Topological superfluid in one-dimensional ultracold atomic system with spin-orbit coupling

We propose a one-dimensional Hamiltonian H _1D which supports Majorana fermions when d _{x² ? y²}-wave superfluid appears in the ultracold atomic system and obtain the phase diagrams both for the time-reversal-invariant (TRI) case and time-reversal-symmetry-breaking (TRSB) case. From the phase diagrams, we find that the Majorana doublets and the single Majorana fermions exist in the topological superfluid (TSF) regions for the TRI case and the TRSB case, respectively, and we can reach these regions by tuning the chemical potential μ and spin-orbit coupling α _R . Importantly, the spin-orbit coupling has been realized in ultracold atoms by the recent experimental achievement of synthetic gauge field, therefore, our one-dimensional ultra-cold atomic system described by H _1D is a promising platform to find the mysterious Majorana fermions.     

Electronic transport through a Majorana bound state coupled to a T-shaped quantum-dot system with Coulomb interaction

Using the Green’s function technique, we respectively investigate the electron transport properties of two spin components through the system of a T-shaped double quantum dot structure coupled to a Majorana bound state, in which only one quantum dot is connected with two metallic leads. We explore the interplay between the Fano effect and the MBSs for different dot-MBS coupling strength λ, dot-dot coupling strength t, and MBS-MBS coupling strength ε_M in the noninteracting case. Then the Coulomb interaction and magnetic field effect on the conductance spectra are investigated. Our results indicate that G_↓(ω) is not affected by the Majorana bound states, but a “0.5” conductance signature occurs in the vicinities of Fermi level of G_↑(ω). This robust property persists for a wide range of dot-dot coupling strength and dot-MBS coupling strength, but it can be destroyed by Coulomb interaction in quantum dots. By adjusting the size and direction of magnetic field around the quantum dots, the “0.5” conductance signature damaged by U can be restored. At last, the spin magnetic moments of two dots by applying external magnetic field are also predicted.     

Calculation of magnetic field in the region of the superconducting winding of window frame dipole for particle accelerators

The necessity of simulations in design of superconducting dipole magnets is due to the following circumstances. First, the critical current as a function of the magnetic field I _c(B) for the multicore superconducting cable which drops strongly requires the knowledge of the value of maximum magnetic field “felt” by its coils for estimation of the working current of the magnet. Second, for choosing the optimal number of coils of the winding (1 or 2) and the working current of the magnet, the ratio of B _max for the inner and outer layers of the dipole magnet winding should be known. Since usually the length of the dipole magnet exceeds many times its transverse size, in this work all calculations of B(x, y) are performed in the transverse plane crossing the center of the magnet. The field at the central point is chosen to be B(0, 0) = 2 T (this is the characteristic working value close to the maximum value in the dipole magnet of this type). In this work, the results of calculation of B(x, y) for single-and double-layered windings with 8 and 16 coils from circular hollow cable are presented.     

Superconducting spin filter

Consider two normal leads coupled to a superconductor; the first lead is biased while the second one and the superconductor are grounded. In general, a finite current I₂(V₁, 0) is induced in grounded lead 2; its magnitude depends on the competition between processes of Andreev and normal quasiparticle transmission from lead 1 to lead 2. It is known that, in the tunneling limit, when normal leads are weakly coupled to the superconductor, I₂(V₁, 0)=0 if |V₁|<Δ, and the system is in the clean limit. In other words, Andreev and normal tunneling processes compensate each other. We consider the general case: the voltages are below the gap, the system is either dirty or clean. It is shown that I₂(V₁, 0)=0 for general configuration of the normal leads; if the first lead injects spin-polarized current then I₂=0, but spin current in lead 2 is finite. A XISIN structure, where X is a source of the spin-polarized current, could be applied as a filter separating spin current from charge current. We do an analytical progress calculating I₁(V₁, V₂), I₂(V₁, V₂).     

