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Sample records for deformed harmonic-oscillator basis

  1. Macroscopic detection of deformed QM by the harmonic oscillator

    NASA Astrophysics Data System (ADS)

    Maziashvili, Michael

    2017-08-01

    Based on the nonperturbative analysis, we show that the classical motion of harmonic oscillator derived from the deformed QM is manifestly in contradiction with observations (to the first order in deformation parameter as it has been pointed out in Bawaj et al. (2015)). For this reason, we take an alternate way for estimating the effect and discuss its possible observational manifestations in macrophysics.

  2. Probing deformed commutators with macroscopic harmonic oscillators

    PubMed Central

    Bawaj, Mateusz; Biancofiore, Ciro; Bonaldi, Michele; Bonfigli, Federica; Borrielli, Antonio; Di Giuseppe, Giovanni; Marconi, Lorenzo; Marino, Francesco; Natali, Riccardo; Pontin, Antonio; Prodi, Giovanni A.; Serra, Enrico; Vitali, David; Marin, Francesco

    2015-01-01

    A minimal observable length is a common feature of theories that aim to merge quantum physics and gravity. Quantum mechanically, this concept is associated with a nonzero minimal uncertainty in position measurements, which is encoded in deformed commutation relations. In spite of increasing theoretical interest, the subject suffers from the complete lack of dedicated experiments and bounds to the deformation parameters have just been extrapolated from indirect measurements. As recently proposed, low-energy mechanical oscillators could allow to reveal the effect of a modified commutator. Here we analyze the free evolution of high-quality factor micro- and nano-oscillators, spanning a wide range of masses around the Planck mass mP (≈22 μg). The direct check against a model of deformed dynamics substantially lowers the previous limits on the parameters quantifying the commutator deformation. PMID:26088965

  3. Solution of the Skyrme Hartree Fock Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (V) HFODD(v2.08k)

    NASA Astrophysics Data System (ADS)

    Dobaczewski, J.; Olbratowski, P.

    2005-05-01

    We describe the new version (v2.08k) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock or Skyrme-Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. Similarly as in the previous version (v2.08i), all symmetries can be broken, which allows for calculations with angular frequency and angular momentum tilted with respect to the mass distribution. In the new version, three minor errors have been corrected. New Version Program SummaryTitle of program: HFODD; version: 2.08k Catalogue number: ADVA Catalogue number of previous version: ADTO (Comput. Phys. Comm. 158 (2004) 158) Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVA Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Does the new version supersede the previous one: yes Computers on which this or another recent version has been tested: SG Power Challenge L, Pentium-II, Pentium-III, AMD-Athlon Operating systems under which the program has been tested: UNIX, LINUX, Windows-2000 Programming language used: Fortran Memory required to execute with typical data: 10M words No. of bits in a word: 64 No. of lines in distributed program, including test data, etc.: 52 631 No. of bytes in distributed program, including test data, etc.: 266 885 Distribution format:tar.gz Nature of physical problem: The nuclear mean-field and an analysis of its symmetries in realistic cases are the main ingredients of a description of nuclear states. Within the Local Density Approximation, or for a zero-range velocity-dependent Skyrme interaction, the nuclear mean-field is local and velocity dependent. The locality allows for an effective and fast solution of the self-consistent Hartree-Fock equations, even for heavy nuclei, and for various nucleonic ( n-particle n-hole) configurations, deformations, excitation energies, or angular momenta. Similar Local Density Approximation in the particle-particle channel, which is equivalent to using a zero

  4. Quantum Harmonic Oscillator State Control in a Squeezed Fock Basis.

    PubMed

    Kienzler, D; Lo, H-Y; Negnevitsky, V; Flühmann, C; Marinelli, M; Home, J P

    2017-07-21

    We demonstrate control of a trapped-ion quantum harmonic oscillator in a squeezed Fock state basis, using engineered Hamiltonians analogous to the Jaynes-Cummings and anti-Jaynes-Cummings forms. We demonstrate that for squeezed Fock states with low n the engineered Hamiltonians reproduce the sqrt[n] scaling of the matrix elements which is typical of Jaynes-Cummings physics, and also examine deviations due to the finite wavelength of our control fields. Starting from a squeezed vacuum state, we apply sequences of alternating transfer pulses which allow us to climb the squeezed Fock state ladder, creating states up to excitations of n=6 with up to 8.7 dB of squeezing, as well as demonstrating superpositions of these states. These techniques offer access to new sets of states of the harmonic oscillator which may be applicable for precision metrology or quantum information science.

  5. Quantum Harmonic Oscillator State Control in a Squeezed Fock Basis

    NASA Astrophysics Data System (ADS)

    Kienzler, D.; Lo, H.-Y.; Negnevitsky, V.; Flühmann, C.; Marinelli, M.; Home, J. P.

    2017-07-01

    We demonstrate control of a trapped-ion quantum harmonic oscillator in a squeezed Fock state basis, using engineered Hamiltonians analogous to the Jaynes-Cummings and anti-Jaynes-Cummings forms. We demonstrate that for squeezed Fock states with low n the engineered Hamiltonians reproduce the √{n } scaling of the matrix elements which is typical of Jaynes-Cummings physics, and also examine deviations due to the finite wavelength of our control fields. Starting from a squeezed vacuum state, we apply sequences of alternating transfer pulses which allow us to climb the squeezed Fock state ladder, creating states up to excitations of n =6 with up to 8.7 dB of squeezing, as well as demonstrating superpositions of these states. These techniques offer access to new sets of states of the harmonic oscillator which may be applicable for precision metrology or quantum information science.

  6. Dynamical deformations of three-dimensional Lie algebras in Bianchi classification over the harmonic oscillator

    SciTech Connect

    Paal, Eugen; Virkepu, Jueri

    2009-05-15

    Operadic Lax representations for the harmonic oscillator are used to construct the dynamical deformations of three-dimensional (3D) real Lie algebras in the Bianchi classification. It is shown that the energy conservation of the harmonic oscillator is related to the Jacobi identities of the dynamically deformed algebras. Based on this observation, it is proved that the dynamical deformations of 3D real Lie algebras in the Bianchi classification over the harmonic oscillator are Lie algebras.

  7. Effective field theory in the harmonic oscillator basis

    NASA Astrophysics Data System (ADS)

    Binder, S.; Ekström, A.; Hagen, G.; Papenbrock, T.; Wendt, K. A.

    2016-04-01

    We develop interactions from chiral effective field theory (EFT) that are tailored to the harmonic oscillator basis. As a consequence, ultraviolet convergence with respect to the model space is implemented by construction and infrared convergence can be achieved by enlarging the model space for the kinetic energy. In oscillator EFT, matrix elements of EFTs formulated for continuous momenta are evaluated at the discrete momenta that stem from the diagonalization of the kinetic energy in the finite oscillator space. By fitting to realistic phase shifts and deuteron data we construct an effective interaction from chiral EFT at next-to-leading order. Many-body coupled-cluster calculations of nuclei up to 132Sn converge fast for the ground-state energies and radii in feasible model spaces.

  8. Effective field theory in the harmonic oscillator basis

    SciTech Connect

    Binder, S.; Ekström, Jan A.; Hagen, Gaute; Papenbrock, Thomas F.; Wendt, Kyle A.

    2016-04-25

    In this paper, we develop interactions from chiral effective field theory (EFT) that are tailored to the harmonic oscillator basis. As a consequence, ultraviolet convergence with respect to the model space is implemented by construction and infrared convergence can be achieved by enlarging the model space for the kinetic energy. In oscillator EFT, matrix elements of EFTs formulated for continuous momenta are evaluated at the discrete momenta that stem from the diagonalization of the kinetic energy in the finite oscillator space. By fitting to realistic phase shifts and deuteron data we construct an effective interaction from chiral EFT at next-to-leading order. Finally, many-body coupled-cluster calculations of nuclei up to 132Sn converge fast for the ground-state energies and radii in feasible model spaces.

  9. Effective field theory in the harmonic oscillator basis

    DOE PAGES

    Binder, S.; Ekström, Jan A.; Hagen, Gaute; ...

    2016-04-25

    In this paper, we develop interactions from chiral effective field theory (EFT) that are tailored to the harmonic oscillator basis. As a consequence, ultraviolet convergence with respect to the model space is implemented by construction and infrared convergence can be achieved by enlarging the model space for the kinetic energy. In oscillator EFT, matrix elements of EFTs formulated for continuous momenta are evaluated at the discrete momenta that stem from the diagonalization of the kinetic energy in the finite oscillator space. By fitting to realistic phase shifts and deuteron data we construct an effective interaction from chiral EFT at next-to-leadingmore » order. Finally, many-body coupled-cluster calculations of nuclei up to 132Sn converge fast for the ground-state energies and radii in feasible model spaces.« less

  10. Effective field theory in the harmonic oscillator basis

    SciTech Connect

    Binder, S.; Ekström, Jan A.; Hagen, Gaute; Papenbrock, Thomas F.; Wendt, Kyle A.

    2016-04-25

    In this paper, we develop interactions from chiral effective field theory (EFT) that are tailored to the harmonic oscillator basis. As a consequence, ultraviolet convergence with respect to the model space is implemented by construction and infrared convergence can be achieved by enlarging the model space for the kinetic energy. In oscillator EFT, matrix elements of EFTs formulated for continuous momenta are evaluated at the discrete momenta that stem from the diagonalization of the kinetic energy in the finite oscillator space. By fitting to realistic phase shifts and deuteron data we construct an effective interaction from chiral EFT at next-to-leading order. Finally, many-body coupled-cluster calculations of nuclei up to 132Sn converge fast for the ground-state energies and radii in feasible model spaces.

  11. An algebraic cluster model based on the harmonic oscillator basis

    NASA Technical Reports Server (NTRS)

    Levai, Geza; Cseh, J.

    1995-01-01

    We discuss the semimicroscopic algebraic cluster model introduced recently, in which the internal structure of the nuclear clusters is described by the harmonic oscillator shell model, while their relative motion is accounted for by the Vibron model. The algebraic formulation of the model makes extensive use of techniques associated with harmonic oscillators and their symmetry group, SU(3). The model is applied to some cluster systems and is found to reproduce important characteristics of nuclei in the sd-shell region. An approximate SU(3) dynamical symmetry is also found to hold for the C-12 + C-12 system.

  12. Cooper pair of superconductivity in the coordinate representation and q-deformed harmonic oscillator

    NASA Astrophysics Data System (ADS)

    Van Ngu, Man; Gia Vinh, Ngo; Lan, Nguyen Tri; Thanh, Luu Thi Kim; Viet, Nguyen Ai

    2016-06-01

    In this work we study the similarity between the wave functions of q -deformed harmonic oscillator and wave functions of Cooper pair. The wave functions of Cooper pairs in coordinate-space have an “onion-like” layered structure with exponent decay (Boltzmann) envelope modulation. The ground state wave function of q -deform harmonic oscillator has the form of oscillate functions with Gaussian decay envelope modulation. The corresponding between Boltzmann and Gaussian forms of envelope functions and their quantum similarity are discussed.

  13. Some applications using the connection between q-deformed harmonic oscillator and symmetric and asymmetric potentials

    NASA Astrophysics Data System (ADS)

    Gia Vinh, Ngo; Van Ngu, Man; Lan, Nguyen Tri; Thanh, Luu Thi Kim; Dung, Nguyen Thi; Viet, Nguyen Ai

    2017-06-01

    In our previous article, the connections between q-deformed harmonic oscillator and the two types of asymmetric (Morse-like) and symmetric (inverse square cosine form) potentials have been investigated. The use of these relations in an inverse way to investigate the properties of q-deformed harmonic oscillators has been proposed. In this work, we explore the possibility of using this approach to study some real physical systems, such as diatomic molecules, phonon, etc.

  14. Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (VII) HFODD (v2.49t): A new version of the program

    SciTech Connect

    Schunck, Nicolas F; McDonnell, J.; Sheikh, J. A.; Staszczak, A.; Stoitsov, Mario; Dobaczewski, J.; Toivanen, P.

    2012-01-01

    We describe the new version (v2.49t) of the code HFODD which solves the nuclear Skyrme Hartree-Fock (HF) or Skyrme Hartree-Fock-Bogolyubov (HFB) problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following physics features: (i) the isospin mixing and projection, (ii) the finite temperature formalism for the HFB and HF+BCS methods, (iii) the Lipkin translational energy correction method, (iv) the calculation of the shell correction. A number of specific numerical methods have also been implemented in order to deal with large-scale multi-constraint calculations and hardware limitations: (i) the two-basis method for the HFB method, (ii) the Augmented Lagrangian Method (ALM) for multi-constraint calculations, (iii) the linear constraint method based on the approximation of the RPA matrix for multi-constraint calculations, (iv) an interface with the axial and parity-conserving Skyrme-HFB code HFBTHO, (v) the mixing of the HF or HFB matrix elements instead of the HF fields. Special care has been paid to using the code on massively parallel leadership class computers. For this purpose, the following features are now available with this version: (i) the Message Passing Interface (MPI) framework, (ii) scalable input data routines, (iii) multi-threading via OpenMP pragmas, (iv) parallel diagonalization of the HFB matrix in the simplex breaking case using the ScaLAPACK library. Finally, several little significant errors of the previous published version were corrected.

  15. Solution of the Skyrme-Hartree-Fock-Bogolyubovequations in the Cartesian deformed harmonic-oscillator basis. (VIII) HFODD (v2.73y): A new version of the program

    NASA Astrophysics Data System (ADS)

    Schunck, N.; Dobaczewski, J.; Satuła, W.; Bączyk, P.; Dudek, J.; Gao, Y.; Konieczka, M.; Sato, K.; Shi, Y.; Wang, X. B.; Werner, T. R.

    2017-07-01

    We describe the new version (v2.73y) of the code HFODD which solves the nuclear Skyrme Hartree-Fock or Skyrme Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following new features: (i) full proton-neutron mixing in the particle-hole channel for Skyrme functionals, (ii) the Gogny force in both particle-hole and particle-particle channels, (iii) linear multi-constraint method at finite temperature, (iv) fission toolkit including the constraint on the number of particles in the neck between two fragments, calculation of the interaction energy between fragments, and calculation of the nuclear and Coulomb energy of each fragment, (v) the new version 200d of the code HFBTHO, together with an enhanced interface between HFBTHO and HFODD, (vi) parallel capabilities, significantly extended by adding several restart options for large-scale jobs, (vii) the Lipkin translational energy correction method with pairing, (viii) higher-order Lipkin particle-number corrections, (ix) interface to a program plotting single-particle energies or Routhians, (x) strong-force isospin-symmetry-breaking terms, and (xi) the Augmented Lagrangian Method for calculations with 3D constraints on angular momentum and isospin. Finally, an important bug related to the calculation of the entropy at finite temperature and several other little significant errors of the previous published version were corrected.

  16. Solution of the Skyrme-Hartree–Fock–Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (VIII) HFODD (v2.73y): A new version of the program

    DOE PAGES

    Schunck, N.; Dobaczewski, J.; Satuła, W.; ...

    2017-03-27

    Here, we describe the new version (v2.73y) of the code hfodd which solves the nuclear Skyrme Hartree–Fock or Skyrme Hartree–Fock–Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following new features: (i) full proton–neutron mixing in the particle–hole channel for Skyrme functionals, (ii) the Gogny force in both particle–hole and particle–particle channels, (iii) linear multi-constraint method at finite temperature, (iv) fission toolkit including the constraint on the number of particles in the neck between two fragments, calculation of the interaction energy between fragments, and calculation of the nuclear and Coulomb energy ofmore » each fragment, (v) the new version 200d of the code hfbtho, together with an enhanced interface between HFBTHO and HFODD, (vi) parallel capabilities, significantly extended by adding several restart options for large-scale jobs, (vii) the Lipkin translational energy correction method with pairing, (viii) higher-order Lipkin particle-number corrections, (ix) interface to a program plotting single-particle energies or Routhians, (x) strong-force isospin-symmetry-breaking terms, and (xi) the Augmented Lagrangian Method for calculations with 3D constraints on angular momentum and isospin. Finally, an important bug related to the calculation of the entropy at finite temperature and several other little significant errors of the previous published version were corrected.« less

  17. Axially deformed solution of the Skyrme-Hartree-Fock-Bogoliubov equations using the transformed harmonic oscillator basis (II) HFBTHO v2.00d: A new version of the program

    NASA Astrophysics Data System (ADS)

    Stoitsov, M. V.; Schunck, N.; Kortelainen, M.; Michel, N.; Nam, H.; Olsen, E.; Sarich, J.; Wild, S.

    2013-06-01

    We describe the new version 2.00d of the code HFBTHO that solves the nuclear Skyrme-Hartree-Fock (HF) or Skyrme-Hartree-Fock-Bogoliubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the modified Broyden method for non-linear problems, (ii) optional breaking of reflection symmetry, (iii) calculation of axial multipole moments, (iv) finite temperature formalism for the HFB method, (v) linear constraint method based on the approximation of the Random Phase Approximation (RPA) matrix for multi-constraint calculations, (vi) blocking of quasi-particles in the Equal Filling Approximation (EFA), (vii) framework for generalized energy density with arbitrary density-dependences, and (viii) shared memory parallelism via OpenMP pragmas. Program summaryProgram title: HFBTHO v2.00d Catalog identifier: ADUI_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUI_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License version 3 No. of lines in distributed program, including test data, etc.: 167228 No. of bytes in distributed program, including test data, etc.: 2672156 Distribution format: tar.gz Programming language: FORTRAN-95. Computer: Intel Pentium-III, Intel Xeon, AMD-Athlon, AMD-Opteron, Cray XT5, Cray XE6. Operating system: UNIX, LINUX, WindowsXP. RAM: 200 Mwords Word size: 8 bits Classification: 17.22. Does the new version supercede the previous version?: Yes Catalog identifier of previous version: ADUI_v1_0 Journal reference of previous version: Comput. Phys. Comm. 167 (2005) 43 Nature of problem: The solution of self-consistent mean-field equations for weakly-bound paired nuclei requires a correct description of the asymptotic properties of nuclear quasi-particle wave functions. In the present implementation, this is achieved by using the single-particle wave functions

  18. Constructing quantum logic gates using q-deformed harmonic oscillator algebras

    NASA Astrophysics Data System (ADS)

    Altintas, Azmi Ali; Ozaydin, Fatih; Yesilyurt, Can; Bugu, Sinan; Arik, Metin

    2014-04-01

    We study two-level q-deformed angular momentum states, and using q-deformed harmonic oscillators, we provide a framework for constructing qubits and quantum gates. We also present the construction of some basic one-qubit and two-qubit quantum logic gates.

  19. Application of Elliott's SU(3) model to the triaxially deformed harmonic oscillators

    SciTech Connect

    Sugawara-Tanabe, Kazuko

    2011-05-06

    We have introduced new bosons corresponding to the integral ratio of three frequencies for a harmonic oscillator potential, by means of a non-linear transformation which realizes the SU(3) group as a dynamical symmetry group, and which leaves the anisotropic harmonic oscillator Hamiltonian invariant. The classification of the single-particle levels based on this covering group predicts magic numbers depending on the deformation parameters {delta} and {gamma}. The special cases with tan {gamma} = 1/{radical}(3)({gamma} = 30 deg.) and {radical}(3)/5({gamma}{approx}19 deg.) are discussed.

  20. Application of Elliott's SU(3) model to the triaxially deformed harmonic oscillators

    NASA Astrophysics Data System (ADS)

    Sugawara-Tanabe, Kazuko

    2011-05-01

    We have introduced new bosons corresponding to the integral ratio of three frequencies for a harmonic oscillator potential, by means of a non-linear transformation which realizes the SU(3) group as a dynamical symmetry group, and which leaves the anisotropic harmonic oscillator Hamiltonian invariant. The classification of the single-particle levels based on this covering group predicts magic numbers depending on the deformation parameters δ and γ. The special cases with tan γ = 1/√3 (γ = 30°) and √3 /5(γ˜19°) are discussed.

  1. RLC circuit realization of a q-deformed harmonic oscillator with time dependent mass

    NASA Astrophysics Data System (ADS)

    Batouli, J.; El Baz, M.; Maaouni, A.

    2015-08-01

    We consider an RLC circuit type realization of a q-deformed harmonic oscillator. The differential equations of motion characterizing this circuit are derived, and it is shown that the RLC circuit gets modified as a result of the q-deformation. The natural frequency, the capacitance and the external power source are all modified and become q-dependent. The energy aspects of the circuit are also studied and the effects of the deformation are shown.

  2. Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis.. (VI) HFODD (v2.40h): A new version of the program

    NASA Astrophysics Data System (ADS)

    Dobaczewski, J.; Satuła, W.; Carlsson, B. G.; Engel, J.; Olbratowski, P.; Powałowski, P.; Sadziak, M.; Sarich, J.; Schunck, N.; Staszczak, A.; Stoitsov, M.; Zalewski, M.; Zduńczuk, H.

    2009-11-01

    We describe the new version (v2.40h) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock or Skyrme-Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented: (i) projection on good angular momentum (for the Hartree-Fock states), (ii) calculation of the GCM kernels, (iii) calculation of matrix elements of the Yukawa interaction, (iv) the BCS solutions for state-dependent pairing gaps, (v) the HFB solutions for broken simplex symmetry, (vi) calculation of Bohr deformation parameters, (vii) constraints on the Schiff moments and scalar multipole moments, (viii) the DT2h transformations and rotations of wave functions, (ix) quasiparticle blocking for the HFB solutions in odd and odd-odd nuclei, (x) the Broyden method to accelerate the convergence, (xi) the Lipkin-Nogami method to treat pairing correlations, (xii) the exact Coulomb exchange term, (xiii) several utility options, and we have corrected three insignificant errors. New version program summaryProgram title: HFODD (v2.40h) Catalogue identifier: ADFL_v2_2 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADFL_v2_2.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 79 618 No. of bytes in distributed program, including test data, etc.: 372 548 Distribution format: tar.gz Programming language: FORTRAN-77 and Fortran-90 Computer: Pentium-III, AMD-Athlon, AMD-Opteron Operating system: UNIX, LINUX, Windows XP Has the code been

  3. Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis.. (VII) HFODD (v2.49t): A new version of the program

    NASA Astrophysics Data System (ADS)

    Schunck, N.; Dobaczewski, J.; McDonnell, J.; Satuła, W.; Sheikh, J. A.; Staszczak, A.; Stoitsov, M.; Toivanen, P.

    2012-01-01

    We describe the new version (v2.49t) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock (HF) or Skyrme-Hartree-Fock-Bogolyubov (HFB) problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following physics features: (i) the isospin mixing and projection, (ii) the finite-temperature formalism for the HFB and HF + BCS methods, (iii) the Lipkin translational energy correction method, (iv) the calculation of the shell correction. A number of specific numerical methods have also been implemented in order to deal with large-scale multi-constraint calculations and hardware limitations: (i) the two-basis method for the HFB method, (ii) the Augmented Lagrangian Method (ALM) for multi-constraint calculations, (iii) the linear constraint method based on the approximation of the RPA matrix for multi-constraint calculations, (iv) an interface with the axial and parity-conserving Skyrme-HFB code HFBTHO, (v) the mixing of the HF or HFB matrix elements instead of the HF fields. Special care has been paid to using the code on massively parallel leadership class computers. For this purpose, the following features are now available with this version: (i) the Message Passing Interface (MPI) framework, (ii) scalable input data routines, (iii) multi-threading via OpenMP pragmas, (iv) parallel diagonalization of the HFB matrix in the simplex-breaking case using the ScaLAPACK library. Finally, several little significant errors of the previous published version were corrected. New version program summaryProgram title:HFODD (v2.49t) Catalogue identifier: ADFL_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADFL_v3_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public Licence v3 No. of lines in distributed program, including test data, etc.: 190 614 No. of bytes in distributed program, including test data, etc.: 985 898 Distribution

  4. Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (IV) HFODD (v2.08i): a new version of the program

    NASA Astrophysics Data System (ADS)

    Dobaczewski, J.; Olbratowski, P.

    2004-04-01

    We describe the new version (v2.08i) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock or Skyrme-Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, all symmetries can be broken, which allows for calculations with angular frequency and angular momentum tilted with respect to the mass distribution. The new version contains an interface to the LAPACK subroutine ZHPEVX. Program summaryTitle of the program:HFODD (v2.08i) Catalogue number: ADTO Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADTO Reference in CPC for earlier version of program: J. Dobaczewski and J. Dudek, Comput. Phys. Commun. 131 (2000) 164 (v1.75r) Catalogue number of previous version: ADML Licensing provisions: none Does the new version supersede the previous one: yes Computers on which the program has been tested: SG Power Challenge L, Pentium-II, Pentium-III, AMD-Athlon Operating systems: UNIX, LINUX, Windows-2000 Programming language used: FORTRAN-77 and FORTRAN-90 Memory required to execute with typical data: 10 Mwords No. of bits in a word: The code is written in single-precision for the use on a 64-bit processor. The compiler option -r8 or +autodblpad (or equivalent) has to be used to promote all real and complex single-precision floating-point items to double precision when the code is used on a 32-bit machine. Has the code been vectorised?: Yes No. of bytes in distributed program, including test data, etc.: 265352 No. of lines in distributed program: 52656 Distribution format: tar gzip file Nature of physical problem: The nuclear mean-field and an analysis of its symmetries in realistic cases are the main ingredients of a description of nuclear states. Within the Local Density Approximation, or for a zero-range velocity-dependent Skyrme interaction, the nuclear mean-field is local and velocity dependent. The locality allows for

  5. Energy spectrum inverse problem of q-deformed harmonic oscillator and entanglement of composite bosons

    NASA Astrophysics Data System (ADS)

    Sang, Nguyen Anh; Thu Thuy, Do Thi; Loan, Nguyen Thi Ha; Lan, Nguyen Tri; Viet, Nguyen Ai

    2017-06-01

    Using the simple deformed three-level model (D3L model) proposed in our early work, we study the entanglement problem of composite bosons. Consider three first energy levels are known, we can get two energy separations, and can define the level deformation parameter δ. Using connection between q-deformed harmonic oscillator and Morse-like anharmonic potential, the deform parameter q also can be derived explicitly. Like the Einstein’s theory of special relativity, we introduce the observer e˙ects: out side observer (looking from outside the studying system) and inside observer (looking inside the studying system). Corresponding to those observers, the outside entanglement entropy and inside entanglement entropy will be defined.. Like the case of Foucault pendulum in the problem of Earth rotation, our deformation energy level investigation might be useful in prediction the environment e˙ect outside a confined box.

  6. Four-body continuum-discretized coupled-channels calculations using a transformed harmonic oscillator basis

    SciTech Connect

    Rodriguez-Gallardo, M.; Arias, J. M.; Gomez-Camacho, J.; Moro, A. M.; Johnson, R. C.; Tostevin, J. A.; Thompson, I. J.

    2008-06-15

    The scattering of a weakly bound three-body system by a target is discussed. A transformed harmonic oscillator basis is used to provide an appropriate discrete and finite basis for treating the continuum part of the spectrum of the projectile. The continuum-discretized coupled-channels framework is used for the scattering calculations. The formalism is applied to different reactions, {sup 6}He+{sup 12}C at 229.8 MeV, {sup 6}He+{sup 64}Zn at 10 and 13.6 MeV, and {sup 6}He+{sup 208}Pb at 22 MeV, induced by the Borromean nucleus {sup 6}He. Both the Coulomb and nuclear interactions with a target are taken into account.

  7. Some properties of an infinite family of deformations of the harmonic oscillator

    NASA Astrophysics Data System (ADS)

    Quesne, Christiane

    2010-12-01

    In memory of Marcos Moshinsky, who promoted the algebraic study of the harmonic oscillator, some results recently obtained on an infinite family of deformations of such a system are reviewed. This set, which was introduced by Tremblay, Turbiner, and Winternitz, consists in some Hamiltonians Hk on the plane, depending on a positive real parameter k. Two algebraic extensions of Hk are described. The first one, based on the elements of the dihedral group D2k and a Dunkl operator formalism, provides a convenient tool to prove the superintegrability of Hk for odd integer k. The second one, employing two pairs of fermionic operators, leads to a supersymmetric extension of Hk of the same kind as the familiar Freedman and Mende super-Calogero model. Some connection between both extensions is also outlined.

  8. The q-DEFORMED SCHRÖDINGER Equation of the Harmonic Oscillator on the Quantum Euclidean Space

    NASA Astrophysics Data System (ADS)

    Carow-Watamura, Ursula; Watamura, Satoshi

    We consider the q-deformed Schrödinger equation of the harmonic oscillator on the N-dimensional quantum Euclidean space. The creation and annihilation operators are found, which systematically produce all energy levels and eigenfunctions of the Schrödinger equation. In order to get the q series representation of the eigenfunction, we also give an alternative way to solve the Schrödinger equation which is based on the q analysis. We represent the Schrödinger equation by the q difference equation and solve it by using q polynomials and q exponential functions.

  9. Analytical transformed harmonic oscillator basis for continuum discretized coupled channels calculations

    SciTech Connect

    Moro, A. M.; Arias, J. M.; Gomez-Camacho, J.; Perez-Bernal, F.

    2009-11-15

    A new method for continuum discretization in continuum-discretized coupled-channels calculations is proposed. The method is based on an analytic local-scale transformation of the harmonic-oscillator wave functions proposed for other purposes in a recent work [Karatagladis et al., Phys. Rev. C 71, 064601 (2005)]. The new approach is compared with the standard method of continuum discretization in terms of energy bins for the reactions d+{sup 58}Ni at 80 MeV, {sup 6}Li+{sup 40}Ca at 156 MeV, and {sup 6}He+{sup 208}Pb at 22 MeV and 240 MeV/nucleon. In all cases very good agreement between both approaches is found.

  10. Workshop on Harmonic Oscillators

    NASA Technical Reports Server (NTRS)

    Han, D. (Editor); Kim, Y. S. (Editor); Zachary, W. W. (Editor)

    1993-01-01

    Proceedings of a workshop on Harmonic Oscillators held at the College Park Campus of the University of Maryland on March 25 - 28, 1992 are presented. The harmonic oscillator formalism is playing an important role in many branches of physics. This is the simplest mathematical device which can connect the basic principle of physics with what is observed in the real world. The harmonic oscillator is the bridge between pure and applied physics.

  11. Covariant harmonic oscillators: 1973 revisited

    NASA Technical Reports Server (NTRS)

    Noz, M. E.

    1993-01-01

    Using the relativistic harmonic oscillator, a physical basis is given to the phenomenological wave function of Yukawa which is covariant and normalizable. It is shown that this wave function can be interpreted in terms of the unitary irreducible representations of the Poincare group. The transformation properties of these covariant wave functions are also demonstrated.

  12. Covariant harmonic oscillators and coupled harmonic oscillators

    NASA Technical Reports Server (NTRS)

    Han, Daesoo; Kim, Young S.; Noz, Marilyn E.

    1995-01-01

    It is shown that the system of two coupled harmonic oscillators shares the basic symmetry properties with the covariant harmonic oscillator formalism which provides a concise description of the basic features of relativistic hadronic features observed in high-energy laboratories. It is shown also that the coupled oscillator system has the SL(4,r) symmetry in classical mechanics, while the present formulation of quantum mechanics can accommodate only the Sp(4,r) portion of the SL(4,r) symmetry. The possible role of the SL(4,r) symmetry in quantum mechanics is discussed.

  13. On the moment of inertia of a quantum harmonic oscillator

    SciTech Connect

    Khamzin, A. A. Sitdikov, A. S.; Nikitin, A. S.; Roganov, D. A.

    2013-04-15

    An original method for calculating the moment of inertia of the collective rotation of a nucleus on the basis of the cranking model with the harmonic-oscillator Hamiltonian at arbitrary frequencies of rotation and finite temperature is proposed. In the adiabatic limit, an oscillating chemical-potential dependence of the moment of inertia is obtained by means of analytic calculations. The oscillations of the moment of inertia become more pronounced as deformations approach the spherical limit and decrease exponentially with increasing temperature.

  14. The Quantum Group as a Symmetry ---The Schrödinger Equation of the N-Dimensional q-Deformed Harmonic Oscillator---

    NASA Astrophysics Data System (ADS)

    Carow-Watamura, U.; Watamura, S.

    With the aim to construct a dynamical model with quantum group symmetry, the q-deformed Schrödinger equation of the harmonic oscillator on the N-dimensional quantum Euclidian space is investigated. After reviewing the differential calculus on the q-Euclidian space, the q-analog of the creation-annihilation operator is constructed. It is shown that it produces systematically all eigenfunctions of the Schrödinger equation and eigenvalues. We also present an alternative way to solve the Schrödinger equation which is based on the q-analysis. We represent the Schrödinger equation by the q-difference equation and solve it by using q-polynomials and q-exponential functions. The problem of the involution corresponding to the reality condition is discussed.

  15. The q-harmonic oscillators, q-coherent states and the q-symplecton

    NASA Technical Reports Server (NTRS)

    Biedenharn, L. C.; Lohe, M. A.; Nomura, Masao

    1993-01-01

    The recently introduced notion of a quantum group is discussed conceptually and then related to deformed harmonic oscillators ('q-harmonic oscillators'). Two developments in applying q-harmonic oscillators are reviewed: q-coherent states and the q-symplecton.

  16. Scaling properties of the harmonic oscillator basis calculations for N = Z nuclei in the infrared limit with the JISP16 potential

    NASA Astrophysics Data System (ADS)

    Constantinou, Chrysovalantis; Caprio, Mark A.; Vary, James P.; Maris, Pieter

    2014-03-01

    It has recently been found that when no-core configuration interaction (NCCI) calculations of low-mass nuclei are plotted against an infrared momentum cutoff λsc (scaling cutoff), a universal curve is obtained for the energy and the RMS radius. The plotted results must have an ultraviolet (UV) cutoff ΛUV greater than or equal to the intrinsic cutoff ΛNN of the interaction. This assures that UV convergence is reached. The scaling property then allows for the performance of extrapolations in the IR limit. Here we conduct NCCI calculations in the harmonic oscillator basis with the JISP16 potential. In the IR limit we obtain universal curves for N = Z nuclei up to and including 8Be . An extrapolation in the IR limit for the ground state energy and the RMS radius is performed, and extrapolated results are obtained. Supported by US DOE (DE-FG02-95ER-40934, DESC0008485 SciDAC/NUCLEI, DE-FG02-87ER40371), US NSF (0904782), and Research Corporation for Science Advancement (Cottrell Scholar Award). Computational resources provided by NERSC (US DOE DE-AC02-05CH11231).

  17. Galilean covariant harmonic oscillator

    NASA Technical Reports Server (NTRS)

    Horzela, Andrzej; Kapuscik, Edward

    1993-01-01

    A Galilean covariant approach to classical mechanics of a single particle is described. Within the proposed formalism, all non-covariant force laws defining acting forces which become to be defined covariantly by some differential equations are rejected. Such an approach leads out of the standard classical mechanics and gives an example of non-Newtonian mechanics. It is shown that the exactly solvable linear system of differential equations defining forces contains the Galilean covariant description of harmonic oscillator as its particular case. Additionally, it is demonstrated that in Galilean covariant classical mechanics the validity of the second Newton law of dynamics implies the Hooke law and vice versa. It is shown that the kinetic and total energies transform differently with respect to the Galilean transformations.

  18. Synchronous Discrete Harmonic Oscillator

    SciTech Connect

    Antippa, Adel F.; Dubois, Daniel M.

    2008-10-17

    We introduce the synchronous discrete harmonic oscillator, and present an analytical, numerical and graphical study of its characteristics. The oscillator is synchronous when the time T for one revolution covering an angle of 2{pi} in phase space, is an integral multiple N of the discrete time step {delta}t. It is fully synchronous when N is even. It is pseudo-synchronous when T/{delta}t is rational. In the energy conserving hyperincursive representation, the phase space trajectories are perfectly stable at all time scales, and in both synchronous and pseudo-synchronous modes they cycle through a finite number of phase space points. Consequently, both the synchronous and the pseudo-synchronous hyperincursive modes of time-discretization provide a physically realistic and mathematically coherent, procedure for dynamic, background independent, discretization of spacetime. The procedure is applicable to any stable periodic dynamical system, and provokes an intrinsic correlation between space and time, whereby space-discretization is a direct consequence of background-independent time-discretization. Hence, synchronous discretization moves the formalism of classical mechanics towards that of special relativity. The frequency of the hyperincursive discrete harmonic oscillator is ''blue shifted'' relative to its continuum counterpart. The frequency shift has the precise value needed to make the speed of the system point in phase space independent of the discretizing time interval {delta}t. That is the speed of the system point is the same on the polygonal (in the discrete case) and the circular (in the continuum case) phase space trajectories.

  19. Relativistic harmonic oscillator revisited

    SciTech Connect

    Bars, Itzhak

    2009-02-15

    The familiar Fock space commonly used to describe the relativistic harmonic oscillator, for example, as part of string theory, is insufficient to describe all the states of the relativistic oscillator. We find that there are three different vacua leading to three disconnected Fock sectors, all constructed with the same creation-annihilation operators. These have different spacetime geometric properties as well as different algebraic symmetry properties or different quantum numbers. Two of these Fock spaces include negative norm ghosts (as in string theory), while the third one is completely free of ghosts. We discuss a gauge symmetry in a worldline theory approach that supplies appropriate constraints to remove all the ghosts from all Fock sectors of the single oscillator. The resulting ghost-free quantum spectrum in d+1 dimensions is then classified in unitary representations of the Lorentz group SO(d,1). Moreover, all states of the single oscillator put together make up a single infinite dimensional unitary representation of a hidden global symmetry SU(d,1), whose Casimir eigenvalues are computed. Possible applications of these new results in string theory and other areas of physics and mathematics are briefly mentioned.

  20. Relativistic Harmonic Oscillators and Hadronic Structures in the Quantum-Mechanics Curriculum

    ERIC Educational Resources Information Center

    Kim, Y. S.; Noz, Marilyn E.

    1978-01-01

    A relativistic harmonic-oscillator formalism which is mathematically simple as the nonrelativistic harmonic oscillator is given. In view of its effectiveness in describing Lorentz-deformed hadrons, the inclusion of this formalism in a first-year graduate course will make the results of high-energy experiments more understandable. (BB)

  1. Symmetry Based No Core Shell Model in a Deformed Basis

    NASA Astrophysics Data System (ADS)

    Kekejian, David; Draayer, Jerry; Launey, Kristina

    2017-01-01

    To address current limitations of shell-model descriptions of large spatial deformation and cluster structures, we adopt a no-core shell model with a deformed harmonic oscillator basis and implement an angular momentum projection in a symmetry-adapted scheme. This approach allows us to reach larger model spaces as a result of computational memory savings for calculations of highly deformed states, such as the Hoyle state in C-12. The method is first tested with schematic interactions, but the ultimate goal is to carry forward calculations with realistic nucleon-nucleon interactions in future work. Supported by the U.S. NSF (OCI-0904874, ACI-1516338) and the U.S. DOE (DE-SC0005248), and benefitted from computing resources provided by Blue Waters and LSU's Center for Computation & Technology.

  2. Harmonic oscillator and nuclear pseudospin

    SciTech Connect

    Lisboa, Ronai; Malheiro, Manuel; Castro, Antonio S. de; Alberto, Pedro; Fiolhais, Manuel

    2004-12-02

    A generalized relativistic harmonic oscillator for spin 1/2 particles is studied. The Dirac Hamiltonian contains a scalar S and a vector V quadratic potentials in the radial coordinate, as well as a tensor potential U, linear in r. Setting either {sigma} = S + V or {delta} = V - S to zero, analytical solutions for bound states are found. The eingenenergies and their nonrelativistic limits are presented and particular cases are discussed, especially the case {sigma} = 0, for which pseudospin symmetry is exact.

  3. Symmetries of coupled harmonic oscillators

    NASA Technical Reports Server (NTRS)

    Han, D.; Kim, Y. S.

    1993-01-01

    It is shown that the system of two coupled harmonic oscillators possesses many interesting symmetries. It is noted that the symmetry of a single oscillator is that of the three-parameter group Sp(2). Thus two uncoupled oscillator exhibits a direct product of two Sp(2) groups, with six parameters. The coupling can be achieved through a rotation in the two-dimensional space of two oscillator coordinates. The closure of the commutation relations for the generators leads to the ten-parameter group Sp(4) which is locally isomorphic to the deSitter group O(3,2).

  4. The harmonic oscillator behind all aberrations

    SciTech Connect

    Wolf, Kurt Bernardo

    2010-12-23

    The group-theoretical structure of the harmonic oscillator appears in many guises. Originally developed by Marcos Moshinsky among several others for applications in nuclear physics, we point out here that the harmonic oscillator structure appears in aberrations of geometric optics, particularly in their classification by rank, symplectic spin and weight. And further, the finite harmonic oscillator appears again in the nonlinear transformations of finite Hamiltonian systems, when applied to the parallel processing of signals.

  5. Coherent states for the relativistic harmonic oscillator

    NASA Technical Reports Server (NTRS)

    Aldaya, Victor; Guerrero, J.

    1995-01-01

    Recently we have obtained, on the basis of a group approach to quantization, a Bargmann-Fock-like realization of the Relativistic Harmonic Oscillator as well as a generalized Bargmann transform relating fock wave functions and a set of relativistic Hermite polynomials. Nevertheless, the relativistic creation and annihilation operators satisfy typical relativistic commutation relations of the Lie product (vector-z, vector-z(sup dagger)) approximately equals Energy (an SL(2,R) algebra). Here we find higher-order polarization operators on the SL(2,R) group, providing canonical creation and annihilation operators satisfying the Lie product (vector-a, vector-a(sup dagger)) = identity vector 1, the eigenstates of which are 'true' coherent states.

  6. Harmonic oscillator states in aberration optics

    NASA Technical Reports Server (NTRS)

    Wolf, Kurt Bernardo

    1993-01-01

    The states of the three-dimensional quantum harmonic oscillator classify optical aberrations of axis-symmetric systems due to the isomorphism between the two mathematical structures. Cartesian quanta and angular momentum classifications have their corresponding aberration classifications. The operation of concatenation of optical elements introduces a new operation between harmonic oscillator states.

  7. Quantum wormholes and harmonic oscillators

    NASA Technical Reports Server (NTRS)

    Garay, Luis J.

    1993-01-01

    The quantum state of a wormhole can be represented by a path integral over all asymptotically Euclidean four-geometries and all matter fields which have prescribed values, the arguments of the wave function, on a three-surface which divides the space time manifold into two disconnected parts. Minisuperspace models which consist of a homogeneous massless scalar field coupled to a Friedmann-Robertson-Walker space time are considered. Once the path integral over the lapse function is performed, the requirement that the space time be asymptotically Euclidean can be accomplished by fixing the asymptotic gravitational momentum in the remaining path integral. It is argued that there does not exist any wave function which corresponds to asymptotic field configurations such that the effective gravitational constant is negative in the asymptotic region. Then, the wormhole wave functions can be written as linear combinations of harmonic oscillator wave functions.

  8. Instanton solutions on the polymer harmonic oscillator

    NASA Astrophysics Data System (ADS)

    Austrich-Olivares, Joan A.; Garcia-Chung, Angel; Vergara, J. David

    2017-06-01

    We have computed, using instanton methods, the first allowed energy band for the polymer harmonic oscillator. The eigenvalues within the band are labelled by a discrete parameter λ which results from the non-separability of the polymer Hilbert space. It is shown throughout the article the role played by λ in the full quantization of the polymer harmonic oscillator. The result is consistent with the band structure of the standard quantum pendulum but with pure point spectrum. Consequently, an effective infinite degeneracy emerges in the formal limit μ/l0 \\to 0 where l 0 is the characteristic length of the vacuum eigenfunction of a quantum harmonic oscillator.

  9. Harmonic Oscillators as Bridges between Theories

    NASA Astrophysics Data System (ADS)

    Kim, Y. S.; Noz, Marilyn E.

    2005-03-01

    Other than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other is to formulate the problem in terms of two-by-two matrices. If two oscillators are coupled, the problem combines both two-by-two matrices and harmonic oscillators. This method then becomes a powerful research tool to cover many different branches of physics. Indeed, the concept and methodology in one branch of physics can be translated into another through the common mathematical formalism. It is noted that the present form of quantum mechanics is largely a physics of harmonic oscillators. Special relativity is the physics of the Lorentz group which can be represented by the group of by two-by-two matrices commonly called SL(2, c). Thus the coupled harmonic oscillators can therefore play the role of combining quantum mechanics with special relativity. Both Paul A. M. Dirac and Richard P. Feynman were fond of harmonic oscillators, while they used different approaches to physical problems. Both were also keenly interested in making quantum mechanics compatible with special relativity. It is shown that the coupled harmonic oscillators can bridge these two different approaches to physics.

  10. The harmonic oscillator and nuclear physics

    NASA Technical Reports Server (NTRS)

    Rowe, D. J.

    1993-01-01

    The three-dimensional harmonic oscillator plays a central role in nuclear physics. It provides the underlying structure of the independent-particle shell model and gives rise to the dynamical group structures on which models of nuclear collective motion are based. It is shown that the three-dimensional harmonic oscillator features a rich variety of coherent states, including vibrations of the monopole, dipole, and quadrupole types, and rotations of the rigid flow, vortex flow, and irrotational flow types. Nuclear collective states exhibit all of these flows. It is also shown that the coherent state representations, which have their origins in applications to the dynamical groups of the simple harmonic oscillator, can be extended to vector coherent state representations with a much wider range of applicability. As a result, coherent state theory and vector coherent state theory become powerful tools in the application of algebraic methods in physics.

  11. Second International Workshop on Harmonic Oscillators

    NASA Technical Reports Server (NTRS)

    Han, Daesoo (Editor); Wolf, Kurt Bernardo (Editor)

    1995-01-01

    The Second International Workshop on Harmonic Oscillators was held at the Hotel Hacienda Cocoyoc from March 23 to 25, 1994. The Workshop gathered 67 participants; there were 10 invited lecturers, 30 plenary oral presentations, 15 posters, and plenty of discussion divided into the five sessions of this volume. The Organizing Committee was asked by the chairman of several Mexican funding agencies what exactly was meant by harmonic oscillators, and for what purpose the new research could be useful. Harmonic oscillators - as we explained - is a code name for a family of mathematical models based on the theory of Lie algebras and groups, with applications in a growing range of physical theories and technologies: molecular, atomic, nuclear and particle physics; quantum optics and communication theory.

  12. Kraus representation of a damped harmonic oscillator and its application

    SciTech Connect

    Liu Yuxi; Oezdemir, Sahin K.; Miranowicz, Adam; Imoto, Nobuyuki

    2004-10-01

    By definition, the Kraus representation of a harmonic oscillator suffering from the environment effect, modeled as the amplitude damping or the phase damping, is directly given by a simple operator algebra solution. As examples and applications, we first give a Kraus representation of a single qubit whose computational basis states are defined as bosonic vacuum and single particle number states. We further discuss the environment effect on qubits whose computational basis states are defined as the bosonic odd and even coherent states. The environment effects on entangled qubits defined by two different kinds of computational basis are compared with the use of fidelity.

  13. Pisot q-coherent states quantization of the harmonic oscillator

    NASA Astrophysics Data System (ADS)

    Gazeau, J. P.; del Olmo, M. A.

    2013-03-01

    We revisit the quantized version of the harmonic oscillator obtained through a q-dependent family of coherent states. For each q, 0deformed integers form Fibonacci-like sequences of integers. We then examine the main characteristics of the corresponding quantum oscillator: localization in the configuration and in the phase spaces, angle operator, probability distributions and related statistical features, time evolution and semi-classical phase space trajectories.

  14. Quantum nondemolition measurements of harmonic oscillators

    NASA Technical Reports Server (NTRS)

    Thorne, K. S.; Caves, C. M.; Zimmermann, M.; Sandberg, V. D.; Drever, R. W. P.

    1978-01-01

    Measuring systems to determine the real component of the complex amplitude of a harmonic oscillator are described. This amplitude is constant in the absence of driving forces, and the uncertainty principle accounts for the fact that only the real component can be measured precisely and continuously ('quantum nondemolition measurement'). Application of the measuring systems to the detection of gravitational waves is considered.

  15. Group Theory of Covariant Harmonic Oscillators

    ERIC Educational Resources Information Center

    Kim, Y. S.; Noz, Marilyn E.

    1978-01-01

    A simple and concrete example for illustrating the properties of noncompact groups is presented. The example is based on the covariant harmonic-oscillator formalism in which the relativistic wave functions carry a covariant-probability interpretation. This can be used in a group theory course for graduate students who have some background in…

  16. Background independent duals of the harmonic oscillator.

    PubMed

    Husain, Viqar

    2006-06-09

    We show that a class of topological field theories are quantum duals of the harmonic oscillator. This is demonstrated by establishing a correspondence between the creation and annihilation operators and nonlocal gauge invariant observables of the topological field theory. The example is used to discuss some issues concerning background independence and the relation of vacuum energy to the problem of time in quantum gravity.

  17. Group Theory of Covariant Harmonic Oscillators

    ERIC Educational Resources Information Center

    Kim, Y. S.; Noz, Marilyn E.

    1978-01-01

    A simple and concrete example for illustrating the properties of noncompact groups is presented. The example is based on the covariant harmonic-oscillator formalism in which the relativistic wave functions carry a covariant-probability interpretation. This can be used in a group theory course for graduate students who have some background in…

  18. Quantum harmonic oscillator in a thermal bath

    NASA Technical Reports Server (NTRS)

    Zhang, Yuhong

    1993-01-01

    The influence functional path-integral treatment of quantum Brownian motion is briefly reviewed. A newly derived exact master equation of a quantum harmonic oscillator coupled to a general environment at arbitrary temperature is discussed. It is applied to the problem of loss of quantum coherence.

  19. Condition for minimal harmonic oscillator action

    NASA Astrophysics Data System (ADS)

    Moriconi, M.

    2017-08-01

    We provide an elementary proof that the action for the physical trajectory of the one-dimensional harmonic oscillator is guaranteed to be a minimum if and only if τ<π/ω , where τ is the elapsed time and ω is the oscillator's natural frequency.

  20. Markovian evolution of strongly coupled harmonic oscillators

    NASA Astrophysics Data System (ADS)

    Joshi, Chaitanya; Öhberg, Patrik; Cresser, James D.; Andersson, Erika

    2014-12-01

    We investigate how to model Markovian evolution of coupled harmonic oscillators, each of them interacting with a local environment. When the coupling between the oscillators is weak, dissipation may be modeled using local Lindblad terms for each of the oscillators in the master equation, as is commonly done. When the coupling between oscillators is strong, this model may become invalid. We derive a master equation for two coupled harmonic oscillators that are subject to individual heat baths modeled by a collection of harmonic oscillators and show that this master equation in general contains nonlocal Lindblad terms. We compare the resulting time evolution with that obtained for dissipation through local Lindblad terms for each individual oscillator and show that the evolution is different in the two cases. In particular, the two descriptions give different predictions for the steady state and for the entanglement between strongly coupled oscillators. This shows that when describing strongly coupled harmonic oscillators, one must take great care in how dissipation is modeled and that a description using local Lindblad terms may fail. This may be particularly relevant when attempting to generate entangled states of strongly coupled quantum systems.

  1. Pisot q-coherent states quantization of the harmonic oscillator

    SciTech Connect

    Gazeau, J.P.; Olmo, M.A. del

    2013-03-15

    We revisit the quantized version of the harmonic oscillator obtained through a q-dependent family of coherent states. For each q, 0deformed integers form Fibonacci-like sequences of integers. We then examine the main characteristics of the corresponding quantum oscillator: localization in the configuration and in the phase spaces, angle operator, probability distributions and related statistical features, time evolution and semi-classical phase space trajectories. - Highlights: Black-Right-Pointing-Pointer Quantized version of the harmonic oscillator (HO) through a q-family of coherent states. Black-Right-Pointing-Pointer For q,0Deformed numbers are Fibonacci-like integer sequences (1/q a quadratic unit Pisot number). Black-Right-Pointing-Pointer We examine the main physical characteristics of the corresponding quantum oscillator.

  2. Coherent states for the nonlinear harmonic oscillator

    SciTech Connect

    Ghosh, Subir

    2012-06-15

    Wave packets for the quantum nonlinear oscillator are considered in the generalized coherent state framework. To first order in the nonlinearity parameter the coherent state behaves very similar to its classical counterpart. The position expectation value oscillates in a simple harmonic manner. The energy-momentum uncertainty relation is time independent as in a harmonic oscillator. Various features (such as the squeezed state nature) of the coherent state have been discussed.

  3. Quantum harmonic oscillator with superoscillating initial datum

    SciTech Connect

    Buniy, R. V.; Struppa, D. C.; Colombo, F.; Sabadini, I.

    2014-11-15

    In this paper, we study the evolution of superoscillating initial data for the quantum driven harmonic oscillator. Our main result shows that superoscillations are amplified by the harmonic potential and that the analytic solution develops a singularity in finite time. We also show that for a large class of solutions of the Schrödinger equation, superoscillating behavior at any given time implies superoscillating behavior at any other time.

  4. Ground-state isolation and discrete flows in a rationally extended quantum harmonic oscillator

    NASA Astrophysics Data System (ADS)

    Cariñena, José F.; Plyushchay, Mikhail S.

    2016-11-01

    Ladder operators for the simplest version of a rationally extended quantum harmonic oscillator (REQHO) are constructed by applying a Darboux transformation to the quantum harmonic oscillator system. It is shown that the physical spectrum of the REQHO carries a direct sum of a trivial and an infinite-dimensional irreducible representation of the polynomially deformed bosonized osp (1 |2 ) superalgebra. In correspondence with this the ground state of the system is isolated from other physical states but can be reached by ladder operators via nonphysical energy eigenstates, which belong to either an infinite chain of similar eigenstates or to the chains with generalized Jordan states. We show that the discrete chains of the states generated by ladder operators and associated with physical energy levels include six basic generalized Jordan states, in comparison with the two basic Jordan states entering in analogous discrete chains for the quantum harmonic oscillator.

  5. Information theories for time-dependent harmonic oscillator

    SciTech Connect

    Choi, Jeong Ryeol; Kim, Min-Soo; Kim, Daeyeoul; Maamache, Mustapha; Menouar, Salah; Nahm, In Hyun

    2011-06-15

    Highlights: > Information theories for the general time-dependent harmonic oscillator based on invariant operator method. > Time dependence of entropies and entropic uncertainty relation. > Characteristics of Shannon information and Fisher information. > Application of information theories to particular systems that have time-dependent behavior. - Abstract: Information theories for the general time-dependent harmonic oscillator are described on the basis of invariant operator method. We obtained entropic uncertainty relation of the system and discussed whether it is always larger than or equal to the physically allowed minimum value. Shannon information and Fisher information are derived by means of density operator that satisfies Liouville-von Neumann equation and their characteristics are investigated. Shannon information is independent of time, but Fisher information is explicitly dependent on time as the time functions of the Hamiltonian vary. We can regard that the Fisher information is a local measure since its time behavior is largely affected by local arrangements of the density, whilst the Shannon information plays the role of a global measure of the spreading of density. To promote the understanding, our theory is applied to special systems, the so-called quantum oscillator with time-dependent frequency and strongly pulsating mass system.

  6. Time evolution of a time-dependent inverted harmonic oscillator in arbitrary dimensions

    NASA Astrophysics Data System (ADS)

    Guo, Guang-Jie; Ren, Zhong-Zhou; Ju, Guo-Xing; Guo, Xiao-Yong

    2012-03-01

    The time evolution of a time-dependent inverted harmonic oscillator (TDIHO) of arbitrary dimensions is investigated. Using the algebraic method, we obtain the exact orthogonal basis of solutions of a TDIHO in which the dimensionality d and angular momentum l appear as parameters, and also discuss its properties. With the wavepacket as the initial state, the general expressions of sojourn time of a TDIHO are given. The method is also applied to the inverted Caldirola-Kanai harmonic oscillator. The results show that the sojourn time appears as an increasing function of the dissipation parameter in arbitrary dimensions, but a decreasing function of the dimensionality.

  7. Quantum Harmonic Oscillator Subjected to Quantum Vacuum Fluctuations

    SciTech Connect

    Gevorkyan, A. S.; Burdik, C.; Oganesyan, K. B.

    2010-05-04

    Spontaneous transitions between bound states of an atomic system, 'Lamb Shift' of energy level, as well as many other phenomena in real nonrelativistic quantum systems are connected with the influence of quantum vacuum fluctuations which are impossible to consider in the limits of standard quantum-mechanical approaches. The joint system 'quantum harmonic oscillator (QHO)+ environment' is described in terms of complex probabilistic processes (CPP) which satisfies a stochastic differential equation (SDE) of Langevin-Schroedinger (L-Sch) type. On the basis of orthogonal CPP, the method of stochastic density matrix (SDM) is developed. The energy spectrum of QHO and a possibility of infringement of detailed balance of transitions between quantum levels including spontaneous decay of <> are investigated by the SDM method.

  8. Chiral potential renormalized in harmonic-oscillator space

    NASA Astrophysics Data System (ADS)

    Yang, C.-J.

