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.
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.)
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.)
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.
Using Coupled Harmonic Oscillators to Model Some Greenhouse Gas Molecules
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.
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.
Harmonic Oscillator Model for Radin's Markov-Chain Experiments
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.
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.
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.
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…
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…
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.
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.
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.
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.
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.
Relativistic harmonic oscillator revisited
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.
Synchronous Discrete Harmonic Oscillator
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.
NASA Astrophysics Data System (ADS)
Hamerly, Ryan; Marandi, Alireza; Jankowski, Marc; Fejer, M. M.; Yamamoto, Yoshihisa; Mabuchi, Hideo
2016-12-01
We develop reduced models that describe half-harmonic generation in a synchronously pumped optical parametric oscillator above threshold, where nonlinearity, dispersion, and group-velocity mismatch are all relevant. These models are based on (1) an eigenmode expansion for low pump powers, (2) a simultonlike sech-pulse ansatz for intermediate powers, and (3) dispersionless box-shaped pulses for high powers. Analytic formulas for pulse compression, degenerate vs nondegenerate operation, and stability are derived and compared to numerical and experimental results.
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.
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.
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.
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.
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.
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).
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.
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.
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.
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.
Application of Elliott's SU(3) model to the triaxially deformed harmonic oscillators
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.
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.
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.
Harmonic oscillator and nuclear pseudospin
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.
The harmonic oscillator behind all aberrations
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.
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.
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.
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.
Coherent states for the nonlinear harmonic oscillator
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.
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.
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.
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.
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.
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.
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.
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.
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.
On the moment of inertia of a quantum harmonic oscillator
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.
Quantum harmonic oscillator with superoscillating initial datum
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.
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.
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…
Background independent duals of the harmonic oscillator.
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.
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…
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.
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.
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.
Finite quantum kinematics of the harmonic oscillator
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.
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.
NASA Astrophysics Data System (ADS)
Scafetta, Nicola
2013-11-01
Power spectra of global surface temperature (GST) records (available since 1850) reveal major periodicities at about 9.1, 10-11, 19-22 and 59-62 years. Equivalent oscillations are found in numerous multisecular paleoclimatic records. The Coupled Model Intercomparison Project 5 (CMIP5) general circulation models (GCMs), to be used in the IPCC Fifth Assessment Report (AR5, 2013), are analyzed and found not able to reconstruct this variability. In particular, from 2000 to 2013.5 a GST plateau is observed while the GCMs predicted a warming rate of about 2 °C/century. In contrast, the hypothesis that the climate is regulated by specific natural oscillations more accurately fits the GST records at multiple time scales. For example, a quasi 60-year natural oscillation simultaneously explains the 1850-1880, 1910-1940 and 1970-2000 warming periods, the 1880-1910 and 1940-1970 cooling periods and the post 2000 GST plateau. This hypothesis implies that about 50% of the ~ 0.5 °C global surface warming observed from 1970 to 2000 was due to natural oscillations of the climate system, not to anthropogenic forcing as modeled by the CMIP3 and CMIP5 GCMs. Consequently, the climate sensitivity to CO2 doubling should be reduced by half, for example from the 2.0-4.5 °C range (as claimed by the IPCC, 2007) to 1.0-2.3 °C with a likely median of ~ 1.5 °C instead of ~ 3.0 °C. Also modern paleoclimatic temperature reconstructions showing a larger preindustrial variability than the hockey-stick shaped temperature reconstructions developed in early 2000 imply a weaker anthropogenic effect and a stronger solar contribution to climatic changes. The observed natural oscillations could be driven by astronomical forcings. The ~ 9.1 year oscillation appears to be a combination of long soli-lunar tidal oscillations, while quasi 10-11, 20 and 60 year oscillations are typically found among major solar and heliospheric oscillations driven mostly by Jupiter and Saturn movements. Solar models based
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…
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…
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).
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.
Brownian motion with adhesion: harmonic oscillator with fluctuating mass.
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.
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.
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.
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.
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.
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.
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.
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.
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.
BAYESIAN ANALYSIS OF MULTIPLE HARMONIC OSCILLATIONS IN THE SOLAR CORONA
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.
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.
Effective field theory in the harmonic oscillator basis
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 ^{132}Sn converge fast for the ground-state energies and radii in feasible model spaces.
Effective field theory in the harmonic oscillator basis
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
Effective field theory in the harmonic oscillator basis
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 ^{132}Sn converge fast for the ground-state energies and radii in feasible model spaces.
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.
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.
Operation of higher harmonic oscillations in free-electron lasers.
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.
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.
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…
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…
Driven harmonic oscillator as a quantum simulator for open systems
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.
Harmonic and Anharmonic Behaviour of a Simple Oscillator
ERIC Educational Resources Information Center
O'Shea, Michael J.
2009-01-01
We consider a simple oscillator that exhibits harmonic and anharmonic regimes and analyse its behaviour over the complete range of possible amplitudes. The oscillator consists of a mass "m" fixed at the midpoint of a horizontal rope. For zero initial rope tension and small amplitude the period of oscillation, tau, varies as tau is approximately…
Thermal conduction in a chain of colliding harmonic oscillators revisited.
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.
Non-Markovian quantum Brownian motion of a harmonic oscillator
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.
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.
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.
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.
Probing deformed commutators with macroscopic harmonic oscillators
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
The effect of singular potentials on the harmonic oscillator
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.
Kraus representation of a damped harmonic oscillator and its application
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.
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.
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…
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…
Harmonic response of a class of finite extensibility nonlinear oscillators
NASA Astrophysics Data System (ADS)
Febbo, M.
2011-06-01
Finite extensibility oscillators are widely used to simulate those systems that cannot be extended to infinity. For example, they are used when modelling the bonds between molecules in a polymer or DNA molecule or when simulating filaments of non-Newtonian liquids. In this paper, the dynamic behavior of a harmonically driven finite extensibility oscillator is presented and studied. To this end, the harmonic balance method is applied to determine the amplitude-frequency and amplitude-phase equations. The distinguishable feature in this case is the bending of the amplitude-frequency curve to the frequency axis, making it asymptotically approach the limit of maximum elongation of the oscillator, which physically represents the impossibility of the system reaching this limit. Also, the stability condition that defines stable and unstable steady-state solutions is derived. The study of the effect of the system parameters on the response reveals that a decreasing value of the damping coefficient or an increasing value of the excitation amplitude leads to the appearance of a multi-valued response and to the existence of a jump phenomenon. In this sense, the critical amplitude of the excitation, which means here a certain value of external excitation that results in the occurrence of jump phenomena, is also derived. Numerical experiments to observe the effects of system parameters on the frequency-amplitude response are performed and compared with analytical calculations. At a low value of the damping coefficient or at a high value of excitation amplitude, the agreement is poor for low frequencies but good for high frequencies. It is demonstrated that the disagreement is caused by the neglect of higher-order harmonics in the analytical formulation. These higher-order harmonics, which appear as distinguishable peaks at certain values in the frequency response curves, are possible to calculate considering not the linearized frequency of the oscillator but its actual
Braenzel, J.; Schnürer, M.; Steinke, S.; Priebe, G.; Sandner, W.; Andreev, A.; Platonov, K.
2013-08-15
Theoretical and experimental investigations of the dynamics of a relativistically oscillating plasma slab reveal spectral line splitting in laser driven harmonic spectra, leading to double harmonic series. Both series are well characterized with harmonics arising by two fundamental frequencies. While a relativistic oscillation of the critical density drives the harmonic emission, the splitting is a result of an additional acceleration during the laser pulse duration. In comparison with the oscillatory movement, this acceleration is rather weak and can be described by a plasma shock wave driven by the pressure of light. We introduce particle in cell simulations and an analytical model explaining the harmonic line splitting. The derived analytical formula gives direct access between the splitting in the harmonic spectrum and the acceleration of the plasma surface.
Harmonic phase detector for phase locking of cryogenic terahertz oscillators
NASA Astrophysics Data System (ADS)
Kalashnikov, Konstantin V.; Khudchenko, Andrey V.; Koshelets, Valery P.
2013-09-01
We present a simple and effective way to phase lock terahertz cryogenic oscillators. Extreme nonlinearity of a superconductor-insulator-superconductor tunnel junction allows its implementation as a cryogenic high-harmonic phase detector (HPD), which is used both for mixing a terahertz oscillator signal with a microwave reference and for generating a phase error feedback signal that is directly applied to the oscillator for its phase locking. An integration of the HPD with a cryogenic flux-flow oscillator results in synchronization bandwidth as wide as 70 MHz (significantly exceeding conventional room-temperature system bandwidth), providing phase locking of 84% emitted power for 15 MHz oscillator linewidth.
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.
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.
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.
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.
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.
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.
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.
