19,794 research outputs found
An intrinsic Hamiltonian formulation of the dynamics of LC-circuits
First, the dynamics of LC-circuits are formulated as a Hamiltonian system defined with respect to a Poisson bracket which may be degenerate, i.e., nonsymplectic. This Poisson bracket is deduced from the network graph of the circuit and captures the dynamic invariants due to Kirchhoff's laws. Second, the antisymmetric relations defining the Poisson bracket are realized as a physical network using the gyrator element and partially dualizing the network graph constraints. From the network realization of the Poisson bracket, the reduced standard Hamiltonian system as well as the realization of the embedding standard Hamiltonian system are deduce
Multiport Impedance Quantization
With the increase of complexity and coherence of superconducting systems made
using the principles of circuit quantum electrodynamics, more accurate methods
are needed for the characterization, analysis and optimization of these quantum
processors. Here we introduce a new method of modelling that can be applied to
superconducting structures involving multiple Josephson junctions, high-Q
superconducting cavities, external ports, and voltage sources. Our technique,
an extension of our previous work on single-port structures [1], permits the
derivation of system Hamiltonians that are capable of representing every
feature of the physical system over a wide frequency band and the computation
of T1 times for qubits. We begin with a black box model of the linear and
passive part of the system. Its response is given by its multiport impedance
function Zsim(w), which can be obtained using a finite-element electormagnetics
simulator. The ports of this black box are defined by the terminal pairs of
Josephson junctions, voltage sources, and 50 Ohm connectors to high-frequency
lines. We fit Zsim(w) to a positive-real (PR) multiport impedance matrix Z(s),
a function of the complex Laplace variable s. We then use state-space
techniques to synthesize a finite electric circuit admitting exactly the same
impedance Z(s) across its ports; the PR property ensures the existence of this
finite physical circuit. We compare the performance of state-space algorithms
to classical frequency domain methods, justifying their superiority in
numerical stability. The Hamiltonian of the multiport model circuit is obtained
by using existing lumped element circuit quantization formalisms [2, 3]. Due to
the presence of ideal transformers in the model circuit, these quantization
methods must be extended, requiring the introduction of an extension of the
Kirchhoff voltage and current laws
Slider-pinning Rigidity: a Maxwell-Laman-type Theorem
We define and study slider-pinning rigidity, giving a complete combinatorial
characterization. This is done via direction-slider networks, which are a
generalization of Whiteley's direction networks.Comment: Accepted, to appear in Discrete and Computational Geometr
Loop Equations as a Generalized Virasoro Constraints
The loop equations in the lattice gauge theory are represented in the
form of constraints imposed on a generating functional for the Wilson loop
correlators. These constraints form a closed algebra with respect to
commutation. This algebra generalizes the Virasoro one, which is known to
appear in one-matrix models in the same way. The realization of this algebra in
terms of the infinitesimal changes of generators of the loop space is given.
The representations on the tensor fields on the loop space, generalizing the
integer spin conformal fields, are constructed. The structure constants of the
algebra under consideration being independent of the coupling constants, almost
all the results are valid in the continuum.Comment: 7 pages, LaTex (3 LaTex figures), SMI-94-
The standard model at low energies
The hadronic sector of the standard model at low energies is described by a
non--decoupling effective field theory, chiral perturbation theory. An
introduction is given to the construction of effective chiral Lagrangians, both
in the purely mesonic sector and with inclusion of baryons. The connection
between the relativistic formulation and the heavy baryon approach to chiral
perturbation theory with baryons is reviewed.Comment: Lectures given at the 6th Indian-Summer School on Intermediate Energy
Physics, Prague, Aug. 1993, Latex, 26 pages (with a4.sty), UWThPh-1993-3
Naturalness from runaways in direct mediation
Postulating that the NMSSM singlet is a meson of a microscopic confining
theory opens up new model-building possibilities. Based on this, we construct
calculable models of direct mediation that solve the mu/Bmu problem and
simultaneously lead to realistic phenomenology. The singlet that couples to the
Higgs fields develops a runaway produced by soft interactions, then stabilized
by a small superpotential perturbation. The mechanism is first realized in an
O'Raifeartaigh model of direct gauge mediation with metastable supersymmetry
breaking. Focusing then on the microscopic theory, we argue that super QCD with
massless and massive flavors in the free magnetic phase gives rise to this
dynamics in the infrared. A deformation of the SQCD superpotential leads to
large spontaneous R-symmetry breaking, gaugino masses naturally at the scale of
the Higgs mass parameters, and absence of CP violating phases.Comment: 31 pages. Version 2: Reference added, minor change
Three-dimensional simplicial gravity and combinatorics of group presentations
We demonstrate how some problems arising in simplicial quantum gravity can be
successfully addressed within the framework of combinatorial group theory. In
particular, we argue that the number of simplicial 3-manifolds having a fixed
homology type grows exponentially with the number of tetrahedra they are made
of. We propose a model of 3D gravity interacting with scalar fermions, some
restriction of which gives the 2-dimensional self-avoiding-loop-gas matrix
model. We propose a qualitative picture of the phase structure of 3D simplicial
gravity compatible with the numerical experiments and available analytical
results.Comment: 24 page
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