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

On the solutions of the nonlinear Liouville hierarchy

We investigate the initial-value problem of the non-linear Liouville hierarchy. For the general form of the interaction potential we construct an explicit solution in terms of an expansion over particle clusters whose evolution is described by the corresponding-order cumulant of evolution operators of a system of finitely many particles. For the initial data from the space of integrable functions the existence of a strong solution of the Cauchy problem is proved.Comment: 9 page

The spectral shift function and Levinson's theorem for quantum star graphs

We consider the Schr\"odinger operator on a star shaped graph with $n$ edges joined at a single vertex. We derive an expression for the trace of the difference of the perturbed and unperturbed resolvent in terms of a Wronskian. This leads to representations for the perturbation determinant and the spectral shift function, and to an analog of Levinson's formula

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

On Rigorous Derivation of the Enskog Kinetic Equation

We develop a rigorous formalism for the description of the kinetic evolution of infinitely many hard spheres. On the basis of the kinetic cluster expansions of cumulants of groups of operators of finitely many hard spheres the nonlinear kinetic Enskog equation and its generalizations are justified. It is established that for initial states which are specified in terms of one-particle distribution functions the description of the evolution by the Cauchy problem of the BBGKY hierarchy and by the Cauchy problem of the generalized Enskog kinetic equation together with a sequence of explicitly defined functionals of a solution of stated kinetic equation is an equivalent. For the initial-value problem of the generalized Enskog equation the existence theorem is proved in the space of integrable functions.Comment: 28 page

And yet it moves: Recovery of volitional control after spinal cord injury

Preclinical and clinical neurophysiological and neurorehabilitation research has generated rather surprising levels of recovery of volitional sensory-motor function in persons with chronic motor paralysis following a spinal cord injury. The key factor in this recovery is largely activity-dependent plasticity of spinal and supraspinal networks. This key factor can be triggered by neuromodulation of these networks with electrical and pharmacological interventions. This review addresses some of the systems-level physiological mechanisms that might explain the effects of electrical modulation and how repetitive training facilitates the recovery of volitional motor control. In particular, we substantiate the hypotheses that: (1) in the majority of spinal lesions, a critical number and type of neurons in the region of the injury survive, but cannot conduct action potentials, and thus are electrically non-responsive; (2) these neuronal networks within the lesioned area can be neuromodulated to a transformed state of electrical competency; (3) these two factors enable the potential for extensive activity-dependent reorganization of neuronal networks in the spinal cord and brain, and (4) propriospinal networks play a critical role in driving this activity-dependent reorganization after injury. Real-time proprioceptive input to spinal networks provides the template for reorganization of spinal networks that play a leading role in the level of coordination of motor pools required to perform a given functional task. Repetitive exposure of multi-segmental sensory-motor networks to the dynamics of task-specific sensory input as occurs with repetitive training can functionally reshape spinal and supraspinal connectivity thus re-enabling one to perform complex motor tasks, even years post injury

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

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