Search results for "formula"
showing 10 items of 755 documents
Numerical Hydrodynamics in Special Relativity
2003
This review is concerned with a discussion of numerical methods for the solution of the equations of special relativistic hydrodynamics (SRHD). Particular emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods in SRHD. Results obtained with different numerical SRHD methods are compared, and two astrophysical applications of SRHD flows are discussed. An evaluation of the various numerical methods is given and future developments are analyzed.
Fundamental Principles of Quantum Mechanics
2001
There are two alternative methods of quantizing a system: a) quantization via the Feynman Path Integral (equivalent to Schwinger’s Action Principle); b) canonical quantization.
Comparison of two non-primitive methods for path integral simulations: Higher-order corrections vs. an effective propagator approach
2002
Two methods are compared that are used in path integral simulations. Both methods aim to achieve faster convergence to the quantum limit than the so-called primitive algorithm (PA). One method, originally proposed by Takahashi and Imada, is based on a higher-order approximation (HOA) of the quantum mechanical density operator. The other method is based upon an effective propagator (EPr). This propagator is constructed such that it produces correctly one and two-particle imaginary time correlation functions in the limit of small densities even for finite Trotter numbers P. We discuss the conceptual differences between both methods and compare the convergence rate of both approaches. While th…
Engineering NonBinary Rydberg Interactions via Phonons in an Optical Lattice
2019
Coupling electronic and vibrational degrees of freedom of Rydberg atoms held in optical tweezer arrays offers a flexible mechanism for creating and controlling atom-atom interactions. We find that the state-dependent coupling between Rydberg atoms and local oscillator modes gives rise to two- and three-body interactions which are controllable through the strength of the local confinement. This approach even permits the cancellation of two-body terms such that three-body interactions become dominant. We analyze the structure of these interactions on two-dimensional bipartite lattice geometries and explore the impact of three-body interactions on system ground state on a square lattice. Focus…
Triple resonant four-wave mixing boosts the yield of continuous coherent vacuum ultraviolet generation.
2012
Efficient continuous-wave four-wave mixing by using three different fundamental wavelengths with individual detunings to resonances of the nonlinear medium is shown. Up to 6 μW of vacuum ultraviolet light at 121 nm can be generated, which corresponds to an increase of three orders of magnitude in efficiency. This opens the field of quantum information processing by Rydberg entanglement of trapped ions.
Glueball masses from ratios of path integrals
2011
By generalizing our previous work on the parity symmetry, the partition function of a Yang-Mills theory is decomposed into a sum of path integrals each giving the contribution from multiplets of states with fixed quantum numbers associated to parity, charge conjugation, translations, rotations and central conjugations. Ratios of path integrals and correlation functions can then be computed with a multi-level Monte Carlo integration scheme whose numerical cost, at a fixed statistical precision and at asymptotically large times, increases power-like with the time extent of the lattice. The strategy is implemented for the SU(3) Yang-Mills theory, and a full-fledged computation of the mass and …
Neutrino-dark matter connections in gauge theories
2019
We discuss the connection between the origin of neutrino masses and the properties of dark matter candidates in the context of gauge extensions of the Standard Model. We investigate minimal gauge theories for neutrino masses where the neutrinos are predicted to be Dirac or Majorana fermions. We find that the upper bound on the effective number of relativistic species provides a strong constraint in the scenarios with Dirac neutrinos. In the context of theories where the lepton number is a local gauge symmetry spontaneously broken at the low scale, the existence of dark matter is predicted from the condition of anomaly cancellation. Applying the cosmological bound on the dark matter relic de…
Charge and magnetic moment of the neutrino in the background field method and in the linear R-xi(L) gauge
1999
We present a computation of the charge and the magnetic moment of the neutrino in the recently developed electro-weak Background Field Method and in the linear $R_{\xi}^L$ gauge. First, we deduce a formal Ward-Takahashi identity which implies the immediate cancellation of the neutrino electric charge. This Ward-Takahashi identity is as simple as that for QED. The computation of the (proper and improper) one loop vertex diagrams contributing to the neutrino electric charge is also presented in an arbitrary gauge, checking in this way the Ward-Takahashi identity previously obtained. Finally, the calculation of the magnetic moment of the neutrino, in the minimal extension of the Standard Model…
On the evaluation of a certain class of Feynman diagrams in x-space: Sunrise-type topologies at any loop order
2005
We review recently developed new powerful techniques to compute a class of Feynman diagrams at any loop order, known as sunrise-type diagrams. These sunrise-type topologies have many important applications in many different fields of physics and we believe it to be timely to discuss their evaluation from a unified point of view. The method is based on the analysis of the diagrams directly in configuration space which, in the case of the sunrise-type diagrams and diagrams related to them, leads to enormous simplifications as compared to the traditional evaluation of loops in momentum space. We present explicit formulae for their analytical evaluation for arbitrary mass configurations and arb…
Neutrino masses in the Standard Model effective field theory
2021
We would like to thank Xiao-Dong Ma for help in understanding some of the computations in Ref. [27]. We would like to thank Guilherme Guedes, Maria Ramos, Jose Santiago, and Arcadi Santamaria for useful discussions. M. C. is supported by the Spanish MINECO under the Ramon y Cajal program and partially by the Ministry of Science and Innovation under Grant No. FPA201678220-C3-1/3-P (FEDER), Spanish State Research Agency (Agencia Estatal de Investigacion) under Grant No. PID2019-106087 GB-C21/C22 (10.13039/501100011033) as well as by the Junta de Andalucia Grants No. FQM 101 and No. A-FQM-211-UGR18, and No. P18-FR-4314 (FEDER). A. T. is supported by the Generalitat Valenciana under Grant No. P…