Nonlinear dynamics of plasma oscillations modeled by an anharmonic oscillator
Enjieu Kadji, H. G.; Nana Nbendjo, B. R.; Chabi Orou, J. B.; Talla, P. K.
2008-03-15
This paper considers nonlinear dynamics of plasma oscillations modeled by an anharmonic oscillator. These plasma oscillations are described by a nonlinear differential equation of the form xe+{epsilon}(1+x{sup 2})x+x+{kappa}x{sup 2}+{delta}x{sup 3}=F cos {omega}t. The amplitudes of the forced harmonic, superharmonic, and subharmonic oscillatory states are obtained using the harmonic balance technique and the multiple time scales method. Admissible values of the amplitude of the external strength are derived. Bifurcation sequences displayed by the model for each type of oscillatory states are performed numerically through the fourth-order Runge-Kutta scheme.
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.
Violation of smooth observable macroscopic realism in a harmonic oscillator.
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.
Measuring nonlinear functionals of quantum harmonic oscillator states.
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.
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.
Single trapped ion as a time-dependent harmonic oscillator
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.
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.''
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.
Entanglement prethermalization in an interaction quench between two harmonic oscillators.
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.
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.
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.
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.
Nonequilibrium work distribution of a quantum harmonic oscillator.
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.
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.
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.
34 GHz second-harmonic peniotron oscillator
NASA Astrophysics Data System (ADS)
Dressman, Lawrence Jude
Harmonic operation of gyro-devices has been proposed as a way to lower the magnetic field required to a level feasible with normal (i.e., non-superconducting) magnets. The problem is, however, that gyrotron efficiency drops dramatically at harmonics greater than two, making development of such a device of limited utility. A promising solution to this quandary is the development of a related device, the peniotron, which is believed capable of achieving both high efficiency and harmonic operation resulting in a reduction of the required axial magnetic field. Although the physics of the peniotron interaction, including its high electronic conversion efficiency, has been understood and experimentally verified, demonstration of characteristics consistent with a practical device has been more elusive. This is the goal of this effort---specifically, to demonstrate high device efficiency (defined as the actual power output as a fraction of the electron beam power) with an electron beam generated by a compact cusp electron gun consistent in size and performance with other microwave vacuum electron devices. The cavity design process revealed that the pi/2 mode couples easily to the output circular waveguide. In fact, the transition to circular waveguide produced such a low reflection coefficient that an iris was needed at the cavity output to achieve the desired Q. Integral couplers were also designed to couple directly into the slotted cavity for diagnostic purposes for simplicity in this proof-of-principle physics experiment. This eliminated the need for a high-power circular vacuum window and allowed the diagnostic coupling to be made in standard WR-28 rectangular waveguide. Although mode competition did prevent the second-harmonic peniotron mode from being tuned over its entire range of magnetic field, the peniotron mode was stable over a range sufficient to allow useful experimental data to be obtained. However, another unexpected problem which occurred during execution
Harmonic Emission from High Power Gyrotron Oscillators.
1984-05-01
rd ( 0. () 2 4 39 . * .. . . a.. . . As discussed in Section 2.1, for the Gaussian ki k1l Leff/2. This relationship with the near cutoff and near...linear changes in I he IF fre- quency by equat ion (3.1). The tlilne scale onl the sCope was cal ibra 1 ed by changing 93 RD -A145 621 HARMONIC EMISSION...cial mi. lin’neaatra pro~ rd helpful in findin~g the comrwq RI: bmpfel "lr kriw" Ife .1.1. eftoai -Olvtoo %*a- fairlh *lattir In ’feur (&*#ft. *vrfil
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.
Geometric phase and nonadiabatic effects in an electronic harmonic oscillator.
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.
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.
Harmonic and anharmonic oscillations investigated by using a microcomputer-based Atwood's machine
NASA Astrophysics Data System (ADS)
Pecori, Barbara; Torzo, Giacomo; Sconza, Andrea
1999-03-01
We describe how the Atwood's machine, interfaced to a personal computer through a rotary encoder, is suited for investigating harmonic and anharmonic oscillations, exploiting the buoyancy force acting on a body immersed in water. We report experimental studies of oscillators produced by driving forces of the type F=-kxn with n=1,2,3, and F=-k sgn(x). Finally we suggest how this apparatus can be used for showing to the students a macroscopic model of interatomic forces.
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, 0oscillator: 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.
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.
Reaching Synchronization in Networked Harmonic Oscillators With Outdated Position Data.
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.
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.
Quantum Harmonic Oscillator State Control in a Squeezed Fock Basis.
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.
Increase of Boltzmann entropy in a quantum forced harmonic oscillator.
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.
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.
Equilibrium and stationary nonequilibrium states in a chain of colliding harmonic oscillators
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.
Fisher Information and Shannon Entropy in Confined 1D Harmonic Oscillator
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.
High gain amplifiers: Power oscillations and harmonic generation
Dattoli, G.; Ottaviani, P. L.; Pagnutti, S.
2007-08-01
We discuss the power oscillations in saturated high gain free electron laser amplifiers and show that the relevant period can be written in terms of the gain length. We use simple arguments following from the solution of the pendulum equation in terms of Jacobi elliptic functions. Nontrivial effects due to nonlinear harmonic generation and inhomogeneous broadening are discussed too, as well as the saturated dynamics of short pulses.
Dynamical properties of the delta-kicked harmonic oscillator.
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.
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.
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.
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.
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.
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.
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.
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.
Spatial analysis of harmonic oscillation of gypsy moth outbreak intensity.
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.
Pisot q-coherent states quantization of the harmonic oscillator
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, 0oscillator: 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,0
oscillator.
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.
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.
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.
MODEL HARMONIZATION POTENTIAL AND BENEFITS
The IPCS Harmonization Project, which is currently ongoing under the auspices of the WHO, in the context of chemical risk assessment or exposure modeling, does not imply global standardization. Instead, harmonization is thought of as an effort to strive for consistency among appr...
MODEL HARMONIZATION POTENTIAL AND BENEFITS
The IPCS Harmonization Project, which is currently ongoing under the auspices of the WHO, in the context of chemical risk assessment or exposure modeling, does not imply global standardization. Instead, harmonization is thought of as an effort to strive for consistency among appr...
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.
Detecting the harmonics of oscillations with time-variable frequencies
NASA Astrophysics Data System (ADS)
Sheppard, L. W.; Stefanovska, A.; McClintock, P. V. E.
2011-01-01
A method is introduced for the spectral analysis of complex noisy signals containing several frequency components. It enables components that are independent to be distinguished from the harmonics of nonsinusoidal oscillatory processes of lower frequency. The method is based on mutual information and surrogate testing combined with the wavelet transform, and it is applicable to relatively short time series containing frequencies that are time variable. Where the fundamental frequency and harmonics of a process can be identified, the characteristic shape of the corresponding oscillation can be determined, enabling adaptive filtering to remove other components and nonoscillatory noise from the signal. Thus the total bandwidth of the signal can be correctly partitioned and the power associated with each component then can be quantified more accurately. The method is first demonstrated on numerical examples. It is then used to identify the higher harmonics of oscillations in human skin blood flow, both spontaneous and associated with periodic iontophoresis of a vasodilatory agent. The method should be equally relevant to all situations where signals of comparable complexity are encountered, including applications in astrophysics, engineering, and electrical circuits, as well as in other areas of physiology and biology.
Information theories for time-dependent harmonic oscillator
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.
Self Phase-Locked Sub-Harmonic Optical Parametric Oscillators
NASA Astrophysics Data System (ADS)
Zondy, J.-J.; Laclau, V.; Bancel, A.; Douillet, A.; Tallet, A.; Ressayre, E.; Le Berre, M.
2002-04-01
We analyse a novel class of non-degenerate, doubly (DRO) or triply (TRO) resonant optical parametric oscillators (OPOs) producing signal and idler waves that are sub-harmonics of the pump frequency (3ω → 2ω, ω), and subject to an additional resonant coupling via the second-harmonic generation (SHG) of the idler wave (ω + ω → 2ω). At exact 3 ÷ 2 ÷ 1 non-degeneracy, self phase-locking among the three waves is theoretically predicted, freezing the well-known quantum phase diffusion noise in conventional oscillators. Three possible phase states corresponding to the same intensity state emerge. When slightly detuned from the 3 ÷ 2 ÷ 1 point, and under some specific conditions, the OPO:SHG cascading is expected to lead to a passively mode-locked cw-OPO providing two frequency combs peaked around the signal and idler frequencies. We report our attempt to observe both types of self-phase-locked (SPL) operation in a single-grating (OPO-only section) periodically poled lithium niobate (PPLN) oscillator, under the very weak self injection-locking by non-phase matched spontaneous idler SHG.
