1,171 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
Coherent states of a charged particle in a uniform magnetic field
The coherent states are constructed for a charged particle in a uniform
magnetic field based on coherent states for the circular motion which have
recently been introduced by the authors.Comment: 2 eps figure
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
Magnetic and spectral properties of multi-sublattice oxides SrY2O4:Er3+ and SrEr2O4
SrEr2O4 is a geometrically frustrated magnet which demonstrates rather
unusual properties at low temperatures including a coexistence of long- and
short-range magnetic order, characterized by two different propagation vectors.
In the present work, the effects of crystal fields (CF) in this compound
containing four magnetically inequivalent erbium sublattices are investigated
experimentally and theoretically. We combine the measurements of the CF levels
of the Er3+ ions made on a powder sample of SrEr2O4 using neutron spectroscopy
with site-selective optical and electron paramagnetic resonance measurements
performed on single crystal samples of the lightly Er-doped nonmagnetic
analogue, SrY2O4. Two sets of CF parameters corresponding to the Er3+ ions at
the crystallographically inequivalent lattice sites are derived which fit all
the available experimental data well, including the magnetization and dc
susceptibility data for both lightly doped and concentrated samples.Comment: 14 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
f-Oscillators and Nonlinear Coherent States
The notion of f-oscillators generalizing q-oscillators is introduced. For
classical and quantum cases, an interpretation of the f-oscillator is provided
as corresponding to a special nonlinearity of vibration for which the frequency
of oscillation depends on the energy. The f-coherent states (nonlinear coherent
states) generalizing q-coherent states are constructed. Applied to quantum
optics, photon distribution function, photon number means, and dispersions are
calculated for the f-coherent states as well as the Wigner function and
Q-function. As an example, it is shown how this nonlinearity may affect the
Planck distribution formula.Comment: Latex, 32 pages, accepted by Physica Script
Supersymmetry of the Nonstationary Schr\"odinger equation and Time-Dependent Exactly Solvable Quantum Models
New exactly solvable quantum models are obtained with the help of the
supersymmetric extencion of the nonstationary Schr/"odinger equation.Comment: Talk at the 8th International Conference "Symmetry Methods in
Physics". Dubna, Russia, 28 July - 2 August, 199
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
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