8,611 research outputs found

### 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

### 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

### 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

### 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.

### The density matrix in the de Broglie-Bohm approach

If the density matrix is treated as an objective description of individual
systems, it may become possible to attribute the same objective significance to
statistical mechanical properties, such as entropy or temperature, as to
properties such as mass or energy. It is shown that the de Broglie-Bohm
interpretation of quantum theory can be consistently applied to density
matrices as a description of individual systems. The resultant trajectories are
examined for the case of the delayed choice interferometer, for which Bell
appears to suggest that such an interpretation is not possible. Bell's argument
is shown to be based upon a different understanding of the density matrix to
that proposed here.Comment: 15 pages, 4 figure

### In Switzerland: Vor der Sennhuette

https://digitalcommons.library.umaine.edu/mmb-ps/2877/thumbnail.jp

### 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
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