Feynman's Model Research Articles

Analysis of data for γp → f 1(1285)p photoproduction* *Partially supported by the National Natural Science Foundation of China (12175240, 12147153, 11635009, 12305097, 12305137), the Fundamental Research Funds for the Central Universities, and the China Postdoctoral Science Foundation (2021M693141, 2021M693142)

The photoproduction of the meson off the proton target is investigated within an effective Lagrangian approach. The t-channel ρ- and ω-exchange diagrams, u-channel nucleon-exchange diagram, generalized contact term, and s-channel pole diagrams of the nucleon and a minimal number of nucleon resonances are taken into account in constructing the reaction amplitudes to describe the experimental data. Three different models, that is, the Feynman, Regge, and interpolated Regge models, are employed, where the t-channel reaction amplitudes are constructed in Feynman, Regge, and interpolated Regge types, respectively. The results show that neither the Feynman model with two nucleon resonances nor the interpolated Regge model with one nucleon resonance can satisfactorily reproduce the available data for . Nevertheless, in the Regge model, when any one of the , , , , , , , , and resonances is considered, the data can be well described. The resulting resonance parameters are consistent with those advocated in the Particle Data Group (PDG) review. Further analysis shows that, in the high-energy region, the peaks of differential cross sections at forward angles are dominated by the contributions from t-channel ρ- and ω-exchange diagrams, while in low-energy region, the s-channel pole diagrams of resonances also provide significant contributions to the cross sections.

Full counting statistics and fluctuation theorem for the currents in the discrete model of Feynman's ratchet.

We provide a detailed investigation of the fluctuations of the currents in the discrete model of Feynman's ratchet proposed by Jarzynski and Mazonka in 1999. Two macroscopic currents are identified, with the corresponding affinities determined using Schnakenberg's graph analysis. We also investigate full counting statistics of the two currents and show that fluctuation theorem holds for their joint probability distribution. Moreover, fluctuation-dissipation relation, Onsager reciprocal relation and their nonlinear generalizations are numerically shown to be satisfied in this model.

Editorial

Editorial

Pion-induced production with baryon off proton target

In this work, the reaction is investigated with an effective Lagrangian approach. The contributions from the Born terms, including the s, t, and u channel, are considered, and the Regge model and the Feynman model are applied to treat the t-channel contribution. The existing experimental data can be reproduced with the best-fitted χ 2 being 2.38 and 1.54 for the Feynman and Regge models, respectively. Moreover, it is found that the contribution from the t channel is dominant in the cross-section. The contribution of the u channel is mainly distributed at backward angles, and the contribution from the s channel is small and negligible. In the Feynman model, the contribution of the t-channel K exchange is much larger than the contribution of the exchange, while in the Regge model the contribution of the t-channel K exchange is comparable to that of the exchange. Prediction about the differential cross-section of the reaction is also presented, which is helpful for clarifying the role of the Regge treatment. The current results suggest high-precision experimental measurements which can be performed at J-PARC and COMPASS.

Studying X(2100) hadronic decays and predicting its pion and kaon induced productions

The newly observed $X(2100)$ by the BESIII Collaboration inspires our interest in studying the light meson system, especially axial-vector mesons. Since the $X(2100)$ has $J^P=1^+$ possibilities but cannot be distinguished only by mass, we make use of flux-tube model to study the strong decay behavior of $X(2100)$ under this assignment. The experimental width of the newly reported $X(2100)$ can be reproduced in our calculation, which favors an assignment of $X(2100)$ as the second radial excitation of $h_1(1380)$ with $I(J^P)=0(1^+)$. And the $\mathcal{B}(X(2100)\to \phi \eta^\prime)$ has a sizable contribution to the total width. Furthermore, we focus on the production of $X(2100)$ and its flavour partner $h_1(1965)$ induced by pion and kaon on a proton target with the Feynman model and the Regge model, which is an available platform to further identify their nature. The numerical results indicate that the total cross section are similar in the two models. When the range of momentum ${\mathrm{p_{Lab}}}$ is 10 to 30 GeV/$c$, the total cross sections for $\pi^-p\to X(2100)n$ and $K^-p\to X(2100)\Lambda$ are predicted to be at an order of magnitude of 0.1 $\mu$b. Whereas, the total cross section for $\pi^-p\to h_1(1965)n$ is near an order of magnitude of 10 $\mu$b when $p_{\mathrm{Lab}}$ is from 10 to 30 GeV/$c$, and much larger than that of reaction $K^-p\to h_1(1965)\Lambda$. These predictions can provide some valuable information to search for $X(2100)$ and $h_1(1965)$ in experiments at J-PARC, COMPASS, OKA@U-70 and SPS@CERN.

