scholarly journals Three-dimensional Majorana fermions in chiral superconductors

2016 ◽  
Vol 2 (12) ◽  
pp. e1601835 ◽  
Author(s):  
Vladyslav Kozii ◽  
Jörn W. F. Venderbos ◽  
Liang Fu
Keyword(s):  
Angular Momentum ◽  
Bound States ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Majorana Fermions ◽  
Spin Orbit ◽  
Nuclear Spins ◽  
Topology Analysis ◽  
Resonance Spin ◽  
Comprehensive Classification

Using a systematic symmetry and topology analysis, we establish that three-dimensional chiral superconductors with strong spin-orbit coupling and odd-parity pairing generically host low-energy nodal quasiparticles that are spin-nondegenerate and realize Majorana fermions in three dimensions. By examining all types of chiral Cooper pairs with total angular momentumJformed by Bloch electrons with angular momentumjin crystals, we obtain a comprehensive classification of gapless Majorana quasiparticles in terms of energy-momentum relation and location on the Fermi surface. We show that the existence of bulk Majorana fermions in the vicinity of spin-selective point nodes is rooted in the nonunitary nature of chiral pairing in spin-orbit–coupled superconductors. We address experimental signatures of Majorana fermions and find that the nuclear magnetic resonance spin relaxation rate is significantly suppressed for nuclear spins polarized along the nodal direction as a consequence of the spin-selective Majorana nature of nodal quasiparticles. Furthermore, Majorana nodes in the bulk have nontrivial topology and imply the presence of Majorana bound states on the surface, which form arcs in momentum space. We conclude by proposing the heavy fermion superconductor PrOs4Sb12and related materials as promising candidates for nonunitary chiral superconductors hosting three-dimensional Majorana fermions.

Bound States in Three Dimensions: The Atom

2021 ◽  
pp. 82-92
Author(s):  
Duncan G. Steel
Keyword(s):  
Angular Momentum ◽  
Quantum Number ◽  
Bound States ◽  
Laguerre Polynomials ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Spherical Coordinates ◽  
Quantum Numbers ◽  
Energy Plus ◽  
Charged Nucleus

In this chapter, we go to three dimensions in space and look at the solution of the time independent Schrödinger equation for the hydrogen atom. The Hamiltonian is then the kinetic energy plus the potential energy due to the Coulomb coupling between the positively charged nucleus and the electron. We construct the angular momentum operator and find that the partial differential equation for the angular momentum eigenfunctions of the spherical coordinates θ,ϕ is the same as the angular part of the ∇2 operator in spherical coordinates. The angular momentum eigenfunctions are the spherical harmonics, with two quantum numbers, l and m, and the solution to the radial part of the Hamiltonian including the Coulomb potential are Laguerre polynomials with one quantum number, called the principle quantum number, n. The hydrogen wave function is the product of a Laguerre polynomial and a spherical harmonic with three quantum numbers. Since these are two- and three-dimensional functions for angular momentum and hydrogen respectively, they are best understood in a series of plots. The chapter concludes by giving the historical letter names to specific orbitals, since they continue to be used today.

RETARDATION EFFECTS IN COVARIANT THREE-DIMENSIONAL BOUND STATE WAVE FUNCTIONS

2005 ◽  
Vol 14 (06) ◽  
pp. 931-947 ◽  
Author(s):  
F. PILOTTO ◽  
M. DILLIG
Keyword(s):  
Bound States ◽  
Three Dimensional ◽  
Bound State ◽  
Relative Energy ◽  
Wave Functions ◽  
Three Dimensions ◽  
State Wave ◽  
Scalar Diquark ◽  
Bound State Wave Function ◽  
Retardation Effects

We investigate the influence of retardation effects on covariant 3-dimensional wave functions for bound hadrons. Within a quark-(scalar) diquark representation of a baryon, the four-dimensional Bethe–Salpeter equation is solved for a 1-rank separable kernel which simulates Coulombic attraction and confinement. We project the manifestly covariant bound state wave function into three dimensions upon integrating out the non-static energy dependence and compare it with solutions of three-dimensional quasi-potential equations obtained from different kinematical projections on the relative energy variable. We find that for long-range interactions, as characteristic in QCD, retardation effects in bound states are of crucial importance.

Phase separation in spin-orbit-angular-momentum coupling Bose–Einstein condensate systems

2020 ◽  
Vol 34 (23) ◽  
pp. 2050241
Author(s):  
Jin Xu ◽  
Jinbin Li
Keyword(s):  
Angular Momentum ◽  
Phase Separation ◽  
Coupling Strength ◽  
Interaction Strength ◽  
Einstein Condensate ◽  
Three Dimensions ◽  
Pitaevskii Equation ◽  
Spin Orbit ◽  
Bose Einstein Condensate ◽  
Bose Einstein

We study the phase separation in three-component spin-orbit-angular-momentum coupled Bose–Einstein condensate with spin-1 in three dimensions. Different types of phase-separation are acquired upon an increase of the coupling strength, magnetic gradient strength, spin-dependent interaction strength and particle number above a critical value. Increasing the value of coupling strength and other related parameters shows distinct behaviors which are produced by repulsion for large strengths of spin-orbit angular-momentum (SOAM) coupling. The present investigation is carried out through a numerical Crank–Nicolson method of the underlying mean-field Gross–Pitaevskii equation.

