44 research outputs found
Origin of the exponential decay of the Loschmidt echo in integrable systems
We address the time decay of the Loschmidt echo, measuring the sensitivity of quantum dynamics to small Hamiltonian perturbations, in one-dimensional integrable systems. Using a semiclassical analysis, we show that the Loschmidt echo may exhibit a well-pronounced regime of exponential decay, similar to the one typically observed in quantum systems whose dynamics is chaotic in the classical limit. We derive an explicit formula for the exponential decay rate in terms of the spectral properties of the unperturbed and perturbed Hamilton operators and the initial state. In particular, we show that the decay rate, unlike in the case of the chaotic dynamics, is directly proportional to the strength of the Hamiltonian perturbation. Finally, we compare our analytical predictions against the results of a numerical computation of the Loschmidt echo for a quantum particle moving inside a one-dimensional box with Dirichlet-Robin boundary conditions, and find the two in good agreement
Huygens-Fresnel-Kirchhoff construction for quantum propagators with application to diffraction in space and time
We address the phenomenon of diffraction of non-relativistic matter waves on openings in absorbing screens. To this end, we expand the full quantum propagator, connecting two points on the opposite sides of the screen, in terms of the free particle propagator and spatio-temporal properties of the opening. Our construction, based on the Huygens-Fresnel principle, describes the quantum phenomena of diffraction in space and diffraction in time, as well as the interplay between the two. We illustrate the method by calculating diffraction patterns for localized wave packets passing through various time-dependent openings in one and two spatial dimensions
Perturbations and chaos in quantum maps
The local density of states (LDOS) is a distribution that characterizes the
effect of perturbations on quantum systems. Recently, it was proposed a
semiclassical theory for the LDOS of chaotic billiards and maps. This theory
predicts that the LDOS is a Breit-Wigner distribution independent of the
perturbation strength and also gives a semiclassical expression for the LDOS
witdth. Here, we test the validity of such an approximation in quantum maps
varying the degree of chaoticity, the region in phase space where the
perturbation is applying and the intensity of the perturbation. We show that
for highly chaotic maps or strong perturbations the semiclassical theory of the
LDOS is accurate to describe the quantum distribution. Moreover, the width of
the LDOS is also well represented for its semiclassical expression in the case
of mixed classical dynamics.Comment: 9 pages, 11 figures. Accepted for publication in Phys. Rev.
Disruption of coordination between arm, trunk, and center of pressure displacement in patients with hemiparesis
To determine how arm movements influence postural sway in the upright position after stroke, interactions between arm, trunk, and center of pressure (CoP) displacements in the sagittal direction were investigated in participants with hemiparesis and healthy subjects. Participants swung both arms sagittally in either of 2 directions (in-phase, anti-phase) and at 2 speeds (preferred, fast) while standing on separate force plates. Variables measured included amplitude and frequency of arm swinging, shoulder and trunk range of motion, CoP displacements under each foot and of the whole body, and the relationships between the arm, trunk, and CoP displacements. CoP displacements under the non-paretic leg were greater than those under the paretic leg, which may in part be related to the larger amplitude of swinging of the non-paretic arm. CoP displacements under each foot were not related to arm swinging during in-phase swinging at the preferred speed in healthy subjects. When speed of arm swinging was increased, however, the CoP moved in a direction opposite to the arm movement. In contrast, in individuals with hemiparesis, CoPs and arms moved in the same direction for both speeds. During anti-phase swinging in healthy subjects, the trunk counterbalanced the arm movements, while in participants with hemiparesis, the trunk moved with the affected arm. Results show that stroke resulted in abnormal patterns of arm-trunk-CoP interactions that may be related to a greater involvement of the trunk in arm transport, an altered pattern of coordination between arm and CoP displacements, and an impaired ability of the damaged nervous system to adapt postural synergies to changes in movement velocity
Wave packet autocorrelation functions for quantum hard-disk and hard-sphere billiards in the high-energy, diffraction regime
We consider the time evolution of a wave packet representing a quantum
particle moving in a geometrically open billiard that consists of a number of
fixed hard-disk or hard-sphere scatterers. Using the technique of multiple
collision expansions we provide a first-principle analytical calculation of the
time-dependent autocorrelation function for the wave packet in the high-energy
