Addenda and corrections to work done on the path-integral approach to classical mechanics

In this paper we continue the study of the path-integral formulation of classical mechanics and in particular we better clarify, with respect to previous papers, the geometrical meaning of the variables entering this formulation. With respect to the first paper with the same title, we {\it correct} here the set of transformations for the auxiliary variables $\lambda_{a}$. We prove that under this new set of transformations the Hamiltonian ${\widetilde{\cal H}}$, appearing in our path-integral, is an exact scalar and the same for the Lagrangian. Despite this different transformation, the variables $\lambda_{a}$ maintain the same operatorial meaning as before but on a different functional space. Cleared up this point we then show that the space spanned by the whole set of variables ($\phi, c, \lambda,\bar c$) of our path-integral is the cotangent bundle to the {\it reversed-parity} tangent bundle of the phase space ${\cal M}$ of our system and it is indicated as $T^{\star}(\Pi T{\cal M})$. In case the reader feel uneasy with this strange {\it Grassmannian} double bundle, we show in this paper that it is possible to build a different path-integral made only of {\it bosonic} variables. These turn out to be the coordinates of $T^{\star}(T^{\star}{\cal M})$ which is the double cotangent bundle of phase-space.Comment: Title changed, appendix expanded, few misprints fixe

Distillation by repeated measurements: continuous spectrum case

Repeated measurements on a part of a bipartite system strongly affect the other part not measured, whose dynamics is regulated by an effective contracted evolution operator. When the spectrum of this operator is discrete, the latter system is driven into a pure state irrespective of the initial state, provided the spectrum satisfies certain conditions. We here show that even in the case of continuous spectrum an effective distillation can occur under rather general conditions. We confirm it by applying our formalism to a simple model.Comment: 4 pages, 2 figure

A 9Cr-1Mo steel as a mercury containment material for the SNAP-8 boiler

9Cr-1Mo steel as mercury containment material for SNAP-8 boile

Initial state maximizing the nonexponentially decaying survival probability for unstable multilevel systems

The long-time behavior of the survival probability for unstable multilevel systems that follows the power-decay law is studied based on the N-level Friedrichs model, and is shown to depend on the initial population in unstable states. A special initial state maximizing the asymptote of the survival probability at long times is found and examined by considering the spontaneous emission process for the hydrogen atom interacting with the electromagnetic field.Comment: 5 pages, 1 table. Accepted for publication in Phys. Rev.

Reflection and Transmission in a Neutron-Spin Test of the Quantum Zeno Effect

The dynamics of a quantum system undergoing frequent "measurements", leading to the so-called quantum Zeno effect, is examined on the basis of a neutron-spin experiment recently proposed for its demonstration. When the spatial degrees of freedom are duely taken into account, neutron-reflection effects become very important and may lead to an evolution which is totally different from the ideal case.Comment: 26 pages, 6 figure

Muscle plasticity related to changes in tubulin and αB-crystallin levels induced by eccentric contraction in rat skeletal muscles

We used the model of eccentric contraction of the hindlimb muscle by Ochi et al. to examine the role of eccentric contraction in muscle plasticity. This model aims to focus on stimulated skeletal muscle responses by measuring tissue weights and tracing the quantities of αB-crystallin and tubulin. The medial gastrocnemius muscle (GCM) responded to electrically induced eccentric contraction (EIEC) with significant increases in tissue weight (p < 0.01) and the ratio of tissue weight to body weight (p < 0.05); however, there was a decrease in soleus muscle weight after EIEC. EIEC in the GCM caused contractile-induced sustenance of the traced proteins, but the soleus muscle exhibited a remarkable decrease in α-tubulin and a 19% decrease in αB-crystallin. EIEC caused fast-to-slow myosin heavy chain (MHC) isoform type-oriented shift within both the GCM and soleus muscle. These results have shown that different MHC isoform type-expressing slow and fast muscles commonly undergo fast-to-slow type MHC isoform transformation. This suggests that different levels of EIEC affected each of the slow and fast muscles to induce different quantitative changes in the expression of αB-crystallin and α-tubulin

Exponential behavior of a quantum system in a macroscopic medium

An exponential behavior at all times is derived for a solvable dynamical model in the weak-coupling, macroscopic limit. Some implications for the quantum measurement problem are discussed, in particular in connection with dissipation.Comment: 8 pages, report BA-TH/94-17

An quantum approach of measurement based on the Zurek's triple model

In a close form without referring the time-dependent Hamiltonian to the total system, a consistent approach for quantum measurement is proposed based on Zurek's triple model of quantum decoherence [W.Zurek, Phys. Rev. D 24, 1516 (1981)]. An exactly-solvable model based on the intracavity system is dealt with in details to demonstrate the central idea in our approach: by peeling off one collective variable of the measuring apparatus from its many degrees of freedom, as the pointer of the apparatus, the collective variable de-couples with the internal environment formed by the effective internal variables, but still interacts with the measured system to form a triple entanglement among the measured system, the pointer and the internal environment. As another mechanism to cause decoherence, the uncertainty of relative phase and its many-particle amplification can be summed up to an ideal entanglement or an Shmidt decomposition with respect to the preferred basis.Comment: 22pages,3figure

Initial wave packets and the various power-law decreases of scattered wave packets at long times

The long time behavior of scattered wave packets $\psi (x,t)$ from a finite-range potential is investigated, by assuming $\psi (x,t)$ to be initially located outside the potential. It is then shown that $\psi (x,t)$ can asymptotically decrease in the various power laws at long time, according to its initial characteristics at small momentum. As an application, we consider the square-barrier potential system and demonstrate that $\psi (x,t)$ exhibits the asymptotic behavior $t^{-3/2}$, while another behavior like $t^{-5/2}$ can also appear for another $\psi (x,t)$.Comment: 5 pages, 1 figur

Zeno Dynamics of von Neumann Algebras

The dynamical quantum Zeno effect is studied in the context of von Neumann algebras. We identify a localized subalgebra on which the Zeno dynamics acts by automorphisms. The Zeno dynamics coincides with the modular dynamics of that subalgebra, if an additional assumption is satisfied. This relates the modular operator of that subalgebra to the modular operator of the original algebra by a variant of the Kato-Lie-Trotter product formula.Comment: Revised version; further typos corrected; 9 pages, AMSLaTe