scholarly journals Bound states in the continuum in open acoustic resonators

2015 ◽  
Vol 780 ◽  
pp. 370-387 ◽  
Author(s):  
A. A. Lyapina ◽  
D. N. Maksimov ◽  
A. S. Pilipchuk ◽  
A. F. Sadreev
Keyword(s):  
Bound States ◽  
Three Dimensional ◽  
Life Time ◽  
Three Dimensions ◽  
Destructive Interference ◽  
Acoustic Resonators ◽  
Coupled Mode ◽  
Resonant Modes ◽  
Axisymmetric Duct ◽  
The Continuum

We consider bound states in the continuum (BSCs) or embedded trapped modes in two- and three-dimensional acoustic axisymmetric duct–cavity structures. We demonstrate numerically that, under variation of the length of the cavity, multiple BSCs occur due to the Friedrich–Wintgen two-mode full destructive interference mechanism. The BSCs are detected by tracing the resonant widths to the points of the collapse of Fano resonances where one of the two resonant modes acquires infinite life-time. It is shown that the approach of the acoustic coupled mode theory cast in the truncated form of a two-mode approximation allows us to analytically predict the BSC frequencies and shape functions to a good accuracy in both two and three dimensions.

scholarly journals Stationary scalar and vector clouds around Kerr–Newman black holes

2020 ◽  
Vol 29 (11) ◽  
pp. 2041013
Author(s):  
Nuno M. Santos ◽  
Carlos A. R. Herdeiro
Keyword(s):  
Black Holes ◽  
Angular Momentum ◽  
Bound States ◽  
Total Angular Momentum ◽  
Radial Direction ◽  
Three Dimensional ◽  
Proca Equation ◽  
Dimensional Parameter ◽  
Atomic Orbitals ◽  
Quantum Numbers

Massive bosons in the vicinity of Kerr–Newman black holes can form pure bound states when their phase angular velocity fulfills the synchronization condition, i.e. at the threshold of superradiance. The presence of these stationary clouds at the linear level is intimately linked to the existence of Kerr black holes with synchronized hair at the nonlinear level. These configurations are very similar to the atomic orbitals of the electron in a hydrogen atom. They can be labeled by four quantum numbers: [Formula: see text], the number of nodes in the radial direction; [Formula: see text], the orbital angular momentum; [Formula: see text], the total angular momentum; and [Formula: see text], the azimuthal total angular momentum. These synchronized configurations are solely allowed for particular values of the black holes mass, angular momentum and electric charge. Such quantization results in an existence surface in the three-dimensional parameter space of Kerr–Newman black holes. The phenomenology of stationary scalar clouds has been widely addressed over the last years. However, there is a gap in the literature concerning their vector cousins. Following the separability of the Proca equation in Kerr(–Newman) spacetime, this paper explores and compares scalar and vector stationary clouds around Kerr and Kerr–Newman black holes, extending previous research.

MASS MATRICES AND MONOPOLES IN THREE-DIMENSIONAL FLUX PHASE MODELS

1992 ◽  
Vol 06 (25) ◽  
pp. 1569-1576
Author(s):  
G.C. SEGRE
Keyword(s):  
Bound States ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Spin States ◽  
Mass Matrices ◽  
Phase Models

Chiral spin states in two dimensions can be generalized to three dimensions by introducing effective monopoles to generate the background fluxes. We explore some generalizations of chiral spin states and the consequences of chiral rotations on the charges of dyons, particle-monopole bound states.

convergent-beam diffraction from surfaces

1987 ◽  
Vol 45 ◽  
pp. 30-33
Author(s):  
J. A. Eades ◽  
A. E. Smith ◽  
D. F. Lynch
Keyword(s):  
Reciprocal Lattice ◽  
Three Dimensional ◽  
Grazing Incidence ◽  
Three Dimensions ◽  
Plane Figure ◽  
Transmission Electron ◽  
Convergent Beam ◽  
Beam Patterns ◽  
Beam Diffraction

It is quite simple (in the transmission electron microscope) to obtain convergent-beam patterns from the surface of a bulk crystal. The beam is focussed onto the surface at near grazing incidence (figure 1) and if the surface is flat the appropriate pattern is obtained in the diffraction plane (figure 2). Such patterns are potentially valuable for the characterization of surfaces just as normal convergent-beam patterns are valuable for the characterization of crystals.There are, however, several important ways in which reflection diffraction from surfaces differs from the more familiar electron diffraction in transmission.GeometryIn reflection diffraction, because of the surface, it is not possible to describe the specimen as periodic in three dimensions, nor is it possible to associate diffraction with a conventional three-dimensional reciprocal lattice.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

scholarly journals Free partition functions and an averaged holographic duality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nima Afkhami-Jeddi ◽  
Henry Cohn ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Partition Function ◽  
Spectral Gap ◽  
Central Charge ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Partition Functions ◽  
General Constraints ◽  
Dimensional Gravity ◽  
Holographic Duality

Abstract We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with U(1)c×U(1)c symmetry and a composite boundary graviton. Additionally, for small central charge c, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.

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