Harmonic Oscillations in Homeostatic Controllers: Dynamics of the p53 Regulatory System
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
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.
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.
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.
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.
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.
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.
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
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.
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.
Non-unique monopole oscillations of harmonically confined Yukawa systems
NASA Astrophysics Data System (ADS)
Ducatman, Samuel; Henning, Christian; Kaehlert, Hanno; Bonitz, Michael
2008-11-01
Recently it was shown that the Breathing Mode (BM), the mode of uniform radial expansion and contraction, which is well known from harmonically confined Coulomb systems [1], does not exist in general for other systems [2]. As a consequence the monopole oscillation (MO), the radial collective excitation, is not unique, but there are several MO with different frequencies. Within this work we show simulation results of those monopole oscillations of 2-dimensional harmonically confined Yukawa systems, which are known from, e.g., dusty plasma crystals [3,4]. We present the corresponding spectrum of the particle motion, including analysis of the frequencies found, and compare with theoretical investigations.[1] D.H.E. Dubin and J.P. Schiffer, Phys. Rev. E 53, 5249 (1996)[2] C. Henning at al., accepted for publication in Phys. Rev. Lett. (2008)[3] A. Melzer et al., Phys. Rev. Lett. 87, 115002 (2001)[4] M. Bonitz et al., Phys. Rev. Lett. 96, 075001 (2006)
Dissipative quantum trajectories in complex space: Damped harmonic oscillator
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.
1-GHz harmonically pumped femtosecond optical parametric oscillator frequency comb.
Balskus, K; Leitch, S M; Zhang, Z; McCracken, R A; Reid, D T
2015-01-26
We present the first example of a femtosecond optical parametric oscillator frequency comb harmonically-pumped by a 333-MHz Ti:sapphire laser to achieve a stabilized signal comb at 1-GHz mode spacing in the 1.1-1.6-µm wavelength band. Simultaneous locking of the comb carrier-envelope-offset and repetition frequencies is achieved with uncertainties over 1 s of 0.27 Hz and 5 mHz respectively, which are comparable with those of 0.27 Hz and 1.5 mHz achieved for 333-MHz fundamental pumping. The phase-noise power-spectral density of the CEO frequency integrated from 1 Hz-64 kHz was 2.8 rad for the harmonic comb, 1.0 rad greater than for fundamental pumping. The results show that harmonic operation does not substantially compromise the frequency-stability of the comb, which is shown to be limited only by the Rb atomic frequency reference used.
Heat and work fluctuations for a harmonic oscillator.
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
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.
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
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.
Observation of harmonic gyro-backward-wave oscillation in a 100 GHz CARM oscillator experiment
NASA Astrophysics Data System (ADS)
McCowan, Robert B.; Sullivan, Carol A.; Gold, Steven H.; Fliflet, Arne W.
1991-02-01
A cyclotron autoresonance maser (CARM) oscillator experiment is reported, using a 600 keV, 200 A electron beam, and a whispering gallery-mode rippled-wall Bragg cavity. This device was designed to produce tens of megawatts of radiation at 100 GHz from a CARM interaction, but instead has produced only moderate powers (tens of kWs) in fundamental gyrotron modes near 35 GHz, in third-harmonic-gyro-BWO modes, and possible third-harmonic gyrotron modes at frequencies near the expected CARM frequency, with no discernable CARM radiation. The lack of observable CARM radiation is attributed to excessive ripple on the voltage waveform and to mode competition. Calculations of the spectrum and growth rate of the backward-wave oscillations are consistent with the experimental observation.
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.
Oscillator Seeding of a High Gain Harmonic Generation FEL in a Radiator-First Configuration
Gandhi, P.; Wurtele, J.; Penn, G.; Reinsch, M.
2012-05-20
A longitudinally coherent X-ray pulse from a high repetition rate free electron laser (FEL) is desired for a wide variety of experimental applications. However, generating such a pulse with a repetition rate greater than 1 MHz is a significant challenge. The desired high repetition rate sources, primarily high harmonic generation with intense lasers in gases or plasmas, do not exist now, and, for the multi-MHz bunch trains that superconducting accelerators can potentially produce, are likely not feasible with current technology. In this paper, we propose to place an oscillator downstream of a radiator. The oscillator generates radiation that is used as a seed for a high gain harmonic generation (HGHG) FEL which is upstream of the oscillator. For the first few pulses the oscillator builds up power and, until power is built up, the radiator has no HGHG seed. As power in the oscillator saturates, the HGHG is seeded and power is produced. The dynamics and stability of this radiator-first scheme is explored analytically and numerically. A single-pass map is derived using a semi-analytic model for FEL gain and saturation. Iteration of the map is shown to be in good agreement with simulations. A numerical example is presented for a soft X-ray FEL.
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.
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)
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…
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…
Quantum Harmonic Oscillator Subjected to Quantum Vacuum Fluctuations
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 <
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.
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.
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.
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.
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.
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.
Derivation of exact master equation with stochastic description: dissipative harmonic oscillator.
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.
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
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.
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.
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…
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.
Edge Event-Triggered Synchronization in Networks of Coupled Harmonic Oscillators.
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.
Calorimetric measurement of work for a driven harmonic oscillator.
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.
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.
Data harmonization and model performance
NASA Astrophysics Data System (ADS)
The Joint Committee on Urban Storm Drainage of the International Association for Hydraulic Research (IAHR) and International Association on Water Pollution Research and Control (IAWPRC) was formed in 1982. The current committee members are (no more than two from a country): B. C. Yen, Chairman (USA); P. Harremoes, Vice Chairman (Denmark); R. K. Price, Secretary (UK); P. J. Colyer (UK), M. Desbordes (France), W. C. Huber (USA), K. Krauth (FRG), A. Sjoberg (Sweden), and T. Sueishi (Japan).The IAHR/IAWPRC Joint Committee is forming a Task Group on Data Harmonization and Model Performance. One objective is to promote international urban drainage data harmonization for easy data and information exchange. Another objective is to publicize available models and data internationally. Comments and suggestions concerning the formation and charge of the Task Group are welcome and should be sent to: B. C. Yen, Dept. of Civil Engineering, Univ. of Illinois, 208 N. Romine St., Urbana, IL 61801.
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.
ERIC Educational Resources Information Center
Nicolaides, Cleanthes A.; Constantoudis, Vasilios
2009-01-01
In Planck's model of the harmonic oscillator (HO) a century ago, both the energy and the phase space were quantized according to epsilon[subscript n] = nhv, n = 0, 1, 2..., and [double integral]dp[subscript x] dx = h. By referring to just these two relations, we show how the adoption of "cycle-averaged phase-space states" (CAPSSs) leads to the…
ERIC Educational Resources Information Center
Nicolaides, Cleanthes A.; Constantoudis, Vasilios
2009-01-01
In Planck's model of the harmonic oscillator (HO) a century ago, both the energy and the phase space were quantized according to epsilon[subscript n] = nhv, n = 0, 1, 2..., and [double integral]dp[subscript x] dx = h. By referring to just these two relations, we show how the adoption of "cycle-averaged phase-space states" (CAPSSs) leads to the…
Anomalous diffusive behavior of a harmonic oscillator driven by a Mittag-Leffler noise.
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.
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.
Wood, William E.; Osseward, Peter J.; Roseberry, Thomas K.; Perkel, David J.
2013-01-01
Complex motor skills are more difficult to perform at certain points in the day (for example, shortly after waking), but the daily trajectory of motor-skill error is more difficult to predict. By undertaking a quantitative analysis of the fundamental frequency (FF) and amplitude of hundreds of zebra finch syllables per animal per day, we find that zebra finch song follows a previously undescribed daily oscillation. The FF and amplitude of harmonic syllables rises across the morning, reaching a peak near mid-day, and then falls again in the late afternoon until sleep. This oscillation, although somewhat variable, is consistent across days and across animals and does not require serotonin, as animals with serotonergic lesions maintained daily oscillations. We hypothesize that this oscillation is driven by underlying physiological factors which could be shared with other taxa. Song production in zebra finches is a model system for studying complex learned behavior because of the ease of gathering comprehensive behavioral data and the tractability of the underlying neural circuitry. The daily oscillation that we describe promises to reveal new insights into how time of day affects the ability to accomplish a variety of complex learned motor skills. PMID:24312654
Sonic horizon formation for oscillating Bose-Einstein condensates in isotropic harmonic potential
Wang, Ying; Zhou, Yu; Zhou, Shuyu
2016-01-01
We study the sonic horizon phenomena of the oscillating Bose-Einstein condensates in isotropic harmonic potential. Based on the Gross-Pitaevskii equation model and variational method, we derive the original analytical formula for the criteria and lifetime of the formation of the sonic horizon, demonstrating pictorially the interaction parameter dependence for the occur- rence of the sonic horizon and damping effect of the system distribution width. Our analytical results corroborate quantitatively the particular features of the sonic horizon reported in previous numerical study. PMID:27922129
Sonic horizon formation for oscillating Bose-Einstein condensates in isotropic harmonic potential.
