scholarly journals Shape-invariant quantum Hamiltonian with position-dependent effective mass through second-order supersymmetry

2007 ◽  
Vol 40 (26) ◽  
pp. 7265-7281 ◽  
Author(s):  
A Ganguly ◽  
L M Nieto
2010 ◽  
Vol 24 (25n26) ◽  
pp. 4901-4914 ◽  
Author(s):  
J. W. CLARK ◽  
V. A. KHODEL ◽  
M. V. ZVEREV

In a number of strongly-interacting Fermi systems, the existence of a quantum critical point (QCP) is signaled by a divergent density of states and effective mass at zero temperature. Competing scenarios and corresponding mechanisms for the QCP are contrasted and analyzed. The conventional scenario invokes critical fluctuations of a collective mode in the close vicinity of a second-order phase transition and attributes divergence of the effective mass to a coincident vanishing of the quasiparticle pole strength. It is argued that this collective scenario is disfavored by certain experimental observations as well as theoretical inconsistencies, including violation of conservation laws applicable in the strongly interacting medium. An alternative topological scenario for the QCP is developed self-consistently within the general framework of Landau quasiparticle theory. In this scenario, the topology of the Fermi surface is transfigured when the quasiparticle group velocity vanishes at the QCP, yet the quasiparticle picture remains meaningful and no symmetry is broken. The topological scenario is found to explain the non-Fermi-liquid behavior observed experimentally in Yb-based heavy-fermion systems close to the QCP. This study suggests that integration of the topological scenario with the theory of second-order, symmetry-breaking quantum phase transitions will furnish a proper foundation for theoretical understanding of the extended QCP region.


2016 ◽  
Vol 56 (3) ◽  
pp. 224 ◽  
Author(s):  
Petra Košťáková ◽  
Pavel Stovicek

<p>We consider an invariant quantum Hamiltonian <em>H</em> = −Δ<em><sub>LB</sub></em> + <em>V</em> in the <em>L</em><sup>2</sup> space based on a Riemannian manifold <em>˜M</em> with a discrete symmetry group Γ. To any unitary representation Λ of Γ one can relate another operator on <em>M</em> = <em>˜M</em> /Γ, called <em>H</em><sub>Λ</sub>, which formally corresponds to the same differential operator as <em>H</em> but which is determined by quasi-periodic boundary conditions. As originally observed by Schulman in theoretical physics and Sunada in mathematics, one can construct the propagator associated with <em>H</em><sub>Λ</sub> provided one knows the propagator associated with <em>H</em>. This approach is reviewed and demonstrated on a quantum model describing a charged particle on the plane with two Aharonov-Bohm vortices. The construction of the propagator is explained in full detail including all substantial intermediate steps.</p>


Author(s):  
W. L. Bell

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.


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