Search results for "Eigenvalues"
showing 10 items of 315 documents
Pattern selection in the 2D FitzHugh–Nagumo model
2018
We construct square and target patterns solutions of the FitzHugh–Nagumo reaction–diffusion system on planar bounded domains. We study the existence and stability of stationary square and super-square patterns by performing a close to equilibrium asymptotic weakly nonlinear expansion: the emergence of these patterns is shown to occur when the bifurcation takes place through a multiplicity-two eigenvalue without resonance. The system is also shown to support the formation of axisymmetric target patterns whose amplitude equation is derived close to the bifurcation threshold. We present several numerical simulations validating the theoretical results.
Dynamics of a Quantum Particle in Asymmetric Bistable Potential with Environmental Noise
2011
In this work we analyze the dynamics of a quantum particle subject to an asymmetric bistable potential and interacting with a thermal reservoir. We obtain the time evolution of the population distributions in both energy and position eigenstates of the particle, for different values of the coupling strength with the thermal bath. The calculation is carried out using the Feynman-Vernon functional under the discrete variable representation.
Driven harmonic oscillators in the adiabatic Magnus approximation
1993
The time evolution of driven harmonic oscillators is determined by applying the Magnus expansion in the basis set of instantaneous eigenstates of the total Hamiltonian. It is shown that the first-order approximation already provides transition probabilities close to the exact values even in the intermediate regime.
Transition cancellations of 87Rb and 85Rb atoms in a magnetic field
2020
We have analyzed the magnetic field dependencies of the intensities of all the optical transitions between magnetic sublevels of hyperfine levels, excited with σ + , π , and σ − polarized light, for the D 1 and D 2 lines of 87 R b and 85 R b atoms. Depending on the type of transition and the quantum numbers of the involved levels, the Hamiltonian matrices are of 1 × 1 , 2 × 2 , 3 × 3 , or 4 × 4 dimension. As an example, analytical expressions are presented for the case of 2 × 2 dimension matrices for the D 1 line of both isotopes. Eigenvalues and eigenkets are given, and the expression for the transition intensity as a function of B has been determined. It is found that some π transitions o…
Graphical representation of non-absorbing polarization devices
2000
A graphical representation of general non-absorbing polarization devices operating under normal plane-wave incidence is presented. The representation is based on a four-dimensional spherical parametrization of the Jones matrix of this kind of polarization devices. The graphical representation takes the form of a solid cylinder. The projection of the point representing the device over the base of the cylinder gives the corresponding polarization eigenvectors represented in the complex plane, while the height of the point in the cylinder is the phase of its eigenvalue. Some simple examples like wave-plates and rotators are discussed. The representation may represent a useful tool to identify …
Multifractal Properties of Eigenstates in Weakly Disordered Two-Dimensional Systems without Magnetic Field
1992
In order to investigate the electronic states in weakly disordered 2D samples very large (up to 180 000 * 180 000) secular matrices corresponding to the Anderson Hamiltonian are diagonalized. The analysis of the resulting wave functions shows multifractal fluctuations on all length scales in the considered systems. The set of generalized (fractal) dimensions and the singularity spectrum of the fractal measure are determined in order to completely characterize the eigenfunctions.
Identification of spatially confined states in two-dimensional quasiperiodic lattices.
1995
We study the electronic eigenstates on several two-dimensional quasiperiodic lattices, such as the Penrose lattice and random-tiling lattices, using a tight-binding Hamiltonian in the vertex model. The infinitely degenerate states at E=0 are especially investigated. We present a systematic procedure which allows us to identify numerically the spatially strongly localized so-called confined states.
Tunneling-charging Hamiltonian of a Cooper-pair pump
2001
General properties of the tunneling-charging Hamiltonian of a Cooper pair pump are examined with emphasis on the symmetries of the model. An efficient block-diagonalization scheme and a compatible Fourier expansion of the eigenstates is constructed and applied in order to gather information on important observables. Systematics of the adiabatic pumping with respect to all of the model parameters are obtained and the link to the geometrical Berry's phase is identified.
The bound state in the spectrum of the Lee–Friedrichs Hamiltonian
2000
Abstract The spectrum of the Lee–Friedrichs Hamiltonian, describing a two-level system embedded in a continuum, is considered. An appropriate discretization of the field modes is performed before taking the continuum limit. It is shown that the existence of an eigenstate with negative energy (bound state) is related to the nonanalyticity of the Friedrichs spectral representation. This negative energy state is a dressed state and its physical properties are studied in some significant cases.
Preparation of coherent superposition in a three-state system by adiabatic passage
2004
We examine the topology of eigenenergy surfaces associated to a three-state system driven by two quasi-resonant fields. We deduce mechanisms that allow us to generate various coherent superposition of two states using an additional field, far off resonances. We report the numerical validations in mercury atoms as a model system, creating the coherent superpositions of two excited states and of two states coupled by a Raman process.