    2016-12-01

    We renormalize the chiral effective field theory potential in harmonic-oscillator (HO) model space. The low energy constants (LECs) are utilized to absorb not just the ultraviolet part of the physics due to the cutoff, but also the infrared part due to the truncation of model space. We use the inverse J -matrix method to reproduce the nucleon-nucleon scattering phase shifts in the given model space. We demonstrate that by including the NLO correction, the nucleon-nucleon scattering in the continuum could be well reproduced in the truncated HO trap space up to laboratory energy Tlab=100 MeV with number of HO basis nmax as small as 10. A perturbative power counting starts at subleading order is adopted in this work, and how to extract the perturbative contribution is demonstrated. This work serves as the input to perform ab initio calculations.

  9. A possible generalization of the harmonic oscillator potential

    NASA Technical Reports Server (NTRS)

    Levai, Geza

    1995-01-01

    A four-parameter potential is analyzed, which contains the three-dimensional harmonic oscillator as a special case. This potential is exactly solvable and retains several characteristics of the harmonic oscillator, and also of the Coulomb problem. The possibility of similar generalizations of other potentials is also pointed out.

  10. Finite quantum kinematics of the harmonic oscillator

    SciTech Connect

    Shiri-Garakani, Mohsen; Finkelstein, David Ritz

    2006-03-15

    Arbitrarily small changes in the commutation relations suffice to transform the usual singular quantum theories into regular quantum theories. This process is an extension of canonical quantization that we call general quantization. Here we apply general quantization to the time-independent linear harmonic oscillator. The unstable Heisenberg group becomes the stable group SO(3). This freezes out the zero-point energy of very soft or very hard oscillators, like those responsible for the infrared or ultraviolet divergencies of usual field theories, without much changing the medium oscillators. It produces pronounced violations of equipartition and of the usual uncertainty relations for soft or hard oscillators, and interactions between the previously uncoupled excitation quanta of the oscillator, weakly attractive for medium quanta, strongly repulsive for soft or hard quanta.

  11. Finite quantum theory of the harmonic oscillator

    NASA Astrophysics Data System (ADS)

    Shiri-Garakani, Mohsen

    We apply the Segal process of group simplification to the linear harmonic oscillator. The result is a finite quantum theory with three quantum constants h, h', h″ instead of the usual one. We compare the classical (CLHO), quantum (QLHO), and finite (FLHO) linear harmonic oscillators and their canonical or unitary groups. The FLHO is isomorphic to a dipole rotator with N = l(l + 1) ˜ 1/(h ' h″) states and Hamiltonian H = A(Lx)2 + B(Ly)2, and the physically interesting case has N ≫ 1. The position and momentum variables are quantized with uniform finite spectra. For fixed quantum constants and large N ≫ 1 there are three broad classes of FLHO: soft, medium, and hard, with B/A ≪ 1, B/A ˜ 1, and B/A ≫ 1 respectively. The field oscillators responsible for infra-red and ultraviolet divergences are soft and hard respectively. Medium oscillators have B/A ˜ 1 and approximate the QLHO. They have ˜ N low-lying states with nearly the same zero-point energy and level spacing as the QLHO, and nearly obeying the Heisenberg uncertainty principle and the equipartition principle. The corresponding rotators are nearly polarized along the z axis with Lz ˜ +/-l. The soft and hard FLHO's have infinitesimal 0-point energy and grossly violate equipartition and the Heisenberg uncertainty principle. They do not resemble the QLHO at all. Their low-lying energy states correspond to rotators with Lx ˜ 0 or Ly ˜ 0 instead of Lz ˜ +/-l. Soft oscillators have frozen momentum, because their maximum potential energy is too small to produce one quantum of momentum. Hard oscillators have frozen position, because their maximum kinetic energy is too small to excite one quantum of position.

  12. Harmonic oscillator interaction with squeezed radiation

    NASA Technical Reports Server (NTRS)

    Dodonov, V. V.; Nikonov, D. E.

    1993-01-01

    Although the problem of electromagnetic radiation by a quantum harmonic oscillator is considered in textbooks on quantum mechanics, some of its aspects have remained unclear until now. By this, we mean that usually the initial quantum states of both the oscillator and the field are assumed to be characterized by a definite energy level of the oscillator and definite occupation numbers of the field modes. In connection with growing interest in squeezed states, it would be interesting to analyze the general case when the initial states of both subsystems are arbitrary superpositions of energy eigenstates. This problem was considered in other work, where the power of the spontaneous emission was calculated in the case of an arbitrary oscillator's initial state, but the field was initially in a vacuum state. In the present article, we calculate the rate of the oscillator average energy, squeezing, and correlation parameter change under the influence of an arbitrary external radiation field. Some other problems relating to the interaction between quantum particles (atoms) or oscillators where the electromagnetic radiation is an arbitrary (in particular squeezed) state were investigated.

  13. Improving Density Functionals with Quantum Harmonic Oscillators

    NASA Astrophysics Data System (ADS)

    Tkatchenko, Alexandre

    2013-03-01

    Density functional theory (DFT) is the most widely used and successful approach for electronic structure calculations. However, one of the pressing challenges for DFT is developing efficient functionals that can accurately capture the omnipresent long-range electron correlations, which determine the structure and stability of many molecules and materials. Here we show that, under certain conditions, the problem of computing the long-range correlation energy of interacting electrons can be mapped to a system of coupled quantum harmonic oscillators (QHOs). The proposed model allows us to synergistically combine concepts from DFT, quantum chemistry, and the widely discussed random-phase approximation for the correlation energy. In the dipole limit, the interaction energy for a system of coupled QHOs can be calculated exactly, thereby leading to an efficient and accurate model for the many-body dispersion energy of complex molecules and materials. The studied examples include intermolecular binding energies, the conformational hierarchy of DNA structures, the geometry and stability of molecular crystals, and supramolecular host-guest complexes (A. Tkatchenko, R. A. DiStasio Jr., R. Car, M. Scheffler, Phys. Rev. Lett. 108, 236402 (2012); R. A. DiStasio Jr., A. von Lilienfeld, A. Tkatchenko, PNAS 109, 14791 (2012); A. Tkatchenko, D. Alfe, K. S. Kim, J. Chem. Theory and Comp. (2012), doi: 10.1021/ct300711r; A. Tkatchenko, A. Ambrosetti, R. A. DiStasio Jr., arXiv:1210.8343v1).

  14. Driven harmonic oscillator as a quantum simulator for open systems

    SciTech Connect

    Piilo, Jyrki; Maniscalco, Sabrina

    2006-09-15

    We show theoretically how a driven harmonic oscillator can be used as a quantum simulator for the non-Markovian damped harmonic oscillator. In the general framework, our results demonstrate the possibility to use a closed system as a simulator for open quantum systems. The quantum simulator is based on sets of controlled drives of the closed harmonic oscillator with appropriately tailored electric field pulses. The non-Markovian dynamics of the damped harmonic oscillator is obtained by using the information about the spectral density of the open system when averaging over the drives of the closed oscillator. We consider single trapped ions as a specific physical implementation of the simulator, and we show how the simulator approach reveals physical insight into the open system dynamics, e.g., the characteristic quantum mechanical non-Markovian oscillatory behavior of the energy of the damped oscillator, usually obtained by the non-Lindblad-type master equation, can have a simple semiclassical interpretation.

  15. Harmonic oscillator in quantum rotational spectra: Molecules and nuclei

    NASA Technical Reports Server (NTRS)

    Pavlichenkov, Igor M.

    1995-01-01

    The mapping of a rotational dynamics on a harmonic oscillator is considered. The method used for studying the stabilization of the rigid top rotation around the intermediate moment of inertial axix by orbiting particle is described.

  16. A harmonic oscillator having “volleyball damping”

    NASA Astrophysics Data System (ADS)

    Mickens, R. E.; Oyedeji, K.; Rucker, S. A.

    2006-05-01

    Volleyball damping corresponds to linear damping up to a certain critical velocity, with zero damping above this value. The dynamics of a linear harmonic oscillator is investigated with this damping mechanism.

  17. Relation of squeezed states between damped harmonic and simple harmonic oscillators

    NASA Technical Reports Server (NTRS)

    Um, Chung-In; Yeon, Kyu-Hwang; George, Thomas F.; Pandey, Lakshmi N.

    1993-01-01

    The minimum uncertainty and other relations are evaluated in the framework of the coherent states of the damped harmonic oscillator. It is shown that the coherent states of the damped harmonic oscillator are the squeezed coherent states of the simple harmonic oscillator. The unitary operator is also constructed, and this connects coherent states with damped harmonic and simple harmonic oscillators.

  18. Analytic energy-level densities of separable harmonic oscillators including approximate hindered rotor corrections

    NASA Astrophysics Data System (ADS)

    Döntgen, M.

    2016-09-01

    Energy-level densities are key for obtaining various chemical properties. In chemical kinetics, energy-level densities are used to predict thermochemistry and microscopic reaction rates. Here, an analytic energy-level density formulation is derived using inverse Laplace transformation of harmonic oscillator partition functions. Anharmonic contributions to the energy-level density are considered approximately using a literature model for the transition from harmonic to free motions. The present analytic energy-level density formulation for rigid rotor-harmonic oscillator systems is validated against the well-studied CO+O˙ H system. The approximate hindered rotor energy-level density corrections are validated against the well-studied H2O2 system. The presented analytic energy-level density formulation gives a basis for developing novel numerical simulation schemes for chemical processes.

  19. Fourier methods for the perturbed harmonic oscillator in linear and nonlinear Schrödinger equations.

    PubMed

    Bader, Philipp; Blanes, Sergio

    2011-04-01

    We consider the numerical integration of the Gross-Pitaevskii equation with a potential trap given by a time-dependent harmonic potential or a small perturbation thereof. Splitting methods are frequently used with Fourier techniques since the system can be split into the kinetic and remaining part, and each part can be solved efficiently using fast Fourier transforms. Splitting the system into the quantum harmonic-oscillator problem and the remaining part allows us to get higher accuracies in many cases, but it requires us to change between Hermite basis functions and the coordinate space, and this is not efficient for time-dependent frequencies or strong nonlinearities. We show how to build methods that combine the advantages of using Fourier methods while solving the time-dependent harmonic oscillator exactly (or with a high accuracy by using a Magnus integrator and an appropriate decomposition).

  20. Digitization of the harmonic oscillator in extended relativity

    NASA Astrophysics Data System (ADS)

    Friedman, Yaakov

    2013-06-01

    Extended relativistic dynamics (ERD) admits only solutions that have speed bounded by the speed of light c and acceleration bounded by an assumed universal maximal acceleration am. Here we explore the harmonic oscillator under ERD. For oscillators with small natural frequency ω, we recover the classical solutions, while for large ω, the solutions differ significantly from the classical one. The solutions for large ω are a ‘digitization’ of the standard signals of the classical harmonic oscillator. The spectrum of these signals coincides with the energy spectrum of the quantum harmonic oscillator. While for small ω, the thermal radiation is a wave type, for large ω, it becomes pulses of radiation. This provides a possible explanation for the difference in the blackbody radiation for small and large ω and is another indication of the validity of ERD.

  1. Predicting charmonium and bottomonium spectra with a quark harmonic oscillator

    NASA Technical Reports Server (NTRS)

    Norbury, J. W.; Badavi, F. F.; Townsend, L. W.

    1986-01-01

    The nonrelativistic quark model is applied to heavy (nonrelativistic) meson (two-body) systems to obtain sufficiently accurate predictions of the spin-averaged mass levels of the charmonium and bottomonium spectra as an example of the three-dimensional harmonic oscillator. The present calculations do not include any spin dependence, but rather, mass values are averaged for different spins. Results for a charmed quark mass value of 1500 MeV/c-squared show that the simple harmonic oscillator model provides good agreement with experimental values for 3P states, and adequate agreement for the 3S1 states.

  2. Violation of smooth observable macroscopic realism in a harmonic oscillator.

    PubMed

    Leshem, Amir; Gat, Omri

    2009-08-14

    We study the emergence of macrorealism in a harmonic oscillator subject to consecutive measurements of a squeezed action. We demonstrate a breakdown of dynamical realism in a wide parameter range that is maximized in a scaling limit of extreme squeezing, where it is based on measurements of smooth observables, implying that macroscopic realism is not valid in the harmonic oscillator. We propose an indirect experimental test of these predictions with entangled photons by demonstrating that local realism in a composite system implies dynamical realism in a subsystem.

  3. Predicting charmonium and bottomonium spectra with a quark harmonic oscillator

    NASA Technical Reports Server (NTRS)

    Norbury, J. W.; Badavi, F. F.; Townsend, L. W.

    1986-01-01

    The nonrelativistic quark model is applied to heavy (nonrelativistic) meson (two-body) systems to obtain sufficiently accurate predictions of the spin-averaged mass levels of the charmonium and bottomonium spectra as an example of the three-dimensional harmonic oscillator. The present calculations do not include any spin dependence, but rather, mass values are averaged for different spins. Results for a charmed quark mass value of 1500 MeV/c-squared show that the simple harmonic oscillator model provides good agreement with experimental values for 3P states, and adequate agreement for the 3S1 states.

  4. Geometric approach to nonlinear coherent states using the Higgs model for harmonic oscillator

    NASA Astrophysics Data System (ADS)

    Mahdifar, A.; Roknizadeh, R.; Naderi, M. H.

    2006-06-01

    In this paper, we investigate the relation between the curvature of the physical space and the deformation function of the deformed oscillator algebra using the nonlinear coherent states approach. For this purpose, we study two-dimensional harmonic oscillators on the flat surface and on a sphere by applying the Higgs model. With the use of their algebras, we show that the two-dimensional oscillator algebra on a surface can be considered as a deformed one-dimensional oscillator algebra where the effect of the curvature of the surface appears as a deformation function. We also show that the curvature of the physical space plays the role of deformation parameter. Then we construct the associated coherent states on the flat surface and on a sphere and compare their quantum statistical properties, including quadrature squeezing and antibunching effect.

  5. A Simple Mechanical Model for the Isotropic Harmonic Oscillator

    ERIC Educational Resources Information Center

    Nita, Gelu M.

    2010-01-01

    A constrained elastic pendulum is proposed as a simple mechanical model for the isotropic harmonic oscillator. The conceptual and mathematical simplicity of this model recommends it as an effective pedagogical tool in teaching basic physics concepts at advanced high school and introductory undergraduate course levels. (Contains 2 figures.)

  6. Revisiting the quantum harmonic oscillator via unilateral Fourier transforms

    NASA Astrophysics Data System (ADS)

    Nogueira, Pedro H. F.; de Castro, Antonio S.

    2016-01-01

    The literature on the exponential Fourier approach to the one-dimensional quantum harmonic oscillator problem is revised and criticized. It is shown that the solution of this problem has been built on faulty premises. The problem is revisited via the Fourier sine and cosine transform method and the stationary states are properly determined by requiring definite parity and square-integrable eigenfunctions.

  7. Symmetry algebra of a generalized anisotropic harmonic oscillator

    NASA Technical Reports Server (NTRS)

    Castanos, O.; Lopez-Pena, R.

    1993-01-01

    It is shown that the symmetry Lie algebra of a quantum system with accidental degeneracy can be obtained by means of the Noether's theorem. The procedure is illustrated by considering a generalized anisotropic two dimensional harmonic oscillator, which can have an infinite set of states with the same energy characterized by an u(1,1) Lie algebra.

  8. The Study of Damped Harmonic Oscillations Using an Electronic Counter

    ERIC Educational Resources Information Center

    Wadhwa, Ajay

    2009-01-01

    We study damped harmonic oscillations in mechanical systems like the loaded spring and simple pendulum with the help of an oscillation measuring electronic counter. The experimental data are used in a software program that solves the differential equation for damped vibrations of any system and determines its position, velocity and acceleration as…

  9. The Study of Damped Harmonic Oscillations Using an Electronic Counter

    ERIC Educational Resources Information Center

    Wadhwa, Ajay

    2009-01-01

    We study damped harmonic oscillations in mechanical systems like the loaded spring and simple pendulum with the help of an oscillation measuring electronic counter. The experimental data are used in a software program that solves the differential equation for damped vibrations of any system and determines its position, velocity and acceleration as…

  10. Nonequilibrium work distribution of a quantum harmonic oscillator.

    PubMed

    Deffner, Sebastian; Lutz, Eric

    2008-02-01

    We calculate analytically the work distribution of a quantum harmonic oscillator with arbitrary time-dependent angular frequency. We provide detailed expressions for the work probability density for adiabatic and nonadiabatic processes, in the limits of low and high temperature. We further verify the validity of the quantum Jarzynski equality.

  11. Free Fall and Harmonic Oscillations: Analyzing Trampoline Jumps

    ERIC Educational Resources Information Center

    Pendrill, Ann-Marie; Eager, David

    2015-01-01

    Trampolines can be found in many gardens and also in some playgrounds. They offer an easily accessible vertical motion that includes free fall. In this work, the motion on a trampoline is modelled by assuming a linear relation between force and deflection, giving harmonic oscillations for small amplitudes. An expression for the cycle-time is…

  12. A Look at Damped Harmonic Oscillators through the Phase Plane

    ERIC Educational Resources Information Center

    Daneshbod, Yousef; Latulippe, Joe

    2011-01-01

    Damped harmonic oscillations appear naturally in many applications involving mechanical and electrical systems as well as in biological systems. Most students are introduced to harmonic motion in an elementary ordinary differential equation (ODE) course. Solutions to ODEs that describe simple harmonic motion are usually found by investigating the…

  13. A Simple Mechanical Model for the Isotropic Harmonic Oscillator

    ERIC Educational Resources Information Center

    Nita, Gelu M.

    2010-01-01

    A constrained elastic pendulum is proposed as a simple mechanical model for the isotropic harmonic oscillator. The conceptual and mathematical simplicity of this model recommends it as an effective pedagogical tool in teaching basic physics concepts at advanced high school and introductory undergraduate course levels. (Contains 2 figures.)

  14. The One-Dimensional Damped Forced Harmonic Oscillator Revisited

    ERIC Educational Resources Information Center

    Flores-Hidalgo, G.; Barone, F. A.

    2011-01-01

    In this paper we give a general solution to the problem of the damped harmonic oscillator under the influence of an arbitrary time-dependent external force. We employ simple methods accessible for beginners and useful for undergraduate students and professors in an introductory course of mechanics.

  15. A Look at Damped Harmonic Oscillators through the Phase Plane

    ERIC Educational Resources Information Center

    Daneshbod, Yousef; Latulippe, Joe

    2011-01-01

    Damped harmonic oscillations appear naturally in many applications involving mechanical and electrical systems as well as in biological systems. Most students are introduced to harmonic motion in an elementary ordinary differential equation (ODE) course. Solutions to ODEs that describe simple harmonic motion are usually found by investigating the…

  16. Free Fall and Harmonic Oscillations: Analyzing Trampoline Jumps

    ERIC Educational Resources Information Center

    Pendrill, Ann-Marie; Eager, David

    2015-01-01

    Trampolines can be found in many gardens and also in some playgrounds. They offer an easily accessible vertical motion that includes free fall. In this work, the motion on a trampoline is modelled by assuming a linear relation between force and deflection, giving harmonic oscillations for small amplitudes. An expression for the cycle-time is…

  17. Renormalized reaction and relaxation rates for harmonic oscillator model

    NASA Astrophysics Data System (ADS)

    Gorbachev, Yuriy E.

    2017-07-01

    The thermal dissociation process is considered within the method of solving the kinetic equations for spatially inhomogeneous reactive gas mixtures developed in the previous papers. For harmonic oscillator model explicit expressions for reaction and relaxation rates in the renormalized form are derived.

  18. Quantum kicked harmonic oscillator in contact with a heat bath

    NASA Astrophysics Data System (ADS)

    Prado Reynoso, M. Á.; López Vázquez, P. C.; Gorin, T.

    2017-02-01

    We consider the quantum harmonic oscillator in contact with a finite-temperature bath, modeled by the Caldeira-Leggett master equation. Applying periodic kicks to the oscillator, we study the system in different dynamical regimes between classical integrability and chaos, on the one hand, and ballistic or diffusive energy absorption, on the other. We then investigate the influence of the heat bath on the oscillator in each case. Phase-space techniques allow us to simulate the evolution of the system efficiently. In this way, we calculate high-resolution Wigner functions at long times, where the system approaches a quasistationary cyclic evolution. Thereby, we perform an accurate study of the thermodynamic properties of a nonintegrable, quantum chaotic system in contact with a heat bath at finite temperature. In particular, we find that the heat transfer between harmonic oscillator and heat bath is governed by Fourier's law.

  19. Reaching Synchronization in Networked Harmonic Oscillators With Outdated Position Data.

    PubMed

    Song, Qiang; Yu, Wenwu; Cao, Jinde; Liu, Fang

    2016-07-01

    This paper studies the synchronization problem for a network of coupled harmonic oscillators by proposing a distributed control algorithm based only on delayed position states, i.e., outdated position states stored in memory. The coupling strength of the network is conveniently designed according to the absolute values and the principal arguments of the nonzero eigenvalues of the network Laplacian matrix. By analyzing a finite number of stability switches of the network with respect to the variation in the time delay, some necessary and sufficient conditions are derived for reaching synchronization in networked harmonic oscillators with positive and negative coupling strengths, respectively, and it is shown that the time delay should be taken from a set of intervals bounded by some critical values. Simulation examples are given to illustrate the effectiveness of the theoretical analysis.

  20. Increase of Boltzmann entropy in a quantum forced harmonic oscillator

    NASA Astrophysics Data System (ADS)

    Campisi, Michele

    2008-11-01

    Recently, a quantum-mechanical proof of the increase of Boltzmann entropy in quantum systems that are coupled to an external classical source of work has been given. Here we illustrate this result by applying it to a forced quantum harmonic oscillator. We show plots of the actual temporal evolution of work and entropy for various forcing protocols. We note that entropy and work can be partially or even fully returned to the source, although both work and entropy balances are non-negative at all times in accordance with the minimal work principle and the Clausius principle, respectively. A necessary condition for the increase of entropy is that the initial distribution is decreasing (e.g., canonical). We show evidence that for a nondecreasing distribution (e.g., microcanonical), the quantum expectation of entropy may decrease slightly. Interestingly, the classical expectation of entropy cannot decrease, irrespective of the initial distribution, in the forced harmonic oscillator.

  1. Increase of Boltzmann entropy in a quantum forced harmonic oscillator.

    PubMed

    Campisi, Michele

    2008-11-01

    Recently, a quantum-mechanical proof of the increase of Boltzmann entropy in quantum systems that are coupled to an external classical source of work has been given. Here we illustrate this result by applying it to a forced quantum harmonic oscillator. We show plots of the actual temporal evolution of work and entropy for various forcing protocols. We note that entropy and work can be partially or even fully returned to the source, although both work and entropy balances are non-negative at all times in accordance with the minimal work principle and the Clausius principle, respectively. A necessary condition for the increase of entropy is that the initial distribution is decreasing (e.g., canonical). We show evidence that for a nondecreasing distribution (e.g., microcanonical), the quantum expectation of entropy may decrease slightly. Interestingly, the classical expectation of entropy cannot decrease, irrespective of the initial distribution, in the forced harmonic oscillator.

  2. Geometric phase and nonadiabatic effects in an electronic harmonic oscillator.

    PubMed

    Pechal, M; Berger, S; Abdumalikov, A A; Fink, J M; Mlynek, J A; Steffen, L; Wallraff, A; Filipp, S

    2012-04-27

    Steering a quantum harmonic oscillator state along cyclic trajectories leads to a path-dependent geometric phase. Here we describe its experimental observation in an electronic harmonic oscillator. We use a superconducting qubit as a nonlinear probe of the phase, which is otherwise unobservable due to the linearity of the oscillator. We show that the geometric phase is, for a variety of cyclic paths, proportional to the area enclosed in the quadrature plane. At the transition to the nonadiabatic regime, we study corrections to the phase and dephasing of the qubit caused by qubit-resonator entanglement. In particular, we identify parameters for which this dephasing mechanism is negligible even in the nonadiabatic regime. The demonstrated controllability makes our system a versatile tool to study geometric phases in open quantum systems and to investigate their potential for quantum information processing.

  3. Equity prices as a simple harmonic oscillator with noise

    NASA Astrophysics Data System (ADS)

    Ataullah, Ali; Tippett, Mark

    2007-08-01

    The centred return on the London Stock Exchange's FTSE All Share Index is modelled as a simple harmonic oscillator with noise over the period from 1 January, 1994 until 30 June 2006. Our empirical results are compatible with the hypothesis that there is a period in the FTSE All Share Index of between two and two and one half years. This means the centred return will on average continue to increase for about a year after reaching the minimum in its oscillatory cycle; alternatively, it will continue on average to decline for about a year after reaching a maximum. Our analysis also shows that there is potential to exploit the harmonic nature of the returns process to earn abnormal profits. Extending our analysis to the low energy states of a quantum harmonic oscillator is also suggested.

  4. Dynamical properties of the delta-kicked harmonic oscillator.

    PubMed

    Kells, G A; Twamley, J; Heffernan, D M

    2004-01-01

    We propose an efficient procedure for numerically evolving the quantum dynamics of delta-kicked harmonic oscillator. The method allows for longer and more accurate simulations of the system as well as a simple procedure for calculating the system's Floquet eigenstates and quasienergies. The method is used to examine the dynamical behavior of the system in cases where the ratio of the kicking frequency to the system's natural frequency is both rational and irrational.

  5. Measuring nonlinear functionals of quantum harmonic oscillator states.

    PubMed

    Pregnell, K L

    2006-02-17

    Using only linear interactions and a local parity measurement we show how entanglement can be detected between two harmonic oscillators. The scheme generalizes to measure both linear and nonlinear functionals of an arbitrary oscillator state. This leads to many applications including purity tests, eigenvalue estimation, entropy, and distance measures--all without the need for nonlinear interactions or complete state reconstruction. Remarkably, experimental realization of the proposed scheme is already within the reach of current technology with linear optics.

  6. Energy-dependent harmonic oscillator in noncommutative space

    NASA Astrophysics Data System (ADS)

    Benchikha, A.; Merad, M.; Birkandan, T.

    2017-06-01

    In noncommutative quantum mechanics, the energy-dependent harmonic oscillator problem is studied by solving the Schrödinger equation in polar coordinates. The presence of the noncommutativity in space coordinates and the dependence on energy for the potential yield energy-dependent mass and potential. The correction of normalization condition is calculated and the parameter-dependences of the results are studied graphically.

  7. Coherent and squeezed states for the 3D harmonic oscillator

    NASA Astrophysics Data System (ADS)

    Mazouz, Amel; Bentaiba, Mustapha; Mahieddine, Ali

    2017-01-01

    A three-dimensional harmonic oscillator is studied in the context of generalized coherent states. We construct its squeezed states as eigenstates of linear contribution of ladder operators which are associated to the generalized Heisenberg algebra. We study the probability density to show the compression effect on the squeezed states. Our analysis reveals that squeezed states give us some freedom on the precise knowledge of position of the particle while maintaining the Heisenberg uncertainty relation minimum, squeezed states remains squeezed states over time.

  8. An analogue of the Berry phase for simple harmonic oscillators

    NASA Astrophysics Data System (ADS)

    Suslov, S. K.

    2013-03-01

    We evaluate a variant of Berry's phase for a ‘missing’ family of the square integrable wavefunctions for the linear harmonic oscillator, which cannot be derived by the separation of variables (in a natural way). Instead, it is obtained by the action of the maximal kinematical invariance group on the standard solutions. A simple closed formula for the phase (in terms of elementary functions) is found here by integration with the help of a computer algebra system.

  9. Oscillation death and revival by coupling with damped harmonic oscillator

    NASA Astrophysics Data System (ADS)

    Varshney, Vaibhav; Saxena, Garima; Biswal, Bibhu; Prasad, Awadhesh

    2017-09-01

    Dynamics of nonlinear oscillators augmented with co- and counter-rotating linear damped harmonic oscillator is studied in detail. Depending upon the sense of rotation of augmenting system, the collective dynamics converges to either synchronized periodic behaviour or oscillation death. Multistability is observed when there is a transition from periodic state to oscillation death. In the periodic region, the system is found to be in mixed synchronization state, which is characterized by the newly defined "relative phase angle" between the different axes.

  10. Generalized relativistic harmonic oscillator in minimal length quantum mechanics

    NASA Astrophysics Data System (ADS)

    Castro, L. B.; E Obispo, A.

    2017-07-01

    We solve the generalized relativistic harmonic oscillator in 1  +  1 dimensions in the presence of a minimal length. Using the momentum space representation, we explore all the possible signs of the potentials and discuss their bound-state solutions for fermions and antifermions. Furthermore, we also find an isolated solution from the Sturm-Liouville scheme. All cases already analyzed in the literature are obtained as particular cases.

  11. Alpha clustering near nuclear surface and harmonic-oscillator excitations

    NASA Astrophysics Data System (ADS)

    Horiuchi, W.; Suzuki, Y.

    2017-06-01

    We quantify how it is difficult to describe an alpha(α)-cluster state with single-particle harmonic-oscillator (HO) bases in the low-lying16O states by counting the number of HO quanta of12 C+n+n+p+p five-body wave functions. We also discuss how many HO quanta are needed for describing a localized α cluster near the nuclear surface towards understanding of the shell and cluster coexistence in heavier nuclei.

  12. Driven damped harmonic oscillator resonance with an Arduino

    NASA Astrophysics Data System (ADS)

    Goncalves, A. M. B.; Cena, C. R.; Bozano, D. F.

    2017-07-01

    In this paper we propose a simple experimental apparatus that can be used to show quantitative and qualitative results of resonance in a driven damped harmonic oscillator. The driven oscillation is made by a servo motor, and the oscillation amplitude is measured by an ultrasonic position sensor. Both are controlled by an Arduino board. The frequency of free oscillation measured was campatible with the resonance frequency that was measured.

  13. Using Coupled Harmonic Oscillators to Model Some Greenhouse Gas Molecules

    SciTech Connect

    Go, Clark Kendrick C.; Maquiling, Joel T.

    2010-07-28

    Common greenhouse gas molecules SF{sub 6}, NO{sub 2}, CH{sub 4}, and CO{sub 2} are modeled as harmonic oscillators whose potential and kinetic energies are derived. Using the Euler-Lagrange equation, their equations of motion are derived and their phase portraits are plotted. The authors use these data to attempt to explain the lifespan of these gases in the atmosphere.

  14. Observations of Harmonic Oscillations and ELM Magnetic Precursors in NSTX

    NASA Astrophysics Data System (ADS)

    Kelly, F.; Fredrickson, E.; Bell, R.; Tritz, K.; Maingi, R.; Takahashi, H.

    2010-11-01

    Recent experiments in the National Spherical Torus Experiment (NSTX) demonstrated the progressive suppression of edge localized modes (ELMs) with increasing lithium deposition. Sufficient lithium suppressed ELMs and made the occurrence of low-frequency, low-n harmonics more frequent. Signatures of these harmonic oscillations with a significant edge component were observed in both the high-n Mirnov magnetic and soft X-ray diagnostics of NSTX. Two distinct sets of harmonic oscillations can be observed during some ELM-free periods. The harmonic oscillations are consistent with modes localized in the edge with the frequency of the n = 1 harmonic near the rotation frequency of the edge plasma. NSTX magnetic diagnostics also observe distinctive signatures of ELMs. Transient n = 1 and n = 2 mode bursts and occasional higher n modes with frequency in the 30 to 90 kHz range occurred simultaneous with the increase in fast Da signal. These bursts of n = 1 and n = 2 modes resemble a model simulation of ELMs by T. Evans in which a bifurcation of magnetic topology is driven by nonlinear feedback amplification of thermoelectric currents from linear peeling-ballooning modes.

  15. Collision-induced squeezing in a harmonic oscillator

    NASA Technical Reports Server (NTRS)

    Lee, Hai-Woong

    1993-01-01

    The concept of squeezing has so far been applied mainly to light, as is evidenced by the number of research works on the subject of squeezed light. Since, in quantum mechanics, both light and the simple harmonic oscillator are described within the same mathematical framework, there is of course no difficulty in applying the concept to the simple harmonic oscillator as well. In fact, the theoretical development of squeezed states and squeezed light owes much to the physical insights that one obtains as the analogy between light and the harmonic oscillator is exploited. The example presented shows clearly that two states with different phases in general have different degrees of squeezing, even if they have the same state distribution. This means that, even if one considers collision processes that produce the same state distribution, the degree of squeezing obtained during and after the collisions can be quite different, depending on how the phases phi(sub n) of the probability amplitudes develop in time as the collisions proceed. It is therefore evident that, for a detailed study of collision-induced squeezing, further study on the time development of the phases in collisions and its relation to collision parameters such as potential energy surfaces and collision energy is needed.

  16. Teaching from a Microgravity Environment: Harmonic Oscillator and Pendulum

    NASA Astrophysics Data System (ADS)

    Benge, Raymond; Young, Charlotte; Davis, Shirley; Worley, Alan; Smith, Linda; Gell, Amber

    2009-04-01

    This presentation reports on an educational experiment flown in January 2009 as part of NASA's Microgravity University program. The experiment flown was an investigation into the properties of harmonic oscillators in reduced gravity. Harmonic oscillators are studied in every introductory physics class. The equation for the period of a harmonic oscillator does not include the acceleration due to gravity, so the period should be independent of gravity. However, the equation for the period of a pendulum does include the acceleration due to gravity, so the period of a pendulum should appear longer under reduced gravity (such as lunar or Martian gravity) and shorter under hyper-gravity. These environments can be simulated aboard an aircraft. Video of the experiments being performed aboard the aircraft is to be used in introductory physics classes. Students will be able to record information from watching the experiment performed aboard the aircraft in a similar manner to how they collect data in the laboratory. They can then determine if the experiment matches theory. Video and an experimental procedure are being prepared based upon this flight, and these materials will be available for download by faculty anywhere with access to the internet who wish to use the experiment in their own classrooms.

  17. Thermal conduction in a chain of colliding harmonic oscillators revisited.

    PubMed

    Sano, M M; Kitahara, K

    2001-11-01

    Thermal conduction in a chain of colliding harmonic oscillators, sometimes called the ding-dong model, is investigated. We first argue that this system is equivalent to the Dawson plasma sheet model. Next we show the Lyapunov analysis for this system to characterize its dynamical property. Finally, we reconsider the numerical study of thermal conduction for this system using the Green-Kubo relation and the direct simulation of Fourier law. Both show that thermal conduction is normal in that kappa(N,T) approximately equals N(0), at least, at low temperature in a large system.

  18. Quantum harmonic oscillator: an elementary derivation of the energy spectrum

    NASA Astrophysics Data System (ADS)

    Borghi, Riccardo

    2017-03-01

    An elementary treatment of the quantum harmonic oscillator is proposed. No previous knowledge of linear differential equation theory or Fourier analysis are required, but rather only a few basics of elementary calculus. The pivotal role in our analysis is played by the sole particle localization constraint, which implies square integrability of stationary-state wavefunctions. The oscillator ground-state characterization is then achieved in a way that could be grasped, in principle, even by first-year undergraduates. A very elementary approach to build up and to characterize all higher-level energy eigenstates completes our analysis.

  19. Heat transport along a chain of coupled quantum harmonic oscillators

    NASA Astrophysics Data System (ADS)

    de Oliveira, Mário J.

    2017-04-01

    I study the heat transport properties of a chain of coupled quantum harmonic oscillators in contact at its ends with two heat reservoirs at distinct temperatures. My approach is based on the use of an evolution equation for the density operator which is a canonical quantization of the classical Fokker-Planck-Kramers equation. I set up the evolution equation for the covariances and obtain the stationary covariances at the stationary states from which I determine the thermal conductance in closed form when the interparticle interaction is small. The conductance is finite in the thermodynamic limit implying an infinite thermal conductivity.

  20. The effect of singular potentials on the harmonic oscillator

    SciTech Connect

    Filgueiras, C.; Silva, E.O.; Oliveira, W.; Moraes, F.

    2010-11-15

    We address the problem of a quantum particle moving under interactions presenting singularities. The self-adjoint extension approach is used to guarantee that the Hamiltonian is self-adjoint and to fix the choice of boundary conditions. We specifically look at the harmonic oscillator added of either a {delta}-function potential or a Coulomb potential (which is singular at the origin). The results are applied to Landau levels in the presence of a topological defect, the Calogero model and to the quantum motion on the noncommutative plane.

  1. Brownian motion with adhesion: harmonic oscillator with fluctuating mass.

    PubMed

    Gitterman, M; Klyatskin, V I

    2010-05-01

    In contrast to the cases usually studied of a harmonic oscillator subject to a random force (Brownian motion) or having random frequency or random damping, we consider a random mass which corresponds to an oscillator for which the particles of the surrounding medium adhere to it for some (random) time after the collision, thereby changing the oscillator mass. This model, which describes Brownian motion with adhesion, can be useful for the analysis of chemical and biological solutions as well as nanotechnological devices. We consider dichotomous noise and its limiting case, white noise.

  2. Analysis of transonic flow about harmonically oscillating airfoils and wings

    NASA Technical Reports Server (NTRS)

    Weatherill, W. H.; Ehlers, F. E.

    1980-01-01

    A finite difference method for analyzing the unsteady transonic flow about harmonically oscillating wings is discussed. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting partial differential equations for small disturbances. Initial solutions were obtained using relaxation procedures, but the solution range proved to be limited in terms of Mach number and reduced frequency. Recent two-dimensional results are presented which have been obtained with direct solution procedures in which the difference equations are solved 'all at once' and these provide reasonable correlation for practical values of Mach number and reduced frequency.

  3. Harmonic Oscillator Model for Radin's Markov-Chain Experiments

    NASA Astrophysics Data System (ADS)

    Sheehan, D. P.; Wright, J. H.

    2006-10-01

    The conscious observer stands as a central figure in the measurement problem of quantum mechanics. Recent experiments by Radin involving linear Markov chains driven by random number generators illuminate the role and temporal dynamics of observers interacting with quantum mechanically labile systems. In this paper a Lagrangian interpretation of these experiments indicates that the evolution of Markov chain probabilities can be modeled as damped harmonic oscillators. The results are best interpreted in terms of symmetric equicausal determinism rather than strict retrocausation, as posited by Radin. Based on the present analysis, suggestions are made for more advanced experiments.

  4. Harmonic Oscillator Model for Radin's Markov-Chain Experiments

    SciTech Connect

    Sheehan, D. P.; Wright, J. H.

    2006-10-16

    The conscious observer stands as a central figure in the measurement problem of quantum mechanics. Recent experiments by Radin involving linear Markov chains driven by random number generators illuminate the role and temporal dynamics of observers interacting with quantum mechanically labile systems. In this paper a Lagrangian interpretation of these experiments indicates that the evolution of Markov chain probabilities can be modeled as damped harmonic oscillators. The results are best interpreted in terms of symmetric equicausal determinism rather than strict retrocausation, as posited by Radin. Based on the present analysis, suggestions are made for more advanced experiments.

  5. Elementary derivation of the quantum propagator for the harmonic oscillator

    NASA Astrophysics Data System (ADS)

    Shao, Jiushu

    2016-10-01

    Operator algebra techniques are employed to derive the quantum evolution operator for the harmonic oscillator. The derivation begins with the construction of the annihilation and creation operators and the determination of the wave function for the coherent state as well as its time-dependent evolution, and ends with the transformation of the propagator in a mixed position-coherent-state representation to the desired one in configuration space. Throughout the entire procedure, besides elementary operator manipulations, it is only necessary to solve linear differential equations and to calculate Gaussian integrals.

  6. Random reverse-cyclic matrices and screened harmonic oscillator

    NASA Astrophysics Data System (ADS)

    Srivastava, Shashi C. L.; Jain, Sudhir R.

    2012-04-01

    We have calculated the joint probability distribution function for random reverse-cyclic matrices and shown that it is related to an N-body exactly solvable model. We refer to this well-known model potential as a screened harmonic oscillator. The connection enables us to obtain all the correlations among the particle positions moving in a screened harmonic potential. The density of nontrivial eigenvalues of this ensemble is found to be of the Wigner form and admits a hole at the origin, in contrast to the semicircle law of the Gaussian orthogonal ensemble of random matrices. The spacing distributions assume different forms ranging from Gaussian-like to Wigner.

  7. Non-Markovian quantum Brownian motion of a harmonic oscillator

    SciTech Connect

    Tang, J.

    1994-02-01

    We apply the density-matrix method to the study of quantum Brownian motion of a harmonic oscillator coupled to a heat bath, a system investigated previously by Caldeira and Leggett using a different method. Unlike the earlier work, in our derivation of the master equation the non-Markovian terms are maintained. Although the same model of interaction is used, discrepancy is found between their results and our equation in the Markovian limit. We also point out that the particular interaction model used by both works cannot lead to the phenomenological generalized Langevin theory of Kubo.

  8. Pure Gaussian states from quantum harmonic oscillator chains with a single local dissipative process

    NASA Astrophysics Data System (ADS)

    Ma, Shan; Woolley, Matthew J.; Petersen, Ian R.; Yamamoto, Naoki

    2017-03-01

    We study the preparation of entangled pure Gaussian states via reservoir engineering. In particular, we consider a chain consisting of (2\\aleph +1) quantum harmonic oscillators where the central oscillator of the chain is coupled to a single reservoir. We then completely parametrize the class of (2\\aleph +1) -mode pure Gaussian states that can be prepared by this type of quantum harmonic oscillator chain. This parametrization allows us to determine the steady-state entanglement properties of such quantum harmonic oscillator chains.

  9. Dissipative quantum trajectories in complex space: Damped harmonic oscillator

    NASA Astrophysics Data System (ADS)

    Chou, Chia-Chun

    2016-10-01

    Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton-Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation for the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.

  10. Dissipative quantum trajectories in complex space: Damped harmonic oscillator

    SciTech Connect

    Chou, Chia-Chun

    2016-10-15

    Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton–Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation for the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.

  11. Exact master equation and quantum decoherence of two coupled harmonic oscillators in a general environment.

    PubMed

    Chou, Chung-Hsien; Yu, Ting; Hu, B L

    2008-01-01

    In this paper we derive an exact master equation for two coupled quantum harmonic oscillators interacting via bilinear coupling with a common environment at arbitrary temperature made up of many harmonic oscillators with a general spectral density function. We first show a simple derivation based on the observation that the two harmonic oscillator model can be effectively mapped into that of a single harmonic oscillator in a general environment plus a free harmonic oscillator. Since the exact one harmonic oscillator master equation is available [B. L. Hu, J. P. Paz, and Y. Zhang, Phys. Rev. D 45, 2843 (1992)], the exact master equation with all its coefficients for this two harmonic oscillator model can be easily deduced from the known results of the single harmonic oscillator case. In the second part we give an influence functional treatment of this model and provide explicit expressions for the evolutionary operator of the reduced density matrix which are useful for the study of decoherence and disentanglement issues. We show three applications of this master equation: on the decoherence and disentanglement of two harmonic oscillators due to their interaction with a common environment under Markovian approximation, and a derivation of the uncertainty principle at finite temperature for a composite object, modeled by two interacting harmonic oscillators. The exact master equation for two, and its generalization to N, harmonic oscillators interacting with a general environment are expected to be useful for the analysis of quantum coherence, entanglement, fluctuations, and dissipation of mesoscopic objects toward the construction of a theoretical framework for macroscopic quantum phenomena.

  12. Exact solution of a quantum forced time-dependent harmonic oscillator

    NASA Technical Reports Server (NTRS)

    Yeon, Kyu Hwang; George, Thomas F.; Um, Chung IN

    1992-01-01

    The Schrodinger equation is used to exactly evaluate the propagator, wave function, energy expectation values, uncertainty values, and coherent state for a harmonic oscillator with a time dependent frequency and an external driving time dependent force. These quantities represent the solution of the classical equation of motion for the time dependent harmonic oscillator.

  13. The Harmonic Oscillator with a Gaussian Perturbation: Evaluation of the Integrals and Example Applications

    ERIC Educational Resources Information Center

    Earl, Boyd L.

    2008-01-01

    A general result for the integrals of the Gaussian function over the harmonic oscillator wavefunctions is derived using generating functions. Using this result, an example problem of a harmonic oscillator with various Gaussian perturbations is explored in order to compare the results of precise numerical solution, the variational method, and…

  14. The Two-Capacitor Problem Revisited: A Mechanical Harmonic Oscillator Model Approach

    ERIC Educational Resources Information Center

    Lee, Keeyung

    2009-01-01

    The well-known two-capacitor problem, in which exactly half the stored energy disappears when a charged capacitor is connected to an identical capacitor, is discussed based on the mechanical harmonic oscillator model approach. In the mechanical harmonic oscillator model, it is shown first that "exactly half" the work done by a constant applied…

  15. The Two-Capacitor Problem Revisited: A Mechanical Harmonic Oscillator Model Approach

    ERIC Educational Resources Information Center

    Lee, Keeyung

    2009-01-01

    The well-known two-capacitor problem, in which exactly half the stored energy disappears when a charged capacitor is connected to an identical capacitor, is discussed based on the mechanical harmonic oscillator model approach. In the mechanical harmonic oscillator model, it is shown first that "exactly half" the work done by a constant applied…

  16. The Harmonic Oscillator with a Gaussian Perturbation: Evaluation of the Integrals and Example Applications

    ERIC Educational Resources Information Center

    Earl, Boyd L.

    2008-01-01

    A general result for the integrals of the Gaussian function over the harmonic oscillator wavefunctions is derived using generating functions. Using this result, an example problem of a harmonic oscillator with various Gaussian perturbations is explored in order to compare the results of precise numerical solution, the variational method, and…

  17. BAYESIAN ANALYSIS OF MULTIPLE HARMONIC OSCILLATIONS IN THE SOLAR CORONA

    SciTech Connect

    Arregui, I.; Asensio Ramos, A.; Diaz, A. J.

    2013-03-01

    The detection of multiple mode harmonic kink oscillations in coronal loops enables us to obtain information on coronal density stratification and magnetic field expansion using seismology inversion techniques. The inference is based on the measurement of the period ratio between the fundamental mode and the first overtone and theoretical results for the period ratio under the hypotheses of coronal density stratification and magnetic field expansion of the wave guide. We present a Bayesian analysis of multiple mode harmonic oscillations for the inversion of the density scale height and magnetic flux tube expansion under each of the hypotheses. The two models are then compared using a Bayesian model comparison scheme to assess how plausible each one is given our current state of knowledge.

  18. Ecological optimization of an irreversible harmonic oscillators Carnot heat engine

    NASA Astrophysics Data System (ADS)

    Liu, Xiaowei; Chen, Lingen; Wu, Feng; Sun, Fengrui

    2009-12-01

    A model of an irreversible quantum Carnot heat engine with heat resistance, internal irreversibility and heat leakage and many non-interacting harmonic oscillators is established in this paper. Based on the quantum master equation and semi-group approach, equations of some important performance parameters, such as power output, efficiency, exergy loss rate and ecological function for the irreversible quantum Carnot heat engine are derived. The optimal ecological performance of the heat engine in the classical limit is analyzed with numerical examples. Effects of internal irreversibility and heat leakage on the ecological performance are discussed. A performance comparison of the quantum heat engine under maximum ecological function and maximum power conditions is also performed.

  19. Single trapped ion as a time-dependent harmonic oscillator

    SciTech Connect

    Menicucci, Nicolas C.; Milburn, G. J.

    2007-11-15

    We show how a single trapped ion may be used to test a variety of important physical models realized as time-dependent harmonic oscillators. The ion itself functions as its own motional detector through laser-induced electronic transitions. Alsing et al., [Phys. Rev. Lett. 94, 220401 (2005)] proposed that an exponentially decaying trap frequency could be used to simulate (thermal) Gibbons-Hawking radiation in an expanding universe, but the Hamiltonian used was incorrect. We apply our general solution to this experimental proposal, correcting the result for a single ion and showing that while the actual spectrum is different from the Gibbons-Hawking case, it nevertheless shares an important experimental signature with this result.

  20. Phase-space treatment of the driven quantum harmonic oscillator

    NASA Astrophysics Data System (ADS)

    Campos, Diógenes

    2017-03-01

    A recent phase-space formulation of quantum mechanics in terms of the Glauber coherent states is applied to study the interaction of a one-dimensional harmonic oscillator with an arbitrary time-dependent force. Wave functions of the simultaneous values of position q and momentum p are deduced, which in turn give the standard position and momentum wave functions, together with expressions for the ηth derivatives with respect to q and p, respectively. Afterwards, general formulae for momentum, position and energy expectation values are obtained, and the Ehrenfest theorem is verified. Subsequently, general expressions for the cross-Wigner functions are deduced. Finally, a specific example is considered to numerically and graphically illustrate some results.

  1. A method of solving simple harmonic oscillator Schroedinger equation

    NASA Technical Reports Server (NTRS)

    Maury, Juan Carlos F.

    1995-01-01

    A usual step in solving totally Schrodinger equation is to try first the case when dimensionless position independent variable w is large. In this case the Harmonic Oscillator equation takes the form (d(exp 2)/dw(exp 2) - w(exp 2))F = 0, and following W.K.B. method, it gives the intermediate corresponding solution F = exp(-w(exp 2)/2), which actually satisfies exactly another equation, (d(exp 2)/dw(exp 2) + 1 - w(exp 2))F = 0. We apply a different method, useful in anharmonic oscillator equations, similar to that of Rampal and Datta, and although it is slightly more complicated however it is also more general and systematic.

  2. A Perturbation of the Dunkl Harmonic Oscillator on the Line

    NASA Astrophysics Data System (ADS)

    Álvarez López, Jesús A.; Calaza, Manuel

    2015-07-01

    Let J_σ be the Dunkl harmonic oscillator on R (σ>-1/2). For 00, it is proved that, if σ>u-1/2, then the operator U=J_σ+ξ|x|^{-2u}, with appropriate domain, is essentially self-adjoint in L^2({R},|x|^{2σ} dx), the Schwartz space S is a core of overline U^{1/2}, and overline U has a discrete spectrum, which is estimated in terms of the spectrum of overline{J_σ}. A generalization J_{σ,τ} of J_σ is also considered by taking different parameters σ and τ on even and odd functions. Then extensions of the above result are proved for J_{σ,τ}, where the perturbation has an additional term involving, either the factor x^{-1} on odd functions, or the factor x on even functions. Versions of these results on R_+ are derived.

  3. The Acoustic Simple Harmonic Oscillator: Experimental Verification and Applications

    NASA Astrophysics Data System (ADS)

    Matteson, Sam

    2009-04-01

    In his famous volume, The Sensations of Tone, published in 1877, Hermann Helmholtz introduced a resonator that was central to his investigations of acoustics. This talk revisits the device that Helmholtz described and examines it as a manifestation of an acoustic simple harmonic oscillator (SHO). The presentation demonstrates that an enclosed volume which communicates with the outside world via a narrow tube exhibits a single strong frequency response in analogy to a mechanical SHO, along with weaker resonances of the air in the short pipe that comprises the ``neck.'' The investigations, furthermore, report results of a straightforward experiment that confirms the SHO model (with damping) and that is very accessible to undergraduate students using inexpensive equipment and internet-obtainable freeware. The current work also extends the analysis to include applications of the Helmholtz Resonator to several folk instruments, namely, the ocarina, whistling, and the ``bottle band.''

  4. Excitation with quantum light. I. Exciting a harmonic oscillator

    NASA Astrophysics Data System (ADS)

    Carreño, J. C. López; Laussy, F. P.

    2016-12-01

    We present a two-part study of the excitation of an optical target by quantum light. In this first part, we introduce the problematic and address the first case of interest, that of exciting the quantum harmonic oscillator, corresponding to, e.g., a single-mode passive cavity or a noninteracting bosonic field. We introduce a mapping of the Hilbert space that allows to chart usefully the accessible regions. We then consider the quantum excitation from single-photon sources in the form of a two-level system under various regimes of (classical) pumping: incoherent, coherent, and in the Mollow triplet regime. We close this first part with an overview of the material to be covered in the subsequent work.

  5. Free fall and harmonic oscillations: analyzing trampoline jumps

    NASA Astrophysics Data System (ADS)

    Pendrill, Ann-Marie; Eager, David

    2015-01-01

    Trampolines can be found in many gardens and also in some playgrounds. They offer an easily accessible vertical motion that includes free fall. In this work, the motion on a trampoline is modelled by assuming a linear relation between force and deflection, giving harmonic oscillations for small amplitudes. An expression for the cycle-time is obtained in terms of maximum normalized force from the trampoline and the harmonic frequency. A simple expression is obtained for the ratio between air-time and harmonic period, and the maximum g-factor. The results are compared to experimental results, including accelerometer data showing 7g during bounces on a small trampoline in an amusement park play area. Similar results are obtained on a larger garden trampoline, and even larger accelerations have been measured for gymnastic trampolines.

  6. Avoiding dissipation in a system of three quantum harmonic oscillators

    NASA Astrophysics Data System (ADS)

    Manzano, Gonzalo; Galve, Fernando; Zambrini, Roberta

    2013-03-01

    We analyze the symmetries in an open quantum system composed by three coupled and detuned harmonic oscillators in the presence of a common heat bath. It is shown analytically how to engineer the couplings and frequencies of the system so as to have several degrees of freedom unaffected by decoherence, irrespective of the specific spectral density or initial state of the bath. This partial thermalization allows observing asymptotic entanglement at moderate temperatures, even in the nonresonant case. This latter feature cannot be seen in the simpler situation of only two oscillators, highlighting the richer structural variety of the three-body case. When departing from the strict conditions for partial thermalization, a hierarchical structure of dissipation rates for the normal modes is observed, leading to a long transient where quantum correlations such as the quantum discord are largely preserved, as well as to synchronous dynamics of the oscillators quadratures.

  7. Revised calculation of four-particle harmonic-oscillator transformation brackets matrix

    NASA Astrophysics Data System (ADS)

    Mickevičius, S.; Germanas, D.; Kalinauskas, R. K.

    2013-02-01

    In this article we present a new, considerably enhanced and more rapid method for calculation of the matrix of four-particle harmonic-oscillator transformation brackets (4HOB). The new method is an improved version of 4HOB matrix calculations which facilitates the matrix calculation by finding the eigenvectors of the 4HOB matrix explicitly. Using this idea the new Fortran code for fast and 4HOB matrix calculation is presented. The calculation time decreases more than a few hundred times for large matrices. As many problems of nuclear and hadron physics structure are modeled on the harmonic oscillator (HO) basis our presented method can be useful for large-scale nuclear structure and many-particle identical fermion systems calculations. Program summaryTitle of program: HOTB_M Catalogue identifier: AEFQ_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFQ_v3_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License version 3 No. of lines in distributed program, including test data, etc.: 2149 No. of bytes in distributed program, including test data, etc.: 17576 Distribution format: tar.gz Programming language: Fortran 90. Computer: Any computer with Fortran 90 compiler. Operating system: Windows, Linux, FreeBSD, True64 Unix. RAM: Up to a few Gigabytes (see Tables 1 and 2 included in the distribution package) Classification: 17.16, 17.17. Catalogue identifier of previous version: AEFQ_v2_0 Journal reference of previous version: Comput. Phys. Comm. 182(2011)1377 Does the new version supersede the previous version?: Yes Nature of problem: Calculation of the matrix of the 4HOB in a more effective way, which allows us to calculate the matrix of the brackets up to a few hundred times more rapidly than in a previous version. Solution method: The method is based on compact expressions of 4HOB, presented in [1] and its simplifications presented in this paper. Reasons for new version

  8. Quantum Encoding and Entanglement in Terms of Phase Operators Associated with Harmonic Oscillator

    NASA Astrophysics Data System (ADS)

    Singh, Manu Pratap; Rajput, B. S.

    2016-10-01

    Realization of qudit quantum computation has been presented in terms of number operator and phase operators associated with one-dimensional harmonic oscillator and it has been demonstrated that the representations of generalized Pauli group, viewed in harmonic oscillator operators, allow the qudits to be explicitly encoded in such systems. The non-Hermitian quantum phase operators contained in decomposition of the annihilation and creation operators associated with harmonic oscillator have been analysed in terms of semi unitary transformations (SUT) and it has been shown that the non-vanishing analytic index for harmonic oscillator leads to an alternative class of quantum anomalies. Choosing unitary transformation and the Hermitian phase operator free from quantum anomalies, the truncated annihilation and creation operators have been obtained for harmonic oscillator and it has been demonstrated that any attempt of removal of quantum anomalies leads to absence of minimum uncertainty.

  9. Random phase approximation in a deformed Hartree-Fock basis

    SciTech Connect

    Gering, M.Z.I.; Heiss, W.D.

    1984-03-01

    The validity of the random phase approximation in a deformed Hartree-Fock basis is investigated in a soluble model. There is strong evidence that the random phase approximation reproduces well the vibrational excitations of the system. Within the framework of the Green's function technique, the significance of the deformed single particle basis is established.

