38,503 research outputs found
Berry phase in a non-isolated system
We investigate the effect of the environment on a Berry phase measurement
involving a spin-half. We model the spin+environment using a biased spin-boson
Hamiltonian with a time-dependent magnetic field. We find that, contrary to
naive expectations, the Berry phase acquired by the spin can be observed, but
only on timescales which are neither too short nor very long. However this
Berry phase is not the same as for the isolated spin-half. It does not have a
simple geometric interpretation in terms of the adiabatic evolution of either
bare spin-states or the dressed spin-resonances that remain once we have traced
out the environment. This result is crucial for proposed Berry phase
measurements in superconducting nanocircuits as dissipation there is known to
be significant.Comment: 4 pages (revTeX4) 2 fig. This version has MAJOR changes to equation
On the propagation of semiclassical Wigner functions
We establish the difference between the propagation of semiclassical Wigner
functions and classical Liouville propagation. First we re-discuss the
semiclassical limit for the propagator of Wigner functions, which on its own
leads to their classical propagation. Then, via stationary phase evaluation of
the full integral evolution equation, using the semiclassical expressions of
Wigner functions, we provide the correct geometrical prescription for their
semiclassical propagation. This is determined by the classical trajectories of
the tips of the chords defined by the initial semiclassical Wigner function and
centered on their arguments, in contrast to the Liouville propagation which is
determined by the classical trajectories of the arguments themselves.Comment: 9 pages, 1 figure. To appear in J. Phys. A. This version matches the
one set to print and differs from the previous one (07 Nov 2001) by the
addition of two references, a few extra words of explanation and an augmented
figure captio
Non-quantized Dirac monopoles and strings in the Berry phase of anisotropic spin systems
The Berry phase of an anisotropic spin system that is adiabatically rotated
along a closed circuit C is investigated. It is shown that the Berry phase
consists of two contributions: (i) a geometric contribution which can be
interpreted as the flux through C of a non-quantized Dirac monopole, and (ii) a
topological contribution which can be interpreted as the flux through C of a
Dirac string carrying a non-quantized flux, i.e., a spin analogue of the
Aharonov-Bohm effect. Various experimental consequences of this novel effect
are discussed.Comment: 4 pages, 3 figures (RevTeX + eps); v2 (revised paper): 4 pages, 4
figure
The Limiting Speed of the Bacterial Flagellar Motor
Recent experiments on the bacterial flagellar motor have shown that the
structure of this nanomachine, which drives locomotion in a wide range of
bacterial species, is more dynamic than previously believed. Specifically, the
number of active torque-generating units (stators) was shown to vary across
applied loads. This finding invalidates the experimental evidence reporting
that limiting (zero-torque) speed is independent of the number of active
stators. Here, we propose that, contrary to previous assumptions, the maximum
speed of the motor is not universal, but rather increases as additional
torque-generators are recruited. This result arises from our assumption that
stators disengage from the motor for a significant portion of their
mechanochemical cycles at low loads. We show that this assumption is consistent
with current experimental evidence and consolidate our predictions with
arguments that a processive motor must have a high duty ratio at high loads.Comment: 8 pages, 3 figures (main text); 7 pages, 3 figures (supplementary
Non-adiabatic Arbitary Geometric Gates in 2-qubit NMR Model
We study a 2-qubit nuclear spin system for realizing an arbitrary geometric
quantum phase gate by means of non-adiabatic operation. A single magnetic pulse
with multi harmonic frequencies is applied to manipulate the quantum states of
2-qubit instantly. Using resonant transition approximation, the time dependent
Hamiltonian of two nuclear spins can be solved analytically. The time evolution
of the wave function is obtained without adiabatic approximation. The
parameters of magnetic pulse, such as the frequency, amplitude, phase of each
harmonic part as well as the time duration of the pulse, are determined for
achieving an arbitrary non-adiabatic geometric phase gate. The derivation of
non-adiabatic geometric controlled phase gates and A-A phase are also
addressed.Comment: 7 pages, 1 figur
Robust point correspondence applied to two and three-dimensional image registration
