the associated surface shearing and Poynting flux. The emerged flux influences the system's global polarity, leading in some cases to a polarity reversal while inhibiting background dynamo from doing so in some others. The emerged magnetic flux is slowly advected poleward, while being diffused and assimilated by the background dynamo field.Comment: Accepted for publication in Ap

Subfactor realisation of modular invariants

We study the problem of realising modular invariants by braided subfactors and the related problem of classifying nimreps. We develop the fusion rule structure of these modular invariants. This structure is useful tool in the analysis of modular data from quantum double subfactors, particularly those of the double of cyclic groups, the symmetric group on 3 letters and the double of the subfactors with principal graph the extended Dynkin diagram D_5^(1). In particular for the double of S_3, 14 of the 48 modular modular invariants are nimless, and only 28 of the remaining 34 nimble invariants can be realised by subfactors

Coupling the solar surface and the corona: coronal rotation, Alfv\'en wave-driven polar plumes

The dynamical response of the solar corona to surface and sub-surface perturbations depends on the chromospheric stratification, and specifically on how efficiently these layers reflect or transmit incoming Alfv\'en waves. While it would be desirable to include the chromospheric layers in the numerical simulations used to study such phenomena, that is most often not feasible. We defined and tested a simple approximation allowing the study of coronal phenomena while taking into account a parametrised chromospheric reflectivity. We addressed the problems of the transmission of the surface rotation to the corona and that of the generation of polar plumes by Alfv\'en waves (Pinto et al., 2010, 2011). We found that a high (yet partial) effective chromospheric reflectivity is required to properly describe the angular momentum balance in the corona and the way the surface differential rotation is transmitted upwards. Alfv\'en wave-driven polar plumes maintain their properties for a wide range of values for the reflectivity, but they become bursty (and eventually disrupt) when the limit of total reflection is attained.Comment: Solar Wind 13: Proceedings of the Thirteenth International Solar Wind Conferenc

The Phase Structure of the Weakly Coupled Lattice Schwinger Model

The weak coupling expansion is applied to the single flavour Schwinger model with Wilson fermions on a symmetric toroidal lattice of finite extent. We develop a new analytic method which permits the expression of the partition function as a product of pure gauge expectation values whose zeroes are the Lee-Yang zeroes of the model. Application of standard finite-size scaling techniques to these zeroes recovers previous numerical results for the small and moderate lattice sizes to which those studies were restricted. Our techniques, employable for arbitrarily large lattices, reveal the absence of accumulation of these zeroes on the real hopping parameter axis at constant weak gauge coupling. The consequence of this previously unobserved behaviour is the absence of a zero fermion mass phase transition in the Schwinger model with single flavour Wilson fermions at constant weak gauge coupling.Comment: 8 pages, 2 figures, insert to figure 2 include