We study the structure of the energy-momentum tensor of radial excitations of Q-balls in scalar field theories with U(1) symmetry. The obtained numerical results for the 1 ≤ N ≤ 23 excitations allow us to study in detail patterns how the solutions behave with N . We show that although the fields φ(r) and energy-momentum tensor densities exhibit a remarkable degree of complexity, the properties of the solutions scale with N with great regularity. This is to best of our knowledge the first study of the D-term d1 for excited states, and we demonstrate that it is negative -in agreement with results from literature on the d1 of ground state particles.
The D-term is, like mass and spin, a fundamental property related to the energymomentum tensor. Yet it is not known experimentally for any particle. In all theoretical studies so far the D-terms of various particles were found negative. Early works gave rise to the assumption the negative sign could be related to stability. The emerging question is whether it is possible to find a field-theoretical system with a positive D-term. To shed some light on this question we investigate Q-clouds, an extreme parametric limit in the Q-ball system. Q-clouds are classically unstable solutions which delocalize, spread out over all space forming an infinitely dilute gas of free quanta, and are even energetically unstable against tunneling to plane waves. In short, these extremely unstable field configurations provide an ideal candidate system for our purposes. By studying the energy-momentum tensor we show that at any stage of the Q-cloud limit one deals with perfectly well-defined and, when viewed in appropriately scaled coordinates, non-dissipating non-topological solitonic solutions. We investigate in detail their properties, and find new physical interpretations by observing that Q-clouds resemble BPS Skyrmions in certain aspects, and correspond to universal non-perturbative solutions in (complex) |Φ| 4 theory. In particular, we show that also Q-cloud solutions have negative D-terms. Our findings do not prove that D-terms must always be negative. But they indicate that it is unlikely to realize a positive D-term in a consistent physical system.
A non-perturbative approach to the solution of the time-dependent, two-center Dirac equation is presented with a special emphasis on the proper treatment of the potential of the nuclei. In order to account for the full multipole expansion of this potential, we express eigenfunctions of the two-center Hamiltonian in terms of well-known solutions of the "monopole" problem that employs solely the spherically-symmetric part of the interaction. When combined with the coupled-channel method, such a wavefunction-expansion technique allows for an accurate description of the electron dynamics in the field of moving ions for a wide range of internuclear distances. To illustrate the applicability of the proposed approach, the probabilities of the K-as well as L-shell ionization of hydrogen-like ions in the course of nuclear α-decay and slow ion-ion collisions have been calculated.center system at a fixed internuclear distance R. The performance of the coupled-channel methods depends, therefore, on the efficiency of the spectrum generation of the time-independent Hamiltonian at each required R.
We study the energy-momentum tensor of stable, meta-stable and unstable Q-balls in scalar field theories with U(1) symmetry. We calculate properties such as charge, mass, mean square radii and the constant d1 ("D-term") as functions of the phase space angular velocity ω. We discuss the limits when ω approaches the boundaries of the region in which solutions exist, and derive analytical results for the quantities in these limits. The central result of this work is the rigorous proof that d1 is strictly negative for all finite energy solutions in the Q-ball system. We also show that for Q-balls stability is a sufficient, but not necessary, condition for d1 to be negative.
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