Quantum Kinetic Evolution of Marginal Observables

We develop a rigorous formalism for the description of the evolution of observables of quantum systems of particles in the mean-field scaling limit. The corresponding asymptotics of a solution of the initial-value problem of the dual quantum BBGKY hierarchy is constructed. Moreover, links of the evolution of marginal observables and the evolution of quantum states described in terms of a one-particle marginal density operator are established. Such approach gives the alternative description of the kinetic evolution of quantum many-particle systems to generally accepted approach on basis of kinetic equations.Comment: 18 page

Towards Rigorous Derivation of Quantum Kinetic Equations

We develop a rigorous formalism for the description of the evolution of states of quantum many-particle systems in terms of a one-particle density operator. For initial states which are specified in terms of a one-particle density operator the equivalence of the description of the evolution of quantum many-particle states by the Cauchy problem of the quantum BBGKY hierarchy and by the Cauchy problem of the generalized quantum kinetic equation together with a sequence of explicitly defined functionals of a solution of stated kinetic equation is established in the space of trace class operators. The links of the specific quantum kinetic equations with the generalized quantum kinetic equation are discussed.Comment: 25 page

The von Neumann Hierarchy for Correlation Operators of Quantum Many-Particle Systems

The Cauchy problem for the von Neumann hierarchy of nonlinear equations is investigated. One describes the evolution of all possible states of quantum many-particle systems by the correlation operators. A solution of such nonlinear equations is constructed in the form of an expansion over particle clusters whose evolution is described by the corresponding order cumulant (semi-invariant) of evolution operators for the von Neumann equations. For the initial data from the space of sequences of trace class operators the existence of a strong and a weak solution of the Cauchy problem is proved. We discuss the relationships of this solution both with the $s$-particle statistical operators, which are solutions of the BBGKY hierarchy, and with the $s$-particle correlation operators of quantum systems.Comment: 26 page

Slightly broken higher spin symmetry: general structure of correlators

We explore a class of CFT’s with higher spin currents and charges. Away from the free or N = ∞ limit the non-conservation of currents is governed by operators built out of the currents themselves, which deforms the algebra of charges by, and together with, its action on the currents. This structure is encoded in a certain A∞/L∞-algebra. Under quite general assumptions we construct invariants of the deformed higher spin symmetry, which are candidate correlation functions. In particular, we show that there is a finite number of independent structures at the n-point level. The invariants are found to have a form reminiscent of a one-loop exact theory. In the case of Chern-Simons vector models the uniqueness of the invariants implies the three-dimensional bosonization duality in the large-N limit

Structure and Biochemical Study of Nanocomposite Bioconstruction for Restoration of Bone-cartilaginous Defects

Porous and strong nanocomposite bioconstructions were formed by laser evaporation of an aqueous dispersion of carbon nanotubes in a protein matrix. The homogeneous dispersion was exposed to laser irradiation to create solid constructions. Continuous laser radiation with a wavelength of 970 nm and a power of 5-7 W was used. The porosity of nanocomposite bioconstructions was studied by the method of lowtemperature nitrogen porosimetry and X-ray microtomography, the tensile strength and relative elongation of bioconstructions were evaluated, and their biocompatibility was tested in vitro. It was found that with an increase of the carbon nanotube’s concentration, a slight decrease in strength (3-15 %), a decrease in the pore size (20- 40 %), and an increase in the degree of deformation (10-12 %) were observed. At the same time, the mechanical parameters of the bioconstructions met the requirements for the materials for the restoration of bone-cartilaginous defects. Using optical microscopy and the MTT-test, proliferative activity and structural features of bone tissue cells on the surface of nanocomposite bioconstructions were evaluated. Studies have shown no toxic or inhibitory effect on cells. The results of the studies can talk about the advantage of nanocomposite bioconstructions using as an implant material for improving the growth of biological cells and regenerating damaged biotissues. Keywords: Nanocomposites, laser radiation, mechanical properties, porosity, X-ray microtomography, biocompatibilit

Sampling of quantum dynamics at long time

The principle of energy conservation leads to a generalized choice of transition probability in a piecewise adiabatic representation of quantum(-classical) dynamics. Significant improvement (almost an order of magnitude, depending on the parameters of the calculation) over previous schemes is achieved. Novel perspectives for theoretical calculations in coherent many-body systems are opened.Comment: Revised versio

Electrophysiological Guidance of Epidural Electrode Array Implantation over the Human Lumbosacral Spinal Cord to Enable Motor Function after Chronic Paralysis.

Epidural electrical stimulation (EES) of the spinal cord has been shown to restore function after spinal cord injury (SCI). Characterization of EES-evoked motor responses has provided a basic understanding of spinal sensorimotor network activity related to EES-enabled motor activity of the lower extremities. However, the use of EES-evoked motor responses to guide EES system implantation over the spinal cord and their relation to post-operative EES-enabled function in humans with chronic paralysis attributed to SCI has yet to be described. Herein, we describe the surgical and intraoperative electrophysiological approach used, followed by initial EES-enabled results observed in 2 human subjects with motor complete paralysis who were enrolled in a clinical trial investigating the use of EES to enable motor functions after SCI. The 16-contact electrode array was initially positioned under fluoroscopic guidance. Then, EES-evoked motor responses were recorded from select leg muscles and displayed in real time to determine electrode array proximity to spinal cord regions associated with motor activity of the lower extremities. Acceptable array positioning was determined based on achievement of selective proximal or distal leg muscle activity, as well as bilateral muscle activation. Motor response latencies were not significantly different between intraoperative recordings and post-operative recordings, indicating that array positioning remained stable. Additionally, EES enabled intentional control of step-like activity in both subjects within the first 5 days of testing. These results suggest that the use of EES-evoked motor responses may guide intraoperative positioning of epidural electrodes to target spinal cord circuitry to enable motor functions after SCI

