1,903 research outputs found
Higher order approximation of isochrons
Phase reduction is a commonly used techinque for analyzing stable
oscillators, particularly in studies concerning synchronization and phase lock
of a network of oscillators. In a widely used numerical approach for obtaining
phase reduction of a single oscillator, one needs to obtain the gradient of the
phase function, which essentially provides a linear approximation of isochrons.
In this paper, we extend the method for obtaining partial derivatives of the
phase function to arbitrary order, providing higher order approximations of
isochrons. In particular, our method in order 2 can be applied to the study of
dynamics of a stable oscillator subjected to stochastic perturbations, a topic
that will be discussed in a future paper. We use the Stuart-Landau oscillator
to illustrate the method in order 2
Simulations of magnetic and magnetoelastic properties of Tb2Ti2O7 in paramagnetic phase
Magnetic and magnetoelastic properties of terbium titanate pyrochlore in
paramagnetic phase are simulated. The magnetic field and temperature
dependences of magnetization and forced magnetostriction in Tb2Ti2O7 single
crystals and polycrystalline samples are calculated in the framework of
exchange charge model of crystal field theory and a mean field approximation.
The set of electron-deformation coupling constants has been determined.
Variations of elastic constants with temperature and applied magnetic field are
discussed. Additional strong softening of the crystal lattice at liquid helium
temperatures in the magnetic field directed along the rhombic symmetry axis is
predicted.Comment: 13 pages, 4 figures, 2 table
Space-Time Complexity in Hamiltonian Dynamics
New notions of the complexity function C(epsilon;t,s) and entropy function
S(epsilon;t,s) are introduced to describe systems with nonzero or zero Lyapunov
exponents or systems that exhibit strong intermittent behavior with
``flights'', trappings, weak mixing, etc. The important part of the new notions
is the first appearance of epsilon-separation of initially close trajectories.
The complexity function is similar to the propagator p(t0,x0;t,x) with a
replacement of x by the natural lengths s of trajectories, and its introduction
does not assume of the space-time independence in the process of evolution of
the system. A special stress is done on the choice of variables and the
replacement t by eta=ln(t), s by xi=ln(s) makes it possible to consider
time-algebraic and space-algebraic complexity and some mixed cases. It is shown
that for typical cases the entropy function S(epsilon;xi,eta) possesses
invariants (alpha,beta) that describe the fractal dimensions of the space-time
structures of trajectories. The invariants (alpha,beta) can be linked to the
transport properties of the system, from one side, and to the Riemann
invariants for simple waves, from the other side. This analog provides a new
meaning for the transport exponent mu that can be considered as the speed of a
Riemann wave in the log-phase space of the log-space-time variables. Some other
applications of new notions are considered and numerical examples are
presented.Comment: 27 pages, 6 figure
Structural and Magnetic Investigations of Single-Crystals of the Neodymium Zirconate Pyrochlore, Nd2Zr2O7
We report structural and magnetic properties studies of large high quality
single-crystals of the frustrated magnet, NdZrO. Powder x-ray
diffraction analysis confirms that NdZrO adopts the pyrochlore
structure. Room-temperature x-ray diffraction and time-of-flight neutron
scattering experiments show that the crystals are stoichiometric in composition
with no measurable site disorder. The temperature dependence of the magnetic
susceptibility shows no magnetic ordering at temperatures down to 0.5 K. Fits
to the magnetic susceptibility data using a Curie-Weiss law reveal a
ferromagnetic coupling between the Nd moments. Magnetization versus field
measurements show a local Ising anisotropy along the axes of the
Nd ions in the ground state. Specific heat versus temperature
measurements in zero applied magnetic field indicate the presence of a thermal
anomaly below K, but no evidence of magnetic ordering is observed down
to 0.5 K. The experimental temperature dependence of the single-crystal bulk dc
susceptibility and isothermal magnetization are analyzed using crystal field
theory and the crystal field parameters and exchange coupling constants
determined.Comment: 10 pages, 6 figures, 4 tables. Accepted for publication in Physical
Review
Observation of a red-blue detuning asymmetry in matter-wave superradiance
We report the first experimental observations of strong suppression of
