Search results for "equation"
showing 10 items of 4219 documents
Analytical design of soliton molecules in fibers
2016
We present an analytical method for designing fiber systems for a highly stable propagation of soliton molecules. This analytical design uses the variational equations of the soliton molecule to determine the parameters of the most suitable fiber system for any desired soliton, thus reducing dramatically the cost of the whole procedure of design, for both the appropriate fiber system and the desired soliton molecule.
Analytical description of lobster eye and similar multi-foil optics
2015
Analytical equations describing lobster eye optical parameters on dependence on its geometric parameters are presented. The paper partially gives review of main previously known results. At next, the paper gives new results discussing parameters, that were not included to previously published models but may be significant. The results are applicable for a Schmidt as well as for an Angel lobster eye and for some related multi-foil systems.
Rotational States of the Helium Trimer in the Symmetry-Adapted Hyperradial-Adiabatic Approach
2003
We have searched for bound rotationally excited states of the helium trimer using the symmetry-adapted hyperradial adiabatic approach. Since the calculated J p = 2+ and J p = 1− potential curves are both completely repulsive, we infer that there are no bound rotational states of 4He3. A recent adiabatic calculation [1] based on the direct solution of the Coriolis-coupled Schrodinger equation agrees with this conclusion.
Dynamics of mean-field spin models from basic results in abstract differential equations
1992
The infinite-volume limit of the dynamics of (generalized) mean-field spin models is obtained through a direct analysis of the equations of motion, in a large class of representations of the spin algebra. The resulting dynamics fits into a general framework for systems with long-range interaction: variables at infinity appear in the time evolution of local variables and spontaneous symmetry breaking with an energy gap follows from this mechanism. The independence of the construction of the approximation scheme in finite volume is proven. © 1992 Plenum Publishing Corporation.
High-momentum tails as magnetic-structure probes for strongly correlatedSU(κ)fermionic mixtures in one-dimensional traps
2016
A universal ${k}^{\ensuremath{-}4}$ decay of the large-momentum tails of the momentum distribution, fixed by Tan's contact coefficients, constitutes a direct signature of strong correlations in a short-range interacting quantum gas. Here we consider a repulsive multicomponent Fermi gas under harmonic confinement, as in the experiment of G. Pagano et al. [Nat. Phys. 10, 198 (2014)], realizing a gas with tunable $\text{SU}(\ensuremath{\kappa})$ symmetry. We exploit an exact solution at infinite repulsion to show a direct correspondence between the value of the Tan's contact for each of the $\ensuremath{\kappa}$ components of the gas and the Young tableaux for the ${S}_{N}$ permutation symmetr…
Modal expansions in lasers outside the uniform-field limit
2003
We show that, in lasers characterized by a slow population dynamics, the expansion of the electric field on longitudinal modes is useful even beyond the uniform-field limit. The dynamical behavior of the laser above the second threshold can be well reproduced by a set of ordinary differential equations, whose integration is much faster than that of the complete Maxwell–Bloch equations. The conditions for the uniform-field limit are also clarified.
Noise-induced effects in population dynamics
2002
We investigate the role of noise in the nonlinear relaxation of two ecosystems described by generalized Lotka-Volterra equations in the presence of multiplicative noise. Specifically we study two cases: (i) an ecosystem with two interacting species in the presence of periodic driving; (ii) an ecosystem with a great number of interacting species with random interaction matrix. We analyse the interplay between noise and periodic modulation for case (i) and the role of the noise in the transient dynamics of the ecosystem in the presence of an absorbing barrier in case (ii). We find that the presence of noise is responsible for the generation of temporal oscillations and for the appearance of s…
Population dynamics based on ladder bosonic operators
2021
Abstract We adopt an operatorial method, based on truncated bosons, to describe the dynamics of populations in a closed region with a non trivial topology. The main operator that includes the various mechanisms and interactions between the populations is the Hamiltonian, constructed with the density and transport operators. The whole evolution is derived from the Schrodinger equation, and the densities of the populations are retrieved from the normalized expected values of the density operators. We show that this approach is suitable for applications in very large domain, solving the computational issues that typically occur when using an Hamiltonian based on fermionic ladder operators.
Stimulated nutation echo: application to the driven decoherence study
2003
We study experimentally the dynamical and decay properties of the stimulated nutation echo (SNE) in a two-level spin system, the signal of which allows the observation timescale of the driven coherence relaxation to be extended. This signal appears in the transient response of the system to the second pulse at time τ1 from its start and coinciding with the duration of the first pulse. The information about the first pulse duration is imprinted into the population difference of the inhomogeneously broadened ensemble of the two-level absorbers. The decay of the SNE signal has two contributions. One originates from the population decay during the time τ between the two pulses. Another is cause…
Chaos and nonlinearities in high harmonic generation
2016
Linearity is a fundamental postulate of quantum mechanics which is occasionally the subject of debate. This paper investigates the possibility of checking this assumption by using a laser field. We study the corrections caused by the presence of a small nonlinearity in the Hamiltonian of a quantum system. As a model we use a simplified two-level quantum system whose states are coupled by a small off-diagonal term proportional to the population of the upper level. The nonlinearity causes spontaneous decay of the upper level, shift and broadening of the line and the sensitive dependence of the final state on the initial condition. The presence of a strong laser field, resonant with the atomic…