Radiation reaction and quantum damped harmonic oscillator

By taking a Klein-Gordon field as the environment of an harmonic oscillator and using a new method for dealing with quantum dissipative systems (minimal coupling method), the quantum dynamics and radiation reaction for a quantum damped harmonic oscillator investigated. Applying perturbation method, some transition probabilities indicating the way energy flows between oscillator, reservoir and quantum vacuum, obtainedComment: 12 pages. Accepted for publication in Mod. Phys. Lett.

Experimental investigations of control principles of involuntary movement: a comprehensive review of the Kohnstamm phenomenon

The Kohnstamm phenomenon refers to the observation that if one pushes the arm hard outwards against a fixed surface for about 30 s, and then moves away from the surface and relaxes, an involuntary movement of the arm occurs, accompanied by a feeling of lightness. Central, peripheral and hybrid theories of the Kohnstamm phenomenon have been advanced. Afferent signals may be irrelevant if purely central theories hold. Alternatively, according to peripheral accounts, altered afferent signalling actually drives the involuntary movement. Hybrid theories suggest afferent signals control a centrally-programmed aftercontraction via negative position feedback control or positive force feedback control. The Kohnstamm phenomenon has provided an important scientific method for comparing voluntary with involuntary movement, both with respect to subjective experience, and for investigating whether involuntary movements can be brought under voluntary control. A full review of the literature reveals that a hybrid model best explains the Kohnstamm phenomenon. On this model, a central adaptation interacts with afferent signals at multiple levels of the motor hierarchy. The model assumes that a Kohnstamm generator sends output via the same pathways as voluntary movement, yet the resulting movement feels involuntary due to a lack of an efference copy to cancel against sensory inflow. This organisation suggests the Kohnstamm phenomenon could represent an amplification of neuromotor processes normally involved in automatic postural maintenance. Future work should determine which afferent signals contribute to the Kohnstamm phenomenon, the location of the Kohnstamm generator, and the principle of feedback control operating during the aftercontraction

Vacuum Photon Splitting in Lorentz-Violating Quantum Electrodynamics

Radiative corrections arising from Lorentz violation in the fermion sector induce a nonzero amplitude for vacuum photon splitting. At one loop, the on-shell amplitude acquires both CPT-even and CPT-odd contributions forbidden in conventional electrodynamics.Comment: 4 pages, minor wording changes, references added, accepted in Physical Review Letter

Looking for a time independent Hamiltonian of a dynamical system

In this paper we introduce a method for finding a time independent Hamiltonian of a given dynamical system by canonoid transformation. We also find a condition that the system should satisfy to have an equivalent time independent formulation. We study the example of damped oscillator and give the new time independent Hamiltonian for it, which has the property of tending to the standard Hamiltonian of the harmonic oscillator as damping goes to zero.Comment: Some references added, LATEX fixing

Fruit and vegetable juice fermentation with Bifidobacteria

Consumers are becoming more interested in healthy nutrition. To meet consumer requirements, the possibility of the fruit and vegetable juice fermentation by bifidobacteria was investigated. Sour cherry, orange, carrot, and tomato juice was fermented with five Bifidobacterium strains (from human origin and starter culture). The tested strains have grown well in orange, carrot, and tomato juices. The B. longum Bb-46 strain demonstrated the best growth activities. It was found that ratio of the produced acetic and lactic acids are dependent on the Bifidobacterium strain rather than on the fermentation medium. The most intensive inhibition was observed against the Campylobacter jejuni strain. In course of the fermentation the antioxidant capacities slightly decreased, except when the orange juice was fermented with B. lactis Bb-12 and B. longum A4.8. The obtained results may contribute to the design of a novel functional food product