Topological superconductivity and the fractional Josephson effect in quasi-one dimensional wires on a plane

A time-reversal invariant topological superconductivity is suggested to be realized in a quasi-one-dimensional structure on a plane, which is fabricated by filling the superconducting materials into the periodic channel of dielectric matrices like zeolite and asbestos under high pressure. The topological superconducting phase sets up in the presence of large spin–orbit interactions when intra-wire s-wave and inter-wire d-wave pairings take place. Kramers pairs of Majorana bound states emerge at the edges of each wire. We analyze effects of the Zeeman magnetic field on Majorana zero-energy states. In-plane magnetic field was shown to make asymmetric the energy dispersion, nevertheless Majorana fermions survive due to protection of a particle–hole symmetry. Tunneling of Majorana quasiparticle from the end of one wire to the nearest-neighboring one yields edge fractional Josephson current with 4π-periodicity.     

ESR-Linienbreite der Ionen der Eisengruppe in Lösungen

Electron spin resonance linewidths of ions belonging to the first transition group with quenched orbital angular momentum are calculated using a modified relaxationmatrix theory including third and fourth order perturbation terms. We base our calculation on a Hamiltonian, which depends on electron spin, nuclear spin, orbital angular momentum, rotation of the whole complex, and vibration of the ligands. Quadrupol effects, intermolecular electron-electron and electron-nucleus interactions are neglected. The results show that the well-known formula of the transverse relaxation time derived by using the spin-Hamiltonian is correct, if first the contribution of the rotational spin orbit process is taken in consideration and second the rotational correlation timeτ _c is replaced byτ _v =(1/τ _c +1/τ(0))^?1. 1/τ(0) describes the linewidth of the lowest energy value of the electrostatic energy of unpaired electrons in the ligand field. The linewidth arises from the normal modes of the complex; the calculation gives τ(0)=l0^?11...10^?12 sec.     

Effect of spin structures and nesting on the shape of the fermi surface and pseudogap anisotropy in the <Emphasis Type="Italic">t</Emphasis>-<Emphasis Type="Italic">t</Emphasis>′-<Emphasis Type="Italic">U</Emphasis> Hubbard models

The effect of two types of spin structures on the shape of the Fermi surface and on the map of photoemission intensities for the t-t′-U Hubbard model is investigated. The stripe phase with a period of 8α and the spiral spin structure are calculated in the mean field approximation. It is shown that, in contrast to electron-type doping, hole-doped models are unstable to the formation of such structures. Pseudogap anisotropy is different for h-and e-doping and is determined by the spin structure. In accordance with ARPES data for La_2?xSr_xCuO₄, the stripe phase is characterized by quasi-one-dimensional FS segments in the vicinity of points M(±π, 0) and by suppression of the spectral density for k _x =k _y . It is shown that spiral structures exhibit polarization anisotropy: different segments of the FS correspond to electrons with different spin polarizations.     

Longitudinal scaling of elliptic flow in Landau hydrodynamics

This study presents a generalization of the Landau hydrodynamic solution for multiparticle production applied to non-central relativistic heavy-ion collisions. The obtained results show the longitudinal scaling of elliptic flow, v ₂, as a function of rapidity shifted by beam rapidity (y ? y _beam ) for different energies (\(\sqrt {s_{NN} } = 62.4 GeV\) and 200 GeV) and for different systems (Au-Au and Cu-Cu). It is argued that the elliptic flow and its longitudinal scaling are due to the initial transverse energy density distribution and initial longitudinal thickness effect.     

Spin on a 4D Feynman Checkerboard

We discretize the Weyl equation for a massless, spin-1/2 particle on a time-diagonal, hypercubic spacetime lattice with null faces. The amplitude for a step of right-handed chirality is proportional to the spin projection operator in the step direction, while for left-handed it is the orthogonal projector. Iteration yields a path integral for the retarded propagator, with matrix path amplitude proportional to the product of projection operators. This assigns the amplitude i ^±T 3^?B/2 2^?N to a path with N steps, B bends, and T right-handed minus left-handed bends, where the sign corresponds to the chirality. Fermion doubling does not occur in this discrete scheme. A Dirac mass m introduces the amplitude i ?? m to flip chirality in any given time step ??, and a Majorana mass similarly introduces a charge conjugation amplitude.     

