Search results for "Formalism"
showing 10 items of 357 documents
Quantum motion of a neutron in a wave-guide in the gravitational field
2006
We study theoretically the quantum motion of a neutron in a horizontal waveguide in the gravitational field of the Earth. The waveguide in question is equipped with a mirror below and a rough surface absorber above. We show that such a system acts as a quantum filter, i.e. it effectively absorbs quantum states with sufficiently high transversal energy but transmits low-energy states. The states transmitted are determined mainly by the potential well formed by the gravitational field of the Earth and the mirror. The formalism developed for quantum motion in an absorbing waveguide is applied to the description of the recent experiment on the observation of the quantum states of neutrons in th…
Pseudo-fermions in an electronic loss-gain circuit
2013
In some recent papers a loss-gain electronic circuit has been introduced and analyzed within the context of PT-quantum mechanics. In this paper we show that this circuit can be analyzed using the formalism of the so-called pseudo-fermions. In particular we discuss the time behavior of the circuit, and we construct two biorthogonal bases associated to the Liouville matrix $\Lc$ used in the treatment of the dynamics. We relate these bases to $\Lc$ and $\Lc^\dagger$, and we also show that a self-adjoint Liouville-like operator could be introduced in the game. Finally, we describe the time evolution of the circuit in an {\em Heisenberg-like} representation, driven by a non self-adjoint hamilton…
Distillation by repeated measurements: Continuous spectrum case
2010
Repeated measurements on a part of a bipartite system strongly affect the other part not measured, whose dynamics is regulated by an effective contracted evolution operator. When the spectrum of this operator is discrete, the latter system is driven into a pure state irrespective of the initial state, provided the spectrum satisfies certain conditions. We here show that even in the case of continuous spectrum an effective distillation can occur under rather general conditions. We confirm it by applying our formalism to a simple model.
Geometric phases and criticality in spin systems
2006
A general formalism of the relation between geometric phases produced by circularly evolving interacting spin systems and their criticality behavior is presented. This opens up the way for the use of geometric phases as a tool to study regions of criticality without having to undergo a quantum phase transition. As a concrete example a spin-1/2 chain with XY interactions is presented and the corresponding geometric phases are analyzed. The generalization of these results to the case of an arbitrary spin system provides an explanation for the existence of such a relation.
$a_0-f_0$ mixing in the Khuri-Treiman equations for $\eta\to 3\pi$
2015
A reliable determination of the isospin breaking double quark mass ratio from precise experimental data on $\eta\to 3\pi$ decays should be based on the chiral expansion of the amplitude supplemented with a Khuri-Treiman type dispersive treatment of the final-state interactions. We discuss an extension of this formalism which allows to estimate the effects of the $a_0(980)$ and $f_0(980)$ resonances and their mixing on the $\eta\to 3\pi$ amplitudes. Matrix generalisations of the equations describing elastic $\pi\pi$ rescattering with $I=0,\,2$ are introduced which accomodate both $\pi\pi/K\bar{K}$ and $\eta\pi/K\bar{K}$ coupled-channel rescattering. Isospin violation induced by the physical …
Exclusive semileptonic heavy meson decays including lepton mass effects
1990
We discuss the exclusive semi-leptonic (s.l.) bottom meson decaysB→D(D*)+l+v where we include non-zero lepton mass effects in the kinematics and dynamics. We develop the general formalism for the non-zero lepton mass case. We then look at how rates, spectra and angular correlations are affected by non-zero lepton masses in the context of a specific spectator quark model. Numerical results are presented for s.l. decays involving thee-, μ- and τ-leptons. We also discuss the s.l. decaysB→π(ρ),D→K(K*) and the free quark decay model.
Global frequency and intensity analysis of the / / / band system of 12 C 2 H 4 at 10 μm using the D 2h Top Data System
2016
Abstract A global frequency and intensity analysis of the infrared tetrad of 12C2H4 located in the 600 – 1500 cm − 1 region was carried out using the tensorial formalism developed in Dijon for X2Y4 asymmetric-top molecules. It relied on spectroscopic information available in the literature and retrieved from high-resolution Fourier transform infrared spectra recorded in Brussels in the frame of either the present or previous work. In particular, 645 and 131 line intensities have been respectively measured for the weak ν10 and ν4 bands. Including the Coriolis interactions affecting the upper vibrational levels 101, 71, 41 and 121, a total of 10 757 line positions and 1645 line intensities ha…
Line positions and intensities in the band of ethylene near : An experimental and theoretical study
2008
Abstract Recently, we built a tensorial formalism adapted to the spectroscopy of X2Y4 molecules. It is based on formalisms developed in Dijon for spherical-top molecules. This approach has the advantages to allow a systematic development of rovibrational interactions and to make global analyses easier to perform. We used this tool to carry out an analysis of the ν 12 band of 12C2H4 near 1450 cm - 1 , both in frequencies and intensities. 1240 line positions and 871 intensities, measured in a set of spectra recorded in Brussels, with global root mean square deviations of 1.6 × 10 - 4 cm - 1 and 1.88 % , respectively.
EPM calculations of E2/M1 mixing ratios for even samarium isotopes 146–152Sm
1987
Abstract The M1 operator and the E2/M1 mixing ratios, Δ (E2/M1), are discussed in the framework of the extended phonon projection model (EPM). The model is applied to 146, 148, 150, 152 Sm to describe their M1 properties. Comparison is made between the EPM, the consistent- Q formalism (CQF) of the basic interacting-boson approximation (IBA-1) and the experimental Δ(E2/M1) data. Both theoretical approaches give reasonably good results and parameter systematics.
Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude
2015
In this article we complete our formalism relating the finite-volume energy spectrum of a scalar quantum field theory to the three-to-three scattering amplitude, ${\cal M}_3$. In previous work we found a quantization condition relating the spectrum to a non-standard infinite-volume quantity, denoted ${\cal K}_{{\rm df},3}$. Here we present the relation between ${\cal K}_{{\rm df},3}$ and ${\cal M}_3$. We then discuss briefly how our now completed formalism can be practically implemented to extract ${\cal M}_3$ from the finite-volume energy spectrum.