Search results for "Eigenvalues"

Detuning-induced robustness of a three-state Landau-Zener model against dissipation

2019

A three-state system subjected to a time-dependent Hamiltonian whose bare energies undergo one or more crossings, depending on the relevant parameters, is considered, also taking into account the role of dissipation in the adiabatic following of the Hamiltonian eigenstates. Depending on the fact that the bare energies are equidistant or not, the relevant population transfer turns out to be very sensitive to the environmental interaction or relatively robust. The physical mechanisms on the basis of this behavior are discussed in detail.

Modelling excitonic energy transfer in the photosynthetic unit of purple bacteria

2009

Abstract Molecular mechanics and quantum chemical configuration interaction calculations in combination with exciton theory were used to predict vibronic energies and eigenstates of light harvesting antennae and the reaction centre and to evaluate excitation energy transfer rates in the photosynthetic unit of purple bacteria. Excitation energy transfer rates were calculated by using the transition matrix formalism and exciton basis sets of the interacting antenna systems. Energy transfer rates of 600–800 fs from B800 ring to B850 ring in the LH2 antenna, 3–10 ps from LH2 to LH2 antenna, 2–8 ps from LH2 to LH1 antenna and finally 30–70 ps from LH1 to the reaction centre were obtained. Depend…

Numerical modelling of asymmetric boudinage

2002

Abstract Asymmetric boudinage structures are commonly used as shear sense indicators but their development is incompletely understood. This paper describes the influence of initial shape and kinematic parameters on the evolution of boudin trains using a numerical approach based on the finite difference code FLAC. Boudin trains are simulated as a series of competent objects embedded in a soft matrix subjected to general monoclinic ductile flow. Deformation of boudin trains includes heterogeneous stretching, rotation of boudins and offset along the neck regions. The sense of relative boudin offset is mainly influenced by the initial orientation of the interboudin plane in the boudinaging laye…

Deformed quons and bi-coherent states

2017

We discuss how a q-mutation relation can be deformed replacing a pair of conjugate operators with two other and unrelated operators, as it is done in the construction of pseudo-fermions, pseudo-bosons and truncated pseudo-bosons. This deformation involves interesting mathematical problems and suggests possible applications to pseudo-hermitian quantum mechanics. We construct bi-coherent states associated to $\D$-pseudo-quons, and we show that they share many of their properties with ordinary coherent states. In particular, we find conditions for these states to exist, to be eigenstates of suitable annihilation operators and to give rise to a resolution of the identity. Two examples are discu…

Finite-dimensional pseudo-bosons: a non-Hermitian version of the truncated harmonic oscillator

2018

We propose a deformed version of the commutation rule introduced in 1967 by Buchdahl to describe a particular model of the truncated harmonic oscillator. The rule we consider is defined on a $N$-dimensional Hilbert space $\Hil_N$, and produces two biorhogonal bases of $\Hil_N$ which are eigenstates of the Hamiltonians $h=\frac{1}{2}(q^2+p^2)$, and of its adjoint $h^\dagger$. Here $q$ and $p$ are non-Hermitian operators obeying $[q,p]=i(\1-Nk)$, where $k$ is a suitable orthogonal projection operator. These eigenstates are connected by ladder operators constructed out of $q$, $p$, $q^\dagger$ and $p^\dagger$. Some examples are discussed.

Two-dimensional Noncommutative Swanson Model and Its Bicoherent States

2019

We introduce an extended version of the Swanson model, defined on a two-dimensional noncommutative space, which can be diagonalized exactly by making use of pseudo-bosonic operators. Its eigenvalues are explicitly computed and the biorthogonal sets of eigenstates of the Hamiltonian and of its adjoint are explicitly constructed.We also show that it is possible to construct two displacement-like operators from which a family of bi-coherent states can be obtained. These states are shown to be eigenstates of the deformed lowering operators, and their projector allows to produce a suitable resolution of the identity in a dense subspace of \(\mathcal{L}^\mathrm{2}\, (\mathbb{R}^\mathrm{2})\).

2017

It has been shown in previous papers that classes of (minimal asymmetric) informationally-complete positive operator valued measures (IC-POVMs) in dimension d can be built using the multiparticle Pauli group acting on appropriate fiducial states. The latter states may also be derived starting from the Poincare upper half-plane model H . To do this, one translates the congruence (or non-congruence) subgroups of index d of the modular group into groups of permutation gates, some of the eigenstates of which are the sought fiducials. The structure of some IC-POVMs is found to be intimately related to the Kochen-Specker theorem.

Invariant Markov semigroups on quantum homogeneous spaces

2019

Invariance properties of linear functionals and linear maps on algebras of functions on quantum homogeneous spaces are studied, in particular for the special case of expected coideal *-subalgebras. Several one-to-one correspondences between such invariant functionals are established. Adding a positivity condition, this yields one-to-one correspondences of invariant quantum Markov semigroups acting on expected coideal *-subalgebras and certain convolution semigroups of states on the underlying compact quantum group. This gives an approach to classifying invariant quantum Markov semigroups on these quantum homogeneous spaces. The generators of these semigroups are viewed as Laplace operators …

Existence and gap-bifurcation of multiple solutions to certain nonlinear eigenvalue problems

1993

IN THIS PAPER we study: (i) a class of operator equations in an abstract Hilbert space; and (ii) the L2-theory of certain nonlinear Schrodinger equations which can be viewed as special cases of (i). In order to describe the type of abstract nonlinear eigenvalue problems to be discussed, consider a real Hilbert space H with scalar product (* , *) and norm II.11 and let S be a (not necessarily bounded) positive self-adjoint linear operator in li. We write S in the form

Principal eigenvalue of a very badly degenerate operator and applications

2007

Abstract In this paper, we define and investigate the properties of the principal eigenvalue of the singular infinity Laplace operator Δ ∞ u = ( D 2 u D u | D u | ) ⋅ D u | D u | . This operator arises from the optimal Lipschitz extension problem and it plays the same fundamental role in the calculus of variations of L ∞ functionals as the usual Laplacian does in the calculus of variations of L 2 functionals. Our approach to the eigenvalue problem is based on the maximum principle and follows the outline of the celebrated work of Berestycki, Nirenberg and Varadhan [H. Berestycki, L. Nirenberg, S.R.S. Varadhan, The principal eigenvalue and maximum principle for second-order elliptic operator…