  10. Edge Event-Triggered Synchronization in Networks of Coupled Harmonic Oscillators.

    PubMed

    Wei, Bo; Xiao, Feng; Dai, Ming-Zhe

    2016-08-30

    The synchronization problems of networks of coupled harmonic oscillators are addressed by the edge event-triggered approach in this paper. The network dynamics with respect to edge states are presented and a new edge event-triggered control protocol is designed. Combined with the periodic event-detecting and edge event-triggered approach, sufficient conditions that guarantee the synchronization of coupled harmonic oscillators are presented. Two event-detecting rules are given to achieve the synchronization of coupled harmonic oscillators with low resource consumption. Finally, simulations are conducted to illustrate the effectiveness of the edge event-triggered control algorithm.

  11. Damping of a harmonic oscillator in a squeezed vacuum without rotating-wave approximation

    NASA Astrophysics Data System (ADS)

    Hassan, S. S.; Joshi, A.; Frege, O. M.; Emam, W.

    2007-09-01

    A single harmonic oscillator interacting with a broadband squeezed reservoir is analyzed within the framework of master equation without invoking the rotating-wave approximation. The dynamical evolution and photon statistics of the system are investigated by studying mean photon number and second order intensity-intensity correlation function, respectively, under resonance condition which show transient oscillations at twice the harmonic oscillator frequency. The transient fluorescent spectrum reveals asymmetric features. Inclusion of vacuum and field-dependent frequency shifts affects the thermal equilibrium value of the average photon number of the harmonic oscillator.

  12. Feinberg-Horodecki states of a time-dependent mass distribution harmonic oscillator

    NASA Astrophysics Data System (ADS)

    Eshghi, M.; Sever, R.; Ikhdair, S. M.

    2016-07-01

    The solution of the Feinberg-Horodecki (FH) equation for a time-dependent mass (TDM) harmonic oscillator quantum system is studied. A certain interaction is applied to a mass m(t) to provide a particular spectrum of stationary energies. The related spectrum of the harmonic oscillator potential V(t) acting on the TDM m(t) oscillators is found. We apply the time version of the asymptotic iteration method (AIM) to calculate analytical expressions of the TDM stationary state energies and their wave functions. It is shown that the obtained solutions reduce to those of simple harmonic oscillator as the time-dependent mass reduces to m0.

  13. Spatial analysis of harmonic oscillation of gypsy moth outbreak intensity.

    PubMed

    Haynes, Kyle J; Liebhold, Andrew M; Johnson, Derek M

    2009-03-01

    Outbreaks of many forest-defoliating insects are synchronous over broad geographic areas and occur with a period of approximately 10 years. Within the range of the gypsy moth in North America, however, there is considerable geographic heterogeneity in strength of periodicity and the frequency of outbreaks. Furthermore, gypsy moth outbreaks exhibit two significant periodicities: a dominant period of 8-10 years and a subdominant period of 4-5 years. In this study, we used a simulation model and spatially referenced time series of outbreak intensity data from the Northeastern United States to show that the bimodal periodicity in the intensity of gypsy moth outbreaks is largely a result of harmonic oscillations in gypsy moth abundance at and above a 4 km(2) scale of resolution. We also used geographically weighted regression models to explore the effects of gypsy moth host-tree abundance on the periodicity of gypsy moths. We found that the strength of 5-year cycles increased relative to the strength of 10-year cycles with increasing host tree abundance. We suggest that this pattern emerges because high host-tree availability enhances the growth rates of gypsy moth populations.

  14. Entanglement prethermalization in an interaction quench between two harmonic oscillators.

    PubMed

    Ikeda, Tatsuhiko N; Mori, Takashi; Kaminishi, Eriko; Ueda, Masahito

    2017-02-01

    Entanglement prethermalization (EP) refers to a quasi-stationary nonequilibrium state of a composite system in which each individual subsystem looks thermal but the entire system remains nonthermal due to quantum entanglement between subsystems. We theoretically study the dynamics of EP following a coherent split of a one-dimensional harmonic potential in which two interacting bosons are confined. This problem is equivalent to that of an interaction quench between two harmonic oscillators. We show that this simple model captures the bare essentials of EP; that is, each subsystem relaxes to an approximate thermal equilibrium, whereas the total system remains entangled. We find that a generalized Gibbs ensemble exactly describes the total system if we take into account nonlocal conserved quantities that act nontrivially on both subsystems. In the presence of a symmetry-breaking perturbation, the relaxation dynamics of the system exhibits a quasi-stationary EP plateau and eventually reaches thermal equilibrium. We analytically show that the lifetime of EP is inversely proportional to the magnitude of the perturbation.

  15. Observations of ELM Magnetic Precursors and Harmonic Oscillations in NSTX

    NASA Astrophysics Data System (ADS)

    Kelly, F.; Frederickson, E.; Bell, R.; Tritz, K.; Takahashi, H.; Maingi, R.; NSTX Collaboration

    2011-10-01

    Recent experiments on NSTX have shown n=1 dominant and n=2 mode ELM magnetic precursors with mode frequency in the 30 to 90 kHz range. The growing magnetic oscillations measured with the NSTX high-n Mirnov diagnostic occurred simultaneous with the onset of the increase in fast D α signal. These bursts of dominantly n=1, some n=2 and fewer higher modes resemble the predictions of a model simulation of ELMs by T. Evans in which a feedback amplification mechanism causes explosive growth of the separatrix topology driven by thermoelectric currents in flux tubes connecting the divertor plates. The n=1 mode remained dominant as wall recycling was reduced with lithium conditioning and n=3 RMP was applied, suggesting the trigger mechanism remained the same. Sufficient lithium suppressed ELMs and made the occurrence of low-frequency, low-n Harmonics Oscillations (HOs) more frequent. The HOs are consistent with modes localized in the edge with the frequency of the n = 1 harmonic near the rotation frequency of the edge plasma. Work supported in part by US DOE contract no. DE-AC02-09CH11466.

  16. Calorimetric measurement of work for a driven harmonic oscillator.

    PubMed

    Sampaio, Rui; Suomela, Samu; Ala-Nissila, Tapio

    2016-12-01

    A calorimetric measurement has recently been proposed as a promising technique to measure thermodynamic quantities in a dissipative superconducting qubit. These measurements rely on the fact that the system is projected into energy eigenstates whenever energy is exchanged with the environment. This requirement imposes a restriction on the class of systems that can be measured in this way. Here we extend the calorimetric protocol to the measurement of work in a driven quantum harmonic oscillator. We employ a scheme based on a two-level approximation that makes use of an experimentally accessible quantity and show how it relates to the work obtained through the standard two-measurement protocol. We find that the average work is well approximated in the underdamped regime for short driving times and, in the overdamped regime, for any driving time. However, this approximation fails for the variance and higher moments of work at finite temperatures. Furthermore, we show how to relate the work statistics obtained through this scheme to the work statistics given by the two-measurement protocol.

  17. The Study of a Dampened Driven Harmonic Oscillator

    NASA Astrophysics Data System (ADS)

    Findley, Tiffany; Yoshida, Sanichiro; Bankston, Daniel; Lovell, Clinton

    2003-03-01

    The dynamics of a pendulum are studied with a suspended mirror used in a Laser Interferometer Gravitational-wave Observatory (LIGO) detector in mind. We are interested in modeling the motion of the suspended mirrors in the context of a damped driven harmonic oscillator. A model mirror was constructed and suspended by wire to a block that was driven by a mechanical oscillator. To measure the frequency dependence of the pitch and yaw motions, the mirror reflected a laser beam onto a measurement plane. A CCD camera took periodic pictures of the measurement plane, thus capturing the movement of the beam due to the movement of the mirror. These pictures were then analyzed to determine the dynamics of the pendulum at the driving frequency. The resonant frequencies and damping coefficient were estimated from free oscillations of the pendulum. The pendular motion of the three-dimensional pendulum will also be analyzed. We will compare our results with data from LIGO to understand the dynamics of the mirror.

  18. Heat and work fluctuations for a harmonic oscillator.

    PubMed

    Sabhapandit, Sanjib

    2012-02-01

    The formalism of Kundu et al. [J. Stat. Mech. P03007 (2011)], for computing the large deviations of heat flow in harmonic systems, is applied to the case of single Brownian particle in a harmonic trap and coupled to two heat baths at different temperatures. The large-τ form of the moment generating function ≈g(λ)exp[τμ(λ)], of the total heat flow Q from one of the baths to the particle in a given time interval τ, is studied and exact explicit expressions are obtained for both μ(λ) and g(λ). For a special case of the single particle problem that corresponds to the work done by an external stochastic force on a harmonic oscillator coupled to a thermal bath, the large-τ form of the moment generating function is analyzed to obtain the exact large deviation function as well as the complete asymptotic forms of the probability density function of the work.

  19. Entanglement prethermalization in an interaction quench between two harmonic oscillators

    NASA Astrophysics Data System (ADS)

    Ikeda, Tatsuhiko N.; Mori, Takashi; Kaminishi, Eriko; Ueda, Masahito

    2017-02-01

    Entanglement prethermalization (EP) refers to a quasi-stationary nonequilibrium state of a composite system in which each individual subsystem looks thermal but the entire system remains nonthermal due to quantum entanglement between subsystems. We theoretically study the dynamics of EP following a coherent split of a one-dimensional harmonic potential in which two interacting bosons are confined. This problem is equivalent to that of an interaction quench between two harmonic oscillators. We show that this simple model captures the bare essentials of EP; that is, each subsystem relaxes to an approximate thermal equilibrium, whereas the total system remains entangled. We find that a generalized Gibbs ensemble exactly describes the total system if we take into account nonlocal conserved quantities that act nontrivially on both subsystems. In the presence of a symmetry-breaking perturbation, the relaxation dynamics of the system exhibits a quasi-stationary EP plateau and eventually reaches thermal equilibrium. We analytically show that the lifetime of EP is inversely proportional to the magnitude of the perturbation.

  20. Calorimetric measurement of work for a driven harmonic oscillator

    NASA Astrophysics Data System (ADS)

    Sampaio, Rui; Suomela, Samu; Ala-Nissila, Tapio

    2016-12-01

    A calorimetric measurement has recently been proposed as a promising technique to measure thermodynamic quantities in a dissipative superconducting qubit. These measurements rely on the fact that the system is projected into energy eigenstates whenever energy is exchanged with the environment. This requirement imposes a restriction on the class of systems that can be measured in this way. Here we extend the calorimetric protocol to the measurement of work in a driven quantum harmonic oscillator. We employ a scheme based on a two-level approximation that makes use of an experimentally accessible quantity and show how it relates to the work obtained through the standard two-measurement protocol. We find that the average work is well approximated in the underdamped regime for short driving times and, in the overdamped regime, for any driving time. However, this approximation fails for the variance and higher moments of work at finite temperatures. Furthermore, we show how to relate the work statistics obtained through this scheme to the work statistics given by the two-measurement protocol.

  1. Entanglement dynamics for a conditionally kicked harmonic oscillator

    NASA Astrophysics Data System (ADS)

    Arrais, Eric G.; Sales, J. S.; de Almeida, N. G.

    2016-08-01

    The time evolution of the quantum kicked harmonic oscillator (KHO) is described by the Floquet operator which maps the state of the system immediately before one kick onto the state at a time immediately after the next. Quantum KHO is characterized by three parameters: the coupling strength V 0, the so-called Lamb-Dicke parameter η whose square is proportional to the effective Planck constant {{\\hslash }}{{eff}}, and the ratio T of the natural frequency of the oscillator and the kick frequency. To a given coupling strength and depending on T being a natural or irrational number, the phase space of the classical kicked oscillator can display different behaviors, as for example, stochastic webs or quasicrystal structures, thus showing a chaotic or localized behavior that is mirrored in the quantum phase space. On the other hand, the classical limit is studied letting {{\\hslash }}{{eff}} become negligible. In this paper we investigate how the ratio T, considered as integer, rational or irrational, influences the entanglement dynamics of the quantum KHO and study how the entanglement dynamics behaves when varying either V 0 or {{\\hslash }}{{eff}} parameters.

  2. On quantum harmonic oscillator being subjected to absolute potential state

    NASA Astrophysics Data System (ADS)

    Nityayogananda, Swami

    2017-01-01

    In a quantum harmonic oscillator (QHO), the energy of the oscillator increases with increased frequency. In this paper, assuming a boundary condition that the product of momentum and position, or the product of energy density and position remains constant in the QHO, it is established that a particle subjected to increasing frequencies becomes gradually subtler to transform into a very high dormant potential energy. This very high dormant potential energy is referred to as `like-potential' energy in this paper. In the process a new wave function is generated. This new function, which corresponds to new sets of particles, has scope to raise the quantum oscillator energy (QOE) up to infinity. It is proposed to show that this high energy does not get cancelled but remains dormant. Further, it is proposed that the displacement about the equilibrium goes to zero when the vibration of the oscillator stops and then the QOE becomes infinity - this needs further research. The more the QOE, the greater will be the degree of dormancy. A simple mathematical model has been derived here to discuss the possibilities that are involved in the QHO under the above-mentioned boundary conditions.

  3. Coherent states and uncertainty relations for the damped harmonic oscillator with time-dependent frequency

    NASA Technical Reports Server (NTRS)

    Yeon, Kyu-Hwang; Um, Chung-In; George, Thomas F.; Pandey, Lakshmi N.

    1993-01-01

    Starting with evaluations of propagator and wave function for the damped harmonic oscillator with time-dependent frequency, exact coherent states are constructed. These coherent states satisfy the properties which coherent states should generally have.

  4. Phase of the quantum harmonic oscillator with applications to optical polarization

    NASA Technical Reports Server (NTRS)

    Shepard, Scott R.

    1993-01-01

    The phase of the quantum harmonic oscillator, the temporal distribution of a particle in a square-well potential, and a quantum theory of angles are derived from a general theory of complementarity. Schwinger's harmonic oscillator model of angular momenta is modified for the case of photons. Angular distributions for systems of identical and distinguishable particles are discussed. Unitary and antiunitary time reversal operators are then presented and applied to optical polarization states in birefringent media.

  5. Brownian motion of a harmonic oscillator in a noninertial reference frame.

    PubMed

    Jiménez-Aquino, J I; Romero-Bastida, M

    2013-08-01

    The Brownian motion of a charged harmonic oscillator in the presence of additional force fields, such as a constant magnetic field and arbitrary time-dependent electric and mechanical forces, is studied in a rotational reference frame under uniform motion. By assuming an isotropic surrounding medium (a scalar friction constant), we solve explicitly the Smoluchowski equation associated with the Langevin equation for the charged harmonic oscillator and calculate the mean square displacements along and orthogonal to the rotation axis.

  6. Amplitude and phase representation of quantum invariants for the time-dependent harmonic oscillator

    SciTech Connect

    Fernandez Guasti, M.; Moya-Cessa, H.

    2003-06-01

    The correspondence between classical and quantum invariants is established. The Ermakov-Lewis quantum invariant of the time-dependent harmonic oscillator is translated from the coordinate and momentum operators into amplitude and phase operators. In doing so, Turski's phase operator as well as Susskind-Glogower operators are generalized to the time-dependent harmonic-oscillator case. A quantum derivation of the Manley-Rowe relations is shown as an example.

  7. Study of continuous variable entanglement in multipartite harmonic oscillator systems

    NASA Astrophysics Data System (ADS)

    Landau, Mayer Amitai

    In this thesis we investigate the entanglement of Schrodinger cat states that derive from harmonic oscillator models. In order to extend the finite dimensional framework of entanglement to the infinite dimensional case we consider only initial conditions that have some type of symmetry. Systems with symmetry usually have fewer important parameters. In our case, symmetry allows us to discard the bulk of the Hilbert space as irrelevant to our particular entanglement problem. We are then left with an effectively finite dimensional Hilbert space, and the developed entanglement framework can therefore be followed. The dimension we derive for the reduced Hilbert space in each subsystem is equal to the number of coherent states in the Schrodinger cat superposition. We investigate the entanglement vs. time of our Schrodinger cat state for closed and open systems. For closed systems, we place no limit on the number of coherently summed linearly independent coherent states. So the dimension of our effective Hilbert space can be quite high. We also place no restriction on the number of subsystems (or parties). Consequently, we use the entanglement measure developed by Barnum, Knill, Ortiz, and Viola (BKOV). This is the only measure to our knowledge that has no restriction on the dimension of the Hilbert space or the number of subsystems. We also place no constraint on the magnitude of our coherent states. The coherent value may be quite large, or quite small. We find that the entanglement of the Schrodinger cat state has nontrivial dependence on the above mentioned three variables. That is, the entanglement is a non-separable function of the values of the coherent states, the number of coherent states in the superposition, and the number of partitions of the Hilbert space. For open systems, we model the reservoir as a harmonic oscillator zero temperature bath. Due to the interactions with the bath the Schrodinger cat state becomes a mixed density matrix. To investigate the

  8. Generalized su(1,1) coherent states for pseudo harmonic oscillator and their nonclassical properties

    NASA Astrophysics Data System (ADS)

    Mojaveri, B.; Dehghani, A.

    2013-08-01

    In this paper we define a non-unitary displacement operator, which by acting on the vacuum state of the pseudo harmonic oscillator (PHO), generates new class of generalized coherent states (GCSs). An interesting feature of this approach is that, contrary to the Klauder-Perelomov and Barut-Girardello approaches, it does not require the existence of dynamical symmetries associated with the system under consideration. These states admit a resolution of the identity through positive definite measures on the complex plane. We have shown that the realization of these states for different values of the deformation parameters leads to the well-known Klauder-Perelomov and Barut-Girardello CSs associated with the su(1,1) Lie algebra. This is why we call them the generalized su(1,1) CSs for the PHO. Finally, study of some statistical characters such as squeezing, anti-bunching effect and sub-Poissonian statistics reveals that the constructed GCSs have indeed nonclassical features.

  9. Benchmark Calculation of Radial Expectation Value \\varvec{< r^{-2} \\rangle } for Confined Hydrogen-Like Atoms and Isotropic Harmonic Oscillators

    NASA Astrophysics Data System (ADS)

    Yu, Rong Mei; Zan, Li Rong; Jiao, Li Guang; Ho, Yew Kam

    2017-09-01

    Spatially confined atoms have been extensively investigated to model atomic systems in extreme pressures. For the simplest hydrogen-like atoms and isotropic harmonic oscillators, numerous physical quantities have been established with very high accuracy. However, the expectation value of < r^{-2} > which is of practical importance in many applications has significant discrepancies among calculations by different methods. In this work we employed the basis expansion method with cut-off Slater-type orbitals to investigate these two confined systems. Accurate values for several low-lying bound states were obtained by carefully examining the convergence with respect to the size of basis. A scaling law for < rn > was derived and it is used to verify the accuracy of numerical results. Comparison with other calculations show that the present results establish benchmark values for this quantity, which may be useful in future studies.

  10. Equilibration and thermalization of the dissipative quantum harmonic oscillator in a nonthermal environment.

    PubMed

    Pagel, D; Alvermann, A; Fehske, H

    2013-01-01

    We study the dissipative quantum harmonic oscillator with general nonthermal preparations of the harmonic oscillator bath. The focus is on equilibration of the oscillator in the long-time limit and the additional requirements for thermalization. Our study is based on the exact solution of the microscopic model obtained by means of operator equations of motion, which provides us with the time evolution of the central oscillator density matrix in terms of the propagating function. We find a hierarchy of conditions for thermalization, together with the relation of the asymptotic temperature to the energy distribution in the initial bath state. We discuss the presence and absence of equilibration for the example of an inhomogeneous chain of harmonic oscillators, and we illustrate the general findings about thermalization for the nonthermal environment that results from a quench.

  11. Planck scale corrections to the harmonic oscillator, coherent, and squeezed states

    NASA Astrophysics Data System (ADS)

    Bosso, Pasquale; Das, Saurya; Mann, Robert B.

    2017-09-01

    The generalized uncertainty principle (GUP) is a modification of Heisenberg's Principle predicted by several theories of quantum gravity. It consists of a modified commutator between the position and momentum. In this work, we compute potentially observable effects that GUP implies for the harmonic oscillator, coherent, and squeezed states in quantum mechanics. In particular, we rigorously analyze the GUP-perturbed harmonic oscillator Hamiltonian, defining new operators that act as ladder operators on the perturbed states. We use these operators to define the new coherent and squeezed states. We comment on potential applications.

  12. Anomalous diffusive behavior of a harmonic oscillator driven by a Mittag-Leffler noise.

    PubMed

    Viñales, A D; Wang, K G; Despósito, M A

    2009-07-01

    The diffusive behavior of a harmonic oscillator driven by a Mittag-Leffler noise is studied. Using the Laplace analysis we derive exact expressions for the relaxation functions of the particle in terms of generalized Mittag-Leffler functions and its derivatives from a generalized Langevin equation. Our results show that the oscillator displays an anomalous diffusive behavior. In the strictly asymptotic limit, the dynamics of the harmonic oscillator corresponds to an oscillator driven by a noise with a pure power-law autocorrelation function. However, at short and intermediate times the dynamics has qualitative difference due to the presence of the characteristic time of the noise.

  13. On the effects of a screw dislocation and a linear potential on the harmonic oscillator

    NASA Astrophysics Data System (ADS)

    Bueno, M. J.; Furtado, C.; Bakke, K.

    2016-09-01

    Quantum effects on the harmonic oscillator due to the presence of a linear scalar potential and a screw dislocation are investigated. By searching for bound states solutions, it is shown that an Aharonov-Bohm-type effect for bound states and a restriction of the values of the angular frequency of the harmonic oscillator can be obtained, where the allowed values are determined by the topology of the screw dislocation and the quantum numbers associated with the radial modes and the angular momentum. As particular cases, the angular frequency and the energy levels associated with the ground state and the first excited state of the system are obtained.

  14. Hamiltonian of mean force and a damped harmonic oscillator in an anisotropic medium

    NASA Astrophysics Data System (ADS)

    Jafari, Marjan; Kheirandish, Fardin

    2017-01-01

    The quantum dynamics of a damped harmonic oscillator is investigated in the presence of an anisotropic heat bath. The medium is modeled by a continuum of three dimensional harmonic oscillators and anisotropic coupling is treated by introducing tensor coupling functions. Starting from a classical Lagrangian, the total system is quantized in the framework of the canonical quantization. Following the Fano technique, the Hamiltonian of the system is diagonalized in terms of creation and annihilation operators that are linear combinations of the basic dynamical variables. Using the diagonalized Hamiltonian, the mean force internal energy, free energy and entropy of the damped oscillator are calculated.

  15. Time-dependent Hartree approximation and time-dependent harmonic oscillator model

    NASA Astrophysics Data System (ADS)

    Blaizot, J. P.; Schulz, H.

    1982-03-01

    We present an analytically soluble model for studying nuclear collective motion within the framework of the time-dependent Hartree (TDH) approximation. The model reduces the TDH equations to the Schrödinger equation of a time-dependent harmonic oscillator. Using canonical transformations and coherent states we derive a few properties of the time-dependent harmonic oscillator which are relevant for applications. We analyse the role of the normal modes in the time evolution of a system governed by TDH equations. We show how these modes couple together due to the anharmonic terms generated by the non-linearity of the theory.

  16. Generalized seniority on a deformed single-particle basis

    NASA Astrophysics Data System (ADS)

    Jia, L. Y.

    2017-09-01

    Recently, I proposed a fast computing scheme for generalized seniority on a spherical single-particle basis [J. Phys. G: Nucl. Part. Phys. 42, 115105 (2015), 10.1088/0954-3899/42/11/115105]. This work redesigns the scheme to make it applicable to deformed single-particle basis. The algorithm is applied to the rare-earth-metal nucleus 94 64 158Gd for intrinsic (body-fixed frame) neutron excitations under the low-momentum NN interaction Vlow -k. By allowing as many as four broken pairs, I compute the lowest 300 intrinsic states of several multipolarities. These states converge well to the exact ones, showing generalized seniority is very effective in truncating the deformed shell model. Under realistic interactions, the picture remains approximately valid: The ground state is a coherent pair condensate and the pairs gradually break up as excitation energy increases.

  17. Modeling Stretching Modes of Common Organic Molecules with the Quantum Mechanical Harmonic Oscillator: An Undergraduate Vibrational Spectroscopy Laboratory Exercise

    ERIC Educational Resources Information Center

    Parnis, J. Mark; Thompson, Matthew G. K.

    2004-01-01

    An introductory undergraduate physical organic chemistry exercise that introduces the harmonic oscillator's use in vibrational spectroscopy is developed. The analysis and modeling exercise begins with the students calculating the stretching modes of common organic molecules with the help of the quantum mechanical harmonic oscillator (QMHO) model.

  18. Modeling Stretching Modes of Common Organic Molecules with the Quantum Mechanical Harmonic Oscillator: An Undergraduate Vibrational Spectroscopy Laboratory Exercise

    ERIC Educational Resources Information Center

    Parnis, J. Mark; Thompson, Matthew G. K.

    2004-01-01

    An introductory undergraduate physical organic chemistry exercise that introduces the harmonic oscillator's use in vibrational spectroscopy is developed. The analysis and modeling exercise begins with the students calculating the stretching modes of common organic molecules with the help of the quantum mechanical harmonic oscillator (QMHO) model.

  19. On the damping of the angular momentum of a spherical harmonic oscillator as a model for heavy ion collisions

    SciTech Connect

    Isar, A.; Sandulescu, A. ); Scheid, W. )

    1990-05-01

    In the frame of the Lindblad theory of open quantum systems, the spherical harmonic oscillator with opening operators linear in the coordinates and the momenta of the considered system is analyzed. Explicit expressions for the damping of the energy, angular momentum and its projection, including the coupling of the harmonic oscillator due to the environment, are obtained.

  20. Discrete Excitation Spectrum of a Classical Harmonic Oscillator in Zero-Point Radiation

    NASA Astrophysics Data System (ADS)

    Huang, Wayne Cheng-Wei; Batelaan, Herman

    2015-03-01

    We report that upon excitation by a single pulse, a classical harmonic oscillator immersed in the classical electromagnetic zero-point radiation exhibits a discrete harmonic spectrum in agreement with that of its quantum counterpart. This result is interesting in view of the fact that the vacuum field is needed in the classical calculation to obtain the agreement.

  1. Nonsingular parametric oscillators Darboux-related to the classical harmonic oscillator

    NASA Astrophysics Data System (ADS)

    Rosu, H. C.; Cornejo-Pérez, O.; Chen, P.

    2012-12-01

    Interesting nonsingular parametric oscillators which are Darboux-related to the classical harmonic oscillator and have periodic dissipative/gain features are identified through a modified factorization method. The same method is applied to the upside-down (hyperbolic) “oscillator” for which the obtained Darboux partners show transient underdamped features.

  2. The Adiabatic Invariant of the n-Degree-of-Freedom Harmonic Oscillator

    ERIC Educational Resources Information Center

    Devaud, M.; Leroy, V.; Bacri, J.-C.; Hocquet, T.

    2008-01-01

    In this graduate-level theoretical paper, we propose a general derivation of the adiabatic invariant of the n-degree-of-freedom harmonic oscillator, available whichever the physical nature of the oscillator and of the parametrical excitation it undergoes. This derivation is founded on the use of the classical Glauber variables and ends up with…

  3. Fisher Information and Shannon Entropy in Confined 1D Harmonic Oscillator

    SciTech Connect

    Stevanovic, Ljiljana

    2010-01-21

    Study of the linear harmonic oscillator confined in the square well with impenetrable walls is of great interest since its application for modeling parabolic quantum well semiconductor heterostructures. Fisher information and Shannon entropy, as a complexity measure for its ground and some excited energy levels are reported here.

  4. Note on the Time-Dependent Damped and Forced Harmonic Oscillator.

    ERIC Educational Resources Information Center

    Leach, P. G. L.

    1978-01-01

    A Hamiltonian for the time-dependent damped and forced harmonic oscillator is derived. A simple time-dependent linear canonical transformation transforms the Hamiltonian to one whose solution is readily obtained. The wave function for the corresponding quantum mechanical problem is given. (Author/GA)

  5. The harmonic oscillator and the position dependent mass Schroedinger equation: isospectral partners and factorization operators

    SciTech Connect

    Morales, J.; Ovando, G.; Pena, J. J.

    2010-12-23

    One of the most important scientific contributions of Professor Marcos Moshinsky has been his study on the harmonic oscillator in quantum theory vis a vis the standard Schroedinger equation with constant mass [1]. However, a simple description of the motion of a particle interacting with an external environment such as happen in compositionally graded alloys consist of replacing the mass by the so-called effective mass that is in general variable and dependent on position. Therefore, honoring in memoriam Marcos Moshinsky, in this work we consider the position-dependent mass Schrodinger equations (PDMSE) for the harmonic oscillator potential model as former potential as well as with equi-spaced spectrum solutions, i.e. harmonic oscillator isospectral partners. To that purpose, the point canonical transformation method to convert a general second order differential equation (DE), of Sturm-Liouville type, into a Schroedinger-like standard equation is applied to the PDMSE. In that case, the former potential associated to the PDMSE and the potential involved in the Schroedinger-like standard equation are related through a Riccati-type relationship that includes the equivalent of the Witten superpotential to determine the exactly solvable positions-dependent mass distribution (PDMD)m(x). Even though the proposed approach is exemplified with the harmonic oscillator potential, the procedure is general and can be straightforwardly applied to other DEs.

  6. Novel Approach for Solving the Equation of Motion of a Simple Harmonic Oscillator. Classroom Notes

    ERIC Educational Resources Information Center

    Gauthier, N.

    2004-01-01

    An elementary method, based on the use of complex variables, is proposed for solving the equation of motion of a simple harmonic oscillator. The method is first applied to the equation of motion for an undamped oscillator and it is then extended to the more important case of a damped oscillator. It is finally shown that the method can readily be…

  7. Generalized uncertainty principle corrections to the simple harmonic oscillator in phase space

    NASA Astrophysics Data System (ADS)

    Das, Saurya; Robbins, Matthew P. G.; Walton, Mark A.

    2016-01-01

    We compute Wigner functions for the harmonic oscillator including corrections from generalized uncertainty principles (GUPs), and study the corresponding marginal probability densities and other properties. We show that the GUP corrections to the Wigner functions can be significant, and comment on their potential measurability in the laboratory.

  8. Note on the Time-Dependent Damped and Forced Harmonic Oscillator.

    ERIC Educational Resources Information Center

    Leach, P. G. L.

    1978-01-01

    A Hamiltonian for the time-dependent damped and forced harmonic oscillator is derived. A simple time-dependent linear canonical transformation transforms the Hamiltonian to one whose solution is readily obtained. The wave function for the corresponding quantum mechanical problem is given. (Author/GA)

  9. The Adiabatic Invariant of the n-Degree-of-Freedom Harmonic Oscillator

    ERIC Educational Resources Information Center

    Devaud, M.; Leroy, V.; Bacri, J.-C.; Hocquet, T.

    2008-01-01

    In this graduate-level theoretical paper, we propose a general derivation of the adiabatic invariant of the n-degree-of-freedom harmonic oscillator, available whichever the physical nature of the oscillator and of the parametrical excitation it undergoes. This derivation is founded on the use of the classical Glauber variables and ends up with…

  10. Convergence for Fourier Series Solutions of the Forced Harmonic Oscillator II

    ERIC Educational Resources Information Center

    Fay, Temple H.

    2002-01-01

    This paper compliments two recent articles by the author in this journal concerning solving the forced harmonic oscillator equation when the forcing is periodic. The idea is to replace the forcing function by its Fourier series and solve the differential equation term-by-term. Herein the convergence of such series solutions is investigated when…

  11. Adaptive radial basis function mesh deformation using data reduction

    NASA Astrophysics Data System (ADS)

    Gillebaart, T.; Blom, D. S.; van Zuijlen, A. H.; Bijl, H.

    2016-09-01

    Radial Basis Function (RBF) mesh deformation is one of the most robust mesh deformation methods available. Using the greedy (data reduction) method in combination with an explicit boundary correction, results in an efficient method as shown in literature. However, to ensure the method remains robust, two issues are addressed: 1) how to ensure that the set of control points remains an accurate representation of the geometry in time and 2) how to use/automate the explicit boundary correction, while ensuring a high mesh quality. In this paper, we propose an adaptive RBF mesh deformation method, which ensures the set of control points always represents the geometry/displacement up to a certain (user-specified) criteria, by keeping track of the boundary error throughout the simulation and re-selecting when needed. Opposed to the unit displacement and prescribed displacement selection methods, the adaptive method is more robust, user-independent and efficient, for the cases considered. Secondly, the analysis of a single high aspect ratio cell is used to formulate an equation for the correction radius needed, depending on the characteristics of the correction function used, maximum aspect ratio, minimum first cell height and boundary error. Based on the analysis two new radial basis correction functions are derived and proposed. This proposed automated procedure is verified while varying the correction function, Reynolds number (and thus first cell height and aspect ratio) and boundary error. Finally, the parallel efficiency is studied for the two adaptive methods, unit displacement and prescribed displacement for both the CPU as well as the memory formulation with a 2D oscillating and translating airfoil with oscillating flap, a 3D flexible locally deforming tube and deforming wind turbine blade. Generally, the memory formulation requires less work (due to the large amount of work required for evaluating RBF's), but the parallel efficiency reduces due to the limited

  12. On the Quantum Potential and Pulsating Wave Packet in the Harmonic Oscillator

    SciTech Connect

    Dubois, Daniel M.

    2008-10-17

    A fundamental mathematical formalism related to the Quantum Potential factor, Q, is presented in this paper. The Schroedinger equation can be transformed to two equations depending on a group velocity and a density of presence of the particle. A factor, in these equations, was called ''Quantum Potential'' by D. Bohm and B. Hiley. In 1999, I demonstrated that this Quantum Potential, Q, can be split in two Quantum Potentials, Q{sub 1}, and Q{sub 2}, for which the relation, Q=Q{sub 1}+Q{sub 2}, holds. These two Quantum Potentials depend on a fundamental new variable, what I called a phase velocity, u, directly related to the probability density of presence of the wave-particle, given by the modulus of the wave function. This paper gives some further developments for explaining the Quantum Potential for oscillating and pulsating Gaussian wave packets in the Harmonic Oscillator. It is shown that the two Quantum Potentials play a central role in the interpretation of quantum mechanics. A breakthrough in the formalism of the Quantum Mechanics could be provoked by the physical properties of these Quantum Potentials. The probability density of presence of the oscillating and pulsating Gaussian wave packets in the Harmonic Oscillator is directly depending on the ratio Q{sub 2}/Q{sub 1} of the two Quantum Potentials. In the general case, the energy of these Gaussian wave packets is not constant, but is oscillating. The energy is given by the sum of the kinetic energy, T, the potential energy, V, and the two Quantum Potentials: E=T+V+Q{sub 1}+Q{sub 2}. For some conditions, given in the paper, the energy can be a constant. The first remarkable result is the fact that the first Quantum Potential, Q{sub 1}, is related to the ground state energy, E{sub 0}, of the Quantum Harmonic Oscillator: Q{sub 1}=h-bar {omega}/2=E{sub 0}. The second result is related to the property of the second Quantum Potential, Q{sub 2}, which plays the role of an anti-potential, Q{sub 2}=-V(x), where V is

  13. A study of the orthogonal polynomials associated with the quantum harmonic oscillator on constant curvature spaces

    NASA Astrophysics Data System (ADS)

    Vignat, C.; Lamberti, P. W.

    2009-10-01

    Recently, Cariñena, et al. [Ann. Phys. 322, 434 (2007)] introduced a new family of orthogonal polynomials that appear in the wave functions of the quantum harmonic oscillator in two-dimensional constant curvature spaces. They are a generalization of the Hermite polynomials and will be called curved Hermite polynomials in the following. We show that these polynomials are naturally related to the relativistic Hermite polynomials introduced by Aldaya et al. [Phys. Lett. A 156, 381 (1991)], and thus are Jacobi polynomials. Moreover, we exhibit a natural bijection between the solutions of the quantum harmonic oscillator on negative curvature spaces and on positive curvature spaces. At last, we show a maximum entropy property for the ground states of these oscillators.

  14. Entropy evolution of a damped harmonic oscillator driven by quasimonochromatic noise and external periodic force

    NASA Astrophysics Data System (ADS)

    Qin, Jie; Ning, Lijuan

    2017-08-01

    This paper addresses the entropy evolution of a damped harmonic oscillator driven by quasimonochromatic noise (QMN). Due to QMN is distinct from white noise, so this paper studied the effect of QMN noise on the upper bound of time derivative of entropy for a damped harmonic oscillator. Through the comparison of probability density function (PDF) and the upper bound for the time derivative of entropy, we find that the entropy evolution is also a useful tool to describe the system dynamic behavior. Then we discuss the interplay of the parameters of QMN, damping constant, the frequency of oscillator and external periodic force and their effects on the upper bound for the rate of entropy change. Finally, some beneficial conclusions are obtained.

  15. Coherent dynamics of a flux qubit coupled to a harmonic oscillator.

    PubMed

    Chiorescu, I; Bertet, P; Semba, K; Nakamura, Y; Harmans, C J P M; Mooij, J E

    2004-09-09

    In the emerging field of quantum computation and quantum information, superconducting devices are promising candidates for the implementation of solid-state quantum bits (qubits). Single-qubit operations, direct coupling between two qubits and the realization of a quantum gate have been reported. However, complex manipulation of entangled states-such as the coupling of a two-level system to a quantum harmonic oscillator, as demonstrated in ion/atom-trap experiments and cavity quantum electrodynamics-has yet to be achieved for superconducting devices. Here we demonstrate entanglement between a superconducting flux qubit (a two-level system) and a superconducting quantum interference device (SQUID). The latter provides the measurement system for detecting the quantum states; it is also an effective inductance that, in parallel with an external shunt capacitance, acts as a harmonic oscillator. We achieve generation and control of the entangled state by performing microwave spectroscopy and detecting the resultant Rabi oscillations of the coupled system.

  16. Coupled harmonic oscillators for the measurement of a weak classical force at the standard quantum limit

    SciTech Connect

    Leaci, Paola; Ortolan, Antonello

    2007-12-15

    We discuss limitations in precision measurements of a weak classical force coupled to quantum mechanical systems, the so-called standard quantum limit (SQL). Among the several contexts exploiting the measurement of classical signals, gravitational wave (GW) detection is of paramount importance. In this framework, we analyze the quantum limited sensitivity of a free test mass, a quantum mechanical harmonic oscillator, two harmonic oscillators with equal masses and different resonance frequencies, and finally two mechanical oscillators with different masses and resonating at the same frequency. The sensitivity analysis of the latter two cases illustrates the potentialities of back-action reduction and classical impedance matching schemes, respectively. By examining coupled quantum oscillators as detectors of classical signals, we found a viable path to approach the SQL for planned or operating GW detectors, such as DUAL and AURIGA.

  17. Damped harmonic oscillator model for analyzing the dynamic characteristics of STM system

    NASA Astrophysics Data System (ADS)

    Liu, A. P.; Yao, X. X.; Wang, X.; Yang, D. X.; Zhang, X. M.

    2015-09-01

    Recognizing and distinguishing the dynamic characteristics of scanning tunneling microscopy (STM) system is fatal for studying STM image. In this paper, a method for analyzing system’s characteristics by using a damped harmonic oscillator model is presented. The model is driven by random force and all of its properties are described by damping and periodic. For the general solution of such harmonic oscillator’s Langevin equation is deduced and the auto-correlation function (ACF) is obtained for fitting curve. It is shown that damping and periodic property of the two curves have a good agreement by comparing the fitting curve with the auto-correlation curve of time series dates which are acquired by STM. It could be concluded that the damped harmonic oscillator model and auto-correlation method are feasible for analyzing the dynamic characteristics of STM system.

  18. Bound States Energies of a Harmonic Oscillator Perturbed by Point Interactions

    NASA Astrophysics Data System (ADS)

    Ferkous, N.; Boudjedaa, T.

    2017-03-01

    We determine explicitly the exact transcendental bound states energies equation for a one-dimensional harmonic oscillator perturbed by a single and a double point interactions via Green’s function techniques using both momentum and position space representations. The even and odd solutions of the problem are discussed. The corresponding limiting cases are recovered. For the harmonic oscillator with a point interaction in more than one dimension, divergent series appear. We use to remove this divergence an exponential regulator and we obtain a transcendental equation for the energy bound states. The results obtained here are consistent with other investigations using different methods. Supported by the Algerian Ministry of Higher Education and Scientific Research under the CNEPRU project No. D01720140001

  19. Equilibrium and stationary nonequilibrium states in a chain of colliding harmonic oscillators

    PubMed

    Sano

    2000-02-01

    Equilibrium and nonequilibrium properties of a chain of colliding harmonic oscillators (ding-dong model) are investigated. Our chain is modeled as harmonically bounded particles that can only interact with neighboring particles by hard-core interaction. Between the collisions, particles are just independent harmonic oscillators. We are especially interested in the stationary nonequilibrium state of the ding-dong model coupled with two stochastic heat reservoirs (not thermostated) at the ends, whose temperature is different. We check the Gallavotti-Cohen fluctuation theorem [G. Gallavoti and E. G. D. Cohen, Phys. Rev. Lett. 74, 2694 (1995)] and also the Evans-Searles identity [D. Evans and D. Searles, Phys. Rev. E. 50, 1994 (1994)] numerically. It is verified that the former theorem is satisfied for this system, although the system is not a thermostated system.

  20. Transformations of the perturbed two-body problem to unperturbed harmonic oscillators

    NASA Technical Reports Server (NTRS)

    Szebehely, V.; Bond, V.

    1983-01-01

    Singular, nonlinear, and Liapunov unstable equations are made regular and linear through transformations that change the perturbed planar problem of two bodies into unperturbed and undamped harmonic oscillators with constant coefficients, so that the stable solution may be immediately written in terms of the new variables. The use of arbitrary and special functions for the transformations allows the systematic discussion of previously introduced and novel anomalies. For the case of the unperturbed two-body problem, it is proved that if transformations are power functions of the radial variable, only the eccentric and the true anomalies (with the corresponding transformations of the radial variable) will result in harmonic oscillators. The present method significantly reduces computation requirements in autonomous space operations.

  1. Experimental demonstration of a technique for generation of arbitrary harmonic oscillator states.

    NASA Astrophysics Data System (ADS)

    Ben-Kish, A.; Demarco, B.; Rowe, M.; Meyer, V.; Britton, J.; Itano, W. M.; Jelenković, B. M.; Langer, C.; Leibfried, D.; Rosenband, T.; Wineland, D. J.

    2002-05-01

    Synthesizing arbitrary quantum states is at the heart of such diverse fields as quantum computation and reaction control in chemistry. For harmonic oscillator states, particular interactions (in general, non-linear) can be used to generate special states such as squeezed states. However, it is usually intractable to realize the interactions required to create arbitrary states. Law and Eberly [1] have devised a technique for arbitrary harmonic oscillator state generation that couples the oscillator to a two-level atomic or spin system and applies a sequence of operations that use simple interactions. We demonstrate the general features of this technique on the harmonic motion of a single trapped ^9Be^+ ion and extend it to the generation of arbitrary spin-oscillator states [2]. [1] C. K. Law and J. H. Eberly, Phys. Rev. Lett. 76, 1055 (1996). [2] B. Kneer and C. K. Law, Phys. Rev. A 57, 2096 (1998).

  2. Superdiffusion of Energy in a Chain of Harmonic Oscillators with Noise

    NASA Astrophysics Data System (ADS)

    Jara, Milton; Komorowski, Tomasz; Olla, Stefano

    2015-10-01

    We consider a one dimensional infinite chain of harmonic oscillators whose dynamics is perturbed by a stochastic term conserving energy and momentum. We prove that in the unpinned case the macroscopic evolution of the energy converges to the solution of the fractional diffusion equation . For a pinned system we prove that its energy evolves diffusively, generalizing some results of Basile and Olla (J. Stat. Phys. 155(6):1126-1142, 2014).

  3. Transient energy excitation in shortcuts to adiabaticity for the time-dependent harmonic oscillator

    SciTech Connect

    Chen Xi; Muga, J. G.

    2010-11-15

    We study for the time-dependent harmonic oscillator the transient energy excitation in speed-up processes ('shortcuts to adiabaticity') designed to reproduce the initial populations at some predetermined final frequency and time. We provide lower bounds and examples. Implications for the limits imposed to the process times and for the principle of unattainability of the absolute zero, in a single expansion or in quantum refrigerator cycles, are drawn.

  4. Quantum-trajectory approach to the stochastic thermodynamics of a forced harmonic oscillator.

    PubMed

    Horowitz, Jordan M

    2012-03-01

    I formulate a quantum stochastic thermodynamics for the quantum trajectories of a continuously monitored forced harmonic oscillator coupled to a thermal reservoir. Consistent trajectory-dependent definitions are introduced for work, heat, and entropy, through engineering the thermal reservoir from a sequence of two-level systems. Within this formalism the connection between irreversibility and entropy production is analyzed and confirmed by proving a detailed fluctuation theorem for quantum trajectories. Finally, possible experimental verifications are discussed.

  5. Calculation of the convex roof for an open entangled harmonic oscillator system

    SciTech Connect

    Landau, Mayer A.; Stroud, C. R. Jr.

    2010-05-15

    We explicitly calculate the time dependence of entanglement via the convex roof extension for a system of noninteracting harmonic oscillators. These oscillators interact only indirectly with each other by way of a zero-temperature bath. The initial state of the oscillators is taken to be that of an entangled Schroedinger-cat state. This type of initial condition leads to superexponential decay of the entanglement when the initial state has the same symmetry as the interaction Hamiltonian.

  6. Geometric phase and topology of elastic oscillations and vibrations in model systems: Harmonic oscillator and superlattice

    NASA Astrophysics Data System (ADS)

    Deymier, P. A.; Runge, K.; Vasseur, J. O.

    2016-12-01

    We illustrate the concept of geometric phase in the case of two prototypical elastic systems, namely the one-dimensional harmonic oscillator and a one-dimensional binary superlattice. We demonstrate formally the relationship between the variation of the geometric phase in the spectral and wave number domains and the parallel transport of a vector field along paths on curved manifolds possessing helicoidal twists which exhibit non-conventional topology.

  7. Dynamics of SU(1,1) coherent states for the damped harmonic oscillator

    SciTech Connect

    Choi, Jeong Ryeol; Yeon, Kyu Hwang

    2009-05-15

    Gerry, Ma, and Vrscay [Phys. Rev. A 39, 668 (1989)] studied the time evolution of SU(1,1) coherent states for the damped harmonic oscillator by introducing the Kanai-Caldirola Hamiltonian. The purposes of this Brief Report are to demonstrate that there are somewhat serious errors on their results and to correct them. Most of the figures given in their work are reproduced with correction in order to facilitate our explanation of results.

  8. Quantum optics. Quantum harmonic oscillator state synthesis by reservoir engineering.

    PubMed

    Kienzler, D; Lo, H-Y; Keitch, B; de Clercq, L; Leupold, F; Lindenfelser, F; Marinelli, M; Negnevitsky, V; Home, J P

    2015-01-02

    The robust generation of quantum states in the presence of decoherence is a primary challenge for explorations of quantum mechanics at larger scales. Using the mechanical motion of a single trapped ion, we utilize reservoir engineering to generate squeezed, coherent, and displaced-squeezed states as steady states in the presence of noise. We verify the created state by generating two-state correlated spin-motion Rabi oscillations, resulting in high-contrast measurements. For both cooling and measurement, we use spin-oscillator couplings that provide transitions between oscillator states in an engineered Fock state basis. Our approach should facilitate studies of entanglement, quantum computation, and open-system quantum simulations in a wide range of physical systems. Copyright © 2015, American Association for the Advancement of Science.

  9. Steady-state entanglement of harmonic oscillators via dissipation in a single superconducting artificial atom

    NASA Astrophysics Data System (ADS)

    Wang, Fei; Nie, Wei; Feng, Xunli; Oh, C. H.

    2016-07-01

    The correlated emission lasing (CEL) is experimentally demonstrated in harmonic oscillators coupled via a single three-level artificial atom [Phys. Rev. Lett. 115, 223603 (2015), 10.1103/PhysRevLett.115.223603] in which two-mode entanglement only exists in a certain time period when the harmonic oscillators are resonant with the atomic transitions. Here we examine this system and show that it is possible to obtain the steady-state entanglement when the two harmonic oscillators are resonant with Rabi sidebands. Applying dressed atomic states and Bogoliubov-mode transformation, we obtain the analytical results of the variance sum of a pair of Einstein-Podolsky-Rosen (EPR)-like operators. The stable entanglement originates from the dissipation process of the Bogoliubov modes because the atomic system can act as a reservoir in dressed state representation. We also show that the entanglement is robust against the dephasing rates of the superconducing atom, which is expected to have important applications in quantum information processing.

  10. Derivation of exact master equation with stochastic description: dissipative harmonic oscillator.

    PubMed

    Li, Haifeng; Shao, Jiushu; Wang, Shikuan

    2011-11-01

    A systematic procedure for deriving the master equation of a dissipative system is reported in the framework of stochastic description. For the Caldeira-Leggett model of the harmonic-oscillator bath, a detailed and elementary derivation of the bath-induced stochastic field is presented. The dynamics of the system is thereby fully described by a stochastic differential equation, and the desired master equation would be acquired with statistical averaging. It is shown that the existence of a closed-form master equation depends on the specificity of the system as well as the feature of the dissipation characterized by the spectral density function. For a dissipative harmonic oscillator it is observed that the correlation between the stochastic field due to the bath and the system can be decoupled, and the master equation naturally results. Such an equation possesses the Lindblad form in which time-dependent coefficients are determined by a set of integral equations. It is proved that the obtained master equation is equivalent to the well-known Hu-Paz-Zhang equation based on the path-integral technique. The procedure is also used to obtain the master equation of a dissipative harmonic oscillator in time-dependent fields.

  11. Using harmonic oscillators to determine the spot size of Hermite-Gaussian laser beams

    NASA Technical Reports Server (NTRS)

    Steely, Sidney L.

    1993-01-01

    The similarity of the functional forms of quantum mechanical harmonic oscillators and the modes of Hermite-Gaussian laser beams is illustrated. This functional similarity provides a direct correlation to investigate the spot size of large-order mode Hermite-Gaussian laser beams. The classical limits of a corresponding two-dimensional harmonic oscillator provide a definition of the spot size of Hermite-Gaussian laser beams. The classical limits of the harmonic oscillator provide integration limits for the photon probability densities of the laser beam modes to determine the fraction of photons detected therein. Mathematica is used to integrate the probability densities for large-order beam modes and to illustrate the functional similarities. The probabilities of detecting photons within the classical limits of Hermite-Gaussian laser beams asymptotically approach unity in the limit of large-order modes, in agreement with the Correspondence Principle. The classical limits for large-order modes include all of the nodes for Hermite Gaussian laser beams; Sturm's theorem provides a direct proof.

  12. Noncommutative quantum mechanics of a harmonic oscillator under linearized gravitational waves

    SciTech Connect

    Saha, Anirban; Gangopadhyay, Sunandan; Saha, Swarup

    2011-01-15

    We consider the quantum dynamics of a harmonic oscillator in noncommutative space under the influence of linearized gravitational waves (GWs) in the long-wavelength and low-velocity limit. Following the prescription in Saha and Gangopadhyay [Phys. Lett. B 681, 96 (2009)] we quantize the system. The Hamiltonian of the system is solved by using standard algebraic iterative methods. The solution shows signatures of the coordinate noncommutativity via alterations in the oscillation frequency of the harmonic oscillator system from its commutative counterpart. Moreover, it is found that the response of the harmonic oscillator to periodic GWs, when their frequencies match, will oscillate with a time scale imposed by the noncommutative parameter. We expect this noncommutative signature to show up as some noise source in the GW detection experiments since the recent phenomenological upper bounds set on the spatial noncommutative parameter imply a length scale comparable to the length variations due to the passage of gravitational waves, detectable in the present-day GW detectors.

  13. Brownian motion of a classical harmonic oscillator in a magnetic field.

    PubMed

    Jiménez-Aquino, J I; Velasco, R M; Uribe, F J

    2008-05-01

    In this paper, the stochastic diffusion process of a charged classical harmonic oscillator in a constant magnetic field is exactly described through the analytical solution of the associated Langevin equation. Due to the presence of the magnetic field, stochastic diffusion takes place across and along the magnetic field. Along the magnetic field, the Brownian motion is exactly the same as that of the ordinary one-dimensional classical harmonic oscillator, which was very well described in Chandrasekhar's celebrated paper [Rev. Mod. Phys. 15, 1 (1943)]. Across the magnetic field, the stochastic process takes place on a plane, perpendicular to the magnetic field. For internally Gaussian white noise, this planar-diffusion process is exactly described through the first two moments of the positions and velocities and their corresponding cross correlations. In the absence of the magnetic field, our analytical results are the same as those calculated by Chandrasekhar for the ordinary harmonic oscillator. The stochastic planar diffusion is also well characterized in the overdamped approximation, through the solutions of the Langevin equation.

  14. Containment control for coupled harmonic oscillators with multiple leaders under directed topology

    NASA Astrophysics Data System (ADS)

    Xu, Chengjie; Zheng, Ying; Su, Housheng; Wang, Hua O.

    2015-02-01

    This paper investigates the problem of containment control for coupled harmonic oscillators with multiple leaders under directed topology. Using tools from matrix, graph and stability theories, necessary and sufficient conditions are obtained for coupled harmonic oscillators under continuous-time and sampled-data-based protocols, respectively. When the continuous-time protocol is used, it is proved that every follower will ultimately converge to the convex hull spanned by the leaders if and only if there exists at least one leader that has a directed path to that follower at any time. When the sampled-data-based protocol is used, it is shown that the containment can be achieved if and only if: (1) an appropriate sampling period is chosen and (2) for every follower, there exists at least one leader that has a directed path to that follower at any time. And we also give the containment conditions for coupled harmonic oscillators under undirected topology as a special case. Finally, numerical simulations are presented to illustrate the theoretical findings.

  15. The harmonic oscillator on Riemannian and Lorentzian configuration spaces of constant curvature

    NASA Astrophysics Data System (ADS)

    Cariñena, José F.; Rañada, Manuel F.; Santander, Mariano

    2008-03-01

    The harmonic oscillator as a distinguished dynamical system can be defined not only on the Euclidean plane but also on the sphere and on the hyperbolic plane, and more generally on any configuration space with constant curvature and metric of any signature, either Riemannian (definite positive) or Lorentzian (indefinite). In this paper we study the main properties of these "curved" harmonic oscillators simultaneously on any such configuration space, using a Cayley-Klein (CK)-type approach, with two free parameters κ1,κ2 which altogether correspond to the possible values for curvature and signature type: the generic Riemannian and Lorentzian spaces of constant curvature (sphere S2, hyperbolic plane H2, AntiDeSitter sphere AdS1+1, and DeSitter sphere dS1+1) appear in this family, with Euclidean and Minkowski spaces as flat particular cases. We solve the equations of motion for the curved harmonic oscillator and obtain explicit expressions for the orbits by using three different methods: by direct integration, by obtaining the general CK version of Binet's equation, and finally as a consequence of its superintegrable character. The orbits are conics with center at the potential origin on any CK space, thereby extending this well known Euclidean property to any constant curvature configuration space. The final part of the article, that has a more geometric character, presents pertinent results of the theory of conics on spaces of constant curvature.

  16. Multiparameter deformation theory for quantum confined systems

    SciTech Connect

    Aleixo, A. N. F.; Balantekin, A. B.

    2009-11-15

    We introduce a generalized multiparameter deformation theory applicable to all supersymmetric and shape-invariant systems. Taking particular choices for the deformation factors used in the construction of the deformed ladder operators, we show that we can generalize the one-parameter quantum-deformed harmonic oscillator models and build alternative multiparameter deformed models that are also shape invariant like the primary undeformed system.

  17. HOTB: High precision parallel code for calculation of four-particle harmonic oscillator transformation brackets

    NASA Astrophysics Data System (ADS)

    Stepšys, A.; Mickevicius, S.; Germanas, D.; Kalinauskas, R. K.

    2014-11-01

    This new version of the HOTB program for calculation of the three and four particle harmonic oscillator transformation brackets provides some enhancements and corrections to the earlier version (Germanas et al., 2010) [1]. In particular, new version allows calculations of harmonic oscillator transformation brackets be performed in parallel using MPI parallel communication standard. Moreover, higher precision of intermediate calculations using GNU Quadruple Precision and arbitrary precision library FMLib [2] is done. A package of Fortran code is presented. Calculation time of large matrices can be significantly reduced using effective parallel code. Use of Higher Precision methods in intermediate calculations increases the stability of algorithms and extends the validity of used algorithms for larger input values. Catalogue identifier: AEFQ_v4_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEFQ_v4_0.html Program obtainable from: CPC Program Library, Queen’s University of Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 Number of lines in programs, including test data, etc.: 1711 Number of bytes in distributed programs, including test data, etc.: 11667 Distribution format: tar.gz Program language used: FORTRAN 90 with MPI extensions for parallelism Computer: Any computer with FORTRAN 90 compiler Operating system: Windows, Linux, FreeBSD, True64 Unix Has the code been vectorized of parallelized?: Yes, parallelism using MPI extensions. Number of CPUs used: up to 999 RAM(per CPU core): Depending on allocated binomial and trinomial matrices and use of precision; at least 500 MB Catalogue identifier of previous version: AEFQ_v1_0 Journal reference of previous version: Comput. Phys. Comm. 181, Issue 2, (2010) 420-425 Does the new version supersede the previous version? Yes Nature of problem: Calculation of matrices of three-particle harmonic oscillator brackets (3HOB) and four-particle harmonic oscillator brackets (4HOB) in a more

  18. Single particle calculations for a Woods-Saxon potential with triaxial deformations, and large Cartesian oscillator basis

    NASA Astrophysics Data System (ADS)

    Mohammed-Azizi, B.; Medjadi, D. E.