On Ohm’s law in the thin current sheets of the Earth’s magnetosphere

The analytical and numerical dependences of the total transverse current on an electric field, the normal component of a magnetic field and the ion and electron temperatures are obtained using analytical approximation of numerical results provided by a self-consistent model of the magnetospheric thin sheet. The dependence of current on the parameters ?, T _i , b _n is shown to be nonlinear. The relative contributions of different plasma components into the total current are estimated.     

Quantenstatistik eines Gases mit verschiedener Bahn- und Spintemperatur

A system of particles with spin in a magnetic field may possess an orbital temperatureT _o different from the spin temperatureT _s (?0), if it is possible to neglect the energetic interaction between the orbital and the spin system. The calculation of the quantum statistical most probable distribution of identical independent particles on the orbital and spin energy levels yields the introduction of three Lagrange multipliers—according to the fact that the orbital and the spin energy and the number of particles are fixed—representing the orbital and spin temperature and a generalizedPlanck's “characteristic function”. Apart from the Boltzmann-approximation being valid in the case of small spin values forT _o ?T _e (T _e =customary degeneration temperature) and arbitraryT _s ?0, the distributions and the orbital and the spin energy depend onboth the temperaturesT _o andT _s coming from the principle of exclusion forFermi resp.Bose particles. The equations of state are discussed. There are four heat capacities, which possess characteristic peaks. In stead of the well-known temperature independence of the paramagnetism of degenerated conducting electrons one obtains χ～T _o /T _s . The behaviour of the Einstein-condensation of aBose gas is considered.     

Spin correlation in pp elastic scattering and in pion production near threshold

An internal polarized gas target in conjunction with a beam of polarized protons stored in the IUCF Cooler storage ring has been used to measure analyzing power and spin correlation parameters between 200 MeV and 450 MeV over a wide range of angles. A consistent absolute beam and target polarization calibration was established by ramping the stored protons up and down in energy. The analyzing power A _y and the spin correlations A _xx , A _yy and A _xz were measured with transverse beam polarization, while determination of A _zz required the development of a longitudinally polarized beam. First experiments on the spin dependence on π₀-production have recently been carried out.     

Thermoelectric effect in the Kondo dot side-coupled to a Majorana mode

We investigate the linear thermoelectric response of an interacting quantum dot side-coupled by one of two Majorana modes hosted by a topological superconducting wire. We employ the numerical renormalization group technique to obtain the thermoelectrical conductance L in the Kondo regime while the background temperature T, the Majorana-dot coupling Γ _m , and the overlap ε _m between the two Majorana modes are tuned. We distinguish two transport regimes in which L displays different features: the weak- (Γ _m <T _K ) and strong-coupling (Γ _m >T _K ) regimes, where T _K is the Kondo temperature. For an infinitely long nanowire where the Majorana modes do not overlap (ε _m = 0), the thermoelectrical conductance in the weak-coupling regime exhibits a peak at T ~ Γ _m <T _K . This peak is ascribed to the anti-Fano resonance between the asymmetric Kondo resonance and the zero-energy Majorana bound state. In the strong-coupling regime, on the other hand, the Kondo-induced peak in L is affected by the induced Zeeman splitting in the dot. For finite but small overlap (0 <ε _m <Γ _m ), the interference between the two Majorana modes restores the Kondo effect in a smaller energy scale Γ′ _m and gives rise to an additional peak in Γ ~ Γ′ _m, whose sign is opposite to that at T ~ Γ _m . In the strong-coupling regime this additional peak can cause a non-monotonic behavior of L with respect to the dot gate. Finally, in order to identify the fingerprint of Majorana physics, we compare the Majorana case with its counterpart in which the Majorana bound states are replaced by a (spin-polarized) ordinary bound state and find that the thermoelectric features for finite ε _m are the genuine effect of the Majorana physics.     

