Search results for "Miti"
showing 10 items of 1065 documents
Eigenvalues of non-hermitian matrices: a dynamical and an iterative approach. Application to a truncated Swanson model
2020
We propose two different strategies to find eigenvalues and eigenvectors of a given, not necessarily Hermitian, matrix (Formula presented.). Our methods apply also to the case of complex eigenvalues, making the strategies interesting for applications to physics and to pseudo-Hermitian quantum mechanics in particular. We first consider a dynamical approach, based on a pair of ordinary differential equations defined in terms of the matrix (Formula presented.) and of its adjoint (Formula presented.). Then, we consider an extension of the so-called power method, for which we prove a fixed point theorem for (Formula presented.) useful in the determination of the eigenvalues of (Formula presented…
A Note on States and Traces from Biorthogonal Sets
2019
In this paper, following Bagarello, Trapani, and myself, we generalize the Gibbs states and their related KMS-like conditions. We have assumed that H 0 , H are closed and, at least, densely defined, without giving information on the domain of these operators. The problem we address in this paper is therefore to find a dense domain D that allows us to generalize the states of Gibbs and take them in their natural environment i.e., defined in L &dagger
On the representation of integers by indefinite binary Hermitian forms
2011
Given an integral indefinite binary Hermitian form f over an imaginary quadratic number field, we give a precise asymptotic equivalent to the number of nonequivalent representations, satisfying some congruence properties, of the rational integers with absolute value at most s by f, as s tends to infinity.
THE BISHOP-PHELPS-BOLLOBAS PROPERTY FOR HERMITIAN FORMS ON HILBERT SPACES
2013
Effect of foot health and quality of life in patients with Parkinson disease: A prospective case-control investigation.
2022
Financiado para publicación en acceso aberto: Universidade da Coruña/CISUG [Abstract] Background Parkinson's disease (PD) is a common neurodegenerative disorder, characterised by the presence of motor disturbances. Therefore, it can be related to musculoskeletal and orthopaedic problems, particularly in the foot status, that are linked to a negative effect on overall health, mobility and social function. Objective The aim was to analyse the impact of foot health and quality of life in patients with Parkinson's disease and people without Parkinson's disease, with normalised reference scores, in the light of the values recorded with regard to foot health status and overall health. Material an…
Bi-coherent states as generalized eigenstates of the position and the momentum operators
2022
AbstractIn this paper, we show that the position and the derivative operators, $${{\hat{q}}}$$ q ^ and $${{\hat{D}}}$$ D ^ , can be treated as ladder operators connecting various vectors of two biorthonormal families, $${{{\mathcal {F}}}}_\varphi $$ F φ and $${{{\mathcal {F}}}}_\psi $$ F ψ . In particular, the vectors in $${{{\mathcal {F}}}}_\varphi $$ F φ are essentially monomials in x, $$x^k$$ x k , while those in $${{{\mathcal {F}}}}_\psi $$ F ψ are weak derivatives of the Dirac delta distribution, $$\delta ^{(m)}(x)$$ δ ( m ) ( x ) , times some normalization factor. We also show how bi-coherent states can be constructed for these $${{\hat{q}}}$$ q ^ and $${{\hat{D}}}$$ D ^ , both as con…
Reconstruction of Hamiltonians from given time evolutions
2010
In this paper we propose a systematic method to solve the inverse dynamical problem for a quantum system governed by the von Neumann equation: to find a class of Hamiltonians reproducing a prescribed time evolution of a pure or mixed state of the system. Our approach exploits the equivalence between an action of the group of evolution operators over the state space and an adjoint action of the unitary group over Hermitian matrices. The method is illustrated by two examples involving a pure and a mixed state.
Searching for exceptional points and inspecting non-contractivity of trace distance in (anti-) PT -symmetric systems
2022
Non-Hermitian systems with parity-time ($\mathcal{PT}$) symmetry and anti-$\mathcal{PT}$ symmetry give rise to exceptional points (EPs) with intriguing properties related to, e.g., chiral transport and enhanced sensitivity, due to the coalescence of eigenvectors. In this paper, we propose a powerful and easily computable tool, based on the Hilbert-Schmidt speed (HSS), which does not require the diagonalization of the evolved density matrix, to detect exactly the EPs and hence the critical behavior of the (anti-)$\mathcal{PT}\!-$symmetric systems, especially high-dimensional ones. Our theoretical predictions, made without the need for modification of the Hilbert space, which is performed by …
Exotic interactions mediated by a non-Hermitian photonic bath
2022
Photon-mediated interactions between quantum emitters in engineered photonic baths is an emerging area of quantum optics. At the same time, non-Hermitian (NH) physics is currently thriving, spurred by the exciting possibility to access new physics in systems ruled by non-trivial NH Hamiltonians - in particular photonic lattices - which can challenge longstanding tenets such as the Bloch theory of bands. Here, we combine these two fields and study the exotic interaction between emitters mediated by the photonic modes of a lossy photonic lattice described by a NH Hamiltonian. We show in a paradigmatic case study that structured losses in the field can seed exotic emission properties. Photons …
Changes in climatic signals of English oak tree-ring width and cross-section area of earlywood vessels in Latvia during the period 1900–2009
2012
Abstract We investigated changes in response of wood formation in English oak (Quercus robur L.) to climatic factors since 1900. It was hypothesised that the effect of winter and spring temperatures has weakened, while summer precipitation has become limiting. Increment cores were taken from 40 sites across Latvia. Tree-ring width and cross-section area of earlywood vessels were measured and cross-dated. Regional chronologies were built by pooling time series of trees within two regions of Latvia (western and eastern region), which differed in continentality. Climatic signals differed between the proxies (tree-ring width and earlywood vessel cross-section area) and between regions. Mean cro…