Computational study of impulsively generated standing slow acoustic waves in a solar coronal loop

We numerically investigated standing slow acoustic waves impulsively excited in a solar coronal loop by gas pressure and mass density perturbations in one-dimensional space. The corresponding computer model is described by the hydrodynamic equations that are solved numerically by means of the so-called flux limiters methods on uniformly structured mesh. We discuss the fundamental mode and the first harmonic mode which are generated in dependence on position of the initial perturbation in the numerical box. We show how the standing slow acoustic waves are generated in the corona, where they are trapped in space between two dense layers as in the resonator, and how their energy leaks from the corona to the dense layers. We found that this leakage increases with the decrease of the density jump at the transition region. We also studied the case when the perturbation is initiated at the transition region. We found that even in this case the standing wave is formed, but their energetics is influenced by the evaporation of the plasma from the transition region into the corona.     

Conformal transformations and conformal invariance in gravitation

Conformal transformations are frequently used tools in order to study relations between various theories of gravity and Einstein's general relativity theory. In this paper we discuss the rules of these transformations for geometric quantities as well as for the matter energy‐momentum tensor. We show the subtlety of the matter energy‐momentum conservation law which refers to the fact that the conformal transformation “creates” an extra matter term composed of the conformal factor which enters the conservation law. In an extreme case of the flat original spacetime the matter is “created” due to work done by the conformal transformation to bend the spacetime which was originally flat. We discuss how to construct the conformally invariant gravity theories and also find the conformal transformation rules for the curvature invariants R², R_abR^ab, R_abcdR^abcd and the Gauss‐Bonnet invariant in a spacetime of an arbitrary dimension. Finally, we present the conformal transformation rules in the fashion of the duality transformations of the superstring theory. In such a case the transitions between conformal frames reduce to a simple change of the sign of a redefined conformal factor.     

Finite Nilpotent BRST Transformations in Hamiltonian Formulation

We consider the finite field dependent BRST (FFBRST) transformations in the context of Hamiltonian formulation using Batalin-Fradkin-Vilkovisky method. The non-trivial Jacobian of such transformations is calculated in extended phase space. The contribution from Jacobian can be written as exponential of some local functional of fields which can be added to the effective Hamiltonian of the system. Thus, FFBRST in Hamiltonian formulation with extended phase space also connects different effective theories. We establish this result with the help of two explicit examples. We also show that the FFBRST transformations is similar to the canonical transformations in the sector of Lagrange multiplier and its corresponding momenta.     

Finsler gauge transformations and general relativity

The theory of gauge transformations in Finsler space is applied to general relativity. It is seen that the transformations produce new metrics which correspond to the introduction of physical fields. The geodesic equation in the transformed space is equivalent to the equation of motion in the original space where the field is included by a force term. An example is given of a transformation and resulting metric in which the electromagnetic potential is related to parameters of the gauge transformation rather than to gauge potentials. This implies that the electromagnetic field corresponds to a connection instead of a curvature. Another example is given which shows how Weyl or conformal transformations are related to a class of the gauge transformations.     

Anomalous high-energy spin excitations in the high-Tc superconductor-parent antiferromagnet La₂CuO₄

Inelastic neutron scattering is used to investigate the collective magnetic excitations of the high-temperature superconductor-parent antiferromagnet La2CuO4. We find that while the lower energy excitations are well described by spin-wave theory, including one- and two-magnon scattering processes, the high-energy spin waves are strongly damped near the (1/2, 0) position in reciprocal space and merge into a momentum dependent continuum. This anomalous damping indicates the decay of spin waves into other excitations, possibly unbound spinon pairs.     

Squeezed magnetobipolarons in two-dimensional quantum dot

In this Letter, a different method was given for calculating the energies of the magnetobipolarons confined in a parabolic QD (quantum dot). We introduced single-mode squeezed states transformation, which are based on the Lee-Low-Pines and Huybrechts (LLP-H) canonical transformations. This method can provide results not only for the ground state energy but also for the excited states energies. Moreover, it can be applied to the entire range of the electron-phonon coupling strength. Comparing with the results of the LLP-H transformations, we have obtained more accurate results for the ground state energy, excited states energies and binding energy of the bipolarons. It shows that the magnetic field and the quantum dot can facilitate the formation of the bipolarons when η is smaller than some value.     

Relativistic aberrations in quantum phase space

A phase space treatment of special relativity of quantum systems is developed. In this approach a quantum particle remains localized if subject to inertial transformations, the localization occurring in a finite phase space area. Unlike in the non-relativistic case, relativistic transformations generally distort the phase space distribution function, being equivalent to aberrations in optics. The relativistic aberrations of massive particles are in general different from those of optical images.     

Dispersion and uncertainty in multislit matter wave diffraction

We show that single and multislit experiments involving matter waves may be constructed to assess dispersively generated correlations between the position and momentum of a single free particle. These correlations give rise to position dependent phases which develop dynamically as a result of dispersion and may play an important role in the interference patterns. To the extent that initial transverse coherence is preserved throughout the proposed diffraction setup, such interference patterns are noticeably different from those of a classical dispersion free wave.     