Exact solution of the 1D Hubbard model in the atomic limit with inter-site magnetic coupling

In this paper, we present for the first time the exact solution in the narrow-band limit of the 1D extended Hubbard model with nearest-neighbour spin-spin interactions described by an exchange constant J. An external magnetic field h is also taken into account. This result has been obtained in the framework of the Green’s functions formalism, using the composite operator method. By means of this theoretical background, we have studied some relevant features such as double occupancy, magnetization, spin-spin and charge-charge correlation functions and derived a phase diagram for both ferro (J > 0) and anti-ferro (J < 0) coupling in the limit of zero temperature. We also report a study on density of states, specific heat, charge and spin susceptibilities. In the limit of zero temperature, we show that the model exhibits a very rich phase diagram characterized by different magnetic orders and by the coexistence of charge and spin orderings at commensurate filling. Moreover, our analysis at finite temperature of density of states and response functions shows the presence of low-temperature charge and spin excitations near the phase boundaries.     

Volume charge density and radial electric field <Emphasis Type="Italic">E</Emphasis><Subscript><Emphasis Type="Italic">r</Emphasis></Subscript>(<Emphasis Type="Italic">r</Emphasis>) in a moving tokamak plasma

Electric field E _r transverse to the current in a moving quasi-neutral plasma can (and should) be considered using Poisson equations and densities of volume charges emerging in the plasma. In the general case, E _r becomes nonlocal; i.e., remote volume charge densities are not screened but affect the formation of E _r at the points under investigation. This approach is used for describing a phenomenological theory of radial electric field E _r (r) and velocity of toroidal rotation of the plasma in the tokamak. Examples of application of this theory to actual experiments are considered.     

The mass of a static charged sphere

The field of a static, charged sphere is investigated using general relativity. InNordström's exterior solution the parametersm ande, referring to mass and charge, are unrelated, and indeedm can be put equal to zero. It is shown that, if the interior solution is considered,m cannot be put zero unless the matter density is negative. The contribution of the electric field energy to the gravitational mass is estimated using certain special models. A model is given in which the gravitational attraction of the charged matter balances its electrical repulsion. If the radius is allowed to tend to zero, this gives a model of a point charge with finite and non-zero mass and charge.     

On rational functions of first-class complexity

It is proved that, for every rational function of two variables P(x, y) of analytic complexity one, there is either a representation of the form f(a(x) + b(y)) or a representation of the form f(a(x)b(y)), where f(x), a(x), b(x) are nonconstant rational functions of a single variable. Here, if P(x, y) is a polynomial, then f(x), a(x), and b(x) are nonconstant polynomials of a single variable.     

The electric “Meissner effect” in spin superconductor

Spin superconductivity results from the condensation of spin-triplet but charge neutralparticles (e.g., triplet excitons). We present a Laplace-type equation describingelectrostatic properties of spin superconductors. With the phenomenological equationsobtained, we show that there exists an electric “Meissner effect” against the spatialvariation of the electric field along the magnetic moment direction, in particular,(?·?)(?·E). Severaldistinctive characteristics of this electric “Meissner effect” emerge in spinsuperconductors. Firstly, the variation of the electric field(?·?)(?·E) has an abruptdecrease at the boundary, which is analogous to the screen effect for electric fieldE in a uniform dielectric material. Secondly, thesuper-spin current distributes inside or near the boundaries of a spin superconductor,which depends on the magnitude of gradient for the external driven electric field.     

Majorana neutrinos, <Emphasis Type="Italic">CP</Emphasis> violation,neutrinoless double beta and tritium beta decays

If the present or upcoming searches for neutrinoless double beta ((ββ)_0ν) decay give a positive result, the Majorana nature of massive neutrinos will be established. From the determination of the value of the (ββ)_0ν-decay effective Majorana mass parameter (|〈m〉|), it would be possible to obtain information on the type of neutrino mass spectrum. Assuming 3-ν mixing and massive Majorana neutrinos, we discuss the information that a measurement of, or an upper bound on, |〈m〉| can provide on the value of the lightest neutrino mass m₁. With additional data on the neutrino masses obtained in ³H β-decay experiments, it might be possible to establish whether the CP symmetry is violated in the lepton sector. This would require very high precision measurements. If CP invariance holds, the allowed patterns of the relative CP parities of the massive Majorana neutrinos would be determined.