Quantum simulations of relativistic quantum physics in circuit QED

We present a scheme for simulating relativistic quantum physics in circuit quantum electrodynamics. By using three classical microwave drives, we show that a superconducting qubit strongly coupled to a resonator field mode can be used to simulate the dynamics of the Dirac equation and Klein paradox in all regimes. Using the same setup we also propose the implementation of the Foldy-Wouthuysen canonical transformation, after which the time derivative of the position operator becomes a constant of the motion.

Birkhoff normal forms for Fourier integral operators II

Iantchenko, A.; Sj?strand, J., (2001) 'Birkhoff normal forms for Fourier integral operators II', American Journal of Mathematics 124(4) pp.817-850 RAE2008

DERIVATION OF THE ENERGY-TIME UNCERTAINTY RELATION

A derivation from first principles is given of the energy-time uncertainty relation in quantum mechanics. A canonical transformation is made in classical mechanics to a new canonical momentum, which is energy E, and a new canonical coordinate T, which is called tempus, conjugate to the energy. Tempus T, the canonical coordinate conjugate to the energy, is conceptually different from the time t in which the system evolves. The Poisson bracket is a canonical invariant, so that energy and tempus satisfy the same Poisson bracket as do p and q. When the system is quantized, we find the energy-time uncertainty relation DELTAEDELTAT greater-than-or-equal-to HBAR/2. For a conservative system the average of the tempus operator T is the time t plus a constant. For a free particle and a particle acted on by a constant force, the tempus operators are constructed explicitly, and the energy-time uncertainty relation is explicitly verified.

Analytical attitude propagation with non-singular variables and gravity gradient torque for spin stabilized satellite

An analytical approach for the spin stabilized satellite attitude propagation is presented using the non-singular canonical variables to describe the rotational motion. Two sets of variables were introduced for Fukushima in 1994 by a canonical transformation and they are useful when the angle between z-satellite axis of a coordinate system fixed in artificial satellite and the rotational angular momentum vector is zero or when the angle between Z-equatorial axis and rotation angular momentum vector is zero. Analytical solutions for rotational motion equations and torque-free motion are discussed in terms of the elliptic functions and by the application of some simplification to get an approximated solution. These solutions are compared with a numerical solution and the results show a good agreement for many rotation periods. When the mean Hamiltonian associated with the gravity gradient torque is included, an analytical solution is obtained by the application of the successive approximations' method for the satellite in an elliptical orbit. These solutions show that the magnitude of the rotation angular moment is not affected by the gravity gradient torque but this torque causes linear and periodic variations in the angular variables, long and short periodic variations in Z-equatorial component of the rotation angular moment and short periodic variations in x-satellite component of the rotation angular moment. The goal of this analysis is to emphasize the geometrical and physical meaning of the non-singular variables and to validate the approximated analytical solution for the rotational motion without elliptic functions for a non-symmetrical satellite. The analysis can be applied for spin stabilized satellite and in this case the general solution and the approximated solution are coincidence. Then the results can be used in analysis of the space mission of the Brazilian Satellites. (C) 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.

New remarks on the linear constraint self-dual boson and Wess-Zumino terms

In this work we prove in a precise way that the soldering formalism can be applied to the Srivastava chiral boson (SCB), in contradiction with some results appearing in the literature. We promote a canonical transformation that shows directly that the SCB is composed of two Floreanini-Jackiw particles with the same chirality in which the spectrum is a vacuumlike one. As another conflicting result, we prove that a Wess-Zumino (WZ) term used in the literature consists of a scalar field, once again denying the assertion that the WZ term adds a new degree of freedom to the SCB theory in order to modify the physics of the system. © 2001 The American Physical Society.

Variáveis canônicas não singulares e o movimento rotacional de satélites artificiais

Pós-graduação em Física - FEG

Estudo clássico completo do formalismo de Hamilton-Jacobi

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Formal description, compression and transformation of digital pictures

This paper describes the application of vector spaces over Galois fields, for obtaining a formal description of a picture in the form of a very compact, non-redundant, unique syntactic code. Two different methods of encoding are described. Both these methods consist in identifying the given picture as a matrix (called picture matrix) over a finite field. In the first method, the eigenvalues and eigenvectors of this matrix are obtained. The eigenvector expansion theorem is then used to reconstruct the original matrix. If several of the eigenvalues happen to be zero this scheme results in a considerable compression. In the second method, the picture matrix is reduced to a primitive diagonal form (Hermite canonical form) by elementary row and column transformations. These sequences of elementary transformations constitute a unique and unambiguous syntactic code-called Hermite code—for reconstructing the picture from the primitive diagonal matrix. A good compression of the picture results, if the rank of the matrix is considerably lower than its order. An important aspect of this code is that it preserves the neighbourhood relations in the picture and the primitive remains invariant under translation, rotation, reflection, enlargement and replication. It is also possible to derive the codes for these transformed pictures from the Hermite code of the original picture by simple algebraic manipulation. This code will find extensive applications in picture compression, storage, retrieval, transmission and in designing pattern recognition and artificial intelligence systems.

