Planar domain walls in black hole spacetimes

We investigate the behaviour of low-mass, planar domain walls in the so-called $\phi^4$ model of the scalar field on the Schwarzschild and Kerr backgrounds. We focus on a transit of a domain wall through a black hole and solve numerically the equations of motion for a range of parameters of the domain wall and the black hole. We observe a behavior resembling an occurrence of ringing modes. Perturbations of domain walls vanish during latter evolution, suggesting their stability against a passage through the black hole. The results obtained for Kerr and Reissner-Nordstr\"om black holes are also compared.Comment: 13 pages, 8 figure

Stationary solutions of semilinear Schrödinger equations with trapping potentials in supercritical dimensions

summary:Nonlinear Schrödinger equations are usually investigated with the use of the variational methods that are limited to energy-subcritical dimensions. Here we present the approach based on the shooting method that can give the proof of existence of the ground states in critical and supercritical cases. We formulate the assumptions on the system that are sufficient for this method to work. As examples, we consider Schrödinger-Newton and Gross-Pitaevskii equations with harmonic potentials

A nonrelativistic limit for AdS perturbations

The familiar $c\rightarrow \infty$ nonrelativistic limit converts the Klein-Gordon equation in Minkowski spacetime to the free Schroedinger equation, and the Einstein-massive-scalar system without a cosmological constant to the Schroedinger-Newton (SN) equation. In this paper, motivated by the problem of stability of Anti-de Sitter (AdS) spacetime, we examine how this limit is affected by the presence of a negative cosmological constant $\Lambda$. Assuming for consistency that the product $\Lambda c^2$ tends to a negative constant as $c\rightarrow \infty$, we show that the corresponding nonrelativistic limit is given by the SN system with an external harmonic potential which we call the Schrodinger-Newton-Hooke (SNH) system. We then derive the resonant approximation which captures the dynamics of small amplitude spherically symmetric solutions of the SNH system. This resonant system turns out to be much simpler than its general-relativistic version, which makes it amenable to analytic methods. Specifically, in four spatial dimensions, we show that the resonant system possesses a three-dimensional invariant subspace on which the dynamics is completely integrable and hence can be solved analytically. The evolution of the two-lowest-mode initial data (an extensively studied case for the original general-relativistic system), in particular, is described by this family of solutions.Comment: v3: slightly expanded published versio

Ground state in the energy super-critical Gross-Pitaevskii equation with a harmonic potential

The energy super-critical Gross--Pitaevskii equation with a harmonic potential is revisited in the particular case of cubic focusing nonlinearity and dimension d > 4. In order to prove the existence of a ground state (a positive, radially symmetric solution in the energy space), we develop the shooting method and deal with a one-parameter family of classical solutions to an initial-value problem for the stationary equation. We prove that the solution curve (the graph of the eigenvalue parameter versus the supremum) is oscillatory for d = 13. Compared to the existing literature, rigorous asymptotics are derived by constructing three families of solutions to the stationary equation with functional-analytic rather than geometric methods.Comment: 42 page

Spin-dependent potentials: spurious singularity and bounds on contact terms

This work applies a recent theoretical treatment of spin-dependent potentials to experimental searches, in particular in antiprotonic helium. The considered spin-dependent potentials between fermions or spin-polarised macroscopic objects result from an exchange of exotic spin-0 or spin-1 bosons. We address a superficial singularity in one of the potentials, as well as technical issues with contact terms, and use the results to obtain a bound on the pseudovector coupling constants and boson masses.Comment: 4 pages, 4 figure

Constraints on Spin-Spin-Velocity-Dependent Interaction

The existence of exotic spin-dependent forces may shine light on new physics beyond the Standard Model. We utilize two iron shielded SmCo$_5$ electron-spin sources and two optically pumped magnetometers to search for exotic long-range spin-spin-velocity-dependent force. The orientations of spin sources and magnetometers are optimized such that the exotic force is enhanced and common-mode noise is effectively subtracted. We set direct limit on proton-electron interaction in the force range from 1\,cm to 1\,km. Our experiment represents more than ten orders of magnitude improvement than previous works

The bone microstructure from anterior cruciate ligament footprintsis similar after ligament reconstruction and does not affect long‑termoutcomes

Purpose The purpose of this study was to assess the quality of the bone tissue microstructure from the footprints of the anterior cruciate ligament (ACL) and its impact on late follow-up outcomes in patients who undergo anterior cruciate ligament reconstruction (ACLR). Methods The records of 26 patients diagnosed with a completely torn ACL who underwent ACLR were collected. During the surgery performed using the Felmet method, bone blocks from the native ACL footprints were collected. The primary measurements of the bone microstructure were made using a microtomographic scanner. In late follow-up examinations, a GNRB arthrometer was used. Results There was no significant difference in the bone microstructure assessed using micro-CT histomorphometric data according to the blood test results, plain radiographs, age or anthropometric data. There was no difference in the bone volume/total volume ratio or trabecular thickness in the area of the native ACL footprints. Routine preoperative examinations werenot relevant to the quality of the bone microstructure. The elapsed time from an ACL injury to surgery had no relevance to the results of arthrometry. Conclusion The similarities in the microstructure of bone blocks from ACL footprints from the femur and tibia allow the variable use of these blocks to stabilize grafts in the Felmet method. The bone microstructure is not dependent on the time from injury to surgery. Histomorphometric values of the structure of the femoral and tibial ACL footprints have no impact on the long-term stability of the operated knee joint. Trial registration The approval of the Bioethics Committee of the Silesian Medical Chamber in Katowice, Poland (resolution 16/2014) was given for this research

Entangled coherent states under dissipation

We study the evolution of entangled coherent states of the two quantized electromagnetic fields under dissipation. Characteristic time scales for the decay of the negativity are found in the case of large values of the phase space distance among the states of each mode. We also study how the entanglement emerges among the reservoirs.Comment: 13 pages and 4 figures, published versio