Journal of undergraduate reports in physics最新文献

{"title":"Quantum Inequalities and Particle Creation in the Presence of an External, Time-Dependent Mamaev-Trunov Potential","authors":"Kalista Schauer, M. Pfenning, Jared Cochrane","doi":"10.1063/10.0006348","DOIUrl":"https://doi.org/10.1063/10.0006348","url":null,"abstract":"1 United States Military Academy at West Point, West Point, New York 10996-1790, USA a) Corresponding author: kalistaschauer@gmail.com b) michael.pfenning@westpoint.edu c) jared.cochrane.mil@mail.mil Abstract. In 2011, Mr. Dan Solomon proposed a model of a quantized scalar field interacting with a time-dependent Mamaev-Trunov potential in two-dimensional Minkowski spacetime. This model is governed by the Klein-Gordon wave equation with a time-dependent potential. Mr. Solomon claims that this model violates both the classical energy conditions of special relativity and the quantum energy conditions of quantum field theory in curved spacetime. Every classical energy condition can be violated, and their natural replacements are known as quantum inequalities. Mr. Solomon attempted to prove violations of the spatial and temporal quantum inequalities, and he correctly assumed that the negative energy splits into two fluxes at the Cauchy surface, where the potential is turned off. Unfortunately, Solomon neglects the contribution to the energy density due to particle creation when the potential is turned off at time t = 0 . In this project, we calculate the contribution to the stress energy tensor due to particle creation. We show that while the classical energy conditions are violated, the quantum energy inequalities hold, contrary to Mr. Solomon’s statements. SCIENTIFIC BACKGROUND Mathematical Background The mathematical foundation of quantum mechanics consists of wave functions and operators. Wave functions express the state of a system while operators represent observables. Linear algebra is the underlying mathematics of quantum mechanics, where abstract vectors represent wave functions and observables are performed as linear transformations [1]. Quantum mechanics uses Dirac notation to represent a vector as a ‘ket’, shown as . The dual a⟩ ∣ vector for a ket is a ‘bra’, with the inner product ‘bra-ket’ written as . a∣b〉 〈 An inner product space is a vector space over the real or complex numbers containing inner products or dot products. The vector spaces in which wavefunctions exist are called Hilbert spaces. Hilbert spaces are finite-dimensional and span the complex numbers [2]. A Hilbert space is a Banach space where the norm, or mapping, is an inner product. Hilbert spaces are mathematically easier to handle than general Banach spaces due to orthogonality. A Hilbert space is a complete inner product space, an example of which is the collection of square integrable functions,","PeriodicalId":93662,"journal":{"name":"Journal of undergraduate reports in physics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59872472","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Generalized Null Lagrangians for Equations with Special Function Solutions","authors":"Atharva A. Dange, L. Vestal, Z. Musielak","doi":"10.1063/10.0006337","DOIUrl":"https://doi.org/10.1063/10.0006337","url":null,"abstract":"A method to derive general standard and null Lagrangians for second-order differential equations whose solutions are special function of mathematical physics is presented. The general null Lagrangians are used to find the corresponding general gauge functions. All derived Lagrangians are new and in special cases they reduce to those published in the literature. The obtained results are applied to the Bessel, Hermite and Legendre equations, which have many applications in physics, applied mathematics and engineering.","PeriodicalId":93662,"journal":{"name":"Journal of undergraduate reports in physics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47958159","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Simulations and Analysis of Gravitationally Redshifted Kerr Black Hole Accretion Discs","authors":"Benjamin Puzantian, Steven J. Desjardins, Christian Gigualt","doi":"10.1063/1.5129247","DOIUrl":"https://doi.org/10.1063/1.5129247","url":null,"abstract":"The Kerr black hole rotates with two parameters: mass M and angular momentum a and is characterized by the Kerr metric (Taylor and Wheeler 2000). Hence, a binary pair of a black hole and a star can create an accretion disc. A Kerr ray tracer algorithm was used to simulate accretion discs in the Seyfert-1 galaxy. The power law observed flux of relativistic emission lines, and Kerr Fourier image analysis methods were applied to the simulated discs. Simulated image characteristics were analyzed. Power laws were fitted to the simulated data of the Mrk110 accretion disc. Lastly, the simulated images were transformed into Fourier space and characteristics were discussed.","PeriodicalId":93662,"journal":{"name":"Journal of undergraduate reports in physics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1063/1.5129247","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44157183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Noether’s Theorem Applied to the Classical and Schrödinger Wave Equations","authors":"N. Adams, Rebecca Janka, J. R. West","doi":"10.1063/1.5129241","DOIUrl":"https://doi.org/10.1063/1.5129241","url":null,"abstract":"Noether’s Theorem, which relates continuous transformations to conservation laws, is applied to the classical wave equation and the Schrodinger equation. Transformations are derived that lead to invariances and conservation laws.Noether’s Theorem, which relates continuous transformations to conservation laws, is applied to the classical wave equation and the Schrodinger equation. Transformations are derived that lead to invariances and conservation laws.","PeriodicalId":93662,"journal":{"name":"Journal of undergraduate reports in physics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1063/1.5129241","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43063206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An Even Simpler “Truly Elementary” Proof of Bertrand’s Theorem","authors":"J. Galbraith, Jacob Williams","doi":"10.1063/1.5129245","DOIUrl":"https://doi.org/10.1063/1.5129245","url":null,"abstract":"We present a further simplified derivation of a “truly elementary” proof of Bertrand’s theorem, which predicts the exponents in central power-law potentials that produce closed orbits.We present a further simplified derivation of a “truly elementary” proof of Bertrand’s theorem, which predicts the exponents in central power-law potentials that produce closed orbits.","PeriodicalId":93662,"journal":{"name":"Journal of undergraduate reports in physics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1063/1.5129245","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47456358","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effects of Electron-Beam Irradiation on Graphene Oxide","authors":"P. Adamson, S. Williams","doi":"10.1063/1.5129242","DOIUrl":"https://doi.org/10.1063/1.5129242","url":null,"abstract":"Graphene oxide (GO) is a nanofilm composed of graphene with various oxygen functional groups attached. GO is of interest due to its unique mechanical-enhancement properties, its tunable electronic properties, and its potential use in the wide-scale production of graphene. Scanning electron microscopes (SEMs) are frequently used to characterize and study GO films. The purpose of this project was to study the effects of SEM-imaging on GO films. Using an SEM, we irradiated GO samples at electron beam-energies of 10, 20, and 30 keV (at a constant emission current of ~40 micro-amps) for times ranging from 15 minutes to one hour. Raman D- and G-band intensities were used to examine structural modifications/damage to GO samples as a function of beam energy and exposure time. The results suggest that imaging with a 30 keV electron beam for 30 minutes may lead to the formation of amorphous carbon, while imaging with 10 keV or 20 keV beams for 30 minutes does not have a significant effect on GO samples.","PeriodicalId":93662,"journal":{"name":"Journal of undergraduate reports in physics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1063/1.5129242","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42380146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Generalized Non-Standard Lagrangians","authors":"N. Davachi, Z. Musielak","doi":"10.1063/1.5129244","DOIUrl":"https://doi.org/10.1063/1.5129244","url":null,"abstract":"A generalized Lagrange formalism is developed for Ordinary Differential Equations (ODE) with the special function solutions1. The formalism is based on non-standard Lagrangians, which represent a novel family of Lagrangians. It is shown that the Euler-Lagrange equation needs to be supplemented with an auxiliary condition to retrieve the original equation - this is a new phenomenon in the calculus of variations.A generalized Lagrange formalism is developed for Ordinary Differential Equations (ODE) with the special function solutions1. The formalism is based on non-standard Lagrangians, which represent a novel family of Lagrangians. It is shown that the Euler-Lagrange equation needs to be supplemented with an auxiliary condition to retrieve the original equation - this is a new phenomenon in the calculus of variations.","PeriodicalId":93662,"journal":{"name":"Journal of undergraduate reports in physics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1063/1.5129244","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41542083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Using HECTOR for Cross Section Measurements of 102Pd(p,γ)103Ag","authors":"E. Churchman, A. Simon, O. Gomez, R. Kelmar, C. Reingold, S. Kelly","doi":"10.1063/1.5129243","DOIUrl":"https://doi.org/10.1063/1.5129243","url":null,"abstract":"The High EffiCiency TOtal absorption spectrometeR (HECTOR) consists of 16 scintillating crystals that are made of thallium-doped sodium iodide (NaI(Tl)). Each of the crystals is coupled to two photomultiplier tubes (PMT) and the detector is oriented to create a cubic array surrounding a target. This cubic array orientation allows for simultaneous measurements of the individual gamma (γ) rays produced during the de-excitation of the reaction products, creating a coverage of nearly 4π steradian. HECTOR was constructed to measure capture reactions relevant for the nucleosynthesis process at low energies. The work presented here focuses on a (p,γ) reaction on 102Pd, one of the p-nuclei produced during the p-process. The experiment was conducted at the University of Notre Dame using the FN tandem accelerator at the Nuclear Science Lab. A highly enriched 102Pd target was bombarded with a proton (p) beam at energies between 3.5 and 8.0 MeV in 200 keV steps. The measured cross section is compared with experimental data found in literature and theoretical models.The High EffiCiency TOtal absorption spectrometeR (HECTOR) consists of 16 scintillating crystals that are made of thallium-doped sodium iodide (NaI(Tl)). Each of the crystals is coupled to two photomultiplier tubes (PMT) and the detector is oriented to create a cubic array surrounding a target. This cubic array orientation allows for simultaneous measurements of the individual gamma (γ) rays produced during the de-excitation of the reaction products, creating a coverage of nearly 4π steradian. HECTOR was constructed to measure capture reactions relevant for the nucleosynthesis process at low energies. The work presented here focuses on a (p,γ) reaction on 102Pd, one of the p-nuclei produced during the p-process. The experiment was conducted at the University of Notre Dame using the FN tandem accelerator at the Nuclear Science Lab. A highly enriched 102Pd target was bombarded with a proton (p) beam at energies between 3.5 and 8.0 MeV in 200 keV steps. The measured cross section is compared with experimenta...","PeriodicalId":93662,"journal":{"name":"Journal of undergraduate reports in physics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1063/1.5129243","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42596693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}