Quaternionic eigenvalue problem

We discuss the (right) eigenvalue equation for $\mathbb{H}$, $\mathbb{C}$ and $\mathbb{R}$ linear quaternionic operators. The possibility to introduce an isomorphism between these operators and real/complex matrices allows to translate the quaternionic problem into an {\em equivalent} real or complex counterpart. Interesting applications are found in solving differential equations within quaternionic formulations of quantum mechanics.Comment: 13 pages, AMS-Te

Right eigenvalue equation in quaternionic quantum mechanics

We study the right eigenvalue equation for quaternionic and complex linear matrix operators defined in n-dimensional quaternionic vector spaces. For quaternionic linear operators the eigenvalue spectrum consists of n complex values. For these operators we give a necessary and sufficient condition for the diagonalization of their quaternionic matrix representations. Our discussion is also extended to complex linear operators, whose spectrum is characterized by 2n complex eigenvalues. We show that a consistent analysis of the eigenvalue problem for complex linear operators requires the choice of a complex geometry in defining inner products. Finally, we introduce some examples of the left eigenvalue equations and highlight the main difficulties in their solution.Comment: 24 pages, AMS-Te

The octonionic eigenvalue problem

By using a real matrix translation, we propose a coupled eigenvalue problem for octonionic operators. In view of possible applications in quantum mechanics, we also discuss the hermiticity of such operators. Previous difficulties in formulating a consistent octonionic Hilbert space are solved by using the new coupled eigenvalue problem and introducing an appropriate scalar product for the probability amplitudes.Comment: 21 page

Quaternionic potentials in non-relativistic quantum mechanics

We discuss the Schrodinger equation in presence of quaternionic potentials. The study is performed analytically as long as it proves possible, when not, we resort to numerical calculations. The results obtained could be useful to investigate an underlying quaternionic quantum dynamics in particle physics. Experimental tests and proposals to observe quaternionic quantum effects by neutron interferometry are briefly reviewed.Comment: 21 pages, 16 figures (ps), AMS-Te

Spectral properties of a two-orbital Anderson impurity model across a non-Fermi liquid fixed point

We study by NRG the spectral properties of a two-orbital Anderson impurity model in the presence of an exchange splitting which follows either regular or inverted Hund's rules. The phase diagram contains a non-Fermi liquid fixed point separating a screened phase, where conventional Kondo effect occurs, from an unscreened one, where the exchange-splitting takes care of quenching the impurity degrees of freedom. On the Kondo screened side close to this fixed point the impurity density of states shows a narrow Kondo-peak on top of a broader resonance. This narrow peak transforms in the unscreened phase into a narrow pseudo-gap inside the broad resonance. Right at the fixed point only the latter survives. The fixed point is therefore identified by a jump of the density of states at the chemical potential. We also show that particle-hole perturbations which simply shift the orbital energies do not wash out the fixed point, unlike those perturbations which hybridize the two orbitals. Consequently the density-of-state jump at the chemical potential remains finite even away from particle-hole symmetry, and the pseudo-gap stays pinned at the chemical potential, although it is partially filled in. We also discuss the relevance of these results for lattice models which map onto this Anderson impurity model in the limit of large lattice-coordination. Upon approaching the Mott metal-insulator transition, these lattice models necessarily enter a region with a local criticality which reflects the impurity non-Fermi liquid fixed point. However, unlike the impurity, the lattice can get rid of the single-impurity fixed-point instability by spontaneously developing bulk-coherent symmetry-broken phases, which we identify for different lattice models.Comment: 43 pages, 11 figures. Minor corrections in the Appendi

Local land management in Benin with special reference to pastoral groups

A review of local land management experiences in West Africa reveals that the resolution of conflicts over the uses of resources between herders and farmers depends on factors like land and water rights, promotion of the interests of pastoral groups and the Intervention of traditional and modern institutions in conflict resolution. This paper on local land management in Benin with special reference to pastoral groups presents some fmdings in Kemon and Kokey villages. In both villages, land is still under common law to varying degrees despite modern law No 65- 25 of 14* August entitled 'Régime de la propriété foncière'. Crop damage by cattle in areas where agriculture has become more widespread and the blocking of cattle routes are identified as the major causes of conflict between herders and farmers. Resolution of this tension calls for the intervention of local organisations. Conflicts are settled either through amicable settlement or compensation but unfortunately it is the herder in many cases who is still blamed for erop damage

Quaternionic Diffusion by a Potential Step

In looking for qualitative differences between quaternionic and complex formulations of quantum physical theories, we provide a detailed discussion of the behavior of a wave packet in presence of a quaternionic time-independent potential step. In this paper, we restrict our attention to diffusion phenomena. For the group velocity of the wave packet moving in the potential region and for the reflection and transmission times, the study shows a striking difference between the complex and quaternionic formulations which could be matter of further theoretical discussions and could represent the starting point for a possible experimental investigation.Comment: 10 pages, 1 figur

The Effect of Harbor Developments on Future High-Tide Flooding in Miami, Florida

Little is known about the effect of tidal changes on minor flooding in most lagoonal estuaries, often due to a paucity of historical records that predate landscape changes. In this contribution, we recover and apply archival tidal range data to show that the mean tidal range in Miami, Florida, has almost doubled since 1900, from 0.32 to 0.61 m today. A likely cause is the dredging of a ∼15 m deep, 150 m wide harbor entrance channel beginning in the early 20th century, which changed northern Biscayne Bay from a choked inlet system to one with a tidal range close to coastal conditions. To investigate the implications for high-tide flooding, we develop and validate a tidal-inference based methodology that leverages estimates of pre-1900 tidal range to obtain historical tidal predictions and constituents. Next, water level predictions that represent historical and modern water level variations are projected forward in time using different sea level rise scenarios. Results show that the historical increase in tidal range hastened the occurrence of present-day flooding, and that the total integrated number of days with high-tide floods in the 2020–2100 period will be approximately O(103) more under present day tides compared to pre-development conditions. These results suggest that tidal change may be a previously under-appreciated factor in the increasing prevalence of high-tide flooding in lagoonal estuaries, and our methods open the door to improving our understanding of other heavily-altered systems