    2004-01-01

    ). Method of solution: The representative matrix of the Hamiltonian is built by means of the Cartesian basis of the anisotropic harmonic oscillator, and then diagonalized by a set of subroutines of the Eispack library. Two quadrature methods of Gauss are employed to calculate respectively the integrals of the matrix elements of the Hamiltonian, and the integral defining the Coulomb potential. Restrictions: There are two restrictions for the code: The number of the major shells of the basis does not have to exceed Nmax=26. For the largest values of Nmax (˜23-26), the diagonalization takes the major part of the running time, but the global run-time remains reasonable. Typical running time: (With full optimization in the project settings of the Microsoft Visual Fortran 5.0A on Windows XP.) With Nmax=23, for the neutrons case, and for both parities, if we need all eigenenergies and all eigenfunctions of the bound states, the running time is about 80 sec on the AMD Athlon computer at 1 GHz. In this case, the calculation of the matrix elements takes only about 20 sec. If all unbound states are required, the runtime becomes larger.

  19. Single particle calculations for a Woods Saxon potential with triaxial deformations, and large Cartesian oscillator basis (new version code)

    NASA Astrophysics Data System (ADS)

    Mohammed-Azizi, B.; Medjadi, D. E.

    2007-05-01

    and the single particle wave functions are calculated from one-body Hamiltonian including a central field of Woods-Saxon type, a spin-orbit interaction, and the Coulomb potential for the protons. We consider only ellipsoidal (triaxial) shapes. The deformation of the nuclear shape is fixed by the usual Bohr parameters (β,γ). Method of solution: The representative matrix of the Hamiltonian is built by means of the Cartesian basis of the anisotropic harmonic oscillator, and then diagonalized by a set of subroutines of the EISPACK library. Two quadrature methods of Gauss are employed to calculate, respectively, the integrals of the matrix elements of the Hamiltonian, and the integral defining the Coulomb potential. Restrictions: There are two restrictions for the code: The number of the major shells of the basis does not have to exceed N=26. For the largest values of N (˜23-26), the diagonalization takes the major part of the running time, but the global run-time remains reasonable. Typical running time: (With full optimization in the project settings of the Compaq Visual Fortran on Windows XP) With N=23, for the neutrons case, and for both parities, the running time is about 40 sec on the P4 computer at 2.6 GHz. In this case, the calculation of the matrix elements takes only about 17 sec. If all unbound states are required, the runtime becomes larger.

  20. Condition for equivalence of q-deformed and anharmonic oscillators

    NASA Technical Reports Server (NTRS)

    Artoni, M.; Zang, Jun; Birman, Joseph L.

    1993-01-01

    The equivalence between the q-deformed harmonic oscillator and a specific anharmonic oscillator model, by which some new insight into the problem of the physical meaning of the parameter q can be attained, are discussed.

  1. Resonant behavior of a harmonic oscillator with fluctuating mass driven by a Mittag-Leffler noise

    NASA Astrophysics Data System (ADS)

    Zhong, Suchuan; Yang, Jianqiang; Zhang, Lu; Ma, Hong; Luo, Maokang

    2017-02-01

    The resonant behavior of a generalized Langevin equation (GLE) in the presence of a Mittag-Leffler noise is studied analytically in this paper. Considering that a GLE with a Mittag-Leffler friction kernel is very useful for modeling anomalous diffusion processes with long-memory and long-range dependence, and the surrounding molecules do not only collide with the Brownian particle but also adhere to the Brownian particle for random time. Thus, we consider the Brownian particle with fluctuating mass, and the fluctuations of the mass are modelled as a dichotomous noise. Applying the stochastic averaging method, we obtain the exact expression of the output amplitude gain of the system. By studying the impact of the driving frequency and the noise parameters, we find the non-monotonic behaviors of the output amplitude gain. The results indicate that the bona fide SR, the wide sense SR and the conventional SR phenomena occur in the proposed harmonic oscillator with fluctuating mass driven by Mittag-Leffler noise. It is found that when we consider the output amplitude gain versus the driving frequency, the phenomena of stochastic multi-resonance (SMR) with two, three and four peaks are observed, and the quadruple-peaks SR phenomenon had never been observed in previous literature. Besides, when we investigate the dependence of output amplitude gain on the memory exponent, the inverse stochastic resonance (ISR) phenomenon takes place, in contrast to the well-known phenomenon of stochastic resonance. Furthermore, we compare the corresponding ordinary harmonic oscillator without memory to our generalized model, and found that the properties of long-memory and long-range dependence endows our generalized model with more abundant dynamic behaviors than the ordinary harmonic oscillator without memory.

  2. Even and odd coherent states of supersymmetric harmonic oscillators and their nonclassical properties

    NASA Astrophysics Data System (ADS)

    Afshar, Davood; Motamedinasab, Amin; Anbaraki, Azam; Jafarpour, Mojtaba

    2016-02-01

    In this paper, we have constructed even and odd superpositions of supercoherent states, similar to the standard even and odd coherent states of the harmonic oscillator. Then, their nonclassical properties, that is, squeezing and entanglement have been studied. We have observed that even supercoherent states show squeezing behavior for some values of parameters involved, while odd supercoherent states do not show squeezing at all. Also sub-Poissonian statistics have been observed for some ranges of the parameters in both states. We have also shown that these states may be considered as logical qubits which reduce to the Bell states at a limit, with concurrence equal to 1.

  3. Fourth-order master equation for a charged harmonic oscillator interacting with the electromagnetic field

    NASA Astrophysics Data System (ADS)

    Kurt, Arzu; Eryigit, Resul

    2015-12-01

    The master equation for a charged harmonic oscillator coupled to an electromagnetic reservoir is investigated up to fourth order in the interaction strength by using Krylov averaging method. The interaction is in the velocity-coupling form and includes a diamagnetic term. Exact analytical expressions for the second-, the third-, and the fourth-order contributions to mass renormalization, decay constant, normal and anomalous diffusion coefficients are obtained for the blackbody type environment. It is found that, generally, the third- and the fourth-order contributions have opposite signs when their magnitudes are comparable to that of the second-order one.

  4. Dressed Photons Induced Resistance Oscillation and Zero Resistance in Arrayed Simple Harmonic Oscillators with No Impurity

    NASA Astrophysics Data System (ADS)

    Chang, Chih-Chun; Chen, Guang-Yin; Lin, Lee

    2016-11-01

    We investigate a system of an array of N simple harmonic oscillators (SHO) interacting with photons through QED interaction. As the energy of photon is around the spacing between SHO energy levels, energy gaps appear in the dispersion relation of the interacted (dressed) photons. This is quite different from the dispersion relation of free photons. Due to interactions between dressed photonic field and arrayed SHO, the photoresistance of this system shows oscillations and also drops to zero as irradiated by EM field of varying frequencies.

  5. Comment on 'Wave functions of a time-dependent harmonic oscillator in a static magnetic field'

    SciTech Connect

    Maamache, M.; Bounames, A.; Ferkous, N.

    2006-01-15

    We show that the procedure used by Ferreira et al. [Phys. Rev. A 66, 024103 (2002)] is not correct for the following reasons: (i) the invariant I(t) they derived does not satisfy the Liouville-Von Neuman equation. (ii) They found that the eigenvalues of I(t) are time dependent which should not be the case according to the Lewis-Riesenfeld theory. We give a correct procedure to find the solution of the system they considered, i.e., the Schroedinger equation for a two-dimensional harmonic oscillator with time-dependent mass and frequency in the presence of a static magnetic field.

  6. Harmonic oscillators and resonance series generated by a periodic unstable classical orbit

    NASA Technical Reports Server (NTRS)

    Kazansky, A. K.; Ostrovsky, Valentin N.

    1995-01-01

    The presence of an unstable periodic classical orbit allows one to introduce the decay time as a purely classical magnitude: inverse of the Lyapunov index which characterizes the orbit instability. The Uncertainty Relation gives the corresponding resonance width which is proportional to the Planck constant. The more elaborate analysis is based on the parabolic equation method where the problem is effectively reduced to the multidimensional harmonic oscillator with the time-dependent frequency. The resonances form series in the complex energy plane which is equidistant in the direction perpendicular to the real axis. The applications of the general approach to various problems in atomic physics are briefly exposed.

  7. Quantization of a free particle interacting linearly with a harmonic oscillator.

    PubMed

    Mainiero, Thomas; Porter, Mason A

    2007-12-01

    We investigate the quantization of a free particle coupled linearly to a harmonic oscillator. This system, whose classical counterpart has clearly separated regular and chaotic regions, provides an ideal framework for studying the quantization of mixed systems. We identify key signatures of the classically chaotic and regular portions in the quantum system by constructing Husimi distributions and investigating avoided level crossings of eigenvalues as functions of the strength and range of the interaction between the system's two components. We show, in particular, that the Husimi structure becomes mixed and delocalized as the classical dynamics becomes more chaotic.

  8. Thermal conductance of a two-level atom coupled to two quantum harmonic oscillators

    NASA Astrophysics Data System (ADS)

    Guimarães, Pedro H.; Landi, Gabriel T.; de Oliveira, Mário J.

    2017-04-01

    We have determined the thermal conductance of a system consisting of a two-level atom coupled to two quantum harmonic oscillators in contact with heat reservoirs at distinct temperatures. The calculation of the heat flux as well as the atomic population and the rate of entropy production are obtained by the use of a quantum Fokker-Planck-Kramers equation and by a Lindblad master equation. The calculations are performed for small values of the coupling constant. The results coming from both approaches show that the conductance is proportional to the coupling constant squared and that, at high temperatures, it is proportional to the inverse of temperature.

  9. Coherent states for nonlinear harmonic oscillator and some of its properties

    SciTech Connect

    Amir, Naila E-mail: naila.amir@sns.nust.edu.pk; Iqbal, Shahid E-mail: siqbal@sns.nust.edu.pk

    2015-06-15

    A one-dimensional nonlinear harmonic oscillator is studied in the context of generalized coherent states. We develop a perturbative framework to compute the eigenvalues and eigenstates for the quantum nonlinear oscillator and construct the generalized coherent states based on Gazeau-Klauder formalism. We analyze their statistical properties by means of Mandel parameter and second order correlation function. Our analysis reveals that the constructed coherent states exhibit super-Poissonian statistics. Moreover, it is shown that the coherent states mimic the phenomena of quantum revivals and fractional revivals during their time evolution. The validity of our results has been discussed in terms of various parametric bounds imposed by our computational scheme.

  10. Stochastic resonance in a fractional harmonic oscillator subject to random mass and signal-modulated noise

    NASA Astrophysics Data System (ADS)

    Guo, Feng; Zhu, Cheng-Yin; Cheng, Xiao-Feng; Li, Heng

    2016-10-01

    Stochastic resonance in a fractional harmonic oscillator with random mass and signal-modulated noise is investigated. Applying linear system theory and the characteristics of the noises, the analysis expression of the mean output-amplitude-gain (OAG) is obtained. It is shown that the OAG varies non-monotonically with the increase of the intensity of the multiplicative dichotomous noise, with the increase of the frequency of the driving force, as well as with the increase of the system frequency. In addition, the OAG is a non-monotonic function of the system friction coefficient, as a function of the viscous damping coefficient, as a function of the fractional exponent.

  11. Image hiding based on time-averaged fringes produced by non-harmonic oscillations

    NASA Astrophysics Data System (ADS)

    Ragulskis, M.; Aleksa, A.; Navickas, Z.

    2009-12-01

    Image hiding based on time-averaged fringes produced by non-harmonic oscillations is presented in this paper. The secret image is embedded into the background moiré grating. Phase matching and initial stochastic phase deflection algorithms are used to encrypt the image. The decoding of the image is completely visual. The secret embedded image appears when the encrypted image is oscillated according to a predefined law of motion. No secret is leaked when the encrypted image is oscillated harmonically. Numerical experiments are used to illustrate the functionality of the method.

  12. Dressed Photons Induced Resistance Oscillation and Zero Resistance in Arrayed Simple Harmonic Oscillators with No Impurity

    PubMed Central

    Chang, Chih-Chun; Chen, Guang-Yin; Lin, Lee

    2016-01-01

    We investigate a system of an array of N simple harmonic oscillators (SHO) interacting with photons through QED interaction. As the energy of photon is around the spacing between SHO energy levels, energy gaps appear in the dispersion relation of the interacted (dressed) photons. This is quite different from the dispersion relation of free photons. Due to interactions between dressed photonic field and arrayed SHO, the photoresistance of this system shows oscillations and also drops to zero as irradiated by EM field of varying frequencies. PMID:27886252

  13. Quantum entanglement in coupled harmonic oscillator systems: from micro to macro

    NASA Astrophysics Data System (ADS)

    Kao, Jhih-Yuan; Chou, Chung-Hsien

    2016-07-01

    We investigate the entanglement dynamics of several models of coupled harmonic oscillators, whereby a number of properties concerning entanglement have been scrutinized, such as how the environment affects entanglement of a system, and death and revival of entanglement. Among them, there are two models for which we are able to vary their particle numbers easily by assuming identicalness, thereby examining how the particle number affects entanglement. We have found that the upper bound of entanglement between identical oscillators is approximately inversely proportional to the particle number.

  14. Dressed Photons Induced Resistance Oscillation and Zero Resistance in Arrayed Simple Harmonic Oscillators with No Impurity.

    PubMed

    Chang, Chih-Chun; Chen, Guang-Yin; Lin, Lee

    2016-11-25

    We investigate a system of an array of N simple harmonic oscillators (SHO) interacting with photons through QED interaction. As the energy of photon is around the spacing between SHO energy levels, energy gaps appear in the dispersion relation of the interacted (dressed) photons. This is quite different from the dispersion relation of free photons. Due to interactions between dressed photonic field and arrayed SHO, the photoresistance of this system shows oscillations and also drops to zero as irradiated by EM field of varying frequencies.

  15. Molecular Solid EOS based on Quasi-Harmonic Oscillator approximation for phonons

    SciTech Connect

    Menikoff, Ralph

    2014-09-02

    A complete equation of state (EOS) for a molecular solid is derived utilizing a Helmholtz free energy. Assuming that the solid is nonconducting, phonon excitations dominate the specific heat. Phonons are approximated as independent quasi-harmonic oscillators with vibrational frequencies depending on the specific volume. The model is suitable for calibrating an EOS based on isothermal compression data and infrared/Raman spectroscopy data from high pressure measurements utilizing a diamond anvil cell. In contrast to a Mie-Gruneisen EOS developed for an atomic solid, the specific heat and Gruneisen coefficient depend on both density and temperature.

  16. Bohr Hamiltonian with an energy dependent γ-unstable harmonic oscillator potential

    NASA Astrophysics Data System (ADS)

    Budaca, Radu

    2017-01-01

    A new exactly solvable collective solution is realized by inducing a linear energy dependence in the γ-unstable harmonic oscillator potential of the Bohr Hamiltonian and taking the asymptotic limit of the slope parameter. The model preserves the degeneracy features of the U(5) dynamical symmetry but with an expanded energy spectrum and with damped B(E2) rates. The phenomenological interpretation of the model is investigated in comparison to the spherical vibrator collective conditions by means of particular features of the corresponding ground state. Three experimental candidates for the new parameter free model are identified and extensively confronted with the theoretical predictions.

  17. Use of quantum self-friction potentials and forces in standard convention for study of harmonic oscillator

    NASA Astrophysics Data System (ADS)

    Guseinov, I. I.; Mamedov, B. A.

    2017-04-01

    In this paper, the physical nature of quantum usual and self-friction (SF) harmonic oscillators is presented. The procedure for studying these harmonic oscillators is identical; therefore, we can benefit from the theory of the usual harmonic oscillator. To study the SF harmonic oscillator, using analytical formulae for the L^{{(pl^{ * } )}}-SF Laguerre polynomials (L^{{(pl^{ * } )}}-SFLPs) and L^{{(α^{*} )}}-modified SFLPs (L^{{(α^{*} )}}-MSFLPs) in standard convention, the V^{{(pl^{ * } )}}-SF potentials (V^{{(pl^{ * } )}}-SFPs), V^{{(α^{*} )}}-modified SFPs (V^{{(α^{*} )}}-MSFPs), F^{{(pl^{ * } )}}-SF forces (F^{{(pl^{ * } )}}-SFFs) and F^{{(α^{*} )}}-modified SFFs (F^{{(α^{*} )}}-MSFFs) are investigated, where pl^{ * } = 2l + 2 - α^{*} and α^{*} is the integer (α^{*} = α, - ∞ < α ≤ 2) or non-integer (α^{*} ≠ α, - ∞ < α < 3) SF quantum number. We note that the potentials (V^{{(pl^{ * } )}}-SFPs and V^{{(α^{*} )}}-MSFPs), and forces (F^{{(pl^{ * } )}}-SFFs and F^{{(α^{*} )}}-MSFFs), respectively, are independent functions. It is shown that the numerical values of these independent functions are the same, i.e., V_{num}^{{(pl^{ * } )}} = V_{num}^{{(α^{*} )}} and F_{num}^{{(pl^{ * } )}} = F_{num}^{{(α^{*} )}}. The dependence of the SF harmonic oscillator as a function of the distance is analyzed. The presented relationships are valid for arbitrary values of parameters.

  18. On the measurement of a weak classical force coupled to a harmonic oscillator: experimental progress

    SciTech Connect

    Bocko, M.F.; Onofrio, R.

    1996-07-01

    Several high-precision physics experiments are approaching a level of sensitivity at which the intrinsic quantum nature of the experimental apparatus is the dominant source of fluctuations limiting the sensitivity of the measurements. This quantum limit is embodied by the Heisenberg uncertainty principle, which prohibits arbitrarily precise simultaneous measurements of two conjugate observables of a system but allows one-time measurements of a single observable with any precision. The dynamical evolution of a system immediately following a measurement limits the class of observables that may be measured repeatedly with arbitrary precision, with the influence of the measurement apparatus on the system being confined strictly to the conjugate observables. Observables having this feature, and the corresponding measurements performed on them, have been named quantum nondemolition or back-action evasion observables. In a previous review (Caves {ital et} {ital al}., 1980, Rev. Mod. Phys. {bold 52}, 341) a quantum-mechanical analysis of quantum nondemolition measurements of a harmonic oscillator was presented. The present review summarizes the experimental progress on quantum nondemolition measurements and the classical models developed to describe and guide the development of practical implementations of quantum nondemolition measurements. The relationship between the classical and quantum theoretical models is also reviewed. The concept of quantum nondemolition and back-action evasion measurements originated in the context of measurements on a macroscopic mechanical harmonic oscillator, though these techniques may be useful in other experimental contexts as well, as is discussed in the last part of this review. {copyright} {ital 1996 The American Physical Society.}

  19. ABC of ladder operators for rationally extended quantum harmonic oscillator systems

    NASA Astrophysics Data System (ADS)

    Cariñena, José F.; Plyushchay, Mikhail S.

    2017-07-01

    The problem of construction of ladder operators for rationally extended quantum harmonic oscillator (REQHO) systems of a general form is investigated in the light of existence of different schemes of the Darboux-Crum-Krein-Adler transformations by which such systems can be generated from the quantum harmonic oscillator. Any REQHO system is characterized by the number of separated states in its spectrum, the number of ‘valence bands’ in which the separated states are organized, and by the total number of the missing energy levels and their position. All these peculiarities of a REQHO system are shown to be detected and reflected by a trinity (A^+/- , B^+/- , C^+/-) of the basic (primary) lowering and raising ladder operators related between themselves by certain algebraic identities with coefficients polynomially-dependent on the Hamiltonian. We show that all the secondary, higher-order ladder operators are obtainable by a composition of the basic ladder operators of the trinity which form the set of the spectrum-generating operators. Each trinity, in turn, can be constructed from the intertwining operators of the two complementary minimal schemes of the Darboux-Crum-Krein-Adler transformations.

  20. The anisosphere as a new tool for interpreting Foucault pendulum experiments. Part I: harmonic oscillators

    NASA Astrophysics Data System (ADS)

    Verreault, René

    2017-08-01

    In an attempt to explain the tendency of Foucault pendula to develop elliptical orbits, Kamerlingh Onnes derived equations of motion that suggest the use of great circles on a spherical surface as a graphical illustration for an anisotropic bi-dimensional harmonic oscillator, although he did not himself exploit the idea any further. The concept of anisosphere is introduced in this work as a new means of interpreting pendulum motion. It can be generalized to the case of any two-dimensional (2-D) oscillating system, linear or nonlinear, including the case where coupling between the 2 degrees of freedom is present. Earlier pendulum experiments in the literature are revisited and reanalyzed as a test for the anisosphere approach. While that graphical method can be applied to strongly nonlinear cases with great simplicity, this part I is illustrated through a revisit of Kamerlingh Onnes' dissertation, where a high performance pendulum skillfully emulates a 2-D harmonic oscillator. Anisotropy due to damping is also described. A novel experiment strategy based on the anisosphere approach is proposed. Finally, recent original results with a long pendulum using an electronic recording alidade are presented. A gain in precision over traditional methods by 2-3 orders of magnitude is achieved.

  1. Purity and decoherence in the theory of a damped harmonic oscillator.

    PubMed

    Isar, A; Sandulescu, A; Scheid, W

    1999-12-01

    For the generalized master equations derived by Karrlein and Grabert for the microscopic model of a damped harmonic oscillator, the conditions for purity of states are written, in particular for different initial conditions and different types of damping, including Ohmic, Drude, and weak coupling cases, and the Agarwal and Weidlich-Haake models. It is shown that the states which remain pure are the squeezed states with variances that are constant in time. For pure states, generalized nonlinear Schrödinger-type equations corresponding to these master equations are also obtained. Then the condition for purity of states of a damped harmonic oscillator is considered in the framework of Lindblad theory for open quantum systems. For a special choice of the environment coefficients, correlated coherent states with constant variances and covariance are shown to be the only states which remain pure all the time during the evolution of the considered system. In Karrlein-Grabert and Lindblad models, as well as in the particular models considered, expressions for the rate of entropy production are written, and it is shown that state which preserve their purity in time are also states which minimize entropy production and, therefore, are the most stable state under evolution in the presence of the environment, and play an important role in the description of decoherence phenomenon.

  2. Reducibility of 1D quantum harmonic oscillator perturbed by a quasiperiodic potential with logarithmic decay

    NASA Astrophysics Data System (ADS)

    Wang, Zhiguo; Liang, Zhenguo

    2017-04-01

    In this paper we prove an infinite dimensional KAM theorem, in which the assumptions on the derivatives of the perturbation in [24] are weakened from polynomial decay to logarithmic decay. As a consequence, we can apply it to 1D quantum harmonic oscillators and prove the reducibility of the linear harmonic oscillator, T=-\\frac{{{\\text{d}}2}}{\\text{d}{{x}2}}+{{x}2} , on {{L}2}≤ft({R}\\right) perturbed by the quasi-periodic in the time potential V(x,ω t;ω ) with logarithmic decay. This proves the pure-point nature of the spectrum of the Floquet operator K, where K:=-i∑k=1nωk∂∂θk-d2dx2+x2+ɛV(x,θω) is defined on {{L}2}≤ft({R}\\right)\\otimes {{L}2}≤ft({{{T}}n}\\right) , and the potential V(x,θ ;ω ) has logarithmic decay as well as its gradient in ω.

  3. Purity and decoherence in the theory of a damped harmonic oscillator

    NASA Astrophysics Data System (ADS)

    Isar, A.; Sandulescu, A.; Scheid, W.

    1999-12-01

    For the generalized master equations derived by Karrlein and Grabert for the microscopic model of a damped harmonic oscillator, the conditions for purity of states are written, in particular for different initial conditions and different types of damping, including Ohmic, Drude, and weak coupling cases, and the Agarwal and Weidlich-Haake models. It is shown that the states which remain pure are the squeezed states with variances that are constant in time. For pure states, generalized nonlinear Schrödinger-type equations corresponding to these master equations are also obtained. Then the condition for purity of states of a damped harmonic oscillator is considered in the framework of Lindblad theory for open quantum systems. For a special choice of the environment coefficients, correlated coherent states with constant variances and covariance are shown to be the only states which remain pure all the time during the evolution of the considered system. In Karrlein-Grabert and Lindblad models, as well as in the particular models considered, expressions for the rate of entropy production are written, and it is shown that state which preserve their purity in time are also states which minimize entropy production and, therefore, are the most stable state under evolution in the presence of the environment, and play an important role in the description of decoherence phenomenon.

  4. Use of videos for students to see the effect of changing gravity on harmonic oscillators

    NASA Astrophysics Data System (ADS)

    Benge, Raymond; Young, Charlotte; Worley, Alan; Davis, Shirley; Smith, Linda; Gell, Amber

    2010-03-01

    In introductory physics classes, students are introduced to harmonic oscillators such as masses on springs and the simple pendulum. In derivation of the equations describing these systems, the term ``g'' for the acceleration due to gravity cancels in the equation for the period of a mass oscillating on a spring, but it remains in the equation for the period of a pendulum. Frequently there is a homework problem asking how the system described would behave on the Moon, Mars, etc. Students have to have faith in the equations. In January, 2009, a team of community college faculty flew an experiment aboard an aircraft in conjunction with NASA's Microgravity University program. The experiment flown was a study in harmonic oscillator and pendulum behavior under various gravity situations. The aircraft simulated zero gravity, Martian, Lunar, and hypergravity conditions. The experiments were video recorded for students to study the behavior of the systems in varying gravity conditions. These videos are now available on the internet for anyone to use in introductory physics classes.

  5. Solving a fuzzy initial value problem of a harmonic oscillator model

    NASA Astrophysics Data System (ADS)

    Karim, M. A.; Gunawan, A. Y.; Apri, M.; Sidarto, K. A.

    2017-03-01

    Modeling in systems biology is often faced with challenges in terms of measurement uncertainty. This is possibly either due to limitations of available data, environmental or demographic changes. One of typical behavior that commonly appears in the systems biology is a periodic behavior. Since uncertainties would get involved into the systems, the change of solution behavior of the periodic system should be taken into account. To get insight into this issue, in this work a simple mathematical model describing periodic behavior, i.e. a harmonic oscillator model, is considered by assuming its initial value has uncertainty in terms of fuzzy number. The system is known as Fuzzy Initial Value Problems. Some methods to determine the solutions are discussed. First, solutions are examined using two types of fuzzy differentials, namely Hukuhara Differential (HD) and Generalized Hukuhara Differential (GHD). Application of fuzzy arithmetic leads that each type of HD and GHD are formed into α-cut deterministic systems, and then are solved by the Runge-Kutta method. The HD type produces a solution with increasing uncertainty starting from the initial condition. While, GHD type produces an oscillatory solution but only until a certain time and above it the uncertainty becomes monotonic increasing. Solutions of both types certainly do not provide the accuracy for harmonic oscillator model during its evolution. Therefore, we propose the third method, so called Fuzzy Differential Inclusions (FDI), to attack the problem. Using this method, we obtain oscillatory solutions during its evolution.

  6. Harmonic oscillations of laminae in non-Newtonian fluids: A lattice Boltzmann-Immersed Boundary approach

    NASA Astrophysics Data System (ADS)

    De Rosis, Alessandro

    2014-11-01

    In this paper, the fluid dynamics induced by a rigid lamina undergoing harmonic oscillations in a non-Newtonian calm fluid is investigated. The fluid is modelled through the lattice Boltzmann method and the flow is assumed to be nearly incompressible. An iterative viscosity-correction based procedure is proposed to properly account for the non-Newtonian fluid feature and its accuracy is evaluated. In order to handle the mutual interaction between the lamina and the encompassing fluid, the Immersed Boundary method is adopted. A numerical campaign is performed. In particular, the effect of the non-Newtonian feature is highlighted by investigating the fluid forces acting on a harmonically oscillating lamina for different values of the Reynolds number. The findings prove that the non-Newtonian feature can drastically influence the behaviour of the fluid and, as a consequence, the forces acting upon the lamina. Several considerations are carried out on the time history of the drag coefficient and the results are used to compute the added mass through the hydrodynamic function. Moreover, the computational cost involved in the numerical simulations is discussed. Finally, two applications concerning water resources are investigated: the flow through an obstructed channel and the particle sedimentation. Present findings highlight a strong coupling between the body shape, the Reynolds number, and the flow behaviour index.

  7. Harmonic oscillator in heat bath: exact simulation of time-lapse-recorded data and exact analytical benchmark statistics.

    PubMed

    Nørrelykke, Simon F; Flyvbjerg, Henrik

    2011-04-01

    The stochastic dynamics of the damped harmonic oscillator in a heat bath is simulated with an algorithm that is exact for time steps of arbitrary size. Exact analytical results are given for correlation functions and power spectra in the form they acquire when computed from experimental time-lapse recordings. Three applications are discussed: (i) The effects of finite sampling rate and time, described exactly here, are similar for other stochastic dynamical systems--e.g., motile microorganisms and their time-lapse-recorded trajectories. (ii) The same statistics is satisfied by any experimental system to the extent that it is interpreted as a damped harmonic oscillator at finite temperature-such as an AFM cantilever. (iii) Three other models of fundamental interest are limiting cases of the damped harmonic oscillator at finite temperature; it consequently bridges their differences and describes the effects of finite sampling rate and sampling time for these models as well. ©2011 American Physical Society

  8. Universal and deterministic manipulation of the quantum state of harmonic oscillators: a route to unitary gates for Fock state qubits.

    PubMed

    Santos, Marcelo França

    2005-07-01

    We present a simple quantum circuit that allows for the universal and deterministic manipulation of the quantum state of confined harmonic oscillators. The scheme is based on the selective interactions of the referred oscillator with an auxiliary three-level system and a classical external driving source, and enables any unitary operations on Fock states, two by two. One circuit is equivalent to a single qubit unitary logical gate on Fock states qubits. Sequences of similar protocols allow for complete, deterministic, and state-independent manipulation of the harmonic oscillator quantum state.

  9. Double simple-harmonic-oscillator formulation of the thermal equilibrium of a fluid interacting with a coherent source of phonons

    NASA Technical Reports Server (NTRS)

    Defacio, B.; Vannevel, Alan; Brander, O.

    1993-01-01

    A formulation is given for a collection of phonons (sound) in a fluid at a non-zero temperature which uses the simple harmonic oscillator twice; one to give a stochastic thermal 'noise' process and the other which generates a coherent Glauber state of phonons. Simple thermodynamic observables are calculated and the acoustic two point function, 'contrast' is presented. The role of 'coherence' in an equilibrium system is clarified by these results and the simple harmonic oscillator is a key structure in both the formulation and the calculations.

  10. On a q-extension of the linear harmonic oscillator with the continuous orthogonality property on ℝ

    NASA Astrophysics Data System (ADS)

    Alvarez-Nodarse, R.; Atakishiyeva, M. K.; Atakishiyev, N. M.

    2005-11-01

    We discuss a q-analogue of the linear harmonic oscillator in quantum mechanics based on a q-extension of the classical Hermite polynomials H n ( x) recently introduced by us in R. Alvarez-Nodarse et al.: Boletin de la Sociedad Matematica Mexicana (3) 8 (2002) 127. The wave functions in this q-model of the quantum harmonic oscillator possess the continuous orthogonality property on the whole real line ℝ with respect to a positive weight function. A detailed description of the corresponding q-system is carried out.

  11. Solution of the Quantum Harmonic Oscillator Plus a Delta-Function Potential at the Origin: The "Oddness" of Its Even-Parity Solutions

    ERIC Educational Resources Information Center

    Viana-Gomes, J.; Peres, N. M. R.

    2011-01-01

    We derive the energy levels associated with the even-parity wavefunctions of the harmonic oscillator with an additional delta-function potential at the origin. Our results bring to the attention of students a non-trivial and analytical example of a modification of the usual harmonic oscillator potential, with emphasis on the modification of the…

  12. Solution of the Quantum Harmonic Oscillator Plus a Delta-Function Potential at the Origin: The "Oddness" of Its Even-Parity Solutions

    ERIC Educational Resources Information Center

    Viana-Gomes, J.; Peres, N. M. R.

    2011-01-01

    We derive the energy levels associated with the even-parity wavefunctions of the harmonic oscillator with an additional delta-function potential at the origin. Our results bring to the attention of students a non-trivial and analytical example of a modification of the usual harmonic oscillator potential, with emphasis on the modification of the…

  13. Harmonic oscillator representation in the theory of scattering and nuclear reactions

    NASA Technical Reports Server (NTRS)

    Smirnov, Yuri F.; Shirokov, A. M.; Lurie, Yuri, A.; Zaitsev, S. A.

    1995-01-01

    The following questions, concerning the application of the harmonic oscillator representation (HOR) in the theory of scattering and reactions, are discussed: the formulation of the scattering theory in HOR; exact solutions of the free motion Schroedinger equation in HOR; separable expansion of the short range potentials and the calculation of the phase shifts; 'isolated states' as generalization of the Wigner-von Neumann bound states embedded in continuum; a nuclear coupled channel problem in HOR; and the description of true three body scattering in HOR. As an illustration the soft dipole mode in the (11)Li nucleus is considered in a frame of the (9)Li+n+n cluster model taking into account of three body continuum effects.

  14. Semiclassical analysis of long-wavelength multiphoton processes: The periodically driven harmonic oscillator

    NASA Astrophysics Data System (ADS)

    Fox, Ronald F.; Vela-Arevalo, Luz V.

    2002-11-01

    The problem of multiphoton processes for intense, long-wavelength irradiation of atomic and molecular electrons is presented. The recently developed method of quasiadiabatic time evolution is used to obtain a nonperturbative analysis. When applied to the standard vector potential coupling, an exact auxiliary equation is obtained that is in the electric dipole coupling form. This is achieved through application of the Goeppert-Mayer gauge. While the analysis to this point is general and aimed at microwave irradiation of Rydberg atoms, a Floquet analysis of the auxiliary equation is presented for the special case of the periodically driven harmonic oscillator. Closed form expressions for a complete set of Floquet states are obtained. These are used to demonstrate that for the oscillator case there are no multiphoton resonances.

  15. Fourth-order master equation for a charged harmonic oscillator coupled to an electromagnetic field

    NASA Astrophysics Data System (ADS)

    Kurt, Arzu; Eryigit, Resul

    Using Krylov averaging method, we have derived a fourth-order master equation for a charged harmonic oscillator weakly coupled to an electromagnetic field. Interaction is assumed to be of velocity coupling type which also takes into account the diagmagnetic term. Exact analytical expressions have been obtained for the second, the third and the fourth-order corrections to the diffusion and the drift terms of the master equation. We examined the validity range of the second order master equation in terms of the coupling constant and the bath cutoff frequency and found that for the most values of those parameters, the contribution from the third and the fourth order terms have opposite signs and cancel each other. Inclusion of the third and the fourth-order terms is found to not change the structure of the master equation. Bolu, Turkey.

  16. Entanglement in a continuously measured two-level system coupled to a harmonic oscillator

    SciTech Connect

    Hernandez-Concepcion, E.; Alonso, D.; Brouard, S.

    2009-05-15

    The dynamics of a two-level system (TLS) coupled to a harmonic oscillator (HO) is studied under the combined effect of a thermal bath acting on the HO and of a detector continuously measuring one of the components of the spinlike TLS. The analysis focuses on the dynamics of the 'relative entropy of entanglement' (REE) in the one-energy-excitation manifold of the reduced TLS+HO system. For this model system, a stationary state is shown to be reached for which the relative entropy of entanglement is in general nonzero, even though, under certain approximations, the separate effects of bath and detector would be to remove any trace of this resource from the system. Analytical as well as numerical results are obtained for the REE as a function of the different parameters involved in the model definition.

  17. The quantum fidelity for the time-periodic singular harmonic oscillator

    NASA Astrophysics Data System (ADS)

    Combescure, Monique

    2006-03-01

    In this paper we perform an exact study of "quantum fidelity" (also called Loschmidt echo) for the time-periodic quantum harmonic oscillator of the following Hamiltonian: Ĥg(t)≔(P2/2)+f(t)(Q2/2)+(g2/Q2), when compared with the quantum evolution induced by Ĥ0(t) (g=0), in the case where f is a T-periodic function and g a real constant. The reference (initial) state is taken to be an arbitrary "generalized coherent state" in the sense of Perelomov. We show that, starting with a quadratic decrease in time in the neighborhood of t =0, this quantum fidelity may recur to its initial value 1 at an infinite sequence of times tk. We discuss the result when the classical motion induced by Hamiltonian Ĥ0(t) is assumed to be stable versus unstable.

  18. Continuous variable quantum optical simulation for time evolution of quantum harmonic oscillators.

    PubMed

    Deng, Xiaowei; Hao, Shuhong; Guo, Hong; Xie, Changde; Su, Xiaolong

    2016-03-10

    Quantum simulation enables one to mimic the evolution of other quantum systems using a controllable quantum system. Quantum harmonic oscillator (QHO) is one of the most important model systems in quantum physics. To observe the transient dynamics of a QHO with high oscillation frequency directly is difficult. We experimentally simulate the transient behaviors of QHO in an open system during time evolution with an optical mode and a logical operation system of continuous variable quantum computation. The time evolution of an atomic ensemble in the collective spontaneous emission is analytically simulated by mapping the atomic ensemble onto a QHO. The measured fidelity, which is used for quantifying the quality of the simulation, is higher than its classical limit. The presented simulation scheme provides a new tool for studying the dynamic behaviors of QHO.

  19. Energy distribution of the quantum harmonic oscillator under random time-dependent perturbations.

    PubMed

    Garnier, J

    1999-10-01

    This paper investigates the evolution of a quantum particle in a harmonic oscillator driven by time-dependent forces. The perturbations are small, but they act long enough so that we can solve the problem in the asymptotic framework corresponding to a perturbation amplitude that tends to zero and a perturbation duration that tends to infinity. We describe the effective evolution equation of the state vector, which reads as a stochastic partial differential equation. We exhibit a closed-form equation for the transition probabilities, which can be interpreted in terms of a jump process. Using standard probability tools, we are then able to compute explicitly the probabilities for observing the different energy eigenstates and give the exact statistical distribution of the energy of the particle.

  20. Environmental effects in the quantum-classical transition for the delta-kicked harmonic oscillator.

    PubMed

    Carvalho, A R R; de Matos Filho, R L; Davidovich, L

    2004-08-01

    We discuss the roles of the macroscopic limit and different system-environment interactions in a quantum-classical transition for a chaotic system. We consider the kicked harmonic oscillator subject to reservoirs that correspond in the classical case to purely dissipative or purely diffusive behavior, a situation that can be implemented in ion trap experiments. In the dissipative case, we derive an expression for the time at which quantum and classical predictions become different (breaking time) and show that complete quantum-classical correspondence is not possible in the chaotic regime. For the diffusive environment we estimate the minimum value of the diffusion coefficient necessary to retrieve the classical limit and also show numerical evidence that, for diffusion below this threshold, the breaking time behaves, essentially, like that in the case of a system without a reservoir.

  1. Structure of the harmonic oscillator in the space of n-particle Glauber correlators

    NASA Astrophysics Data System (ADS)

    Zubizarreta Casalengua, E.; López Carreño, J. C.; del Valle, E.; Laussy, F. P.

    2017-06-01

    We map the Hilbert space of the quantum harmonic oscillator to the space of Glauber's nth-order intensity correlators, in effect showing "the correlations between the correlators" for a random sampling of the quantum states. In particular, we show how the popular g(2) function is correlated to the mean population and how a recurrent criterion to identify single-particle states or emitters, namely, g ( 2 ) < 1 / 2 , actually identifies states with at most two particles on average. Our charting of the Hilbert space allows us to capture its structure in a simpler and physically more intuitive way that can be used to classify quantum sources by surveying which territory they can access.

  2. The sojourn time of the inverted harmonic oscillator on the noncommutative plane

    NASA Astrophysics Data System (ADS)

    Guo, Guang-Jie; Ren, Zhong-Zhou; Ju, Guo-Xing; Long, Chao-Yun

    2011-10-01

    The sojourn time of the Gaussian wavepacket that is stationed at the center of the inverted harmonic oscillator is investigated on the noncommutative plane in detail. In ordinary commutative space quantum mechanics, the sojourn time of the Gaussian wavepacket is always a monotonically decreasing function of the curvature parameter ω of the potential. However, in this paper, we find that the spatial noncommutativity makes the sojourn time a concave function of ω with a minimum at an inflection point ω0. Furthermore, if ω is larger than a certain critical value the sojourn time will become infinity. Thus, the ordinary intuitive physical picture about the relation between the sojourn time and the shape of the inverted oscillator potential is changed when the spatial noncommutativity is considered.

  3. Alternative descriptions of wave and particle aspects of the harmonic oscillator

    NASA Technical Reports Server (NTRS)

    Schuch, Dieter

    1993-01-01

    The dynamical properties of the wave and particle aspects of the harmonic oscillator can be studied with the help of the time-dependent Schroedinger equation (SE). Especially the time-dependence of maximum and width of Gaussian wave packet solutions allow to show the evolution and connections of those two complementary aspects. The investigation of the relations between the equations describing wave and particle aspects leads to an alternative description of the considered systems. This can be achieved by means of a Newtonian equation for a complex variable in connection with a conservation law for a nonclassical angular momentum-type quantity. With the help of this complex variable, it is also possible to develop a Hamiltonian formalism for the wave aspect contained in the SE, which allows to describe the dynamics of the position and momentum uncertainties. In this case the Hamiltonian function is equivalent to the difference between the mean value of the Hamiltonian operator and the classical Hamiltonian function.

  4. Semiclassical analysis of long-wavelength multiphoton processes: The periodically driven harmonic oscillator

    SciTech Connect

    Fox, Ronald F.; Vela-Arevalo, Luz V.

    2002-11-01

    The problem of multiphoton processes for intense, long-wavelength irradiation of atomic and molecular electrons is presented. The recently developed method of quasiadiabatic time evolution is used to obtain a nonperturbative analysis. When applied to the standard vector potential coupling, an exact auxiliary equation is obtained that is in the electric dipole coupling form. This is achieved through application of the Goeppert-Mayer gauge. While the analysis to this point is general and aimed at microwave irradiation of Rydberg atoms, a Floquet analysis of the auxiliary equation is presented for the special case of the periodically driven harmonic oscillator. Closed form expressions for a complete set of Floquet states are obtained. These are used to demonstrate that for the oscillator case there are no multiphoton resonances.

  5. Relation between the extended time-delayed feedback control algorithm and the method of harmonic oscillators

    NASA Astrophysics Data System (ADS)

    Pyragas, Viktoras; Pyragas, Kestutis

    2015-08-01

    In a recent paper [Phys. Rev. E 91, 012920 (2015), 10.1103/PhysRevE.91.012920] Olyaei and Wu have proposed a new chaos control method in which a target periodic orbit is approximated by a system of harmonic oscillators. We consider an application of such a controller to single-input single-output systems in the limit of an infinite number of oscillators. By evaluating the transfer function in this limit, we show that this controller transforms into the known extended time-delayed feedback controller. This finding gives rise to an approximate finite-dimensional theory of the extended time-delayed feedback control algorithm, which provides a simple method for estimating the leading Floquet exponents of controlled orbits. Numerical demonstrations are presented for the chaotic Rössler, Duffing, and Lorenz systems as well as the normal form of the Hopf bifurcation.

  6. Generalized power-spectrum Larmor formula for an extended charged particle embedded in a harmonic oscillator

    NASA Astrophysics Data System (ADS)

    Marengo, Edwin A.; Khodja, Mohamed R.

    2006-09-01

    The nonrelativistic Larmor radiation formula, giving the power radiated by an accelerated charged point particle, is generalized for a spatially extended particle in the context of the classical charged harmonic oscillator. The particle is modeled as a spherically symmetric rigid charge distribution that possesses both translational and spinning degrees of freedom. The power spectrum obtained exhibits a structure that depends on the form factor of the particle, but reduces, in the limit of an infinitesimally small particle and for the charge distributions considered, to Larmor’s familiar result. It is found that for finite-duration small-enough accelerations as well as perpetual uniform accelerations the power spectrum of the spatially extended particle reduces to that of a point particle. It is also found that when the acceleration is violent or the size parameter of the particle is very large compared to the wavelength of the emitted radiation the power spectrum is highly suppressed. Possible applications are discussed.

  7. Ultra-light and strong: The massless harmonic oscillator and its singular path integral

    NASA Astrophysics Data System (ADS)

    Modanese, Giovanni

    2017-09-01

    In classical mechanics, a light particle bound by a strong elastic force just oscillates at high frequency in the region allowed by its initial position and velocity. In quantum mechanics, instead, the ground state of the particle becomes completely de-localized in the limit m → 0. The harmonic oscillator thus ceases to be a useful microscopic physical model in the limit m → 0, but its Feynman path integral has interesting singularities which make it a prototype of other systems exhibiting a “quantum runaway” from the classical configurations near the minimum of the action. The probability density of the coherent runaway modes can be obtained as the solution of a Fokker-Planck equation associated to the condition S = Smin. This technique can be applied also to other systems, notably to a dimensional reduction of the Einstein-Hilbert action.

  8. Study of the harmonic oscillation on EAST by an eight-channel Doppler Backscattering (DBS) system

    NASA Astrophysics Data System (ADS)

    Zhou, C.; Liu, A. D.; Wang, M. Y.; Hu, J. Q.; Zhang, J.; Li, H.; Lan, T.; Xie, J. L.; Liu, W. D.; Yu, C. X.; Doyle, E. J.; University of California, Los Angeles Collaboration; University of Science; Technology of China Team

    2016-10-01

    The eight-channel DBS system has been installed for turbulence measurements in such plasmas. The frequency range is 55 to 75 GHz, covering the entire H-mode pedestal, with a turbulence wavenumber range of 4-12/cm. A harmonic oscillation has been observed by DBS on EAST during ELMy-free H mode. The fundamental frequency of the coherent oscillation is 12-20 kHz and 2nd-8th harmonic are observed, and the radial coverage is from the edge to rho 0.85. Work supported by the Natural Science Foundation of China (NSFC) under 11475173, 11505184, National Magnetic Confinement Fusion Energy Development Program of China under 2013GB106002 and 2014GB109002, and DOE Grants DE- SC0010424 and DE-SC0010469.

  9. LETTER TO THE EDITOR: Exact energy distribution function in a time-dependent harmonic oscillator

    NASA Astrophysics Data System (ADS)

    Robnik, Marko; Romanovski, Valery G.; Stöckmann, Hans-Jürgen

    2006-09-01

    Following a recent work by Robnik and Romanovski (2006 J. Phys. A: Math. Gen. 39 L35, 2006 Open Syst. Inf. Dyn. 13 197-222), we derive an explicit formula for the universal distribution function of the final energies in a time-dependent 1D harmonic oscillator, whose functional form does not depend on the details of the frequency ω(t) and is closely related to the conservation of the adiabatic invariant. The normalized distribution function is P(x) = \\pi^{-1} (2\\mu^2 - x^2)^{-\\frac{1}{2}} , where x=E_1- \\skew3\\bar{E}_1 ; E1 is the final energy, \\skew3\\bar{E}_1 is its average value and µ2 is the variance of E1. \\skew3\\bar{E}_1 and µ2 can be calculated exactly using the WKB approach to all orders.

  10. Relation between the extended time-delayed feedback control algorithm and the method of harmonic oscillators.

    PubMed

    Pyragas, Viktoras; Pyragas, Kestutis

    2015-08-01

    In a recent paper [Phys. Rev. E 91, 012920 (2015)] Olyaei and Wu have proposed a new chaos control method in which a target periodic orbit is approximated by a system of harmonic oscillators. We consider an application of such a controller to single-input single-output systems in the limit of an infinite number of oscillators. By evaluating the transfer function in this limit, we show that this controller transforms into the known extended time-delayed feedback controller. This finding gives rise to an approximate finite-dimensional theory of the extended time-delayed feedback control algorithm, which provides a simple method for estimating the leading Floquet exponents of controlled orbits. Numerical demonstrations are presented for the chaotic Rössler, Duffing, and Lorenz systems as well as the normal form of the Hopf bifurcation.

  11. A time-discrete harmonic oscillator model of human car-following

    NASA Astrophysics Data System (ADS)

    Wagner, P.

    2011-12-01

    A time-discrete stochastic harmonic oscillator is presented as a model of human car-following behaviour. This describes especially the non-continuous control of a human driver - acceleration changes from time to time at so called action-points and is kept constant in between. Analytical results can be derived which allow to classify the different types of motion possible within this approach. These results show that with weaker control by the human, unstable behaviour of the oscillator becomes more likely. This is in line with common understanding about the causes of accidents. Finally, since even the stochastic behaviour of this model is in parts analytically tractable, the width of the speed-difference and distance fluctuations can be expressed as function of the model's parameter. This allows a fresh view on empirical car-following data and the identification of parameters from real data in the context of the theory presented here.

  12. Stability and multiple bifurcations of a damped harmonic oscillator with delayed feedback near zero eigenvalue singularity.

    PubMed

    Song, Yongli; Zhang, Tonghua; Tadé, Moses O

    2008-12-01

    We investigate the dynamics of a damped harmonic oscillator with delayed feedback near zero eigenvalue singularity. We perform a linearized stability analysis and multiple bifurcations of the zero solution of the system near zero eigenvalue singularity. Taking the time delay as the bifurcation parameter, the presence of steady-state bifurcation, Bogdanov-Takens bifurcation, triple zero, and Hopf-zero singularities is demonstrated. In the case when the system has a simple zero eigenvalue, center manifold reduction and normal form theory are used to investigate the stability and the types of steady-state bifurcation. The stability of the zero solution of the system near the simple zero eigenvalue singularity is completely solved.

  13. The Harmonic Oscillator in the Classical Limit of a Minimal-Length Scenario

    NASA Astrophysics Data System (ADS)

    Quintela, T. S.; Fabris, J. C.; Nogueira, J. A.

    2016-12-01

    In this work, we explicitly solve the problem of the harmonic oscillator in the classical limit of a minimal-length scenario. We show that (i) the motion equation of the oscillator is not linear anymore because the presence of a minimal length introduces an anarmonic term and (ii) its motion is described by a Jacobi sine elliptic function. Therefore, the motion is periodic with the same amplitude and with the new period depending on the minimal length. This result (the change in the period of oscillation) is very important since it enables us to find in a quite simple way the most relevant effect of the presence of a minimal length and consequently traces of the Planck-scale physics. We show applications of our results in spectroscopy and gravity.

  14. Manipulating Fock states of a harmonic oscillator while preserving its linearity

    NASA Astrophysics Data System (ADS)

    Juliusson, K.; Bernon, S.; Zhou, X.; Schmitt, V.; le Sueur, H.; Bertet, P.; Vion, D.; Mirrahimi, M.; Rouchon, P.; Esteve, D.

    2016-12-01

    We present a scheme for controlling the quantum state of a harmonic oscillator by coupling it to an anharmonic multilevel system (MLS) with first- to second-excited-state transition on resonance with the oscillator. In this scheme, which we call ef-resonant, the spurious oscillator Kerr nonlinearity inherited from the MLS is very small, while its Fock states can still be selectively addressed via an MLS transition at a frequency that depends on the number of photons. We implement this concept in a circuit-QED setup with a microwave three-dimensional cavity (the oscillator, with frequency 6.4 GHz and quality factor QO=2 ×106 ) embedding a frequency tunable transmon qubit (the MLS). We characterize the system spectroscopically and demonstrate selective addressing of Fock states and a Kerr nonlinearity below 350 Hz. At times much longer than the transmon coherence times, a nonlinear cavity response with driving power is also observed and explained.

  15. Attractors and Spectral Characteristics of Neural Structures Based on the Model of the Quantum Harmonic Oscillator

    SciTech Connect

    Rigatos, Gerasimos G.

    2007-09-06

    Neural computation based on principles of quantum mechanics can provide improved models of memory processes and brain functioning and is of importance for the realization of quantum computing machines. To this end, this paper studies neural structures with weights that follow the model of the quantum harmonic oscillator. These weights correspond to diffusing particles, which interact to each other as the theory of Brownian motion predicts. The learning of the stochastic weights (convergence of the diffusing particles to an equilibrium) is analyzed. In the case of associative memories the proposed neural model results in an exponential increase of the number of attractors. Spectral analysis shows that the stochastic weights satisfy an equation which is analogous to the principle of uncertainty.

  16. Continuous variable quantum optical simulation for time evolution of quantum harmonic oscillators

    PubMed Central

    Deng, Xiaowei; Hao, Shuhong; Guo, Hong; Xie, Changde; Su, Xiaolong

    2016-01-01

    Quantum simulation enables one to mimic the evolution of other quantum systems using a controllable quantum system. Quantum harmonic oscillator (QHO) is one of the most important model systems in quantum physics. To observe the transient dynamics of a QHO with high oscillation frequency directly is difficult. We experimentally simulate the transient behaviors of QHO in an open system during time evolution with an optical mode and a logical operation system of continuous variable quantum computation. The time evolution of an atomic ensemble in the collective spontaneous emission is analytically simulated by mapping the atomic ensemble onto a QHO. The measured fidelity, which is used for quantifying the quality of the simulation, is higher than its classical limit. The presented simulation scheme provides a new tool for studying the dynamic behaviors of QHO. PMID:26961962

  17. Harmonic Oscillations in Homeostatic Controllers: Dynamics of the p53 Regulatory System

    PubMed Central

    Jolma, Ingunn W.; Ni, Xiao Yu; Rensing, Ludger; Ruoff, Peter

    2010-01-01

    Abstract Homeostatic mechanisms are essential for the protection and adaptation of organisms in a changing and challenging environment. Previously, we have described molecular mechanisms that lead to robust homeostasis/adaptation under inflow or outflow perturbations. Here we report that harmonic oscillations occur in models of such homeostatic controllers and that a close relationship exists between the control of the p53/Mdm2 system and that of a homeostatic inflow controller. This homeostatic control model of the p53 system provides an explanation why large fluctuations in the amplitude of p53/Mdm2 oscillations may arise as part of the homeostatic regulation of p53 by Mdm2 under DNA-damaging conditions. In the presence of DNA damage p53 is upregulated, but is subject to a tight control by Mdm2 and other factors to avoid a premature apoptotic response of the cell at low DNA damage levels. One of the regulatory steps is the Mdm2-mediated degradation of p53 by the proteasome. Oscillations in the p53/Mdm2 system are considered to be part of a mechanism by which a cell decides between cell cycle arrest/DNA repair and apoptosis. In the homeostatic inflow control model, harmonic oscillations in p53/Mdm2 levels arise when the binding strength of p53 to degradation complexes increases. Due to the harmonic character of the oscillations rapid fluctuating noise can lead, as experimentally observed, to large variations in the amplitude of the oscillation but not in their period, a behavior which has been difficult to simulate by deterministic limit-cycle models. In conclusion, the oscillatory response of homeostatic controllers may provide new insights into the origin and role of oscillations observed in homeostatically controlled molecular networks. PMID:20197027

  18. The harmonic oscillator and the position dependent mass Schrödinger equation: isospectral partners and factorization operators

    NASA Astrophysics Data System (ADS)

    Morales, J.; Ovando, G.; Peña, J. J.

    2010-12-01

    One of the most important scientific contributions of Professor Marcos Moshinsky has been his study on the harmonic oscillator in quantum theory vis à vis the standard Schrödinger equation with constant mass [1]. However, a simple description of the motion of a particle interacting with an external environment such as happen in compositionally graded alloys consist of replacing the mass by the so-called effective mass that is in general variable and dependent on position. Therefore, honoring in memoriam Marcos Moshinsky, in this work we consider the position-dependent mass Schrodinger equations (PDMSE) for the harmonic oscillator potential model as former potential as well as with equi-spaced spectrum solutions, i.e. harmonic oscillator isospectral partners. To that purpose, the point canonical transformation method to convert a general second order differential equation (DE), of Sturm-Liouville type, into a Schrödinger-like standard equation is applied to the PDMSE. In that case, the former potential associated to the PDMSE and the potential involved in the Schrödinger-like standard equation are related through a Riccati-type relationship that includes the equivalent of the Witten superpotential to determine the exactly solvable positions-dependent mass distribution (PDMD) m(x). Even though the proposed approach is exemplified with the harmonic oscillator potential, the procedure is general and can be straightforwardly applied to other DEs.

  19. Bound state solution of Dirac equation for 3D harmonics oscillator plus trigonometric scarf noncentral potential using SUSY QM approach

    SciTech Connect

    Cari, C. Suparmi, A.

