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Three-dimensional Quantum Slit Diffraction and Diffraction in Time
Get PDFWe study the quantum slit diffraction problem in three dimensions. In the treatment of diffraction of particles by a slit, it is usually assumed that the motion perpendicular to the slit is classical. Here we take into account the effect of the quantum nature of the motion perpendicular to the slit using the Green function approach [18]. We treat the diffraction of a Gaussian wave packet for general boundary conditions on the shutter. The difference between the standard and our three-dimensional slit diffraction models is analogous to the diffraction in time phenomenon introduced in [16]. We derive corrections to the standard formula for the diffraction pattern, and we point out situations in which this might be observable. In particular, we discuss the diffraction in space and time in the presence of gravity
Multiple backreacted flavour branes
Get PDFWe construct a novel supergravity background holographically dual to the flavoured N = 1 Supersymmetric Yang-Mills theory. We consider flavours of different masses that produce spherical cavities with radii corresponding to the quark masses. The positive beta function blows at some large radial distance corresponding to the Landau pole of the theory. We explore the Wilson loop between two families of light and heavy quarks and observe a screening of the heavy light potential
Einstein’s exploration of a steady-state model of the universe
Get PDFWe present a translation and analysis of an unpublished manuscript by Albert Einstein in which he explored a 'steady-state' model of the universe. The manuscript, which appears to have been written in early 1931, demonstrates that Einstein once considered an expanding cosmos in which the mean density of matter is maintained constant by a continuous formation of matter from empty space. This model is very different to previously known Einsteinian models of the cosmos (both static and dynamic) but anticipates the later steady-state cosmology of Hoyle, Bondi and Gold in some ways. We find that Einstein’s steady-state model contained a fundamental flaw and suggest that it was discarded for this reason. We also suggest that he declined to try again because he realised that a successful steady-state model would require an amendment to the field equations. The abandoned model is of historical significance because it reveals that Einstein debated between steady-state and evolving models of the cosmos decades before a similar debate took place in the cosmological community
On the thermodynamic stability of rotating black holes in higher dimensions—a comparision of thermodynamic ensembles
Get PDFThermodynamic potentials relevant to the micro-canonical, the canonical and the grand-canonical ensembles, associated with rotating black holes in D-dimensions, are analysed and compared. Such black holes are known to be thermodynamically unstable, but the instability is a consequence of a subtle interplay between specific heats and the moments of inertia and it manifests itself differently in the different ensembles. A simple relation between the product of the specific heat and the determinant of the moment of inertia in both the canonical and the grand-canonical ensembles is derived. Myers-Perry black holes in arbitrary dimension are studied in detail. All temperature extrema in the micro-canonical ensemble are determined and classified. The specific heat and the moment of inertia tensor are evaluated in both the canonical and the grand-canonical ensembles in any dimension. All zeros and poles of the specific heats, as a function of the angular momenta, are determined and the eigenvalues of the isentropic moment of inertia tensor are studied and classified. It is further shown that many of the thermodynamic properties of a Myers-Perry black hole in D − 2 dimensions can be obtained from those of a black hole in D dimensions by sending one of the angular momenta to infinity
Rigorous investigation of the reduced density matrix for the ideal Bose gas in harmonic traps by a loop-gas-like approach
Get PDFIn this paper, we rigorously investigate the reduced density matrix (RDM) associated to the ideal Bose gas in harmonic traps. We present a method based on a sum-decomposition of the RDM allowing to treat not only the isotropic trap, but also general anisotropic traps. When focusing on the isotropic trap, the method is analogous to the loop-gas approach developed by W.J. Mullin in [38]. Turning to the case of anisotropic traps, we examine the RDM for some anisotropic trap models corresponding to some quasi-1D and quasi-2D regimes. For such models, we bring out an additional contribution in the local density of particles which arises from the mesoscopic loops. The close connection with the occurrence of generalized-BEC is discussed. Our loop-gas-like approach provides relevant information which can help guide numerical investigations on highly anisotropic systems based on the Path Integral Monte Carlo (PIMC) method
St Mechyll of Anglesey, St Maughold of Man and St Malo of Brittany
Get PDFA late-medieval Welsh poem in honour of the Anglesey saint Mechyll contains features drawn from two other cults, those of the Breton St Malo and the Manx St Maughold. This article surveys the evidence for the interpenetration of these three cults in medieval Man and Anglesey. It describes first the contents of the Welsh poem and the other evidence for the cult of Mechyll. It demonstrates that Mechyll was identified with Malo under his Latin name, Machutus, though the identification itself is unhistorical. The question of the name of Malo-Machutus, the spread of his cult and the hagiography associated with him are then surveyed. It is shown that St Maughold of Man was likewise associated with Machutus, and that much the same thing happened at the Scottish church of Lesmahagow, originally dedicated to St Féchín. The place of Maughold in the Lives of St Patrick is then discussed, confirming that Maughold of Man was the saint associated by Muirchú (c.700) with Patrick’s adversary Mac Cuill. The final question raised is the name of Maughold himself. Though it is unlikely that Maughold and Mechyll were really the same historical individual, the possibility is acknowledged
Flavours in global Klebanov-Witten background
Get PDFWe probe flavour branes in the Klebanov–Witten background in global coordinates. We show that supersymmetric probes correspond to massless flavours and analyse their spectrum of fluctuations. Our studies suggest that the mesons are dissociated by the Casimir energy. The spectrum is equidistant, with a ground state given by the conformal dimension of the operator dual to the fluctuations. We show that the equidistant structure of the spectrum arises from the addition of the angular momenta of the fundamental fields composing the meson operators
Northward channel flow in northern Tibet revealed from 3D magnetotelluric modelling
Get PDFThe Kunlun fault defines one of the major northern tectonic boundaries of the Tibetan plateau. Previous geophysical studies have detected a major change in rheology across this boundary, but it is not clear how this is related to models that have invoked crustal flow. The lithospheric resistivity structure of the Kunlun fault has been investigated by both the INDEPTH III and IV magnetotelluric (MT) transects. All the MT data were processed using modern statistically-robust methods, and have been analysed for directionality and dimensionality. In order to improve understanding of the anisotropic distribution of melt previously revealed by our remodelling of the INDEPTH III MT data, a variant approach on 3D inversion of 2D profiles was investigated to explore and improve lateral resolution. In addition to the apparent surficial deformation associated with the sinistral strike-slip Kunlun fault, the 3D modelling of the INDEPTH MT data reveals that complex deformation processes are occurring at mid-crustal depths in northern Tibet. The 3D MT inversion results, supported by synthetic modelling, particularly confirm and highlight the presence of separate north–south intrusions of conductive material crossing the Kunlun fault into the more resistive Kunlun–Qaidam block. These north–south intrusions are interpreted to be associated with the horizontal channel flow of partially molten Songpan–Ganzi crust into two (or more) separated channels moving northwards and crossing the surficial trace of the Kunlun fault at mid-to-lower crustal depths