Physics

We develop a perturbative method of computing spectral singularities of a Schreodinger operator defined by a general complex potential that vanishes outside a closed interval. These can be realized as zero-width resonances in optical gain media and correspond to a lasing effect that occurs at the threshold gain. Their time-reversed copies yield coherent perfect absorption of light that is also known as an antilaser. We use our general results to establish the exactness of the n-th order perturbation theory for an arbitrary complex potential consisting of n delta-functions, obtain an exact expression for the transfer matrix of these potentials, and examine spectral singularities of complex barrier potentials of arbitrary shape. In the context of optical spectral singularities, these correspond to inhomogeneous gain media.

We have measured the generation and relaxation of excited carriers along their drift direction near the breakdown of the quantum Hall e ect (QHE). The dissipative resistivity xx (x) at current densities close to the critical value for the QHE breakdown was measured as a function of the distance x from the electron injection at x = 0. By injecting "cold" electrons into constrictions at supercritical current levels, the evolution of the breakdown along the drift direction was monitored. After a smooth increase of the resistivity with the drifting distance, an avalanche-like rise towards a saturation value occurs. Drastic changes of the resistivity proÿles with the applied current were found in a narrow range around the critical current. The observed behavior is attributed to impurity-assisted tunneling between Landau levels. By injecting hot electrons (excited in a periodic set of constrictions) into a region with subcritical current density, the relaxation process was analyzed. Inelastic relaxation lengths with typical values in the range from 0.3 to 4 m were found, which agree within 10% with the elastic mean free path determined from the Hall mobility at zero magnetic ÿeld. We conclude that the energy relaxation process is triggered by scattering at impurity potentials. ?

The time evolution of excited charge carriers near the breakdown of the quantum Hall effect is studied within a simple two-Landau-level model. The model incorporates impurity-assisted inter-Landau-level tunneling as the main mechanism, however, with a characteristic length that is much smaller than the scale set by the width of a sample with homogeneous current distribution. Using the carrier drift velocity to convert time into position dependence, we find that the model can reproduce recent experimental results astonishingly well.

The breakdown of the quantum Hall effect, which is observed as an abrupt escalation in the longitudinal resistance with an associated loss in the quantization of Hall voltage is the major obstacle against improving the resistance standard which is currently based on this effect. Graphene is inherently a 2D material and has an unusual band structure that allows the quantization of the Hall resistance even at room temperature. These unique properties of graphene make it a good candidate as a high precision metrological characterization tool for the quantum Hall resistance. The uncertainty in the quantum Hall resistance in graphene has been rapidly improving recently and graphene samples have already been shown to reach the precision of the current best 2DEG samples. In this talk, experimental results on the breakdown of the quantum Hall effect in graphene on SiOx is presented. In narrow graphene samples of 1 micrometer width, the charge inhomogeneity is quite prominent and strongly af...

At present, J1819–1458 is the only rotating radio transient (RRAT) detected in X-rays. We have studied the long-term evolution of this source in the fallback disc model. The model can reproduce the period, period derivative and X-ray luminosity of J1819–1458 simultaneously in the accretion phase at ages ∼ 2 × 10^5 yr. We obtained reasonable model curves with a magnetic dipole field strength B_0 ∼ 5 × 10^11 G on the pole of the neutron star, which is much weaker than the field inferred from the dipole-torque formula. With this B0 and the measured period, we find J1819–1458 below and close to the radio pulsar death line. Our results are not sensitive to initial period, and the source properties can be produced with a large range of disc masses. Our simulations indicate that J1819–1458 is evolving towards the properties of dim isolated neutron stars at later phases of evolution. This implies a close evolutionary link between RRATs and dim isolated neutron stars. For other RRATs with measured period derivatives and unknown X-ray luminosities, we have estimated the lower limits on the B_0 values in the fallback disc model. These limits allow a dipole field distribution for RRATs that could fill the B_0 gap between the estimated B_0 ranges of dim thermal isolated neutron stars and central compact objects in the same model.

A series of detailed work on the long-term evolutions of young neutron star populations, namely anomalous X-ray pulsars (AXPs), soft gamma repeaters (SGRs), dim isolated neutron stars (XDINs), “high-magnetic-field” radio pulsars (HBRPs), and central compact objects (CCOs) showed that the X-ray luminosities, LX, and the rotational properties of these systems can be reached by the neutron stars evolving with fallback discs and conventional dipole fields. Remarkably different individual source properties of these populations are reproduced in the same model as a result of the differences in their initial conditions, magnetic moment, initial rotational period, and the disc properties. In this thesis, we have analysed the properties of the rotating radio transients (RRATs) in the same model. We investigated the long-term evolution of J1819–1458, which is the only RRAT detected in X-rays. The period, period derivative and X-ray luminosity of J1819–1458 can be reproduced simultaneously wit...

Asiri-parlak X-isini kaynaklari (AXK) bir gunes kutlesi icin gecerli Eddington sinirinin 100-1000 kati parlakliga sahip nesnelerdir. Bir goruse gore bu nesneler kutle aktarimi yapan $M \sim 10\,M_{\odot}$ kutleli karadelikler olup isimalari huzmelendigi icin Eddington limiti uzerinde parlakliga sahip olabilmektedir. Baska bir goruse gore ise bu nesneler ortanca kutleli karadelikler ($M \sim 100-1000\,M_{\odot}$) olarak Eddington limiti civarinda kutle aktarimi yapmaktadir. Cok yakin zamanda M82 galaksisindeki AXK NuSTAR J095551$+$6940.8'in X-isini pulsari, yani eslikcisinden kutle aktarimi yapmakta olan bir notron yildizi oldugu, kesfedilmistir. Disk-manyetosfer etkilesiminden yola cikilarak bu nesnenin manyetik alaninin $B \gtrsim 10^{13} {\rm G}$ oldugu gosterilmistir. Bu kadar yuksek manyetik alanlarda kuantum-elektrodinamiksel sureclerin elektron sacilma tesir kesitini kuculterek kritik isima gucunu Eddington limitinin uzerine cikarabilecegi bilinmektedir. M82 X-2'nin Ed...