    2014-09-30

    Dirac equation of 3D harmonics oscillator plus trigonometric Scarf non-central potential for spin symmetric case is solved using supersymmetric quantum mechanics approach. The Dirac equation for exact spin symmetry reduces to Schrodinger like equation. The relativistic energy and wave function for spin symmetric case are simply obtained using SUSY quantum mechanics method and idea of shape invariance.

  20. Research and fabrication of harmonic oscillator with high quality in Si-based MOEMS acceleration seismic geophone

    NASA Astrophysics Data System (ADS)

    Tong, Zhengrong; Wang, Zhiyong; En, De; Chen, Caihe; Li, Xuejiao; Xie, Xiaofang

    2008-03-01

    A kind of photo-electronic integrated acceleration seismic detecting technology, which is novel and precise based on waveguide M-Z interference, is presented. It provieds modern geologic prospect with a novel detection technology. The principle of the photo-electronic integrated acceleration seismic geophone is introduced in this paper. The core of the photo-electronic integrated acceleration is the silicon harmonic oscillator, which is supported by four silicon beams and integrated on the signal beam of the M-Z interferometer. When the seismic mass is subjected to a normal acceleration a z, the acceleration a z, will result in an inertial force F z, causing the mass to move up or down like the piston, until the counter force of the beam suspension equals this inertial force. The principle of the harmonic oscillator is briefly introduced, the factors influencing the anisotropic etching quality of the harmonic oscillator are analyzed in detail. In experiment, the fabrication technology was studied and improved. The high quality harmonic oscillator has been successfully fabricated. It has been applied in the integrated optical chip of "the theory and experiment research of photoelectric integrated acceleration seismic geophone technology".

  1. Sampled-data synchronisation of coupled harmonic oscillators with communication and input delays subject to controller failure

    NASA Astrophysics Data System (ADS)

    Zhao, Liyun; Zhou, Jin; Wu, Quanjun

    2016-01-01

    This paper considers the sampled-data synchronisation problems of coupled harmonic oscillators with communication and input delays subject to controller failure. A synchronisation protocol is proposed for such oscillator systems over directed network topology, and then some general algebraic criteria on exponential convergence for the proposed protocol are established. The main features of the present investigation include: (1) both the communication and input delays are simultaneously addressed, and the directed network topology is firstly considered and (2) the effects of time delays on synchronisation performance are theoretically and numerically investigated. It is shown that in the absence of communication delays, coupled harmonic oscillators can achieve synchronisation oscillatory motion. Whereas if communication delays are nonzero at infinite multiple sampled-data instants, its synchronisation (or consensus) state is zero. This conclusion can be used as an effective control strategy to stabilise coupled harmonic oscillators in practical applications. Furthermore, it is interesting to find that increasing either communication or input delays will enhance the synchronisation performance of coupled harmonic oscillators. Subsequently, numerical examples illustrate and visualise theoretical results.

  2. A Back-to-Front Derivation: The Equal Spacing of Quantum Levels Is a Proof of Simple Harmonic Oscillator Physics

    ERIC Educational Resources Information Center

    Andrews, David L.; Romero, Luciana C. Davila

    2009-01-01

    The dynamical behaviour of simple harmonic motion can be found in numerous natural phenomena. Within the quantum realm of atomic, molecular and optical systems, two main features are associated with harmonic oscillations: a finite ground-state energy and equally spaced quantum energy levels. Here it is shown that there is in fact a one-to-one…

  3. A Back-to-Front Derivation: The Equal Spacing of Quantum Levels Is a Proof of Simple Harmonic Oscillator Physics

    ERIC Educational Resources Information Center

    Andrews, David L.; Romero, Luciana C. Davila

    2009-01-01

    The dynamical behaviour of simple harmonic motion can be found in numerous natural phenomena. Within the quantum realm of atomic, molecular and optical systems, two main features are associated with harmonic oscillations: a finite ground-state energy and equally spaced quantum energy levels. Here it is shown that there is in fact a one-to-one…

  4. Quantization and instability of the damped harmonic oscillator subject to a time-dependent force

    SciTech Connect

    Majima, H. Suzuki, A.

    2011-12-15

    We consider the one-dimensional motion of a particle immersed in a potential field U(x) under the influence of a frictional (dissipative) force linear in velocity (-{gamma}x) and a time-dependent external force (K(t)). The dissipative system subject to these forces is discussed by introducing the extended Bateman's system, which is described by the Lagrangian: L=mxy-U(x+1/2 y)+U(x-1/2 y)+({gamma})/2 (xy-yx)-xK(t)+yK(t), which leads to the familiar classical equations of motion for the dissipative (open) system. The equation for a variable y is the time-reversed of the x motion. We discuss the extended Bateman dual Lagrangian and Hamiltonian by setting U(x{+-}y/2)=1/2 k(x{+-}y/2){sup 2} specifically for a dual extended damped-amplified harmonic oscillator subject to the time-dependent external force. We show the method of quantizing such dissipative systems, namely the canonical quantization of the extended Bateman's Hamiltonian H. The Heisenberg equations of motion utilizing the quantized Hamiltonian H surely lead to the equations of motion for the dissipative dynamical quantum systems, which are the quantum analog of the corresponding classical systems. To discuss the stability of the quantum dissipative system due to the influence of an external force K(t) and the dissipative force, we derived a formula for transition amplitudes of the dissipative system with the help of the perturbation analysis. The formula is specifically applied for a damped-amplified harmonic oscillator subject to the impulsive force. This formula is used to study the influence of dissipation such as the instability due to the dissipative force and/or the applied impulsive force. - Highlights: > A method of quantizing dissipative systems is presented. > In order to obtain the method, we apply Bateman's dual system approach. > A formula for a transition amplitude is derived. > We use the formula to study the instability of the dissipative systems.

  5. HOTB update: Parallel code for calculation of three- and four-particle harmonic oscillator transformation brackets and their matrices using OpenMP

    NASA Astrophysics Data System (ADS)

    Germanas, D.; Stepšys, A.; Mickevičius, S.; Kalinauskas, R. K.

    2017-06-01

    This is a new version of the HOTB code designed to calculate three and four particle harmonic oscillator (HO) transformation brackets and their matrices. The new version uses the OpenMP parallel communication standard for calculations of harmonic oscillator transformation brackets. A package of Fortran code is presented. Calculation time of large matrices, orthogonality conditions and array of coefficients can be significantly reduced using effective parallel code. Other functionalities of the original code (for example calculation of single harmonic oscillator brackets) have not been modified.

  6. The stochastic electrodynamic solution of the charged harmonic oscillator in a constant uniform magnetic field

    NASA Astrophysics Data System (ADS)

    Davis, Brian Thompson

    1998-07-01

    An isotropic three-dimensional non-relativistic charged harmonic oscillator immersed in the stochastic zero point field, an applied classical radiation field, and a constant uniform magnetic field is treated. The method followed is that of previous work [1, 2, 3, 4] with no static magnetic field present. Starting from a non-runaway classical stochastic motion equation, an appropriate conjugate momentum is derived. The classical position/conjugate momentum phase space distribution, a product of Dirac delta distributions, is ensemble averaged. The Liouville equation for this ensemble averaged phase space distribution, along with a separate independent equation that the distribution must satisfy, are derived in dipole approximation. The Weyl transformed Liouville, equation is used to derive a stochastic Schroedinger equation valid to first order in the Larmor frequency. The stochastic equation is the same as the quantum one to this order, except for the presence of radiation reaction vector potentials that produce spontaneous emission without quantization of the applied radiation field. The ensemble averaged Weyl transformed phase space distribution is also shown to be separable into a product of Schroedinger eigenfunctions, in general. Electric dipole spectra and transition probabilities for spontaneous emission and resonant absorption are calculated using the stochastic Schroedinger equation and its exact solutions. The results are compared to the corresponding predictions of quantum electrodynamics and found to be in agreement.

  7. Rotational shear effects on edge harmonic oscillations in DIII-D quiescent H-mode discharges

    NASA Astrophysics Data System (ADS)

    Chen, Xi; Burrell, K. H.; Ferraro, N. M.; Osborne, T. H.; Austin, M. E.; Garofalo, A. M.; Groebner, R. J.; Kramer, G. J.; Luhmann, N. C., Jr.; McKee, G. R.; Muscatello, C. M.; Nazikian, R.; Ren, X.; Snyder, P. B.; Solomon, W. M.; Tobias, B. J.; Yan, Z.

    2016-07-01

    In the quiescent H-mode (QH-mode) regime, edge harmonic oscillations (EHOs) play an important role in avoiding transient edge localized mode (ELM) power fluxes by providing benign and continuous edge particle transport. A detailed theoretical, experimental and modeling comparison has been made of low-n (n  ⩽  5) EHO in DIII-D QH-mode plasmas. The calculated linear eigenmode structure from the extended magentoohydrodynamics (MHD) code M3D-C1 matches closely the coherent EHO properties from external magnetics data and internal measurements using the ECE, BES, ECE-Imaging and microwave imaging reflectometer (MIR) diagnostics, as well as the kink/peeling mode properties found by the ideal MHD code ELITE. Numerical investigations indicate that the low-n EHO-like solutions from M3D-C1 are destabilized by rotation and/or rotational shear while high-n modes are stabilized. This effect is independent of the rotation direction, suggesting that EHOs can be destabilized in principle with rotation in either direction. The modeling results are consistent with observations of EHO, support the proposed theory of the EHO as a low-n kink/peeling mode destabilized by edge E  ×  B rotational shear, and improve our understanding and confidence in creating and sustaining QH-mode in present and future devices.

  8. Rotational Shear Effects on Edge Harmonic Oscillations in DIII-D Quiescent H-mode Discharges

    NASA Astrophysics Data System (ADS)

    Chen, Xi; Burrell, K. H.; Ferraro, N. M.; Osborne, T. H.; Austin, M. E.; Garofalo, A. M.; Groebner, R. J.; Kramer, G. J.; Luhmann, N. C., Jr.; McKee, G. R.; Muscatello, C. M.; Nazikian, R.; Ren, X.; Snyder, P. B.; Solomon, Wm.; Tobias, B. J.; Yan, Z.

    2015-11-01

    In quiescent H-mode (QH) regime, the edge harmonic oscillations (EHO) play an important role in avoiding the transient ELM power fluxes by providing benign and continuous edge particle transport. A detailed theoretical, experimental and modeling comparison has been made of low-n (n <= 5) EHO in DIII-D QH-mode plasmas. The calculated linear eigenmode structure from the extended MHD code M3D-C1 matches closely the coherent EHO properties from external magnetics data and internal measurements using the ECE, BES, ECE-I and MIR diagnostics, as well as the kink/peeling mode properties of the ideal MHD code ELITE. The numerical investigations indicate that the low-n EHO-like solutions from M3D-C1 are destabilized by the toroidal rotational shear while high-n modes are stabilized. This effect is independent of the rotation direction, suggesting that the low-n EHO can be destabilized in principle with rotation in both directions. These modeling results are consistent with experimental observations of the EHO and support the proposed theory of the EHO as a rotational shear driven kink/peeling mode.

  9. Development and applications of algorithms for calculating the transonic flow about harmonically oscillating wings

    NASA Technical Reports Server (NTRS)

    Ehlers, F. E.; Weatherill, W. H.; Yip, E. L.

    1984-01-01

    A finite difference method to solve the unsteady transonic flow about harmonically oscillating wings was investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The differential equation for the unsteady velocity potential is linear with spatially varying coefficients and with the time variable eliminated by assuming harmonic motion. An alternating direction implicit procedure was investigated, and a pilot program was developed for both two and three dimensional wings. This program provides a relatively efficient relaxation solution without previously encountered solution instability problems. Pressure distributions for two rectangular wings are calculated. Conjugate gradient techniques were developed for the asymmetric, indefinite problem. The conjugate gradient procedure is evaluated for applications to the unsteady transonic problem. Different equations for the alternating direction procedure are derived using a coordinate transformation for swept and tapered wing planforms. Pressure distributions for swept, untaped wings of vanishing thickness are correlated with linear results for sweep angles up to 45 degrees.

  10. Stability of the ground state of a harmonic oscillator in a monochromatic wave.

    PubMed

    Berman, Gennady P.; James, Daniel F. V.; Kamenev, Dmitry I.

    2001-09-01

    The stability of the ground state of a harmonic oscillator in a monochromatic wave is studied. This model describes, in particular, the dynamics of a cold ion in a linear ion trap, interacting with two laser fields with close frequencies. The stability of the "classical ground state"-the vicinity of the point (x=0,p=0)-is analyzed analytically and numerically. For the quantum case, a method for studying a stability of the quantum ground state is developed, based on the quasienergy representation. It is demonstrated that stability of the ground state may be substantially improved by increasing the resonance number, l, where l=Omega/omega+delta, Omega and omega are, respectively, the wave frequency and the oscillator frequency, l=1,2, em leader, mid R:deltamid R:<1; or by detuning the system from exact resonance, so that delta not equal 0. The influence of a large-amplitude wave (in the presence of chaos) on the stability of the ground state is analyzed for different parameters of the model in both the quantum and classical cases. (c) 2001 American Institute of Physics.

  11. Floquet topological system based on frequency-modulated classical coupled harmonic oscillators

    NASA Astrophysics Data System (ADS)

    Salerno, Grazia; Ozawa, Tomoki; Price, Hannah M.; Carusotto, Iacopo

    2016-02-01

    We theoretically propose how to observe topological effects in a generic classical system of coupled harmonic oscillators, such as classical pendula or lumped-element electric circuits, whose oscillation frequency is modulated fast in time. Making use of Floquet theory in the high-frequency limit, we identify a regime in which the system is accurately described by a Harper-Hofstadter model where the synthetic magnetic field can be externally tuned via the phase of the frequency modulation of the different oscillators. We illustrate how the topologically protected chiral edge states, as well as the Hofstadter butterfly of bulk bands, can be observed in the driven-dissipative steady state under a monochromatic drive. In analogy with the integer quantum Hall effect, we show how the topological Chern numbers of the bands can be extracted from the mean transverse shift of the steady-state oscillation amplitude distribution. Finally, we discuss the regime where the analogy with the Harper-Hofstadter model breaks down.

  12. Thermodynamical analysis of a quantum heat engine based on harmonic oscillators.

    PubMed

    Insinga, Andrea; Andresen, Bjarne; Salamon, Peter

    2016-07-01

    Many models of heat engines have been studied with the tools of finite-time thermodynamics and an ensemble of independent quantum systems as the working fluid. Because of their convenient analytical properties, harmonic oscillators are the most frequently used example of a quantum system. We analyze different thermodynamical aspects with the final aim of the optimization of the performance of the engine in terms of the mechanical power provided during a finite-time Otto cycle. The heat exchange mechanism between the working fluid and the thermal reservoirs is provided by the Lindblad formalism. We describe an analytical method to find the limit cycle and give conditions for a stable limit cycle to exist. We explore the power production landscape as the duration of the four branches of the cycle are varied for short times, intermediate times, and special frictionless times. For short times we find a periodic structure with atolls of purely dissipative operation surrounding islands of divergent behavior where, rather than tending to a limit cycle, the working fluid accumulates more and more energy. For frictionless times the periodic structure is gone and we come very close to the global optimal operation. The global optimum is found and interestingly comes with a particular value of the cycle time.

  13. Are There Signatures of Harmonic Oscillator Shells Far from Stability? First Spectroscopy of 110Zr

    NASA Astrophysics Data System (ADS)

    Paul, N.; Corsi, A.; Obertelli, A.; Doornenbal, P.; Authelet, G.; Baba, H.; Bally, B.; Bender, M.; Calvet, D.; Château, F.; Chen, S.; Delaroche, J.-P.; Delbart, A.; Gheller, J.-M.; Giganon, A.; Gillibert, A.; Girod, M.; Heenen, P.-H.; Lapoux, V.; Libert, J.; Motobayashi, T.; Niikura, M.; Otsuka, T.; Rodríguez, T. R.; Roussé, J.-Y.; Sakurai, H.; Santamaria, C.; Shimizu, N.; Steppenbeck, D.; Taniuchi, R.; Togashi, T.; Tsunoda, Y.; Uesaka, T.; Ando, T.; Arici, T.; Blazhev, A.; Browne, F.; Bruce, A. M.; Carroll, R.; Chung, L. X.; Cortés, M. L.; Dewald, M.; Ding, B.; Flavigny, F.; Franchoo, S.; Górska, M.; Gottardo, A.; Jungclaus, A.; Lee, J.; Lettmann, M.; Linh, B. D.; Liu, J.; Liu, Z.; Lizarazo, C.; Momiyama, S.; Moschner, K.; Nagamine, S.; Nakatsuka, N.; Nita, C.; Nobs, C. R.; Olivier, L.; Patel, Z.; Podolyák, Zs.; Rudigier, M.; Saito, T.; Shand, C.; Söderström, P.-A.; Stefan, I.; Orlandi, R.; Vaquero, V.; Werner, V.; Wimmer, K.; Xu, Z.

    2017-01-01

    The first measurement of the low-lying states of the neutron-rich 110Zr and 112Mo was performed via in-beam γ -ray spectroscopy after one proton removal on hydrogen at ˜200 MeV /nucleon . The 21+ excitation energies were found at 185(11) keV in 110Zr, and 235(7) keV in 112Mo, while the R42=E (41+)/E (21+) ratios are 3.1(2), close to the rigid rotor value, and 2.7(1), respectively. These results are compared to modern energy density functional based configuration mixing models using Gogny and Skyrme effective interactions. We conclude that first levels of 110Zr exhibit a rotational behavior, in agreement with previous observations of lighter zirconium isotopes as well as with the most advanced Monte Carlo shell model predictions. The data, therefore, do not support a harmonic oscillator shell stabilization scenario at Z =40 and N =70 . The present data also invalidate predictions for a tetrahedral ground state symmetry in 110Zr.

  14. Application of functional analysis to perturbation theory of differential equations. [nonlinear perturbation of the harmonic oscillator

    NASA Technical Reports Server (NTRS)

    Bogdan, V. M.; Bond, V. B.

    1980-01-01

    The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.

  15. On The Exact and JWKB Solution of 1D Quantum Harmonic Oscillator by Mathematica

    NASA Astrophysics Data System (ADS)

    Deniz, Coşkun

    2016-04-01

    Although being the fundamental semiclassical approximation method mainly used in quantum mechanics and optical waveguides, JWKB method along with the application of the associated JWKB asymptotic matching rules is known to give exact solutions for the Quantum Harmonic Oscillator (QHO). Asymptotically matched JWKB solutions are typically accurate or exact in the entire domain except for a narrow domain around the classical turning points where potential energy equals the total energy of the related quantum mechanical system. So, one has to cope with this diverging behavior at the classical turning points since it prohibits us from using continuity relations at the related boundaries to determine the required JWKB coefficients. Here, a computational diagram and related mathematica codes to surmount the problem by applying parity matching for even and odd JWKB solutions rather than boundary continuities are being presented. In effect, JWKB coefficients as well as the conversion factor for the dimensionless form of the Schrodingers equation, which is common to both exact and JWKB solutions, is being successfully obtained.

  16. Rotational shear effects on edge harmonic oscillations in DIII-D quiescent H-mode discharges

    SciTech Connect

    Chen, Xi; Burrell, Keith H.; Ferraro, Nathaniel M.; Osborne, Thomas H.; Austin, Max E.; Garofalo, Andrea M.; Groebner, Richard J.; Kramer, Gerrit J.; Luhmann, Jr., Neville C.; McKee, George R.; Muscatello, C. M.; Nazikian, R.; Ren, X.; Snyder, P. B.; Solomon, W. M.; Tobias, B. J.; Yan, Z.

    2016-06-21

    In the quiescent H-mode (QH-mode) regime, edge harmonic oscillations (EHO) play an important role in avoiding transient edge localized mode (ELM) power fluxes by providing benign and continuous edge particle transport. A detailed theoretical, experimental and modeling comparison has been made of low-n (n ≤ 5) EHO in DIII-D QH-mode plasmas. The calculated linear eigenmode structure from the extended MHD code M3D-C1 matches closely the coherent EHO properties from external magnetics data and internal measurements using the ECE, BES, ECE-Imaging and microwave imaging reflectometer (MIR) diagnostics, as well as the kink/peeling mode properties found by the ideal MHD code ELITE. Numerical investigations indicate that the low-n EHO-like solutions from M3D-C1 are destabilized by the rotational shear while high-n modes are stabilized. This effect is independent of the rotation direction, suggesting that EHO can be destabilized in principle with rotation in either direction. Furthermore, the modeling results are consistent with observations of the EHO, support the proposed theory of the EHO as a rotational shear driven kink/peeling mode, and improve our understanding and confidence in creating and sustaining QH-mode in present and future devices.

  17. Nonlinear spectroscopic theory of displaced harmonic oscillators with differing curvatures: a correlation function approach.

    PubMed

    Fidler, Andrew F; Engel, Gregory S

    2013-10-03

    We present a theory for a bath model in which we approximate the adiabatic nuclear potential surfaces on the ground and excited electronic states by displaced harmonic oscillators that differ in curvature. Calculations of the linear and third-order optical response functions employ an effective short-time approximation coupled with the cumulant expansion. In general, all orders of correlation contribute to the optical response, indicating that the solvation process cannot be described as Gaussian within the model. Calculations of the linear absorption and fluorescence spectra resulting from the theory reveal a stronger temperature dependence of the Stokes shift along with a general asymmetry between absorption and fluorescence line shapes, resulting purely from the difference in the phonon side band. We discuss strategies for controlling spectral tuning and energy-transfer dynamics through the manipulation of the excited-state and ground-state curvature. Calculations of the nonlinear response also provide insights into the dynamics of the system-bath interactions and reveal that multidimensional spectroscopies are sensitive to a difference in curvature between the ground- and excited-state adiabatic surfaces. This extension allows for the elucidation of short-time dynamics of dephasing that are accessible in nonlinear spectroscopic methods.

  18. Thermodynamical analysis of a quantum heat engine based on harmonic oscillators

    NASA Astrophysics Data System (ADS)

    Insinga, Andrea; Andresen, Bjarne; Salamon, Peter

    2016-07-01

    Many models of heat engines have been studied with the tools of finite-time thermodynamics and an ensemble of independent quantum systems as the working fluid. Because of their convenient analytical properties, harmonic oscillators are the most frequently used example of a quantum system. We analyze different thermodynamical aspects with the final aim of the optimization of the performance of the engine in terms of the mechanical power provided during a finite-time Otto cycle. The heat exchange mechanism between the working fluid and the thermal reservoirs is provided by the Lindblad formalism. We describe an analytical method to find the limit cycle and give conditions for a stable limit cycle to exist. We explore the power production landscape as the duration of the four branches of the cycle are varied for short times, intermediate times, and special frictionless times. For short times we find a periodic structure with atolls of purely dissipative operation surrounding islands of divergent behavior where, rather than tending to a limit cycle, the working fluid accumulates more and more energy. For frictionless times the periodic structure is gone and we come very close to the global optimal operation. The global optimum is found and interestingly comes with a particular value of the cycle time.

  19. Phase space path integral approach to harmonic oscillator with a time-dependent force constant

    NASA Astrophysics Data System (ADS)

    Janakiraman, Deepika; Sebastian, K. L.

    2015-09-01

    The quantum statistical mechanical propagator for a harmonic oscillator with a time-dependent force constant, mω2(t) , has been investigated in the past and was found to have only a formal solution in terms of the solutions of certain ordinary differential equations. Such path integrals are frequently encountered in semiclassical path integral evaluations and having exact analytical expressions for such path integrals is of great interest. In a previous work, we had obtained the exact propagator for motion in an arbitrary time-dependent harmonic potential in the overdamped limit of friction using phase space path integrals in the context of Lévy flights - a result that can be easily extended to Brownian motion. In this paper, we make a connection between the overdamped Brownian motion and the imaginary time propagator of quantum mechanics and thereby get yet another way to evaluate the latter exactly. We find that explicit analytic solution for the quantum statistical mechanical propagator can be written when the time-dependent force constant has the form ω2(t) =λ2(t) - dλ(t)/dt, where λ(t) is any arbitrary function of t and use it to evaluate path integrals which have not been evaluated previously. We also employ this method to arrive at a formal solution of the propagator for both Lévy flights and Brownian subjected to a time-dependent harmonic potential in the underdamped limit of friction.

  20. Rotational shear effects on edge harmonic oscillations in DIII-D quiescent H-mode discharges

    SciTech Connect

    Chen, Xi; Burrell, Keith H.; Ferraro, Nathaniel M.; Osborne, Thomas H.; Austin, Max E.; Garofalo, Andrea M.; Groebner, Richard J.; Kramer, Gerrit J.; Luhmann, Jr., Neville C.; McKee, George R.; Muscatello, C. M.; Nazikian, R.; Ren, X.; Snyder, P. B.; Solomon, W. M.; Tobias, B. J.; Yan, Z.

    2016-06-21

    In the quiescent H-mode (QH-mode) regime, edge harmonic oscillations (EHO) play an important role in avoiding transient edge localized mode (ELM) power fluxes by providing benign and continuous edge particle transport. A detailed theoretical, experimental and modeling comparison has been made of low-n (n ≤ 5) EHO in DIII-D QH-mode plasmas. The calculated linear eigenmode structure from the extended MHD code M3D-C1 matches closely the coherent EHO properties from external magnetics data and internal measurements using the ECE, BES, ECE-Imaging and microwave imaging reflectometer (MIR) diagnostics, as well as the kink/peeling mode properties found by the ideal MHD code ELITE. Numerical investigations indicate that the low-n EHO-like solutions from M3D-C1 are destabilized by the rotational shear while high-n modes are stabilized. This effect is independent of the rotation direction, suggesting that EHO can be destabilized in principle with rotation in either direction. Furthermore, the modeling results are consistent with observations of the EHO, support the proposed theory of the EHO as a rotational shear driven kink/peeling mode, and improve our understanding and confidence in creating and sustaining QH-mode in present and future devices.

  1. Rotational shear effects on edge harmonic oscillations in DIII-D quiescent H-mode discharges

    DOE PAGES

    Chen, Xi; Burrell, Keith H.; Ferraro, Nathaniel M.; ...

    2016-06-21

    In the quiescent H-mode (QH-mode) regime, edge harmonic oscillations (EHO) play an important role in avoiding transient edge localized mode (ELM) power fluxes by providing benign and continuous edge particle transport. A detailed theoretical, experimental and modeling comparison has been made of low-n (n ≤ 5) EHO in DIII-D QH-mode plasmas. The calculated linear eigenmode structure from the extended MHD code M3D-C1 matches closely the coherent EHO properties from external magnetics data and internal measurements using the ECE, BES, ECE-Imaging and microwave imaging reflectometer (MIR) diagnostics, as well as the kink/peeling mode properties found by the ideal MHD code ELITE.more » Numerical investigations indicate that the low-n EHO-like solutions from M3D-C1 are destabilized by the rotational shear while high-n modes are stabilized. This effect is independent of the rotation direction, suggesting that EHO can be destabilized in principle with rotation in either direction. Furthermore, the modeling results are consistent with observations of the EHO, support the proposed theory of the EHO as a rotational shear driven kink/peeling mode, and improve our understanding and confidence in creating and sustaining QH-mode in present and future devices.« less

  2. Are There Signatures of Harmonic Oscillator Shells Far from Stability? First Spectroscopy of ^{110}Zr.

    PubMed

    Paul, N; Corsi, A; Obertelli, A; Doornenbal, P; Authelet, G; Baba, H; Bally, B; Bender, M; Calvet, D; Château, F; Chen, S; Delaroche, J-P; Delbart, A; Gheller, J-M; Giganon, A; Gillibert, A; Girod, M; Heenen, P-H; Lapoux, V; Libert, J; Motobayashi, T; Niikura, M; Otsuka, T; Rodríguez, T R; Roussé, J-Y; Sakurai, H; Santamaria, C; Shimizu, N; Steppenbeck, D; Taniuchi, R; Togashi, T; Tsunoda, Y; Uesaka, T; Ando, T; Arici, T; Blazhev, A; Browne, F; Bruce, A M; Carroll, R; Chung, L X; Cortés, M L; Dewald, M; Ding, B; Flavigny, F; Franchoo, S; Górska, M; Gottardo, A; Jungclaus, A; Lee, J; Lettmann, M; Linh, B D; Liu, J; Liu, Z; Lizarazo, C; Momiyama, S; Moschner, K; Nagamine, S; Nakatsuka, N; Nita, C; Nobs, C R; Olivier, L; Patel, Z; Podolyák, Zs; Rudigier, M; Saito, T; Shand, C; Söderström, P-A; Stefan, I; Orlandi, R; Vaquero, V; Werner, V; Wimmer, K; Xu, Z

    2017-01-20

    The first measurement of the low-lying states of the neutron-rich ^{110}Zr and ^{112}Mo was performed via in-beam γ-ray spectroscopy after one proton removal on hydrogen at ∼200  MeV/nucleon. The 2_{1}^{+} excitation energies were found at 185(11) keV in ^{110}Zr, and 235(7) keV in ^{112}Mo, while the R_{42}=E(4_{1}^{+})/E(2_{1}^{+}) ratios are 3.1(2), close to the rigid rotor value, and 2.7(1), respectively. These results are compared to modern energy density functional based configuration mixing models using Gogny and Skyrme effective interactions. We conclude that first levels of ^{110}Zr exhibit a rotational behavior, in agreement with previous observations of lighter zirconium isotopes as well as with the most advanced Monte Carlo shell model predictions. The data, therefore, do not support a harmonic oscillator shell stabilization scenario at Z=40 and N=70. The present data also invalidate predictions for a tetrahedral ground state symmetry in ^{110}Zr.

  3. Characterizing classical periodic orbits from quantum Green's functions in two-dimensional integrable systems: Harmonic oscillators and quantum billiards

    NASA Astrophysics Data System (ADS)

    Chen, Y. F.; Tung, J. C.; Tuan, P. H.; Yu, Y. T.; Liang, H. C.; Huang, K. F.

    2017-01-01

    A general method is developed to characterize the family of classical periodic orbits from the quantum Green's function for the two-dimensional (2D) integrable systems. A decomposing formula related to the beta function is derived to link the quantum Green's function with the individual classical periodic orbits. The practicality of the developed formula is demonstrated by numerically analyzing the 2D commensurate harmonic oscillators and integrable quantum billiards. Numerical analyses reveal that the emergence of the classical features in quantum Green's functions principally comes from the superposition of the degenerate states for 2D harmonic oscillators. On the other hand, the damping factor in quantum Green's functions plays a critical role to display the classical features in mesoscopic regime for integrable quantum billiards, where the physical function of the damping factor is to lead to the coherent superposition of the nearly degenerate eigenstates.

  4. Characterizing classical periodic orbits from quantum Green's functions in two-dimensional integrable systems: Harmonic oscillators and quantum billiards.

    PubMed

    Chen, Y F; Tung, J C; Tuan, P H; Yu, Y T; Liang, H C; Huang, K F

    2017-01-01

    A general method is developed to characterize the family of classical periodic orbits from the quantum Green's function for the two-dimensional (2D) integrable systems. A decomposing formula related to the beta function is derived to link the quantum Green's function with the individual classical periodic orbits. The practicality of the developed formula is demonstrated by numerically analyzing the 2D commensurate harmonic oscillators and integrable quantum billiards. Numerical analyses reveal that the emergence of the classical features in quantum Green's functions principally comes from the superposition of the degenerate states for 2D harmonic oscillators. On the other hand, the damping factor in quantum Green's functions plays a critical role to display the classical features in mesoscopic regime for integrable quantum billiards, where the physical function of the damping factor is to lead to the coherent superposition of the nearly degenerate eigenstates.

  5. Variational study of a two-level system coupled to a harmonic oscillator in an ultrastrong-coupling regime

    SciTech Connect

    Hwang, Myung-Joong; Choi, Mahn-Soo

    2010-08-15

    The nonclassical behavior of a two-level system coupled to a harmonic oscillator is investigated in the ultrastrong coupling regime. We revisit the variational solution of the ground state and find that the existing solutions do not account accurately for nonclassical effects such as squeezing. We suggest a trial wave function and demonstrate that it has an excellent accuracy for the quantum correlation effects as well as for the energy.

  6. Harmonic Oscillation at a Mud Volcano in the West Nile Delta

    NASA Astrophysics Data System (ADS)

    Lefeldt, M. R.; Hoelz, S.; Bialas, J.; Brueckmann, W.

    2009-12-01

    We present results from an Ocean Bottom Seismometer (OBS) Network that has been installed for a period of 8 months at North Alex Mud Volcano (NAMV) in the West Nile Delta at 500 m water depth. All six OBS stations were equipped with both a hydrophone and a 3-component geophone. In addition to local seismicity, i.e. seismic signals from NAMV, records from these stations also show large earthquakes that occurred in the Mediterranean, e.g. a Mw=6.7 event that took place offshore Crete at the 1st of July 2009. Records from OBS stations, which were located on the Mud Volcano’s conduit, differ markedly from records of the stations positioned outside of the mud volcano. While onset and waveform of P- and S-wave are comparable at all stations, an OBS on top of the NAMV central conduit record a long-wavelength ground movement even several minutes after the signal has died at any other station. Spectral analysis shows distinguished peaks for this movement at periods of 11.1s; 5.6s; 2.8s and 1.9s, which implies a harmonic oscillation in resonance of the entire conduit. Thus, large seismic events seem to be able to stimulate mud volcanoes to all natural oscillations, comparable to the 1s - 5d modes of a stimulated membrane. Since the diameter of the central NAMV conduit is known from seafloor bathymetry and 3-D seismic images, modeling of the resonance wavelength might allow to construct depth and seismic velocities within it. In turn, seismic velocities could be related to gas content. Furthermore, when oscillating in resonance, the slow movement of the NAMV surface means a pressure change in the upper sedimentary layers. We present evidence that this causes degassing of the conduit. Gas pressures in the conduit are expected to be in equilibrium with the surrounding pressure. Lowering the surrounding pressure causes the mentioned effect, in agreement with Henry’s law. We show that in case of a harmonic oscillation, large amplitude noise in the high-frequency spectra of

  7. Entropy of orthogonal polynomials with Freud weights and information entropies of the harmonic oscillator potential

    NASA Astrophysics Data System (ADS)

    Van Assche, W.; Yáñez, R. J.; Dehesa, J. S.

    1995-08-01

    The information entropy of the harmonic oscillator potential V(x)=1/2λx2 in both position and momentum spaces can be expressed in terms of the so-called ``entropy of Hermite polynomials,'' i.e., the quantity Sn(H):= -∫-∞+∞H2n(x)log H2n(x) e-x2dx. These polynomials are instances of the polynomials orthogonal with respect to the Freud weights w(x)=exp(-||x||m), m≳0. Here, a very precise and general result of the entropy of Freud polynomials recently established by Aptekarev et al. [J. Math. Phys. 35, 4423-4428 (1994)], specialized to the Hermite kernel (case m=2), leads to an important refined asymptotic expression for the information entropies of very excited states (i.e., for large n) in both position and momentum spaces, to be denoted by Sρ and Sγ, respectively. Briefly, it is shown that, for large values of n, Sρ+1/2logλ≂log(π√2n/e)+o(1) and Sγ-1/2log λ≂log(π√2n/e)+o(1), so that Sρ+Sγ≂log(2π2n/e2)+o(1) in agreement with the generalized indetermination relation of Byalinicki-Birula and Mycielski [Commun. Math. Phys. 44, 129-132 (1975)]. Finally, the rate of convergence of these two information entropies is numerically analyzed. In addition, using a Rakhmanov result, we describe a totally new proof of the leading term of the entropy of Freud polynomials which, naturally, is just a weak version of the aforementioned general result.

  8. Microwave Imaging Reflectometry for the study of Edge Harmonic Oscillations on DIII-D

    NASA Astrophysics Data System (ADS)

    Ren, X.; Chen, M.; Chen, X.; Domier, C. W.; Ferraro, N. M.; Kramer, G. J.; Luhmann, N. C., Jr.; Muscatello, C. M.; Nazikian, R.; Shi, L.; Tobias, B. J.; Valeo, E.

    2015-10-01

    Quiescent H-mode (QH-mode) is an ELM free mode of operation in which edge-localized harmonic oscillations (EHOs) are believed to enhance particle transport, thereby stabilizing ELMs and preventing damage to the divertor and plasma facing components. Microwave Imaging Reflectometer (MIR) enabling direct comparison between the measured and simulated 2D images of density fluctuations near the edge can determine the 2D structure of density oscillation, which can help to explain the physics behind EHO modes. MIR data sometimes indicate a counter-propagation between dominant (n=1) and higher harmonic modes of coherent EHOs in the steep gradient regions of the pedestal. To preclude diagnostic artifacts, we have performed forward modeling that includes possible optical mis-alignments to show that offsets between transmitting and receiving antennas do not account for this feature. We have also simulated the non-linear structure of the EHO modes, which induces multiple harmonics that are properly charaterized in the synthetic diagnostic. By excluding mis-alignments of optics as well as patially eliminating non-linearity of EHO mode structure as possible explanation for the data, counter-propagation observed in MIR data, which is not corroborated by external Mirnov coil array measurements, may be due to subtleties of the eigenmode structure, such as an inversion radius consistent with a magnetic island. Similar effects are observed in analysis of internal ECE-Imaging and BES data. The identification of a non-ideal structure motivates further exploration of nonlinear models of this instability. A shorter version of this contribution is due to be published in PoS at: 1st EPS conference on Plasma Diagnostics

  9. Scaling of Harmonic Oscillator Eigenfunctions and Their Nodal Sets Around the Caustic

    NASA Astrophysics Data System (ADS)

    Hanin, Boris; Zelditch, Steve; Zhou, Peng

    2017-03-01

    We study the scaling asymptotics of the eigenspace projection kernels Π_{hbar, E}(x,y) of the isotropic Harmonic Oscillator {hat{H}_{hbar} = - hbar^2 Δ +|x|^2} of eigenvalue {E = hbar(N + d/2)} in the semi-classical limit {hbar to 0} . The principal result is an explicit formula for the scaling asymptotics of Π_{hbar, E}(x,y) for x, y in a {hbar^{2/3}} neighborhood of the caustic C_E as {hbar → 0.} The scaling asymptotics are applied to the distribution of nodal sets of Gaussian random eigenfunctions around the caustic as {hbar to 0} . In previous work we proved that the density of zeros of Gaussian random eigenfunctions of {hat{H}_{hbar}} have different orders in the Planck constant {hbar} in the allowed and forbidden regions: In the allowed region the density is of order {hbar^{-1}} while it is {hbar^{-1/2}} in the forbidden region. Our main result on nodal sets is that the density of zeros is of order {hbar^{-2/3}} in an {hbar^{2/3}} -tube around the caustic. This tube radius is the `critical radius'. For annuli of larger inner and outer radii {hbar^{α}} with {0 < α < 2/3} we obtain density results that interpolate between this critical radius result and our prior ones in the allowed and forbidden region. We also show that the Hausdorff ( d-2)-dimensional measure of the intersection of the nodal set with the caustic is of order {hbar^{- 2/3}}.

  10. Twist deformation of rotationally invariant quantum mechanics

    SciTech Connect

    Chakraborty, B.; Kuznetsova, Z.; Toppan, F.

    2010-11-15

    Noncommutative quantum mechanics in 3D is investigated in the framework of an abelian Drinfeld twist which deforms a given Hopf algebra structure. Composite operators (of coordinates and momenta) entering the Hamiltonian have to be reinterpreted as primitive elements of a dynamical Lie algebra which could be either finite (for the harmonic oscillator) or infinite (in the general case). The deformed brackets of the deformed angular momenta close the so(3) algebra. On the other hand, undeformed rotationally invariant operators can become, under deformation, anomalous (the anomaly vanishes when the deformation parameter goes to zero). The deformed operators, Taylor-expanded in the deformation parameter, can be selected to minimize the anomaly. We present the deformations (and their anomalies) of undeformed rotationally invariant operators corresponding to the harmonic oscillator (quadratic potential), the anharmonic oscillator (quartic potential), and the Coulomb potential.

  11. Single particle calculations for a Woods-Saxon potential with triaxial deformations, and large Cartesian oscillator basis (TRIAXIAL 2014, Third version of the code Triaxial)

    NASA Astrophysics Data System (ADS)

    Mohammed-Azizi, B.; Medjadi, D. E.

    2014-11-01

    , WINDOWS 7, LINUX. RAM: 256 Mb (depending on nmax). Swap file: 4Gb (depending on nmax) Classification: 17.7. Does the new version supersede the previous version?: Yes Catalogue identifier of previous version: ADSK_v2_0 Journal reference of previous version: Comput. Phys. Comm. 176 (2007) 634 Nature of problem: The Single particle energies and the single particle wave functions are calculated from one-body Hamiltonian including a central field of Woods-Saxon type, a spin-orbit interaction, and the Coulomb potential for the protons. We consider only ellipsoidal (triaxial) shapes. The deformation of the nuclear shape is fixed by the usual Bohr parameters (β,γ). Solution method: The representative matrix of the Hamiltonian is built by means of the Cartesian basis of the anisotropic harmonic oscillator, and then diagonalized by a set of subroutines of the EISPACK library. Two quadrature methods of Gauss are employed to calculate respectively the integrals of the matrix elements of the Hamiltonian, and the integral defining the Coulomb potential. Two quantum numbers are conserved: the parity and the signature. Due to the Kramers degeneracy, only positive signature is considered. Therefore, calculations are made for positive and negative parity separately (with positive signature only). Reasons for new version: Now, there are several ways to obtain the eigenvalues and the eigenfunctions. The eigenvalues can be obtained from the subroutine ‘eigvals’ or from the array ‘energies’ or also from the formatted files ‘valuu.dat’, ‘eigenvalo.dat’, ‘eigenva.dat’ or better from the unformatted file ‘eigenvaunf.dat’. The eigenfunctions can be obtained straightforwardly in configuration space from the subroutine ‘eigfunc’ or by their components on the oscillator basis from the subroutine ‘compnts’. The latter are also recorded on a formatted file ‘componento.dat’ or on an unformatted file ‘componentounf.dat’. Summary of revisions: This version is

  12. Form of the effective interaction in harmonic-oscillator-based effective theory

    NASA Astrophysics Data System (ADS)

    Haxton, W. C.

    2008-03-01

    I explore the form of the effective interaction in harmonic-oscillator-based effective theory (HOBET) in leading order (LO) through next-to-next-to-next-to-leading order (NLO3). Because the included space in a HOBET (as in the shell model) is defined by the oscillator energy, both long-distance (low-momentum) and short-distance (high-momentum) degrees of freedom reside in the high-energy excluded space. A HOBET effective interaction is developed in which a short-range contact-gradient expansion, free of operator mixing and corresponding to a systematic expansion in nodal quantum numbers, is combined with an exact summation of the relative kinetic energy. By this means the very strong coupling of the included (P) and excluded (Q) spaces by the kinetic energy is removed. One finds a simple and rather surprising result, that the interplay of QT and QV is governed by a single parameter κ, the ratio of an observable, the binding energy |E|, to a parameter in the effective theory, the oscillator energy ℏω. Once the functional dependence on κ is identified, the remaining order-by-order subtraction of the short-range physics residing in Q becomes systematic and rapidly converging. Numerical calculations are used to demonstrate how well the resulting expansion reproduces the running of Heff from high scales to a typical shell-model scale of 8ℏω. At NLO3 various global properties of Heff are reproduced to a typical accuracy of 0.01%, or about 1 keV, at 8ℏω. Channel-by-channel variations in convergence rates are similar to those found in effective field theory approaches. The state dependence of the effective interaction has been a troubling problem in nuclear physics and is embodied in the energy dependence of Heff(|E|) in the Bloch-Horowitz formalism. It is shown that almost all of this state dependence is also extracted in the procedures followed here, isolated in the analytic dependence of Heff on κ. Thus there exists a simple, Hermitian Heff that can be use

  13. A model of the two-dimensional quantum harmonic oscillator in an AdS_3 background

    NASA Astrophysics Data System (ADS)

    Frick, R.

    2016-10-01

    In this paper we study a model of the two-dimensional quantum harmonic oscillator in a three-dimensional anti-de Sitter background. We use a generalized Schrödinger picture in which the analogs of the Schrödinger operators of the particle are independent of both the time and the space coordinates in different representations. The spacetime independent operators of the particle induce the Lie algebra of Killing vector fields of the AdS_3 spacetime. In this picture, we have a metamorphosis of the Heisenberg uncertainty relations.

  14. Wigner distribution function and entropy of the damped harmonic oscillator within the theory of the open quantum systems

    NASA Technical Reports Server (NTRS)

    Isar, Aurelian

    1995-01-01

    The harmonic oscillator with dissipation is studied within the framework of the Lindblad theory for open quantum systems. By using the Wang-Uhlenbeck method, the Fokker-Planck equation, obtained from the master equation for the density operator, is solved for the Wigner distribution function, subject to either the Gaussian type or the delta-function type of initial conditions. The obtained Wigner functions are two-dimensional Gaussians with different widths. Then a closed expression for the density operator is extracted. The entropy of the system is subsequently calculated and its temporal behavior shows that this quantity relaxes to its equilibrium value.

  15. New ladder operators for a rational extension of the harmonic oscillator and superintegrability of some two-dimensional systems

    NASA Astrophysics Data System (ADS)

    Marquette, Ian; Quesne, Christiane

    2013-10-01

    New ladder operators are constructed for a rational extension of the harmonic oscillator associated with type III Hermite exceptional orthogonal polynomials and characterized by an even integer m. The eigenstates of the Hamiltonian separate into m + 1 infinite-dimensional unitary irreducible representations of the corresponding polynomial Heisenberg algebra. These ladder operators are used to construct a higher-order integral of motion for two superintegrable two-dimensional systems separable in cartesian coordinates. The polynomial algebras of such systems provide for the first time an algebraic derivation of the whole spectrum through their finite-dimensional unitary irreducible representations.

  16. Deformation quantization and boundary value problems

    NASA Astrophysics Data System (ADS)

    Tarkhanov, Nikolai

    2016-11-01

    We describe a natural construction of deformation quantization on a compact symplectic manifold with boundary. On the algebra of quantum observables a trace functional is defined which as usual annihilates the commutators. This gives rise to an index as the trace of the unity element. We formulate the index theorem as a conjecture and examine it by the classical harmonic oscillator.

  17. Incremental approach for radial basis functions mesh deformation with greedy algorithm

    NASA Astrophysics Data System (ADS)

    Selim, Mohamed M.; Koomullil, Roy P.; Shehata, Ahmed S.

    2017-07-01

    Mesh Deformation is an important element of any fluid-structure interaction simulation. In this article, a new methodology is presented for the deformation of volume meshes using incremental radial basis function (RBF) based interpolation. A greedy algorithm is used to select a small subset of the surface nodes iteratively. Two incremental approaches are introduced to solve the RBF system of equations: 1) block matrix inversion based approach and 2) modified LU decomposition approach. The use of incremental approach decreased the computational complexity of solving the system of equations within each greedy algorithm's iteration from O (n3) to O (n2). Results are presented from an accuracy study using specified deformations on a 2D surface. Mesh deformations for bending and twisting of a 3D rectangular supercritical wing have been demonstrated. Outcomes showed the incremental approaches reduce the CPU time up to 67% as compared to a traditional RBF matrix solver. Finally, the proposed mesh deformation approach was integrated within a fluid-structure interaction solver for investigating a flow induced cantilever beam vibration.

  18. Complex Vector Formalism of Harmonic Oscillator in Geometric Algebra: Particle Mass, Spin and Dynamics in Complex Vector Space

    NASA Astrophysics Data System (ADS)

    Muralidhar, K.

    2014-03-01

    Elementary particles are considered as local oscillators under the influence of zeropoint fields. Such oscillatory behavior of the particles leads to the deviations in their path of motion. The oscillations of the particle in general may be considered as complex rotations in complex vector space. The local particle harmonic oscillator is analyzed in the complex vector formalism considering the algebra of complex vectors. The particle spin is viewed as zeropoint angular momentum represented by a bivector. It has been shown that the particle spin plays an important role in the kinematical intrinsic or local motion of the particle. From the complex vector formalism of harmonic oscillator, for the first time, a relation between mass and bivector spin has been derived in the form . Where, is the angular velocity bivector of complex rotations, is the velocity of light. The unit vector acts as an operator on the idempotents and to give the eigen values The constant represents two fold nature of the equation corresponding to particle and antiparticle states. Further the above relation shows that the mass of the particle may be interpreted as a local spatial complex rotation in the rest frame. This gives an insight into the nature of fundamental particles. When a particle is observed from an arbitrary frame of reference, it has been shown that the spatial complex rotation dictates the relativistic particle motion. The mathematical structure of complex vectors in space and spacetime is developed.

  19. Relating pseudospin and spin symmetries through charge conjugation and chiral transformations: The case of the relativistic harmonic oscillator

    SciTech Connect

    Castro, A.S. de; Alberto, P.; Lisboa, R.; Malheiro, M.

    2006-05-15

    We solve the generalized relativistic harmonic oscillator in 1+1 dimensions, i.e., including a linear pseudoscalar potential and quadratic scalar and vector potentials which have equal or opposite signs. We consider positive and negative quadratic potentials and discuss in detail their bound-state solutions for fermions and antifermions. The main features of these bound states are the same as the ones of the generalized three-dimensional relativistic harmonic oscillator bound states. The solutions found for zero pseudoscalar potential are related to the spin and pseudospin symmetry of the Dirac equation in 3+1 dimensions. We show how the charge conjugation and {gamma}{sup 5} chiral transformations relate the several spectra obtained and find that for massless particles the spin and pseudospin symmetry-related problems have the same spectrum but different spinor solutions. Finally, we establish a relation of the solutions found with single-particle states of nuclei described by relativistic mean-field theories with scalar, vector, and isoscalar tensor interactions and discuss the conditions in which one may have both nucleon and antinucleon bound states.

  20. Nuclear longitudinal form factors for axially deformed charge distributions expanded by nonorthogonal basis functions

    NASA Astrophysics Data System (ADS)

    Liu, Jian; Zhang, Jinjuan; Xu, Chang; Ren, Zhongzhou

    2017-05-01

    In this paper, the nuclear longitudinal form factors are systematically studied from the intrinsic charge multipoles. For axially deformed nuclei, two different types of density profiles are used to describe their charge distributions. For the same charge distributions expanded with different basis functions, the corresponding longitudinal form factors are derived and compared with each other. Results show the multipoles Cλ of longitudinal form factors are independent of the basis functions of charge distributions. Further numerical calculations of longitudinal form factors of 12C indicates that the C 0 multipole reflects the contributions of spherical components of all nonorthogonal basis functions. For deformed nuclei, their charge RMS radii can also be determined accurately by the C 0 measurement. The studies in this paper examine the model-independent properties of electron scattering, which are useful for interpreting electron scattering experiments on exotic deformed nuclei. Supported by National Natural Science Foundation of China (11505292, 11175085, 11575082, 11235001, 11275138, and 11447226), by Shandong Provincial Natural Science Foundation, China (BS2014SF007), Fundamental Research Funds for Central Universities (15CX02072A).

  1. Research on the Dynamic Problems of 3D Cross Coupling Quantum Harmonic Oscillator by Virtue of Intermediate Representation | x> λ, ν

    NASA Astrophysics Data System (ADS)

    Xu, Shi-Min; Xu, Xing-Lei; Li, Hong-Qi

    2008-06-01

    The intermediate representation (namely intermediate coordinate-momentum representation) | x> λ, ν are introduced and employed to research the expression of the operator tauhat{p}+σhat{x} in intermediate representation | x> λ, ν . The systematic Hamilton operator hat{H} of 3D cross coupling quantum harmonic oscillator was diagonalized by virtue of quadratic form theory. The quantity of λ, ν, τand σ were figured out. The dynamic problems of 3D cross coupling quantum harmonic oscillator are researched by virtue of intermediate representation. The energy eigen-value and eigenwave function of 3D cross coupling quantum harmonic oscillator were obtained in intermediate representation. The importance of intermediate representation was discussed. The results show that the Radon transformation of Wigner operator is just the projectional operator | x> λ, ν λ, ν < x|, and the Radon transformation of Wigner function is just a margin distribution.

  2. Perelomov and Barut-Girardello SU(1, 1) Coherent States for Harmonic Oscillator in One-Dimensional Half Space

    NASA Astrophysics Data System (ADS)

    Liu, Q. H.; Zhuo, H.

    The Perelomov and the Barut-Girardello SU(1, 1) coherent states for harmonic oscillator in one-dimensional half space are constructed. Results show that the uncertainty products ΔxΔp for these two coherent states are bound from below √ {9/4-6/π } that is the uncertainty for the ground state, and the mean values for position x and momentum p in classical limit go over to their classical quantities respectively. In classical limit, the uncertainty given by Perelomov coherent does not vanish, and the Barut-Girardello coherent state reveals a node structure when positioning closest to the boundary x = 0 which has not been observed in coherent states for other systems.

  3. Harmonic oscillator wave functions of a self-assembled InAs quantum dot measured by scanning tunneling microscopy.

    PubMed

    Teichmann, Karen; Wenderoth, Martin; Prüser, Henning; Pierz, Klaus; Schumacher, Hans W; Ulbrich, Rainer G

    2013-08-14

    InAs quantum dots embedded in an AlAs matrix inside a double barrier resonant tunneling diode are investigated by cross-sectional scanning tunneling spectroscopy. The wave functions of the bound quantum dot states are spatially and energetically resolved. These bound states are known to be responsible for resonant tunneling phenomena in such quantum dot diodes. The wave functions reveal a textbook-like one-dimensional harmonic oscillator behavior showing up to five equidistant energy levels of 80 meV spacing. The derived effective oscillator mass of m* = 0.24m0 is 1 order of magnitude higher than the effective electron mass of bulk InAs that we attribute to the influence of the surrounding AlAs matrix. This underlines the importance of the matrix material for tailored QD devices with well-defined properties.

  4. Van der Waals interactions in density functional theory by combining the quantum harmonic oscillator-model with localized Wannier functions.

    PubMed

    Silvestrelli, Pier Luigi

    2013-08-07

    We present a new scheme to include the van der Waals (vdW) interactions in approximated Density Functional Theory (DFT) by combining the quantum harmonic oscillator model with the maximally localized Wannier function technique. With respect to the recently developed DFT/vdW-WF2 method, also based on Wannier Functions, the new approach is more general, being no longer restricted to the case of well separated interacting fragments. Moreover, it includes higher than pairwise energy contributions, coming from the dipole-dipole coupling among quantum oscillators. The method is successfully applied to the popular S22 molecular database, and also to extended systems, namely graphite and H2 adsorbed on the Cu(111) metal surface (in this case metal screening effects are taken into account). The results are also compared with those obtained by other vdW-corrected DFT schemes.

  5. Optimal control equations for the one dimensional quantum harmonic oscillator under the influence of external dipole effects

    SciTech Connect

    Ayvaz, Muzaffer; Demiralp, Metin

    2012-12-10

    This study focuses on the construction of the optimal control equations for one dimensional quantum harmonic oscillator under the influence of external dipol effects and the solution of these equations by using Fluctuationlessness Theorem and a recently developed scheme called Characteristic Evolutions Method. The dipole function of the system has been taken as odd cubic spatial polynomial. Optimal control equations of the system under consideration are constructed by using expectation values of the position and the momentum operators instead of the wave and costate evolutions. It is shown that, the resulting equations are systems of ordinary differential equations and there are infinitely many ODEs. The solution strategy is based on the approximation of the expectation values for the operator products in the sense of Fluctuationlessness Theorem.

  6. Canonical averaging in the second order quantized Hamilton dynamics by extension of the coherent state thermodynamics of the harmonic oscillator.

    PubMed

    Heatwole, Eric; Prezhdo, Oleg V

    2007-05-28

    A conceptually simple approximation to quantum mechanics, quantized Hamilton dynamics (QHD) includes zero-point energy, tunneling, dephasing, and other important quantum effects in a classical-like description. The hierarchy of coupled differential equations describing the time evolution of observables in QHD can be mapped in the second order onto a classical system with double the dimensionality of the original system. While QHD excels at dynamics with a single initial condition, the correct method for generating thermal initial conditions in QHD remains an open question. Using the coherent state representation of thermodynamics of the harmonic oscillator (HO) [Schnack, Europhys. Lett. 45, 647 (1999)], we develop canonical averaging for the second order QHD [Prezhdo, J. Chem. Phys. 117, 2995 (2002)]. The methodology is exact for the free particle and HO, and shows good agreement with quantum results for a variety of quartic potentials.

