47,430 research outputs found
Symmetry and quaternionic integrable systems
Given a hyperkahler manifold M, the hyperkahler structure defines a triple of
symplectic structures on M; with these, a triple of Hamiltonians defines a so
called hyperhamiltonian dynamical system on M. These systems are integrable
when can be mapped to a system of quaternionic oscillators. We discuss the
symmetry of integrable hyperhamiltonian systems, i.e. quaternionic oscillators;
and conversely how these symmetries characterize, at least in the Euclidean
case, integrable hyperhamiltonian systems.Comment: 26 page
An introduction to operational quantum dynamics
In the summer of 2016, physicists gathered in Torun, Poland for the 48th
annual Symposium on Mathematical Physics. This Symposium was special; it
celebrated the 40th anniversary of the discovery of the
Gorini-Kossakowski-Sudarshan-Lindblad master equation, which is widely used in
quantum physics and quantum chemistry. This article forms part of a Special
Volume of the journal Open Systems & Information Dynamics arising from that
conference; and it aims to celebrate a related discovery -- also by Sudarshan
-- that of Quantum Maps (which had their 55th anniversary in the same year).
Nowadays, much like the master equation, quantum maps are ubiquitous in physics
and chemistry. Their importance in quantum information and related fields
cannot be overstated. In this manuscript, we motivate quantum maps from a
tomographic perspective, and derive their well-known representations. We then
dive into the murky world beyond these maps, where recent research has yielded
their generalisation to non-Markovian quantum processes.Comment: Submitted to Special OSID volume "40 years of GKLS
Behavioral Modelling of Digital Devices Via Composite Local-Linear State-Space Relations
This paper addresses the generation of accurate and efficient behavioral models of digital ICs. The proposed approach is based on the approximation of the device port characteristics by means of composite local linear state-space relations whose parameters can effectively be estimated from device port transient responses via well-established system identification techniques. The proposedmodels have been proven to overcome some inherent limitations of the state-of-the-art models used so far, and they can effectively be implemented in any commercial tool as Simulation Program with Integrated Circuit Emphasis (SPICE) subcircuits or VHDL-AMS hardware descriptions. A systematic study of the performances of the proposed state-space models is carried out on a synthetic test device. The effectiveness of the proposed approach has been demonstrated on a real application problem involving commercial devices and a data link of a mobile phon
Towards a Field Theory of the Plateau Transition
We suggest a procedure for calculating correlation functions of the local
densities of states (DOS) at the plateau transitions in the Integer Quantum
Hall effect (IQHE). We argue that their correlation functions are appropriately
described in terms of the SL()/SU(2) WZNW model (at the usual Ka{\v
c}--Moody point and with the level ). In this model we have
identified the operators corresponding to the local DOS, and derived the
partial differential equation determining their correlation functions. The OPEs
for powers of the local DOS obtained from this equation are in agreement with
available results.Comment: typos corrected, a revised versio
Formalization of Complex Vectors in Higher-Order Logic
Complex vector analysis is widely used to analyze continuous systems in many
disciplines, including physics and engineering. In this paper, we present a
higher-order-logic formalization of the complex vector space to facilitate
conducting this analysis within the sound core of a theorem prover: HOL Light.
Our definition of complex vector builds upon the definitions of complex numbers
and real vectors. This extension allows us to extensively benefit from the
already verified theorems based on complex analysis and real vector analysis.
To show the practical usefulness of our library we adopt it to formalize
electromagnetic fields and to prove the law of reflection for the planar waves.Comment: 15 pages, 1 figur
Invariance of visual operations at the level of receptive fields
Receptive field profiles registered by cell recordings have shown that
mammalian vision has developed receptive fields tuned to different sizes and
orientations in the image domain as well as to different image velocities in
space-time. This article presents a theoretical model by which families of
idealized receptive field profiles can be derived mathematically from a small
set of basic assumptions that correspond to structural properties of the
environment. The article also presents a theory for how basic invariance
properties to variations in scale, viewing direction and relative motion can be
obtained from the output of such receptive fields, using complementary
selection mechanisms that operate over the output of families of receptive
fields tuned to different parameters. Thereby, the theory shows how basic
invariance properties of a visual system can be obtained already at the level
of receptive fields, and we can explain the different shapes of receptive field
profiles found in biological vision from a requirement that the visual system
should be invariant to the natural types of image transformations that occur in
its environment.Comment: 40 pages, 17 figure
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