Wang, Ying; Zhou, Yu; Zhou, Shuyu
2016-12-06
We study the sonic horizon phenomena of the oscillating Bose-Einstein condensates in isotropic harmonic potential. Based on the Gross-Pitaevskii equation model and variational method, we derive the original analytical formula for the criteria and lifetime of the formation of the sonic horizon, demonstrating pictorially the interaction parameter dependence for the occur- rence of the sonic horizon and damping effect of the system distribution width. Our analytical results corroborate quantitatively the particular features of the sonic horizon reported in previous numerical study.
Molecular Solid EOS based on Quasi-Harmonic Oscillator approximation for phonons
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.
Brownian motion of a harmonic oscillator in a noninertial reference frame.
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.
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.
Amplitude and phase representation of quantum invariants for the time-dependent harmonic oscillator
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.
Dynamics in the Kuramoto model with a bi-harmonic coupling function
NASA Astrophysics Data System (ADS)
Yuan, Di; Cui, Haitao; Tian, Junlong; Xiao, Yi; Zhang, Yingxin
2016-09-01
We study a variant of the Kuramoto model with a bi-harmonic coupling function, in which oscillators with positive first harmonic coupling strength are conformists and oscillators with negative first harmonic coupling strength are contrarians. We show that the model displays different synchronous dynamics and different dynamics may be characterized by the phase distributions of oscillators. There exist stationary synchronous states, travelling wave states, π state and, most interestingly, another type of nonstationary state: an oscillating π state. The phase distribution oscillates in a confined region and the phase difference between conformists and contrarians oscillates around π with a constant amplitude and a constant period in oscillating π state. Finally, the bifurcation diagram of the model in the parameter space is presented.
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.
Purity and decoherence in the theory of a damped harmonic oscillator.
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.
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.
Continuous variable quantum optical simulation for time evolution of quantum harmonic oscillators.
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.
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.
Continuous variable quantum optical simulation for time evolution of quantum harmonic oscillators
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
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.
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.
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…
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…
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 (
On the measurement of a weak classical force coupled to a harmonic oscillator: experimental progress
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.}
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.
Calculation of the convex roof for an open entangled harmonic oscillator system
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.
Double Fourier Harmonic Balance Method for Nonlinear Oscillators by Means of Bessel Series
2014-10-16
Double Fourier harmonic balance method for nonlinear oscillators by means of Bessel series T.C. Lipscombe∗1 and C.E. Mungan†2 1Catholic University of...expressed in terms of a Bessel series, and the sums of many such series are known or can be developed. The method is illustrated for five different... Bessel series, work-energy theorem, nonlinear oscillator, pendulum. 1 Introduction Nonlinear oscillators are ubiquitous in physical and engineering
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).
Modeling Bloch oscillations in nanoscale Josephson junctions
NASA Astrophysics Data System (ADS)
Vora, Heli; Kautz, R. L.; Nam, S. W.; Aumentado, J.
2017-08-01
Bloch oscillations in nanoscale Josephson junctions with a Coulomb charging energy comparable to the Josephson coupling energy are explored within the context of a model previously considered by Geigenmüller and Schön that includes Zener tunneling and treats quasiparticle tunneling as an explicit shot-noise process. The dynamics of the junction quasicharge are investigated numerically using both Monte Carlo and ensemble approaches to calculate voltage-current characteristics in the presence of microwaves. We examine in detail the origin of harmonic and subharmonic Bloch steps at dc biases I =(n /m )2 e f induced by microwaves of frequency f and consider the optimum parameters for the observation of harmonic (m =1 ) steps. We also demonstrate that the GS model allows a detailed semiquantitative fit to experimental voltage-current characteristics previously obtained at the Chalmers University of Technology, confirming and strengthening the interpretation of the observed microwave-induced steps in terms of Bloch oscillations.
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
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.
Nonlinear harmonic generation in finite amplitude black hole oscillations
NASA Astrophysics Data System (ADS)
Papadopoulos, Philippos
2002-04-01
The nonlinear generation of harmonics in gravitational perturbations of black holes is explored using numerical relativity based on an ingoing light-cone framework. Localized, finite, perturbations of an isolated black hole are parametrized by amplitude and angular harmonic form. The response of the black hole spacetime is monitored and its harmonic content analyzed to identify the strength of the nonlinear generation of harmonics as a function of the initial data amplitude. It is found that overwhelmingly the black hole responds at the harmonic mode perturbed, even for spacetimes with 10% of the black hole mass radiated. The coefficients for down and up scattering in harmonic space are computed for a range of couplings. Down scattering, leading to smoothing out of angular structure, is found to be equally as or more efficient than the up scatterings that would lead to increased rippling. The details of this nonlinear balance may form the quantitative mechanism by which black holes avoid fission even for arbitrary strong distortions.
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.
A neural network model of harmonic detection
NASA Astrophysics Data System (ADS)
Lewis, Clifford F.
2003-04-01
Harmonic detection theories postulate that a virtual pitch is perceived when a sufficient number of harmonics is present. The harmonics need not be consecutive, but higher harmonics contribute less than lower harmonics [J. Raatgever and F. A. Bilsen, in Auditory Physiology and Perception, edited by Y. Cazals, K. Horner, and L. Demany (Pergamon, Oxford, 1992), pp. 215-222 M. K. McBeath and J. F. Wayand, Abstracts of the Psychonom. Soc. 3, 55 (1998)]. A neural network model is presented that has the potential to simulate this operation. Harmonics are first passed through a bank of rounded exponential filters with lateral inhibition. The results are used as inputs for an autoassociator neural network. The model is trained using harmonic data for symphonic musical instruments, in order to test whether it can self-organize by learning associations between co-occurring harmonics. It is shown that the trained model can complete the pattern for missing-fundamental sounds. The Performance of the model in harmonic detection will be compared with experimental results for humans.
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.
Entanglement in a continuously measured two-level system coupled to a harmonic oscillator
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.
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.
The finite harmonic oscillator and its associated sequences
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
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.
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.
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.
On the Quantum Potential and Pulsating Wave Packet in the Harmonic Oscillator
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
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.
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.
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.
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.
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
Vibrational spectroscopy and relaxation of an anharmonic oscillator coupled to harmonic bath.
Joutsuka, Tatsuya; Ando, Koji
2011-05-28
The vibrational spectroscopy and relaxation of an anharmonic oscillator coupled to a harmonic bath are examined to assess the applicability of the time correlation function (TCF), the response function, and the semiclassical frequency modulation (SFM) model to the calculation of infrared (IR) spectra. These three approaches are often used in connection with the molecular dynamics simulations but have not been compared in detail. We also analyze the vibrational energy relaxation (VER), which determines the line shape and is itself a pivotal process in energy transport. The IR spectra and VER are calculated using the generalized Langevin equation (GLE), the Gaussian wavepacket (GWP) method, and the quantum master equation (QME). By calculating the vibrational frequency TCF, a detailed analysis of the frequency fluctuation and correlation time of the model is provided. The peak amplitude and width in the IR spectra calculated by the GLE with the harmonic quantum correction are shown to agree well with those by the QME though the vibrational frequency is generally overestimated. The GWP method improves the peak position by considering the zero-point energy and the anharmonicity although the red-shift slightly overshoots the QME reference. The GWP also yields an extra peak in the higher-frequency region than the fundamental transition arising from the difference frequency of the center and width oscillations of a wavepacket. The SFM approach underestimates the peak amplitude of the IR spectra but well reproduces the peak width. Further, the dependence of the VER rate on the strength of an excitation pulse is discussed. © 2011 American Institute of Physics
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.
Quantum optics. Quantum harmonic oscillator state synthesis by reservoir engineering.
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.
Schulze-Halberg, Axel E-mail: xbataxel@gmail.com; Wang, Jie
2015-07-15
We obtain series solutions, the discrete spectrum, and supersymmetric partners for a quantum double-oscillator system. Its potential features a superposition of the one-parameter Mathews-Lakshmanan interaction and a one-parameter harmonic or inverse harmonic oscillator contribution. Furthermore, our results are transferred to a generalized Pöschl-Teller model that is isospectral to the double-oscillator system.
Stability of the ground state of a harmonic oscillator in a monochromatic wave.
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.
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.
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)
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.
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)
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…
Fourier methods for the perturbed harmonic oscillator in linear and nonlinear Schrödinger equations.
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).