  7. Realization of quantum gates based on three-dimensional harmonic oscillator in a time-varying electromagnetic field

    NASA Astrophysics Data System (ADS)

    Gautam, Kumar; Chauhan, Garv; Rawat, Tarun Kumar; Parthasarathy, Harish; Sharma, Navneet

    2015-09-01

    This paper presents the design of a given quantum unitary gate by perturbing a three-dimensional (3-D) quantum harmonic oscillator with a time-varying but spatially constant electromagnetic field. The idea is based on expressing the radiation- perturbed Hamiltonian as the sum of the unperturbed Hamiltonian and O( e) and perturbations and then solving the Schrödinger equation to obtain the evolution operator at time T up to , and this is a linear-quadratic function of the perturbing electromagnetic field values over the time interval [0, T]. Setting the variational derivative of the error energy with respect to the electromagnetic field values with an average electromagnetic field energy constraint leads to the optimal electromagnetic field solution, a linear integral equation. The reliability of such a gate design procedure in the presence of heat bath coupling is analysed, and finally, an example illustrating how atoms and molecules can be approximated using oscillators is presented.

  8. Constructive influence of noise flatness and friction on the resonant behavior of a harmonic oscillator with fluctuating frequency.

    PubMed

    Laas, Katrin; Mankin, Romi; Rekker, Astrid

    2009-05-01

    The influences of noise flatness and friction coefficient on the long-time behavior of the first two moments and the correlation function for the output signal of a harmonic oscillator with fluctuating frequency subjected to an external periodic force are considered. The colored fluctuations of the oscillator frequency are modeled as a trichotomous noise. The study is a follow up of the previous investigation of a stochastic oscillator [Phys. Rev. E 78, 031120 (2008)], where the connection between the occurrence of energetic instability and stochastic multiresonance is established. Here we report some unexpected results not considered in the previous work. Notably, we have found a nonmonotonic dependence of several stochastic resonance characteristics such as spectral amplification, variance of the output signal, and signal-to-noise ratio on the friction coefficient and on the noise flatness. In particular, in certain parameter regions spectral amplification exhibits a resonancelike enhancement at intermediate values of the friction coefficient.

  9. Chaos in axially symmetric potentials with octupole deformation

    SciTech Connect

    Heiss, W.D.; Nazmitdinov, R.G.; Radu, S. Departamento de Fisica Teorica C-XI, Universidad Autonoma de Madrid, E-28049, Madrid )

    1994-04-11

    Classical and quantum mechanical results are reported for the single particle motion in a harmonic oscillator potential which is characterized by a quadrupole deformation and an additional octupole deformation. The chaotic character of the motion is strongly dependent on the quadrupole deformation in that for a prolate deformation virtually no chaos is discernible while for the oblate case the motion shows strong chaos when the octupole term is turned on.

  10. An Efficient Radial Basis Function Mesh Deformation Scheme within an Adjoint-Based Aerodynamic Optimization Framework

    NASA Astrophysics Data System (ADS)

    Poirier, Vincent

    Mesh deformation schemes play an important role in numerical aerodynamic optimization. As the aerodynamic shape changes, the computational mesh must adapt to conform to the deformed geometry. In this work, an extension to an existing fast and robust Radial Basis Function (RBF) mesh movement scheme is presented. Using a reduced set of surface points to define the mesh deformation increases the efficiency of the RBF method; however, at the cost of introducing errors into the parameterization by not recovering the exact displacement of all surface points. A secondary mesh movement is implemented, within an adjoint-based optimization framework, to eliminate these errors. The proposed scheme is tested within a 3D Euler flow by reducing the pressure drag while maintaining lift of a wing-body configured Boeing-747 and an Onera-M6 wing. As well, an inverse pressure design is executed on the Onera-M6 wing and an inverse span loading case is presented for a wing-body configured DLR-F6 aircraft.

  11. Sorting on the basis of deformability of single cells in a femtosecond laser fabricated optofluidic device

    NASA Astrophysics Data System (ADS)

    Bragheri, F.; Paiè, P.; Yang, T.; Nava, G.; Martınez Vázquez, R.; Di Tano, M.; Veglione, M.; Minzioni, P.; Mondello, C.; Cristiani, I.; Osellame, R.

    2015-03-01

    Optical stretching is a powerful technique for the mechanical phenotyping of single suspended cells that exploits cell deformability as an inherent functional marker. Dual-beam optical trapping and stretching of cells is a recognized tool to investigate their viscoelastic properties. The optical stretcher has the ability to deform cells through optical forces without physical contact or bead attachment. In addition, it is the only method that can be combined with microfluidic delivery, allowing for the serial, high-throughput measurement of the optical deformability and the selective sorting of single specific cells. Femtosecond laser micromachining can fabricate in the same chip both the microfluidic channel and the optical waveguides, producing a monolithic device with a very precise alignment between the components and very low sensitivity to external perturbations. Femtosecond laser irradiation in a fused silica chip followed by chemical etching in hydrofluoric acid has been used to fabricate the microfluidic channels where the cells move by pressure-driven flow. With the same femtosecond laser source two optical waveguides, orthogonal to the microfluidic channel and opposing each other, have been written inside the chip. Here we present an optimized writing process that provides improved wall roughness of the micro-channels allowing high-quality imaging. In addition, we will show results on cell sorting on the basis of mechanical properties in the same device: the different deformability exhibited by metastatic and tumorigenic cells has been exploited to obtain a metastasis-cells enriched sample. The enrichment is verified by exploiting, after cells collection, fluorescence microscopy.

  12. Accurate and robust extraction of brain regions using a deformable model based on radial basis functions.

    PubMed

    Liu, Jia-Xiu; Chen, Yong-Sheng; Chen, Li-Fen

    2009-10-15

    Brain extraction from head magnetic resonance (MR) images is a classification problem of segmenting image volumes into brain and non-brain regions. It is a difficult task due to the convoluted brain surface and the inapparent brain/non-brain boundaries in images. This paper presents an automated, robust, and accurate brain extraction method which utilizes a new implicit deformable model to well represent brain contours and to segment brain regions from MR images. This model is described by a set of Wendland's radial basis functions (RBFs) and has the advantages of compact support property and low computational complexity. Driven by the internal force for imposing the smoothness constraint and the external force for considering the intensity contrast across boundaries, the deformable model of a brain contour can efficiently evolve from its initial state toward its target by iteratively updating the RBF locations. In the proposed method, brain contours are separately determined on 2D coronal and sagittal slices. The results from these two views are generally complementary and are thus integrated to obtain a complete 3D brain volume. The proposed method was compared to four existing methods, Brain Surface Extractor, Brain Extraction Tool, Hybrid Watershed Algorithm, and Model-based Level Set, by using two sets of MR images as well as manual segmentation results obtained from the Internet Brain Segmentation Repository. Our experimental results demonstrated that the proposed approach outperformed these four methods when jointly considering extraction accuracy and robustness.

  13. Microwave Imaging Reflectometry for the study of Edge Harmonic Oscillations on DIII-D [Microwave Imaging Reflectometry (MIR) for the study of Edge Harmonic Oscillations (EHOs) on DIII-D

    SciTech Connect

    Ren, X.; Chen, M.; Chen, X.; Domier, C. W.; Ferraro, N. M.; Kramer, G. J.; Luhmann, Jr., N. C.; Muscatello, C. M.; Nazikian, R.; Shi, L.; Tobias, B. J.; Valeo, E.

    2015-10-23

    Quiescent H-mode (QH) is an ELM free mode of operation in which edge-localized harmonic oscillations (EHOs) are believed to enhance particle transport, thereby stabilizing ELMs and preventing damage to the divertor and plasma facing components. Microwave Imaging Reflectometer (MIR) enabling direct comparison between the measured and simulated 2D images of density fluctuations near the edge can determine the 2D structure of density oscillation which can help to explain the physics behind EHO modes. MIR data sometimes indicates a counter-propagation between higher (n>1) and dominant (n=1) harmonics of coherent EHOs in the steep gradient regions of the pedestal. To preclude diagnostic artifacts, we have performed forward modeling that includes possible optical misalignments to show that offsets between transmitting and receiving antennas do not account for this feature. We have also simulated the non-uniform rotation of the EHO structure, which induces multiple harmonics that are properly characterized in the synthetic diagnostic. Excluding these possible explanations for the data, the counter-propagation observed in MIR data, which is not corroborated by external Mirnov coil array measurements, may be due to subtleties of the eigenmode structure, such as an inversion radius consistent with a magnetic island. Similar effects are observed in analysis of internal ECE-Imaging and BES data. Furthermore, the identification of a non-ideal structure motivates further exploration of nonlinear models of this instability.

  14. Microwave Imaging Reflectometry for the study of Edge Harmonic Oscillations on DIII-D [Microwave Imaging Reflectometry (MIR) for the study of Edge Harmonic Oscillations (EHOs) on DIII-D

    DOE PAGES

    Ren, X.; Chen, M.; Chen, X.; ...

    2015-10-23

    Quiescent H-mode (QH) is an ELM free mode of operation in which edge-localized harmonic oscillations (EHOs) are believed to enhance particle transport, thereby stabilizing ELMs and preventing damage to the divertor and plasma facing components. Microwave Imaging Reflectometer (MIR) enabling direct comparison between the measured and simulated 2D images of density fluctuations near the edge can determine the 2D structure of density oscillation which can help to explain the physics behind EHO modes. MIR data sometimes indicates a counter-propagation between higher (n>1) and dominant (n=1) harmonics of coherent EHOs in the steep gradient regions of the pedestal. To preclude diagnosticmore » artifacts, we have performed forward modeling that includes possible optical misalignments to show that offsets between transmitting and receiving antennas do not account for this feature. We have also simulated the non-uniform rotation of the EHO structure, which induces multiple harmonics that are properly characterized in the synthetic diagnostic. Excluding these possible explanations for the data, the counter-propagation observed in MIR data, which is not corroborated by external Mirnov coil array measurements, may be due to subtleties of the eigenmode structure, such as an inversion radius consistent with a magnetic island. Similar effects are observed in analysis of internal ECE-Imaging and BES data. Furthermore, the identification of a non-ideal structure motivates further exploration of nonlinear models of this instability.« less

  15. Computer-simulation calculations of the electronic stopping of fast heavy charges by a classical harmonic oscillator

    SciTech Connect

    Jakas, M. M.; Perez de la Rosa, F. J.; Custidiano, E. R.

    2003-09-01

    The accuracy of Bohr's and more recent analytical calculations of the electronic stopping of heavy charges by a classical harmonic oscillator is analyzed. According to results in this paper, for |{xi}|{>=}100 ({xi} being the Bohr stopping parameter) the present simulations agree with previous theoretical calculations, whereas for smaller |{xi}| values, discrepancies are evident. In fact, for |{xi}|<100 the stopping cross section seems to be sensitive to the sign of the ion charge. The so-called Barkas effect is unambiguously observed and positively charged projectiles appear to have a larger stopping compared to that of negative ones at the same {xi}. Bohr's calculations, however, seem to reproduce the stopping of negative charges relatively well, but those of positive ions are consequently underestimated. By giving the electron an initial velocity, the so-called inner-shell effect on the stopping can be readily studied. The present simulations show that previous analytical predictions of this effect do not account for the present results.

  16. Classical and quantum harmonic oscillators with time dependent mass and frequency: A new class of exactly solvable model

    NASA Astrophysics Data System (ADS)

    Mandal, Swapan

    2017-03-01

    The classical harmonic oscillator with time dependent mass and frequency is investigated to obtain a closed form exact analytical solution. It is found that the closed form analytical solutions are indeed possible if the time dependent mass of the oscillator is inversely proportional to the time dependent frequency. The scaled wronskian obtained from the linearly independent solutions of the equation of motion of the classical oscillator is used to obtain the solution corresponding to its quantum mechanical counterpart. The analytical solution of the present oscillator is used to obtain the squeezing effects of the input coherent light. In addition to the possibilities of getting the squeezed states, the present solution will be of use for investigating various quantum statistical properties of the radiation fields. As an example, we investigate the antibunching of the input thermal (chaotic) light coupled to the oscillator. Therefore, the appearance of the photon antibunching does not warrant the squeezing and vice-versa. The exact solution is obtained at the cost of the stringent condition where the product of time dependent mass and frequency of the oscillator is time invariant.

  17. Maxwell speed distribution and analogue Hawking-Unruh temperature in an ontological model of a Harmonic oscillator ground state

    NASA Astrophysics Data System (ADS)

    Budiyono, Agung; Gunara, Bobby Eka; Okamura, Makoto; Nakamura, Katsuhiro

    2015-03-01

    Within an ontological (hidden variable) model of quantum fluctuation, one can discuss the actual properties of a system regardless (independent) of measurement. Here we apply an ontological model proposed earlier to investigate a Harmonic oscillator in the quantum mechanical ground state. We first show that the actual speed of the oscillator fluctuates randomly following the Maxwell-Boltzmann distribution. On the other hand, the actual energy obeys a broad Gamma distribution with an average 3 ħ ω / 2, where ω is the classical angular frequency, so that one may conclude that the outcome of a single energy measurement reveals the average of the actual energy. The distribution of actual speed (energy) thus formally resembles the distribution of speed (energy) of an ideal gas in thermal equilibrium of temperature Tg = ħ ω / 2. We shall then argue that Tg can be written in a form analogous to the Hawking temperature for a Schwarzschild black hole in which the average distance of the oscillator from the origin plays the analogous role of the radius of the black hole event horizon. It can also be written in a form analogous to the Unruh temperature experienced by a body moving with a uniform acceleration. In the analogy, the oscillator suffers an effective acceleration which balances the attractive force of the trapping Harmonic potential, thus keeps its average position away from the origin.

  18. Using Monte Carlo ray tracing simulations to model the quantum harmonic oscillator modes observed in uranium nitride

    SciTech Connect

    Lin, J. Y. Y.; Aczel, Adam A; Abernathy, Douglas L; Nagler, Stephen E; Buyers, W. J. L.; Granroth, Garrett E

    2014-01-01

    Recently an extended series of equally spaced vibrational modes was observed in uranium nitride (UN) by performing neutron spectroscopy measurements using the ARCS and SEQUOIA time-of- flight chopper spectrometers [A.A. Aczel et al, Nature Communications 3, 1124 (2012)]. These modes are well described by 3D isotropic quantum harmonic oscillator (QHO) behavior of the nitrogen atoms, but there are additional contributions to the scattering that complicate the measured response. In an effort to better characterize the observed neutron scattering spectrum of UN, we have performed Monte Carlo ray tracing simulations of the ARCS and SEQUOIA experiments with various sample kernels, accounting for the nitrogen QHO scattering, contributions that arise from the acoustic portion of the partial phonon density of states (PDOS), and multiple scattering. These simulations demonstrate that the U and N motions can be treated independently, and show that multiple scattering contributes an approximate Q-independent background to the spectrum at the oscillator mode positions. Temperature dependent studies of the lowest few oscillator modes have also been made with SEQUOIA, and our simulations indicate that the T-dependence of the scattering from these modes is strongly influenced by the uranium lattice.

  19. Using Monte Carlo ray tracing simulations to model the quantum harmonic oscillator modes observed in uranium nitride

    NASA Astrophysics Data System (ADS)

    Lin, J. Y. Y.; Aczel, A. A.; Abernathy, D. L.; Nagler, S. E.; Buyers, W. J. L.; Granroth, G. E.

    2014-04-01

    Recently an extended series of equally spaced vibrational modes was observed in uranium nitride (UN) by performing neutron spectroscopy measurements using the ARCS and SEQUOIA time-of-flight chopper spectrometers [A. A. Aczel et al., Nat. Commun. 3, 1124 (2012), 10.1038/ncomms2117]. These modes are well described by three-dimensional isotropic quantum harmonic oscillator (QHO) behavior of the nitrogen atoms, but there are additional contributions to the scattering that complicate the measured response. In an effort to better characterize the observed neutron scattering spectrum of UN, we have performed Monte Carlo ray tracing simulations of the ARCS and SEQUOIA experiments with various sample kernels, accounting for nitrogen QHO scattering, contributions that arise from the acoustic portion of the partial phonon density of states, and multiple scattering. These simulations demonstrate that the U and N motions can be treated independently, and show that multiple scattering contributes an approximate Q-independent background to the spectrum at the oscillator mode positions. Temperature-dependent studies of the lowest few oscillator modes have also been made with SEQUOIA, and our simulations indicate that the T dependence of the scattering from these modes is strongly influenced by the uranium lattice.

  20. Sampled-data-based consensus and containment control of multiple harmonic oscillators: A motion-planning approach.

    PubMed

    Liu, Yongfang; Zhao, Yu; Chen, Guanrong

    2016-11-01

    This paper studies the distributed consensus and containment problems for a group of harmonic oscillators with a directed communication topology. First, for consensus without a leader, a class of distributed consensus protocols is designed by using motion planning and Pontryagin's principle. The proposed protocol only requires relative information measurements at the sampling instants, without requiring information exchange over the sampled interval. By using stability theory and the properties of stochastic matrices, it is proved that the distributed consensus problem can be solved in the motion planning framework. Second, for the case with multiple leaders, a class of distributed containment protocols is developed for followers such that their positions and velocities can ultimately converge to the convex hull formed by those of the leaders. Compared with the existing consensus algorithms, a remarkable advantage of the proposed sampled-data-based protocols is that the sampling periods, communication topologies and control gains are all decoupled and can be separately designed, which relaxes many restrictions in controllers design. Finally, some numerical examples are given to illustrate the effectiveness of the analytical results.

  1. Further investigation of a finite difference procedure for analyzing the transonic flow about harmonically oscillating airfoils and wings

    NASA Technical Reports Server (NTRS)

    Weatherill, W. H.; Ehlers, F. E.; Yip, E.; Sebastian, J. D.

    1980-01-01

    Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. The steady velocity potential is obtained first from the well-known nonlinear equation for steady transonic flow. The unsteady velocity potential is then obtained from a linear differential equation in complex form with spatially varying coefficients. Since sinusoidal motion is assumed, the unsteady equation is independent of time. An out-of-core direct solution procedure was developed and applied to two-dimensional sections. Results are presented for a section of vanishing thickness in subsonic flow and an NACA 64A006 airfoil in supersonic flow. Good correlation is obtained in the first case at values of Mach number and reduced frequency of direct interest in flutter analyses. Reasonable results are obtained in the second case. Comparisons of two-dimensional finite difference solutions with exact analytic solutions indicate that the accuracy of the difference solution is dependent on the boundary conditions used on the outer boundaries. Homogeneous boundary conditions on the mesh edges that yield complex eigenvalues give the most accurate finite difference solutions. The plane outgoing wave boundary conditions meet these requirements.

  2. Simulation and analysis of magnetic resonance elastography wave images using coupled harmonic oscillators and Gaussian local frequency estimation.

    PubMed

    Braun, J; Buntkowsky, G; Bernarding, J; Tolxdorff, T; Sack, I

    2001-06-01

    New methods for simulating and analyzing Magnetic Resonance Elastography (MRE) images are introduced. To simulate a two-dimensional shear wave pattern, the wave equation is solved for a field of coupled harmonic oscillators with spatially varying coupling and damping coefficients in the presence of an external force. The spatial distribution of the coupling and the damping constants are derived from an MR image of the investigated object. To validate the simulation as well as to derive the elasticity modules from experimental MRE images, the wave patterns are analyzed using a Local Frequency Estimation (LFE) algorithm based on Gauss filter functions with variable bandwidths. The algorithms are tested using an Agar gel phantom with spatially varying elasticity constants. Simulated wave patterns and LFE results show a high agreement with experimental data. Furthermore, brain images with estimated elasticities for gray and white matter as well as for exemplary tumor tissue are used to simulate experimental MRE data. The calculations show that already small distributions of pathologically changed brain tissue should be detectable by MRE even within the limit of relatively low shear wave excitation frequency around 0.2 kHz.

  3. Structure and Behavior of the Edge Harmonic Oscillation in Quiescent H-Mode Plasmas on DIII-D

    NASA Astrophysics Data System (ADS)

    McKee, G. R.; Yan, Z.; Burrell, K. H.; Garofalo, A. M.; Grierson, B. A.; Solomon, W. M.

    2013-10-01

    The edge harmonic oscillation (EHO) is a steady-state, pedestal-localized instability that is observed in high-performance, ELM-free Quiescent H-mode plasmas. The spatiotemporal characteristics of the EHO have been measured in QH-mode plasmas with a 2D BES array that measures low-k density fluctuations. The skewness of the fluctuation distribution increases radially from -0.5 to +1 near the separatrix, consistent with the radially varying and highly non-sinusoidal harmonic structure. These fluctuation characteristics are qualitatively consistent with an outward particle transport driven by the EHO. The density fluctuation (ñ / n) profile peaks inside the pedestal, near ρ = 0.90-0.95, and is observed from ρ = 0 . 85 to the separatrix; the fundamental frequency is typically in the range of 5-15 kHz. The radial structure of the oscillation has a monotonically varying phase shift of approximately 180 degrees across the outer plasma region that changes direction with plasma current, suggesting that the mode structure is impacted by the high edge toroidal rotation velocity. Work supported by the US Department of Energy under DE-FG02-08ER54999, DE-FC02-04ER54698, and DE-AC02-09CH11466.

  4. Sampled-data-based consensus and containment control of multiple harmonic oscillators: A motion-planning approach

    NASA Astrophysics Data System (ADS)

    Liu, Yongfang; Zhao, Yu; Chen, Guanrong

    2016-11-01

    This paper studies the distributed consensus and containment problems for a group of harmonic oscillators with a directed communication topology. First, for consensus without a leader, a class of distributed consensus protocols is designed by using motion planning and Pontryagin's principle. The proposed protocol only requires relative information measurements at the sampling instants, without requiring information exchange over the sampled interval. By using stability theory and the properties of stochastic matrices, it is proved that the distributed consensus problem can be solved in the motion planning framework. Second, for the case with multiple leaders, a class of distributed containment protocols is developed for followers such that their positions and velocities can ultimately converge to the convex hull formed by those of the leaders. Compared with the existing consensus algorithms, a remarkable advantage of the proposed sampled-data-based protocols is that the sampling periods, communication topologies and control gains are all decoupled and can be separately designed, which relaxes many restrictions in controllers design. Finally, some numerical examples are given to illustrate the effectiveness of the analytical results.

  5. Rényi entropies of the highly-excited states of multidimensional harmonic oscillators by use of strong Laguerre asymptotics

    NASA Astrophysics Data System (ADS)

    Ivanovich Aptekarev, Alexander; Nikolaevich Tulyakov, Dmitry; Valero Toranzo, Irene; Sanchez Dehesa, Jesús

    2016-03-01

    The Rényi entropies Rp [ ρ ], p> 0, ≠ 1 of the highly-excited quantum states of the D-dimensional isotropic harmonic oscillator are analytically determined by use of the strong asymptotics of the orthogonal polynomials which control the wavefunctions of these states, the Laguerre polynomials. This Rydberg energetic region is where the transition from classical to quantum correspondence takes place. We first realize that these entropies are closely connected to the entropic moments of the quantum-mechanical probability ρn(r) density of the Rydberg wavefunctions Ψn,l, { μ }(r); so, to the ℒp-norms of the associated Laguerre polynomials. Then, we determine the asymptotics n → ∞ of these norms by use of modern techniques of approximation theory based on the strong Laguerre asymptotics. Finally, we determine the dominant term of the Rényi entropies of the Rydberg states explicitly in terms of the hyperquantum numbers (n,l), the parameter order p and the universe dimensionality D for all possible cases D ≥ 1. We find that (a) the Rényi entropy power decreases monotonically as the order p is increasing and (b) the disequilibrium (closely related to the second order Rényi entropy), which quantifies the separation of the electron distribution from equiprobability, has a quasi-Gaussian behavior in terms of D.

  6. Rényi entropies of the highly-excited states of multidimensional harmonic oscillators by use of strong Laguerre asymptotics

    NASA Astrophysics Data System (ADS)

    Aptekarev, Alexander Ivanovich; Tulyakov, Dmitry Nikolaevich; Toranzo, Irene Valero; Dehesa, Jesús Sanchez

    2016-03-01

    The Rényi entropies R p [ ρ ], p> 0, ≠ 1 of the highly-excited quantum states of the D-dimensional isotropic harmonic oscillator are analytically determined by use of the strong asymptotics of the orthogonal polynomials which control the wavefunctions of these states, the Laguerre polynomials. This Rydberg energetic region is where the transition from classical to quantum correspondence takes place. We first realize that these entropies are closely connected to the entropic moments of the quantum-mechanical probability ρ n (r) density of the Rydberg wavefunctions Ψ n,l, { μ }(r); so, to the ℒ p -norms of the associated Laguerre polynomials. Then, we determine the asymptotics n → ∞ of these norms by use of modern techniques of approximation theory based on the strong Laguerre asymptotics. Finally, we determine the dominant term of the Rényi entropies of the Rydberg states explicitly in terms of the hyperquantum numbers (n,l), the parameter order p and the universe dimensionality D for all possible cases D ≥ 1. We find that (a) the Rényi entropy power decreases monotonically as the order p is increasing and (b) the disequilibrium (closely related to the second order Rényi entropy), which quantifies the separation of the electron distribution from equiprobability, has a quasi-Gaussian behavior in terms of D.

  7. Harmonic oscillations of a lamina in a viscous fluid near a solid surface: A lattice Boltzmann-immersed boundary approach

    NASA Astrophysics Data System (ADS)

    De Rosis, Alessandro

    2014-12-01

    In this paper, a rigid thickless lamina is immersed in a quiescent viscous fluid and it undergoes transverse finite amplitude harmonic oscillations near a solid surface. The surrounding flow physics is computed through the lattice Boltzmann method. In order to account for the presence of the lamina in the lattice fluid background, the Immersed Boundary method is adopted. Several scenarios are investigated by varying the distance between the initial position of the lamina and the solid wall. For a given lamina-solid surface distance, the effect of the Reynolds number is investigated, together with the influence of the Keulegan-Carpenter number. Findings in terms of drag coefficient show that the force exerted by the encompassing fluid upon the lamina is remarkably influenced by the distance from the solid surface, especially for low values of the Reynolds number. Moreover, such results are confirmed by the computation of the hydrodynamic function. In fact, it highlights that the added mass effect and the non-linear damping experienced by the oscillating lamina grow as the above mentioned distance and the Reynolds number reduce.

  8. The Extended Projector Method and the Trotter - Approximation Applied to the Study of Few Level Systems Coupled to Harmonic Oscillators.

    NASA Astrophysics Data System (ADS)

    Vanhimbeeck, Marc

    In this thesis a technique is developed to determine the low-energy eigensolutions of an unspecified few-level system which is coupled both linearly and quadratically to a finite collection of harmonic oscillators. The method is based on the second-order symmetrized Trotter-Suzuki approximation for e^{lambda} ^{H} with H standing for the Hamiltonian of the quantum mechanical system. Taking lambda = -beta (real), we use e ^{beta}^{H} as a projection operator which sorts out the low-energy eigenstates from the decomposition of an initially randomly constructed system-state. Once the eigenstates are found, a second approximation on the time propagator e ^{-itH} is applied in order to determine some relevant time-correlation functions for the systems under study. Next to a general formulation of the theory we also provide a study of some example systems. The coupled two-level system is shown to account phenomenologically for the anomalous isotope shift which was observed in the Raman spectrum of the tunneling Li^+ defect in KCl. Furthermore, we examine the low-energy eigenvalues and Ham-reduction factors for some of the cubic Jahn-Teller (JT) systems. The triplet systems T otimes tau _2 and T otimes epsilon are studied with a linear JT-interaction but for the E otimes epsilon doublet system a quadratic warping is included in the description. The results are in good agreement with the literature and confirm the applicability of the method.

  9. On square-integrability of solutions of the stationary Schrödinger equation for the quantum harmonic oscillator in two dimensional constant curvature spaces

    SciTech Connect

    Noguera, Norman; Rózga, Krzysztof

    2015-07-15

    In this work, one provides a justification of the condition that is usually imposed on the parameters of the hypergeometric equation, related to the solutions of the stationary Schrödinger equation for the harmonic oscillator in two-dimensional constant curvature spaces, in order to determine the solutions which are square-integrable. One proves that in case of negative curvature, it is a necessary condition of square integrability and in case of positive curvature, a necessary condition of regularity. The proof is based on the analytic continuation formulas for the hypergeometric function. It is observed also that the same is true in case of a slightly more general potential than the one for harmonic oscillator.

  10. Adaptive Runge-Kutta integration for stiff systems: Comparing Nosé and Nosé-Hoover dynamics for the harmonic oscillator

    NASA Astrophysics Data System (ADS)

    Graham Hoover, William; Clinton Sprott, Julien; Griswold Hoover, Carol

    2016-10-01

    We describe the application of adaptive (variable time step) integrators to stiff differential equations encountered in many applications. Linear harmonic oscillators subject to nonlinear thermal constraints can exhibit either stiff or smooth dynamics. Two closely related examples, Nosé's dynamics and Nosé-Hoover dynamics, are both based on Hamiltonian mechanics and generate microstates consistent with Gibbs' canonical ensemble. Nosé's dynamics is stiff and can present severe numerical difficulties. Nosé-Hoover dynamics, although it follows exactly the same trajectory, is smooth and relatively trouble-free. We emphasize the power of adaptive integrators to resolve stiff problems such as the Nosé dynamics for the harmonic oscillator. The solutions also illustrate the power of computer graphics to enrich numerical solutions.

  11. Oscillations of the crystal-melt interface caused by harmonic oscillations of the pulling rate for the cylindrical phase of crystal growth

    NASA Astrophysics Data System (ADS)

    Vasil'ev, M. G.

    2017-02-01

    A technique for measuring the crystal cross-sectional area with a weight sensor based on the difference between its readings at the extreme rod positions in the stepwise and continuous modes of modulation of the pulling rate is proposed for the low-thermal gradient Czochralski method. A change in the crystallization rate at harmonic oscillations of the pulling rate is estimated with the aim of conserving the quality of the growing crystal for this measurement method.

  12. Bifurcation of quiescent H-mode to a wide pedestal regime in DIII-D and advances in the understanding of edge harmonic oscillations

    DOE PAGES

    Chen, Xi; Burrell, K. H.; Osborne, T. H.; ...

    2017-06-14

    New experimental studies and modelling of the coherent edge harmonic oscillation (EHO), which regulates the conventional Quiescent H-mode (QH-mode) edge, validate the proposed hypothesis of edge rotational shear in destabilizing the low-n kink-peeling mode as the additional drive mechanism for the EHO. The observed minimum edge E×B shear required for the EHO decreases linearly with pedestal collisionalitymore » $$\

  13. Smoothly deformed light

    NASA Technical Reports Server (NTRS)

    Stenholm, Stig

    1993-01-01

    A single mode cavity is deformed smoothly to change its electromagnetic eigenfrequency. The system is modeled as a simple harmonic oscillator with a varying period. The Wigner function of the problem is obtained exactly by starting with a squeezed initial state. The result is evaluated for a linear change of the cavity length. The approach to the adiabatic limit is investigated. The maximum squeezing is found to occur for smooth change lasting only a fraction of the oscillational period. However, only a factor of two improvement over the adiabatic result proves to be possible. The sudden limit cannot be investigated meaningfully within the model.

  14. Harmonic oscillator potential with a quartic anharmonicity in the prolate γ-rigid collective geometrical model

    NASA Astrophysics Data System (ADS)

    Budaca, Radu

    2015-12-01

    An analytical expression for the energy spectrum of the ground and β bands was obtained in the axially symmetric γ-rigid regime of the Bohr-Mottelson Hamiltonian with a general quartic anharmonic oscillator potential in the β shape variable. As the Schrodinger equation for such a potential is not exactly solvable, the energy formula is derived on the basis of the JWKB approximation. Due to the scaling property of the quartic oscillator problem, the resulting energy depends on a single parameter up to an overall multiplicative constant. The upper limit of the domain of values for the free parameter is established by comparing the ground state eigenvalues with the corresponding numerically calculated results. Studying the behavior of the potential and of the whole energy spectrum as function of the free parameter, one establishes the present model's place between other γ-rigid models. The agreement with experiment is achieved through model fits for few near-vibrational nuclei.

  15. Addendum to "An update on the classical and quantum harmonic oscillators on the sphere and the hyperbolic plane in polar coordinates" [Phys. Lett. A 379 (26-27) (2015) 1589-1593

    NASA Astrophysics Data System (ADS)

    Quesne, C.

    2016-02-01

    The classical and quantum solutions of a nonlinear model describing harmonic oscillators on the sphere and the hyperbolic plane, derived in polar coordinates in a recent paper (Quesne, 2015) [1], are extended by the inclusion of an isotonic term.

  16. Structural basis of inter-protofilament interaction and lateral deformation of microtubules

    PubMed Central

    Sui, Haixin; Downing, Kenneth H.

    2010-01-01

    Summary The diverse functions of microtubules require stiff structures possessing sufficient lateral flexibility to enable bending with high curvature. We used cryo-electron microscopy to investigate the molecular basis for these critical mechanical properties. High-quality structural maps were used to build pseudo-atomic models of microtubules containing 11 to 16 protofilaments, representing a wide range of lateral curvature. Protofilaments in all these microtubules were connected primarily via inter-protofilament interactions between the M loops, and the H1′-S2 and H2-S3 loops. We postulate that the tolerance of the loop-loop interactions to lateral deformation provides the capacity for high-curvature bending without breaking. On the other hand, the local molecular architecture that surrounds these connecting loops contributes to the overall rigidity. Inter-protofilament interactions in the seam region are similar to those in the normal helical regions, suggesting that the existence of the seam does not significantly affect the mechanical properties of microtubules. PMID:20696402

  17. Energy level promotion in the correlation from the tunnelling-doubled harmonic oscillator to the bi-rotor: application to internal rotation in molecules.

    PubMed

    Ross, Stephen C; Yamada, Koichi M T

    2007-11-21

    A surprisingly rich variety of phenomena are revealed in the energy level correlation between the limits of a tunnelling doubled harmonic oscillator and a bi-rotor. Some levels are found to have their vibrational quantum number "promoted" upon removal of the barrier to rotation, other levels, which we dub "invariant", are found to be completely independent of the barrier, while yet other levels exhibit a smooth transition between these limits. The general nature of these features can be understood in terms of the different degeneracies of the limiting cases. The elucidation of these effects aids the understanding of the rotational-vibrational energy levels of molecules having two internal rotor moieties.

  18. Investigation of Bohr Hamiltonian in the presence of time-dependent Manning-Rosen, harmonic oscillator and double ring shaped potentials

    NASA Astrophysics Data System (ADS)

    Sobhani, Hadi; Hassanabadi, Hassan

    2016-08-01

    This paper contains study of Bohr Hamiltonian considering time-dependent form of two important and famous nuclear potentials and harmonic oscillator. Dependence on time in interactions is considered in general form. In order to investigate this system, a powerful mathematical method has been employed, so-called Lewis-Riesenfeld dynamical invariant method. Appropriate dynamical invariant for considered system has been constructed. Then its eigen functions and the wave function are derived. At the end, we discussed about physical meaning of the results.

  19. Franck-Condon factors perturbed by damped harmonic oscillators: Solvent enhanced X 1Ag ↔ A1B1u absorption and fluorescence spectra of perylene

    NASA Astrophysics Data System (ADS)

    Wang, Chen-Wen; Yang, Ling; Zhu, Chaoyuan; Yu, Jian-Guo; Lin, Sheng-Hsien

    2014-08-01

    Damped harmonic oscillators are utilized to calculate Franck-Condon factors within displaced harmonic oscillator approximation. This is practically done by scaling unperturbed Hessian matrix that represents local modes of force constants for molecule in gaseous phase, and then by diagonalizing perturbed Hessian matrix it results in direct modification of Huang-Rhys factors which represent normal modes of solute molecule perturbed by solvent environment. Scaling parameters are empirically introduced for simulating absorption and fluorescence spectra of an isolated solute molecule in solution. The present method is especially useful for simulating vibronic spectra of polycyclic aromatic hydrocarbon molecules in which hydrogen atom vibrations in solution can be scaled equally, namely the same scaling factor being applied to all hydrogen atoms in polycyclic aromatic hydrocarbons. The present method is demonstrated in simulating solvent enhanced X 1Ag ↔ A1B1u absorption and fluorescence spectra of perylene (medium-sized polycyclic aromatic hydrocarbon) in benzene solution. It is found that one of six active normal modes v10 is actually responsible to the solvent enhancement of spectra observed in experiment. Simulations from all functionals (TD) B3LYP, (TD) B3LYP35, (TD) B3LYP50, and (TD) B3LYP100 draw the same conclusion. Hence, the present method is able to adequately reproduce experimental absorption and fluorescence spectra in both gas and solution phases.

  20. A dynamical basis for crustal deformation and seismotectonic block movements in central Europe

    NASA Technical Reports Server (NTRS)

    Liu, H.-S.

    1983-01-01

    The stress field in the earth's crust as inferred from satellite gravity data causes crustal deformation and seismotectonic block movements in central Europe. The satellite-determined stresses in the crust of central Europe are consistent with earthquake focal mechanisms, joint-orientation and in situ stress measurements.

  1. Shape Invariance in Deformation Quantization

    NASA Astrophysics Data System (ADS)

    Rasinariu, Constantin

    2013-03-01

    Shape invariance is a powerful solvability condition, that allows for complete knowledge of the energy spectrum, and eigenfunctions of a system. After a short introduction into the deformation quantization formalism, this work explores the implications of the supersymmetric quantum mechanics and shape invariance techniques to the phase space formalism. We show that shape invariance induces a new set of relations between the Wigner functions of the system, that allows for their direct calculation, once we know one of them. The simple harmonic oscillator and the Morse potential are presented as examples. I would like to acknowledge a sabbatical leave and grant from Columbia College Chicago that made this work possible.

  2. Probing deformed quantum commutators

    NASA Astrophysics Data System (ADS)

    Rossi, Matteo A. C.; Giani, Tommaso; Paris, Matteo G. A.

    2016-07-01

    Several quantum gravity theories predict a minimal length at the order of magnitude of the Planck length, under which the concepts of space and time lose their physical meaning. In quantum mechanics, the insurgence of such a minimal length can be described by introducing a modified position-momentum commutator, which in turn yields a generalized uncertainty principle, where the uncertainty on position measurements has a lower bound. The value of the minimal length is not predicted by theories and must be estimated experimentally. In this paper, we address the quantum bound to the estimability of the minimal uncertainty length by performing measurements on a harmonic oscillator, which is analytically solvable in the deformed algebra induced by the deformed commutation relations.

  3. Biomechanical Basis of Shoulder Osseous Deformity and Contracture in a Rat Model of Brachial Plexus Birth Palsy.

    PubMed

    Crouch, Dustin L; Hutchinson, Ian D; Plate, Johannes F; Antoniono, Jennifer; Gong, Hao; Cao, Guohua; Li, Zhongyu; Saul, Katherine R

    2015-08-05

    The purpose of this study was to investigate the relative contributions of two proposed mechanisms, strength imbalance and impaired longitudinal muscle growth, to osseous and postural deformity in a rat model of brachial plexus birth palsy (BPBP). Thirty-two Sprague-Dawley rat pups were divided into four groups on the basis of surgical interventions to induce a strength imbalance, impaired growth, both a strength imbalance and impaired growth (a combined mechanism), and a sham condition in the left forelimb. Maximum passive external shoulder rotation angle (ERmax) was measured bilaterally at four and eight weeks postoperatively. After the rats were killed at eight weeks, the glenohumeral geometry (on microcomputed tomography) and shoulder muscle architecture properties were measured bilaterally. Bilateral muscle mass and optimal length differences were greatest in the impaired growth and combined mechanism groups, which also exhibited >15° lower ERmax (p < 0.05; four weeks postoperatively), 14° to 18° more glenoid declination (p < 0.10), and 0.76 to 0.94 mm more inferior humeral head translation (p < 0.10) on the affected side. Across all four groups, optimal muscle length was significantly correlated with at least one osseous deformity measure for six of fourteen muscle compartments crossing the shoulder on the affected side (p < 0.05). In the strength imbalance group, the glenoid was 5° more inclined and the humeral head was translated 7.5% more posteriorly on the affected side (p < 0.05). Impaired longitudinal muscle growth and shoulder deformity were most pronounced in the impaired growth and combined mechanism groups, which underwent neurectomy. Strength imbalance was associated with osseous deformity to a lesser extent. Treatments to alleviate shoulder deformity should address mechanical effects of both strength imbalance and impaired longitudinal muscle growth, with an emphasis on developing new treatments to promote growth in muscles affected by BPBP

  4. Quantum Optimal Control of Single Harmonic Oscillator under Quadratic Controls together with Linear Dipole Polarizability: A Fluctuation Free Expectation Value Dynamical Perspective

    NASA Astrophysics Data System (ADS)

    Ayvaz, Muzaffer; Demiralp, Metin

    2011-09-01

    In this study, the optimal control equations for one dimensional quantum harmonic oscillator under the quadratic control operators together with linear dipole polarizability effects are constructed in the sense of Heisenberg equation of motion. A numerical technique based on the approximation to the non-commuting quantum mechanical operators from the fluctuation free expectation value dynamics perspective in the classical limit is also proposed for the solution of optimal control equations which are ODEs with accompanying boundary conditions. The dipole interaction of the system is considered to be linear, and the observable whose expectation value will be suppressed during the control process is considered to be quadratic in terms of position operator x. The objective term operator is also assumed to be quadratic.

  5. Quantum Optimal Control of Single Harmonic Oscillator under Quadratic Controls together with Linear Dipole Polarizability: A Fluctuation Free Expectation Value Dynamical Perspective

    SciTech Connect

    Ayvaz, Muzaffer; Demiralp, Metin

    2011-09-14

    In this study, the optimal control equations for one dimensional quantum harmonic oscillator under the quadratic control operators together with linear dipole polarizability effects are constructed in the sense of Heisenberg equation of motion. A numerical technique based on the approximation to the non-commuting quantum mechanical operators from the fluctuation free expectation value dynamics perspective in the classical limit is also proposed for the solution of optimal control equations which are ODEs with accompanying boundary conditions. The dipole interaction of the system is considered to be linear, and the observable whose expectation value will be suppressed during the control process is considered to be quadratic in terms of position operator x. The objective term operator is also assumed to be quadratic.

  6. Connection between quantum systems involving the fourth Painlevé transcendent and k-step rational extensions of the harmonic oscillator related to Hermite exceptional orthogonal polynomial

    NASA Astrophysics Data System (ADS)

    Marquette, Ian; Quesne, Christiane

    2016-05-01

    The purpose of this communication is to point out the connection between a 1D quantum Hamiltonian involving the fourth Painlevé transcendent PIV, obtained in the context of second-order supersymmetric quantum mechanics and third-order ladder operators, with a hierarchy of families of quantum systems called k-step rational extensions of the harmonic oscillator and related with multi-indexed Xm1,m2,…,mk Hermite exceptional orthogonal polynomials of type III. The connection between these exactly solvable models is established at the level of the equivalence of the Hamiltonians using rational solutions of the fourth Painlevé equation in terms of generalized Hermite and Okamoto polynomials. We also relate the different ladder operators obtained by various combinations of supersymmetric constructions involving Darboux-Crum and Krein-Adler supercharges, their zero modes and the corresponding energies. These results will demonstrate and clarify the relation observed for a particular case in previous papers.

  7. Entropy and Information of a harmonic oscillator in a time-varying electric field in 2D and 3D noncommutative spaces

    NASA Astrophysics Data System (ADS)

    Nascimento, J. P. G.; Aguiar, V.; Guedes, I.

    2017-07-01

    We analyze the noncommutativity effects on the Fisher information (F r ˆ , p ˆ) and Shannon entropies (S r ˆ , p ˆ) of a harmonic oscillator immersed in a time-varying electric field in two and three dimensions. We find the exact solutions of the respective time-dependent Schrödinger equation and use them to calculate the Fisher information and the Shannon entropy for the simplest case corresponding to the lowest-lying state of each system. While there is no problem in defining the Shannon entropy for noncommutating spaces, the definition of the Fisher information have to be modified to satisfy the Cramer-Rao inequalities. For both systems we observe how the Fisher information and Shannon entropy in position and momentum change due to the noncommutativity of the space. We verify that the Bialynicki-Birula-Mycielski (BBM) entropic uncertainty relation still holds in the systems considered.

  8. Coherence and decoherence processes of a harmonic oscillator coupled with finite temperature field: Exact eigenbasis solution of Kossakowski-Linblad's equation

    NASA Astrophysics Data System (ADS)

    Tay, Buang Ann

    The eigenvalue problem of Kossakowski-Linblad's kinetic equation associated with the reduced density matrix of a harmonic oscillator interacting with a thermal bath in equilibrium is solved. The solution gives rise to a complete orthogonal eigenbasis endowed with Hilbert space structure that has a weighted norm. We find that the eigenfunctions at finite temperature can be obtained from the eigenfunction at zero temperature through a hyperbolic rotation on the position variables. This transformation enables the extension of the simple harmonic oscillator density matrix to that of a finite temperature. We further investigate the decay of these extended states under our dissipative kinetic equation. Furthermore, the Hilbert space structure enables the proof of a H -theorem in this system. We apply the eigenbasis expansion of an initial state to analyze decoherence as well as coherence processes. We find that coherence process occurs at a longer time scale compared to decoherence process. The time scales of both processes are estimated with the eigenbasis expansion. In the same way we analyze the evolution of the coherent state. We show that in addition to the ordinary decay time, we found another time scale which is defined by the time when the motion of the peak of the coherent state become comparative to the width of the coherent state. In contrast to the ordinary decay time this new relaxation time depends on the initial value of the momentum of the oscillator. We also find that our eigenbasis is applicable to a class of non-linear interactions, with a slight extension of the form of transport coefficients due to the non-linear interactions.

  9. A remarkable spectral feature of the Schrödinger Hamiltonian of the harmonic oscillator perturbed by an attractive δ‧-interaction centred at the origin: double degeneracy and level crossing

    NASA Astrophysics Data System (ADS)

    Albeverio, Sergio; Fassari, Silvestro; Rinaldi, Fabio

    2013-09-01

    We rigorously define the self-adjoint Hamiltonian of the harmonic oscillator perturbed by an attractive δ‧-interaction, of strength β, centred at 0 (the bottom of the confining parabolic potential), by explicitly providing its resolvent. Our approach is based on a ‘coupling constant renormalization’, related to a technique originated in quantum field theory and implemented in the rigorous mathematical construction of the self-adjoint operator representing the negative Laplacian perturbed by the δ-interaction in two and three dimensions. The way the δ‧-interaction enters in our Hamiltonian corresponds to the one originally discussed for the free Hamiltonian (instead of the harmonic oscillator one) by P Sěba. It should not be confused with the δ‧-potential perturbation of the harmonic oscillator discussed, e.g., in a recent paper by Gadella, Glasser and Nieto (also introduced by P Sěba as a perturbation of the one-dimensional free Laplacian and recently investigated in that context by Golovaty, Hryniv and Zolotaryuk). We investigate in detail the spectrum of our perturbed harmonic oscillator. The spectral structure differs from that of the one-dimensional harmonic oscillator perturbed by an attractive δ-interaction centred at the origin: the even eigenvalues are not modified at all by the δ‧-interaction. Moreover, all the odd eigenvalues, regarded as functions of β, exhibit the rather remarkable phenomenon called ‘level crossing’ after first producing the double degeneracy of all the even eigenvalues for the value \\beta = \\beta _0 = \\frac{{2\\sqrt \\pi }}{{B\\left( {\\frac{3}{4},\\frac{1}{2}} \\right)}} \\cong 1.47934(B( ·, ·) being the beta function). Dedicated to Professor Gianfausto Dell'Antonio on the occasion of his 80th birthday.

  10. Exact analytical expressions and numerical analysis of two-center Franck Condon factors and matrix elements over displaced harmonic oscillator wave functions

    NASA Astrophysics Data System (ADS)

    Guseinov, I. I.; Mamedov, B. A.; Ekenoğlu, A. S.

    2006-08-01

    A detailed study is undertaken, using various techniques, in deriving analytical formula of Franck-Condon overlap integrals and matrix elements of various functions of power (x), exponential (exp(-2cx)) and Gaussian (exp(-cx)) over displaced harmonic oscillator wave functions with arbitrary frequencies. The results suggested by previous experience with various algorithms are presented in mathematically compact form and consist of generalization. The relationships obtained are valid for the arbitrary values of parameters and the computation results are in good agreement with the literature. The numerical results illustrate clearly a further reduction in calculation times. Program summaryProgram name:FRANCK Catalogue identifier:ADXX_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXX_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Programming language:Mathematica 5.0 Computer:Pentium M 1.4 GHz Operating system:Mathematica 5.0 RAM:512 MB No. of lines in distributed program, including test data, etc.:825 No. of bytes in distributed program, including test data, etc.:16 344 Distribution format:tar.gz Nature of problem:The programs calculate the Franck-Condon factors and matrix elements over displaced harmonic oscillator wave functions with arbitrary quantum numbers (n,n), frequencies (a,a) and displacement (d) for the various functions of power (x), exponential (exp(-2cx)) and Gaussian (exp(-cx)). Solution method:The Franck-Condon factors and matrix elements are evaluated using binomial coefficients and basic integrals. Restrictions:The results obtained by the present programs show great numerical stability for arbitrary quantum numbers (n,n), frequencies (a,a) and displacement (d). Unusual features:None Running time:As an example, for the value of Franck-Condon Overlap Integral I(d;α,α)=0.004405001887372332 with n=3, n=2, a=4, a=3, d=2, the compilation time in a Pentium M 1.4 GHz computer is 0.18 s. Execution

  11. UF-CHERS Measurements of Ion Temperature and Toroidal Rotation Fluctuations Associated with the Edge Harmonic Oscillation in Quiescent H-mode Plasmas

    NASA Astrophysics Data System (ADS)

    Truong, D. D.; Fonck, R. J.; McKee, G. R.; Yan, Z.; Grierson, B. A.

    2016-10-01

    The UF-CHERS (Ultra Fast CHarge Exchange Recombination Spectroscopy) diagnostic at DIII-D measures local, long-wavelength ion temperature and toroidal velocity fluctuations at turbulence-relevant spatiotemporal scales from emission of the CVI n=8 ->7 transition. During Quiescent H-mode (QH-mode) plasmas, which offer ELM-free improved confinement, UF-CHERS measurements observed coherent, low frequency (fo 10kHz) pedestal oscillations in Ti and vtor at the Edge Harmonic Oscillation (EHO) frequency while several modes between 35-75 kHz are suppressed when the EHO appears. Although broadband ion temperature and density fluctuations were reduced by the EHO, the toroidal rotation showed increased fluctuation amplitude. Investigating ion temperature and toroidal fluctuations associated with the EHO may provide insights into the saturated instability driving the EHO. Supported by DOE Grants DE-FG02-08ER54999, DE-FC02-04ER54698, and NSF GRFP Grant DGE-1256259.

  12. An investigation of several factors involved in a finite difference procedure for analyzing the transonic flow about harmonically oscillating airfoils and wings

    NASA Technical Reports Server (NTRS)

    Ehlers, F. E.; Sebastian, J. D.; Weatherill, W. H.

    1979-01-01

    Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. Since sinusoidal motion is assumed, the unsteady equation is independent of time. Three finite difference investigations are discussed including a new operator for mesh points with supersonic flow, the effects on relaxation solution convergence of adding a viscosity term to the original differential equation, and an alternate and relatively simple downstream boundary condition. A method is developed which uses a finite difference procedure over a limited inner region and an approximate analytical procedure for the remaining outer region. Two investigations concerned with three-dimensional flow are presented. The first is the development of an oblique coordinate system for swept and tapered wings. The second derives the additional terms required to make row relaxation solutions converge when mixed flow is present. A finite span flutter analysis procedure is described using the two-dimensional unsteady transonic program with a full three-dimensional steady velocity potential.

  13. Connection between quantum systems involving the fourth Painlevé transcendent and k-step rational extensions of the harmonic oscillator related to Hermite exceptional orthogonal polynomial

    SciTech Connect

    Marquette, Ian; Quesne, Christiane

    2016-05-15

    The purpose of this communication is to point out the connection between a 1D quantum Hamiltonian involving the fourth Painlevé transcendent P{sub IV}, obtained in the context of second-order supersymmetric quantum mechanics and third-order ladder operators, with a hierarchy of families of quantum systems called k-step rational extensions of the harmonic oscillator and related with multi-indexed X{sub m{sub 1,m{sub 2,…,m{sub k}}}} Hermite exceptional orthogonal polynomials of type III. The connection between these exactly solvable models is established at the level of the equivalence of the Hamiltonians using rational solutions of the fourth Painlevé equation in terms of generalized Hermite and Okamoto polynomials. We also relate the different ladder operators obtained by various combinations of supersymmetric constructions involving Darboux-Crum and Krein-Adler supercharges, their zero modes and the corresponding energies. These results will demonstrate and clarify the relation observed for a particular case in previous papers.

  14. A novel model of interaction between high frequency electromagnetic non-ionizing fields and microtubules viewed as coupled two-degrees of freedom harmonic oscillators.

    PubMed

    Caligiuri, Luigi Maxmilian

    2015-01-01

    The question regarding the potential biological and adverse health effects of non-ionizing electromagnetic fields on living organisms is of primary importance in biophysics and medicine. Despite the several experimental evidences showing such occurrence in a wide frequency range from extremely low frequency to microwaves, a definitive theoretical model able to explain a possible mechanism of interaction between electromagnetic fields and living matter, especially in the case of weak and very weak intensities, is still missing. In this paper it has been suggested a possible mechanism of interaction involving the resonant absorption of electromagnetic radiation by microtubules. To this aim these have been modeled as non-dissipative forced harmonic oscillators characterized by two coupled "macroscopic" degrees of freedom, respectively describing longitudinal and transversal vibrations induced by the electromagnetic field. We have shown that the proposed model, although at a preliminary stage, is able to explain the ability of even weak electromagnetic radiating electromagnetic fields to transfer high quantities of energy to living systems by means of a resonant mechanism, so capable to easily damage microtubules structure.

  15. Relation of deformed nonlinear algebras with linear ones

    NASA Astrophysics Data System (ADS)

    Nowicki, A.; Tkachuk, V. M.

    2014-01-01

    The relation between nonlinear algebras and linear ones is established. For a one-dimensional nonlinear deformed Heisenberg algebra with two operators we find the function of deformation for which this nonlinear algebra can be transformed to a linear one with three operators. We also establish the relation between the Lie algebra of total angular momentum and corresponding nonlinear one. This relation gives a possibility to simplify and to solve the eigenvalue problem for the Hamiltonian in a nonlinear case using the reduction of this problem to the case of linear algebra. It is demonstrated in an example of a harmonic oscillator.

  16. Comparison between the Morse eigenfunctions and deformed oscillator wavefunctions

    SciTech Connect

    Recamier, J.; Mochan, W. L.; Gorayeb, M.; Paz, J. L.

    2008-04-15

    In this work we introduce deformed creation and annihilation operators which differ from the usual harmonic oscillator operators a, a{sup {dagger}} by a number operator function A circumflex = a circumflex f(n circumflex ), A circumflex {sup {dagger}} = f(n circumflex )a circumflex {sup {dagger}}. We construct the deformed coordinate and momentum in terms of the deformed operators and maintain only up to first order terms in the deformed operators. By application of the deformed annihilation operator upon the vacuum state we get the ground state wavefunction in the configuration space and the wavefunctions for excited states are obtained by repeated application of the deformed creation operator. Finally, we compare the wavefunctions obtained with the deformed operators with the corresponding Morse eigenfunctions.

  17. Evaluation of high-resolution sea ice models on the basis of statistical and scaling properties of Arctic sea ice drift and deformation

    NASA Astrophysics Data System (ADS)

    Girard, L.; Weiss, J.; Molines, J. M.; Barnier, B.; Bouillon, S.

    2009-08-01

    Sea ice drift and deformation from models are evaluated on the basis of statistical and scaling properties. These properties are derived from two observation data sets: the RADARSAT Geophysical Processor System (RGPS) and buoy trajectories from the International Arctic Buoy Program (IABP). Two simulations obtained with the Louvain-la-Neuve Ice Model (LIM) coupled to a high-resolution ocean model and a simulation obtained with the Los Alamos Sea Ice Model (CICE) were analyzed. Model ice drift compares well with observations in terms of large-scale velocity field and distributions of velocity fluctuations although a significant bias on the mean ice speed is noted. On the other hand, the statistical properties of ice deformation are not well simulated by the models: (1) The distributions of strain rates are incorrect: RGPS distributions of strain rates are power law tailed, i.e., exhibit "wild randomness," whereas models distributions remain in the Gaussian attraction basin, i.e., exhibit "mild randomness." (2) The models are unable to reproduce the spatial and temporal correlations of the deformation fields: In the observations, ice deformation follows spatial and temporal scaling laws that express the heterogeneity and the intermittency of deformation. These relations do not appear in simulated ice deformation. Mean deformation in models is almost scale independent. The statistical properties of ice deformation are a signature of the ice mechanical behavior. The present work therefore suggests that the mechanical framework currently used by models is inappropriate. A different modeling framework based on elastic interactions could improve the representation of the statistical and scaling properties of ice deformation.

  18. Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields

    SciTech Connect

    Ibarra-Sierra, V.G.; Sandoval-Santana, J.C.; Cardoso, J.L.; Kunold, A.