The derivation and solution of the modal flux equations for backscattering in a duct in the presence of random space and time fluctuations

Abstract

In this paper we first derive the equations governing the energy fluxes propagating in each of the modes of a duct. In each mode there is a forward and backward component and the equations are intended to treat ducts in which backscattering plays a major role. The modal fluxes are coupled since there is transfer of energy between the modes that occurs as a result of random time and space sound-speed fluctuations in the medium in the duct. Since the fluctuations are both space and time dependent the governing equations are radiation transport equations. This is not the case if the fluctuations depend only on space. The basic method is to develop a coupled set of equations for the energy spectra in the modes and then to integrate over the frequency to obtain the fluxes. In the second section of this paper the modal flux equations are solved. A numerical result is presented to show how energy is transferred between modes. It is also shown how the reflected energy varies as a function of duct length.     

Equivalence of model space techniques and the renormalization group for a separable model problem

Lee–Suzuki similarity transformations and Krenciglowa–Kuo folded diagrams are two common methods used to derive energy independent model space effective interactions for nuclear many-body systems. We demonstrate that these two methods are equivalent to a Renormalization Group (RG) analysis of a well-studied problem in quantum mechanics. The effective low-momentum potentials V_eff obtained from model space methods are shown to obey the same scaling equation for V_eff that RG arguments predict. This indicates that model space methods might be of interest to those studying low-energy nuclear physics using Effective Field Theories (EFT). We find the new result that all of the different energy independent model space techniques yield a unique low-momentum V_eff when applied to the toy model under consideration.     

The spacetime of double field theory: Review,remarks, and outlook

We review double field theory (DFT) with emphasis on the doubled spacetime and its generalized coordinate transformations, which unify diffeomorphisms and b‐field gauge transformations. We illustrate how the composition of generalized coordinate transformations fails to associate. Moreover, in dimensional reduction, the O(d,d) T‐duality transformations of fields can be obtained as generalized diffeomorphisms. Restricted to a half‐dimensional subspace, DFT includes ‘generalized geometry’, but is more general in that local patches of the doubled space may be glued together with generalized coordinate transformations. Indeed, we show that for certain T‐fold backgrounds with non‐geometric fluxes, there are generalized coordinate transformations that induce, as gauge symmetries of DFT, the requisite O(d,d;ℤ) monodromy transformations. Finally we review recent results on the α^′ extension of DFT which, reduced to the half‐dimensional subspace, yields intriguing modifications of the basic structures of generalized geometry.     

Floquet states and geometrical phase of a multi-level system in cyclic evolution

We study the electronic states of a mesoscopic system whose Hamiltonian has a complicated static multi-level energy structure and undergoes periodic evolution in time. By using the Floquet theory, we derive the quasienergies, the Floquet states, and the geometrical phase. It is shown numerically that the geometrical phase is strongly dependent on the evolution circuits in the parameter space and on the evolution frequency of the varying Hamiltonian. In some cases the nonadiabatic geometric phases can exhibit chaotic behavior. We also show a trend of phase compensation in pairs of states which could restore the phase coherence if the pairing occurs.     

Finite Hamiltonian systems: Linear transformations and aberrations

Finite Hamiltonian systems contain operators of position, momentum, and energy, having a finite number N of equally-spaced eigenvalues. Such systems are under the æis of the algebra su(2), and their phase space is a sphere. Rigid motions of this phase space form the group SU(2); overall phases complete this to U(2). But since N-point states can be subject to U(N) ?U(2) transformations, the rest of the generators will provide all N ² unitary transformations of the states, which appear as nonlinear transformations—aberrations—of the system phase space. They are built through the “finite quantization” of a classical optical system.     

External Electric Field Effect on Hydrogenic Donor Impurity in Zinc-Blende InGaN Quantum Dot

The binding energy of a hydrogenic donor impurity in zinc-blende (ZB) InGaN quantum dot (QD) is calculated in the framework of effective-mass envelope-function theory using the plane wave basis. It is shown that the donor binding energy is highly dependent on the impurity position, QD size and the external electric field. The symmetry of the electron probability distribution is broken and the maximum of the donor binding energy is shifted from the centre of QD in the presence of the external electric field. The degenerating energy levels for symmetrical positions with respect to the centre of QD are split. The splitting increases with the increase of QD height while the splitting increases up to a maximum value and then decreases with the increase of QD radius.     

Local BRS transformations and OSp(3,1¦2) symmetry of Yang-Mills theories

We consider a certain local generalization of BRS transformations of Yang-Mills theory in which the anti-commuting parameter is space time dependent. While these are not exact symmetries, they do lead to a new nontrivial WT identity. We make a precise connection between the “local BRS” and the broken orthosymplectic symmetry recently found in superspace formulation of Yang-Mills theory by showing that the local BRS WT identity is precisely the WT identity obtained in the superspace formulation via a superrotation. This “local BRS” WT identity could lead to new consequences not contained in the usual BRS WT identity.     

BRST-BV quantization of gauge theories with global symmetries

We consider the general gauge theory with a closed irreducible gauge algebra possessing the non-anomalous global (super)symmetry in the case when the gauge fixing procedure violates the global invariance of classical action. The theory is quantized in the framework of BRST-BV approach in the form of functional integral over all fields of the configuration space. It is shown that the global symmetry transformations are deformed in the process of quantization and the full quantum action is invariant under such deformed global transformations in the configuration space. The deformed global transformations are calculated in an explicit form in the one-loop approximation.