Harmonic mode competition in a terahertz gyrotron backward-wave oscillator
Kao, S. H.; Chiu, C. C.; Chang, P. C.; Wu, K. L.; Chu, K. R.
2012-10-15
Electron cyclotron maser interactions at terahertz (THz) frequencies require a high-order-mode structure to reduce the wall loss to a tolerable level. To generate THz radiation, it is also essential to employ cyclotron harmonic resonances to reduce the required magnetic field strength to a value within the capability of the superconducting magnets. However, much weaker harmonic interactions in a high-order-mode structure lead to serious mode competition problems. The current paper addresses harmonic mode competition in the gyrotron backward wave oscillator (gyro-BWO). We begin with a comparative study of the mode formation and oscillation thresholds in the gyro-BWO and gyromonotron. Differences in linear features result in far fewer 'windows' for harmonic operation of the gyro-BWO. Nonlinear consequences of these differences are examined in particle simulations of the multimode competition processes in the gyro-BWO, which shed light on the competition criteria between modes of different as well as the same cyclotron harmonic numbers. The viability of a harmonic gyro-BWO is assessed on the basis of the results obtained.
Noncommutative quantum mechanics of a harmonic oscillator under linearized gravitational waves
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.
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.
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.
Coherent dynamics of a flux qubit coupled to a harmonic oscillator.
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.
Time-Variant Least Squares Harmonic Modeling
2003-01-01
SNR situations. We show applicability to high accuracy speech pitch and heart sound beat epoch estimation. 1. INTRODUCTION Harmonic modeling...techniques have been successfully used for low bit-rate speech coding; however their performance degrades at low SNR . The LSH model is capable of...producing more accurate and robust harmonic analysis, even at very low SNR ; however, as will be shown, its performance degrades significantly with rapid
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.
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.
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.
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
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'
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
Whitfield, Troy W; Martyna, Glenn J
2007-02-21
In the effort to develop atomistic models capable of accurately describing nanoscale systems with complex interfaces, it has become clear that simple treatments with rigid charge distributions and dispersion coefficients selected to generate bulk properties are insufficient to predict important physical properties. The quantum Drude oscillator model, a system of one-electron pseudoatoms whose "pseudoelectrons" are harmonically bound to their respective "pseudonuclei," is capable of treating many-body polarization and dispersion interactions in molecular systems on an equal footing due to the ability of the pseudoatoms to mimic the long-range interactions that characterize real materials. Using imaginary time path integration, the Drude oscillator model can, in principle, be solved in computer operation counts that scale linearly with the number of atoms in the system. In practice, however, standard expressions for the energy and pressure, including the commonly used virial estimator, have extremely large variances that require untenably long simulation times to generate converged averages. In this paper, low-variance estimators for the internal energy are derived, in which the large zero-point energy of the oscillators does not contribute to the variance. The new estimators are applicable to any system of harmonic oscillators coupled to one another (or to the environment) via an arbitrary set of anharmonic interactions. The variance of the new estimators is found to be much smaller than standard estimators in three example problems, a one-dimensional anharmonic oscillator and quantum Drude models of the xenon dimer and solid (fcc) xenon, respectively, yielding 2-3 orders of magnitude improvement in computational efficiency.
A two phase harmonic model for left ventricular function.
Dubi, Shay; Dubi, Chen; Dubi, Yonatan
2007-11-01
A minimal model for mechanical motion of the left ventricle is proposed. The model assumes the left ventricle to be a harmonic oscillator with two distinct phases, simulating the systolic and diastolic phases, at which both the amplitude and the elastic constant of the oscillator are different. Taking into account the pressure within the left ventricle, the model shows qualitative agreement with functional parameters of the left ventricle. The model allows for a natural explanation of heart failure with preserved systolic left ventricular function, also termed diastolic heart failure. Specifically, the rise in left ventricular filling pressures following increased left-ventricular wall stiffness is attributed to a mechanism aimed at preserving heart rate and cardiac output.
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.
Harmonically pumped femtosecond optical parametric oscillator with multi-gigahertz repetition rate.
Tian, Wenlong; Wang, Zhaohua; Zhu, Jiangfeng; Wei, Zhiyi
2016-12-26
We report a multi-gigahertz (GHz) repetition-rate femtosecond MgO:PPLN optical parametric oscillator (OPO) harmonically pumped by a 75.6 MHz Kerr-lens mode-locked Yb:KGW laser. By fractionally increasing the OPO cavity length, we obtained OPO operation up to the 493rd harmonic of the pump laser repetition rate, corresponding to a repetition rate as high as 37.3 GHz. Using a 1.5% output coupler, we are able to extract signal pulses with up to 260 mW average power at the 102nd harmonic (7.7 GHz) and 90 mW at the 493rd harmonic (37.3 GHz) under 2 W pump power. The measured relative standard deviations of the fundamental and the 102nd harmonic signal power were recorded to be 0.5% and 2.1%, respectively. The signal pulse durations at different harmonics were measured in the range of 160-230 fs.
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.
Coherent states for nonlinear harmonic oscillator and some of its properties
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.
Bifurcation analysis of a non-linear hysteretic oscillator under harmonic excitation
NASA Astrophysics Data System (ADS)
Il Chang, Seo
2004-09-01
The steady state oscillations of a system incorporating a non-linear hysteretic damper are studied analytically by applying a perturbation technique. The hysteretic damper of the system subject to harmonic resonant force is modelled by combining a Maxwell's model and Kelvin-Voigt's model in series. The non-linearity is imposed by replacing a spring element by a cubic-non-linear spring. The response of the system is described by two coupled second order differential equations including a non-linear constitutive equation. Proper rescaling of the variables and parameters of the equations of motion leads to a set of weakly non-linear equations of motion to which the method of averaging is applied. The bifurcation analysis of the reduced four-dimensional amplitude- and phase-equations of motion shows typical non-linear behaviors including saddle-node and Hopf bifurcations and separate solution branch. By the stability analysis, the saddle-node and Hopf bifurcation sets are obtained in parameter spaces. The software package AUTO is used to numerically study the bifurcation sets and limit cycle solutions bifurcating from the Hopf bifurcation points. It is shown that the limit cycle responses of the averaged system exist over broad parameter ranges.
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.
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
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.
NASA Technical Reports Server (NTRS)
Bgattacharyya, Sudip; Strohmayer, E.
2005-01-01
We report on a study of the evolution of burst oscillation properties during the rising phase of X-ray bursts from 4U 1636-536 observed with the proportional counter array (PCA) on board the Rossi X-Ray Timing Explorer (RXTE) . We present evidence for significant harmonic structure of burst oscillation pulses during the early rising phases of bursts. This is the first such detection in burst rise oscillations, and is very important for constraining neutron star structure parameters and the equation of state models of matter at the core of a neutron star. The detection of harmonic content only during the initial portions of the burst rise is consistent with the theoretical expectation that with time the thermonuclear burning region becomes larger, and hence the fundamental and harmonic amplitudes both diminish. We also find, for the first time from this source, strong evidence of oscillation frequency increase during the burst rise. The timing behavior of harmonic content, amplitude, and frequency of burst rise oscillations may be important in understanding the spreading of thermonuclear flames under the extreme physical conditions on neutron star surfaces.
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).
Transient energy excitation in shortcuts to adiabaticity for the time-dependent harmonic oscillator
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.
Quantum-trajectory approach to the stochastic thermodynamics of a forced harmonic oscillator.
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.
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.
Dynamics of SU(1,1) coherent states for the damped harmonic oscillator
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.
Two families of super-harmonic resonances in a time-delayed nonlinear oscillator
NASA Astrophysics Data System (ADS)
Ji, J. C.
2015-08-01
Two stable bifurcating periodic solutions are numerically found to coexist in a time-delayed nonlinear oscillator by using different initial conditions, after the trivial equilibrium loses its stability via two-to-one resonant Hopf bifurcations. These two coexisting solutions have different amplitudes and frequency components with one having the frequencies of Hopf bifurcations while the other containing different frequencies from those of Hopf bifurcations. The dynamic interaction of the periodic excitation and the two coexisting solutions can induce two families of super-harmonic resonances, when the forcing frequency is approximately at half the lower frequency component of the stable bifurcating solutions. It is found that the forced response under two families of super-harmonic resonances exhibits qualitatively different dynamic behaviour. In addition, one family of super-harmonic resonances may suddenly disappear when the excitation magnitude reaches a certain value and then the forced response becomes non-resonant response. The other family of super-harmonic resonances can be established by adjusting the forcing frequency accordingly. Time trajectories, phase portraits, frequency spectra, basin of attraction and bifurcation diagrams are given to characterise the different dynamic behaviours of the time-delayed nonlinear oscillator.
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.
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.
Brownian motion of a classical harmonic oscillator in a magnetic field.
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.
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.
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.
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.
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.
