Longtime dynamics for the Landau Hamiltonian with a time dependent magnetic field

We consider the decay $\pi^- \to l \, \bar{\nu}_l$ ($l=e^-,\,\mu^-$) in the presence of an arbitrary large uniform magnetic field, using the symmetric gauge. The consequences of the axial symmetry of the problem and the issue of angular momentum conservation are discussed in detail. In particular, we analyze the projection of both the canonical and the mechanical total angular momenta along the direction of the magnetic field. It is found that while the former is conserved in the symmetric gauge, the latter is not conserved in both the symmetric and Landau gauges. We derive an expression for the integrated $\pi^- \to l \, \bar{\nu}_l$ width that coincides exactly with the one we previously found using the Landau gauge, providing an explicit test of the gauge independence of that result. Such an expression implies that for nonzero magnetic fields the decay width does not vanish in the limit in which the outgoing charged leptons can be considered as massless, i.e. it does not exhibit the helicity suppression found in the case of no external field.

Contribution of time-dependent electric and magnetic fields to the dynamics of magnetic storms

We investigated the quantum states of a free electron with time-dependenteffective mass subjected to a time-dependent magnetic field by solving theSchrödinger equation under the choice of Landau and symmetric gauges. Usingthe invariant operator and unitary transformation methods together, wederived exact wavefunctions of the system. The wavefunctions rely on thesolution of associated classical dynamical systems. We confirmed that thequantum analysis of the system under the two gauges coincides mutually.

We study two quantum mechanical systems on the noncommutative plane using a representation independent approach. First, in the context of the Landau problem, we obtain an explicit expression for the gauge transformation that connects the Landau and the symmetric gauge in noncommutative space. This lead us to conclude that the usual form of the symmetric gauge A⃗=−β2Ŷ,β2X̂, in which the constant β is interpreted as the magnetic field, is not true in noncommutative space. We also be able to establish a precise definition of β as a function of the magnetic field, for which the equivalence between the symmetric and Landau gauges is held in noncommutative plane. Using the symmetric gauge, we obtain results for the spectrum of the quantum Hall system, its transverse conductivity in the presence of an electric field, and other static observables. These results amend the literature on quantum Hall effect in the noncommutative plane in which the incorrect form of the symmetric gauge, in noncommutative space, is assumed. We also study the non-equilibrium dynamics of simple observables for this system. On the other hand, we study the dynamics of the harmonic oscillator in non-commutative space and show that, in general, it exhibits quasi-periodic behavior, in striking contrast with its commutative version. The study of dynamics reveals itself as a most powerful tool to characterize and understand the effects of non-commutativity.

In this work, we have studied, for the first time, the impact of a realistic picture of a time dependent electric and magnetic field on the shear and bulk viscosities of the medium. Both the electric and magnetic fields are considered to be exponentially decaying with time, and the study is valid in the regime where the magnetic field strength is weak (eB≪T2). The evaluation has been done in the kinetic theory framework wherein we have solved the relativistic Boltzmann transport equation within the relaxation time approximation collision kernel. We have shown that the constant weak field results as well as the B=0 results in the literature can be obtained as special cases of our general results. We have observed that the shear and bulk viscosities increase with time or equivalently, increase with the decrease of the strength of the magnetic field. To connect these observations with experiments, we have calculated the thermalization time, shear viscosity to entropy ratio (η/s), and bulk viscosity to entropy ratio (ζ/s). Published by the American Physical Society 2025

We consider a quantum spinless nonrelativistic charged particle moving in the plane under the action of a time-dependent magnetic field, described by means of the linear vector potential , with two fixed values of the gauge parameter : (the circular gauge) and (the Landau gauge). While the magnetic field is the same in all the cases, the systems with different values of the gauge parameter are not equivalent for nonstationary magnetic fields due to different structures of induced electric fields, whose lines of force are circles for and straight lines for . We derive general formulas for the time-dependent mean values of the energy and magnetic moment, as well as for their variances, for an arbitrary function . They are expressed in terms of solutions to the classical equation of motion , with . Explicit results are found in the cases of the sudden jump of magnetic field, the parametric resonance, the adiabatic evolution, and for several specific functions , when solutions can be expressed in terms of elementary or hypergeometric functions. These examples show that the evolution of the mentioned mean values can be rather different for the two gauges, if the evolution is not adiabatic. It appears that the adiabatic approximation fails when the magnetic field goes to zero. Moreover, the sudden jump approximation can fail in this case as well. The case of a slowly varying field changing its sign seems especially interesting. In all the cases, fluctuations of the magnetic moment are very strong, frequently exceeding the square of the mean value.

NONEQUILIBRIUM MULTICRITICAL BEHAVIOR IN ANISOTROPIC HEISENBERG FERROMAGNET DRIVEN BY OSCILLATING MAGNETIC FIELD

In order to accurately position biological material and cells, it is a useful way to label those particles with magnetic nanoparticles (MNPs) and target them via static or time-dependent magnetic fields. The aim of our work is to generate tailored magnetic fields to optimize the magnetic nanoparticle assisted gene transfer, cell positioning and drug targeting.The first step in the design of the magnetic field generators is the determination of the basic geometry using analytical equations. Subsequently, the geometry will be optimized by numerical field calculations. The trajectories of the magnetic nanoparticles have to be calculated with respect to the physiological boundary conditions like blood flow and pressure as well as size and geometry of the target tissue.It is possible to estimate the amount of particles which can be retained by the external magnetic field source at the target location. This is done by combining the numerical calculations of the magnetic field, structural mechanics and hydrodynamics within the target area with the magnetic and geometric properties of the particles or complexes. During all those consecutive steps we construct several prototypes of field generators which will be tested in experiments. According to these results we build static as well as time-dependent adequate magnetic field sources and optimize them and the underlying physical model in an iterative approach.We want to aspire a magnetic field that will be able to exactly transport and position nucleic acids, viral particles and magnetic nanoparticle labeled cells in vitro, in vivo and ex vivo.

