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2015

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Articles 1 - 30 of 162

Full-Text Articles in Physics

New Exactly Solvable Hamiltonians - Shape Invariance And Self-Similarity, David Barclay, Ranabir Dutt, Asim Gangopadhyaya, Avinash Khare, A. Pagnamenta, Uday Sukhatne Dec 2015

New Exactly Solvable Hamiltonians - Shape Invariance And Self-Similarity, David Barclay, Ranabir Dutt, Asim Gangopadhyaya, Avinash Khare, A. Pagnamenta, Uday Sukhatne

Asim Gangopadhyaya

We discuss in some detail the self-similar potentials of Shabat and Spiridonov which are reflectionless and have an infinite number of bound states. We demonstrate that these self-similar potentials are in fact shape invariant potentials within the formalism of supersymmetric quantum mechanics. In particular, using a scaling ansatz for the change of parameters, we obtain a large class of new, reflectionless, shape invariant potentials of which the Shabat-Spiridonov ones are a special case. These new potentials can be viewed as q-deformations of the single soliton solution corresponding to the Rosen-Morse potential. Explicit expressions for the energy eigenvalues, eigenfunctions and transmission …

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Generation Of A Complete Set Of Additive Shape-Invariant Potentials From An Euler Equation, Jonathan Bougie, Asim Gangopadhyaya, Jeffrey Mallow Dec 2015

Generation Of A Complete Set Of Additive Shape-Invariant Potentials From An Euler Equation, Jonathan Bougie, Asim Gangopadhyaya, Jeffrey Mallow

Asim Gangopadhyaya

In supersymmetric quantum mechanics, shape invariance is a sufficient condition for solvability. We show that all conventional additive shape-invariant superpotentials that are independent of ħ can be generated from two partial differential equations. One of these is equivalent to the one-dimensional Euler equation expressing momentum conservation for inviscid fluid flow, and it is closed by the other. We solve these equations, generate the set of all conventional shape-invariant superpotentials, and show that there are no others in this category. We then develop an algorithm for generating all additive shape-invariant superpotentials including those that depend on ħ explicitly.

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Supersymmetry And The Tunneling Problem In An Asymmetric Double Well, Asim Gangopadhyaya, Prasanta Panigrahi, Uday Sukhatne Dec 2015

Supersymmetry And The Tunneling Problem In An Asymmetric Double Well, Asim Gangopadhyaya, Prasanta Panigrahi, Uday Sukhatne

Asim Gangopadhyaya

The techniques of supersymmetric quantum mechanics are applied to the calculation of the energy difference between the ground state and the first excited state of an asymmetric double well. This splitting, originating from the tunneling effect, is computed via a systematic, rapidly converging perturbation expansion. Perturbative calculations to any order can be easily carried out using a logarithmic perturbation theory. Our approach yield substantially better results than alternative widely used semiclassical analyses.

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Magnet Traveling Through A Conducting Pipe: A Variation On The Analytical Approach, Benjamin Irvine, Matthew Kemnetz, Asim Gangopadhyaya, Thomas Ruubel Dec 2015

Magnet Traveling Through A Conducting Pipe: A Variation On The Analytical Approach, Benjamin Irvine, Matthew Kemnetz, Asim Gangopadhyaya, Thomas Ruubel

Asim Gangopadhyaya

We present an analytical study of magnetic damping. In particular, we investigate the dynamics of a cylindrical neodymium magnet as it moves through a conducting tube. Owing to the very high degree of uniformity of the magnetization for neodymium magnets, we are able to provide completely analytical results for the electromotive force generated in the pipe and the consequent retarding force. Our analytical expressions are shown to have excellent agreement with experimental observations.

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Noncentral Potentials And Spherical Harmonics Using Supersymmetry And Shape Invariance, Ranabir Dutt, Asim Gangopadhyaya, Uday Sukhatne Dec 2015

Noncentral Potentials And Spherical Harmonics Using Supersymmetry And Shape Invariance, Ranabir Dutt, Asim Gangopadhyaya, Uday Sukhatne

Asim Gangopadhyaya

It is shown that the operator methods of supersymmetric quantum mechanics and the concept of shape invariance can profitably be used to derive properties of spherical harmonics in a simple way. The same operator techniques can also be applied to several problems with noncentral vector and scalar potentials. As examples, we analyze the bound state spectra of an electron in a Coulomb plus an Aharonov – Bohm field and/or in the magnetic field of a Dirac monopole.