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.
Rotational shear effects on edge harmonic oscillations in DIII-D quiescent H-mode discharges
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.
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.
Rotational shear effects on edge harmonic oscillations in DIII-D quiescent H-mode discharges
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.
Rotational shear effects on edge harmonic oscillations in DIII-D quiescent H-mode discharges
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
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.
Quantum spatial-periodic harmonic model for daily price-limited stock markets
NASA Astrophysics Data System (ADS)
Meng, Xiangyi; Zhang, Jian-Wei; Xu, Jingjing; Guo, Hong
2015-11-01
We investigate the behaviors of stocks in daily price-limited stock markets by purposing a quantum spatial-periodic harmonic model. The stock price is considered to be oscillating and damping in a quantum spatial-periodic harmonic oscillator potential well. A complicated non-linear relation including inter-band positive correlation and intra-band negative correlation between the volatility and trading volume of a stock is numerically derived with the energy band structure of the model concerned. The effectiveness of price limit is re-examined, with some observed characteristics of price-limited stock markets in China studied by applying our quantum model.
Modeling nonlinearities in MEMS oscillators.
Agrawal, Deepak K; Woodhouse, Jim; Seshia, Ashwin A
2013-08-01
We present a mathematical model of a microelectromechanical system (MEMS) oscillator that integrates the nonlinearities of the MEMS resonator and the oscillator circuitry in a single numerical modeling environment. This is achieved by transforming the conventional nonlinear mechanical model into the electrical domain while simultaneously considering the prominent nonlinearities of the resonator. The proposed nonlinear electrical model is validated by comparing the simulated amplitude-frequency response with measurements on an open-loop electrically addressed flexural silicon MEMS resonator driven to large motional amplitudes. Next, the essential nonlinearities in the oscillator circuit are investigated and a mathematical model of a MEMS oscillator is proposed that integrates the nonlinearities of the resonator. The concept is illustrated for MEMS transimpedance-amplifier- based square-wave and sine-wave oscillators. Closed-form expressions of steady-state output power and output frequency are derived for both oscillator models and compared with experimental and simulation results, with a good match in the predicted trends in all three cases.
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…
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…
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
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.
Thermodynamical analysis of a quantum heat engine based on harmonic oscillators.
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.
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.
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
A Improved Transmission System Harmonic Modeling Technique.
NASA Astrophysics Data System (ADS)
Akram, Muhammad Fayyaz
1994-01-01
The development of a comprehensive approach to the modeling of electric power transmission systems at harmonic frequencies is presented. For harmonic analysis it is not practically possible to model a large transmission system with its neighboring interconnected systems in detail due to computer time and memory limitations. A large number of components of a large system also makes switching studies a recognized problem with respect to the desired accuracy, and required engineering and computer time. Current methods depend on the trial and error approach or the individual analyst's knowledge of the system, which are imprecise and expensive to develop at harmonic frequencies. The approach to solve this problem involves the development of a formal method for dividing large-scale transmission systems into a main study system and a group of external systems. Then, using an efficient and appropriate method of adjoint network sensitivity analysis, the size of the system model is reduced, keeping the same frequency characteristics as that of the original system. This reduction in model size in turn accommodates larger transmission system size and increases the accuracy and computational efficiency. An efficient and accurate method is also presented that determines the relative importance of external system equivalents on the harmonic impedance of a transmission network. The bilinear theorem provides an economical method of determining the appropriate locations for simplification of external systems. Using this technique, the system model error bounds can be fixed and the high error range of the external system equivalent impedance can be reduced. For filter designs, the most important issue of computing harmonic impedance boundaries is improved by using an efficient adjoint network sensitivity analysis. Using this sensitivity analysis an order of critical components is developed. The number of outage contingencies to be analyzed is reduced by a large factor which
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.
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.
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.
RESONANT HARMONIC GENERATION AND NONLINEAR OPTICS.
OSCILLATORS, *QUANTUM THEORY, *OPTICS, HARMONIC GENERATORS, OSCILLATORS, HARMONIC GENERATORS, OSCILLATORS, HARMONIC GENERATORS, NONLINEAR SYSTEMS, QUARTZ, TOURMALINE , ZINC COMPOUNDS, OXIDES, HYDRATES, NIOBATES, TENSOR ANALYSIS.
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.
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.
Comment on 'Wave functions of a time-dependent harmonic oscillator in a static magnetic field'
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.
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.
Quantization of a free particle interacting linearly with a harmonic oscillator.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
A generalized harmonic balance method for forced non-linear oscillations: the subharmonic cases
NASA Astrophysics Data System (ADS)
Wu, J. J.
1992-12-01
This paper summarizes and extends results in two previous papers, published in conference proceedings, on a variant of the generalized harmonic balance method (GHB) and its application to obtain subharmonic solutions of forced non-linear oscillation problems. This method was introduced as an alternative to the method of multiple scales, and it essentially consists of two parts. First, the part of the multiple scales method used to reduce the problem to a set of differential equations is used to express the solution as a sum of terms of various harmonics with unknown, time dependent coefficients. Second, the form of solution so obtained is substituted into the original equation and the coefficients of each harmonic are set to zero. Key equations of approximations for a subharmonic case are derived for the cases of both "small" damping and excitations, and "Large" damping and excitations, which are shown to be identical, in the intended order of approximation, to those obtained by Nayfeh using the method of multiple scales. Detailed numerical formulations, including the derivation of the initial conditions, are presented, as well as some numerical results for the frequency-response relations and the time evolution of various harmonic components. Excellent agreement is demonstrated between results by GHB and by integrating the original differential equation directly. The improved efficiency in obtaining numerical solutions using GHB as compared with integrating the original differential equation is demonstrated also. For the case of large damping and excitations and for non-trivial solutions, it is noted that there exists a threshold value of the force beyond which no subharmonic excitations are possible.
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.
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 » $$\
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.
Electron-bunch lengthening on higher-harmonic oscillations in storage-ring free-electron lasers.
Sei, Norihiro; Ogawa, Hiroshi; Okuda, Shuichi
2017-09-01
The influence of higher-harmonic free-electron laser (FEL) oscillations on an electron beam have been studied by measuring its bunch length at the NIJI-IV storage ring. The bunch length and the lifetime of the electron beam were measured, and were observed to have become longer owing to harmonic lasing, which is in accord with the increase of the FEL gain. It was demonstrated that the saturated FEL power could be described by the theory of bunch heating, even for the harmonic lasing. Cavity-length detuning curves were measured for the harmonic lasing, and it was found that the width of the detuning curve was proportional to a parameter that depended on the bunch length. These experimental results will be useful for developing compact resonator-type FELs by using higher harmonics in the extreme-ultraviolet and the X-ray regions.
Electron-bunch lengthening on higher-harmonic oscillations in storage-ring free-electron lasers
Ogawa, Hiroshi; Okuda, Shuichi
2017-01-01
The influence of higher-harmonic free-electron laser (FEL) oscillations on an electron beam have been studied by measuring its bunch length at the NIJI-IV storage ring. The bunch length and the lifetime of the electron beam were measured, and were observed to have become longer owing to harmonic lasing, which is in accord with the increase of the FEL gain. It was demonstrated that the saturated FEL power could be described by the theory of bunch heating, even for the harmonic lasing. Cavity-length detuning curves were measured for the harmonic lasing, and it was found that the width of the detuning curve was proportional to a parameter that depended on the bunch length. These experimental results will be useful for developing compact resonator-type FELs by using higher harmonics in the extreme-ultraviolet and the X-ray regions. PMID:28862612
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.
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…
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…
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.
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.
Energy distribution of the quantum harmonic oscillator under random time-dependent perturbations.
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.
Environmental effects in the quantum-classical transition for the delta-kicked harmonic oscillator.
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.
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.
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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Xiong, Huai; Kong, Xianren; Li, Haiqin; Yang, Zhenguo
2017-01-01
This paper considers dynamics of bilinear hysteretic systems, which are widely used for vibration control and vibration absorption such as magneto-rheological damper, metal-rubber. The method of incremental harmonic balance (IHB) technique that hysteresis is considered in the corrective term is improved in order to determine periodic solutions of bilinear hysteretic systems. The improved continuation method called two points tracing algorithm which is stable to the turning point makes the calculation more efficient for tracing amplitude-frequency response. Precise Hsu's method for analysing the stability of periodic solutions is introduced. The effects of different parameters of bilinear hysteretic oscillator on the response are discussed numerically. Some numerical simulations of considered bilinear hysteretic systems, including a single DOF and a 2DOF system, are effectively obtained by the modified IHB method and the results compare very well with the 4-oder Runge-Kutta method.
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.
NASA Astrophysics Data System (ADS)
Gaiko, Nick V.; van Horssen, Wim T.
