Narrow Results

This paper is a part of an ongoing study on the diamagnetic behavior of a 3-dimensional quantum gas of non-interacting charged particles subjected to an external uniform magnetic field together with a random electric potential. We prove the existence of an almost-sure non-random thermodynamic limit for the grand-canonical pressure, magnetization and zero-field orbital magnetic susceptibility. We also give an explicit formulation of these thermodynamic limits. Our results cover a wide class of physically relevant random potentials which model not only crystalline disordered solids, but also amorphous solids.

The original formulation of the Bohr–van Leeuwen (BvL) theorem states that, in a uniform magnetic field and in thermal equilibrium, the magnetization of an electron gas in the classical Drude–Lorentz model vanishes identically. This stems from classical statistics which assign the canonical momenta all values ranging from -∞ to ∞ that makes the free energy density magnetic-field-independent. When considering a classical (Maxwell–Boltzmann) interacting electron gas, it is usually admitted that the BvL theorem holds upon condition that the potentials modeling the interactions are particle-velocities-independent and do not cause the system to rotate after turning on the magnetic field. From a rigorous viewpoint, when treating large macroscopic systems, one expects the BvL theorem to hold provided the thermodynamic limit of the free energy density exists (and the equivalence of ensemble holds). This requires suitable assumptions on the many-body interactions potential and on the possible external potentials to prevent the system from collapsing or flying apart. Starting from quantum statistical mechanics, the purpose of this paper is to give, within the linear-response theory, a proof of the BvL theorem in the semiclassical limit when considering a dilute electron gas in the canonical conditions subjected to a class of translational invariant external potentials.

Experiments were performed in vacuum to examine a modified Kaluza–Klein theory. Originally proposed by Mbelek and Lachièze-Rey, the 5D Kaluza–Klein-$\psi$ theory includes an external scalar field $\psi$ to couple gravitational and electromagnetic fields and can be used to explain some misunderstood phenomena in physics. The theory predicts that a pendulum will experience detectable forces exceeding predictions from classical electromagnetism when interacting with a scalar field. In this experiment, a dielectric mirror is hung as a pendulum inside a vacuum chamber and its oscillations are examined with two laser interferometers. In proximity to the pendulum, different solenoids and toroids will induce magnetic fields that can also be shielded to a great extent using a Gauss chamber. The experiments were conducted in a vacuum chamber to allow the measurement of torsion angles as low as 0.1arcsec above the noise, as well as 0.1$\mu$m translations of the pendulum. The phenomenon observed differs from what was observed by Mbelek at ambient pressure in both magnitude and behavior. Dummy test results hint at the presence of convection effects to explain the pendulum’s rotation, which was eliminated under higher vacuum and by placing a wall between the solenoid and pendulum. In the presence of stronger magnetic fields, the pendulum’s translation was observed to agree with effects predicted by a consideration of diamagnetic effects.

Xu et al. observed enhanced Nernst effect and Iguchi et al. observed patched diamagnetism, both well above T_c in underdoped high-T_c superconductors (HTSCs). A new mechanism is proposed here, which seems to naturally explain, at least qualitatively, these observations, as well as the d-wave nature and continuity of pseudogap and pairing gap, the tunneling conductance above T_c, as well as T*(x), T_ν(x), T_c(x), etc. This mechanism combines features of dynamic charged stripes, preformed pairs, and spin-bags: At appropriete doping levels, the doped holes (and perhaps also electrons) will promote the formation of anti-phase islands in short-range anti-ferromagnetic order. On the boundary of each such island reside two doped carriers; the unscreened Coulomb repulsion between them stabilizes the island's size. Superconductivity results when such "pre-formed pairs" Bose-condense.

Magnetic properties of harmonically trapped charged ideal spin-1/2 fermions in a uniform magnetic field are studied. It is shown that the magnetism of charged spin-1/2 fermions can be explained by a competition between the diamagnetic and paramagnetic effects, where a variable spin factor is introduced to describe the strength of paramagnetic effect. As the spin factor increases, a crossover from diamagnetic region to paramagnetic region appears. Moreover, the critical values of spin factor are obtained at low-temperature and under weak magnetic field, respectively. Spin-1/2 fermions display distinct magnetic behaviors from spinless case.

