Non-cyclic Geometric Phase due to Spatial Evolution in a Neutron Interferometer

We present a split-beam neutron interferometric experiment to test the non-cyclic geometric phase tied to the spatial evolution of the system: the subjacent two-dimensional Hilbert space is spanned by the two possible paths in the interferometer and the evolution of the state is controlled by phase shifters and absorbers. A related experiment was reported previously by Hasegawa et al. [Phys. Rev. A 53, 2486 (1996)] to verify the cyclic spatial geometric phase. The interpretation of this experiment, namely to ascribe a geometric phase to this particular state evolution, has met severe criticism from Wagh [Phys. Rev. A 59, 1715 (1999)]. The extension to a non-cyclic evolution manifests the correctness of the interpretation of the previous experiment by means of an explicit calculation of the non-cyclic geometric phase in terms of paths on the Bloch-sphere.Comment: 4 pages, revtex

Quasi-Lagrangian Systems of Newton Equations

Systems of Newton equations of the form $\ddot{q}=-{1/2}A^{-1}(q)\nabla k$ with an integral of motion quadratic in velocities are studied. These equations generalize the potential case (when A=I, the identity matrix) and they admit a curious quasi-Lagrangian formulation which differs from the standard Lagrange equations by the plus sign between terms. A theory of such quasi-Lagrangian Newton (qLN) systems having two functionally independent integrals of motion is developed with focus on two-dimensional systems. Such systems admit a bi-Hamiltonian formulation and are proved to be completely integrable by embedding into five-dimensional integrable systems. They are characterized by a linear, second-order PDE which we call the fundamental equation. Fundamental equations are classified through linear pencils of matrices associated with qLN systems. The theory is illustrated by two classes of systems: separable potential systems and driven systems. New separation variables for driven systems are found. These variables are based on sets of non-confocal conics. An effective criterion for existence of a qLN formulation of a given system is formulated and applied to dynamical systems of the Henon-Heiles type.Comment: 50 pages including 9 figures. Uses epsfig package. To appear in J. Math. Phy

Dynamics of the Tippe Top -- properties of numerical solutions versus the dynamical equations

We study the relationship between numerical solutions for inverting Tippe Top and the structure of the dynamical equations. The numerical solutions confirm oscillatory behaviour of the inclination angle $\theta(t)$ for the symmetry axis of the Tippe Top. They also reveal further fine features of the dynamics of inverting solutions defining the time of inversion. These features are partially understood on the basis of the underlying dynamical equations

Magnetic phase diagram of CePt3B1-xSix

We present a study of the main bulk properties (susceptibility, magnetization, resistivity and specific heat) of CePt_3B_(1-x)Si-x, an alloying system that crystallizes in a noncentrosymmetric lattice, and derive the magnetic phase diagram. The materials at the end point of the alloying series have previously been studied, with CePt_3B established as a material with two different magnetic phases at low temperatures (antiferromagnetic below T_N = 7.8 K, weakly ferromagnetic below T_C ~ 5 K), while CePt3Si is a heavy fermion superconductor (T_c = 0.75 K) coexisting with antiferromagnetism (T_N = 2.2 K). From our experiments we conclude that the magnetic phase diagram is divided into two regions. In the region of low Si content (up to x ~ 0.7) the material properties resemble those of CePt3B. Upon increasing the Si concentration further the magnetic ground state continuously transforms into that of CePt3Si. In essence, we argue that CePt_3B can be understood as a low pressure variant of CePt3Si.Comment: 7pages, 9figure