2016-11-01
In this paper, the free transverse vibrations of a vertically moving string with a harmonically time-varying length are studied. The string length variations are assumed to be small. By using the multiple-timescales perturbation method in conjunction with a Fourier series approach, we determine the resonance frequencies and derive the non-secularity conditions in the form of an infinite dimensional system of coupled ordinary differential equations. This system describes the long time behavior of the amplitudes of the oscillations. Then, the eigenvalues of the obtained system are studied by the Galerkin truncation method, and applicability of this method is discussed. Apart from this, the dynamic stability of the solution is investigated by an energy analysis. Additionally, resonance detuning is considered.
Modelling harmonic generation measurements in solids.
Best, S R; Croxford, A J; Neild, S A
2014-02-01
Harmonic generation measurements typically make use of the plane wave result when extracting values for the nonlinearity parameter, β, from experimental measurements. This approach, however, ignores the effects of diffraction, attenuation, and receiver integration which are common features in a typical experiment. Our aim is to determine the importance of these effects when making measurements of β over different sample dimensions, or using different input frequencies. We describe a three-dimensional numerical model designed to accurately predict the results of a typical experiment, based on a quasi-linear assumption. An experiment is designed to measure the axial variation of the fundamental and second harmonic amplitude components in an ultrasonic beam, and the results are compared with those predicted by the model. The absolute β values are then extracted from the experimental data using both the simulation and the standard plane wave result. A difference is observed between the values returned by the two methods, which varies with axial range and input frequency.
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.
Impact oscillations and wear of loosely supported rod subject to harmonic load
NASA Astrophysics Data System (ADS)
Knudsen, J.; Massih, A. R.
2004-12-01
The non-linear dynamic behaviour of a damped rod oscillator with elastic two-sided amplitude constraints is analyzed using finite element method. Symmetric and asymmetric elastic double-impact motions, both harmonic and sub-harmonic, are studied by way of a Poincaré mapping that relates the states at subsequent impacts. It is found that by increasing the forcing frequency ( ω) for the beam at a certain frequency a stable period one motion turns into a stable period two motion without bifurcation and subsequently moves to an infinite number of solutions characteristic of chaotic behaviour through a cyclic fold bifurcation. By further increasing ω a series of windows in the bifurcation diagram (impact velocity vs. ω) comprising periodic solutions within the chaotic domain appear. The kinds of bifurcations involved are discussed. Furthermore, impact work-rate of the beam, i.e., the rate of energy dissipation to the impacting surfaces, is calculated. Computations show that the work-rate for asymmetric orbits is substantially higher than for symmetric orbits at or near the same frequency. For the vibro-impacting beam, under conditions that exhibit a stable attractor, calculation of work-rate allows prediction of the "lifetime" of the contacting beam due to fretting-wear damage by extending the stable branch and using the local gap between contacting surfaces as a control parameter.
Spherical harmonic stacking for the singlets of Earth's normal modes of free oscillation
NASA Astrophysics Data System (ADS)
Chao, Benjamin F.; Ding, Hao
2014-08-01
We extend the spherical harmonic stacking (SHS) method of Buland et al. (1979) for the radial (vertical) component in the seismogram to the transverse (horizontal) components of the displacement field. Taking advantage of the orthogonality of the spherical harmonic functions (scalar and vectorial), SHS isolates and accentuates the signals of individual singlets of the Earth's normal modes of free oscillation. We apply the SHS on the broadband Incorporated Research Institutions for Seismology (IRIS) seismograms from up to 97 IRIS seismic stations for the 2004 Sumatra-Andaman earthquake, in experiments targeted to spheroidal as well as toroidal modes—2S1, 0S3, 2S2, 3S1, 1S3, 0T2, and 0T3. We report the complete resolution of the singlet frequencies of these multiplets, some for the first time, and estimate the singlets' complex frequencies using the frequency domain autoregressive method of Chao and Gilbert (1980). The latter contain useful information to be used in inversions for the 3-D structure of the Earth's interior.
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.
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".
Non-Sticking Oscillation Formulae for Coulomb Friction Under Harmonic Loading
NASA Astrophysics Data System (ADS)
HONG, H.-K.; LIU, C.-S.
2001-07-01
In this paper, a new estimate for periodic non-sticking (i.e., zero stop per cycle) solutions is presented for the steady state responses of the Coulomb friction oscillator subjected to harmonic loading. Compared with the Den Hartog (1931 Transactions of the American Society of Mechanical Engineers53, 107-115 [1]) estimate, the new estimate leads to the same formulae for the maximum displacement and its time lag, but only the new estimate offers the closed-form formulae for the maximum velocity and its time lag. More importantly, a simple formula is derived for estimating the minimum driving force amplitude needed to prevent an oscillating object from sticking to the friction surface on which it slides. The validity of the assumptions made for the new estimate and the accuracy of the formulae developed are confirmed by comparing with the exact solutions (Hong and Liu 2000 Journal of Sound and Vibration229, 1171-1192 [2]). It is also found that there exists the best driving force amplitude for maximum dissipation efficiency.
Oscillating water column structural model
Copeland, Guild; Bull, Diana L; Jepsen, Richard Alan; Gordon, Margaret Ellen
2014-09-01
An oscillating water column (OWC) wave energy converter is a structure with an opening to the ocean below the free surface, i.e. a structure with a moonpool. Two structural models for a non-axisymmetric terminator design OWC, the Backward Bent Duct Buoy (BBDB) are discussed in this report. The results of this structural model design study are intended to inform experiments and modeling underway in support of the U.S. Department of Energy (DOE) initiated Reference Model Project (RMP). A detailed design developed by Re Vision Consulting used stiffeners and girders to stabilize the structure against the hydrostatic loads experienced by a BBDB device. Additional support plates were added to this structure to account for loads arising from the mooring line attachment points. A simplified structure was designed in a modular fashion. This simplified design allows easy alterations to the buoyancy chambers and uncomplicated analysis of resulting changes in buoyancy.
Quantum dephasing of a two-state system by a nonequilibrium harmonic oscillator
Martens, Craig C.
2013-07-14
In this paper, we investigate coherent quantum dynamics in a nonequilibrium environment. We focus on a two-state quantum system strongly coupled to a single classical environmental oscillator, and explore the effect of nonstationary statistical properties of the oscillator on the quantum evolution. A simple nonequilibrium model, consisting of an oscillator with a well-defined initial phase which undergoes subsequent diffusion, is introduced and studied. Approximate but accurate analytic expressions for the evolution of the off-diagonal density matrix element of the quantum system are derived in the second-order cumulant approximation. The effect of the initial phase choice on the subsequent quantum evolution is quantified. It is observed that the initial phase can have a significant effect on the preservation of coherence on short time scales, suggesting this variable as a control parameter for optimizing coherence in many-body quantum systems.
Quantum dephasing of a two-state system by a nonequilibrium harmonic oscillator.
Martens, Craig C
2013-07-14
In this paper, we investigate coherent quantum dynamics in a nonequilibrium environment. We focus on a two-state quantum system strongly coupled to a single classical environmental oscillator, and explore the effect of nonstationary statistical properties of the oscillator on the quantum evolution. A simple nonequilibrium model, consisting of an oscillator with a well-defined initial phase which undergoes subsequent diffusion, is introduced and studied. Approximate but accurate analytic expressions for the evolution of the off-diagonal density matrix element of the quantum system are derived in the second-order cumulant approximation. The effect of the initial phase choice on the subsequent quantum evolution is quantified. It is observed that the initial phase can have a significant effect on the preservation of coherence on short time scales, suggesting this variable as a control parameter for optimizing coherence in many-body quantum systems.
Casimir friction force and energy dissipation for moving harmonic oscillators. II
NASA Astrophysics Data System (ADS)
Høye, J. S.; Brevik, I.
2011-01-01
This paper is a second in a series devoted to the study of a two-oscillator system in linear relative motion (the first one published as a letter in [J.S. Høye, I. Brevik, Europhys. Lett. 91, 60003 (2010)]). The main idea behind considering this kind of system is to use it as a simple model for Casimir friction. In the present paper we extend our previous theory so as to obtain the change in the oscillator energy to second order in the perturbation, even though we employ first order perturbation theory only. The results agree with, and confirm, our earlier results obtained via different routes. The friction force is finite at finite temperatures, whereas in the case of two oscillators moving with constant relative velocity the force becomes zero at zero temperature, due to slowly varying coupling.
Robust identification of harmonic oscillator parameters using the adjoint Fokker-Planck equation
NASA Astrophysics Data System (ADS)
Boujo, E.; Noiray, N.