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Supersymmetric Quantum Mechanics And Solvable Models, Asim Gangopadhyaya, Jonathan Bougie, Jeffrey Mallow, C. Rasinariu Dec 2015

Supersymmetric Quantum Mechanics And Solvable Models, Asim Gangopadhyaya, Jonathan Bougie, Jeffrey Mallow, C. Rasinariu

Asim Gangopadhyaya

We review solvable models within the framework of supersymmetric quantum mechanics (SUSYQM). In SUSYQM, the shape invariance condition insures solvability of quantum mechanical problems. We review shape invariance and its connection to a consequent potential algebra. The additive shape invariance condition is specified by a difference-differential equation; we show that this equation is equivalent to an infinite set of partial differential equations. Solving these equations, we show that the known list of h-independent superpotentials is complete. We then describe how these equations could be extended to include superpotentials that do depend on h.

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Comment On "Ideal Capacitor Circuits And Energy Conservation" By K. Mita And M. Boufaida [Am. J. Phys. 67 (8), 737-739 (1999)], Asim Gangopadhyaya, Jeffrey Mallow Dec 2015

Comment On "Ideal Capacitor Circuits And Energy Conservation" By K. Mita And M. Boufaida [Am. J. Phys. 67 (8), 737-739 (1999)], Asim Gangopadhyaya, Jeffrey Mallow

Asim Gangopadhyaya

No abstract provided.

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Semiclassical Approach To Quantum-Mechanical Problems With Broken Supersymmetry, Ranabir Dutt, Asim Gangopadhyaya, Avinash Khare, A. Pagnamenta, Uday Sukhatne Dec 2015

Semiclassical Approach To Quantum-Mechanical Problems With Broken Supersymmetry, Ranabir Dutt, Asim Gangopadhyaya, Avinash Khare, A. Pagnamenta, Uday Sukhatne

Asim Gangopadhyaya

The semiclassical WKB approximation method is reexamined in the context of nonrelativistic quantum-mechanical bound-state problems with broken supersymmetry (SUSY). This gives rise to an alternative quantization condition (denoted by BSWKB) which is different from the standard WKB formula and also different from the previously studied supersymmetric (SWKB) formula for unbroken SUSY. It is shown that to leading order in ħ, the BSWKB condition yields exact energy eigenvalues for shape-invariant potentials with broken SUSY (harmonic oscillator, Pöschl-Teller I and II) which are known to be analytically solvable. Further, we show explicitly that the higher-order corrections to these energy eigenvalues, up to …

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Renormalization Group Equations In Broken Supersymmetric Theories Using Superspace Methods, Asim Gangopadhyaya, Darwin Chang Dec 2015

Renormalization Group Equations In Broken Supersymmetric Theories Using Superspace Methods, Asim Gangopadhyaya, Darwin Chang

Asim Gangopadhyaya

We apply the superfield method with the spurion technique to derive the renormalization-group equations in broken supersymmetric theories. We point out some possible ambiguities in this procedure and show that it is in general necessary to express the supersymmetry-breaking terms in explicit D-type form. We also found that it is possible to construct broken supersymmetric theories where some of the symmetry-breaking parameters do not receive any infinite renormalization.

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Comment On ‘‘The Hidden Symmetry For A Quantum System With An Infinitely Deep Square-Well Potential By Shi-Hai Dong And Zhong-Qi Ma [Am. J. Phys. 70 (5) 520-521 (2002)], Asim Gangopadhyaya, Jeffrey Mallow Dec 2015

Comment On ‘‘The Hidden Symmetry For A Quantum System With An Infinitely Deep Square-Well Potential By Shi-Hai Dong And Zhong-Qi Ma [Am. J. Phys. 70 (5) 520-521 (2002)], Asim Gangopadhyaya, Jeffrey Mallow

Asim Gangopadhyaya

No abstract provided.

