There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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Principles Of Optics Electromagnetic Theory Of Propagation Interference And Diffraction Of Light

In the real world, a realistic setting for computer vision or multimedia recognition problems is that we have some classes containing lots of training data and many classes contain a small amount of training data. Therefore, how to use frequent classes to help learning rare classes for which it is harder to collect the training data is an open question. Learning with Shared Information is an emerging topic in machine learning, computer vision and multimedia analysis. There are different level of components that can be shared during concept modeling and machine learning stages, such as sharing generic object parts, sharing attributes, sharing transformations, sharing regularization parameters and sharing training examples, etc. Regarding the specific methods, multi-task learning, transfer learning and deep learning can be seen as using different strategies to share information. These learning with shared information methods are very effective in solving real-world large-scale problems. This special issue aims at gathering the recent advances in learning with shared information methods and their applications in computer vision and multimedia analysis. Both state-of-the-art works, as well as literature reviews, are welcome for submission. Papers addressing interesting real-world computer vision and multimedia applications are especially encouraged. Topics of interest include, but are not limited to:  • Multi-task learning or transfer learning for large-scale computer vision and multimedia analysis • Deep learning for large-scale computer vision and multimedia analysis • Multi-modal approach for large-scale computer vision and multimedia analysis • Different sharing strategies, e.g., sharing generic object parts, sharing attributes, sharing transformations, sharing regularization parameters and sharing training examples, • Real-world computer vision and multimedia applications based on learning with shared information, e.g., event detection, object recognition, object detection, action recognition, human head pose estimation, object tracking, location-based services, semantic indexing. • New datasets and metrics to evaluate the benefit of the proposed sharing ability for the specific computer vision or multimedia problem. • Survey papers regarding the topic of learning with shared information.  Authors who are unsure whether their planned submission is in scope may contact the guest editors prior to the submission deadline with an abstract, in order to receive feedback.

IEEE transactions on pattern analysis and machine intelligence

Course Description This is an advanced course in which we explore the field of Statistical Optics. Topics covered include such subjects as the statistical properties of natural (thermal) and laser light, spatial and temporal coherence, effects of partial coherence on optical imaging instruments, effects on imaging due to randomly inhomogeneous media, and a statistical treatment of the detection of light. Development of this more comprehensive model of the behavior of light draws upon the use of tools traditionally available to the electrical engineer, such as linear system theory and the theory of stochastic processes.

http://ieeexplore.ieee.org/iel5/3/23094/01073023.pdf

Statistical optics

A possible sighting of Majorana states Nearly 80 years ago, the Italian physicist Ettore Majorana proposed the existence of an unusual type of particle that is its own antiparticle, the so-called Majorana fermion. The search for a free Majorana fermion has so far been unsuccessful, but bound Majorana-like collective excitations may exist in certain exotic superconductors. Nadj-Perge et al. created such a topological superconductor by depositing iron atoms onto the surface of superconducting lead, forming atomic chains (see the Perspective by Lee). They then used a scanning tunneling microscope to observe enhanced conductance at the ends of these chains at zero energy, where theory predicts Majorana states should appear. Science, this issue p. 602; see also p. 547 Scanning tunneling microscopy is used to observe signatures of Majorana states at the ends of iron atom chains. [Also see Perspective by Lee] Majorana fermions are predicted to localize at the edge of a topological superconductor, a state of matter that can form when a ferromagnetic system is placed in proximity to a conventional superconductor with strong spin-orbit interaction. With the goal of realizing a one-dimensional topological superconductor, we have fabricated ferromagnetic iron (Fe) atomic chains on the surface of superconducting lead (Pb). Using high-resolution spectroscopic imaging techniques, we show that the onset of superconductivity, which gaps the electronic density of states in the bulk of the Fe chains, is accompanied by the appearance of zero-energy end-states. This spatially resolved signature provides strong evidence, corroborated by other observations, for the formation of a topological phase and edge-bound Majorana fermions in our atomic chains.

/pdf/observation-of-majorana-fermions-in-ferromagnetic-atomic-5451hode2h.pdf

Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor

We introduce a general and systematic theoretical framework for operational dynamic modeling (ODM) by combining a kinematic description of a model with the evolution of the dynamical average values. The kinematics includes the algebra of the observables and their defined averages. The evolution of the average values is drawn in the form of Ehrenfest-like theorems. We show that ODM is capable of encompassing wide-ranging dynamics from classical non-relativistic mechanics to quantum field theory. The generality of ODM should provide a basis for formulating novel theories.