Productions of f1(1420) in pion and kaon induced reactions

The $f_{1}(1420)$ productions via pion and kaon induced reactions on a proton target are investigated in an effective Lagrangian approach. Two treatments of the $t$-channel Born term, the Feynman model and the Regge model, are introduced to calculate the total and differential cross sections of the $\pi^{-}p\rightarrow f_{1}(1420)n$ and $K^{-}p\rightarrow f_{1}(1420)\Lambda $ reactions. The numerical results indicate that the experimental data of the total cross section of the $\pi ^{-}p\rightarrow f_{1}(1420)n$ reaction can be reproduced in both the Feynman and the Regge models. Based on the parameters determined in the pion induced reaction, the cross sections of the $K^{-}p\rightarrow f_{1}(1420)\Lambda $ reaction, about which there is little data found in the literature, are predicted in the same beam momentum range. It is found that the line shapes of the total cross section obtained in a kaon induced reaction with two treatments are quite different. The cross sections for both reactions are at an order of magnitude of $\mu$b, or larger, at a beam momenta up to 10 GeV/c. The differential cross sections for both pion and kaon induced reactions are also present. It is found that in the Regge model, the $t$ channel provides a sharp increase at extreme forward angles. The results suggest that the experimental study of the $f_1(1420)$ in the kaon induced reaction on a proton target is as promising as in the pion induced reaction. Such an experimental measurement is also very helpful to clarify the production mechanism of the $f_1(1420)$.

Solvable problems in classical representation

Some solvable problems are considered in a classical representation: namely, the harmonic oscillator, the non-relativistic model of confinement of quarks and the time-dependent Feynman model. In a classical representation, the harmonic oscillator $$V(x)=\frac{1}{2}m\omega ^2x^2$$ transforms into an equation, which formally coincides with the radial Schrodinger equation for Sturmian states of a hydrogen atom with an energy $$ {\mathcal {E}} = -2 / \omega ^ 2 $$ , an effective charge $$ {\mathcal {Z}} = 2E_n / \omega ^ 2 $$ and an orbital quantum number $$ l = -1 / 2 $$ . The problem of V-type potential $$V(x)=F|x|$$ describing the confinement of quarks transforms again into the Airy equation. The classical solution of the time-dependent Feynman model $$V(x,t)=\frac{1}{2}m\omega ^2x^2+\alpha (t)x$$ after projection on the eigen-states in classical representation gives results for inelastic transitions which coincide with the exact results obtained by Feynman in a purely quantum approach. The analysis of harmonic oscillator, V-type potential and the Feynman model gives a new integral relation between the Laguerre polynomials and the square of the Hermite polynomials, the Airy function and the square of the Airy function, quadratic form of the Laguerre polynomials and quadratic form of the generalized Laguerre polynomials.

Photoproduction ofa2(1320)in a Regge model

In this work, the photoproduction of $a_{2}(1320)$ off a proton target is investigated within an effective Lagrangian approach and the Regge model. The theoretical result indicates that the shapes of {the} total and differential cross sections of the $\gamma p\rightarrow a_{2}^{+}n$ reaction within the Feynman (isobar) model are much different from that of the Reggeized treatment. The obtained cross section is compared with the existing experimental results at low energies. The $a_{2}(1320)$ production cross section at high energies can be tested by the COMPASS experiment, which can provide important information for clarifying the role of the Reggeized treatment at that energy range.

