Search results for "quantization"
showing 10 items of 253 documents
On a possible origin of quantum groups
1991
A Poisson bracket structure having the commutation relations of the quantum group SLq(2) is quantized by means of the Moyal star-product on C∞(ℝ2), showing that quantum groups are not exactly quantizations, but require a quantization (with another parameter) in the background. The resulting associative algebra is a strongly invariant nonlinear star-product realization of the q-algebra Uq(sl(2)). The principle of strong invariance (the requirement that the star-commutator is star-expressed, up to a phase, by the same function as its classical limit) implies essentially the uniqueness of the commutation relations of Uq(sl(2)).
Soliton Statistical Mechanics: Statistical Mechanics of the Quantum and Classical Integrable Models
1988
It is shown how the Bethe Ansatz (BA) analysis for the quantum statistical mechanics of the Nonlinear Schrodinger Model generalises to the other quantum integrable models and to the classical statistical mechanics of the classical integrable models. The bose-fermi equivalence of these models plays a fundamental role even at classical level. Two methods for calculating the quantum or classical free energies are developed: one generalises the BA method the other uses functional integral methods. The familiar classical action-angle variables of the integrable models developed for the real line R are used throughout, but the crucial importance of periodic boundary conditions is recognized and t…
Improved moment scaling estimation for multifractal signals
2018
A fundamental problem in the analysis of multifractal processes is to estimate the scaling exponent K(q) of moments of different order q from data. Conventional estimators use the empirical moments μ^[subscript r][superscript q]=⟨ | ε[subscript r](τ)|[superscript q]⟩ of wavelet coefficients ε[subscript r](τ), where τ is location and r is resolution. For stationary measures one usually considers "wavelets of order 0" (averages), whereas for functions with multifractal increments one must use wavelets of order at least 1. One obtains K^(q) as the slope of log(μ^[subscript r][superscript q]) against log(r) over a range of r. Negative moments are sensitive to measurement noise and quantization.…
Propagating single photons from an open cavity: Description from universal quantization
2022
Over the last decades, quantum optics has evolved from high quality factor cavities in the early experiments toward new cavity designs involving leaky modes. Despite very reliable models, in the concepts of cavity quantum electrodynamics, photon leakage is most of the time treated phenomenologically. Here, we take a different approach, and starting from first principles, we define an inside-outside representation which is derived from the original true-mode representation, in which one can determine effective Hamiltonian and Poynting vector. Contrary to the phenomenological model, they allow a full description of a leaking single photon produced in the cavity and propagating in free space. …
Looking for magnetic monopoles at LHC with diphoton events
2012
Magnetic monopoles have been a subject of interest since Dirac established the relation between the existence of monopoles and charge quantization. The intense experimental search carried thus far has not met with success. The Large Hadron Collider is reaching energies never achieved before allowing the search for exotic particles in the TeV mass range. In a continuing effort to discover these rare particles we propose here other ways to detect them. We study the observability of monopoles and monopolium, a monopole-antimonopole bound state, at the Large Hadron Collider in the $\gamma \gamma$ channel for monopole masses in the range 500-1000 GeV. We conclude that LHC is an ideal machine to …
Quantum counter-propagation in open optical cavities via the quasi-normal-mode approach
2006
By using the quasi-normal-mode (QNM) formalism in a second quantization scheme, the problem of the counter-propagation of electromagnetic fields inside optical cavities is studied. The links between QNM operators and canonical destruction and creation operators describing the external free field, as well as the field correlation functions, are found and discussed. An application of the theory is performed for open cavities whose refractive index satisfies symmetric properties.
Parton distribution functions of heavy mesons on the light front
2019
The parton distribution functions (PDFs) of heavy mesons are evaluated from their light-front wave functions, which are obtained from a basis light-front quantization in the leading Fock sector representation. We consider the mass eigenstates from an effective Hamiltonian consisting of the confining potential adopted from light-front holography in the transverse direction, a longitudinal confinement, and a one-gluon exchange interaction with running coupling. We present the gluon and the sea quark PDFs which we generate dynamically from the QCD evolution of the valence quark distributions.
Ultrarelativistic quark-nucleus scattering in a light-front Hamiltonian approach
2020
We investigate the scattering of a quark on a heavy nucleus at high energies using the time-dependent basis light-front quantization (tBLFQ) formalism, which is the first application of the tBLFQ formalism in QCD. We present the real-time evolution of the quark wave function in a strong classical color field of the relativistic nucleus, described as the color glass condensate. The quark and the nucleus color field are simulated in the QCD SU(3) color space. We calculate the total and the differential cross sections, and the quark distribution in coordinate and color spaces using the tBLFQ approach. We recover the eikonal cross sections in the eikonal limit. We find that the differential cro…
Perturbative quantum field theory
2000
pQFT In this chapter we repeat the main steps towards a derivation of the Feynman rules, following the well-known path of canonical quantization. This is standard material, and readers who are not acquainted with such topics are referred to [Bjorken and Drell 1965, Bogoliubov and Shirkov 1980, Itzykson and Zuber 1980, Kaku 1993, Weinberg 1995, Peskin and Schroeder 1995, Teller 1997]. We hope that the short summary given here, similar to that in [Kreimer 1997a], is helpful for readers who want to refresh their memory. Having introduced Feynman rules, we next introduce Schwinger–Dyson equations as a motivation for the introduction of Z -factors. We remark on dimensional regularization and giv…
Tuning the Pseudospin Polarization of Graphene by a Pseudomagnetic Field.
2016
One of the intriguing characteristics of honeycomb lattices is the appearance of a pseudo-magnetic field as a result of mechanical deformation. In the case of graphene, the Landau quantization resulting from this pseudo-magnetic field has been measured using scanning tunneling microscopy. Here we show that a signature of the pseudo-magnetic field is a local sublattice symmetry breaking observable as a redistribution of the local density of states. This can be interpreted as a polarization of graphene's pseudospin due to a strain induced pseudo-magnetic field, in analogy to the alignment of a real spin in a magnetic field. We reveal this sublattice symmetry breaking by tunably straining grap…