Narrow Results

Phase structure of the (2 + 1)-dimensional model with four-fermion interaction of spin-½ quasiparticles (electrons) both in the fermion–antifermion (or chiral) and fermion–fermion (or superconducting) channels is considered at nonzero chemical potential μ and under the influence of an in-plane, i.e. parallel to a system sheet, external magnetic field B_‖. It is shown that at sufficiently large values of μ and/or B_‖ the Cooper pairing (or superconducting) phase appears in the system at arbitrary relation between coupling constants, provided that there is an (arbitrary small) attractive interaction in the superconducting channel. In particular, at sufficiently weak attractive interaction in the chiral channel, the Cooper pairing occurs even at infinitesimal values of μ and/or B_‖. The superconducting phase of the model is always a paramagnetic one.

In the article we review observational features of black holes where an influence of a gravitational field is dominant and we must use strong gravitational field approach for GR. Recent X-ray observations of microquasars and Seyfert galaxies reveal broad emission lines in their spectra, which can arise in the innermost parts of accretion disks. Simulations indicate that at low inclination angle the line is measured by a distant observer as characteristic two-peak profile. However, at high inclination angles (> 85°) two additional peaks arise. This phenomenon was discovered by Matt et al. (1993) using the Schwarzschild black hole metric to analyze such an effect. They assumed that the effect is applicable to a Kerr metric far beyond the range of parameters that they exploited. We check and confirm their hypothesis about such a structure of the spectral line shape for the Kerr metric case. We discuss how analysis of the iron spectral line shapes could give an information about an upper limit of magnetic field near black hole horizon.

We mainly study the Zeeman effect on electronic structure of carbon nanotori in the presence of magnetic field (B) perpendicular to the tori's plane. As a function of magnetic flux (ϕ), the energy gap (E_g) and density of states (DOS) near the Fermi level are obtained in the case of with and without considering the Zeeman effect. Without spin-B interaction, the ϕ-dependent electronic structure would exhibit the periodical Aharonov–Bohm (AB) oscillation. A magnetic-field-induced semiconductor-metal transition is indicated in the variation of energy gap and DOS of armchair tori. The Zeeman effect on electronic structure is notable at relatively large ϕ (~100ϕ₀, with ϕ₀ = h/e), e.g., more phase transition points may appear in the E_g - B dependence for armchair tori, and the destruction of periodical AB oscillation is distinct due to the Zeeman effect. These results may be observed by scanning tunneling spectroscopy measurement.

The spin dynamics in solid state systems is governed by the competition between spin-orbit interaction (SOI) and the Zeeman effect. The SOI couples orbital motion of electron spins with an electric field. The Zeeman effect lifts the spin degeneracy in a magnetic field. In InGaAs-based 2DEGs, it is known that the Rashba SOI energy E_SOI can be controlled by an electric field applied on the gate electrode.¹ In the presence of SOI, weak localization (WL) due to time reversal symmetric interference changes to weak anti-localization (WAL). We have found crossover from WL to WAL by applying the gate voltage in InGaAs 2DEGs. Applying an in-plane magnetic field to the 2DEG does not affect the orbital motion of the electrons, but only modifies the Zeeman spin splitting energy E_Z. This allows tuning the ratio between E_SOI and E_Z very accurately.

We have studied how the interplay between SOI and Zeeman coupling affects the electron transport and the spin dynamics in InGaAs-based 2DEGs. From the quantitative analysis of the magnetoconductance, measured in the presence of an in-plane magnetic field, we conclude that this interplay results in a spin-induced breaking of time reversal symmetry (TRS) and in an enhancement of the spin relaxation time. Both effects are due to a partial alignment of the electron spin along the applied magnetic field, and are found to be in excellent agreement with recent theoretical predictions.² We find that the electron dephasing time saturates when E_Z becomes comparable to E_SOI. Moreover, we show that the spin-induced electron dephasing time is a universal function of the ratio E_Z/E_SOI within the experimental accuracy, i.e. it is independent of any details of the quantum well.³ This universal behavior is explained by the recent theory.⁴