K*0Λphotoproduction off a neutron

Inspired by the preliminary experimental data by the CLAS Collaboration, the $K^{\ast 0}\Lambda$ photoproduction off a neutron is studied within an effective Lagrangian approach. The contributions from the Born terms including $s$, $u$, and $t$ channels are considered to calculate the amplitude, with which the cross sections are calculated and compared with preliminary CLAS data. The theoretical results indicate that the contribution from the $K$-exchange $t$ channel plays a dominant role for the $K^{\ast 0}\Lambda$ photoproduction. The contribution from the $\kappa$ exchange is found one order of magnitude smaller than that from the $K$ exchange. Both the Regge model and the Feynman model are applied to treat the $t$-channel contribution. The discrepancy between two models is found small in the energy range of CLAS data and predicted to become obvious at energies higher than 3 GeV. More precise experimental data especially at backward angles will be helpful to further understand the interaction mechanism of the $K^{\ast 0}\Lambda$ photoproduction.

Energy Blocks — A Physical Model for Teaching Energy Concepts

Most physics educators would agree that energy is a very useful, albeit abstract topic. It is therefore important to use various methods to help the student internalize the concept of energy itself and its related ideas. These methods include using representations such as energy bar graphs, energy pie charts, or energy tracking diagrams. Activities and analogies like Energy Theater and Richard Feynman's blocks, as well as the popular money (or wealth) analogy, can also be very effective. The goal of this paper is to describe a physical model of Feynman's blocks that can be employed by instructors to help students learn the following energy-related concepts: The factors affecting each individual mechanical energy storage mode (this refers to what has been traditionally called a form of energy, and while the Modeling Method of instruction is not the focus of this paper, much of the energy related language used is specific to the Modeling Method). For example, how mass or height affects gravitational energy;Energy conservation; andThe graphical relationships between the energy storage mode and a factor affecting it. For example, the graphical relationship between elastic energy and the change in length of a spring.

From microscopic to macroscopic description of Josephson dynamics in one-dimensional arrays of weakly-coupled superconducting islands

By starting from a microscopic quantum mechanical description of Josephson dynamics of a one-dimensional array of N coupled superconductors, we obtain a set of linear differential equations for the system order parameter and for additional macroscopic physical quantities. With opportune considerations, we adapt this description to two coupled superconductors, obtaining the celebrated Feynman model for Josephson junctions. These results confirm the correspondence between the microscopic picture and the semi-classical Ohta’s model adopted in describing the superconducting phase dynamics in multi-barrier Josephson junctions.

Feynman's and Ohta's models of a Josephson junction

The Josephson equations are derived by means of the weakly coupled two-level quantum system model given by Feynman. Adopting a simplified version of Ohta's model, starting from Feynman's model, the strict voltage–frequency Josephson relation is derived. The contribution of Ohta's approach to the comprehension of the additional term given by the classical external system is recognized. Extension of the model to double-barrier Josephson junctions and multilayered systems is finally briefly commented on.

ChargedK*photoproduction in a Regge model

We investigate $\gamma p \to K^{*+} \Lambda$ reaction within a Regge approach. For the gauge invariance of the scattering amplitude, we reggeize the s-channel and contact term amplitudes as well as the $t$-channel amplitude. We obtain the decreasing behavior of the total cross section as the CLAS's preliminary data show. We also calculate spin density matrices, and find clear differences between our Regge model and the previous Feynman (isobar) model.

