Search results for "LIMIT"
showing 10 items of 2826 documents
correction to ƒB
1991
Abstract The 1/m corrections to the B-meson decay constant ƒB (and the D-meson decay constant ƒD) of the heavy quark effective theory are calculated in the Green function approach. The corrections are found to be sensitive to the difference of the meson mass mB and the heavy quark mass mb. For mb=4.81 GeV we obtain a 100% correction to the heavy quark limit mb=mB. The scaling law of the ratio ƒB/ƒD is, however, quite well satisfied because of cancellations. For reasonable values of quark masses we obtain ƒ B = (130±20) MeV and ƒ D = (170±10) MeV .
Electromagnetic lattice gauge invariance in two-dimensional discrete-time quantum walks
2018
International audience; Gauge invariance is one of the more important concepts in physics. We discuss this concept in connection with the unitary evolution of discrete-time quantum walks in one and two spatial dimensions, when they include the interaction with synthetic, external electromagnetic fields. One introduces this interaction as additional phases that play the role of gauge fields. Here, we present a way to incorporate those phases, which differs from previous works. Our proposal allows the discrete derivatives, that appear under a gauge transformation, to treat time and space on the same footing, in a way which is similar to standard lattice gauge theories. By considering two step…
Asymptotic analysis of the form-factors of the quantum spin chains
2020
Since a long-time, the quantum integrable systems have remained an area where modern mathematical methods have given an access to interesting results in the study of physical systems. The exact computations, both numerical and asymptotic, of the correlation function is one of the most important subject of the theory of the quantum integrable models. In this context an approach based on the calculation of form factors has been proved to be a more effective one. In this thesis, we develop a new method based on the algebraic Bethe ansatz is proposed for the computation of the form-factors in thermodynamic limit. It is applied to and described in the context of isotropic XXX Heisenberg chain, w…
Can a quantum nondemolition measurement improve the sensitivity of an atomic magnetometer?
2004
Noise properties of an idealized atomic magnetometer that utilizes spin squeezing induced by a continuous quantum nondemolition measurement are considered. Such a magnetometer measures spin precession of $N$ atomic spins by detecting optical rotation of far-detuned light. Fundamental noise sources include the quantum projection noise and the photon shot-noise. For measurement times much shorter than the spin-relaxation time observed in the absence of light ($\tau_{\rm rel}$) divided by $\sqrt{N}$, the optimal sensitivity of the magnetometer scales as $N^{-3/4}$, so an advantage over the usual sensitivity scaling as $N^{-1/2}$ can be achieved. However, at longer measurement times, the optimi…
Quantum Criticality in a Bosonic Josephson Junction
2011
In this paper we consider a bosonic Josephson junction described by a two-mode Bose-Hubbard model, and we thoroughly analyze a quantum phase transition occurring in the system in the limit of infinite bosonic population. We discuss the relation between this quantum phase transition and the dynamical bifurcation occurring in the spectrum of the Discrete Self Trapping equations describing the system at the semiclassical level. In particular, we identify five regimes depending on the strength of the effective interaction among bosons, and study the finite-size effects arising from the finiteness of the bosonic population. We devote a special attention to the critical regime which reduces to th…
Quantum fluctuations and coherence in high-precision single-electron capture.
2012
The phase of a single quantum state is undefined unless the history of its creation provides a reference point. Thus quantum interference may seem hardly relevant for the design of deterministic single-electron sources which strive to isolate individual charge carriers quickly and completely. We provide a counterexample by analyzing the non-adiabatic separation of a localized quantum state from a Fermi sea due to a closing tunnel barrier. We identify the relevant energy scales and suggest ways to separate the contributions of quantum non-adiabatic excitation and backtunneling to the rare non-capture events. In the optimal regime of balanced decay and non-adiabaticity, our simple electron tr…
Scaling of Berry's phase close to the Dicke quantum phase transition
2006
We discuss the thermodynamic and finite size scaling properties of the geometric phase in the adiabatic Dicke model, describing the super-radiant phase transition for an $N$ qubit register coupled to a slow oscillator mode. We show that, in the thermodynamic limit, a non zero Berry phase is obtained only if a path in parameter space is followed that encircles the critical point. Furthermore, we investigate the precursors of this critical behavior for a system with finite size and obtain the leading order in the 1/N expansion of the Berry phase and its critical exponent.
Symmetry-protected intermediate trivial phases in quantum spin chains
2015
Symmetry-protected trivial (SPt) phases of matter are the product-state analogue of symmetry-protected topological (SPT) phases. This means, SPt phases can be adiabatically connected to a product state by some path that preserves the protecting symmetry. Moreover, SPt and SPT phases can be adiabatically connected to each other when interaction terms that break the symmetries protecting the SPT order are added in the Hamiltonian. It is also known that spin-1 SPT phases in quantum spin chains can emerge as effective intermediate phases of spin-2 Hamiltonians. In this paper we show that a similar scenario is also valid for SPt phases. More precisely, we show that for a given spin-2 quantum cha…
Dynamical bifurcation as a semiclassical counterpart of a quantum phase transition
2011
We illustrate how dynamical transitions in nonlinear semiclassical models can be recognized as phase transitions in the corresponding -- inherently linear -- quantum model, where, in a Statistical Mechanics framework, the thermodynamic limit is realized by letting the particle population go to infinity at fixed size. We focus on lattice bosons described by the Bose-Hubbard (BH) model and Discrete Self-Trapping (DST) equations at the quantum and semiclassical level, respectively. After showing that the gaussianity of the quantum ground states is broken at the phase transition, we evaluate finite populations effects introducing a suitable scaling hypothesis; we work out the exact value of the…
All spin-1 topological phases in a single spin-2 chain
2014
Here we study the emergence of different Symmetry-Protected Topological (SPT) phases in a spin-2 quantum chain. We consider a Heisenberg-like model with bilinear, biquadratic, bicubic, and biquartic nearest-neighbor interactions, as well as uniaxial anisotropy. We show that this model contains four different effective spin-1 SPT phases, corresponding to different representations of the $(\mathbb{Z}_2 \times \mathbb{Z}_2) + T$ symmetry group, where $\mathbb{Z}_2$ is some $\pi$-rotation in the spin internal space and $T$ is time-reversal. One of these phases is equivalent to the usual spin-1 Haldane phase, while the other three are different but also typical of spin-1 systems. The model also …