Majorana zero modes in a quantum Ising chain with longer-ranged interactions

A one-dimensional Ising model in a transverse field can be mapped onto a system of spinless fermions with p-wave superconductivity. In the weak-coupling BCS regime, it exhibits a zero energy Majorana mode at each end of the chain. Here, we consider a variation of the model, which represents a superconductor with longer ranged kinetic energy and pairing amplitudes, as is likely to occur in more realistic systems. It possesses a richer zero temperature phase diagram and has several quantum phase transitions. From an exact solution of the model these phases can be classified according to the number of Majorana zero modes of an open chain: 0, 1, or 2 at each end. The model posseses a multicritical point where phases with 0, 1, and 2 Majorana end modes meet. The number of Majorana modes at each end of the chain is identical to the topological winding number of the Anderson's pseudospin vector that describes the BCS Hamiltonian. The topological classification of the phases requires a unitary time-reversal symmetry to be present. When this symmetry is broken, only the number of Majorana end modes modulo 2 can be used to distinguish two phases. In one of the regimes, the wave functions of the two phase shifted Majorana zero modes decays exponentially in space but but in an oscillatory manner. The wavelength of oscillation is identical to the asymptotic connected spin-spin correlation of the XY-model in a transverse field to which our model is dual.Comment: 11 pages, 8 figures; brief clarifying comments added; few new references; this version is accepted in Phys. Rev.

CP1CP^{1} model with Hopf term and fractional spin statistics

We reconsider the $CP^{1}$ model with the Hopf term by using the Batalin-Fradkin-Tyutin (BFT) scheme, which is an improved version of the Dirac quantization method. We also perform a semi-classical quantization of the topological charge Q sector by exploiting the collective coordinates to explicitly show the fractional spin statistics.Comment: 15 page

Oscillating instanton solutions in curved space

We investigate oscillating instanton solutions of a self-gravitating scalar field between degenerate vacua. We show that there exist O(4)-symmetric oscillating solutions in a de Sitter background. The geometry of this solution is finite and preserves the $Z_{2}$ symmetry. The nontrivial solution corresponding to tunneling is possible only if the effect of gravity is taken into account. We present numerical solutions of this instanton, including the phase diagram of solutions in terms of the parameters of the present work and the variation of energy densities. Our solutions can be interpreted as solutions describing an instanton-induced domain wall or braneworld-like object rather than a kink-induced domain wall or braneworld. The oscillating instanton solutions have a thick wall and the solutions can be interpreted as a mechanism providing nucleation of the thick wall for topological inflation. We remark that $Z_{2}$ invariant solutions also exist in a flat and anti-de Sitter background, though the physical significance is not clear.Comment: 25 pages, 11 figues. Some typos corrected, references added, and Ch3. modified according to referee's comment

The false vacuum bubble nucleation due to a nonminimally coupled scalar field

We study the possibility of forming the false vacuum bubble nucleated within the true vacuum background via the true-to-false vacuum phase transition in curved spacetime. We consider a semiclassical Euclidean bubble in the Einstein theory of gravity with a nonminimally coupled scalar field. In this paper we present the numerical computations as well as the approximate analytical computations. We mention the evolution of the false vacuum bubble after nucleation.Comment: 23 pages, 12 figures, References added, minor correctio

Investigation of Rheological Properties of Blended Cement Pastes Using Rotational Viscometer and Dynamic Shear Rheometer

To successfully process concrete, it is necessary to predict and control its flow behavior. However, the workability of concrete is not completely measured or specified by current standard tests. Furthermore, it is only with a clear picture of cement hydration and setting that full prediction and control of concrete performance can be generalized. In order to investigate the rheological properties of blended cement pastes, a rotational viscometer (RV) was used to determine the flow characteristics of ordinary and blended pastes to provide assurance that it can be pumped and handled. Additionally, a dynamic shear rheometer (DSR) was used to characterize both the viscous and elastic components of pastes. Ordinary Portland cement paste and blended pastes (slag, fly ash, and silica fume) were investigated in this study. /e stress and strain of the blended specimens were measured by the DSR, which characterizes both viscous and elastic behaviors by measuring the complex shear modulus (the ratio of total shear stress to total shear strain) and phase angle (an indicator of the relative amounts of recoverable and nonrecoverable deformation) of materials. Cement pastes generally exhibit different rheological behaviors with respect to age, mineral admixture type, and cement replacement level

Semi-orthogonal subspaces for value mediate a tradeoff between binding and generalization

