Search results for "Invariant"

Topological Hamiltonian as an exact tool for topological invariants

2012

We propose the concept of `topological Hamiltonian' for topological insulators and superconductors in interacting systems. The eigenvalues of topological Hamiltonian are significantly different from the physical energy spectra, but we show that topological Hamiltonian contains the information of gapless surface states, therefore it is an exact tool for topological invariants.

Λ(1405) resonance as a superposition of two states

2008

Chiral unitarity models have shown the existence of two states with the same quantum numbers in the vicinity of the Λ(1405), both contributing to the final experimental invariant mass distribution. The K − p → π 0 π 0 Σ 0 reaction, discussed in detail in this work, gives maximal possible weight to the second Λ(1405) state, which is narrower and of higher energy than the nominal Λ(1405). The calculated distribution of π 0 Σ 0 states forming the Λ(1405) is in agreement with a recent experimental data, and shows a peak at 1420 MeV and a relatively narrow width of Γ = 38 MeV. In contrast, the π − p → K 0 πΣ reaction gives more weight to the pole at lower energy and with a larger width. The data…

U(N) invariant dynamics for a simplified loop quantum gravity model

2011

The implementation of the dynamics in Loop Quantum Gravity (LQG) is still an open problem. Here, we discuss a tentative dynamics for the simplest class of graphs in LQG: Two vertices linked with an arbitrary number of edges. We use the recently introduced U(N) framework in order to construct SU(2) invariant operators and define a global U(N) symmetry that will select the homogeneous/isotropic states. Finally, we propose a Hamiltonian operator invariant under area-preserving deformations of the boundary surface and we identify possible connections of this model with Loop Quantum Cosmology.

Central region in relativistic heavy ion collisions; results from hydrodynamic calculations and cascade simulation

1988

Results of three dimensional hydrodynamic calculations with boost invariant longitudinal expansion are presented with special emphasis on the transverse momentum spectra of hadrons and production rates of dileptons. The effect and signatures of transverse collective motion are discussed in detail. The hydrodynamic results which are based on the assumption of the existence of a first order phase transition and formation of an equilibrium mixed phase are compared with cascade simulation where the mixed phase is modelled in terms of plasma droplets embedded in a pion gas. The comparison shows a great deal of similarity between the two approaches lending further support for the hydrodynamic app…

2014

We investigate the performance of different control techniques for ion transport in state-of-the-art segmented miniaturized ion traps. We employ numerical optimization of classical trajectories and quantum wavepacket propagation as well as analytical solutions derived from invariant based inverse engineering and geometric optimal control. We find that accurate shuttling can be performed with operation times below the trap oscillation period. The maximum speed is limited by the maximum acceleration that can be exerted on the ion. When using controls obtained from classical dynamics for wavepacket propagation, wavepacket squeezing is the only quantum effect that comes into play for a large ra…

Type I vacuum solutions with aligned Papapetrou fields: an intrinsic characterization

2003

We show that Petrov type I vacuum solutions admitting a Killing vector whose Papapetrou field is aligned with a principal bivector of the Weyl tensor are the Kasner and Taub metrics, their counterpart with timelike orbits and their associated windmill-like solutions, as well as the Petrov homogeneous vacuum solution. We recover all these metrics by using an integration method based on an invariant classification which allows us to characterize every solution. In this way we obtain an intrinsic and explicit algorithm to identify them.

On the invariant symmetries of the D-metrics

2007

We analyze the symmetries and other invariant qualities of the $\mathcal{D}$-metrics (type D aligned Einstein Maxwell solutions with cosmological constant whose Debever null principal directions determine shear-free geodesic null congruences). We recover some properties and deduce new ones about their isometry group and about their quadratic first integrals of the geodesic equation, and we analyze when these invariant symmetries characterize the family of metrics. We show that the subfamily of the Kerr-NUT solutions are those admitting a Papapetrou field aligned with the Weyl tensor.

A duality-invariant Einstein-Planck relation and its consequences on micro-black holes.

2013

We discuss the consequences of a duality-invariant Einstein–Planck (DIEP) relation on the equation of state of micro black holes. The results are analogous to those obtained from the "world-crystal" model, but with some significative differences, as for instance a limiting vanishing value for temperature for very small black holes. The model leads to a total evaporation of micro black holes but with the final stage being very slow.

Feynman-diagramme als vektorsysteme invariantentheoretisch behandelt (compton-streuung, elektron-positron-vernichtung

1985

Employing a special contact transformation devised by S. Lie, which takes spheres into lines, we interpret the Feynman diagrams of photon electron scattering in terms of vector systems. This gives a nice kinematic model of Compton scattering. We further compute in detail the transition probabilities of the Compton scattering process by making use of the calculus of chains of complexes from classical invariant theory rather than applying the usual Dirac-matrix technique. In the final paragraph of this paper an application of our calculations to the treatment of myon decay is indicated.

Quasienergy states of trapped ions

2000

The quantum models for a single trapped ion are extended to the description of the collective dynamics for systems of ions confined in quadrupole electromagnetic traps with cylindrical symmetry. A class of quantum Hamiltonians with suitable axial and radial interaction potentials given by homogeneous functions of degree (-2) and invariant under translations and axial rotations are introduced. The considered axial and radial quantum Hamiltonians for the center-of-mass and relative motions are described by collective dynamical systems associated to the symplectic group \(\). Discrete quasienergy spectra are obtained and the corresponding quasienergy states are explicitly realized as \(\) cohe…