Weak Homogeneous Magnetic Field Research Articles

Microscopic derivation of Ginzburg–Landau theory and the BCS critical temperature shift in general external fields

We consider the Bardeen–Cooper–Schrieffer (BCS) free energy functional with weak and macroscopic external electric and magnetic fields and derive the Ginzburg–Landau functional. We also provide an asymptotic formula for the BCS critical temperature as a function of the external fields. This extends our previous results in Deuchert et al. (Microscopic derivation of Ginzburg-Landau theory and the BCS critical temperature shift in a weak homogeneous magnetic field, PMP 4(1), 1–89 (2023)) for the constant magnetic field to general magnetic fields with a nonzero magnetic flux through the unit cell.

Microscopic derivation of Ginzburg-Landau theory and the BCS critical temperature shift in a weak homogeneous magnetic field

Starting from the Bardeen-Cooper-Schrieffer (BCS) free energy functional, we derive the Ginzburg-Landau functional in the presence of a weak homogeneous magnetic field. We also provide an asymptotic formula for the BCS critical temperature as a function of the magnetic field. This extends the previous works arXiv:1102.4001 and arXiv:1410.2352 of Frank, Hainzl, Seiringer and Solovej to the case of external magnetic fields with non-vanishing magnetic flux through the unit cell.

The BCS critical temperature in a weak homogeneous magnetic field

We show that, within a linear approximation of BCS theory, a weak homogeneous magnetic field lowers the critical temperature by an explicit constant times the field strength, up to higher order terms. This provides a rigorous derivation and generalization of results obtained in the physics literature fromWHH theory of the upper critical magnetic field. A new ingredient in our proof is a rigorous phase approximation to control the effects of the magnetic field.

Entanglement in a fermionic spin chain containing a single mobile boson under decoherence

The concurrence between first and the last sites of a fermionic spin chain containing a single boson is rigorously investigated at finite low temperature in the vicinity of a weak homogeneous magnetic field. We consider the boson as a mobile spin-1 particle through the chain and study concurrence without/under decoherence and express some interesting phase flip and bit flip reactions of the pairwise entanglement between first and the last half-spins in the chain. Our investigations show that the concurrence between two considered half-spins has different behavior for various positions of the single boson along the chain. Indeed, we realize that the single boson mobility has an essential role to probe the pairwise entanglement intensity between two spins located at the opposite ends of a fermionic chain. Interestingly, the entanglement remains alive for higher temperatures when the boson is the nearest neighbor of the first fermion. When the boson is at the middle of chain, it is demonstrated that the threshold temperature (at which the concurrence vanishes) versus decoherence rate can be considered as a threshold temperature boundary. These results pave the way to set and interpret the numerical and analytical expressions for utilizing quantum information in realistic scenarios such as quantum state transmission, quantum communication science and quantum information processing, where the both fermion-fermion and fermion-boson correlations should be taken in to account.

Strong coupling between a single nitrogen-vacancy spin and the rotational mode of diamonds levitating in an ion trap

A scheme for strong coupling between a single atomic spin and the rotational mode of levitating nanoparticles is proposed. The idea is based on spin readout of nitrogen-vacancy centers embedded in aspherical nanodiamonds levitating in an ion trap. We show that the asymmetry of the diamond induces a rotational confinement in the ion trap. Using a weak homogeneous magnetic field and a strong microwave driving we then demonstrate that the spin of the nitrogen-vacancy center can be strongly coupled to the rotational mode of the diamond.

Observation of the motional Stark shift in low magnetic fields

We report on the observation of the motional Stark effect of highly excited $^{87}$Rb Rydberg atoms moving in the presence of a weak homogeneous magnetic field in a vapor cell. Employing electromagnetically induced transparency for spectroscopy of an atomic vapor, we observe the velocity-, quantum state- and magnetic field-dependent transition frequencies between the ground and Rydberg excited states. For atoms moving at velocities around $400\,\mathrm{m/s}$, the principal quantum number $n=100$ of the valence electron, and a magnetic field of $B=100\,\mathrm{G}$, we measure a motional Stark shift of $\sim10\,\mathrm{MHz}$. Our experimental results are supported by numerical calculations based on a diagonalization of the effective Hamiltonian governing the valence electron of $^{87}$Rb in the presence of crossed electric and magnetic fields.

Vortex-antivortex pair generation by an in-plane magnetic dipole on a superconducting film

We apply the time-dependent Ginzburg-Landau approach to describe the nucleation of vortex-antivortex pairs in a hybrid system, formed by a thin superconducting film with a single in-plane magnetic dipole on top of it, and to simulate the vortex dynamics in the presence of a direct transport current. At current densities, sufficient to depin vortices and antivortices from a magnetic dipole, it periodically generates vortex-antivortex pairs, producing vortex and antivortex streams which eventually coalesce into phase-slip lines with further increasing current. We demonstrate the possibility to efficiently control the generation rate and trajectories of emitted vortices by the applied current density and an additional weak homogeneous magnetic field.

Hall coefficient in an interacting electron gas

The Hall conductivity in a weak homogeneous magnetic field, $\omega_{c}\tau \ll 1$, is calculated. We have shown that to leading order in $1/\epsilon_{F}\tau$ the Hall coefficient $R_{H}$ is not renormalized by the electron-electron interaction. Our result explains the experimentally observed stability of the Hall coefficient in a dilute electron gas not too close to the metal-insulator transition. We avoid the currently used procedure that introduces an artificial spatial modulation of the magnetic field. The problem of the Hall effect is reformulated in a way such that the magnetic flux associated with the scattering process becomes the central element of the calculation.

On the possible equation of state of a giant molecular cloud

We intend to probe into the nature of the thermodynamical equilibrium of an idealized isothermal, spherical, self-gravitating, giant molecular cloud. The necessity of invoking a frozen in magnetic field has been pointed out for clouds with uniform mass distribution. An equation of state corresponding to the macroscopic statistical equilibrium of the cloud, steeped into a weak homogeneous magnetic field, has also been derived.

On Nucleon Magnetic Moments

The magnetic moments of the proton and neutron are computed for the pseudoscalar-pseudovector symmetric meson field considering the magnetic moments as the time average of the proton and the meson magnetic moments. Using the perturbation theory, the meson contribution is calculated from the self-energy of a nucleon in presence of a weak homogeneous magnetic field where the term due to meson magnetic energy was introduced from the expression for the force exerted on the emitted meson by the magnetic field. The self-energy is made finite with the idea of a fundamental length as introduced by Heisenberg and the cut-off so obtained fits exactly with that suggested by Chew in the extended-source theory. It is also found that mesons need to be present only about 25% of the time to explain the observed magnitudes of the anomalous nucleon magnetic moments.