The virtual Haken conjecture: Experiments and examples

A 3-manifold is Haken if it contains a topologically essential surface. The Virtual Haken Conjecture says that every irreducible 3-manifold with infinite fundamental group has a finite cover which is Haken. Here, we discuss two interrelated topics concerning this conjecture. First, we describe computer experiments which give strong evidence that the Virtual Haken Conjecture is true for hyperbolic 3-manifolds. We took the complete Hodgson-Weeks census of 10,986 small-volume closed hyperbolic 3-manifolds, and for each of them found finite covers which are Haken. There are interesting and unexplained patterns in the data which may lead to a better understanding of this problem. Second, we discuss a method for transferring the virtual Haken property under Dehn filling. In particular, we show that if a 3-manifold with torus boundary has a Seifert fibered Dehn filling with hyperbolic base orbifold, then most of the Dehn filled manifolds are virtually Haken. We use this to show that every non-trivial Dehn surgery on the figure-8 knot is virtually Haken.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper12.abs.htm

On the action principle for a system of differential equations

We consider the problem of constructing an action functional for physical systems whose classical equations of motion cannot be directly identified with Euler-Lagrange equations for an action principle. Two ways of action principle construction are presented. From simple consideration, we derive necessary and sufficient conditions for the existence of a multiplier matrix which can endow a prescribed set of second-order differential equations with the structure of Euler-Lagrange equations. An explicit form of the action is constructed in case if such a multiplier exists. If a given set of differential equations cannot be derived from an action principle, one can reformulate such a set in an equivalent first-order form which can always be treated as the Euler-Lagrange equations of a certain action. We construct such an action explicitly. There exists an ambiguity (not reduced to a total time derivative) in associating a Lagrange function with a given set of equations. We present a complete description of this ambiguity. The general procedure is illustrated by several examples.Comment: 10 page

Covariant Equilibrium Statistical Mechanics

A manifest covariant equilibrium statistical mechanics is constructed starting with a 8N dimensional extended phase space which is reduced to the 6N physical degrees of freedom using the Poincare-invariant constrained Hamiltonian dynamics describing the micro-dynamics of the system. The reduction of the extended phase space is initiated forcing the particles on energy shell and fixing their individual time coordinates with help of invariant time constraints. The Liouville equation and the equilibrium condition are formulated in respect to the scalar global evolution parameter which is introduced by the time fixation conditions. The applicability of the developed approach is shown for both, the perfect gas as well as the real gas. As a simple application the canonical partition integral of the monatomic perfect gas is calculated and compared with other approaches. Furthermore, thermodynamical quantities are derived. All considerations are shrinked on the classical Boltzmann gas composed of massive particles and hence quantum effects are discarded.Comment: 22 pages, 1 figur

Gauge Invariant Hamiltonian Formalism for Spherically Symmetric Gravitating Shells

The dynamics of a spherically symmetric thin shell with arbitrary rest mass and surface tension interacting with a central black hole is studied. A careful investigation of all classical solutions reveals that the value of the radius of the shell and of the radial velocity as an initial datum does not determine the motion of the shell; another configuration space must, therefore, be found. A different problem is that the shell Hamiltonians used in literature are complicated functions of momenta (non-local) and they are gauge dependent. To solve these problems, the existence is proved of a gauge invariant super-Hamiltonian that is quadratic in momenta and that generates the shell equations of motion. The true Hamiltonians are shown to follow from the super-Hamiltonian by a reduction procedure including a choice of gauge and solution of constraint; one important step in the proof is a lemma stating that the true Hamiltonians are uniquely determined (up to a canonical transformation) by the equations of motion of the shell, the value of the total energy of the system, and the choice of time coordinate along the shell. As an example, the Kraus-Wilczek Hamiltonian is rederived from the super-Hamiltonian. The super-Hamiltonian coincides with that of a fictitious particle moving in a fixed two-dimensional Kruskal spacetime under the influence of two effective potentials. The pair consisting of a point of this spacetime and a unit timelike vector at the point, considered as an initial datum, determines a unique motion of the shell.Comment: Some remarks on the singularity of the vector potantial are added and some minor corrections done. Definitive version accepted in Phys. Re