Context dependent non canonical WNT signaling mediates activation of fibroblasts by transforming growth factor-beta

Actions of transforming growth factor-beta are largely context dependent. For instance, TGF-beta is growth inhibitory to epithelial cells and many tumor cell-lines while it stimulates the growth of mesenchymal cells. TGF-beta also activates fibroblast cells to a myofibroblastic phenotype. In order to understand how the responsiveness of fibroblasts to TGF-beta would change in the context of transformation, we have compared the differential gene regulation by TGF-beta in immortal fibroblasts (hFhTERT), transformed fibroblasts (hFhTERT-LTgRAS) and a human fibrosarcoma cell-line (HT1080). The analysis revealed regulation of 6735, 4163, and 3478 probe-sets by TGF-beta in hFhTERT, hFhTERT-LTgRAS and HT1080 cells respectively. Intriguingly, 5291 probe-sets were found to be either regulated in hFhTERT or hFhTERT-LTgRAS cells while 2274 probe-sets were regulated either in hFhTERT or HT1080 cells suggesting that the response of immortal hFhTERT cells to TGF-beta is vastly different compared to the response of both the transformed cells hFhTERT-LTgRAS and HT1080 to TGF-beta. Strikingly, WNT pathway showed enrichment in the hFhTERT cells in Gene Set Enrichment Analysis. Functional studies showed induction of WNT4 by TGF-beta in hFhTERT cells and TGF-beta conferred action of these cells was mediated by WNT4. While TGF-beta activated both canonical and non-canonical WNT pathways in hFhTERT cells, Erk1/2 and p38 Mitogen Activated Protein Kinase pathways were activated in hFhTERT-LTgRAS and HT1080 cells. This suggests that transformation of immortal hFhTERT cells by SV40 large T antigen and activated RAS caused a switch in their response to TGF-beta which matched with the response of HT1080 cells to TGF-beta. These data suggest context dependent activation of non-canonical signaling by TGF-beta. (C) 2015 Published by Elsevier Inc.

BRST quantization and canonical Ward identity of the supersymmetric electromagnetic interaction system

According to the method of path integral quantization for the canonical constrained system in Becchi-Rouet-Stora-Tyutin scheme, the supersymmetric electromagnetic interaction system was quantized. Both the Hamiltonian of the supersymmetric electromagnetic interaction system in phase space and the quantization procedure were simplified. The BRST generator was constructed, and the BRST transformations of supersymmetric fields were gotten; the effective action was calculated, and the generating functional for the Green function was achieved; also, the gauge generator was constructed, and the gauge transformation of the system was obtained. Finally, the Ward-Takahashi identities based on the canonical Noether theorem were calculated, and two relations between proper vertices and propagators were obtained.

Canonical description of the perspective projections

A unique parameterization of the perspective projections in all whole-numbered dimensions is reported. The algorithm for generating a perspective transformation from parameters and for recovering parameters from a transformation is a modification of the Givens orthogonalization algorithm. The algorithm for recovering a perspective transformation from a perspective projection is a modification of Roberts' classical algorithm. Both algorithms have been implemented in Pop-11 with call-out to the NAG Fortran libraries. Preliminary monte-carlo tests show that the transformation algorithm is highly accurate, but that the projection algorithm cannot recover magnitude and shear parameters accurately. However, there is reason to believe that the projection algorithm might improve significantly with the use of many corresponding points, or with multiple perspective views of an object. Previous parameterizations of the perspective transformations in the computer graphics and computer vision literature are discussed.

MODELING THE EVOLUTION OF COMPLEX NETWORKS THROUGH THE PATH-STAR TRANSFORMATION AND OPTIMAL MULTIVARIATE METHODS

The topology of real-world complex networks, such as in transportation and communication, is always changing with time. Such changes can arise not only as a natural consequence of their growth, but also due to major modi. cations in their intrinsic organization. For instance, the network of transportation routes between cities and towns ( hence locations) of a given country undergo a major change with the progressive implementation of commercial air transportation. While the locations could be originally interconnected through highways ( paths, giving rise to geographical networks), transportation between those sites progressively shifted or was complemented by air transportation, with scale free characteristics. In the present work we introduce the path-star transformation ( in its uniform and preferential versions) as a means to model such network transformations where paths give rise to stars of connectivity. It is also shown, through optimal multivariate statistical methods (i.e. canonical projections and maximum likelihood classification) that while the US highways network adheres closely to a geographical network model, its path-star transformation yields a network whose topological properties closely resembles those of the respective airport transportation network.

An extended Weyl-Wigner transformation for special finite spaces

We extend the Weyl-Wigner transformation to those particular degrees of freedom described by a finite number of states using a technique of constructing operator bases developed by Schwinger. Discrete transformation kernels are presented instead of continuous coordinate-momentum pair system and systems such as the one-dimensional canonical continuous coordinate-momentum pair system and the two-dimensional rotation system are described by special limits. Expressions are explicitly given for the spin one-half case. © 1988.