    2015-11-15

    We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra is later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai–Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators. -- Highlights: •We deal with the general quadratic Hamiltonian and a particle in electromagnetic fields. •The evolution operator is worked out through the Lie algebraic approach. •We also obtain the propagator and Heisenberg picture position and momentum operators. •Analytical expressions for a

  19. Efficient and automatic calculation of optical band shapes and resonance Raman spectra for larger molecules within the independent mode displaced harmonic oscillator model.

    PubMed

    Petrenko, Taras; Neese, Frank

    2012-12-21

    In this work, an improved method for the efficient automatic simulation of optical band shapes and resonance Raman (rR) intensities within the "independent mode displaced harmonic oscillator" is described. Despite the relative simplicity of this model, it is able to account for the intensity distribution in absorption (ABS), fluorescence, and rR spectra corresponding to strongly dipole allowed electronic transitions with high accuracy. In order to include temperature-induced effects, we propose a simple extension of the time dependent wavepacket formalism developed by Heller which enables one to derive analytical expressions for the intensities of hot bands in ABS and rR spectra from the dependence of the wavepacket evolution on its initial coordinate. We have also greatly optimized the computational procedures for numerical integration of complicated oscillating integrals. This is important for efficient simulations of higher-order rR spectra and excitation profiles, as well as for the fitting of experimental spectra of large molecules. In particular, the multimode damping mechanism is taken into account for efficient reduction of the upper time limit in the numerical integration. Excited state energy gradient as well as excited state geometry optimization calculations are employed in order to determine excited state dimensionless normal coordinate displacements. The gradient techniques are highly cost-effective provided that analytical excited state derivatives with respect to nuclear displacements are available. Through comparison with experimental spectra of some representative molecules, we illustrate that the gradient techniques can even outperform the geometry optimization method if the harmonic approximation becomes inadequate.

  20. Bifurcation of quiescent H-mode to a wide pedestal regime in DIII-D and advances in the understanding of edge harmonic oscillations

    NASA Astrophysics Data System (ADS)

    Chen, Xi; Burrell, K. H.; Osborne, T. H.; Barada, K.; Ferraro, N. M.; Garofalo, A. M.; Groebner, R. J.; McKee, G. R.; Petty, C. C.; Porkolab, M.; Rhodes, T. L.; Rost, J. C.; Snyder, P. B.; Solomon, W. M.; Yan, Z.; The DIII-D Team

    2017-08-01

    New experimental studies and modelling of the coherent edge harmonic oscillation (EHO), which regulates the conventional Quiescent H-mode (QH-mode) edge, validate the proposed hypothesis of edge rotational shear in destabilizing the low-n kink-peeling mode as the additional drive mechanism for the EHO. The observed minimum edge E  ×  B shear required for the EHO decreases linearly with pedestal collisionality ν \\text{e}\\ast , which is favorable for operating QH-mode in machines with low collisionality and low rotation such as ITER. In addition, the QH-mode regime in DIII-D has recently been found to bifurcate into a new ‘wide-pedestal’ state at low torque in double-null shaped plasmas, characterized by increased pedestal height, width and thermal energy confinement (Burrell 2016 Phys. Plasmas 23 056103, Chen 2017 Nucl. Fusion 57 022007). This potentially provides an alternate path for achieving high performance ELM-stable operation at low torque, in addition to the low-torque QH-mode sustained with applied 3D fields. Multi-branch low-k and intermediate-k turbulences are observed in the ‘wide-pedestal’. New experiments support the hypothesis that the decreased edge E  ×  B shear enables destabilization of broadband turbulence, which relaxes edge pressure gradients, improves peeling-ballooning stability and allows a wider and thus higher pedestal. The ability to accurately predict the critical E  ×  B shear for EHO and maintain high performance QH-mode at low torque is an essential requirement for projecting QH-mode operation to ITER and future machines.

  1. Modeling of Plastic Deformation of Crystalline Materials on the Basis of the Concept of Hardening and Recovery

    NASA Astrophysics Data System (ADS)

    Starenchenko, V. A.; Cherepanov, D. N.; Selivanikova, O. V.

    2014-06-01

    A review is provided and a systematization is proposed for the principal directions of modeling of plastic deformation of crystalline materials and attendant phenomena within the framework of the concept of hardening and recovery. It is suggested that the formulation of the concept of hardening and recovery directly links phenomena taking place in the deformed crystalline material with the defect behavior of the crystal structure. This work considers only mathematical models that assume the formation of defects in the process of deformation. In order to investigate the phenomena observed in the process of deformation, use is made of physical quantities characterizing the defects, such as dislocation density, misorientation boundaries, discontinuities, concentration of point defects, etc. Great attention is given to works of the Tomsk School of Materials Science, which investigate the formation of deformation substructures in a consistent and systematic way.

  2. Decoherence of spin-deformed bosonic model

    SciTech Connect

    Dehdashti, Sh.; Mahdifar, A.; Bagheri Harouni, M.; Roknizadeh, R.

    2013-07-15

    The decoherence rate and some parameters affecting it are investigated for the generalized spin-boson model. We consider the spin-bosonic model when the bosonic environment is modeled by the deformed harmonic oscillators. We show that the state of the environment approaches a non-linear coherent state. Then, we obtain the decoherence rate of a two-level system which is in contact with a deformed bosonic environment which is either in thermal equilibrium or in the ground state. By using some recent realization of f-deformed oscillators, we show that some physical parameters strongly affect the decoherence rate of a two-level system. -- Highlights: •Decoherence of the generalized spin-boson model is considered. •In this model the environment consists of f-oscillators. •Via the interaction, the state of the environment approaches non-linear coherent states. •Effective parameters on decoherence are considered.

  3. A new single-particle basis for nuclear many-body calculations

    NASA Astrophysics Data System (ADS)

    Puddu, G.

    2017-10-01

    Predominantly, harmonic oscillator single-particle wave functions are the preferred choice for a basis in ab initio nuclear many-body calculations. These wave-functions, although very convenient in order to evaluate the matrix elements of the interaction in the laboratory frame, have too fast a fall-off at large distances. In the past, as an alternative to the harmonic oscillator, other single-particle wave functions have been proposed. In this work, we propose a new single-particle basis, directly linked to nucleon–nucleon interaction. This new basis is orthonormal and complete, has the proper asymptotic behavior at large distances and does not contain the continuum which would pose severe convergence problems in nuclear many body calculations. We consider the newly proposed NNLO-opt nucleon–nucleon interaction, without any renormalization. We show that, unlike other bases, this single-particle representation has a computational cost similar to the harmonic oscillator basis with the same space truncation and it gives lower energies for 6He and 6Li.

  4. The most general form of deformation of the Heisenberg algebra from the generalized uncertainty principle

    NASA Astrophysics Data System (ADS)

    Masood, Syed; Faizal, Mir; Zaz, Zaid; Ali, Ahmed Farag; Raza, Jamil; Shah, Mushtaq B.

    2016-12-01

    In this paper, we will propose the most general form of the deformation of Heisenberg algebra motivated by the generalized uncertainty principle. This deformation of the Heisenberg algebra will deform all quantum mechanical systems. The form of the generalized uncertainty principle used to motivate these results will be motivated by the space fractional quantum mechanics, and non-locality in quantum mechanical systems. We also analyse a specific limit of this generalized deformation for one dimensional system, and in that limit, a nonlocal deformation of the momentum operator generates a local deformation of all one dimensional quantum mechanical systems. We analyse the low energy effects of this deformation on a harmonic oscillator, Landau levels, Lamb shift, and potential barrier. We also demonstrate that this deformation leads to a discretization of space.

  5. Modeling of deformation of ground media on the basis of the particle method in a two-dimensional formulation

    NASA Astrophysics Data System (ADS)

    Berezhnoi, D. V.; Gabsalikova, N. F.; Izotov, V. G.; Miheev, V. V.

    2017-06-01

    A two-dimensional version of the soil deformation method based on the particle method is implemented in this paper. For describing the behavior of a continuous medium, the previously used two-parameter “modified” Lennard-Jones interaction potential was chosen. A number of model problems describing the loss of stability of the soil embankment in the field of gravity and the destruction of the soil under the action of the liquid phase are solved.

  6. Franck-Condon factors perturbed by damped harmonic oscillators: Solvent enhanced X {sup 1}A{sub g} ↔ A{sup 1}B{sub 1u} absorption and fluorescence spectra of perylene

    SciTech Connect

    Wang, Chen-Wen; Zhu, Chaoyuan Lin, Sheng-Hsien; Yang, Ling; Yu, Jian-Guo

    2014-08-28

    Damped harmonic oscillators are utilized to calculate Franck-Condon factors within displaced harmonic oscillator approximation. This is practically done by scaling unperturbed Hessian matrix that represents local modes of force constants for molecule in gaseous phase, and then by diagonalizing perturbed Hessian matrix it results in direct modification of Huang–Rhys factors which represent normal modes of solute molecule perturbed by solvent environment. Scaling parameters are empirically introduced for simulating absorption and fluorescence spectra of an isolated solute molecule in solution. The present method is especially useful for simulating vibronic spectra of polycyclic aromatic hydrocarbon molecules in which hydrogen atom vibrations in solution can be scaled equally, namely the same scaling factor being applied to all hydrogen atoms in polycyclic aromatic hydrocarbons. The present method is demonstrated in simulating solvent enhanced X {sup 1}A{sub g} ↔ A{sup 1}B{sub 1u} absorption and fluorescence spectra of perylene (medium-sized polycyclic aromatic hydrocarbon) in benzene solution. It is found that one of six active normal modes v{sub 10} is actually responsible to the solvent enhancement of spectra observed in experiment. Simulations from all functionals (TD) B3LYP, (TD) B3LYP35, (TD) B3LYP50, and (TD) B3LYP100 draw the same conclusion. Hence, the present method is able to adequately reproduce experimental absorption and fluorescence spectra in both gas and solution phases.

  7. Anatomy of the depressor septi nasi muscle: the basis for correction of deformities of the nose/lip junction.

    PubMed

    Barbosa, Marcus Vinícius Jardini; Nahas, Fábio Xerfan; Ferreira, Lydia Masako

    2013-04-01

    The purpose of this study was to analyse the macroscopic aspect of the depressor septi nasi muscle in cadavers according to its relations with the nasolabial region, and to describe a surgical technique developed out of the knowledge gained from its study to take care of nasal tip drooping and gummy smile. Twenty fresh adult cadavers were studied. All of them were men. A transverse incision was done at the gingivo-labial sulcus, through the frenulum, to expose the orbicularis oris and the depressor nasi muscles. These muscles were isolated and their anatomical aspect, localisation, origin, and insertion were registered. Sixteen of the cadavers presented the muscle. From these, 14 were bilateral and two were unilateral. Four cadavers did not present the muscle. Muscular fibres were vertically disposed and presented oblique direction towards the midline, in a quadrangular shape. From the 16 cadavers of the subgroup in whom the muscle was present, 14 originated in the orbicularis oris and its insertion was in the maxilla. Two of the cadavers presented the origin and insertion at the maxilla. According to these findings, a surgical approach of the muscles was proposed to treat the gummy smile deformity during rhinoplasty and two clinical cases are presented. The depressor nasi muscles presented an anatomical variation. In most cases it is intimately related with the orbicularis oris and the maxilla, being a relatively thick structure. We suggest its treatment simultaneously during rhinoplasty for a better result of the nasal tip and it benefits the "tense nose" aspect and the smiling deformity.

  8. Deformation of supersymmetric and conformal quantum mechanics through affine transformations

    NASA Technical Reports Server (NTRS)

    Spiridonov, Vyacheslav

    1993-01-01

    Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional N = 2 supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra. Instead, superpartner Hamiltonians are q-isospectral, i.e. the spectrum of one can be obtained from another (with possible exception of the lowest level) by q(sup 2)-factor scaling. This construction allows easily to rederive a special self-similar potential found by Shabat and to show that for the latter a q-deformed harmonic oscillator algebra of Biedenharn and Macfarlane serves as the spectrum generating algebra. A general class of potentials related to the quantum conformal algebra su(sub q)(1,1) is described. Further possibilities for q-deformation of known solvable potentials are outlined.

  9. Exploring continuum structures with a pseudo-state basis

    SciTech Connect

    Lay, J. A.; Moro, A. M.; Arias, J. M.; Gomez-Camacho, J.

    2010-08-15

    The ability of a recently developed square-integrable discrete basis to represent the properties of the continuum of a two-body system is investigated. The basis is obtained performing a simple analytic local scale transformation to the harmonic oscillator basis. Scattering phase-shifts and the electric transition probabilities B(E1) and B(E2) have been evaluated for several potentials using the proposed basis. Both quantities are found to be in excellent agreement with the exact values calculated from the true scattering states. The basis has been applied to describe the projectile continuum in the {sup 6}He scattering by {sup 12}C and {sup 208}Pb targets at 240 MeV/nucleon and the {sup 11}Be scattering by {sup 12}C at 67 MeV/nucleon. The calculated breakup differential cross sections are found to be in very good agreement with the available experimental data for these reactions.

  10. Core excitation effects in halo nuclei using a transformed oscillator basis

    SciTech Connect

    Lay, J. A.; Arias, J. M.; Moro, A. M.; Gomez-Camacho, J.

    2013-06-10

    A recent generalization of the Transformed Harmonic Oscillator basis, intended to consider core excitations in the structure of one nucleon halo nuclei, is applied to the break up of {sup 11}Be. The reaction studied is {sup 11}Be+{sup 208}Pb at 69 MeV/nucleon. The experimental set up is designed to ensure pure dipole Coulomb excitations. Making use of the Equivalent Photon Method and the electromagnetic transition probabilities obtained with the transformed oscillator basis, a relevant contribution of the quadrupole excitations of the core is found. The inclusion of core excitations is, therefore, necessary for the correct extraction of the dipole electromagnetic transition probability of halo nuclei.

  11. Spectral gaps of spin-orbit coupled particles in deformed traps

    NASA Astrophysics Data System (ADS)

    Marchukov, O. V.; Volosniev, A. G.; Fedorov, D. V.; Jensen, A. S.; Zinner, N. T.

    2013-07-01

    We consider a spin-orbit coupled system of particles in an external trap that is represented by a deformed harmonic oscillator potential. The spin-orbit interaction is a Rashba interaction that does not commute with the trapping potential and requires a full numerical treatment in order to obtain the spectrum. The effect of a Zeeman term is also considered. Our results demonstrate that variable spectral gaps occur as a function of strength of the Rashba interaction and deformation of the harmonic trapping potential. The single-particle density of states and the critical strength for superfluidity vary tremendously with the interaction parameter. The strong variations with Rashba coupling and deformation imply that the few- and many-body physics of spin-orbit coupled systems can be manipulated by variation of these parameters.

  12. Time-dependent q-deformed bi-coherent states for generalized uncertainty relations

    NASA Astrophysics Data System (ADS)

    Gouba, Laure

    2015-07-01

    We consider the time-dependent bi-coherent states that are essentially the Gazeau-Klauder coherent states for the two dimensional noncommutative harmonic oscillator. Starting from some q-deformations of the oscillator algebra for which the entire deformed Fock space can be constructed explicitly, we define the q-deformed bi-coherent states. We verify the generalized Heisenberg's uncertainty relations projected onto these states. For the initial value in time, the states are shown to satisfy a generalized version of Heisenberg's uncertainty relations. For the initial value in time and for the parameter of noncommutativity θ = 0, the inequalities are saturated for the simultaneous measurement of the position-momentum observables. When the time evolves, the uncertainty products are different from their values at the initial time and do not always respect the generalized uncertainty relations.

  13. Quaternary deformation

    SciTech Connect

    Brown, R.D. Jr.

    1990-01-01

    Displaced or deformed rock units and landforms record the past 2 m.y. of faulting, folding, uplift, and subsidence in California. Properly interpreted, such evidence provides a quantitative basis for predicting future earthquake activity and for relating many diverse structures and landforms to the 5 cm/yr of horizontal motion at the boundary between the North American and Pacific plates. Modern techniques of geologic dating and expanded research on earthquake hazards have greatly improved our knowledge of the San Andreas fault system. Much of this new knowledge has been gained since 1965, and that part which concerns crustal deformation during the past 2 m.y. is briefly summarized here.

  14. Solution of the Self-consistent Skyrme Hartree-Fock-Bogoliubov Equations in the Cartesian Deformed Harmonic Oscillator Bssis (VII_HFODD (v.2.73y): a new version of the jprogram

    SciTech Connect

    Schunck, N.; Dobaczewski, J.; Satula, W.; Baczyk, P.; Dudek, J.; Gao, Y.; Konieczka, M.; Sato, K.; Shi, Y.; Wang, X. B.; Werner, T. R.

    2016-10-05

    HFODD is a physics computer code that is used to model the structure of the nucleus. It is an implimentation of the nuclear energy Density Functional Theory (DFT), where the energy of the nucleus is obtained by intergration over space of some phenomenological energy density, which is itself a functional of the neutron and proton densities. In HFODD, the energy density derives from either the Skyre or the Gogny effective two-body interaction between nucleons. Nuclear super-fluidity is treated a the Hartree-Fock-Boboliubov (HFB) approximation. This version is the 8th release of the code; the 7 previous versions have been published in Computer Physics Communications (see references). Version 2.49p was partly developed at LLNL and was released under a GPL License and IM number LLNL-CODE-470611. The currect version 2.73y is the second version that has been partly developed a LLNL.

  15. Dynamic visual cryptography on deformable finite element grids

    NASA Astrophysics Data System (ADS)

    Aleksiene, S.; Vaidelys, M.; Aleksa, A.; Ragulskis, M.

    2017-07-01

    Dynamic visual cryptography scheme based on time averaged moiré fringes on deformable finite element grids is introduced in this paper. A predefined Eigenshape function is used for the selection of the pitch of the moiré grating. The relationship between the pitch of moiré grating, the roots of the zero order Bessel function of the first kind and the amplitude of harmonic oscillations is derived and validated by computational experiments. Phase regularization algorithm is used in the entire area of the cover image in order to embed the secret image and to avoid large fluctuations of the moiré grating. Computational simulations are used to demonstrate the efficiency and the applicability of the proposed image hiding technique.

  16. Nuclear shape phase transition within a conjunction of γ-rigid and γ-stable collective behaviors in deformation-dependent mass formalism

    NASA Astrophysics Data System (ADS)

    Chabab, M.; El Batoul, A.; Lahbas, A.; Oulne, M.

    2016-12-01

    In this paper, we present a theoretical study of a conjunction of γ-rigid and γ-stable collective motions in critical point symmetries of the phase transitions from spherical to deformed shapes of nuclei using an exactly separable version of the Bohr Hamiltonian with a deformation-dependent mass term. The deformation-dependent mass is applied simultaneously to γ-rigid and γ-stable parts of this famous collective Hamiltonian. Moreover, the β part of the problem is described by means of Davidson potential, while the γ-angular part corresponding to axially symmetric shapes is treated by a harmonic oscillator potential. The energy eigenvalues and normalized eigenfunctions of the problem are obtained in compact forms by making use of the asymptotic iteration method. The combined effect of the deformation-dependent mass and rigidity as well as harmonic oscillator stiffness parameters on the energy spectrum and wave functions is duly investigated. Also, the electric quadrupole transition ratios and energy spectrum of some γ-stable and prolate nuclei are calculated and compared with the experimental data as well as with other theoretical models.

  17. Modification of the malus law for the torsional deformation of lyotropic nematics in magnetic field on the basis of statistical approach

    NASA Astrophysics Data System (ADS)

    Golovanov, A. V.; Shapovalov, V. I.

    2010-07-01

    A method based on the statistical approach is proposed to calculate the light intensity for the torsional deformation of lyotropic nematic liquid crystals at violated Mauguin adiabatic approximation. Theoretical dependences of the light intensity on the magnetic field strength are obtained for two limiting cases of lyotropic nematic anchoring with bearing surfaces: infinite and low anchoring energies.

  18. Large deformation of uniaxially loaded slender microbeams on the basis of modified couple stress theory: Analytical solution and Galerkin-based method

    NASA Astrophysics Data System (ADS)

    Kiani, Keivan

    2017-09-01

    Large deformation regime of micro-scale slender beam-like structures subjected to axially pointed loads is of high interest to nanotechnologists and applied mechanics community. Herein, size-dependent nonlinear governing equations are derived by employing modified couple stress theory. Under various boundary conditions, analytical relations between axially applied loads and deformations are presented. Additionally, a novel Galerkin-based assumed mode method (AMM) is established to solve the highly nonlinear equations. In some particular cases, the predicted results by the analytical approach are also checked with those of AMM and a reasonably good agreement is reported. Subsequently, the key role of the material length scale on the load-deformation of microbeams is discussed and the deficiencies of the classical elasticity theory in predicting such a crucial mechanical behavior are explained in some detail. The influences of slenderness ratio and thickness of the microbeam on the obtained results are also examined. The present work could be considered as a pivotal step in better realizing the postbuckling behavior of nano-/micro- electro-mechanical systems consist of microbeams.

  19. Hamiltonian Light-Front Ffield Theory in a Basis Function Approach

    SciTech Connect

    Vary, J.P.; Honkanen, H.; Li, Jun; Maris, P.; Brodsky, S.J.; Harindranath, A.; de Teramond, G.F.; Sternberg, P.; Ng, E.G.; Yang, C.

    2009-05-15

    Hamiltonian light-front quantum field theory constitutes a framework for the non-perturbative solution of invariant masses and correlated parton amplitudes of self-bound systems. By choosing the light-front gauge and adopting a basis function representation, we obtain a large, sparse, Hamiltonian matrix for mass eigenstates of gauge theories that is solvable by adapting the ab initio no-core methods of nuclear many-body theory. Full covariance is recovered in the continuum limit, the infinite matrix limit. There is considerable freedom in the choice of the orthonormal and complete set of basis functions with convenience and convergence rates providing key considerations. Here, we use a two-dimensional harmonic oscillator basis for transverse modes that corresponds with eigensolutions of the soft-wall AdS/QCD model obtained from light-front holography. We outline our approach, present illustrative features of some non-interacting systems in a cavity and discuss the computational challenges.

  20. A new basis set for molecular bending degrees of freedom

    NASA Astrophysics Data System (ADS)

    Jutier, Laurent

    2010-07-01

    We present a new basis set as an alternative to Legendre polynomials for the variational treatment of bending vibrational degrees of freedom in order to highly reduce the number of basis functions. This basis set is inspired from the harmonic oscillator eigenfunctions but is defined for a bending angle in the range θ ɛ[0:π]. The aim is to bring the basis functions closer to the final (ro)vibronic wave functions nature. Our methodology is extended to complicated potential energy surfaces, such as quasilinearity or multiequilibrium geometries, by using several free parameters in the basis functions. These parameters allow several density maxima, linear or not, around which the basis functions will be mainly located. Divergences at linearity in integral computations are resolved as generalized Legendre polynomials. All integral computations required for the evaluation of molecular Hamiltonian matrix elements are given for both discrete variable representation and finite basis representation. Convergence tests for the low energy vibronic states of HCCH++, HCCH+, and HCCS are presented.

  1. (p,q) deformations and (p,q)-vector coherent states of the Jaynes-Cummings model in the rotating wave approximation

    SciTech Connect

    Ben Geloun, Joseph; Govaerts, Jan; Hounkonnou, M. Norbert

    2007-03-15

    Classes of (p,q) deformations of the Jaynes-Cummings model in the rotating wave approximation are considered. Diagonalization of the Hamiltonian is performed exactly, leading to useful spectral decompositions of a series of relevant operators. The latter include ladder operators acting between adjacent energy eigenstates within two separate infinite discrete towers, except for a singleton state. These ladder operators allow for the construction of (p,q)-deformed vector coherent states. Using (p,q) arithmetics, explicit and exact solutions to the associated moment problem are displayed, providing new classes of coherent states for such models. Finally, in the limit of decoupled spin sectors, our analysis translates into (p,q) deformations of the supersymmetric harmonic oscillator, such that the two supersymmetric sectors get intertwined through the action of the ladder operators as well as in the associated coherent states.

  2. How to spoil a good basis set for Rayleigh-Ritz calculations

    SciTech Connect

    Pupyshev, Vladimir I.; Montgomery, H. E. Jr.

    2013-08-15

    For model quantum mechanical systems such as the harmonic oscillator and a particle in an impenetrable box, we consider the set of exact discrete spectrum functions and define the modified basis set by subtraction of the ground state wavefunction from all the other wavefunctions with some real weights. It is demonstrated that the modified set of functions is complete in the space of square integrable functions if and only if the series of the squared weights diverges. A similar, but nonequivalent criterion is derived for convergence of Rayleigh-Ritz ground state energy calculations to the exact ground state energy value with the basis set extension. Some numerical illustrations are provided which demonstrate a wide variety of possible situations for model systems.

  3. Hamiltonian Light-front Field Theory Within an AdS/QCD Basis

    SciTech Connect

    Vary, J.P.; Honkanen, H.; Li, Jun; Maris, P.; Brodsky, S.J.; Harindranath, A.; de Teramond, G.F.; Sternberg, P.; Ng, E.G.; Yang, C.; /LBL, Berkeley

    2009-12-16

    Non-perturbative Hamiltonian light-front quantum field theory presents opportunities and challenges that bridge particle physics and nuclear physics. Fundamental theories, such as Quantum Chromodynamics (QCD) and Quantum Electrodynamics (QED) offer the promise of great predictive power spanning phenomena on all scales from the microscopic to cosmic scales, but new tools that do not rely exclusively on perturbation theory are required to make connection from one scale to the next. We outline recent theoretical and computational progress to build these bridges and provide illustrative results for nuclear structure and quantum field theory. As our framework we choose light-front gauge and a basis function representation with two-dimensional harmonic oscillator basis for transverse modes that corresponds with eigensolutions of the soft-wall AdS/QCD model obtained from light-front holography.

  4. Parity Deformed Jaynes-Cummings Model: “Robust Maximally Entangled States”

    PubMed Central

    Dehghani, A.; Mojaveri, B.; Shirin, S.; Faseghandis, S. Amiri

    2016-01-01

    The parity-deformations of the quantum harmonic oscillator are used to describe the generalized Jaynes-Cummings model based on the λ-analog of the Heisenberg algebra. The behavior is interestingly that of a coupled system comprising a two-level atom and a cavity field assisted by a continuous external classical field. The dynamical characters of the system is explored under the influence of the external field. In particular, we analytically study the generation of robust and maximally entangled states formed by a two-level atom trapped in a lossy cavity interacting with an external centrifugal field. We investigate the influence of deformation and detuning parameters on the degree of the quantum entanglement and the atomic population inversion. Under the condition of a linear interaction controlled by an external field, the maximally entangled states may emerge periodically along with time evolution. In the dissipation regime, the entanglement of the parity deformed JCM are preserved more with the increase of the deformation parameter, i.e. the stronger external field induces better degree of entanglement. PMID:27917882

  5. Parity Deformed Jaynes-Cummings Model: “Robust Maximally Entangled States”

    NASA Astrophysics Data System (ADS)

    Dehghani, A.; Mojaveri, B.; Shirin, S.; Faseghandis, S. Amiri

    2016-12-01

    The parity-deformations of the quantum harmonic oscillator are used to describe the generalized Jaynes-Cummings model based on the λ-analog of the Heisenberg algebra. The behavior is interestingly that of a coupled system comprising a two-level atom and a cavity field assisted by a continuous external classical field. The dynamical characters of the system is explored under the influence of the external field. In particular, we analytically study the generation of robust and maximally entangled states formed by a two-level atom trapped in a lossy cavity interacting with an external centrifugal field. We investigate the influence of deformation and detuning parameters on the degree of the quantum entanglement and the atomic population inversion. Under the condition of a linear interaction controlled by an external field, the maximally entangled states may emerge periodically along with time evolution. In the dissipation regime, the entanglement of the parity deformed JCM are preserved more with the increase of the deformation parameter, i.e. the stronger external field induces better degree of entanglement.

  6. Madelung Deformity.

    PubMed

    Kozin, Scott H; Zlotolow, Dan A

    2015-10-01

    Madelung deformity of the wrist is more common in females and is often associated with Leri Weill dyschondrosteosis, a mesomelic form of dwarfism. Patients with Madelung deformity often report wrist deformity resulting from the prominence of the relatively long ulna. The typical Madelung deformity is associated with a Vickers ligament that creates a tether across the volar-ulnar radial physis that restricts growth across this segment. The distal radius deforms in the coronal (increasing radial inclination) and the sagittal (increasing volar tilt) planes. There is lunate subsidence and the proximal carpal row adapts to the deformity by forming an upside-down pyramid shape or triangle. Treatment depends on the age at presentation, degree of deformity, and magnitude of symptoms. Mild asymptomatic deformity warrants a period of nonsurgical management with serial x-ray examinations because the natural history is unpredictable. Many patients never require surgical intervention. Progressive deformity in the young child with considerable growth potential remaining requires release of Vickers ligament and radial physiolysis to prevent ongoing deterioration Concomitant ulnar epiphysiodesis may be necessary. Advanced asymptomatic deformity in older children with an unacceptable-appearing wrist or symptomatic deformity are indications for surgery. A dome osteotomy of the radius allows 3-dimensional correction of the deformity. Positive radiographic and clinical results after dome osteotomy have been reported. Copyright © 2015 American Society for Surgery of the Hand. Published by Elsevier Inc. All rights reserved.

  7. Applications of Basis Light-Front Quantization to QED

    NASA Astrophysics Data System (ADS)

    Vary, James P.; Zhao, Xingbo; Ilderton, Anton; Honkanen, Heli; Maris, Pieter; Brodsky, Stanley J.

    2014-06-01

    Hamiltonian light-front quantum field theory provides a framework for calculating both static and dynamic properties of strongly interacting relativistic systems. Invariant masses, correlated parton amplitudes and time-dependent scattering amplitudes, possibly with strong external time-dependent fields, represent a few of the important applications. By choosing the light-front gauge and adopting an orthonormal basis function representation, we obtain a large, sparse, Hamiltonian matrix eigenvalue problem for mass eigenstates that we solve by adapting ab initio no-core methods of nuclear many-body theory. In the continuum limit, the infinite matrix limit, we recover full covariance. Guided by the symmetries of light-front quantized theory, we adopt a two-dimensional harmonic oscillator basis for transverse modes that corresponds with eigensolutions of the soft-wall anti-de Sitter/quantum chromodynamics (AdS/QCD) model obtained from light-front holography. We outline our approach and present results for non-linear Compton scattering, evaluated non-perturbatively, where a strong and time-dependent laser field accelerates the electron and produces states of higher invariant mass i.e. final states with photon emission.

  8. Neutron halo in deformed nuclei

    SciTech Connect

    Zhou Shangui; Meng Jie; Ring, P.; Zhao Enguang

    2010-07-15

    Halo phenomena in deformed nuclei are investigated within a deformed relativistic Hartree Bogoliubov (DRHB) theory. These weakly bound quantum systems present interesting examples for the study of the interdependence between the deformation of the core and the particles in the halo. Contributions of the halo, deformation effects, and large spatial extensions of these systems are described in a fully self-consistent way by the DRHB equations in a spherical Woods-Saxon basis with the proper asymptotic behavior at a large distance from the nuclear center. Magnesium and neon isotopes are studied and detailed results are presented for the deformed neutron-rich and weakly bound nucleus {sup 44}Mg. The core of this nucleus is prolate, but the halo has a slightly oblate shape. This indicates a decoupling of the halo orbitals from the deformation of the core. The generic conditions for the occurrence of this decoupling effects are discussed.

  9. Solutions to Kuessner's integral equation in unsteady flow using local basis functions

    NASA Technical Reports Server (NTRS)

    Fromme, J. A.; Halstead, D. W.

    1975-01-01

    The computational procedure and numerical results are presented for a new method to solve Kuessner's integral equation in the case of subsonic compressible flow about harmonically oscillating planar surfaces with controls. Kuessner's equation is a linear transformation from pressure to normalwash. The unknown pressure is expanded in terms of prescribed basis functions and the unknown basis function coefficients are determined in the usual manner by satisfying the given normalwash distribution either collocationally or in the complex least squares sense. The present method of solution differs from previous ones in that the basis functions are defined in a continuous fashion over a relatively small portion of the aerodynamic surface and are zero elsewhere. This method, termed the local basis function method, combines the smoothness and accuracy of distribution methods with the simplicity and versatility of panel methods. Predictions by the local basis function method for unsteady flow are shown to be in excellent agreement with other methods. Also, potential improvements to the present method and extensions to more general classes of solutions are discussed.

  10. Haglund's Deformity

    MedlinePlus

    ... deformity is often called “pump bump” because the rigid backs of pump-style shoes can create pressure ... when walking. In fact, any shoes with a rigid back, such as ice skates, men’s dress shoes ...

  11. Contracture deformity

    MedlinePlus

    Deformity - contracture ... Contracture can be caused by any of the following: Brain and nervous system disorders, such as cerebral ... Follow your health care provider's instructions for treating contracture at home. Treatments may include: Doing exercises and ...

  12. Spinal deformity.

    PubMed

    Bunnell, W P

    1986-12-01

    Spinal deformity is a relatively common disorder, particularly in teenage girls. Early detection is possible by a simple, quick visual inspection that should be a standard part of the routine examination of all preteen and teenage patients. Follow-up observation will reveal those curvatures that are progressive and permit orthotic treatment to prevent further increase in the deformity. Spinal fusion offers correction and stabilization of more severe degrees of scoliosis.

  13. Hamiltonian light-front field theory in a basis function approach

    SciTech Connect

    Vary, J. P.; Honkanen, H.; Li Jun; Maris, P.; Brodsky, S. J.; Harindranath, A.; Sternberg, P.; Ng, E. G.; Yang, C.

    2010-03-15

    Hamiltonian light-front quantum field theory constitutes a framework for the nonperturbative solution of invariant masses and correlated parton amplitudes of self-bound systems. By choosing the light-front gauge and adopting a basis function representation, a large, sparse, Hamiltonian matrix for mass eigenstates of gauge theories is obtained that is solvable by adapting the ab initio no-core methods of nuclear many-body theory. Full covariance is recovered in the continuum limit, the infinite matrix limit. There is considerable freedom in the choice of the orthonormal and complete set of basis functions with convenience and convergence rates providing key considerations. Here we use a two-dimensional harmonic oscillator basis for transverse modes that corresponds with eigensolutions of the soft-wall anti-de Sitter/quantum chromodynamics (AdS/QCD) model obtained from light-front holography. We outline our approach and present illustrative features of some noninteracting systems in a cavity. We illustrate the first steps toward solving quantum electrodynamics (QED) by obtaining the mass eigenstates of an electron in a cavity in small basis spaces and discuss the computational challenges.

  14. Normal ordering for nonlinear deformed ladder operators and the f-generalization of the Stirling and Bell numbers

    NASA Astrophysics Data System (ADS)

    Aleixo, A. N. F.; Balantekin, A. B.

    2015-12-01

    We resolve the normal ordering problem for symmetric ( D ˆ + D ˆ - ) n and asymmetric ( Dˆ + r D ˆ - ) n strings of the nonlinear deformed ladder operators D ˆ ± for supersymmetric and shape-invariant potential systems, where r and n are positive integers. We provide exact and explicit expressions for their normal forms N { ( D ˆ + D ˆ - ) n } and N { ( Dˆ + r D ˆ - ) n } , where in N { . . . } all D ˆ - are at the right side. We find that the solutions involve sequence of expansion coefficients which, for r, n > 1, corresponds to the f-deformed generalization of the classical Stirling and Bell numbers of the second kind. We apply the general formalism for the translational shape-invariant potential systems as well as for the particular case of the harmonic oscillator potential system. We show that these numbers are obtained for families of polynomial expressions generated with the deformations parameters and the parameters related to the forms of the supersymmetric partner potentials.

  15. The impact damped harmonic oscillator in free decay

    NASA Technical Reports Server (NTRS)

    Brown, G. V.; North, C. M.

    1987-01-01

    The impact-damped oscillator in free decay is studied by using time history solutions. A large range of oscillator amplitude is covered. The amount of damping is correlated with the behavior of the impacting mass. There are three behavior regimes: (1) a low amplitude range with less than one impact per cycle and very low damping, (2) a useful middle amplitude range with a finite number of impacts per cycle, and (3) a high amplitude range with an infinite number of impacts per cycle and progressively decreasing damping. For light damping the impact damping in the middle range is: (1) proportional to impactor mass, (2) additive to proportional damping, (3) a unique function of vibration amplitude, (4) proportional to 1-epsilon, where epsilon is the coefficient of restitution, and (5) very roughly inversely proportional to amplitude. The system exhibits jump phenomena and period doublings. An impactor with 2 percent of the oscillator's mass can produce a loss factor near 0.1.

  16. On harmonic oscillators and their Kemmer relativistic forms

    NASA Technical Reports Server (NTRS)

    Debergh, Nathalie; Beckers, Jules

    1993-01-01

    It is shown that Dirac (Kemmer) equations are intimately connected with (para)supercharges coming from (para)supersymmetric quantum mechanics, a nonrelativistic theory. The dimensions of the irreducible representations of Clifford (Kemmer) algebras play a fundamental role in such an analysis. These considerations are illustrated through oscillator like interactions, leading to (para)relativistic oscillators.

  17. Non-Heisenberg states of the harmonic oscillator

    NASA Astrophysics Data System (ADS)

    Dechoum, K.; França, H. M.

    1995-11-01

    The effects of the vacuum electromagnetic fluctuations and the radiation reaction fields on the time development of a simple microscopic system are identified using a new mathematical method. This is done by studying a charged mechanical oscillator (frequency Ω 0) within the realm of stochastic electrodynamics, where the vacuum plays the role of an energy reservoir. According to our approach, which may be regarded as a simple mathematical exercise, we show how the oscillator Liouville equation is transformed into a Schrödinger-like stochastic equation with a free parameter h' with dimensions of action. The role of the physical Planck's constant h is introduced only through the zero-point vacuum electromagnetic fields. The perturbative and the exact solutions of the stochastic Schrödinger-like equation are presented for h'>0. The exact solutions for which h'<(δp) 2 >=(h'/2) 2, which includes the limit of zero indeterminacy (h → 0). We show how the radiation reaction and the vacuum fields govern the evolution of these non-Heisenberg states in phase space, guaranteeing their decay to the stationary state with average energy hΩ 0 /2 and <(δx) 2 ><(δp) 2 >=h 2 /4 at zero temperature. Environmental and thermal effects-are briefly discussed and the connection with similar works within the realm of quantum electrodynamics is also presented. We suggest some other applications of the classical non-Heisenberg states introduced in this paper and we also indicate experiments which might give concrete evidence of these states.

  18. On the measurement of time for the quantum harmonic oscillator

    NASA Technical Reports Server (NTRS)

    Shepard, Scott R.

    1992-01-01

    A generalization of previous treatments of quantum phase is presented. Restrictions on the class of realizable phase statistics are thereby removed; thus, permitting 'phase wavefunction collapse' (and other advantages). This is accomplished by exciting the auxiliary mode of the measurement apparatus in a time-reversed fashion. The mathematical properties of this auxiliary mode are studied in the hope that they will lead to an identification of a physical apparatus which can realize the quantum phase measurement.

  19. Spatial analysis of harmonic oscillation of gypsy moth outbreak intensity

    Treesearch

    Kyle J. Haynes; Andrew M. Liebhold; Derek M. Johnson

    2009-01-01

    Outbreaks of many forest-defoliating insects are synchronous over broad geographic areas and occur with a period of approximately 10 years. Within the range of the gypsy moth in North America, however, there is considerable geographic heterogeneity in strength of periodicity and the frequency of outbreaks. Furthermore, gypsy moth outbreaks exhibit two significant...

  20. Operation of higher harmonic oscillations in free-electron lasers.

    PubMed

    Sei, N; Ogawa, H; Yamada, K

    2012-01-02

    We report for the first time the experimental achievement of a seventh-harmonic free-electron laser (FEL) oscillation. The measured FEL gains and average FEL powers for higher harmonics were identical to those calculated by a one-dimensional FEL theory. The measured linewidths of the higher-harmonic FELs were narrower than that of the fundamental FEL owing to the narrower spectral widths of the spontaneous emissions. By applying the higher-harmonic FEL oscillation to a resonator-type FEL with an advanced accelerator, an x-ray FEL oscillator can be realized at lower electron-beam energy.

  1. Generalized Energy Equipartition in Harmonic Oscillators Driven by Active Baths

    NASA Astrophysics Data System (ADS)

    Maggi, Claudio; Paoluzzi, Matteo; Pellicciotta, Nicola; Lepore, Alessia; Angelani, Luca; Di Leonardo, Roberto

    2014-12-01

    We study experimentally and numerically the dynamics of colloidal beads confined by a harmonic potential in a bath of swimming E. coli bacteria. The resulting dynamics is well approximated by a Langevin equation for an overdamped oscillator driven by the combination of a white thermal noise and an exponentially correlated active noise. This scenario leads to a simple generalization of the equipartition theorem resulting in the coexistence of two different effective temperatures that govern dynamics along the flat and the curved directions in the potential landscape.

  2. Cooling a Harmonic Oscillator by Optomechanical Modification of Its Bath.

    PubMed

    Xu, Xunnong; Purdy, Thomas; Taylor, Jacob M

    2017-06-02

    Optomechanical systems show tremendous promise for the high-sensitivity sensing of forces and modification of mechanical properties via light. For example, similar to neutral atoms and trapped ions, laser cooling of mechanical motion by radiation pressure can take single mechanical modes to their ground state. Conventional optomechanical cooling is able to introduce an additional damping channel to mechanical motion while keeping its thermal noise at the same level, and, as a consequence, the effective temperature of the mechanical mode is lowered. However, the ratio of the temperature to the quality factor remains roughly constant, preventing dramatic advances in quantum sensing using this approach. Here we propose an approach for simultaneously reducing the thermal load on a mechanical resonator while improving its quality factor. In essence, we use the optical interaction to dynamically modify the dominant damping mechanism, providing an optomechanically induced effect analogous to a phononic band gap. The mechanical mode of interest is assumed to be weakly coupled to its heat bath but strongly coupled to a second mechanical mode, which is cooled by radiation pressure coupling to a red-detuned cavity field. We also identify a realistic optomechanical design that has the potential to realize this novel cooling scheme.

  3. Intuitive Solution to Quantum Harmonic Oscillator at Infinity

    ERIC Educational Resources Information Center

    Pye, Cory C.

    2004-01-01

    The attempt to develop the laboratory component of a one-semester quantum chemistry course at Saint Mary's University has led to allowing the students to solve a big problem in quantum chemistry. It is done by subdivision into smaller problems that can be independently tackled by a student with a two-year calculus background.

  4. Synchronizing quantum harmonic oscillators through two-level systems

    NASA Astrophysics Data System (ADS)

    Militello, Benedetto; Nakazato, Hiromichi; Napoli, Anna

    2017-08-01

    Two oscillators coupled to a two-level system which in turn is coupled to an infinite number of oscillators (reservoir) are considered, bringing to light the occurrence of synchronization. A detailed analysis clarifies the physical mechanism that forces the system to oscillate at a single frequency with a predictable and tunable phase difference. Finally, the scheme is generalized to the case of N oscillators and M (

  5. Cooling a Harmonic Oscillator by Optomechanical Modification of Its Bath

    NASA Astrophysics Data System (ADS)

    Xu, Xunnong; Purdy, Thomas; Taylor, Jacob M.

    2017-06-01

    Optomechanical systems show tremendous promise for the high-sensitivity sensing of forces and modification of mechanical properties via light. For example, similar to neutral atoms and trapped ions, laser cooling of mechanical motion by radiation pressure can take single mechanical modes to their ground state. Conventional optomechanical cooling is able to introduce an additional damping channel to mechanical motion while keeping its thermal noise at the same level, and, as a consequence, the effective temperature of the mechanical mode is lowered. However, the ratio of the temperature to the quality factor remains roughly constant, preventing dramatic advances in quantum sensing using this approach. Here we propose an approach for simultaneously reducing the thermal load on a mechanical resonator while improving its quality factor. In essence, we use the optical interaction to dynamically modify the dominant damping mechanism, providing an optomechanically induced effect analogous to a phononic band gap. The mechanical mode of interest is assumed to be weakly coupled to its heat bath but strongly coupled to a second mechanical mode, which is cooled by radiation pressure coupling to a red-detuned cavity field. We also identify a realistic optomechanical design that has the potential to realize this novel cooling scheme.

  6. Entangling Qubits in a One-Dimensional Harmonic Oscillator

    NASA Astrophysics Data System (ADS)

    Owen, Edmund; Dean, Matthew; Barnes, Crispin

    2012-02-01

    We present a method for generating entanglement between qubits associated with a pair of particles interacting in a one-dimensional harmonic potential. By considering the effect of the interaction on the energy spectrum of the system, we show that, under certain approximations, a ``power-of-SWAP" operation is performed on the initial two-qubit quantum state without requiring any time-dependent control. Initialization errors and deviations from our approximation are shown to have a negligible effect on the final state. Using a GPU-accelerated iteration scheme to find numerical solutions to the two-particle time-dependent Schr"odinger equation, we demonstrate that it is possible to generate maximally entangled Bell states between the two qubits with high fidelity for a range of possible interaction potentials.

  7. The finite harmonic oscillator and its associated sequences

    PubMed Central

    Gurevich, Shamgar; Hadani, Ronny; Sochen, Nir

    2008-01-01

    A system of functions (signals) on the finite line, called the oscillator system, is described and studied. Applications of this system for discrete radar and digital communication theory are explained. PMID:18635684

  8. Laser cooling of a harmonic oscillator's bath with optomechanics

    NASA Astrophysics Data System (ADS)

    Xu, Xunnong; Taylor, Jacob

    Thermal noise reduction in mechanical systems is a topic both of fundamental interest for studying quantum physics at the macroscopic level and for application of interest, such as building high sensitivity mechanics based sensors. Similar to laser cooling of neutral atoms and trapped ions, the cooling of mechanical motion by radiation pressure can take single mechanical modes to their ground state. Conventional optomechanical cooling is able to introduce additional damping channel to mechanical motion, while keeping its thermal noise at the same level, and as a consequence, the effective temperature of the mechanical mode is lowered. However, the ratio of temperature to quality factor remains roughly constant, preventing dramatic advances in quantum sensing using this approach. Here we propose an efficient scheme for reducing the thermal load on a mechanical resonator while improving its quality factor. The mechanical mode of interest is assumed to be weakly coupled to its heat bath but strongly coupled to a second mechanical mode, which is cooled by radiation pressure coupling to a red detuned cavity field. We also identify a realistic optomechanical design that has the potential to realize this novel cooling scheme. Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, MD 20742, USA.

  9. Intuitive Solution to Quantum Harmonic Oscillator at Infinity

    ERIC Educational Resources Information Center

    Pye, Cory C.

    2004-01-01

    The attempt to develop the laboratory component of a one-semester quantum chemistry course at Saint Mary's University has led to allowing the students to solve a big problem in quantum chemistry. It is done by subdivision into smaller problems that can be independently tackled by a student with a two-year calculus background.

  10. Crustal deformation

    NASA Astrophysics Data System (ADS)

    Larson, Kristine M.

    1995-07-01

    Geodetic measurements of crustal deformation provide direct tests of geophysical models which are used to describe the dynamics of the Earth. Although geodetic observations have been made throughout history, only in the last several hundred years have they been sufficiently precise for geophysical studies. In the 19th century, these techniques included leveling and triangulation. Approximately 25 years ago, trilateration measurements were initiated by the USGS (United States Geological Survey) to monitor active faults in the United States. Several years later, NASA (National Aeronautics and Space Administration) begin an effort to measure plate tectonic motions on a global scale, using space geodetic techniques, VLBI (Very Long Baseline Interferometry) and SLR (Satellite Laser Ranging). The period covered by this report to the IUGG, 1991-1994, was a transition period in the field of crustal deformation. Trilateration measurements (previously the backbone of measurements across plate boundaries in the western United States and Alaska) have been abandoned. This system was labor-intensive, involved highly trained crews to carry out the observations, and only measured the length between sites. In addition, NASA drastically cut the budgets for VLBI and SLR during this period. Fixed site VLBI systems are still operational, but mobile VLBI measurements in North America have ceased. SLR measurements continue on a global scale, but the remaining crustal deformation measurements are now being made with the Global Positioning System (GPS). Nonetheless, because of the time scales involved, older geodetic data (including leveling, triangulation, and trilateration) continue to be important for many geophysical studies.

  11. [Neurogenic foot deformities].

    PubMed

    Senst, S

    2010-01-01

    There is a multitude of neurological diseases which may lead to neuro-orthopaedic problems and subsequently to neurogenic foot deformities. For this reason the diagnostician will be consistently surprised that there is a great multitude of different foot abnormalities and that not only the typical spastic talipes equines dominates. Of particular significance here is that these deformities almost always develop progressively, whereas most diseases persist per se, cerebral palsy being a typical case in point. However, in MMC (myelomeningocele) patients, there is also the danger of a worsening of the basic problem in the case of tethered cord syndrome. Unlike congenital talipes equinovarus, neuro-orthopaedic talipes equinovarus often shows over- or undercorrection postoperatively due to a shift in muscle imbalance. It is important, therefore, that the basis of conservative therapy include regular physiotherapy and orthoses during the day and, if necessary, at night. Botulinum toxin has been established as an additional measure for spasticity; however, this cannot always prevent surgical intervention, but is able to delay this to a better point in the development of the child/patient. The present article describes the diversity of neurological deformities and presents conservative as well as surgical therapeutic approaches.

  12. Bunionette deformity.

    PubMed

    Cohen, Bruce E; Nicholson, Christopher W

    2007-05-01

    The bunionette, or tailor's bunion, is a lateral prominence of the fifth metatarsal head. Most commonly, bunionettes are the result of a widened 4-5 intermetatarsal angle with associated varus of the metatarsophalangeal joint. When symptomatic, these deformities often respond to nonsurgical treatment methods, such as wider shoes and padding techniques. When these methods are unsuccessful, surgical treatment is based on preoperative radiographs and associated lesions, such as hyperkeratoses. In rare situations, a simple lateral eminence resection is appropriate; however, the risk of recurrence or overresection is high with this technique. Patients with a lateral bow to the fifth metatarsal are treated with a distal chevron-type osteotomy. A widened 4-5 intermetatarsal angle often requires a diaphyseal osteotomy for correction.

  13. Prediction of the critical point of pressure-induced deformation-related phase transitions in aligned single-walled carbon nanotubes on the basis of extreme-low-frequency-shift Raman spectroscopy

    NASA Astrophysics Data System (ADS)

    Shen, Yanting; Zerulla, Dominic

    2017-05-01

    Experimental evidence investigating the high-pressure response (0-9 GPa) of aligned single-walled carbon nanotube (SWNT) arrays in the extreme low Raman shift region (10-100 cm-1, squash mode region) is provided to verify a predictive model for deformation-related phase transitions. In addition to the well-known radial breathing mode (RBM) and despite the technical challenges associated with the detection of Raman signals very close to the exciting laser frequency, clear SWNT squash mode peaks were identified and used to refine the predictive model. Furthermore, this paper investigates and proposes explanations for the detailed behavior of the pressure dependent cross-sectional transition. The results demonstrate experimentally, and confirm earlier theoretical models, that the critical pressure scales ∝1 /O (dt3) against the chirality dependent nanotube diameter dt. Finally, the pressure and chirality dependent Raman upshifts of the squash mode, characterizing the phase transition, are found to be larger than those of the RBM, respectively, confirming the general theoretical prediction of greater environmental sensitivity of squash modes.

  14. States that "look the same" with respect to every basis in a mutually unbiased set

    NASA Astrophysics Data System (ADS)

    Amburg, Ilya; Sharma, Roshan; Sussman, Daniel M.; Wootters, William K.

    2014-12-01

    A complete set of mutually unbiased bases (MUBs) in a Hilbert space of dimension d defines a set of d + 1 orthogonal measurements. Relative to such a set, we define a MUB-balanced state to be a pure state for which the list of probabilities of the d outcomes of any of these measurements is independent of the choice of measurement, up to permutations. In this paper, we explicitly construct a MUB-balanced state for each prime power dimension d for which d = 3 (mod 4). These states have already been constructed by Appleby in unpublished notes, but our presentation here is different in that both the expression for the states themselves and the proof of MUB-balancedness are given in terms of the discrete Wigner function, rather than the density matrix or state vector. The discrete Wigner functions of these states are "rotationally symmetric" in a sense roughly analogous to the rotational symmetry of the energy eigenstates of a harmonic oscillator in the continuous two-dimensional phase space. Upon converting the Wigner function to a density matrix, we find that the states are expressible as real state vectors in the standard basis. We observe numerically that when d is large (and not a power of 3), a histogram of the components of such a state vector appears to form a semicircular distribution.

  15. Deform PF-MT: Particle Filter With Mode Tracker for Tracking Nonaffine Contour Deformations

    PubMed Central

    Vaswani, Namrata; Rathi, Yogesh; Yezzi, Anthony; Tannenbaum, Allen

    2013-01-01

    We propose algorithms for tracking the boundary contour of a deforming object from an image sequence, when the nonaffine (local) deformation over consecutive frames is large and there is overlapping clutter, occlusions, low contrast, or outlier imagery. When the object is arbitrarily deforming, each, or at least most, contour points can move independently. Contour deformation then forms an infinite (in practice, very large), dimensional space. Direct application of particle filters (PF) for large dimensional problems is impractically expensive. However, in most real problems, at any given time, most of the contour deformation occurs in a small number of dimensions (“effective basis space”) while the residual deformation in the rest of the state space (“residual space”) is small. This property enables us to apply the particle filtering with mode tracking (PF-MT) idea that was proposed for such large dimensional problems in recent work. Since most contour deformation is low spatial frequency, we propose to use the space of deformation at a subsampled set of locations as the effective basis space. The resulting algorithm is called deform PF-MT. It requires significant modifications compared to the original PF-MT because the space of contours is a non-Euclidean infinite dimensional space. PMID:19933014

  16. Dislocations: 75 years of Deformation Mechanisms

    NASA Technical Reports Server (NTRS)

    Schneider, Judy

    2009-01-01

    The selection of papers presented in this section reflect on themes to be explored at the "Dislocations: 75 years of Deformation Mechanisms" Symposium to be held at the Annual 2009 TMS meeting. The symposium was sponsored by the Mechanical Behavior of Materials Committee to give tribute to the evolution of a concept that has formed the basis of our mechanistic understanding of how crystalline solids plastically deform and how they fail.

  17. Correlated states and transparency of a barrier for low-energy particles at monotonic deformation of a potential well with dissipation and a stochastic force

    NASA Astrophysics Data System (ADS)

    Vysotskii, V. I.; Vysotskyy, M. V.

    2014-04-01

    The features of the formation of correlated coherent states of a particle in a parabolic potential well at its monotonic deformation (expansion or compression) in finite limits have been considered in the presence of dissipation and a stochastic force. It has been shown that, in both deformation regimes, a correlated coherent state is rapidly formed with a large correlation coefficient | r| → 1, which corresponds at a low energy of the particle to a very significant (by a factor of 1050-10100 or larger) increase in the transparency of the potential barrier at its interaction with atoms (nuclei) forming the "walls" of the potential well or other atoms located in the same well. The efficiency of the formation of correlated coherent states, as well as | r|, increases with an increase in the deformation interval and with a decrease in the deformation time. The presence of the stochastic force acting on the particle can significantly reduce the maximum | r| value and result in the fast relaxation of correlated coherent states with | r| → 0. The effect of dissipation in real systems is weaker than the action of the stochastic force. It has been shown that the formation of correlated coherent states at the fast expansion of the well can underlie the mechanism of nuclear reactions at a low energy, e.g., in microcracks developing in the bulk of metal hydrides loaded with hydrogen or deuterium, as well as in a low-pressure plasma in a variable magnetic field in which the motion of ions is similar to a harmonic oscillator with a variable frequency.

  18. Deformations in VLBI antennas

    NASA Technical Reports Server (NTRS)

    Clark, T. A.; Thomsen, P.

    1988-01-01

    A study is presented of deformations in antennas with the emphasis on their influence on VLBI measurements. The GIFTS structural analysis program has been used to model the VLBI antenna in Fairbanks (Alaska). The report identifies key deformations and studies the effect of gravity, wind, and temperature. Estimates of expected deformations are given.

  19. Description of weakly bound or unbound nuclear states

    SciTech Connect

    Kruppa, A.T.; Nazarewicz, W.

    2004-09-13

    A major theoretical challenge when dealing with weakly bound nuclei is to obtain a consistent microscopic description of bound states, resonances, and the non-resonant continuum. In this talk, resonances in deformed nuclei are described within the coupled-channel approach employing the Gamow state formalism. The coupled-channel method is compared with the expansion schemes employing the harmonic oscillator basis and the Berggren ensemble.

