1,517 research outputs found
Domino D3.1 - Architecture definition
This deliverable presents the concept of operation of Domino. It includes a description of the systems, subsystems and processes that will be taken into account in the model, as well as the general scope of the model. For each of the mechanisms suggested to be modelled in the project, the deliverable provides a set of possible operational concepts and uptake/scope to be deployed
Phase-charge duality in Josephson junction circuits: Role of inertia and effect of microwave irradiation
We investigate the physics of coherent quantum phase slips in two distinct
circuits containing small Josephson junctions: (i) a single junction embedded
in an inductive environment and (ii) a long chain of junctions. Starting from
the standard Josephson Hamiltonian, the single junction circuit can be analyzed
using quasi-classical methods; we formulate the conditions under which the
resulting quasi-charge dynamics is exactly dual to the usual phase dynamics
associated with Josephson tunneling. For the chain we use the fact that its
collective behavior can be characterized by one variable: the number of
quantum phase slips present on it. We conclude that the dynamics of the
conjugate quasi-charge is again exactly dual to the standard phase dynamics of
a single Josephson junction. In both cases we elucidate the role of the
inductance, essential to obtain exact duality. These conclusions have profound
consequences for the behavior of single junctions and chains under microwave
irradiation. Since both systems are governed by a model exactly dual to the
standard resistively and capacitively shunted junction model, we expect the
appearance of current-Shapiro steps. We numerically calculate the corresponding
current-voltage characteristics in a wide range of parameters. Our results are
of interest in view of a metrological current standard
The Domination Number of Grids
In this paper, we conclude the calculation of the domination number of all
grid graphs. Indeed, we prove Chang's conjecture saying that for
every , .Comment: 12 pages, 4 figure
Phase-Charge Duality of a Josephson junction in a fluctuating electromagnetic environment
We have measured the current-voltage characteristics of a single Josephson
junction placed in a high impedance environment. The transfer of Cooper pairs
through the junction is governed by overdamped quasicharge dynamics, leading to
Coulomb blockade and Bloch oscillations. Exact duality exists to the standard
overdamped phase dynamics of a Josephson junction, resulting in a dual shape of
the current-voltage characteristic, with current and voltage changing roles. We
demonstrate this duality with experiments which allow for a quantitative
comparison with a theory that includes the effect of fluctuations due to finite
temperature of the electromagnetic environment
Laplace transformations of hydrodynamic type systems in Riemann invariants: periodic sequences
The conserved densities of hydrodynamic type system in Riemann invariants
satisfy a system of linear second order partial differential equations. For
linear systems of this type Darboux introduced Laplace transformations,
generalising the classical transformations in the scalar case. It is
demonstrated that Laplace transformations can be pulled back to the
transformations of the corresponding hydrodynamic type systems. We discuss
periodic Laplace sequences of with the emphasize on the simplest nontrivial
case of period 2. For 3-component systems in Riemann invariants a complete
discription of closed quadruples is proposed. They turn to be related to a
special quadratic reduction of the (2+1)-dimensional 3-wave system which can be
reduced to a triple of pairwize commuting Monge-Ampere equations. In terms of
the Lame and rotation coefficients Laplace transformations have a natural
interpretation as the symmetries of the Dirac operator, associated with the
(2+1)-dimensional n-wave system. The 2-component Laplace transformations can be
interpreted also as the symmetries of the (2+1)-dimensional integrable
equations of Davey-Stewartson type. Laplace transformations of hydrodynamic
type systems originate from a canonical geometric correspondence between
systems of conservation laws and line congruences in projective space.Comment: 22 pages, Late
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