QUANTUM TIMING AND SYNCHRONIZATION PROBLEMS

Feynman's model of a quantum computer provides an example of a continuous-time quantum walk. Its clocking mechanism is an excitation of a basically linear chain of spins with occasional controlled jumps which allow for motion on a planar graph. The spreading of the wave packet poses limitations on the probability of ever completing the s elementary steps of a computation: an additional amount of storage space δ is needed in order to achieve an assigned completion probability. In this note we study the END instruction, viewed as a measurement of the position of the clocking excitation: a π-pulse indefinitely freezes the contents of the input/output register, with a probability depending only on the ratio δ/s.

The clock of a quantum computer

If the physical agent (the 'pointer', or 'cursor', or 'clocking mechanism') that sequentially scans the T lines of a long computer program is a microscopic system, two quantum phenomena become relevant: spreading of the probability distribution of the pointer along the program lines, and scattering of the probability amplitude at the two endpoints of the physical space allowed for its motion. We show that the first effect determines an upper bound O(T−2/3) on the probability of finding the pointer exactly at the END line. By adding an adequate number δ of further empty lines ('telomers'), one can store the result of the computation up to the moment in which the pointer is scattered back into the active region. This leads to a less severe upper bound O(√δ/T) on the probability of finding the pointer either at the END line or within the additional empty lines. Our analysis is performed in the context of Feynman's model of quantum computation, the only model, to our knowledge, that explicitly includes a physically plausible quantum clocking mechanism in its considerations.

A discrete scheme for the Dirac and Klein–Gordon equations

The 1+1 Klein–Gordon and Dirac equations are converted into finite-dimensional matrix equations by using a projection method. In the Dirac case, the discrete solution converges to the continuum propagator and it can also be rewritten in the form given by the checkerboard model of Feynman.

Feynman's ratchet and pawl: an exactly solvable model.

We introduce a simple, discrete model of Feynman's ratchet and pawl, operating between two heat reservoirs. We solve exactly for the steady-state directed motion and heat flows produced, first in the absence and then in the presence of an external load. We show that the model can act both as a heat engine and as a refrigerator. We finally investigate the behavior of the system near equilibrium, and use our model to confirm general predictions based on linear-response theory.

On the Path Integral of the Relativistic Electron

We revisit the path integral description ofmotion of a relativistic electron. Applying a minor, butwell-motivated conceptional change to Feynman'schessboard model, we obtain exact solutions of the Dirac equation. The calculation is performed by meansof a particularly simple method different from both thecombinatorial approach envisaged by Feynman and itsIsing model correspondence.

Structure, transport and surface properties of dense fluids, especially liquid metals

The initial focus is on the relation between dynamic and static structure in liquid metals such as Rb near freezing. A Feynman-like model of collective modes and some possible generalizations are summarized, and the simple Feynman model is used to evaluate the fourth moment of the dynamic structure factor S(k, w) in terms of the static structure factor S(k) in the long wavelength limit as k tends to zero. Indeed the central role played by S(0), which is in turn proportional to the isothermal compressibility, is a unifying theme throughout the present study. It is then stressed that when a Debye-like assumption is added, the Green—Kubo formula for the longitudinal viscosity can be employed to estimate this transport coefficient for simple sp metals like Rb near freezing. Utilizing a formula for the shear viscosity at melting that goes back to Andrade, new estimates are presented of the bulk viscosity of some sp metals. Via the long wavelength limit S(0) of the static structure factor, the ratio of shear to longitudinal viscosity at the melting temperature Tm is written as proportional to ρk B T m L/σ where σ is the surface tension, L is the surface thickness, of the order of a molecular diameter, and ρ is the atomic number density. This link between viscosities and surface properties seems to be a new result, and its relation to earlier studies is discussed. An important feature introduced here is the surface thickness L.

Josephson equations for the simplest superconducting multilayer system

We extend Feynman's model of a single Josephson junction to the case of three stacked superconducting layers. In order to derive the correct voltage-phase relation, a self consistent approach to this model is used. By this analysis we notice that, if the intermediate electrode is thin enough to allow the overlap of the superconducting order parameters of the outer layers, an additional term appears in the Josephson current-phase relation. Two representative applications are presented for these types of junctions.