The classical continuous XY model - defined as the two-component normalized spin-field - within a time-dependent magnetic field is investigated. It is shown that the dynamics of the spin-field is governed by the elliptic sine-Gordon equation in which the time dependence is built into the time-dependent external magnetic field. This equation is solved by using the covariant Hamilton-Jacobi equation technique and the Backlund transformation method. The reasons for the poor dynamics of the model are discussed.

A theoretical examination of thermal convection for a couple stress fluid which is electrically conducting and possessing significant thermal relaxation time is explored under time dependent magnetic field. Fourier’s law fails for a diverse area of applications such as fluids subjected to rapid heating, strongly confined fluid and nano-devices and hence a non-classical heat conduction law is employed. The heat transport in the system is examined and quantified employing the Lorenz model. The Nusselt number is deduced to quantitate the transfer of heat.KeywordsMagnetic field modulationMaxwell-Cattaneo lawCouple stress fluid

The influence of time-dependent electric and magnetic fields on the dynamic localization of lattice electrons

A uniaxially (along the Z axis) anisotropic Heisenberg ferromagnet, in the presence of time-dependent (but uniform over space) magnetic field, is studied by Monte Carlo simulation. The time-dependent magnetic field was taken as elliptically polarized where the resultant field vector rotates in the X-Z plane. The system is cooled (in the presence of the elliptically polarized magnetic field) from high temperature. As the temperature decreases, it was found that in the low anisotropy limit the system undergoes three successive dynamical phase transitions. These three dynamic transitions were confirmed by studying the temperature variation of dynamic "specific heat." The temperature variation of dynamic specific heat shows three peaks indicating three dynamic transition points.

This work shows the ability to remotely control the paracrine performance of mesenchymal stromal cells (MSCs) in producing an angiogenesis key molecule, vascular endothelial growth factor (VEGF-A), by modulation of an external magnetic field. This work compares for the first time the application of static and dynamic magnetic fields in angiogenesis in vitro model, exploring the effect of magnetic field intensity and dynamic regimes on the VEGF-A secretion potential of MSCs. Tissue scaffolds of gelatin doped with iron oxide nanoparticles (MNPs) were used as a platform for MSC proliferation. Dynamic magnetic field regimes were imposed by cyclic variation of the magnetic field intensity in different frequencies. The effect of the magnetic field intensity on cell behavior showed that higher intensity of 0.45 T was associated with increased cell death and a poor angiogenic effect. It was observed that static and dynamic magnetic stimulation with higher frequencies led to improved angiogenic performance on endothelial cells in comparison with a lower frequency regime. This work showed the possibility to control VEGF-A secretion by MSCs through modulation of the magnetic field, offering attractive perspectives of a non-invasive therapeutic option for several diseases by revascularizing damaged tissues or inhibiting metastasis formation during cancer progression.

We investigated the effect of long-term exposure to modulation magnetic field (MF), insulin, and their combination on blood-brain barrier (BBB) permeability in a diabetic rat model. Fifty-three rats were randomly assigned to one of six groups: sham, exposed to no MF; MF, exposed to MF; diabetes mellitus (DM), DM induced with streptozotocin (STZ); DM plus MF (DMMF); DM plus insulin therapy (DMI); and DM plus insulin therapy plus MF (DMIMF). All the rats underwent Evans blue (EB) measurement to evaluate the BBB 30 days after the beginning of experiments. The rats in MF, DMMF, and DMIMF groups were exposed to MF (B = 5 mT) for 165 min every day for 30 days. Mean arterial blood pressure (MABP), body mass, and serum glucose level of the study rats were recorded. The extravasation of brain EB of the MF, DM, DMMF, DMI, and DMIMF groups was higher than that of the sham group and the extravasation of right hemisphere of the DMIMF group was highest (P < 0.05). The post-procedure body mass of the sham and MF groups were significantly higher than those of the DM and DMMF groups (P < 0.05). In the DM, DMMF, DMI, and DMIMF groups, the baseline glucose was significantly lower than the post-procedure glucose (P < 0.05). DM and MF increase BBB permeability; in combination, they cause more increase in BBB permeability, and insulin decreases their effect on BBB. Improved glucose metabolism may prevent body mass loss and the hypoglycemic effect of MF. DM increases MABP but MF causes no additional effect.

We investigate both pure and mixed states Floquet dynamical quantum phase transition (DQPT) in the periodically time-dependent extended XY model. We exactly show that the proposed Floquet Hamiltonian of interacting spins can be expressed as a sum of noninteracting quasi-spins imposed by an effective time dependent magnetic field (Schwinger-Rabi model). The calculated Chern number indicates that there is a topological transition from nonadiabatic to adiabatic regime. In the adiabatic regime, the quasi-spins trace the time dependent effective magnetic field and then oscillate between spin up and down states. While in the nonadiabatic regime, the quasi-spins cannot follow the time dependent effective magnetic field and feel an average magnetic field. We find the range of driving frequency over which the quasi-spins experience adiabatic cyclic processes. Moreover, we obtain the exact expression of the Loschmidt amplitude and generalized Loschmidt amplitude of the proposed Floquet system. The results represent that both pure and mixed states dynamical phase transition occurs when the system evolves adiabatically. In other words, the minimum required driving frequency for the appearance of Floquet DQPT is equal to the threshold frequency needed for transition from nonadiabatic to adiabatic regime.