Investigation of the long-term evolution of rotating radio transients (RRATs) is important to understand the evolutionary connections between the isolated neutron star populations in a single picture. The X-ray luminosities of RRATs (except one source) are not known. In the fallback disc model, we have developed a method to estimate the dipole field strengths of RRATs without X-ray information. We have found that RRATs could have dipole field strengths, B0, at the poles ranging from ∼7 × 109 to ∼6 × 1011 G which fill the gap between the B0 ranges of central compact objects (CCOs) and dim isolated neutron stars (XDINs) estimated in the same model. In our model, most of RRATs are evolving at ages (∼2–6) × 105 yr, much smaller than their characteristic ages, such that, cooling luminosities of a large fraction of relatively nearby RRATs could be detected by the eROSITA all-sky survey. Many RRATs are located above the upper border of the pulsar death valley with the fields inferred from ...

The recent detection of pulsations from the ultra luminous X-ray source (ULX) NuSTAR J095551+6940.8 in M82 by Bachetti et al. indicates that the object is an accreting neutron star in a high mass X-ray binary (HMXB) system. The super-Eddington luminosity of the object implies that the magnetic field is sufficiently strong to suppress the scattering cross-section unless its beam is viewed at a favourable angle. We show that the torque equilibrium condition for the pulsar indicates the dipole magnetic field of the neutron star is ∼ 10 14 G, two orders of magnitude higher than that estimated by Bachetti et al., and further point to the possibility that even stronger magnetic fields could well be in the higher multipoles. This supports the recent view that magnetars descent from HMXBs.

At present, J1819-1458 is the only rotating radio transient (RRAT) detected in X-rays. We have studied the long-term evolution of this source in the fallback disc model. The model can reproduce the period, period derivative, and X-ray luminosity of J1819-1458 simultaneously in the accretion phase at ages ∼2 × 10 5 yr. We obtained reasonable model curves with a magnetic dipole field strength B 0 ∼ 5 × 10 11 G on the pole of the neutron star, which is much weaker than the field inferred from the dipole-torque formula. With this B 0 and the measured period, we find J1819-1458 below and close to the radio pulsar death line. Our results are not sensitive to initial period, and the source properties can be produced with a large range of disc masses. Our simulations indicate that J1819-1458 is evolving towards the properties of dim isolated neutron stars at later phases of evolution. This implies a close evolutionary link between RRATs and dim isolated neutron stars. For other RRATs with measured period derivatives and unknown X-ray luminosities, we have estimated the lower limits on the B 0 values in the fallback disc model. These limits allow a dipole field distribution for RRATs that could fill the B 0 gap between the estimated B 0 ranges of dim thermal isolated neutron stars and central compact objects in the same model.

The rotational properties and X-ray luminosity of PSR J0726–2612 are close to those of dim isolated neutron stars (XDINs). It was proposed that the source could be the first XDIN with observable pulsed radio emission. We have investigated the long-term evolution of the source to test this possibility in the fallback disc model. Reasonable model curves that can account for the evolution of PSR J0726–2612 consistently with its radio pulsar property are similar to those of high-B radio pulsars with dipole field strength B0 ∼ a few × 1012 G at the pole of the star. In the same model, XDINs are estimated to have relatively weak fields (B0 ≲ 1012 G) locating them well below the pulsar death line. From the simulations, we estimate that PSR J0726–2612 is at an age of t ∼ 5 × 104 yr, and will achieve the rotational properties of a normal radio pulsar within ∼105 yr, rather than the XDIN properties.

We have investigated the detailed torque-reversal behavior of 4U 1626--67 in the framework of the recently developed comprehensive model of the inner disk radius and torque calculations for neutron stars accreting from geometrically thin disks. The model can reproduce the torque -- X-ray luminosity relation across the torque reversals of 4U 1626--67. Our results imply that: (1) rotational equilibrium is reached when the inner disk radius equals the co-rotation radius, $r_\mathrm{co}$, while the conventional Alfven radius is greater than and close to $r_\mathrm{co}$, (2) both spin-up and spin-down torques are operating on either side of torque reversal, (3) with increasing accretion rate the spin-up torque associated with accretion onto the star gradually dominates the spin-down torque exerted by the disk. The torque reversals are the natural outcome of transitions between the well-defined weak-propeller and spin-up phases of the star with a stable geometrically thin accretion disk.

We investigated the detailed torque-reversal behavior of 4U 1626–67 in the framework of the recently developed comprehensive model of the inner disk radius and torque calculations for neutron stars accreting from geometrically thin disks. The model can reproduce the relation between the torque and X-ray luminosity across the torque reversals of 4U 1626–67. Our results imply that: (1) rotational equilibrium is reached when the inner disk radius equals the co-rotation radius, rco, while the conventional Alfvén radius is greater than but close to rco; (2) both spin-up and spin-down torques are operating on either side of torque reversal; and (3) with the increasing accretion rate, the spin-up torque associated with accretion onto the star gradually dominates the spin-down torque exerted by the disk. The torque reversals are the natural outcome of transitions between the well-defined weak-propeller and spin-up phases of the star with a stable, geometrically thin accretion disk.