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,
1 .美国西点军校，纽约西点10996-1790 a)通讯作者:kalistaschauer@gmail.com b) michael.pfenning@westpoint.edu c) jared.cochrane.mil@mail.mil2011年，丹·所罗门提出了一个量子化标量场与二维闵可夫斯基时空中随时间变化的马马耶夫-特鲁诺夫势相互作用的模型。该模型由具有时变势的Klein-Gordon波动方程控制。所罗门先生声称，这个模型既违反了狭义相对论的经典能量条件，也违反了弯曲时空中量子场论的量子能量条件。每一个经典的能量条件都可以被违反，它们的自然替代被称为量子不等式。所罗门先生试图证明违反空间和时间量子不平等，他正确地假设负能量在柯西表面分裂成两个通量，在那里势能被关闭。不幸的是，Solomon忽略了在时间t = 0关闭势时粒子产生对能量密度的贡献。在这个项目中，我们计算了由于粒子产生对应力能量张量的贡献。我们表明，虽然经典能量条件被违反，但量子能量不等式成立，与所罗门先生的陈述相反。科学背景数学背景量子力学的数学基础由波函数和算符组成。波函数表示系统的状态，而算符表示可观测值。线性代数是量子力学的基础数学，其中抽象向量表示波函数，可观测值作为线性变换[1]执行。量子力学使用狄拉克符号来表示一个矢量，如图所示。一个ket的对偶a⟩∣向量是一个' bra '，其内积' bra-ket '写成。a∣b > <内积空间是实数或复数上包含内积或点积的向量空间。波函数存在的向量空间称为希尔伯特空间。希尔伯特空间是有限维的，张成复数[2]。希尔伯特空间是巴拿赫空间，其中范数或映射是内积。由于正交性，希尔伯特空间在数学上比一般巴拿赫空间更容易处理。希尔伯特空间是一个完全的内积空间，其中一个例子是平方可积函数的集合，
{"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}
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.
{"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}
Benjamin Puzantian, Steven J. Desjardins, Christian Gigualt
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.
克尔黑洞的旋转有两个参数:质量M和角动量a，其特征是克尔度规(Taylor and Wheeler 2000)。因此，由黑洞和恒星组成的双星可以形成吸积盘。采用Kerr射线追踪算法模拟Seyfert-1星系中的吸积盘。利用幂律观测的相对论发射谱线通量，采用克尔傅立叶图像分析方法对模拟圆盘进行了分析。分析了模拟图像的特性。对Mrk110吸积盘的模拟数据进行幂律拟合。最后，将模拟图像转换到傅里叶空间，并对其特征进行了讨论。
{"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}
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.
{"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}
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.
{"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}
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.
{"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}
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.
{"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}
E. Churchman, A. Simon, O. Gomez, R. Kelmar, C. Reingold, S. Kelly
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...
{"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}
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