Parameterizing qudit states

Quantum systems with a finite number of states at all times have been a primary element of many physical models in nuclear and elementary particle physics, as well as in condensed matter physics. Today, however, due to a practical demand in the area of developing quantum technologies, a whole set of novel tasks for improving our understanding of the structure of finite-dimensional quantum systems has appeared. In the present article we will concentrate on one aspect of such studies related to the problem of explicit parameterization of state space of an NN-level quantum system. More precisely, we will discuss the problem of a practical description of the unitary SU(N){SU(N)}-invariant counterpart of the NN-level state space BN{\mathcal{B}_N}, i.e., the unitary orbit space BN/SU(N){B_N/SU(N)}. It will be demonstrated that the combination of well-known methods of the polynomial invariant theory and convex geometry provides useful parameterization for the elements of BN/SU(N){B_N/SU(N)}. To illustrate the general situation, a detailed description ofBN/SU(N){B_N/SU(N)} for low-level systems: qubit (N=2{N= 2}), qutrit (N=3{N=3}), quatrit (N=4{N= 4}) - will be given.

Mission Planning of GEO Active Debris Removal Based on Revolver Mode

The mission planning of active debris removal (ADR) of revolver mode on geosynchronous orbit (GEO) is studied in this paper. It is assumed that there are one service satellite, one space depot, and some pieces of space debris in the ADR mission. The service satellite firstly rendezvouses with the debris and then releases the thruster deorbit kits (TDKs), which are carried with the satellite, to push the debris to the graveyard orbit. Space depot will provide replenishment for the service satellite. The purpose of this mission planning is to optimize the ADR sequence of the service satellite, which represents the chronological order, in which the service satellite approaches different debris. In this paper, the mission cost will be stated firstly, and then a mathematical optimization model is proposed. ADR sequence and orbital transfer time are used as designed variables, whereas the fuel consumption in the whole mission is regarded as objective for optimizing, and a specific number of TDKs is also a new constraint. Then, two-level optimization is proposed to solve the mission planning problem, which is low-level for finding optimal transfer orbit using accelerated particle swarm optimization (APSO) algorithm and up-level for finding best mission sequence using immune genetic (IGA) algorithm. Numerical simulations are carried out to demonstrate the effectiveness of the model and the optimization method. Results show that TDK number influences the fuel consumption through impacting the replenishing frequency and TDK redundancy. To reduce fuel consumption, the TDK number should be optimized and designed with suitable replenishing frequency and minimum TDK redundancy.

Influence of Sustainable Development of Space Activities on Earth Ecology

In the age of New Space, faces the global problem of orbit space constraint. Sustainable development of space activities will be possible only when space users implement technologies and practices suitable to avoid accumulating objects in orbit. Artificial debris in orbital space has reached catastrophic proportions. This harm the Earth’s ecology leading to increased steps to transform a planet that is unsuitable for life. Based on the fractal analysis, the graphic interpretation of the components of SWOT-analysis of development of the rocket and space industry is built. It is found that the weak side and threat to the activities of the aerospace industry is the insufficient funding of implemented projects and inefficient distribution of finances between its components: science and production. It is proposed to use blockchain technology as an effective tool for the cybersecurity of space objects. The ecological risks from space activities that affect the Earth’s ecology are analyzed. It is proven that the prevention of severe environmental consequences and minimization of the negative impact of the above threats require the introduction of environmental management systems in space activities.

Effectual topological complexity

We introduce the effectual topological complexity (ETC) of a [Formula: see text]-space [Formula: see text]. This is a [Formula: see text]-equivariant homotopy invariant sitting in between the effective topological complexity of the pair [Formula: see text] and the (regular) topological complexity of the orbit space [Formula: see text]. We study ETC for spheres and surfaces with antipodal involution, obtaining a full computation in the case of the torus. This allows us to prove the vanishing of twice the nontrivial obstruction responsible for the fact that the topological complexity of the Klein bottle is [Formula: see text]. In addition, this gives a counterexample to the possibility — suggested in Pavešić’s work on the topological complexity of a map — that ETC of [Formula: see text] would agree with Farber’s [Formula: see text] whenever the projection map [Formula: see text] is finitely sheeted. We conjecture that ETC of spheres with antipodal action recasts the Hopf invariant one problem, and describe (conjecturally optimal) effectual motion planners.

Examining the Effects of 4He Exposure on the Gut-Brain Axis

Beyond low-Earth orbit, space radiation poses significant risks to astronaut health. Previous studies have shown that the microbial composition of the gastrointestinal (GI) microbiome changes upon exposure to high-linear energy transfer radiation. Interestingly, radiation-induced shifts in GI microbiota composition are linked to various neuropsychological disorders. Herein, we aimed to study changes in GI microbiota and behaviors of rats exposed to whole-body radiation (0, 5 or 25 cGy 4He, 250 MeV/n) at approximately 6 months of age. Fecal samples were collected 24 h prior to 4He irradiation and 24 h and 7 days postirradiation for quantitative PCR analyses to assess fecal levels of spore-forming bacteria (SFB), Bifidobacterium, Lactobacillus and Akkermansia. Rats were also tested in the social odor recognition memory (SORM) test at day 7 after 4He exposure. A subset of rats was euthanized 90 min after completion of the SORM test, and GI tissue from small intestine to colon were prepared for examining overall histological changes and immunohistochemical staining for serotonin (5-HT). No notable pathological changes were observed in GI tissues. Akkermansia spp. and SFB were significantly decreased in the 25 cGy group at 24 h and 7 days postirradiation compared to pre-exposure, respectively. Bifidobacterium and Lactobacillus spp. showed no significant changes. 5-HT production was significantly higher in the proximal small intestine and the cecum in the 25 cGy group compared to the sham group. The 25 cGy group exhibited deficits in recognition in SORM testing at day 7 postirradiation. Taken together, these results suggest a connection between GI microbiome composition, serotonin production, and neurobehavioral performance, and that this connection may be disrupted upon exposure to 25 cGy of 4He ions.

Research on Semi-Physical Simulation Testing of Inter-Satellite Laser Interference in the China Taiji Space Gravitational Wave Detection Program

To guarantee a smooth in-orbit space gravitational wave detection for the Taiji mission, a semi-physical simulation test of inter-satellite laser interference is carried out. The semi-physical simulation test consists of three aspects: the establishment of the inter-satellite laser link, interferometry of the inter-satellite ranging, and simulation of the space environment. With the designed specifications for the semi-physical simulation platform, the test results for the inter-satellite laser interference can be obtained. Based on the semi-physical simulation test, the risks of inter-satellite laser interference technology can be mitigated, laying a solid foundation for the successful detection of in-orbit gravitational waves.

2D ELASTICITY TENSOR INVARIANTS, INVARIANTS DEFINITE POSITIVE CRITERIA

In this paper, we constructed relationships with the differents 2D elasticity tensor invariants. Indeed, let ${\bf A}$ be a 2D elasticity tensor. Rotation group action leads to a pair of Lax in linear elasticity. This pair of Lax leads to five independent invariants chosen among six. The definite positive criteria are established with the determined invariants. We believe that this approach finds interesting applications, as in the one of elastic material classification or approaches in orbit space description.

Correction: Bates et al. Vector Fields and Differential Forms on the Orbit Space of a Proper Action. Axioms 2021, 10, 118

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