  20. Deformable Nanolaminate Optics

    SciTech Connect

    Olivier, S S; Papavasiliou, A P; Barbee, T W; Miles, R R; Walton, C C; Cohn, M B; Chang, K

    2006-05-12

    We are developing a new class of deformable optic based on electrostatic actuation of nanolaminate foils. These foils are engineered at the atomic level to provide optimal opto-mechanical properties, including surface quality, strength and stiffness, for a wide range of deformable optics. We are combining these foils, developed at Lawrence Livermore National Laboratory (LLNL), with commercial metal processing techniques to produce prototype deformable optics with aperture sizes up to 10 cm and actuator spacing from 1 mm to 1 cm and with a range of surface deformation designed to be as much as 10 microns. The existing capability for producing nanolaminate foils at LLNL, coupled with the commercial metal processing techniques being used, enable the potential production of these deformable optics with aperture sizes of over 1 m, and much larger deformable optics could potentially be produced by tiling multiple deformable segments. In addition, based on the fabrication processes being used, deformable nanolaminate optics could potentially be produced with areal densities of less than 1 kg per square m for applications in which lightweight deformable optics are desirable, and deformable nanolaminate optics could potentially be fabricated with intrinsically curved surfaces, including aspheric shapes. We will describe the basic principles of these devices, and we will present details of the design, fabrication and characterization of the prototype deformable nanolaminate optics that have been developed to date. We will also discuss the possibilities for future work on scaling these devices to larger sizes and developing both devices with lower areal densities and devices with curved surfaces.

  1. Study of resonant structures in a deformed mean field by the contour deformation method in momentum space

    NASA Astrophysics Data System (ADS)

    Hagen, G.; Vaagen, J. S.

    2006-03-01

    Solution of the momentum space Schrödinger equation in the case of deformed fields is being addressed. In particular it is shown that a complete set of single-particle states that includes bound, resonant, and complex continuum states may be obtained by the contour deformation method. This generalized basis in the complex energy plane is known as a Berggren basis. The momentum space Schrödinger equation is an integral equation that is easily solved by matrix diagonalization routines even for the case of deformed fields. The method is demonstrated for axial symmetry and a fictitious “deformed He5” but may be extended to more general deformation and applied to truly deformed halo nuclei.

  2. Deformations of superconformal theories

    NASA Astrophysics Data System (ADS)

    Córdova, Clay; Dumitrescu, Thomas T.; Intriligator, Kenneth

    2016-11-01

    We classify possible supersymmetry-preserving relevant, marginal, and irrelevant deformations of unitary superconformal theories in d ≥ 3 dimensions. Our method only relies on symmetries and unitarity. Hence, the results are model independent and do not require a Lagrangian description. Two unifying themes emerge: first, many theories admit deformations that reside in multiplets together with conserved currents. Such deformations can lead to modifications of the supersymmetry algebra by central and non-central charges. Second, many theories with a sufficient amount of supersymmetry do not admit relevant or marginal deformations, and some admit neither. The classification is complicated by the fact that short superconformal multiplets display a rich variety of sporadic phenomena, including supersymmetric deformations that reside in the middle of a multiplet. We illustrate our results with examples in diverse dimensions. In particular, we explain how the classification of irrelevant supersymmetric deformations can be used to derive known and new constraints on moduli-space effective actions.

  3. Deformations of superconformal theories

    SciTech Connect

    Córdova, Clay; Dumitrescu, Thomas T.; Intriligator, Kenneth

    2016-11-22

    Here, we classify possible supersymmetry-preserving relevant, marginal, and irrelevant deformations of unitary superconformal theories in d ≥ 3 dimensions. Our method only relies on symmetries and unitarity. Hence, the results are model independent and do not require a Lagrangian description. Two unifying themes emerge: first, many theories admit deformations that reside in multiplets together with conserved currents. Such deformations can lead to modifications of the supersymmetry algebra by central and noncentral charges. Second, many theories with a sufficient amount of supersymmetry do not admit relevant or marginal deformations, and some admit neither. The classification is complicated by the fact that short superconformal multiplets display a rich variety of sporadic phenomena, including supersymmetric deformations that reside in the middle of a multiplet. We illustrate our results with examples in diverse dimensions. In particular, we explain how the classification of irrelevant supersymmetric deformations can be used to derive known and new constraints on moduli-space effective actions.

  4. Alar Rim Deformities.

    PubMed

    Totonchi, Ali; Guyuron, Bahman

    2016-01-01

    The alar rim plays an important role in nasal harmony. Alar rim flaws are common following the initial rhinoplasty. Classification of the deformities helps with diagnosis and successful surgical correction. Diagnosis of the deformity requires careful observation of the computerized or life-sized photographs. Techniques for treatment of these deformities can easily be learned with attention to detail. Copyright © 2016 Elsevier Inc. All rights reserved.

  5. Deformation properties of lead isotopes

    SciTech Connect

    Tolokonnikov, S. V.; Borzov, I. N.; Lutostansky, Yu. S.; Saperstein, E. E.

    2016-01-15

    The deformation properties of a long lead isotopic chain up to the neutron drip line are analyzed on the basis of the energy density functional (EDF) in the FaNDF{sup 0} Fayans form. The question of whether the ground state of neutron-deficient lead isotopes can have a stable deformation is studied in detail. The prediction of this deformation is contained in the results obtained on the basis of the HFB-17 and HFB-27 Skyrme EDF versions and reported on Internet. The present analysis reveals that this is at odds with experimental data on charge radii and magnetic moments of odd lead isotopes. The Fayans EDF version predicts a spherical ground state for all light lead isotopes, but some of them (for example, {sup 180}Pb and {sup 184}Pb) prove to be very soft—that is, close to the point of a phase transition to a deformed state. Also, the results obtained in our present study are compared with the predictions of some other Skyrme EDF versions, including SKM*, SLy4, SLy6, and UNE1. By and large, their predictions are closer to the results arising upon the application of the Fayans functional. For example, the SLy4 functional predicts, in just the same way as the FaNDF{sup 0} functional, a spherical shape for all nuclei of this region. The remaining three Skyrme EDF versions lead to a deformation of some light lead isotopes, but their number is substantially smaller than that in the case of the HFB-17 and HFB-27 functionals. Moreover, the respective deformation energy is substantially lower, which gives grounds to hope for the restoration of a spherical shape upon going beyond the mean-field approximation, which we use here. Also, the deformation properties of neutron-rich lead isotopes are studied up to the neutron drip line. Here, the results obtained with the FaNDF{sup 0} functional are compared with the predictions of the HFB-17, HFB-27, SKM*, and SLy4 Skyrme EDF versions. All of the EDF versions considered here predict the existence of a region where neutron

  6. A basis-set based Fortran program to solve the Gross Pitaevskii equation for dilute Bose gases in harmonic and anharmonic traps

    NASA Astrophysics Data System (ADS)

    Tiwari, Rakesh Prabhat; Shukla, Alok

    2006-06-01

    Inhomogeneous boson systems, such as the dilute gases of integral spin atoms in low-temperature magnetic traps, are believed to be well described by the Gross-Pitaevskii equation (GPE). GPE is a nonlinear Schrödinger equation which describes the order parameter of such systems at the mean field level. In the present work, we describe a Fortran 90 computer program developed by us, which solves the GPE using a basis set expansion technique. In this technique, the condensate wave function (order parameter) is expanded in terms of the solutions of the simple-harmonic oscillator (SHO) characterizing the atomic trap. Additionally, the same approach is also used to solve the problems in which the trap is weakly anharmonic, and the anharmonic potential can be expressed as a polynomial in the position operators x, y, and z. The resulting eigenvalue problem is solved iteratively using either the self-consistent-field (SCF) approach, or the imaginary time steepest-descent (SD) approach. Iterations can be initiated using either the simple-harmonic-oscillator ground state solution, or the Thomas-Fermi (TF) solution. It is found that for condensates containing up to a few hundred atoms, both approaches lead to rapid convergence. However, in the strong interaction limit of condensates containing thousands of atoms, it is the SD approach coupled with the TF starting orbitals, which leads to quick convergence. Our results for harmonic traps are also compared with those published by other authors using different numerical approaches, and excellent agreement is obtained. GPE is also solved for a few anharmonic potentials, and the influence of anharmonicity on the condensate is discussed. Additionally, the notion of Shannon entropy for the condensate wave function is defined and studied as a function of the number of particles in the trap. It is demonstrated numerically that the entropy increases with the particle number in a monotonic way. Program summaryTitle of program

  7. On q-DEFORMED Para Oscillators and PARA-q Oscillators

    NASA Astrophysics Data System (ADS)

    Kumari, M. Krishna; Shanta, P.; Chaturvedi, S.; Srinivasan, V.

    Three generalized commutation relations for a single mode of the harmonic oscillator which contains para-bose and q oscillator commutation relations are constructed. These are shown to be inequivalent. The coherent states of the annihilation operator for these three cases are also constructed.

  8. First-Order Polynomial Heisenberg Algebras and Coherent States

    NASA Astrophysics Data System (ADS)

    Castillo-Celeita, M.; Fernández C, D. J.

    2016-03-01

    The polynomial Heisenberg algebras (PHA) are deformations of the Heisenberg- Weyl algebra characterizing the underlying symmetry of the supersymmetric partners of the Harmonic oscillator. When looking for the simplest system ruled by PHA, however, we end up with the harmonic oscillator. In this paper we are going to realize the first-order PHA through the harmonic oscillator. The associated coherent states will be also constructed, which turn out to be the well known even and odd coherent states.

  9. Resurgent deformation quantisation

    SciTech Connect

    Garay, Mauricio; Goursac, Axel de; Straten, Duco van

    2014-03-15

    We construct a version of the complex Heisenberg algebra based on the idea of endless analytic continuation. The algebra would be large enough to capture quantum effects that escape ordinary formal deformation quantisation. -- Highlights: •We construct resurgent deformation quantisation. •We give integral formulæ. •We compute examples which show that hypergeometric functions appear naturally in quantum computations.

  10. Tensile deformation of bacterial cellulose composites.

    PubMed

    Astley, Owen M; Chanliaud, Elisabeth; Donald, Athene M; Gidley, Michael J

    2003-03-01

    The polymeric basis for the mechanical properties of primary plant cell walls has been investigated by forming analogous composites based on fermentation of the bacterium Acetobacter xylinus, either alone or in the presence of xyloglucan or pectin. Simultaneous small-angle X-ray scattering and uniaxial deformation experiments has shown how the cellulose microfibrils reorient during deformation. Despite very different stress/strain curves, the reorientation behaviour is similar, regardless of the presence or absence of xyloglucan or pectin. A simple theory has been developed to predict the orientation behaviour. This is qualitatively similar to the measured behaviour, but differs quantitatively.

  11. Deformation mechanisms in experimentally deformed Boom Clay

    NASA Astrophysics Data System (ADS)

    Desbois, Guillaume; Schuck, Bernhard; Urai, Janos

    2016-04-01

    Bulk mechanical and transport properties of reference claystones for deep disposal of radioactive waste have been investigated since many years but little is known about microscale deformation mechanisms because accessing the relevant microstructure in these soft, very fine-grained, low permeable and low porous materials remains difficult. Recent development of ion beam polishing methods to prepare high quality damage free surfaces for scanning electron microscope (SEM) is opening new fields of microstructural investigation in claystones towards a better understanding of the deformation behavior transitional between rocks and soils. We present results of Boom Clay deformed in a triaxial cell in a consolidated - undrained test at a confining pressure of 0.375 MPa (i.e. close to natural value), with σ1 perpendicular to the bedding. Experiments stopped at 20 % strain. As a first approximation, the plasticity of the sample can be described by a Mohr-Coulomb type failure envelope with a coefficient of cohesion C = 0.117 MPa and an internal friction angle ϕ = 18.7°. After deformation test, the bulk sample shows a shear zone at an angle of about 35° from the vertical with an offset of about 5 mm. We used the "Lamipeel" method that allows producing a permanent absolutely plane and large size etched micro relief-replica in order to localize and to document the shear zone at the scale of the deformed core. High-resolution imaging of microstructures was mostly done by using the BIB-SEM method on key-regions identified after the "Lamipeel" method. Detailed BIB-SEM investigations of shear zones show the following: the boundaries between the shear zone and the host rock are sharp, clay aggregates and clastic grains are strongly reoriented parallel to the shear direction, and the porosity is significantly reduced in the shear zone and the grain size is smaller in the shear zone than in the host rock but there is no evidence for broken grains. Comparison of microstructures

  12. Calcaneo-valgus deformity.

    PubMed

    Evans, D

    1975-08-01

    A discussion of the essential deformity in calcaneo-valgus feet develops a theme originally put forward in 1961 on the relapsed club foot (Evans 1961). Whereas in the normal foot the medial and lateral columns are about equal in length, in talipes equino-varus the lateral column is longer and in calcaneo-valgus shorter than the medial column. The suggestion is that in the treatment of both deformities the length of the columns be made equal. A method is described of treating calcaneo-valgus deformity by inserting cortical bone grafts taken from the tibia to elongate the anterior end of the calcaneus.

  13. Large-scale deformed quasiparticle random-phase approximation calculations of the γ -ray strength function using the Gogny force

    NASA Astrophysics Data System (ADS)

    Martini, M.; Péru, S.; Hilaire, S.; Goriely, S.; Lechaftois, F.

    2016-07-01

    Valuable theoretical predictions of nuclear dipole excitations in the whole chart are of great interest for different nuclear applications, including in particular nuclear astrophysics. Here we present large-scale calculations of the E 1 γ -ray strength function obtained in the framework of the axially symmetric deformed quasiparticle random-phase approximation based on the finite-range Gogny force. This approach is applied to even-even nuclei, the strength function for odd nuclei being derived by interpolation. The convergence with respect to the adopted number of harmonic oscillator shells and the cutoff energy introduced in the 2-quasiparticle (2 -q p ) excitation space is analyzed. The calculations performed with two different Gogny interactions, namely D1S and D1M, are compared. A systematic energy shift of the E 1 strength is found for D1M relative to D1S, leading to a lower energy centroid and a smaller energy-weighted sum rule for D1M. When comparing with experimental photoabsorption data, the Gogny-QRPA predictions are found to overestimate the giant dipole energy by typically ˜2 MeV. Despite the microscopic nature of our self-consistent Hartree-Fock-Bogoliubov plus QRPA calculation, some phenomenological corrections need to be included to take into account the effects beyond the standard 2 -q p QRPA excitations and the coupling between the single-particle and low-lying collective phonon degrees of freedom. For this purpose, three prescriptions of folding procedure are considered and adjusted to reproduce experimental photoabsorption data at best. All of them are shown to lead to somewhat similar predictions of the E 1 strength, both at low energies and for exotic neutron-rich nuclei. Predictions of γ -ray strength functions and Maxwellian-averaged neutron capture rates for the whole Sn isotopic chain are also discussed and compared with previous theoretical calculations.

  14. Determination of the Pressure Field in a Reservoir-Deformed Bed Exposed to Vibrowaves

    NASA Astrophysics Data System (ADS)

    Abbasov, É. M.; Agaeva, N. A.

    2017-01-01

    On the basis of theoretical investigations, the authors have determined the pressure field in a deformable bed exposed to vibrowaves. A study has been made of the propagation of various forms of elastic waves in a deformable bed. An analytical expression has been obtained for the bottom-hole pressure with account of the deformation of thebed's reservoir. It has been shown that the degree of attenuation of elastic waves in beds with deformable reservoirs increases strongly compared to undeformable ones.

  15. An improved choice of oscillator basis for banana shaped nuclides

    SciTech Connect

    Chasman, R.R.

    1994-03-01

    The question of the appropriate choice of oscillator basis functions for studying exotic nuclear shapes is raised. Difficulties with the conventional choice of oscillator basis states are noted for shapes having a large banana component. A prescription for an improved oscillator basis to study these shapes is given. It can be applied in a more general context. New calculations with this improved basis are presented for the banana deformation mode. The change of basis gives results that improve the prospects of finding states in the banana minimum for many isotopes of Tl, Pb and Bi.

  16. Casing deformation in Ekofisk

    SciTech Connect

    Yudovich, A. ); Chin, L.Y. ); Morgan, D.R. )

    1989-07-01

    Casing deformation resulting from reservoir compaction occurred in the Ekofisk field operated by Phillips Petroleum Co. Norway and is a serious problem in three of the fields. This study established a relationship between reservoir compaction and casing failure by statistical analyses, finite-element modeling (FEM), and the analyses of deformed casing and logs run through collapsed casings. Ekofisk casing deformation is related primarily to the near well incremental strain, well inclination, and casing diameter. Useful correlations to estimate future probabilities of casing deformation as a function of reservoir variables and well parameters were also obtained. The authors concluded that casing failure induced by reservoir compaction can be minimized through a pressure-maintenance program to reduce strain by drilling with the highest practical angle and by using the largest possible casing in the well.

  17. Rock Deformation Meeting

    NASA Astrophysics Data System (ADS)

    Green, Harry

    The Third Rock Deformation Colloquium was held December 4, 1989, at the AGU Fall Meeting in San Francisco. Steve Kirby of the U.S. Geological Survey, Menlo Park, Calif., reported on actions taken by the rock deformation steering committee. Brian Wernicke of Harvard University, Cambridge, Mass., talked on the structural geology of the Great Basin.The steering committee voted for “Committee on Deformation of Earth Materials” as the name for the AGU technical committee on rock deformation, Kirby said. Considerable discussion has occurred in the steering committee over our relationship to the AGU Mineral Physics Committee. Indeed, Kirby will become chairman of that committee in 1990, underlining the overlap of the two groups. It was agreed that we will pursue closer association with Mineral Physics.

  18. Wrist deformities after fracture.

    PubMed

    Vanheest, Ann

    2006-02-01

    Wrist deformities can occur after fracture because of malunion of the fracture or injury to the growth plate leading to imbalance of growth. Prevention of malunion is paramount by early recognition with proper reduction and casting or fixation with casting. If a mal-union occurs, an osteotomy may be necessary if anticipated growth will not correct the deformity. Injury of the growth plate may lead to wrist deformity in two ways: angular growth or growth arrest. Angular growth deformities are corrected most commonly by osteotomy. Growth arrest of the radius or the ulna leads to an ulnar-positive or an ulnar-negative variance at the wrist. If the ulnar variance is symptomatic, treatment is centered on achieving a level joint. Options for joint leveling procedures include epiphysiodesis or physeal stapling of the longer bone, lengthening osteotomy of the shorter bone, or shortening osteotomy of the longer bone.

  19. Principles of rock deformation

    SciTech Connect

    Nicolas, A.

    1987-01-01

    This text focuses on the recent achievements in the analysis of rock deformation. It gives an analytical presentation of the essential structures in terms of kinetic and dynamic interpretation. The physical properties underlying the interpretation of rock structures are exposed in simple terms. Emphasized in the book are: the role of fluids in rock fracturing; the kinematic analysis of magnetic flow structures; the application of crystalline plasticity to the kinematic and dynamic analysis of the large deformation imprinted in many metamorphic rocks.

  20. Polygonal deformation bands

    NASA Astrophysics Data System (ADS)

    Antonellini, Marco; Mollema, Pauline Nella

    2015-12-01

    We report for the first time the occurrence of polygonal faults in sandstone, which is compelling given that layer-bound polygonal fault systems have been observed so far only in fine-grained sediments such as clay and chalk. The polygonal faults are shear deformation bands that developed under shallow burial conditions via strain hardening in dm-wide zones. The edges of the polygons are 1-5 m long. The shear deformation bands are organized as conjugate faults along each edge of the polygon and form characteristic horst-like structures. The individual deformation bands have slip magnitudes ranging from a few mm to 1.5 cm; the cumulative average slip magnitude in a zone is up to 10 cm. The deformation bands heaves, in aggregate form, accommodate a small isotropic horizontal extension (strain <0.005). The individual shear deformation bands show abutting T-junctions, veering, curving, and merging where they mechanically interact. Crosscutting relationships are rare. The interactions of the deformation bands are similar to those of mode I opening fractures. The documented fault networks have important implications for evaluating the geometry of km-scale polygonal fault systems in the subsurface, top seal integrity, as well as constraining paleo-tectonic stress regimes.

  1. Deformations of superconformal theories

    DOE PAGES

    Córdova, Clay; Dumitrescu, Thomas T.; Intriligator, Kenneth

    2016-11-22

    Here, we classify possible supersymmetry-preserving relevant, marginal, and irrelevant deformations of unitary superconformal theories in d ≥ 3 dimensions. Our method only relies on symmetries and unitarity. Hence, the results are model independent and do not require a Lagrangian description. Two unifying themes emerge: first, many theories admit deformations that reside in multiplets together with conserved currents. Such deformations can lead to modifications of the supersymmetry algebra by central and noncentral charges. Second, many theories with a sufficient amount of supersymmetry do not admit relevant or marginal deformations, and some admit neither. The classification is complicated by the fact thatmore » short superconformal multiplets display a rich variety of sporadic phenomena, including supersymmetric deformations that reside in the middle of a multiplet. We illustrate our results with examples in diverse dimensions. In particular, we explain how the classification of irrelevant supersymmetric deformations can be used to derive known and new constraints on moduli-space effective actions.« less

  2. Experimental Deformation of Magnetite

    NASA Astrophysics Data System (ADS)

    Till, J. L.; Rybacki, E.; Morales, L. F. G.

    2015-12-01

    Magnetite is an important iron ore mineral and the most prominent Fe-oxide phase in the Earth's crust. The systematic occurrence of magnetite in zones of intense deformation in oceanic core complexes suggests that it may play a role in strain localization in some silicate rocks. We performed a series of high-temperature deformation experiments on synthetic magnetite aggregates and natural single crystals to characterize the rheological behavior of magnetite. As starting material, we used fine-grained magnetite powder that was hot isostatically pressed at 1100°C for several hours, resulting in polycrystalline material with a mean grain size of around 40 μm and containing 3-5% porosity. Samples were deformed to 15-20% axial strain under constant load (approximating constant stress) conditions in a Paterson-type gas apparatus for triaxial deformation at temperatures between 900 and 1100°C and 300 MPa confining pressure. The aggregates exhibit typical power-law creep behavior. At high stresses, samples deformed by dislocation creep exhibit stress exponents close to 3, revealing a transition to near-Newtonian creep with stress exponents around 1.3 at lower stresses. Natural magnetite single crystals deformed at 1 atm pressure and temperatures between 950°C and 1150 °C also exhibit stress exponents close to 3, but with lower flow stresses and a lower apparent activation energy than the aggregates. Such behavior may result from the different oxygen fugacity buffers used. Crystallographic-preferred orientations in all polycrystalline samples are very weak and corroborate numerical models of CPO development, suggesting that texture development in magnetite may be inherently slow compared with lower symmetry phases. Comparison of our results with experimental deformation data for various silicate minerals suggests that magnetite should be weaker than most silicates during ductile creep in dry igneous rocks.

  3. Molecular basis for erythrocyte shape

    NASA Astrophysics Data System (ADS)

    Elgsaeter, A.; Mikkelsen, A.

    1991-05-01

    The isolated plasma membrane of the human erythrocytes displays the same shape and shape transformations as the intact cells. It is therefore generally believed that the plasma membrane plays a dominant role in determining erythrocyte shape. The plasma membrane consists of a fluid lipid bilayer to the surface of which is attached a protein skeleton. The two halves of the lipid bilayer and the protein network (gel) are tighly coupled, but at the same time elastically deformable and can slide relative to one another in the plane of the cell membrane. The equilibrium shape of such a structure is determined by the combined mechano-chemical properties of the individual layers and equals the cell shape that for the given cell volume corresponds to the lowest total elastic free energy. The elastic free energy of the lipid bilayer is mainly associated with bending and change in surface area for each of the two lipid monolayer. For the protein membrane skeleton the elastic free energy mainly equals the sum of the local contributions due to shear deformation and surface change. When the mechano-chemical properties of each of the layers are known, calculation of the equilibrium shape is in principle just an exercise in standard continuum mechanics. The elastic properties of pure lipid monolayers have long been qualitatively fairly well known. The changes in lipid bilayer elastic properties resulting from the presence of integral membrane proteins have just recently become better understood. The detailed molecular basis for the elastic properties of the protein membrane skeleton remains unresolved despite many attempts to elucidate the problem. It is widely agreed that the elastic properties are largely accounted for by the highly elongated spectrin molecules, but whether the membrane skelton elasticity is mainly of entropic or entalphic origin is still unsettled.

  4. Infinitesimal deformations of naturally graded filiform Leibniz algebras

    NASA Astrophysics Data System (ADS)

    Khudoyberdiyev, A. Kh.; Omirov, B. A.

    2014-12-01

    In the present paper we describe infinitesimal deformations of complex naturally graded filiform Leibniz algebras. It is known that any n-dimensional filiform Lie algebra can be obtained by a linear integrable deformation of the naturally graded algebra Fn3(0) . We establish that in the same way any n-dimensional filiform Leibniz algebra can be obtained by an infinitesimal deformation of the filiform Leibniz algebras Fn1,Fn2and Fn3(α) . Moreover, we describe the linear integrable deformations of the above-mentioned algebras with a fixed basis of HL2 in the set of all n-dimensional Leibniz algebras. Among these deformations one new rigid algebra has been found.

  5. Deformation behavior and microstructure evolution of wrought magnesium alloys

    NASA Astrophysics Data System (ADS)

    Wang, Shouren; Song, Linghui; Kang, Sukbong; Cho, Jaehyung; Wang, Yingzi

    2013-05-01

    There are many researches on the deformation behavior of wrought magnesium alloys, such as AZ31, AZ80, AZ91, and ZK60 magnesium alloys at different temperatures and strain rates, but few of them focuses on the deformation behavior of AZ41M and ZK60M alloys, especially under the twin-roll casting (TRC) state. Meanwhile, the existing researches only focus on the grain refinement law of the magnesium alloys under deformation conditions, the deformation mechanism has not been revealed yet. The hot compression behavior of AZ41M and ZK60M magnesium alloys under the temperature and strain rate ranges of 250-400 °C and 0.001-1 s-1 are studied by thermal simulation methods using Gleeble 1500 machine and virtual simulation using finite element analysis software. Simulation results show that sine hyperbolic law is the most suitable flow stress model for wider deformation conditions. The most reasonable selected deformation conditions of ZK60M alloy is 350 °C/0.1 s-1 for TRC and 350 °C/1 s-1 for conventional casting (CC), while AZ41M alloy is 300 °C/0.01 s-1 for TRC and 350 °C/0.1 s-1 for CC. Deformation behavior and dynamic recrystallization (DRX) mechanism of them are analyzed at the same deformation conditions. The microstructures of AZ41M and ZK60M alloys are observed at different deformed conditions by optical microscopy (OM) and electron back scatter diffraction (EBSD) and it reveals the flow behavior and deformation mechanism of them. Working harden and work soften contribute to the activation of basal, non-basal slip systems which promote DRX. The proposed research reveals the deformation behavior and mechanism of the AZ41M and ZK 60M magnesium alloys and concludes their optimized deformation parameters and processes and provides a theory basis for their manufacturing and application.

  6. Crustal deformation and earthquakes

    NASA Technical Reports Server (NTRS)

    Cohen, S. C.

    1984-01-01

    The manner in which the Earth's surface deforms during the cycle of stress accumulation and release along major faults is investigated. In an investigation of the crustal deformation associated with a thin channel asthenosphere displacements are reduced from those computed for a half space asthenosphere. A previous finding by other workers that displacements are enhanced when flow is confined to a thin channel is based on several invalid approximations. The major predictions of the finite element model are that the near field postseismic displacements and strain rates are less than those for a half space asthenosphere and that the postseismic strain rates at intermediate distances are greater (in magnitude). The finite width of the asthenosphere ceases to have a significant impact on the crustal deformation pattern when its magnitude exceeds about three lithosphere thicknesses.

  7. Crustal deformation and earthquakes

    NASA Technical Reports Server (NTRS)

    Cohen, S. C.

    1984-01-01

    The manner in which the Earth's surface deforms during the cycle of stress accumulation and release along major faults is investigated. In an investigation of the crustal deformation associated with a thin channel asthenosphere displacements are reduced from those computed for a half space asthenosphere. A previous finding by other workers that displacements are enhanced when flow is confined to a thin channel is based on several invalid approximations. The major predictions of the finite element model are that the near field postseismic displacements and strain rates are less than those for a half space asthenosphere and that the postseismic strain rates at intermediate distances are greater (in magnitude). The finite width of the asthenosphere ceases to have a significant impact on the crustal deformation pattern when its magnitude exceeds about three lithosphere thicknesses.

  8. Interfacial Bubble Deformations

    NASA Astrophysics Data System (ADS)

    Seymour, Brian; Shabane, Parvis; Cypull, Olivia; Cheng, Shengfeng; Feitosa, Klebert

    Soap bubbles floating at an air-water experience deformations as a result of surface tension and hydrostatic forces. In this experiment, we investigate the nature of such deformations by taking cross-sectional images of bubbles of different volumes. The results show that as their volume increases, bubbles transition from spherical to hemispherical shape. The deformation of the interface also changes with bubble volume with the capillary rise converging to the capillary length as volume increases. The profile of the top and bottom of the bubble and the capillary rise are completely determined by the volume and pressure differences. James Madison University Department of Physics and Astronomy, 4VA Consortium, Research Corporation for Advancement of Science.

  9. The Basis System

    SciTech Connect

    Dubois, P.F.

    1989-05-16

    This paper discusses the basis system. Basis is a program development system for scientific programs. It has been developed over the last five years at Lawrence Livermore National Laboratory (LLNL), where it is now used in about twenty major programming efforts. The Basis System includes two major components, a program development system and a run-time package. The run-time package provides the Basis Language interpreter, through which the user does input, output, plotting, and control of the program's subroutines and functions. Variables in the scientific packages are known to this interpreter, so that the user may arbitrarily print, plot, and calculate with, any major program variables. Also provided are facilities for dynamic memory management, terminal logs, error recovery, text-file i/o, and the attachment of non-Basis-developed packages.

  10. Plate motion and deformation

    SciTech Connect

    Minster, B.; Prescott, W.; Royden, L.

    1991-02-01

    Our goal is to understand the motions of the plates, the deformation along their boundaries and within their interiors, and the processes that control these tectonic phenomena. In the broadest terms, we must strive to understand the relationships of regional and local deformation to flow in the upper mantle and the rheological, thermal and density structure of the lithosphere. The essential data sets which we require to reach our goal consist of maps of current strain rates at the earth's surface and the distribution of integrated deformation through time as recorded in the geologic record. Our success will depend on the effective synthesis of crustal kinematics with a variety of other geological and geophysical data, within a quantitative theoretical framework describing processes in the earth's interior. Only in this way can we relate the snapshot of current motions and earth structure provided by geodetic and geophysical data with long-term processes operating on the time scales relevant to most geological processes. The wide-spread use of space-based techniques, coupled with traditional geological and geophysical data, promises a revolution in our understanding of the kinematics and dynamics of plate motions over a broad range of spatial and temporal scales and in a variety of geologic settings. The space-based techniques that best address problems in plate motion and deformation are precise space-geodetic positioning -- on land and on the seafloor -- and satellite acquisition of detailed altimetric and remote sensing data in oceanic and continental areas. The overall science objectives for the NASA Solid Earth Science plan for the 1990's, are to Understand the motion and deformation of the lithosphere within and across plate boundaries'', and to understand the dynamics of the mantle, the structure and evolution of the lithosphere, and the landforms that result from local and regional deformation. 57 refs., 7 figs., 2 tabs.

  11. Micromachined, Electrostatically Deformable Reflectors

    NASA Technical Reports Server (NTRS)

    Bartman, Randall K.; Wang, Paul K. C.; Miller, Linda M.; Kenny, Thomas W.; Kaiser, William J.; Hadaegh, Fred Y.; Agronin, Michael L.

    1995-01-01

    Micromachined, closed-loop, electrostatically actuated reflectors (microCLEARs) provide relatively simple and inexpensive alternatives to large, complex, expensive adaptive optics used to control wavefronts of beams of light in astronomy and in experimental laser weapons. Micromachining used to make deformable mirror, supporting structure, and actuation circuitry. Development of microCLEARs may not only overcome some of disadvantages and limitations of older adaptive optics but may also satisfy demands of potential market for small, inexpensive deformable mirrors in electronically controlled film cameras, video cameras, and other commercial optoelectronic instruments.

  12. Nanolaminate deformable mirrors

    DOEpatents

    Papavasiliou, Alexandros P.; Olivier, Scot S.

    2010-04-06

    A deformable mirror formed out of two layers of a nanolaminate foil attached to a stiff substrate is introduced. Deformation is provided by an electrostatic force between two of the layers. The internal stiffness of the structure allows for high-spatial-frequency shapes. The nanolaminate foil of the present invention allows for a high-quality mirror surface. The device achieves high precision in the vertical direction by using foils with accurately controlled thicknesses, but does not require high precision in the lateral dimensions, allowing such mirrors to be fabricated using crude lithography techniques. Such techniques allow structures up to about the meter scale to be fabricated.

  13. Nanolaminate deformable mirrors

    DOEpatents

    Papavasiliou, Alexandros P.; Olivier, Scot S.

    2009-04-14

    A deformable mirror formed out of two layers of a nanolaminate foil attached to a stiff substrate is introduced. Deformation is provided by an electrostatic force between two of the layers. The internal stiffness of the structure allows for high-spatial-frequency shapes. The nanolaminate foil of the present invention allows for a high-quality mirror surface. The device achieves high precision in the vertical direction by using foils with accurately controlled thicknesses, but does not require high precision in the lateral dimensions, allowing such mirrors to be fabricated using crude lithography techniques. Such techniques allow structures up to about the meter scale to be fabricated.

  14. Safety Basis Report

    SciTech Connect

    R.J. Garrett

    2002-01-14

    As part of the internal Integrated Safety Management Assessment verification process, it was determined that there was a lack of documentation that summarizes the safety basis of the current Yucca Mountain Project (YMP) site characterization activities. It was noted that a safety basis would make it possible to establish a technically justifiable graded approach to the implementation of the requirements identified in the Standards/Requirements Identification Document. The Standards/Requirements Identification Documents commit a facility to compliance with specific requirements and, together with the hazard baseline documentation, provide a technical basis for ensuring that the public and workers are protected. This Safety Basis Report has been developed to establish and document the safety basis of the current site characterization activities, establish and document the hazard baseline, and provide the technical basis for identifying structures, systems, and components (SSCs) that perform functions necessary to protect the public, the worker, and the environment from hazards unique to the YMP site characterization activities. This technical basis for identifying SSCs serves as a grading process for the implementation of programs such as Conduct of Operations (DOE Order 5480.19) and the Suspect/Counterfeit Items Program. In addition, this report provides a consolidated summary of the hazards analyses processes developed to support the design, construction, and operation of the YMP site characterization facilities and, therefore, provides a tool for evaluating the safety impacts of changes to the design and operation of the YMP site characterization activities.

  15. Behavior of lateral-deformation coefficients during elastoplastic deformation of metals

    NASA Astrophysics Data System (ADS)

    Zimin, B. A.; Smirnov, I. V.; Sudenkov, Yu. V.

    2017-06-01

    The results of investigations into variation of the coefficients of lateral deformation (the Poisson ratio) during single-axis tension of samples of steel 12Kh18N10T and St3, titanium VT1, the aluminum alloy D16AM, copper M1, and a magnesium alloy are considered. The technique developed on the basis of the optoacoustic effect and simultaneous measurements of the longitudinal and surface speeds of sound in metallic samples during the tension makes it possible to measure the rates at various stages of the deformation process. The data obtained make it possible to construct the dependences of variation of the lateral-deformation coefficients at all stages of the plastic flow. The correlation of these variations both with known processes of structural reconstructions at various stages of plastic flow and with the process of localization of plastic-shear bands in the aluminum alloy is noted.

  16. Macroscopic modelling of semisolid deformation for considering segregation bands induced by shear deformation

    NASA Astrophysics Data System (ADS)

    Morita, S.; Yasuda, H.; Nagira, T.; Gourlay, C. M.; Yoshiya, M.; Sugiyama, A.

    2012-07-01

    In-situ observation was carried out to observe deformation of semi-solid Fe-2mass%C steel with 65% solid and globular morphology by X-ray radiography. Deformation was predominantly controlled by the rearrangement of globules. The solid particles were pushed into each other and rearrangement caused lower solid fraction regions to form. On the basis of the observation, a macroscopic model that introduces a normal stress acting on the solid due to collisions and rearrangement is proposed. The solid particles are treated as a non-Newtonian fluid. The stiffness parameters, which characterize the flow of the solid, are introduced. Stability of semisolid to fluctuations in solid fraction during simple shear was analysed. Shear deformation can be stably localized in the semisolid with a certain solid fraction range. The model essentially reproduces band segregation formation.

  17. MEMS Actuated Deformable Mirror

    SciTech Connect

    Papavasiliou, A; Olivier, S; Barbee, T; Walton, C; Cohn, M

    2005-11-10

    This ongoing work concerns the creation of a deformable mirror by the integration of MEMS actuators with Nanolaminate foils through metal compression boning. These mirrors will use the advantages of these disparate technologies to achieve dense actuation of a high-quality, continuous mirror surface. They will enable advanced adaptive optics systems in large terrestrial telescopes. While MEMS actuators provide very dense actuation with high precision they can not provide large forces typically necessary to deform conventional mirror surfaces. Nanolaminate foils can be fabricated with very high surface quality while their extraordinary mechanical properties enable very thin, flexible foils to survive the rigors of fabrication. Precise metal compression bonding allows the attachment of the fragile MEMS actuators to the thin nanolaminate foils without creating distortions at the bond sites. This paper will describe work in four major areas: (1) modeling and design, (2) bonding development, (3) nanolaminate foil development, (4) producing a prototype. A first-principles analytical model was created and used to determine the design parameters. A method of bonding was determined that is both strong, and minimizes the localized deformation or print through. Work has also been done to produce nanolaminate foils that are sufficiently thin, flexible and flat to be deformed by the MEMS actuators. Finally a prototype was produced by bonding thin, flexible nanolaminate foils to commercially available MEMS actuators.

  18. Crustal deformation along the San Andreas, California

    NASA Technical Reports Server (NTRS)

    Li, Victor C.

    1992-01-01

    The goal is to achieve a better understanding of the regional and local deformation and crustal straining processes in western North America, particularly the effects of the San Andreas and nearby faults on the spatial and temporal crustal deformation behavior. Construction of theoretical models based on the mechanics of coupled elastic plate, viscoelastic foundation and large scale crack mechanics provide a rational basis for the interpretation of seismic and aseismic anomalies and expedite efforts in forecasting the stability of plate boundary deformation. Special focus is placed on the three dimensional time dependent surface deformation due to localized slippage in a elastic layer coupled to a visco-elastic substrate. The numerical analysis is based on a 3-D boundary element technique. Extension to visco-elastic coupling demands the derivation of 3-D time dependent Green's function. This method was applied to analyze the viscoelastic surface displacements due to a dislocated embedded patch. Surface uplift as a function of time and position are obtained. Comparisons between surface uplift for long and short dislocated patches are made.

  19. Research on wire rope deformation distribution of WR-CVT

    NASA Astrophysics Data System (ADS)

    Zhang, Wu; Guo, Wei; Zhang, Chuanwei; Lu, Zhengxiong; Xu, Xiaobin

    2017-07-01

    A wire rope continuously variable transmissions (WR-CVT) has been introduced in the paper, in view of its less research, this paper mainly studied the deformation distribution of 6×7+IWS bending wire rope. The results shown that in the same section, half of the side strands are in a stretched state and half are in a compressed state. When the transmission ratio i=2.35, the maximum deformation and the minimum deformation are decrease when section U1 to U2, U3 transition. Wire deformation distribution when the transmission ratio i=0.42 is similar to that of i=0.2.35. Wire deformation amount and the deformation difference decrease as the transmission ratio decreases, this shows that the increase in the bending radius of the wire will make the wire deformation more uniform, and the reduction of the deformation difference will also reduce the wear. This study provides a basis for the study of fatigue and wears failure of WR-CVT components.

  20. Determination of stable points in deformation analysis

    NASA Astrophysics Data System (ADS)

    Vodopivec, F.; Savsek-Safic, S.

    2003-04-01

    Determination of displacements of natural and man-made objects is one of the more demanding tasks of the surveying profession. The underlying problem is in the identification of stability and potential hazards of man-made objects in the time of building and later on, as well as earth movements brought about by natural forces or unsupervised land consumption. Due to a constant emergence of displacements, the identification of size, velocity and periodicity of displacements plays an important role especially in civil engineering, mining and related geosciences. The preliminary condition for the deformation analysis is to measure and process the data of respective epochs carefully in the sense of estimating the quality of a given network. In observations, a special emphasis should be given to detecting and eliminating the gross errors. The characteristic point displacements are identified on the basis of at least two epochs and solely on identical network points. This paper aims at presenting the implementation of the Hannover, Asanin and Mihailovic deformation analysis approaches. For the purpose of testing the approaches a trigonometric network in the shape of a sexangle with a centre point was used. The observations and displacements were simulated, accordingly, for pattern generation of normally distributed random variables the Box and Mueller polar generation method was used. On the basis of geodetic observations and with the use of statistical methods the displacements of a given object are determined. Additionally, a comparison regarding the efficiency of stable point identification according to the deformation analysis approaches has been made.

  1. Nanoscale deformation mechanisms in bone.

    PubMed

    Gupta, Himadri S; Wagermaier, Wolfgang; Zickler, Gerald A; Raz-Ben Aroush, D; Funari, Sérgio S; Roschger, Paul; Wagner, H Daniel; Fratzl, Peter

    2005-10-01

    Deformation mechanisms in bone matrix at the nanoscale control its exceptional mechanical properties, but the detailed nature of these processes is as yet unknown. In situ tensile testing with synchrotron X-ray scattering allowed us to study directly and quantitatively the deformation mechanisms at the nanometer level. We find that bone deformation is not homogeneous but distributed between a tensile deformation of the fibrils and a shearing in the interfibrillar matrix between them.

  2. Cosmetic and Functional Nasal Deformities

    MedlinePlus

    ... nasal complaints. Nasal deformity can be categorized as “cosmetic” or “functional.” Cosmetic deformity of the nose results in a less ... taste , nose bleeds and/or recurrent sinusitis . A cosmetic or functional nasal deformity may occur secondary to ...

  3. Spinal osteotomies for rigid deformities.

    PubMed

    Gupta, Munish C; Kebaish, Khalid; Blondel, Benjamin; Klineberg, Eric

    2013-04-01

    Various osteotomies are useful in making a rigid deformity flexible enough for realignment in coronal and sagittal plane. This article defines the osteotomies and their usefulness in treatment of specific rigid deformities. The pedicle subtraction osteotomy and vertebral column resection used in treating rigid deformities are described in detail. Copyright © 2013 Elsevier Inc. All rights reserved.

  4. Partially segmented deformable mirror

    DOEpatents

    Bliss, E.S.; Smith, J.R.; Salmon, J.T.; Monjes, J.A.

    1991-05-21

    A partially segmented deformable mirror is formed with a mirror plate having a smooth and continuous front surface and a plurality of actuators to its back surface. The back surface is divided into triangular areas which are mutually separated by grooves. The grooves are deep enough to make the plate deformable and the actuators for displacing the mirror plate in the direction normal to its surface are inserted in the grooves at the vertices of the triangular areas. Each actuator includes a transducer supported by a receptacle with outer shells having outer surfaces. The vertices have inner walls which are approximately perpendicular to the mirror surface and make planar contacts with the outer surfaces of the outer shells. The adhesive which is used on these contact surfaces tends to contract when it dries but the outer shells can bend and serve to minimize the tendency of the mirror to warp. 5 figures.

  5. Partially segmented deformable mirror

    DOEpatents

    Bliss, Erlan S.; Smith, James R.; Salmon, J. Thaddeus; Monjes, Julio A.

    1991-01-01

    A partially segmented deformable mirror is formed with a mirror plate having a smooth and continuous front surface and a plurality of actuators to its back surface. The back surface is divided into triangular areas which are mutually separated by grooves. The grooves are deep enough to make the plate deformable and the actuators for displacing the mirror plate in the direction normal to its surface are inserted in the grooves at the vertices of the triangular areas. Each actuator includes a transducer supported by a receptacle with outer shells having outer surfaces. The vertices have inner walls which are approximately perpendicular to the mirror surface and make planar contacts with the outer surfaces of the outer shells. The adhesive which is used on these contact surfaces tends to contract when it dries but the outer shells can bend and serve to minimize the tendency of the mirror to warp.

  6. [Babies with cranial deformity].

    PubMed

    Feijen, Michelle M W; Claessens, Edith A W M Habets; Dovens, Anke J Leenders; Vles, Johannes S; van der Hulst, Rene R W J

    2009-01-01

    Plagiocephaly was diagnosed in a baby aged 4 months and brachycephaly in a baby aged 5 months. Positional or deformational plagio- or brachycephaly is characterized by changes in shape and symmetry of the cranial vault. Treatment options are conservative and may include physiotherapy and helmet therapy. During the last two decades the incidence of positional plagiocephaly has increased in the Netherlands. This increase is due to the recommendation that babies be laid on their backs in order to reduce the risk of sudden infant death syndrome. We suggest the following: in cases of positional preference of the infant, referral to a physiotherapist is indicated. In cases of unacceptable deformity of the cranium at the age 5 months, moulding helmet therapy is a possible treatment option.

  7. κ-deformed oscillators: Deformed multiplication versus deformed flip operator and multiparticle clusters

    NASA Astrophysics Data System (ADS)

    Lukierski, J.

    2009-08-01

    We transform the oscillator algebra with κ-deformed multiplication rule, proposed in [1, 2], into the oscillator algebra with κ-deformed flip operator and standard multiplication. We recall that the κ-multiplication of the κ-oscillators puts them off-shell. We study the explicit forms of modified mass-shell conditions in both formulations: with κ-multiplication and with κ-flip operation. On the example of κ-deformed 2-particle states we study the clustered nonfactorizable form of the κ-deformed multiparticle states. We argue that the κ-deformed star product of two free fields leads in similar way to a nonfactorizable κ-deformed bilocal field. We conclude with general remarks concerning the κ-deformed n-particle clusters and κ-deformed star product of n fields.

  8. Advanced Curvature Deformable Mirrors

    DTIC Science & Technology

    2010-09-01

    designs using just a glass wafer and a wafer of Carbon Fiber Reinforced Polymer ( CFRP ). In both cases minimum bend radius decreases and the resonant... matrix is consequently nearly diagonal. The long actuators at the outer edge of the deformable mirror are largely outside the working pupil so their...formal reconstruction of the wave front either explicitly or implicitly in the control matrix . The WFS-DM combination is acting like an analog computer

  9. Surface Deformation Image Analyzer

    DTIC Science & Technology

    2012-09-27

    such as MRI, positron emission tomography (PET) and ultrasound , provide Attorney Docket No. 101700 3 of 36 detailed images of abnormalities...the time frame and cost for treating non-healing wounds. SUMMARY OF THE INVENTION [0012] The present invention provides a device which includes...the surface of interest and the type of deformation anticipated; it may be helpful to treat the surface of interest with a heat source, such as

  10. Covariant deformed oscillator algebras

    NASA Technical Reports Server (NTRS)

    Quesne, Christiane

    1995-01-01

    The general form and associativity conditions of deformed oscillator algebras are reviewed. It is shown how the latter can be fulfilled in terms of a solution of the Yang-Baxter equation when this solution has three distinct eigenvalues and satisfies a Birman-Wenzl-Murakami condition. As an example, an SU(sub q)(n) x SU(sub q)(m)-covariant q-bosonic algebra is discussed in some detail.

  11. Osteotomies for bunionette deformity.

    PubMed

    Weil, Lowell; Weil, Lowell Scott

    2011-12-01

    A variety of surgical osteotomy procedures have been described for the bunionette deformity.Metatarsal osteotomies narrow the forefoot, maintain the length of the metatarsal, and preserve function of the metatarsophalangeal joint. Distal metatarsal osteotomies produce less correction and reduce postoperative disability; however, they pose a risk of inadequate correction because of the small width of the fifth metatarsal head and transfer lesions if shortened or dorsiflexed excessively. The sliding oblique metaphyseal osteotomy described by Smith and Weil (without fixation) and later by Steinke (with fixation) is easy to perform and provides good cancellous bone contact. Fixation is sometimes difficult and bone healing can take a few months owing to the unstable construct of this osteotomy. Kitaoka described a distal chevron osteotomy, which provides lateral pressure relief and reduced plantar pressure. This osteotomy is currently the most common procedure used; however, it may prove difficult to perform if the deformity is large and the bone is narrow. Diaphyseal osteotomies are indicated when greater correction is needed; however, they require more dissection and there is greater postoperative convalescence with non–weight bearing for several weeks. Proximal base osteotomies may be used to address significantly increased 4–5 IMAs or when a large degree of sagittal plane correction is required. Approaches that have been described include opening and closing base wedges and basal chevrons. Advantages to this approach are the ability to avoid epiphyseal plates in pediatric patients and maintain function of the MTPJ, while disadvantages include inherent instability of the location of the osteotomy, embarrassment of intraosseous and extraosseus blood supply of the metatarsal, and technical demand. Non–weight bearing is essential for several weeks. The Scarfette procedure is a combination head–shaft procedure, which is indicated to treat mild to moderate

  12. Deformable micro torque swimmer

    NASA Astrophysics Data System (ADS)

    Ishikawa, Takuji; Tanaka, Tomoyuki; Omori, Toshihiro; Imai, Yohsuke

    2015-11-01

    We investigated the deformation of a ciliate swimming freely in a fluid otherwise at rest. The cell body was modeled as a capsule with a hyper elastic membrane enclosing Newtonian fluid. Thrust forces due to the ciliary beat were modeled as torques distributed above the cell body. Effects of the membrane elasticity, the aspect ratio of cell's reference shape and the density difference between the cell and the surrounding fluid were investigated. The results showed that the cell deformed like heart shape when Capillary number (Ca) was sufficiently large, and the swimming velocity decreased as Ca was increased. The gravity effect on the membrane tension suggested that the upwards and downwards swimming velocities of Paramecium might be reglated by the calcium ion channels distributed locally around the anterior end. Moreover, the gravity induced deformation made a cell directed vertically downwards, which resulted in a positive geotaxis like behavior with physical origin. These results are important to understand physiology of ciliate's biological responses to mechanical stimuli.

  13. Deformation of Wrinkled Graphene

    PubMed Central

    2015-01-01

    The deformation of monolayer graphene, produced by chemical vapor deposition (CVD), on a polyester film substrate has been investigated through the use of Raman spectroscopy. It has been found that the microstructure of the CVD graphene consists of a hexagonal array of islands of flat monolayer graphene separated by wrinkled material. During deformation, it was found that the rate of shift of the Raman 2D band wavenumber per unit strain was less than 25% of that of flat flakes of mechanically exfoliated graphene, whereas the rate of band broadening per unit strain was about 75% of that of the exfoliated material. This unusual deformation behavior has been modeled in terms of mechanically isolated graphene islands separated by the graphene wrinkles, with the strain distribution in each graphene island determined using shear lag analysis. The effect of the size and position of the Raman laser beam spot has also been incorporated in the model. The predictions fit well with the behavior observed experimentally for the Raman band shifts and broadening of the wrinkled CVD graphene. The effect of wrinkles upon the efficiency of graphene to reinforce nanocomposites is also discussed. PMID:25765609

  14. The mechanical basis of Drosophila audition.

    PubMed

    Göpfert, Martin C; Robert, Daniel

    2002-05-01

    In Drosophila melanogaster, antennal hearing organs mediate the detection of conspecific songs. Combining laser Doppler vibrometry, acoustic near-field measurements and anatomical analysis, we have investigated the first steps in Drosophila audition, i.e. the conversion of acoustic energy into mechanical vibrations and the subsequent transmission of vibrations to the auditory receptors in the base of the antenna. Examination of the mechanical responses of the antennal structures established that the distal antennal parts (the funiculus and the arista) together constitute a mechanical entity, the sound receiver. Unconventionally, this receiver is asymmetric, resulting in an unusual, rotatory pattern of vibration; in the presence of sound, the arista and the funiculus together rotate about the longitudinal axis of the latter. According to the mechanical response characteristics, the antennal receiver represents a moderately damped simple harmonic oscillator. The receiver's resonance frequency increases continuously with the stimulus intensity, demonstrating the presence of a non-linear stiffness that may be introduced by the auditory sense organ. This surprising, non-linear effect is relevant for close-range acoustic communication in Drosophila; by improving antennal sensitivity at low song intensities and reducing sensitivity when intensity is high, it brings about dynamic range compression in the fly's auditory system.

  15. Nanoscale Deformable Optics

    NASA Technical Reports Server (NTRS)

    Strauss, Karl F.; Sheldon, Douglas J.

    2011-01-01

    Several missions and instruments in the conceptual design phase rely on the technique of interferometry to create detectable fringe patterns. The intimate emplacement of reflective material upon electron device cells based upon chalcogenide material technology permits high-speed, predictable deformation of the reflective surface to a subnanometer or finer resolution with a very high degree of accuracy. In this innovation, a layer of reflective material is deposited upon a wafer containing (perhaps in the millions) chalcogenic memory cells with the reflective material becoming the front surface of a mirror and the chalcogenic material becoming a means of selectively deforming the mirror by the application of heat to the chalcogenic material. By doing so, the mirror surface can deform anywhere from nil to nanometers in spots the size of a modern day memory cell, thereby permitting realtime tuning of mirror focus and reflectivity to mitigate aberrations caused elsewhere in the optical system. Modern foundry methods permit the design and manufacture of individual memory cells having an area of or equal to the Feature (F) size of the design (assume 65 nm). Fabrication rules and restraints generally require the instantiation of one memory cell to another no closer than 1.5 F, or, for this innovation, 90 nm from its neighbor in any direction. Chalcogenide is a semiconducting glass compound consisting of a combination of chalcogen ions, the ratios of which vary according to properties desired. It has been shown that the application of heat to cells of chalcogenic material cause a large alteration in resistance to the range of 4 orders of magnitude. It is this effect upon which chalcogenidebased commercial memories rely. Upon removal of the heat source, the chalcogenide rapidly cools and remains frozen in the excited state. It has also been shown that the chalcogenide expands in volume because of the applied heat, meaning that the coefficient of expansion of chalcogenic

  16. Neuromechanical Basis of Kinesiology.

    ERIC Educational Resources Information Center

    Enoka, Roger M.

    This textbook provides a scientific basis for the study of human motion. The eight chapters are organized under three major sections. Part One--The Force-Motion Relationship--contains chapters on (1) motion; (2) force; (3) types of movement analysis. In Part Two--The Simple Joint System--chapters concern (4) simple joint system components; (5)…

  17. Neuromechanical Basis of Kinesiology.

    ERIC Educational Resources Information Center

    Enoka, Roger M.

    This textbook provides a scientific basis for the study of human motion. The eight chapters are organized under three major sections. Part One--The Force-Motion Relationship--contains chapters on (1) motion; (2) force; (3) types of movement analysis. In Part Two--The Simple Joint System--chapters concern (4) simple joint system components; (5)…

  18. Diverse deformation patterns of Aleutian volcanoes from InSAR

    USGS Publications Warehouse

    Lu, Zhiming; Dzurisin, D.; Wicks, C.; Power, J.

    2008-01-01

    Interferometric synthetic aperture radar (InSAR) is capable of measuring ground-surface deformation with centimeter-to-subcentimeter precision at a spatial resolution of tens of meters over an area of hundreds to thousands of square kilometers. With its global coverage and all-weather imaging capability, InSAR has become an increasingly important measurement technique for constraining magma dynamics of volcanoes over remote regions such as the Aleutian Islands. The spatial pattern of surface deformation data derived from InSAR images enables the construction of detailed mechanical models to enhance the study of magmatic processes. This paper summarizes the diverse deformation patterns of the Aleutian volcanoes observed with InSAR and demonstrates that deformation patterns and associated magma supply mechanisms in the Aleutians are diverse and vary between volcanoes. These findings provide a basis for improved models and better understanding of magmatic plumbing systems.

  19. Choosing compact support of radial basis function based on landmarks space distribution

    NASA Astrophysics Data System (ADS)

    Yang, Xuan; Pei, Jihong; Zhang, Zhixiong

    2007-12-01

    In image local elastic transformation, compact support radial basis functions are used to implement image elastic deformation. The elastic deformation area is related to the support of the radial basis function. However, how to choose the support based on space distribution of landmarks still is an unresolved problem. In this paper, the relation between the support and three landmarks space locations is analyzed using simple triangle structure for Wendland radial basis function. Moreover, for landmarks set, Delaunay triangle is constructed to obtain the support of each triangle, and the optimal support of radial basis function is chosen as the maximum. Experiments of artificial images and medial images show the feasibility of our conclusions.

  20. Fréchet-algebraic deformation quantizations

    NASA Astrophysics Data System (ADS)

    Waldmann, S.

    2014-09-01

    In this review I present some recent results on the convergence properties of formal star products. Based on a general construction of a Fréchet topology for an algebra with countable vector space basis I discuss several examples from deformation quantization: the Wick star product on the flat phase space m2n gives a first example of a Fréchet algebraic framework for the canonical commutation relations. More interesting, the star product on the Poincare disk can be treated along the same lines, leading to a non-trivial example of a convergent star product on a curved Kahler manifold.