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Gravitational Slingshot , John Dykla, Robert Cacioppo, Asim Gangopadhyaya Dec 2015

Gravitational Slingshot , John Dykla, Robert Cacioppo, Asim Gangopadhyaya

Asim Gangopadhyaya

The slingshot effect is an intriguing phenomenon that has been used effectively by NASA to send spacecraft to outer edges of the solar system. This phenomenon can be satisfactorily explained by Newtonian physics. However, if it is presented as a problem involving four-momentum conservation, the methods of relativistic kinematics easily lead to the conditions necessary for an accelerating as well as a retarding scenario. This problem provides an example that showcases the frequent utility of relativistic methods to analyze problems of Newtonian mechanics.

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Magnetic Transitions In Disordered Gdal2, D. Williams, Paul Shand, Thomas Pekarek, Ralph Skomski, Valeri Petkov, Diandra Leslie-Pelecky Dec 2015

Magnetic Transitions In Disordered Gdal2, D. Williams, Paul Shand, Thomas Pekarek, Ralph Skomski, Valeri Petkov, Diandra Leslie-Pelecky

Thomas M. Pekarek

The role of disorder in magnetic ordering transitions is investigated using mechanically milled GdAl2. Crystalline GdAl2 is a ferromagnet while amorphous GdAl2 is a spin glass. Nanostructured GdAl2 shows a paramagnetic-to-ferromagnetic transition and glassy behavior, with the temperature and magnitude of each transition dependent on the degree and type of disorder. Disorder is parametrized by a Gaussian distribution of Curie temperatures TC with mean TC and breadth Δ TC. A nonzero coercivity is observed at temperatures more than 20 K above the highest TC of any known Gd-Al phase; however, the coercivity decreases with decreasing temperature over the same temperature …

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New Solvable Singular Potentials , R. Dutt, Asim Gangopadhyaya, C. Rasinariu, Uday Sukhatne Dec 2015

New Solvable Singular Potentials , R. Dutt, Asim Gangopadhyaya, C. Rasinariu, Uday Sukhatne

Asim Gangopadhyaya

We obtain three new solvable, real, shape invariant potentials starting from the harmonic oscillator, Pöschl-Teller I and Pöschl-Teller II potentials on the half-axis and extending their domain to the full line, while taking special care to regularize the inverse square singularity at the origin. The regularization procedure gives rise to a delta-function behavior at the origin. Our new systems possess underlying non-linear potential algebras, which can also be used to determine their spectra analytically.

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Inter-Relations Of Solvable Potentials, Asim Gangopadhyaya, Prasanta Panigrahi, Uday Sukhatne Dec 2015

Inter-Relations Of Solvable Potentials, Asim Gangopadhyaya, Prasanta Panigrahi, Uday Sukhatne

Asim Gangopadhyaya

Solvable Natanzon potentials in nonrelativistic quantum mechanics are known to group into two disjoint classes depending on whether the Schrödinger equation can be reduced to a hypergeometric or a confluent hypergeometric equation. All the potentials within each class are connected via point canonical transformations. We establish a connection between the two classes with appropriate limiting procedures and redefinition of parameters, thereby inter-relating all known solvable potentials.

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Disorder-Induced Depression Of The Curie Temperature In Mechanically Milled Gdal2, Marco Morales Torres, D. Williams, Paul Shand, C. Stark, Thomas Pekarek, L. Yue, Valeri Petkov, Diandra Leslie-Pelecky Dec 2015

Disorder-Induced Depression Of The Curie Temperature In Mechanically Milled Gdal2, Marco Morales Torres, D. Williams, Paul Shand, C. Stark, Thomas Pekarek, L. Yue, Valeri Petkov, Diandra Leslie-Pelecky

Thomas M. Pekarek

The effect of disorder on the ferromagnetic transition is investigated in mechanically milled GdAl2. GdAl2is a ferromagnet when crystalline and a spin glass when amorphous. Mechanical milling progressively disorders the alloy, allowing observation of the change from ferromagnetic to a disordered magnetic state. X-ray diffraction and pair-distribution-function analysis are used to determine the grain size, lattice parameter, and mean-squared atomic displacements. The magnetization as a function of temperature is described by a Gaussian distribution of Curie temperatures. The mean Curie temperature decreases with decreasing lattice parameter, where lattice parameter serves as a measure of defect concentration. Two different rates of …