Accurate and robust correspondence calculations are very important in many medical and biological applications. Often, the correspondence calculation forms part of a rigid registration algorithm, but accurate correspondences are especially important for elastic registration algorithms and for quantifying changes over time. In this paper, a new correspondence calculation algorithm, CSM (correspondence by sensitivity to movement), is described. A robust corresponding point is calculated by determining the sensitivity of a correspondence to movement of the point being matched. If the correspondence is reliable, a perturbation in the position of this point should not result in a large movement of the correspondence. A measure of reliability is also calculated. This correspondence calculation method is independent of the registration transformation and has been incorporated into both a 2D elastic registration algorithm for warping serial sections and a 3D rigid registration algorithm for registering pre and postoperative facial range scans. These applications use different methods for calculating the registration transformation and accurate rigid and elastic alignment of images has been achieved with the CSM method. It is expected that this method will be applicable to many different applications and that good results would be achieved if it were to be inserted into other methods for calculating a registration transformation from correspondence
Berry phase, topology, and diabolicity in quantum nano-magnets
A topological theory of the diabolical points (degeneracies) of quantum
magnets is presented. Diabolical points are characterized by their diabolicity
index, for which topological sum rules are derived. The paradox of the the
missing diabolical points for Fe8 molecular magnets is clarified. A new method
is also developed to provide a simple interpretation, in terms of destructive
interferences due to the Berry phase, of the complete set of diabolical points
found in biaxial systems such as Fe8.Comment: 4 pages, 3 figure
The three-body problem and the Hannay angle
The Hannay angle has been previously studied for a celestial circular
restricted three-body system by means of an adiabatic approach. In the present
work, three main results are obtained. Firstly, a formal connection between
perturbation theory and the Hamiltonian adiabatic approach shows that both lead
to the Hannay angle; it is thus emphasised that this effect is already
contained in classical celestial mechanics, although not yet defined nor
evaluated separately. Secondly, a more general expression of the Hannay angle,
valid for an action-dependent potential is given; such a generalised expression
takes into account that the restricted three-body problem is a time-dependent,
two degrees of freedom problem even when restricted to the circular motion of
the test body. Consequently, (some of) the eccentricity terms cannot be
neglected {\it a priori}. Thirdly, we present a new numerical estimate for the
Earth adiabatically driven by Jupiter. We also point out errors in a previous
derivation of the Hannay angle for the circular restricted three-body problem,
with an action-independent potential.Comment: 11 pages. Accepted by Nonlinearit
Decimation and Harmonic Inversion of Periodic Orbit Signals
We present and compare three generically applicable signal processing methods
for periodic orbit quantization via harmonic inversion of semiclassical
recurrence functions. In a first step of each method, a band-limited decimated
periodic orbit signal is obtained by analytical frequency windowing of the
periodic orbit sum. In a second step, the frequencies and amplitudes of the
decimated signal are determined by either Decimated Linear Predictor, Decimated
Pade Approximant, or Decimated Signal Diagonalization. These techniques, which
would have been numerically unstable without the windowing, provide numerically
more accurate semiclassical spectra than does the filter-diagonalization
method.Comment: 22 pages, 3 figures, submitted to J. Phys.
Vector Potential and Berry phase-induced Force
We present a general theoretical framework for the exact treatment of a
hybrid system that is composed of a quantum subsystem and a classical
subsystem. When the quantum subsystem is dynamically fast and the classical
subsystem is slow, a vector potential is generated with a simple canonical
transformation. This vector potential, on one hand, gives rise to the familiar
Berry phase in the fast quantum dynamics; on the other hand, it yields a
Lorentz-like force in the slow classical dynamics. In this way, the pure phase
(Berry phase) of a wavefunction is linked to a physical force.Comment: 4 pages, 1 figur
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