diffraction regime, in which the particle's de Broglie wave length, while being
small compared to the size of the scatterers, is large enough to prevent the
formation of geometric shadow over distances of the order of the particle's
free flight path. The hard-disk or hard-sphere scattering system must be
sufficiently dilute in order for this high-energy diffraction regime to be
achievable. Apart from the overall exponential decay, the autocorrelation
function exhibits a generally complicated sequence of relatively strong peaks
corresponding to partial revivals of the wave packet. Both the exponential
decay (or escape) rate and the revival peak structure are predominantly
determined by the underlying classical dynamics. A relation between the escape
rate, and the Lyapunov exponents and Kolmogorov-Sinai entropy of the
counterpart classical system, previously known for hard-disk billiards, is
strengthened by generalization to three spatial dimensions. The results of the
quantum mechanical calculation of the time-dependent autocorrelation function
agree with predictions of the semiclassical periodic orbit theory.Comment: 24 pages, 13 figure
Semiclassical approach to fidelity amplitude
The fidelity amplitude is a quantity of paramount importance in echo type
experiments. We use semiclassical theory to study the average fidelity
amplitude for quantum chaotic systems under external perturbation. We explain
analytically two extreme cases: the random dynamics limit --attained
approximately by strongly chaotic systems-- and the random perturbation limit,
which shows a Lyapunov decay. Numerical simulations help us bridge the gap
between both extreme cases.Comment: 10 pages, 9 figures. Version closest to published versio
Vector and Tensor Analyzing Powers of the H(d,gamma)He-3 capture reaction
Precise measurements of the deuteron vector analyzing power Ayd and the
tensor analyzing power Ayy of the H(d,gamma)He-3 capture reaction have been
performed at deuteron energies of 29MeV and 45MeV. The data have been compared
to theoretical state-of-the-art calculations available today. Due to the large
sensitivity of polarization observables and the precision of the data light
could be shed on small effects present in the dynamics of the reaction.Comment: 11 pages, 24 figures, submitted for publication to PRC, revised after
referee proces
Measurement of the Electric Form Factor of the Neutron at Q^2=0.5 and 1.0 (GeV/c)^2
The electric form factor of the neutron was determined from measurements of
the \vec{d}(\vec{e},e' n)p reaction for quasielastic kinematics. Polarized
electrons were scattered off a polarized deuterated ammonia target in which the
deuteron polarization was perpendicular to the momentum transfer. The scattered
electrons were detected in a magnetic spectrometer in coincidence with neutrons
in a large solid angle detector. We find G_E^n = 0.0526 +/- 0.0033 (stat) +/-
0.0026 (sys) and 0.0454 +/- 0.0054 +/- 0.0037 at Q^2 = 0.5 and 1.0 (GeV/c)^2,
respectively.Comment: 5 pages, 2 figures, as publishe
Quantum circuits with many photons on a programmable nanophotonic chip
Growing interest in quantum computing for practical applications has led to a
surge in the availability of programmable machines for executing quantum
algorithms. Present day photonic quantum computers have been limited either to
non-deterministic operation, low photon numbers and rates, or fixed random gate
sequences. Here we introduce a full-stack hardware-software system for
executing many-photon quantum circuits using integrated nanophotonics: a
programmable chip, operating at room temperature and interfaced with a fully
automated control system. It enables remote users to execute quantum algorithms
requiring up to eight modes of strongly squeezed vacuum initialized as two-mode
squeezed states in single temporal modes, a fully general and programmable
four-mode interferometer, and genuine photon number-resolving readout on all
outputs. Multi-photon detection events with photon numbers and rates exceeding
any previous quantum optical demonstration on a programmable device are made
possible by strong squeezing and high sampling rates. We verify the
non-classicality of the device output, and use the platform to carry out
proof-of-principle demonstrations of three quantum algorithms: Gaussian boson
sampling, molecular vibronic spectra, and graph similarity
Measurement of the asymmetries in 3(¯e, e′p)d and 3(¯e, e′p)np
Abstract.: The electron target asymmetries A || and A⊥ with target spin parallel and perpendicular to the momentum transfer \ensuremath{\boldsymbol{q}} were measured for both the two- and three-body breakup of 3He in the 3 (¯e, e'p)-reaction. Polarized electrons were scattered off polarized 3He in the quasielastic regime in parallel kinematics with the scattered electron and the knocked-out proton detected using the Three-Spectrometer Facility at MAMI. The results are compared to Faddeev calculations which take into account Final-State Interactions as well as Meson Exchange Currents. The experiment confirms the prediction of a large effect of Final-State Interactions in the asymmetry of the three-body breakup and of an almost negligible one for the two-body breaku