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Unintended Consequences Of Imprecise Notation – An Example From Mechanics, Asim Gangopadhyaya, Gordon Ramsey Dec 2015

Unintended Consequences Of Imprecise Notation – An Example From Mechanics, Asim Gangopadhyaya, Gordon Ramsey

Asim Gangopadhyaya

We present a conundrum that results from the imprecise use of notation for partial derivatives. Taking an example from mechanics, we show that lack of proper care in re presenting partial derivatives in Lagrangian and Hamiltonian formulations paradoxically leads to two different values for the time derivative of the canonical momentum. This problem also exists in other areas of physics,such as thermodynamics.

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Coordinate Realizations Of Deformed Lie Algebras With Three Generator, Ranabir Dutt, Asim Gangopadhyaya, C. Rasinariu, Uday Sukhatne Dec 2015

Coordinate Realizations Of Deformed Lie Algebras With Three Generator, Ranabir Dutt, Asim Gangopadhyaya, C. Rasinariu, Uday Sukhatne

Asim Gangopadhyaya

Differential realizations in coordinate space for deformed Lie algebras with three generators are obtained using bosonic creation and annihilation operators satisfying Heisenberg commutation relations. The unified treatment presented here contains as special cases all previously given coordinate realizations of so(2,1), so(3), and their deformations. Applications to physical problems involving eigenvalue determination in nonrelativistic quantum mechanics are discussed.

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Translational Shape Invariance And The Inherent Potential Algebra, Asim Gangopadhyaya, Jeffrey Mallow, Uday Sukhatne Dec 2015

Translational Shape Invariance And The Inherent Potential Algebra, Asim Gangopadhyaya, Jeffrey Mallow, Uday Sukhatne

Asim Gangopadhyaya

For all quantum-mechanical potentials that are known to be exactly solvable, there are two different, and seemingly independent methods of solution. The first approach is the potential algebra of symmetry groups; the second is supersymmetric quantum mechanics, applied to shape-invariant potentials, which comprise the set of known exactly solvable potentials. Using the underlying algebraic structures of Natanzon potentials, of which the translational shape-invariant potentials are a special subset, we demonstrate the equivalence of the two methods of solution. In addition, we show that, while the algebra for the general Natanzon potential is so(2,2), the subgroup so(2,1) suffices for the shape …

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Anyonic Superconductivity In A Modified Large-U Hubbard Model, Asim Gangopadhyaya, Prasanta Panigrahi Dec 2015

Anyonic Superconductivity In A Modified Large-U Hubbard Model, Asim Gangopadhyaya, Prasanta Panigrahi

Asim Gangopadhyaya

A modified large-U Hubbard model at half filling is analyzed by a mean-field approach. Preserving a local U(1) symmetry of the action, the fluctuations about half filling are studied in the spirit of the commensurate-flux-phase condition. The fluctuations then contribute a Chern-Simons term to the tree-level Lagrangian with a coefficient appropriate to that of a half fermion. With the Coulomb repulsion term, we study the low-energy excitations of the model and show the existence of superconductivity in the presence of a four-Fermi interaction term.

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Superspace Ward Identities In Supersymmetric Gauge Theories, Asim Gangopadhyaya, Darwin Chang Dec 2015

Superspace Ward Identities In Supersymmetric Gauge Theories, Asim Gangopadhyaya, Darwin Chang

Asim Gangopadhyaya

In superspace formulation of supersymmetric gauge theories, gauge invariance requires an infinite set of identities between the infinite set of renormalization constants. Using Ward identities in superspace, the same is derived. These identities at one loop level are also demonstrated.

