Phase Space Geometry in Classical and Quantum Mechanics

Phase space is the state space of classical mechanics, and this manifold is normally endowed only with a symplectic form. The geometry of quantum mechanics is necessarily more complicated. Arguments will be given to show that augmenting the symplectic manifold of classical phase space with a Riemannian metric is sufficient for describing quantum mechanics. In particular, using such spaces, a fully satisfactory geometric version of quantization will be developed and described.Comment: LaTeX, 16 pages, no figure

Dynamics as Shadow of Phase Space Geometry

Starting with the generally well accepted opinion that quantizing an arbitrary Hamiltonian system involves picking out some additional structure on the classical phase space (the {\sl shadow} of quantum mechanics in the classical theory), we describe classical as well as quantum dynamics as a purely geometrical effect by introducing a {\sl phase space metric structure}. This produces an ${\cal O}(\hbar)$ modification of the classical equations of motion reducing at the same time the quantization of an arbitrary Hamiltonian system to standard procedures. Our analysis is carried out in analogy with the adiabatic motion of a charged particle in a curved background (the additional metric structure) under the influence of a universal magnetic field (the classical symplectic structure). This allows one to picture dynamics in an unusual way, and reveals a dynamical mechanism that produces the selection of the right set of physical quantum states.Comment: LaTeX (epsfig macros), 30 pages, 1 figur

Single-hole dynamics in the half-filled two-dimensional Kondo-Hubbard model

We consider the Kondo lattice model in two dimensions at half filling. In addition to the fermionic hopping integral $t$ and the superexchange coupling $J$ the role of a Coulomb repulsion $U$ in the conduction band is investigated. We find the model to display a magnetic order-disorder transition in the U-J plane with a critical value of J_c which is decreasing as a function of U. The single particle spectral function A(k,w) is computed across this transition. For all values of J > 0, and apart from shadow features present in the ordered state, A(k,w) remains insensitive to the magnetic phase transition with the first low-energy hole states residing at momenta k = (\pm \pi, \pm \pi). As J -> 0 the model maps onto the Hubbard Hamiltonian. Only in this limit, the low-energy spectral weight at k = (\pm \pi, \pm \pi) vanishes with first electron removal-states emerging at wave vectors on the magnetic Brillouin zone boundary. Thus, we conclude that (i) the local screening of impurity spins determines the low energy behavior of the spectral function and (ii) one cannot deform continuously the spectral function of the Mott-Hubbard insulator at J=0 to that of the Kondo insulator at J > J_c. Our results are based on both, T=0 Quantum Monte-Carlo simulations and a bond-operator mean-field theory.Comment: 8 pages, 7 figures. Submitted to PR

An approach for Shadow Detection and Removal based on Multiple Light Sources

Shadows in images are essential but sometimes unwanted as they can decline the result of computer vision algorithms. A shadow is obtained by the interaction of light with objects in an image surface. Shadows may letdown the image analysis processes and also cause a poor quality of information which in turn leads to problems in execution of algorithms. In this paper, a method has been proposed to detect and remove the shadows where multiple sources of light is been estimated, as we can take an example of playground stadium where multiple floodlights are fixed, multiple shadows can be observed originating from each of the targets. To successfully track individual target, it is essential to achieve an accurate image of the foreground. Also, an effort has been done to list some of the very crucial techniques related to shadow detection and removal. Many times, the shadow of the background information is merged with the foreground object and makes the process more complex. DOI: 10.17762/ijritcc2321-8169.150517

Mask-ShadowGAN: Learning to Remove Shadows from Unpaired Data

This paper presents a new method for shadow removal using unpaired data, enabling us to avoid tedious annotations and obtain more diverse training samples. However, directly employing adversarial learning and cycle-consistency constraints is insufficient to learn the underlying relationship between the shadow and shadow-free domains, since the mapping between shadow and shadow-free images is not simply one-to-one. To address the problem, we formulate Mask-ShadowGAN, a new deep framework that automatically learns to produce a shadow mask from the input shadow image and then takes the mask to guide the shadow generation via re-formulated cycle-consistency constraints. Particularly, the framework simultaneously learns to produce shadow masks and learns to remove shadows, to maximize the overall performance. Also, we prepared an unpaired dataset for shadow removal and demonstrated the effectiveness of Mask-ShadowGAN on various experiments, even it was trained on unpaired data.Comment: Accepted to ICCV 201