matter-wave superradiance using blue-detuned pump light and demonstrate a
pump-laser detuning asymmetry in the collective atomic recoil motion. In
contrast to all previous theoretical frameworks, which predict that the process
should be symmetric with respect to the sign of the pump-laser detuning, we
find that for condensates the symmetry is broken. With high condensate
densities and red-detuned light, the familiar distinctive multi-order,
matter-wave scattering pattern is clearly visible, whereas with blue-detuned
light superradiance is strongly suppressed. In the limit of a dilute atomic
gas, however, symmetry is restored.Comment: Accepted by Phys. Rev. Let
Supersymmetry of a Nonstationary Pauli Equation
The supersymmetry of the electron in both the nonstationary magnetic and
electric fields in a two-dimensional case is studied. The supercharges which
are the integrals of motion and their algebra are established. Using the
obtained algebra the solutions of nonstationary Pauli equation are generated.Comment: 12 pages, Late
Parity doubling in particle physics
Parity doubling in excited hadrons is reviewed. Parity degeneracy in hadrons
was first experimentally observed 40 years ago. Recently new experimental data
on light mesons caused much excitement and renewed interest to the phenomenon,
which still remains to be enigmatic. The present retrospective review is an
attempt to trace the history of parity doubling phenomenon, thus providing a
kind of introduction to the subject. We begin with early approaches of 1960s
(Regge theory and dynamical symmetries) and end up with the latest trends
(manifestations of broader degeneracies and AdS/QCD). We show the evolution of
various ideas about parity doubling. The experimental evidence for this
phenomenon is scrutinized in the non-strange sector. Some experiments of 1960s
devoted to the search for missing non-strange bosons are re-examined and it is
argued that results of these experiments are encouraging from the modern
perspective.Comment: Version to appear in Int. J. Mod. Phys. A, 63 pages, 9 figure
Coherent states of non-relativistic electron in magnetic-solenoid field
We construct coherent states of a nonrelativistic electron in the
magnetic-solenoid field, which is a superposition of the Aharonov-Bohm field
and a collinear uniform magnetic field. In the problem under consideration
there are two kind of coherent states, the first kind corresponds to classical
trajectories which embrace the solenoid and the second one to trajectories
which do not. Mean coordinates in the constructed coherent states are moving
along classical trajectories, the coherent states maintain their form under the
time evolution, and represent a complete set of functions, which can be useful
in semi classical calculations. In the absence of the Aharonov-Bohm filed these
states are reduced to the well-known in the case of uniform magnetic field
Malkin-Man'ko coherent states.Comment: 11 pages, version accepted for publication in J. Phys. A, 3 figures
adde
Coherent states and related quantizations for unbounded motions
We build coherent states (CS) for unbounded motions along two different
procedures. In the first one we adapt the Malkin-Manko construction for
quadratic Hamiltonians to the motion of a particle in a linear potential. A
generalization to arbitrary potentials is discussed. The second one extends to
continuous spectrum previous constructions of action-angle coherent states in
view of a consistent energy quantization
High resolution infrared absorption spectra, crystal field, and relaxation processes in CsCdBr_3:Pr^3+
High resolution low-temperature absorption spectra of 0.2% Pr^3+ doped
CsCdBr_3 were measured in the spectral region 2000--7000 cm-1. Positions and
widths of the crystal field levels within the 3H5, 3H4, 3F2, and 3F3 multiplets
of the Pr^3+ main center have been determined. Hyperfine structure of several
spectral lines has been found. Crystal field calculations were carried out in
the framework of the semiphenomenological exchange charge model (ECM).
Parameters of the ECM were determined by fitting to the measured total
splittings of the 3H4 and 3H6 multiplets and to the observed in this work
hyperfine splittings of the crystal field levels. One- and two-phonon
relaxation rates were calculated using the phonon Green's functions of the
perfect (CsCdBr_3) and locally perturbed (impurity dimer centers in
CsCdBr_3:Pr^3+) crystal lattice. Comparison with the measured linewidths
confirmed an essential redistribution of the phonon density of states in
CsCdBr_3 crystals doped with rare-earth ions.Comment: 16 pages, 5 tables, 3 figure
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