2,224 research outputs found
Geometric phases for wave packets in a uniform magnetic field
A wave packet of a charged particle always make cyclic circular motion in a
uniform magnetic field, just like a classical particle. The nonadiabatic
geometric phase for an arbitrary wave packet can be expressed in terms of the
mean value of a number operator. For a large class of wave packets, the
geometric phase is proportional to the magnetic flux encircled by the orbit of
the wave packet. For more general wave packets, however, the geometric phase
contains an extra term.Comment: REVTeX4, 7 pages, no figur
Exact solutions of n-level systems and gauge theories
We find a relationship between unitary transformations of the dynamics of
quantum systems with time-dependent Hamiltonians and gauge theories. In
particular, we show that the nonrelativistic dynamics of spin-
particles in a magnetic field can be formulated in a natural way as
an SU(2) gauge theory, with the magnetic field playing the role of the
gauge potential A^i. The present approach can also be applied to systems of n
levels with time-dependent potentials, U(n) being the gauge group. This
geometric interpretation provides a powerful method to find exact solutions of
the Schr\"odinger equation. The root of the present approach rests in the
Hermiticity property of the Hamiltonian operators involved. In addition, the
relationship with true gauge symmetries of n-level quantum systems is
discussed.Comment: LaTeX file, 5 pages, published versio
The Geometric Phase and Ray Space Isometries
We study the behaviour of the geometric phase under isometries of the ray
space. This leads to a better understanding of a theorem first proved by
Wigner: isometries of the ray space can always be realised as projections of
unitary or anti-unitary transformations on the Hilbert space. We suggest that
the construction involved in Wigner's proof is best viewed as an use of the
Pancharatnam connection to ``lift'' a ray space isometry to the Hilbert space.Comment: 17 pages, Latex file, no figures, To appear in Pramana J. Phy
Tops and Writhing DNA
The torsional elasticity of semiflexible polymers like DNA is of biological
significance. A mathematical treatment of this problem was begun by Fuller
using the relation between link, twist and writhe, but progress has been
hindered by the non-local nature of the writhe. This stands in the way of an
analytic statistical mechanical treatment, which takes into account thermal
fluctuations, in computing the partition function. In this paper we use the
well known analogy with the dynamics of tops to show that when subjected to
stretch and twist, the polymer configurations which dominate the partition
function admit a local writhe formulation in the spirit of Fuller and thus
provide an underlying justification for the use of Fuller's "local writhe
expression" which leads to considerable mathematical simplification in solving
theoretical models of DNA and elucidating their predictions. Our result
facilitates comparison of the theoretical models with single molecule
micromanipulation experiments and computer simulations.Comment: 17 pages two figure
Topological Phases near a Triple Degeneracy
We study the pattern of three state topological phases that appear in systems
with real Hamiltonians and wave functions. We give a simple geometric
construction for representing these phases. We then apply our results to
understand previous work on three state phases. We point out that the ``mirror
symmetry'' of wave functions noticed in microwave experiments can be simply
understood in our framework.Comment: 4 pages, 1 figure, to appear in Phys. Rev. Let
Geometric Phase in Entangled Bipartite Systems
The geometric phase (GP) for bipartite systems in transverse external
magnetic fields is investigated in this paper. Two different situations have
been studied. We first consider two non-interacting particles. The results show
that because of entanglement, the geometric phase is very different from that
of the non-entangled case. When the initial state is a Werner state, the
geometric phase is, in general, zero and moreover the singularity of the
geometric phase may appear with a proper evolution time. We next study the
geometric phase when intra-couplings appear and choose Werner states as the
initial states to entail this discussion. The results show that unlike our
first case, the absolute value of the GP is not zero, and attains its maximum
when the rescaled coupling constant is less than 1. The effect of
inhomogeneity of the magnetic field is also discussed.Comment: 5 pages and to be published in Euro. Phys. J.
Quantum Particle-Trajectories and Geometric Phase
"Particle"-trajectories are defined as integrable paths
in projective space.
Quantum states evolving on such trajectories, open or closed, do not
delocalise in projection, the phase associated with the trajectories
being related to the geometric (Berry) phase and the Classical Mechanics
action. High Energy Physics properties of states evolving on
"particle"-trajectories are discussed.Comment: 4 page
Geometric Phases and Mielnik's Evolution Loops
The cyclic evolutions and associated geometric phases induced by
time-independent Hamiltonians are studied for the case when the evolution
operator becomes the identity (those processes are called {\it evolution
loops}). We make a detailed treatment of systems having equally-spaced energy
levels. Special emphasis is made on the potentials which have the same spectrum
as the harmonic oscillator potential (the generalized oscillator potentials)
and on their recently found coherent states.Comment: 11 pages, harvmac, 2 figures available upon request; CINVESTAV-FIS
GFMR 11/9
Noncyclic geometric phase for neutrino oscillation
We provide explicit formulae for the noncyclic geometric phases or
Pancharatnam phases of neutrino oscillations. Since Pancharatnam phase is a
generalization of the Berry phase, our results generalize the previous findings
for Berry phase in a recent paper [Phys. Lett. B, 466 (1999) 262]. Unlike the
Berry phase, the noncyclic geometric phase offers distinctive advantage in
terms of measurement and prediction. In particular, for three-flavor mixing,
our explicit formula offers an alternative means of determining the
CP-violating phase. Our results can also be extended easily to explore
geometric phase associated with neutron-antineutron oscillations
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