Search results for "Eigenvector"
showing 10 items of 303 documents
Critical behaviour of coupled spin chains
1991
The authors investigate, using numerical computation of the eigenvalues of short chains, the critical behaviour of two composite spin models, which interpolate smoothly between isotropic Heisenberg chains with different values of S. For the first model which interpolates between S=1/2 and S=3/2 they find that the model is critical over the whole range and the values of the central charge and critical exponents (scaling dimensions) appear to be constant in the thermodynamic limit. In the second model, which interpolates between S=1/2 and S=1 they find that, except at S=1/2, the central charge is effectively zero, implying a non-critical behaviour.
Tuning nodal line semimetals in trilayered systems
2018
We investigate two-dimensional trilayered quantum systems with multi-orbital conduction bands by focusing on the role played by the layer degree of freedom in setting the character of nodal line semimetals. The layer index can label the electronic states where the electrons reside in the unit cell and can enforce symmetry constraints in the electronic structure by protecting bands crossing. We demonstrate that both the atomic spin-orbit coupling and the removal of local orbital degeneracy can lead to different types of electronic transitions with nodal lines that undergo a changeover from a loop structure enclosing the center of the Brillouin zone to pockets winding around multiple high sym…
A non self-adjoint model on a two dimensional noncommutative space with unbound metric
2013
We demonstrate that a non self-adjoint Hamiltonian of harmonic oscillator type defined on a two-dimensional noncommutative space can be diagonalized exactly by making use of pseudo-bosonic operators. The model admits an antilinear symmetry and is of the type studied in the context of PT-symmetric quantum mechanics. Its eigenvalues are computed to be real for the entire range of the coupling constants and the biorthogonal sets of eigenstates for the Hamiltonian and its adjoint are explicitly constructed. We show that despite the fact that these sets are complete and biorthogonal, they involve an unbounded metric operator and therefore do not constitute (Riesz) bases for the Hilbert space $\L…
The algebra eigenstates method for some systems with spin-like interactions
2006
International audience; An extension of the algebra eigenstates formalism is proposed to solve the eigenvalue equation for a class of problems involving "spin interactions". The method is detailed for the harmonic oscillator, su(2) and su(1, 1) algebras. Special emphasis is given to the resolution of problems in vibronic spectroscopy involving doubly degenerate electronic states.
Bose-Einstein condensation of two interacting particles
2000
We investigate the notion of Bose-Einstein condensation of interacting particles. The definition of the condensate is based on the existence of the dominant eigenvalue of the single-particle density matrix. The statistical properties and the characteristic temperature are computed exactly in the soluble models of two interacting atoms.
On numerical relativistic hydrodynamics and barotropic equations of state
2012
The characteristic formulation of the relativistic hydrodynamic equations (Donat et al 1998 J. Comput. Phys. 146 58), which has been implemented in many relativistic hydro-codes that make use of Godunov-type methods, has to be slightly modified in the case of evolving barotropic flows. For a barotropic equation of state, a removable singularity appears in one of the eigenvectors. The singularity can be avoided by means of a simple renormalization which makes the system of eigenvectors well defined and complete. An alternative strategy for the particular case of barotropic flows is discussed.
Triple magnetopolarons in quantum wells
1997
We derive the equations for eigenstates and eigenenergies of a triple magnetopolaron in quantum-well structures. An iteration procedure for obtaining the wave function and energy including the contributions of diagrams with crossing phonon lines is given. We show that under conditions of exact resonance the middle energy branch of the triply split magnetopolaron state consists of only two out of three bare states. We suggest the experimental verification of this prediction.
Pseudobosons, Riesz bases, and coherent states
2010
In a recent paper, Trifonov suggested a possible explicit model of a PT-symmetric system based on a modification of the canonical commutation relation. Although being rather intriguing, in his treatment many mathematical aspects of the model have just been neglected, making most of the results of that paper purely formal. For this reason we are re-considering the same model and we repeat and extend the same construction paying particular attention to all the subtle mathematical points. From our analysis the crucial role of Riesz bases clearly emerges. We also consider coherent states associated to the model.
Notice of Removal: Stochastic generation of the phononic band structure of lossy and infinite crystals
2017
The concept of the band structure is central to the field of phononic crystals. Indeed, capturing the dispersion of Bloch waves — the eigenmodes of propagation in periodic media — gives invaluable information on allowed propagation modes, their phase and group velocities, local resonances, and band gaps. Band structures are usually obtained by solving an eigenvalue problem defined on a closed and bounded domain, which results in a discrete spectrum. There are at least two cases, however, that cannot be reduced to a simple eigenvalue problem: first, when materials showing dispersive loss are present and second, when the unit-cell extends beyond any bound, as in the case of phononic crystal o…
Floquet perturbative analysis for STIRAP beyond the rotating wave approximation
2009
We present a perturbative analysis of Floquet eigenstates in the context of two delayed laser processes (STIRAP) in three level systems. We show the efficiency of a systematic perturbative development which can be applied as long as no non-linear resonances occur.