A New Look at Calcium Digermanide CaGe2_2: A High-Performing Semimetal Transparent Conducting Material for Ge Optoelectronics

Following a recently manifested guide of how to team up infrared transparency and high electrical conductivity within semimetal materials [C. Cui $et$ $al.$ Prog. Mater. Sci. 2023, 136, 101112], we evaluate an applicability of the calcium digermanide (CaGe$_2$) thin film electrodes for the advanced Ge-based optical devices. Rigorous growth experiments were conducted to define the optimal annealing treatment and thickness of the Ca-Ge mixture for producing stable CaGe$_2$ layers with high figure of merit (FOM) as transparent conducting material. Ab-initio electronic band structure calculations and optical modeling confirmed CaGe$_2$ semimetal nature, which is responsible for a demonstrated high FOM. To test CaGe$_2$ electrodes under actual conditions, a planar Ge photodetector (PD) with metal-semiconductor-metal structure was fabricated, where CaGe$_2$/Ge interface acts as Schottky barrier. The resulting Ge PD with semimetal electrodes outperformed commercially available Ge devices in terms of both photoresponse magnitude and operated spectral range. Moreover, by using femtosecond-laser projection lithography, a mesh CaGe$_2$ electrode with the relative broadband transmittance of 90\% and sheet resistance of 20 $\Omega$/sq. was demonstrated, which further enhanced Ge PD photoresponse. Thus, obtained results suggest that CaGe$_2$ thin films have a great potential in numerous applications promoting the era of advanced Ge optoelectronics.Comment: 12 pages, 4 figure

Lab-Scale Study of the Calcium Carbonate Dissolution and Deposition by Marine Cyanobacterium Phormidium subcapitatum

Suggestions that calcification in marine organisms changes in response to global variations in seawater chemistry continue to be advanced (Wilkinson, 1979; Degens et al. 1985; Kazmierczak et al. 1986; R. Riding 1992). However, the effect of [Na+] on calcification in marine cyanobacteria has not been discussed in detail although [Na+] fluctuations reflect both temperature and sea-level fluctuations. The goal of these lab-scale studies therefore was to study the effect of environmental pH and [Na+] on CaCO3 deposition and dissolution by marine cyanobacterium Phormidium subcapitatum. Marine cyanobacterium P. subcapitatum has been cultivated in ASN-III medium. [Ca2+] fluctuations were monitored with Ca(2+) probe. Na(+) concentrations were determined by the initial solution chemistry. It was found that the balance between CaCO3 dissolution and precipitation induced by P. subcapitatum grown in neutral ASN III medium is very close to zero. No CaCO3 precipitation induced by cyanobacterial growth occurred. Growth of P. subcapitatum in alkaline ASN III medium, however, was accompanied by significant oscillations in free Ca(2+) concentration within a Na(+) concentration range of 50-400 mM. Calcium carbonate precipitation occurred during the log phase of P. subcapitatum growth while carbonate dissolution was typical for the stationary phase of P. subcapitatum growth. The highest CaCO3 deposition was observed in the range of Na(+) concentrations between 200-400 mM. Alkaline pH also induced the clamping of P. subcapitatum filaments, which appeared to have a strong affinity to envelop particles of chemically deposited CaCO3 followed by enlargement of those particles size. EDS analysis revealed the presence of Mg-rich carbonate (or magnesium calcite) in the solution containing 10-100 mM Na(+); calcite in the solution containing 200 mM Na(+); and aragonite in the solution containing with 400 mM Na(+). Typical present-day seawater contains xxmM Na(+). Early (Archean) seawater was likely less saline. The division of marine cyanobacterium P. subcapitatum is associated with periodic deposition and dissolution of CaCO3, the rhythms and intensity of which are dependent on concentrations of both OH(-) and Na(+). Thus, the role of present-day marine cyanobacteria in the global carbonate cycle might be reduced to aggregation and recrystallization of available CaCO3 particles in marine water rather than long-term precipitation and accumulation of CaCO3 deposits. For lower Na(+) concentrations, precipitation of carbonates by cyanobacteria would be even less significant. These results suggest that the lack of calcified cyanobacteria in stromatalite-bearing Precambrian sequences can be explained not only by high dissolved inorganic carbon concentrations but also by lower salinity, as well as possible lower pH compared to present-day oceans

The Generalized Star Product and the Factorization of Scattering Matrices on Graphs

In this article we continue our analysis of Schr\"odinger operators on arbitrary graphs given as certain Laplace operators. In the present paper we give the proof of the composition rule for the scattering matrices. This composition rule gives the scattering matrix of a graph as a generalized star product of the scattering matrices corresponding to its subgraphs. We perform a detailed analysis of the generalized star product for arbitrary unitary matrices. The relation to the theory of transfer matrices is also discussed