Search results for "integral"

Mean field methods in large amplitude nuclear collective motion

1984

The time dependent Hartree-Fock method (TDHF) is reviewed and its success and failure are discussed. It is demonstrated that TDHF is a semiclassical theory which is basically able to describe the time evolution of one-body operators, the energy loss in inclusive deep inelastic collisions, and fusion reactions above the Coulomb barrier. For genuine quantum mechanical processes as e.g. spontaneous fission, subbarrier fusion, phase shifts and the description of bound vibrations, the quantized adiabatic time dependent Hartree-Fock theory (quantized ATDHF) is suggested and reviewed. Realistic three-dimensional calculations for heavy ion systems of A1+A2<32 are presented. Applications to various …

Time-optimal selective pulses of two uncoupled spin-1/2 particles

2018

We investigate the time-optimal solution of the selective control of two uncoupled spin 1/2 particles. Using the Pontryagin Maximum Principle, we derive the global time-optimal pulses for two spins with different offsets. We show that the Pontryagin Hamiltonian can be written as a one-dimensional effective Hamiltonian. The optimal fields can be expressed analytically in terms of elliptic integrals. The time-optimal control problem is solved for the selective inversion and excitation processes. A bifurcation in the structure of the control fields occurs for a specific offset threshold. In particular, we show that for small offsets, the optimal solution is the concatenation of regular and sin…

Power-law running of the effective gluon mass

2007

The dynamically generated effective gluon mass is known to depend non-trivially on the momentum, decreasing sufficiently fast in the deep ultraviolet, in order for the renormalizability of QCD to be preserved. General arguments based on the analogy with the constituent quark masses, as well as explicit calculations using the operator-product expansion, suggest that the gluon mass falls off as the inverse square of the momentum, relating it to the gauge-invariant gluon condensate of dimension four. In this article we demonstrate that the power-law running of the effective gluon mass is indeed dynamically realized at the level of the non-perturbative Schwinger-Dyson equation. We study a gauge…

Foundations of the Quantum Chromodynamics

2015

Quantum chromodynamics (QCD) is a theory to describe the strong interaction in hadrons. It was developed in the history of understanding the structure of the hadrons. In the 1950s, a large number of hadrons were discovered in experiments.

Erratum to: Classical and Quantum Dynamics: From Classical Paths to Path Integrals

2017

Propagators for Particles in an External Magnetic Field

2001

In order to describe the propagation of a scalar particle in an external potential, we begin again with the path integral $$ K(r',t';r,0) = \int_{r,(0)}^{r',(t')} {[dr(t)]} \exp \left\{ {\frac{{\text{i}}} {\hbar }S[r(t)]} \right\} $$ (1) with $$ S[r(t)] = \int_0^{t'} {dt} L(r,\dot r). $$

On Green's function for cylindrically symmetric fields of polarized radiation

2009

Analytic expressions for Green's function describing the process of transfer of polarized radiation in homogeneous isotropic infinite medium in case of cylindrical symmetry and nonconservative scattering are obtained. The solution is based on the set of systems of Abel integral equations of the first kind obtained using the principle of superposition, and the known expression of Green's function for radiation fields with plane-parallel symmetry. Eigenvalue decompositions for the corresponding matrices of generalized spherical functions are found. Using this result the systems of Abel integral equations are diagonalized, and the final solution is obtained.

JEM-X observations of the Be/X-ray binary EXO 2030+375

2003

We have used data from the Joint European Monitor (JEM-X) to perform an X-ray spectral and timing analysis of the 42-s transient pulsar EXO 2030+375 during an X-ray outburst. X-ray pulsations are clearly detected with an average pulse period of 41:66 +- 0:05 s and an average pulse fraction of 60%. The profile of the energy spectrum did not change appreciably throughout the X-ray outburst, although the source shows a slightly softer spectrum during periastron passage in the energy range 9–25 keV. The 5–25 keV X-ray luminosity changed by a factor of 2 throughout the observations, reaching a maximum value of 3x10^36 erg s^−1. These observations allowed us to verify the in-flight instrumental p…

Analysis of Cylindrical Dielectric Resonators in Rectangular Cavities Using a State-Space Integral-Equation Method

2006

In this letter, a state-space integral-equation method in the s-domain has been employed for the accurate analysis of rectangular cavities loaded with cylindrical dielectric resonators. The dielectric obstacles have been treated in terms of their polarization equivalent charge and current densities. The dielectric resonator can be placed at any arbitrary position inside the cavity. The presented technique allows to calculate in a very efficient way a large number of solenoidal modes. The resonant frequencies of dielectric-loaded cavities are calculated and compared with data from literature and a commercial finite element method software, showing a good agreement

Quantum Spin-Tunneling:A Path Integral Approach

1995

We investigate the quantum tunneling of a large spin in a crystal field and an external magnetic field. The twofold degeneracy of the corresponding classical ground state is removed due to tunneling. The tunnel splitting ΔE o of the ground state is calculated by use of a path integral formalism. It is shown that coherent spin state path integrals do not yield a reasonable result. However a “bosonlzation” of the spin system yields excellent results in the semiclassical limit. This result follows from the coherent spin state approach from replacing the spin quantum number s by s + 1/2 which causes a renormalization of the preexponential factor of ΔE o .