Operational dynamic modeling transcending quantum and classical mechanics.

Realistic models of quantum systems must include dissipative interactions with a thermal environment. For weakly-damped systems, while the Lindblad-form Markovian master equation is invaluable for this task, it applies only when the frequencies of any subset of the system’s transitions are degenerate, or their differences are much greater than the transitions’ linewidths. Outside of these regimes the only available efficient description has been the Bloch–Redfield master equation, the efficacy of which has long been controversial due to its failure to guarantee the positivity of the density matrix. The ability to efficiently simulate weakly-damped systems across all regimes is becoming increasingly important, especially in quantum technologies. Here we solve this long-standing problem by deriving a Lindblad-form master equation for weakly-damped systems that is accurate for all regimes. We further show that when this master equation breaks down, so do all time-independent Markovian equations, including the B-R equation. We thus obtain a replacement for the B-R equation for thermal damping that is no less accurate, simpler in structure, completely positive, allows simulation by efficient quantum trajectory methods, and unifies the previous Lindblad master equations. We also show via exact simulations that the new master equation can describe systems in which slowly-varying transition frequencies cross each other during the evolution. System identification tools, developed in systems engineering, play an important role in our analysis. We expect these tools to prove useful in other areas of physics involving complex systems.

/pdf/accurate-lindblad-form-master-equation-for-weakly-damped-10jmlafqok.pdf

Accurate Lindblad-form master equation for weakly damped quantum systems across all regimes

Upon revisiting the Hamiltonian structure of classical wavefunctions in Koopman-von Neumann theory, this paper addresses the long-standing problem of formulating a dynamical theory of classical-quantum coupling. The proposed model not only describes the influence of a classical system onto a quantum one, but also the reverse effect -- the quantum backreaction. These interactions are described by a new Hamiltonian wave equation overcoming shortcomings of currently employed models. For example, the density matrix of the quantum subsystem is always positive-definite. While the Liouville density of the classical subsystem is generally allowed to be unsigned, its sign is shown to be preserved in time for a specific infinite family of hybrid classical-quantum systems. The proposed description is illustrated and compared with previous theories using the exactly solvable model of a degenerate two-level quantum system coupled to a classical harmonic oscillator.

Koopman wavefunctions and classical-quantum correlation dynamics

We demonstrate that the Wigner function of a pure quantum state is a wave function in a specially tuned Dirac bra-ket formalism and argue that the Wigner function is in fact a probability amplitude for the quantum particle to be at a certain point of the classical phase space. Additionally, we establish that in the classical limit, the Wigner function transforms into a classical Koopman-von Neumann wave function rather than into a classical probability distribution. Since probability amplitude need not be positive, our findings provide an alternative outlook on the Wigner function's negativity.

Wigner phase-space distribution as a wave function

The Wigner function is a useful tool for exploring the transition between quantum and classical dynamics, as well as the behavior of quantum chaotic systems. Evolving the Wigner function for open systems has proved challenging, however; a variety of methods have been devised but suffer from being cumbersome and resource intensive. Here we present an efficient fast-Fourier method for evolving the Wigner function that has a complexity of $O(NlogN)$ where $N$ is the size of the array storing the Wigner function. The efficiency, stability, and simplicity of this method allows us to simulate open-system dynamics previously thought to be prohibitively expensive. As a demonstration we simulate the dynamics of both one-particle and two-particle systems under various environmental interactions. For a single particle we also compare the resulting evolution with that of the classical Fokker--Planck and Koopman--von Neumann equations and show that the environmental interactions induce the quantum-to-classical transition as expected. In the case of two interacting particles we show that an environment interacting with one of the particles leads to the loss of coherence of the other.

Denys I. Bondar

Papers

Operational dynamic modeling transcending quantum and classical mechanics.

Accurate Lindblad-form master equation for weakly damped quantum systems across all regimes

Koopman wavefunctions and classical-quantum correlation dynamics

Wigner phase-space distribution as a wave function

Efficient method to generate time evolution of the Wigner function for open quantum systems