Topological Aspects of the Non-adiabatic Berry Phase

The topology of the non-adiabatic parameter space bundle is discussed for evolution of exact cyclic state vectors in Berry's original example of split angular momentum eigenstates. It turns out that the change in topology occurs at a critical frequency. The first Chern number that classifies these bundles is proportional to angular momentum. The non-adiabatic principal bundle over the parameter space is not well-defined at the critical frequency.Comment: 14 pages, Dep. of Physics, Uni. of Texas at Austin, Austin, Texas 78712, to appear in J. Physics

Resonances, Unstable Systems and Irreversibility: Matter Meets Mind

The fundamental time-reversal invariance of dynamical systems can be broken in various ways. One way is based on the presence of resonances and their interactions giving rise to unstable dynamical systems, leading to well-defined time arrows. Associated with these time arrows are semigroups bearing time orientations. Usually, when time symmetry is broken, two time-oriented semigroups result, one directed toward the future and one directed toward the past. If time-reversed states and evolutions are excluded due to resonances, then the status of these states and their associated backwards-in-time oriented semigroups is open to question. One possible role for these latter states and semigroups is as an abstract representation of mental systems as opposed to material systems. The beginnings of this interpretation will be sketched.Comment: 9 pages. Presented at the CFIF Workshop on TimeAsymmetric Quantum Theory: The Theory of Resonances, 23-26 July 2003, Instituto Superior Tecnico, Lisbon, Portugal; and at the Quantum Structures Association Meeting, 7-22 July 2004, University of Denver. Accepted for publication in the Internation Journal of Theoretical Physic

Spin-dependent Bohm trajectories for hydrogen eigenstates

The Bohm trajectories for several hydrogen atom eigenstates are determined, taking into account the additional momentum term that arises from the Pauli current. Unlike the original Bohmian result, the spin-dependent term yields nonstationary trajectories. The relationship between the trajectories and the standard visualizations of orbitals is discussed. The trajectories for a model problem that simulates a 1s-2p transition in hydrogen are also examined.Comment: 11 pages, 3 figure

Measurement, Decoherence and Chaos in Quantum Pinball

The effect of introducing measuring devices in a ``quantum pinball'' system is shown to lead to a chaotic evolution for the particle position as defined in Bohm's approach to Quantum Mechanics.Comment: Latex, uses ioplppt style, two figures. Also can be ftp'd anonymously from: ftp://zaphod.phys.port.ac.uk/pub/papers/paper2

Gamow-Jordan Vectors and Non-Reducible Density Operators from Higher Order S-Matrix Poles

In analogy to Gamow vectors that are obtained from first order resonance poles of the S-matrix, one can also define higher order Gamow vectors which are derived from higher order poles of the S-matrix. An S-matrix pole of r-th order at z_R=E_R-i\Gamma/2 leads to r generalized eigenvectors of order k= 0, 1, ... , r-1, which are also Jordan vectors of degree (k+1) with generalized eigenvalue (E_R-i\Gamma/2). The Gamow-Jordan vectors are elements of a generalized complex eigenvector expansion, whose form suggests the definition of a state operator (density matrix) for the microphysical decaying state of this higher order pole. This microphysical state is a mixture of non-reducible components. In spite of the fact that the k-th order Gamow-Jordan vectors has the polynomial time-dependence which one always associates with higher order poles, the microphysical state obeys a purely exponential decay law.Comment: 39 pages, 3 PostScript figures; sub2.eps may stall some printers and should then be printed out separately; ghostview is o.

Irreversible Quantum Mechanics in the Neutral K-System

The neutral Kaon system is used to test the quantum theory of resonance scattering and decay phenomena. The two dimensional Lee-Oehme-Yang theory with complex Hamiltonian is obtained by truncating the complex basis vector expansion of the exact theory in Rigged Hilbert space. This can be done for K_1 and K_2 as well as for K_S and K_L, depending upon whether one chooses the (self-adjoint, semi-bounded) Hamiltonian as commuting or non-commuting with CP. As an unexpected curiosity one can show that the exact theory (without truncation) predicts long-time 2 pion decays of the neutral Kaon system even if the Hamiltonian conserves CP.Comment: 36 pages, 1 PostScript figure include

Kochen-Specker Obstruction for Position and Momentum Using a Single Degree of Freedom

It is shown that, given a reasonable continuity assumption regarding possessed values, it is possible to construct a Kochen-Specker obstruction for any coordinate and its conjugate momentum, demonstrating that at most one of these two quantities can have a noncontextual value.Comment: This version replaces v1, which contained a faulty continuity condito

TCP over High Speed Variable Capacity Links: A Simulation Study for Bandwidth Allocation

New optical network technologies provide opportunities for fast, controllable bandwidth management. These technologies can now explicitly provide resources to data paths, creating demand driven bandwidth reservation across networks where an applications bandwidth needs can be meet almost exactly. Dynamic synchronous Transfer Mode (DTM) is a gigabit network technology that provides channels with dynamically adjustable capacity. TCP is a reliable end-to-end transport protocol that adapts its rate to the available capacity. Both TCP and the DTM bandwidth can react to changes in the network load, creating a complex system with inter-dependent feedback mechanisms. The contribution of this work is an assessment of a bandwidth allocation scheme for TCP flows on variable capacity technologies. We have created a simulation environment using ns-2 and our results indicate that the allocation of bandwidth maximises TCP throughput for most flows, thus saving valuable capacity when compared to a scheme such as link over-provisioning. We highlight one situation where the allocation scheme might have some deficiencies against the static reservation of resources, and describe its causes. This type of situation warrants further investigation to understand how the algorithm can be modified to achieve performance similar to that of the fixed bandwidth case

Chern number spins of Mn acceptor magnets in GaAs

We determine the effective total spin $J$ of local moments formed from acceptor states bound to Mn ions in GaAs by evaluating their magnetic Chern numbers. We find that when individual Mn atoms are close to the sample surface, the total spin changes from $J = 1$ to $J = 2$, due to quenching of the acceptor orbital moment. For Mn pairs in bulk, the total $J$ depends on the pair orientation in the GaAs lattice and on the separation between the Mn atoms. We point out that Berry curvature variation as a function of local moment orientation can profoundly influence the quantum spin dynamics of these magnetic entities.Comment: 4 pages, 3 figure