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The Electric Field At The Chargeless Interface Between Two Regions Of Space, Asim Gangopadhyaya, Robert Mcnees Dec 2015

The Electric Field At The Chargeless Interface Between Two Regions Of Space, Asim Gangopadhyaya, Robert Mcnees

Asim Gangopadhyaya

A common method for solving Poisson's equation in electrostatics is to patch together two or more solutions of Laplace's equation using boundary conditions on the potential and its gradient. Other methods may generate solutions without the need to check these conditions explicitly, and reconciling these solutions with the appropriate boundary conditions can be surprisingly subtle. As a result, a student may arrive at paradoxical conclusions—even in the case of elementary problems—that seem to be at odds with basic physical intuition. We illustrate this issue by showing how the potential of a uniformly charged ring appears to violate continuity of the …

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Heterotic Conformal Field Theory And Gepner’S Construction, Darwin Chang, Asim Gangopadhyaya, Alok Kumar, Jin Wang Dec 2015

Heterotic Conformal Field Theory And Gepner’S Construction, Darwin Chang, Asim Gangopadhyaya, Alok Kumar, Jin Wang

Asim Gangopadhyaya

We discuss some general properties of heterotic conformal field theory in which conformal anomalies c are different for the left-moving and right-moving sectors. It is precisely this type of theory that can be applied immediately to the construction of heterotic string theory. We discuss a general way of constructing such a theory using free fermions. The construction is then applied to generalize Gepner's construction of superstring solutions using the tensor products of N=2 superconformal field theories.

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Few-Boson Processes In The Presence Of An Attractive Impurity Under One-Dimensional Confinement, Nirav Mehta, Connor Morehead Nov 2015

Few-Boson Processes In The Presence Of An Attractive Impurity Under One-Dimensional Confinement, Nirav Mehta, Connor Morehead

Nirav P Mehta

We consider a few-boson system confined to one dimension with a single distinguishable particle of lesser mass. All particle interactions are modeled with δ functions, but due to the mass imbalance the problem is nonintegrable. Universal few-body binding energies, atom-dimer and atom-trimer scattering lengths, are all calculated in terms of two parameters, namely the mass ratio mL/mH, and ratio gHH/gHL of the δ-function couplings. We specifically identify the values of these ratios for which the atom-dimer or atom-trimer scattering lengths vanish or diverge. We identify regions in this parameter space in which various few-body inelastic processes become energetically allowed. In …

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Imaging Diffractometer With Holographic Encoding Enhancements For Laser Sensing And Characterization, Joesph Binford, Bradley Duncan, Jack Parker, Elizabeth Beecher, Mark Delong Nov 2015

Imaging Diffractometer With Holographic Encoding Enhancements For Laser Sensing And Characterization, Joesph Binford, Bradley Duncan, Jack Parker, Elizabeth Beecher, Mark Delong

Bradley D. Duncan

What is believed to be a novel holographic optical encoding scheme has been developed to enhance the performance of laser sensors designed for the measurement of wavelength and angular trajectory. A prototype holographic imaging diffractometer has been created to reconstruct holographic cueing patterns superimposed in the focal plane of wide-angle scene imagery. Based on experimental pattern metric measurements at the focal plane, a theoretical model is used to compute the laser source wavelength and its apparent propagation direction within the sensor's field of view. The benefits of incorporating holographic enhancements within an imager-based sensor architecture are discussed.

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Optical Sparse Aperture Imaging, Nicholas Miller, Matthew Dierking, Bradley Duncan Nov 2015

Optical Sparse Aperture Imaging, Nicholas Miller, Matthew Dierking, Bradley Duncan

Bradley D. Duncan

The resolution of a conventional diffraction-limited imaging system is proportional to its pupil diameter. A primary goal of sparse aperture imaging is to enhance resolution while minimizing the total light collection area; the latter being desirable, in part, because of the cost of large, monolithic apertures. Performance metrics are defined and used to evaluate several sparse aperture arrays constructed from multiple, identical, circular subapertures. Subaperture piston and∕or tilt effects on image quality are also considered. We selected arrays with compact nonredundant autocorrelations first described by Golay. We vary both the number of subapertures and their relative spacings to arrive at …

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Monte Carlo Simulation Of Multiple Photon Scattering In Sugar Maple Tree Canopies, Michael Greiner, Bradley Duncan, Matthew Dierking Nov 2015

