11,824 research outputs found
Multiple-Scale Analysis of the Quantum Anharmonic Oscillator
Conventional weak-coupling perturbation theory suffers from problems that
arise from resonant coupling of successive orders in the perturbation series.
Multiple-scale perturbation theory avoids such problems by implicitly
performing an infinite reordering and resummation of the conventional
perturbation series. Multiple-scale analysis provides a good description of the
classical anharmonic oscillator. Here, it is extended to study the Heisenberg
operator equations of motion for the quantum anharmonic oscillator. The
analysis yields a system of nonlinear operator differential equations, which is
solved exactly. The solution provides an operator mass renormalization of the
theory.Comment: 12 pages, Revtex, no figures, available through anonymous ftp from
ftp://euclid.tp.ph.ic.ac.uk/papers/ or on WWW at
http://euclid.tp.ph.ic.ac.uk/Papers/papers_95-6_.htm
Visual stimulation of saccades in magnetically tethered Drosophila
Flying fruit flies, Drosophila melanogaster, perform `body saccades', in which they change heading by about 90° in roughly 70 ms. In free flight, visual expansion can evoke saccades, and saccade-like turns are triggered by similar stimuli in tethered flies. However, because the fictive turns in rigidly tethered flies follow a much longer time course, the extent to which these two behaviors share a common neural basis is unknown. A key difference between tethered and free flight conditions is the presence of additional sensory cues in the latter, which might serve to modify the time course of the saccade motor program. To study the role of sensory feedback in saccades, we have developed a new preparation in which a fly is tethered to a fine steel pin that is aligned within a vertically oriented magnetic field, allowing it to rotate freely around its yaw axis. In this experimental paradigm, flies perform rapid turns averaging 35° in 80 ms, similar to the kinematics of free flight saccades. Our results indicate that tethered and free flight saccades share a common neural basis, but that the lack of appropriate feedback signals distorts the behavior performed by rigidly fixed flies. Using our new paradigm, we also investigated the features of visual stimuli that elicit saccades. Our data suggest that saccades are triggered when expanding objects reach a critical threshold size, but that their timing depends little on the precise time course of expansion. These results are consistent with expansion detection circuits studied in other insects, but do not exclude other models based on the integration of local movement detectors
Green Functions for the Wrong-Sign Quartic
It has been shown that the Schwinger-Dyson equations for non-Hermitian
theories implicitly include the Hilbert-space metric. Approximate Green
functions for such theories may thus be obtained, without having to evaluate
the metric explicitly, by truncation of the equations. Such a calculation has
recently been carried out for various -symmetric theories, in both quantum
mechanics and quantum field theory, including the wrong-sign quartic
oscillator. For this particular theory the metric is known in closed form,
making possible an independent check of these approximate results. We do so by
numerically evaluating the ground-state wave-function for the equivalent
Hermitian Hamiltonian and using this wave-function, in conjunction with the
metric operator, to calculate the one- and two-point Green functions. We find
that the Green functions evaluated by lowest-order truncation of the
Schwinger-Dyson equations are already accurate at the (6-8)% level. This
provides a strong justification for the method and a motivation for its
extension to higher order and to higher dimensions, where the calculation of
the metric is extremely difficult
Level Crossings in Complex Two-Dimensional Potentials
Two-dimensional PT-symmetric quantum-mechanical systems with the complex
cubic potential V_{12}=x^2+y^2+igxy^2 and the complex Henon-Heiles potential
V_{HH}=x^2+y^2+ig(xy^2-x^3/3) are investigated. Using numerical and
perturbative methods, energy spectra are obtained to high levels. Although both
potentials respect the PT symmetry, the complex energy eigenvalues appear when
level crossing happens between same parity eigenstates.Comment: 9 pages, 4 figures. Submitted as a conference proceeding of PHHQP
On Pseudo-Hermitian Hamiltonians and Their Hermitian Counterparts
In the context of two particularly interesting non-Hermitian models in
quantum mechanics we explore the relationship between the original Hamiltonian
H and its Hermitian counterpart h, obtained from H by a similarity
transformation, as pointed out by Mostafazadeh. In the first model, due to
Swanson, h turns out to be just a scaled harmonic oscillator, which explains
the form of its spectrum. However, the transformation is not unique, which also
means that the observables of the original theory are not uniquely determined
by H alone. The second model we consider is the original PT-invariant
Hamiltonian, with potential V=igx^3. In this case the corresponding h, which we
are only able to construct in perturbation theory, corresponds to a complicated
velocity-dependent potential. We again explore the relationship between the
canonical variables x and p and the observables X and P.Comment: 9 pages, no figure
Large-amplitude Qn-Qp collectivity in the neutron-rich oxygen isotope 20O
By means of HFB calculations with independent constraints on axial neutron
and proton quadrupole moments Q_n and Q_p, we investigate the large amplitude
isoscalar and isovector deformation properties of the neutron-rich isotope 20O.
Using the particle-number and angular-momentum projected Generator Coordinate
Method, we analyze the collective dynamics in the {Q_n, Q_p} plane. The
parameterization SLy4 of the Skyrme interaction is used for all calculations in
connection with a density-dependent zero-range pairing interaction. Our results
show that already for this moderately neutron-rich nucleus the transition
moments are modified when independent neutron and proton collective dynamics
are allowed.Comment: 8 pages REVTEX, 5 eps figure
Vector Casimir effect for a D-dimensional sphere
The Casimir energy or stress due to modes in a D-dimensional volume subject
to TM (mixed) boundary conditions on a bounding spherical surface is
calculated. Both interior and exterior modes are included. Together with
earlier results found for scalar modes (TE modes), this gives the Casimir
effect for fluctuating ``electromagnetic'' (vector) fields inside and outside a
spherical shell. Known results for three dimensions, first found by Boyer, are
reproduced. Qualitatively, the results for TM modes are similar to those for
scalar modes: Poles occur in the stress at positive even dimensions, and cusps
(logarithmic singularities) occur for integer dimensions . Particular
attention is given the interesting case of D=2.Comment: 20 pages, 1 figure, REVTe
Model of supersymmetric quantum field theory with broken parity symmetry
Recently, it was observed that self-interacting scalar quantum field theories
having a non-Hermitian interaction term of the form ,
where is a real positive parameter, are physically acceptable in the
sense that the energy spectrum is real and bounded below. Such theories possess
PT invariance, but they are not symmetric under parity reflection or time
reversal separately. This broken parity symmetry is manifested in a nonzero
value for , even if is an even integer. This paper extends
this idea to a two-dimensional supersymmetric quantum field theory whose
superpotential is . The resulting quantum
field theory exhibits a broken parity symmetry for all . However,
supersymmetry remains unbroken, which is verified by showing that the
ground-state energy density vanishes and that the fermion-boson mass ratio is
unity.Comment: 20 pages, REVTeX, 11 postscript figure
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