When choosing between options, we must associate their values with the action needed to select them. We hypothesize that the brain solves this binding problem through neural population subspaces. To test this hypothesis, we examined neuronal responses in five reward-sensitive regions in macaques performing a risky choice task with sequential offers. Surprisingly, in all areas, the neural population encoded the values of offers presented on the left and right in distinct subspaces. We show that the encoding we observe is sufficient to bind the values of the offers to their respective positions in space while preserving abstract value information, which may be important for rapid learning and generalization to novel contexts. Moreover, after both offers have been presented, all areas encode the value of the first and second offers in orthogonal subspaces. In this case as well, the orthogonalization provides binding. Our binding-by-subspace hypothesis makes two novel predictions borne out by the data. First, behavioral errors should correlate with putative spatial (but not temporal) misbinding in the neural representation. Second, the specific representational geometry that we observe across animals also indicates that behavioral errors should increase when offers have low or high values, compared to when they have medium values, even when controlling for value difference. Together, these results support the idea that the brain makes use of semi-orthogonal subspaces to bind features together.Comment: arXiv admin note: substantial text overlap with arXiv:2205.0676

WEB-BASED LABORATORY MODULES FOR LINEAR AND ANGULAR KINEMATICS

Two Web-based laboratory modules have been developed and implemented for reinforcing basic concepts in kinematics in the learning of biomechanics. In the linear kinematics module, students digitize the mid-hip, heel and toe on images showing the side views of sprinting, running and jogging and analyze the stride length and time and velocity alTlong these actions. For the angular kinematics module, students digitize the near shoulder, hip, and knee on images of one complete revolution of a forward giant swing of a gymnast and determine the hip angle, the angular velocity and acceleration of the trunk. Evaluations and feedback from biomechanics instructors and students in biomechanics courses have suggested that these modules have the potential to be effective educational tools

Creation of a black hole pair with a domain wall

We study the creation of a black hole (BH) pair separated by a domain wall, in the presence of a cosmological constant. We construct the solution representing a BH pair with a domain wall and compute the Euclidean action to evaluate the probability of the pair creation in the background with a preexisting domain wall. The BHs can be either neutral or magnetically charged ones. We compare the results of the charged case with those of the neutral case with the same cosmological constant. We find that the production rate of a charged BH pair is always suppressed in comparison with that of the neutral one in both four and five dimensions, irrespective of the sign of the cosmological constant. The Euclidean action is equal to the minus of the entropy. Since the horizon area of a BH is decreased as the magnitude of its charge is increased in general, the decreasing creation rate can be understood in terms of the increasing charge. We obtain the explicit confirmation on the relation between the pair creation rate of the charged BHs and the area of horizons in both the four- and five-dimensional cases in the presence of a cosmological constant. The singularity of the domain wall universe with charged BHs, as distinct from that with neutral BHs, can be avoided.Comment: 23 pages, 11 figures, Some typos corrected and references added with respect to the published versio

Scientific Impacts of Wind Direction Errors

An assessment on the scientific impact of random errors in wind direction (less than 45 deg) retrieved from space-based observations under weak wind (less than 7 m/s ) conditions was made. averages, and these weak winds cover most of the tropical, sub-tropical, and coastal oceans. Introduction of these errors in the semi-daily winds causes, on average, 5% changes of the yearly mean Ekman and Sverdrup volume transports computed directly from the winds, respectively. These poleward movements of water are the main mechanisms to redistribute heat from the warmer tropical region to the colder high- latitude regions, and they are the major manifestations of the ocean's function in modifying Earth's climate. Simulation by an ocean general circulation model shows that the wind errors introduce a 5% error in the meridional heat transport at tropical latitudes. The simulation also shows that the erroneous winds cause a pile-up of warm surface water in the eastern tropical Pacific, similar to the conditions during El Nino episode. Similar wind directional errors cause significant change in sea-surface temperature and sea-level patterns in coastal oceans in a coastal model simulation. Previous studies have shown that assimilation of scatterometer winds improves 3-5 day weather forecasts in the Southern Hemisphere. When directional information below 7 m/s was withheld, approximately 40% of the improvement was los

Observation of Scarred Modes in Asymmetrically Deformed Microcylinder Lasers

We report observation of lasing in the scarred modes in an asymmetrically deformed microcavity made of liquid jet. The observed scarred modes correspond to morphology-dependent resonance of radial mode order 3 with their Q values in the range of 10^6. Emission directionality is also observed, corresponding to a hexagonal unstable periodic orbit.Comment: 4 pages, 6 figure