Magnetic Lensing near Ultramagnetized Neutron Stars

Extremely strong magnetic fields change the vacuum index of refraction. This induces a lensing effect that is not unlike the lensing phenomenon in strong gravitational fields. The main difference between the two is the polarization dependency of the magnetic lensing, a behaviour that induces a handful of interesting effects. The main prediction is that the thermal emission of neutron stars with extremely strong magnetic fields is polarized - up to a few percent for the largest fields known. This potentially allows a direct method for measuring their magnetic fields.Comment: To appear in MNRAS, 12 pages, 9 figure

Nonlinear Electromagnetic Waves in Magnetosphere of a Magnetar

We compute electromagnetic wave propagation through the magnetosphere of a magnetar. The magnetosphere is modeled as the QED vacuum and a cold, strongly magnetized plasma. The background field and electromagnetic waves are treated nonperturbatively and can be arbitrarily strong. This technique is particularly useful for examining non-linear effects in propagating waves. Waves travelling through such a medium typically form shocks; on the other hand we focus on the possible existence of waves that travel without evolving. Therefore, in order to examine the nonlinear effects, we make a travelling wave ansatz and numerically explore the resulting wave equations. We discover a class of solutions in a homogeneous plasma which are stabilized against forming shocks by exciting nonorthogonal components which exhibit strong nonlinear behaviour. These waves may be an important part of the energy transmission processes near pulsars and magnetars.Comment: 8 pages, 6 figures, edited for clarity and references added, version accepted for publication by MNRA

Dynamical quantum phase transitions: a brief survey

Nonequilibrium states of closed quantum many-body systems defy a thermodynamic description. As a consequence, constraints such as the principle of equal a priori probabilities in the microcanonical ensemble can be relaxed, which can lead to quantum states with novel properties of genuine nonequilibrium nature. In turn, for the theoretical description it is in general not sufficient to understand nonequilibrium dynamics on the basis of the properties of the involved Hamiltonians. Instead it becomes important to characterize time-evolution operators which adds time as an additional scale to the problem. In these Perspectives we summarize recent progress in the field of dynamical quantum phase transitions, which are phase transitions in time with temporal nonanalyticities in matrix elements of the time-evolution operator. These transitions are not driven by an external control parameter, but rather occur due to sharp internal changes generated solely by unitary real-time dynamics. We discuss the obtained insights on general properties of dynamical quantum phase transitions, their physical interpretation, potential future research directions, as well as recent experimental observations.Comment: 7 pages, 4 figure

Dynamical quantum phase transitions: scaling and universality

Dynamical quantum phase transitions (DQPTs) at critical times appear as non-analyticities during nonequilibrium quantum real-time evolution. Although there is evidence for a close relationship between DQPTs and equilibrium phase transitions, a major challenge is still to connect to fundamental concepts such as scaling and universality. In this work, renormalization group transformations in complex parameter space are formulated for quantum quenches in Ising models showing that the DQPTs are critical points associated with unstable fixed points of equilibrium Ising models. Therefore, these DQPTs obey scaling and universality. On the basis of numerical simulations, signatures of these DQPTs in the dynamical buildup of spin correlations are found with an associated power-law scaling determined solely by the fixed point's universality class. An outlook is given on how to explore this dynamical scaling experimentally in systems of trapped ions.Comment: 4 pages, 3 figures, minor changes, version as publishe

Dynamical quantum phase transitions in systems with broken-symmetry phases

In this work it is shown that dynamical quantum phase transitions in Loschmidt echos control the nonequilibrium dynamics of the order parameter after particular quantum quenches in systems with broken-symmetry phases. A direct connection between Loschmidt echos and the order parameter dynamics is established which links nonequilibrium microscopic probabilities to the system's macroscopic dynamical properties. These concepts are illustrated numerically using exact diagonalization for quantum quenches in the XXZ chain with initial N\'eel states. An outlook is given how to explore these predictions experimentally with ultra-cold gases in optical lattices.Comment: 4 pages, 3 figures, updated reference

Dynamical quantum phase transitions: a review

Quantum theory provides an extensive framework for the description of the equilibrium properties of quantum matter. Yet experiments in quantum simulators have now opened up a route towards generating quantum states beyond this equilibrium paradigm. While these states promise to show properties not constrained by equilibrium principles such as the equal a priori probability of the microcanonical ensemble, identifying general properties of nonequilibrium quantum dynamics remains a major challenge especially in view of the lack of conventional concepts such as free energies. The theory of dynamical quantum phase transitions attempts to identify such general principles by lifting the concept of phase transitions to coherent quantum real-time evolution. This review provides a pedagogical introduction to this field. Starting from the general setting of nonequilibrium dynamics in closed quantum many-body systems, we give the definition of dynamical quantum phase transitions as phase transitions in time with physical quantities becoming nonanalytic at critical times. We summarize the achieved theoretical advances as well as the first experimental observations, and furthermore provide an outlook onto major open questions as well as future directions of research.Comment: Any comments or suggestions are highly welcome, extended presentatio

Quenching a Quantum Critical State by the Order Parameter: Dynamical Quantum Phase Transitions and Quantum Speed Limits

Quantum critical states exhibit strong quantum fluctuations and are therefore highly susceptible to perturbations. In this work we study the dynamical stability against a sudden coupling to these strong fluctuations by quenching the order parameter of the underlying transition. Such a quench can generate superextensive energy fluctuations. This leads to a dynamical quantum phase transition (DQPT) with nonanalytic real-time behavior in the resulting decay of the initial state. By establishing a general connection between DQPTs and quantum speed limits, this allows us to obtain a yet unrecognized quantum speed limit with unconventional system size dependence. These findings are illustrated for the one-dimensional and the infinitely-connected transverse-field Ising model. The main concepts, however, are general and can be applied also to other critical states. An outlook is given onto the implications of the superextensive energy fluctuations on potential restricted thermalization despite of nonintegrability.Comment: 4 pages + supplementary, 3 figures, published versio

QED can explain the non-thermal emission from SGRs and AXPs : Variability

Owing to effects arising from quantum electrodynamics (QED), magnetohydrodynamical fast modes of sufficient strength will break down to form electron-positron pairs while traversing the magnetospheres of strongly magnetised neutron stars. The bulk of the energy of the fast mode fuels the development of an electron-positron fireball. However, a small, but potentially observable, fraction of the energy ($\sim 10^{33}$ ergs) can generate a non-thermal distribution of electrons and positrons far from the star. This paper examines the cooling and radiative output of these particles. Small-scale waves may produce only the non-thermal emission. The properties of this non-thermal emission in the absence of a fireball match those of the quiescent, non-thermal radiation recently observed non-thermal emission from several anomalous X-ray pulsars and soft-gamma repeaters. Initial estimates of the emission as a function of angle indicate that the non-thermal emission should be beamed and therefore one would expect this emission to be pulsed as well. According to this model the pulsation of the non-thermal emission should be between 90 and 180 degrees out of phase from the thermal emission from the stellar surface.Comment: 7 pages, 5 figures, to appear in the proceedings of the conference "Isolated Neutron Stars: from the Interior to the Surface" (April 2006, London), eds. D. Page, R. Turolla, & S. Zane, Astrophysics & Space Scienc