Monte Carlo Simulation Of Multiple Photon Scattering In Sugar Maple Tree Canopies, Michael Greiner, Bradley Duncan, Matthew Dierking

Bradley D. Duncan

Detecting objects hidden beneath forest canopies is a difficult task for optical remote sensing systems. Rather than relying upon the existence of gaps between leaves, as other researchers have done, our ultimate goal is to use light scattered by leaves to image through dense foliage. Herein we describe the development of a Monte Carlo model for simulating the scattering of light as it propagates through the leaves of an extended tree canopy. We measured several parameters, including the gap fraction and maximum leaf-area density, of a nearby sugar maple tree grove and applied them to our model. We report the …

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Improving Mid-Frequency Contrast In Sparse Aperture Optical Imaging Systems Based Upon The Golay-9 Array, Andrew Stokes, Bradley Duncan, Matthew Dierking Nov 2015

Improving Mid-Frequency Contrast In Sparse Aperture Optical Imaging Systems Based Upon The Golay-9 Array, Andrew Stokes, Bradley Duncan, Matthew Dierking

Bradley D. Duncan

Sparse aperture imaging systems are capable of producing high resolution images while maintaining an overall light collection area that is small compared to a fully filled aperture yielding the same resolution. This is advantageous for applications where size, volume, weight and/or cost are important considerations. However, conventional sparse aperture systems pay the penalty of reduced contrast at midband spatial frequencies. This paper will focus on increasing the midband contrast of sparse aperture imaging systems based on the Golay-9 array. This is one of a family of two-dimensional arrays we have previously examined due to their compact, non-redundant autocorrelations. The modulation …

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Periodic, Pseudo-Noise Waveforms For Multi-Function Coherent Ladar, Matthew Dierking, Bradley Duncan Nov 2015

Periodic, Pseudo-Noise Waveforms For Multi-Function Coherent Ladar, Matthew Dierking, Bradley Duncan

Bradley D. Duncan

We report the use of periodic, pseudonoise waveforms in a multifunction coherent ladar system. We exploit the Doppler sensitivity of these waveforms, as well as agile processing, to enable diverse ladar functions, including high range resolution imaging, macro-Doppler imaging, synthetic aperture ladar, and range-resolved micro-Doppler imaging. We present analytic expressions and simulations demonstrating the utility of pseudonoise waveforms for each of the ladar modes. We also discuss a laboratory pseudonoise ladar system that was developed to demonstrate range compression and range-resolved micro-Doppler imaging, as well as the phase recovery common to each of the coherent modes.

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Holographic Aperture Ladar, Bradley Duncan, Matthew Dierking Nov 2015

Holographic Aperture Ladar, Bradley Duncan, Matthew Dierking

Bradley D. Duncan

Holographic aperture ladar is a variant of synthetic aperture ladar that seeks to increase cross-range scene resolution by synthesizing a large effective aperture through the motion of a smaller receiver and through the subsequent proper phasing and correlation of the detected signals in postprocessing. Unlike in conventional synthetic aperture ladar, however, holographic aperture ladar makes use of a two- dimensional translating sensor array, not simply a translating point detector. Also unlike in conventional synthetic aperture ladar, holographic aperture images will be formed in the two orthogonal cross-range dimensions parallel and perpendicular to the sensor platform’s direction of motion. The central …

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Experimental Demonstration Of A Stripmap Holographic Aperture Ladar System, Jason Stafford, Bradley Duncan, Matthew Dierking Nov 2015

Experimental Demonstration Of A Stripmap Holographic Aperture Ladar System, Jason Stafford, Bradley Duncan, Matthew Dierking

Bradley D. Duncan

By synthesizing large effective apertures through the translation of a smaller imaging sensor and the subsequent proper phasing and correlation of detected signals in postprocessing, holographic aperture ladar (HAL) systems seek to increase the resolution of remotely imaged targets. The stripmap HAL process was demonstrated in the laboratory, for the first time to our knowledge. Our results show that the stripmap HAL transformation can precisely account for off-axis transmitter induced phase migrations. This in turn allows multiple pupil plane field segments, sequentially collected across a synthetic aperture, to be coherently mosaiced together. As a direct consequence, we have been able …

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