Search results for "eigenvalues"
showing 10 items of 315 documents
Preparation of macroscopically distinguishable superpositions of circular or linear oscillatory states of a bidimensionally trapped ion
2000
A simple scheme for the generation of two different classes of bidimensional vibrational Schrodinger cat-like states of an isotropically trapped ion is presented. We show that by appropriately adjusting an easily controllable parameter having a clear physical meaning, the states prepared by our procedure are quantum superpositions of either vibrational axial angular momentum eigenstates or Fock states along two orthogonal directions.
A nonlinear eigenvalue problem for the periodic scalar p-Laplacian
2014
We study a parametric nonlinear periodic problem driven by the scalar $p$-Laplacian. We show that if $\hat \lambda_1 >0$ is the first eigenvalue of the periodic scalar $p$-Laplacian and $\lambda> \hat \lambda_1$, then the problem has at least three nontrivial solutions one positive, one negative and the third nodal. Our approach is variational together with suitable truncation, perturbation and comparison techniques.
Prediction of quantum many-body chaos in protactinium atom
2017
Energy level spectrum of protactinium atom (Pa, Z=91) is simulated with a CI calculation. Levels belonging to the separate manifolds of a given total angular momentum and parity $J^\pi$ exhibit distinct properties of many-body quantum chaos. Moreover, an extremely strong enhancement of small perturbations takes place. As an example, effective three-electron interaction is investigated and found to play a significant role in the system. Chaotic properties of the eigenstates allow one to develop a statistical theory and predict probabilities of different processes in chaotic systems.
Can coupled-cluster theory treat conical intersections?
2007
Conical intersections between electronic states are of great importance for the understanding of radiationless ultrafast relaxation processes. In particular, accidental degeneracies of hypersurfaces, i.e., between states of the same symmetry, become increasingly relevant for larger molecular systems. Coupled-cluster theory, including both single and multireference based schemes, offers a size-extensive description of the electronic wave function, but it sacrifices the Hermitian character of the theory. In this contribution, we examine the consequences of anti-Hermitian contributions to the coupling matrix element between near-degenerate states such as linear dependent eigenvectors and compl…
The band structure of double excited states for a linear chain
2000
Abstract The energy band structure in the case of double excited states of finite spin systems (s= 1 2 ) has been investigated. A geometrical construction based on the Bethe Ansatz method for determining eigenstates has been proposed. The formula for energy spectrum in the center and at the border of Brillouin zone has been obtained. Classification of energy bands has been elaborated on and approximated dispersion law for bounded states given. Some problems with application of the Bethe Ansatz in the case of finite system has been pointed out.
An algebraic approach to the Tavis-Cummings problem
2002
An algebraic method is introduced for an analytical solution of the eigenvalue problem of the Tavis-Cummings (TC) Hamiltonian, based on polynomially deformed su(2), i.e. su_n(2), algebras. In this method the eigenvalue problem is solved in terms of a specific perturbation theory, developed here up to third order. Generalization to the N-atom case of the Rabi frequency and dressed states is also provided. A remarkable enhancement of spontaneous emission of N atoms in a resonator is found to result from collective effects.
Anyons and transmutation of statistics via vacuum induced Berry phase
2004
We show that bosonic fields may present anyonic behavior when interacting with a fermion in a Jaynes-Cummings-like model. The proposal is accomplished via the interaction of a two-level system with two quantized modes of a harmonic oscillator; under suitable conditions, the system acquires a fractional geometric phase. A crucial role is played by the entanglement of the system eigenstates, which provides a two-dimensional confinement in the effective evolution of the system, leading to the anyonic behavior. For a particular choice of parameters, we show that it is possible to transmute the statistics of the system continually from fermions to bosons. We also present an experimental proposal…
Multifractal electronic wave functions in disordered systems
1992
Abstract To investigate the electronic states in disordered samples we diagonalize very large secular matrices corresponding to the Anderson Hamiltonian. The resulting probability density of single electronic eigenstates in 1-, 2-, and 3-dimensional samples is analysed by means of a box-counting procedure. By linear regression we obtain the Lipschitz-Holder exponents and the corresponding singularity spectrum, typical for a multifractal set in each case. By means of a Legendre transformation the mass exponents and the generalized dimensions are derived. Consequences for spectroscopic intensities and transport properties are discussed.
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…