Search results for "Quantum"
showing 10 items of 9714 documents
On the Deactivation Mechanisms of Adenine–Thymine Base Pair
2012
In this contribution, the multiconfigurational second-order perturbation theory method based on a complete active space reference wave function (CASSCF/CASPT2) is applied to study all possible single and double proton/hydrogen transfers between the nucleobases in the adenine-thymine (AT) base pair, analyzing the role of excited states with different nature [localized (LE) and charge transfer (CT)], and considering concerted as well as step-wise mechanisms. According to the findings, once the lowest excited states, localized in adenine, are populated during UV irradiation of the Watson-Crick base pair, the proton transfer in the N-O bridge does not require high energy in order to populate a …
Erich Hückel’s Research Agenda During the 1930s: Underpinning Organic Chemistry with Quantum Theory
2009
The foregoing three Sections 1.9.2, 1.9.3 and 1.9.4 have shown how Huckel’s interest in quantum mechanics and its application to problems in chemistry developed. Before turning our attention to a detailed history of Huckel’s theory of double bonding, it seems appropriate to insert a brief sketch of classical models of double bonds in stereochemistry and their limitations. The emphasis will be on controversial aspects of the classical theory important in the development of Huckel’s theory, which prompted him to develop his new ideas about double bonding.
Ultrarelativistic bound states in the spherical well
2016
We address an eigenvalue problem for the ultrarelativistic (Cauchy) operator $(-\Delta )^{1/2}$, whose action is restricted to functions that vanish beyond the interior of a unit sphere in three spatial dimensions. We provide high accuracy spectral datafor lowest eigenvalues and eigenfunctions of this infinite spherical well problem. Our focus is on radial and orbital shapes of eigenfunctions. The spectrum consists of an ordered set of strictly positive eigenvalues which naturally splits into non-overlapping, orbitally labelled $E_{(k,l)}$ series. For each orbital label $l=0,1,2,...$ the label $k =1,2,...$ enumerates consecutive $l$-th series eigenvalues. Each of them is $2l+1$-degenerate. …
Unitary transformations depending on a small parameter
2011
We formulate a unitary perturbation theory for quantum mechanics inspired by the LieDeprit formulation of canonical transformations. The original Hamiltonian is converted into a solvable one by a transformation obtained through a Magnus expansion. This ensures unitarity at every order in a small parameter. A comparison with the standard perturbation theory is provided. We work out the scheme up to order ten with some simple examples.
On the study of the vibrational energy levels of Arsine molecule
2008
Abstract We compare two formalisms applied to the vibrational modes of the molecule of AsH 3 of C 3 v molecular symmetry group. Indeed, the close stretching modes of this molecule may be considered as those of a three-dimensional oscillator whereas the bending modes may be considered either as a one-dimensional oscillator of symmetry A 1 and a two-dimensional oscillator of symmetry E or as an approximate three-dimensional oscillator. So, we have applied the U ( p + 1) formalism to the both stretching and bending modes and introduced coupling terms acting on an appropriate coupled vibrational basis through a local mode formalism. We have then compared the result of our fitting with those ob…
Fault-Reconstruction-Based Cascaded Sliding Mode Observers for Descriptor Linear Systems
2012
Published version of an article from the journal: Mathematical Problems in Engineering. Also available from the publisher:http://dx.doi.org/10.1155/2012/623426 This paper develops a cascaded sliding mode observer method to reconstruct actuator faults for a class of descriptor linear systems. Based on a new canonical form, a novel design method is presented to discuss the existence conditions of the sliding mode observer. Furthermore, the proposed method is extended to general descriptor linear systems with actuator faults. Finally, the effectiveness of the proposed technique is illustrated by a simulation example.
Observer-Based Stabilization of Stochastic Systems with Limited Communication
2012
Published version of an article in the journal: Mathematical Problems in Engineering. Also available from Hindawi: http://dx.doi.org/10.1155/2012/781542 Open Access This paper studies the problem of observer-based stabilization of stochastic nonlinear systems with limited communication. A communication channel exists between the output of the plant and the input of the dynamic controller, which is considered network-induced delays, data packet dropouts, and measurement quantization. A new stability criterion is derived for the stochastic nonlinear system by using the Lyapunov functional approach. Based on this, the design procedure of observer-based controller is presented,which ensures asy…
Robust Observer Design for Takagi-Sugeno Fuzzy Systems with Mixed Neutral and Discrete Delays and Unknown Inputs
2012
Published version of an article from the journal: Mathematical Problems in Engineering. Also available from the publisher:http://dx.doi.org/10.1155/2012/635709 A robust observer design is proposed for Takagi-Sugeno fuzzy neutral models with unknown inputs. The model consists of a mixed neutral and discrete delay, and the disturbances are imposed on both state and output signals. Delay-dependent sufficient conditions for the design of an unknown input T-S observer with time delays are given in terms of linear matrix inequalities. Some relaxations are introduced by using intermediate variables. A numerical example is given to illustrate the effectiveness of the given results.
Spatial correlations of vacuum fluctuations and the Casimir-Polder potential
2003
We calculate the Casimir-Polder intermolecular potential using an effective Hamiltonian recently introduced. We show that the potential can be expressed in terms of the dynamical polarizabilities of the two atoms and the equal-time spatial correlation of the electric field in the vacuum state. This gives support to an interesting physical model recently proposed in the literature, where the potential is obtained from the classical interaction between the instantaneous atomic dipoles induced and correlated by the vacuum fluctuations. Also, the results obtained suggest a more general validity of this intuitive model, for example when external boundaries or thermal fields are present.
Josephson Traveling Wave Parametric Amplifiers as Non-Classical Light Source for Microwave Quantum Illumination
2021
Abstract Detection of low-reflectivity objects can be enriched via the so-called quantum illumination procedure. In order that this quantum procedure outperforms classical detection protocols, entangled states of microwave radiation are initially required. In this paper, we discuss the role of Josephson Traveling Wave Parametric Amplifiers (JTWPAs), based on circuit-QED components, as suitable sources of a two-mode squeezed vacuum state, a special signal-idler entangled state. The obtained wide bandwidth makes the JTWPA an ideal candidate for generating quantum radiation in quantum metrology and information processing applications.