In this letter, a bearing consisting of a disk-shaped NdFeB permanent magnet levitated by a ferrite magnet with a diamagnetic stabilizer made of two bismuth blocks has been statically analyzed. The analysis, including levitation force and stiffness characteristics of this diamagnetic bearing, has been incorporated with the diamagnetic mirror image method based on the finite element and dipole approximation methods. Force equations of the levitated magnet are derived from the potential of the system in terms of magnetic, diamagnetic and gravitational interactions. The dipole approximation and finite element method were compared with each other. It is observed that while the dipole approximation (an analytical method) is successful in predicting the force and stiffness of the bearing, the finite element method, on the other hand, only estimates the levitation force. It is shown that the dipole approach has advantages over the finite element method for various perspectives such as calculation time and precision.

The well-known Bohr–van Leeuwen Theorem states that the orbital diamagnetism of classical charged particles is identically zero in equilibrium. However, results based on real space–time approach using the classical Langevin equation predicts non-zero diamagnetism for classical unbounded (finite or infinite) systems. Here we show that the recently discovered Fluctuation Theorems, namely, the Jarzynski Equality or the Crooks Fluctuation Theorem surprisingly predicts a free energy that depends on magnetic field as well as on the friction coefficient, in outright contradiction to the canonical equilibrium results. However, in the cases where the Langevin approach is consistent with the equilibrium results, the Fluctuation Theorems lead to results in conformity with equilibrium statistical mechanics. The latter is demonstrated analytically through a simple example that has been discussed recently.

Thermodynamics of trapped charged ideal spin-1 bosons confined in a magnetic field are investigated within semi-classical approximation and truncated-summation approach. It is shown that the critical temperature increases slightly at the first, and then decreases slowly with increasing external magnetic field. Charged spin-1 Bose gases present a crossover from diamagnetism to paramagnetism as the spin factor increases. Charged spin-1 Bose gases exhibit distinct thermodynamic behaviors from the spinless case.

The perovskite manganite La${}_{0.7}$Sr${}_{0.3}$MnO₃ compound is used as a component in ceramic ($1-x)$(La${}_{0.7}$Sr${}_{0.3}$MnO${}_3)$-xC composites at x = 0.15–0.85. It is found that every studied specimen is characterized by the linear dependence of the positive magnetoresistance (PMR) on the magnetic field strength at room temperature. The 0.6(La${}_{0.7}$Sr${}_{0.3}$MnO${}_3)$-0.4C composite has the largest magnetoresistance value (15%) at room temperature and intensity of magnetic field $H=15$kOe. A possible mechanism for the PMR of ($1-x)$(La${}_{0.7}$Sr${}_{0.3}$MnO${}_3)$-xC composites is discussed.

Strontium silicate precursor powder was prepared by sol-precipitation. After TGA/DTA measurements, the powder was heated at 973K for 8 hours to obtain the corresponding compound. It is indicated from x-ray diffraction patterns that the major compound is SrSiO₃.

The preparatory conditions of forming strontium silicate powder in an alkaline solution, such as the effects of pH value and alkoxy ligand on the powder, have been studied.

In this study, it is indicated that:

(1) Using various alkoxy groups as the ligand, the less carbon number of alkoxy group has, the much faster of the hydrolysis is. It makes the particle size much bigger.

(2) In various pH values, the higher pH value has, the much faster of the hydrolysis is, and the larger of the particle size becomes.

(3) The sintering behaviours of various particle size powders are also investigated. The more carbon number of alkoxy group has, the bigger the grain size is, the more densification of the bulk density and the less of the linear shrinkage in sintering are. The electrical resistivity of the sintered body is 10⁴~10⁸ ohm-cm, belonging to a semiconductor material.

(4) From the variations of susceptibility with temperature analyzed by SQUID, we found that this compound is diamagnetism substance.

(5) The electrical resistivity and dielectric constant of SrSiO₃ are also determined.

Hall effects of bismuth have been studied theoretically with a special reference to the diamagnetic susceptibility. The conductivity, the Hall conductivity, and the orbital susceptibility are calculated on the basis of the Kubo formula for the 4 × 4 Dirac fermions in three dimension. The Hall coefficient exhibits unexpected peaks at the band-edge and sign change at the center of the band gap. Implications of the present results to bismuth alloys are discussed.