The suppression of WAL is observed by applying in-plane magnetic field because of the enhancement of the spin relaxation time, and this suppression also appears in narrow InGaAs wires since the effective magnetic field direction is confined by wires. In gate fitted narrow wires, the large enhancement of spin relaxation time is obtained when the Rashba SOI is decreased. The spin relaxation time is more than one order longer than that of 2DEG case. This enhancement suggests that the Rashba SOI strength approaches the Dresselhaus SOI strength. We have numerically investigated the angular dependence of in-plane magnetoconductance in disordered wires with both Rashba and Dresselhaus SOIs. A new method is proposed to determine the relative strength of Rashba and Dresselhaus SOI from transport measurements without the need of fitting parameters.⁵ This in-plane magnetic field measurement provides fruitful information on spin related transport.

Note from Publisher: This article contains the abstract only.

Influence of the magnetic field on the properties of the polaron in an asymmetric quantum dot is studied by using the Pekar variation method. The expression of the magnetopolaron ground-state energy is obtained by theoretical derivation. The relationship between the ground-state energy of the magnetopolaron with the transverse confinement strength, the longitudinal confinement strength and the magnetic field cyclotron resonance frequency are further discussed by us. Due to the crystal structure inversion asymmetry and the time inversion asymmetry, the polaron energy causes Rashba spin–orbit splitting and Zeeman splitting. Under the strong and weak magnetic fields, we discuss the dominant position of Rashba effect and Zeeman effect, respectively. Due to the presence of phonons, the polaron is more stable than the bare electron state, and the energy splitting is more stable.

The antiferromagnetic properties of nuclei are studied within the Wigner function moments method. The solution of the time dependent Hartree–Fock–Bogoliubov equations predicts four low-lying $1^{+}$ states. Three of them are known as various scissors modes. Fourth state is disposed below all scissors modes and represents one of three branches of $2^{+}$ multiplet which can exist in spherical nuclei and which is split in deformed nuclei. It is discovered, that the antiferromagnetic properties of nuclei lead to the splitting of $2^{+}$ states already at the zero deformation. It is shown that the splitting caused by nuclear antiferromagnetism is comparable to the Zeeman splitting in an external uniform magnetic field.

We study in the weak field limit the gravitational lensing by spherically symmetric compact object immersed in an asymptotically uniform magnetic field in the presence of plasma and our approach is based on the medium modified Hamiltonian one. We show that the magnetized plasma in the environment of compact object may lead to split of the Einstein cross, creating additional lensed components. Finally we calculate magnification and time delay related to the individual images.

The non-Hermitian aspect of Quantum Mechanics has been of great interest recently. There have been numerous studies on non-Hermitian Hamiltonians written for natural processes. Some studies have even expressed the hydrogen atom in a non-Hermitian basis. In this paper, the principles of non-Hermitian quantum mechanics are applied to the time independent perturbation theory and compared with the Zeeman effect. Here, we have also shown the condition under which the Zeeman Effect results will still be true even though the Hamiltonian taken into consideration is non-Hermitian.

With the gas ionization experiments (Section 1.7) we know that atoms and molecules are made of nuclei and electrons that revolve around them. In this chapter we give representations of these microscopic objects and show how certain atoms or molecular fragments form bonds between them. From the description of the hydrogen atom, the lightest atom in Nature since it contains only one proton and one electron, we will develop a simple model for the bonds between atoms in molecules stable at 25°C. Without making complicated calculations we will be able to predict which bonds between atoms are possible a priori and which structures the molecules containing them have. Atoms are the parts of a Lego® set that can be assembled to make a large number of constructions, but not just any construction (three-dimensional objects with predefined geometries). In Chapter 7, we will develop a slightly more advanced model of the chemical bond. We will examine why some bonds are weaker than others, i.e. which bonds are more or less easily broken by heating…