2017-04-01
We present a model-based output-only method for identifying from time series the parameters governing the dynamics of stochastically forced oscillators. In this context, suitable models of the oscillator's damping and stiffness properties are postulated, guided by physical understanding of the oscillatory phenomena. The temporal dynamics and the probability density function of the oscillation amplitude are described by a Langevin equation and its associated Fokker-Planck equation, respectively. One method consists in fitting the postulated analytical drift and diffusion coefficients with their estimated values, obtained from data processing by taking the short-time limit of the first two transition moments. However, this limit estimation loses robustness in some situations-for instance when the data are band-pass filtered to isolate the spectral contents of the oscillatory phenomena of interest. In this paper, we use a robust alternative where the adjoint Fokker-Planck equation is solved to compute Kramers-Moyal coefficients exactly, and an iterative optimization yields the parameters that best fit the observed statistics simultaneously in a wide range of amplitudes and time scales. The method is illustrated with a stochastic Van der Pol oscillator serving as a prototypical model of thermoacoustic instabilities in practical combustors, where system identification is highly relevant to control.
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.
Quantization and instability of the damped harmonic oscillator subject to a time-dependent force
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.
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.
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.
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.
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.
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.
Xu, L; Chan, H-Y; Alam, S-U; Richardson, D J; Shepherd, D P
2015-07-15
We demonstrate the generation of high-energy, mid-IR, picosecond pulses in a high-harmonic-cavity optical parametric oscillator (OPO) that has a relatively compact cavity with a length that is a small fraction of that required to match the pump repetition rate. The OPO, based on an MgO-doped periodically poled LiNbO3 crystal, is pumped by a fiber master-oscillator-power-amplifier system employing direct amplification and delivering 11-μJ, 150-ps pulses at 1035 nm. For a 1.554-m-long OPO cavity, resonating near-infrared signal pulses with a repetition rate that is the 193rd harmonic of the 1-MHz pump are demonstrated. The mid-infrared idler output pulses, tunable from 2300 nm to 3500 nm, are generated at a 1-MHz repetition rate and have energies as high as 1.5 μJ.
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.
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.
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.
Building Mathematical Models of Simple Harmonic and Damped Motion.
ERIC Educational Resources Information Center
Edwards, Thomas
1995-01-01
By developing a sequence of mathematical models of harmonic motion, shows that mathematical models are not right or wrong, but instead are better or poorer representations of the problem situation. (MKR)
A quantum anharmonic oscillator model for the stock market
NASA Astrophysics Data System (ADS)
Gao, Tingting; Chen, Yu
2017-02-01
A financially interpretable quantum model is proposed to study the probability distributions of the stock price return. The dynamics of a quantum particle is considered an analog of the motion of stock price. Then the probability distributions of price return can be computed from the wave functions that evolve according to Schrodinger equation. Instead of a harmonic oscillator in previous studies, a quantum anharmonic oscillator is applied to the stock in liquid market. The leptokurtic distributions of price return can be reproduced by our quantum model with the introduction of mixed-state and multi-potential. The trend following dominant market, in which the price return follows a bimodal distribution, is discussed as a specific case of the illiquid market.
A model for the harmonic of compressional Pc 5 waves
NASA Technical Reports Server (NTRS)
Takahashi, K.; Zanetti, L. J.; Potemra, T. A.; Acuna, M. H.
1987-01-01
Compressional Pc 5 magnetic waves in the magnetosphere are a unique phenomenon showing a nonsinusoidal waveform in spite of a well-defined period. Although the waveform can be Fourier-decomposed into the fundamental and the second harmonics, the phase between the two is kept constant from event to event, implying that the waveform is not the result of a chance superposition of two magnetospheric eigenmodes. A phenomenological explanation to this waveform is offered using a field-line configuration model that is a modified version of a previously proposed antisymmetric standing wave. In this model, the location of the equatorial node of field-line displacement is assumed to oscillate with the wave, with a peak-to-peak amplitude greater than 10 percent of the wavelength of the standing wave. The predicted waveform at various magnetic latitudes is found to be in excellent agreement with an observation taken near the magnetic equator by the Active Magnetospheric Particle Tracer Explorers/Charge Composition Explorer spacecraft.
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.
Gasulla, Ivana; Sancho, Juan; Capmany, José; Lloret, Juan; Sales, Salvador
2010-12-06
We theoretically and experimentally evaluate the propagation, generation and amplification of signal, harmonic and intermodulation distortion terms inside a Semiconductor Optical Amplifier (SOA) under Coherent Population Oscillation (CPO) regime. For that purpose, we present a general optical field model, valid for any arbitrarily-spaced radiofrequency tones, which is necessary to correctly describe the operation of CPO based slow light Microwave Photonic phase shifters which comprise an electrooptic modulator and a SOA followed by an optical filter and supplements another recently published for true time delay operation based on the propagation of optical intensities. The phase shifter performance has been evaluated in terms of the nonlinear distortion up to 3rd order, for a modulating signal constituted of two tones, in function of the electrooptic modulator input RF power and the SOA input optical power, obtaining a very good agreement between theoretical and experimental results. A complete theoretical spectral analysis is also presented which shows that under small signal operation conditions, the 3rd order intermodulation products at 2Ω1 + Ω2 and 2Ω2 + Ω1 experience a power dip/phase transition characteristic of the fundamental tones phase shifting operation.
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.
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}}.
Teaching Oscillations by a Model of Nanoresonator
ERIC Educational Resources Information Center
Lindell, A.; Viiri, J.
2009-01-01
Nanoscience offers fascinating opportunities for science education as it links the achievements of modern technology to traditional models of science. In this article we present a nanotechnology orientated lesson on oscillations, suitable for physics courses at high schools and universities. The focus of the lesson is in forced oscillations on a…
Teaching Oscillations by a Model of Nanoresonator
ERIC Educational Resources Information Center
Lindell, A.; Viiri, J.
2009-01-01
Nanoscience offers fascinating opportunities for science education as it links the achievements of modern technology to traditional models of science. In this article we present a nanotechnology orientated lesson on oscillations, suitable for physics courses at high schools and universities. The focus of the lesson is in forced oscillations on a…
A Model for Generative Harmonic Dictation.
ERIC Educational Resources Information Center
Bales, W. Kenton
This BASIC computer program designed to help music theory students practice harmonic dictation generates examples for students to use in a drill and practice approach in developing aural skills. To facilitate the implementation of effective generative algorithms, the author has used a non-linear analytical technique similar to the chord symbol…
Hernandez Tenorio, C; Villagran Vargas, E; Serkin, Vladimir N; Aguero Granados, M; Belyaeva, T L; Pena Moreno, R; Morales Lara, L
2005-10-31
The dynamics of dark solitons is studied within the framework of the mathematical model of nonlinear Schroedinger equation (NSE) with an external harmonic potential. A comparative analysis of the solutions of nonstationary problems is performed for a linear harmonic oscillator and the NSE model with a harmonic potential for different signs of the self-action potential. It is shown that the main specific feature of the dynamics of dark NSE solitons in a parabolic trap is the formation of solitons with dynamically changing form factors producing the periodic variation in the modulation depth (the degree of 'blackness') of dark solitons. The oscillation period of the dark soliton does not coincide with the oscillation period of a linear quantum-mechanical oscillator, which is caused by the periodic transformation of the black soliton to the grey one and vice versa. The conditions of applicability of the method of inverse scattering problem are presented, the generalised Lax pair is found, and exact soliton solutions are given for the mathematical NSE model with an external harmonic potential. (solitons)
On Noether's Theorem for the Invariant of the Time-Dependent Harmonic Oscillator
ERIC Educational Resources Information Center
Abe, Sumiyoshi; Itto, Yuichi; Matsunaga, Mamoru
2009-01-01
The time-dependent oscillator describing parametric oscillation, the concept of invariant and Noether's theorem are important issues in physics education. Here, it is shown how they can be interconnected in a simple and unified manner.
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.
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.
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.
Mathematical Modeling of an Oscillating Droplet
NASA Technical Reports Server (NTRS)
Berry, S.; Hyers, R. W.; Racz, L. M.; Abedian, B.; Rose, M. Franklin (Technical Monitor)
2000-01-01
Oscillating droplets are of interest in a number of disciplines. A practical application is the oscillating drop method, which is a technique for measuring surface tension and viscosity of liquid metals. It is especially suited to undercooled and highly reactive metals, because it is performed by electromagnetic levitation. The natural oscillation frequency of the droplets is related to the surface tension of the material, and the decay of oscillations is related to its viscosity. The fluid flow inside the droplet must be laminar in order for this technique to yield good results. Because no experimental method has yet been developed to visualize flow in electromagnetically-levitated oscillating metal droplets, mathematical modeling is required to determine whether or not turbulence occurs. Three mathematical models of the flow: (1) assuming laminar conditions, (2) using the k-epsilon turbulence model, and (3) using the RNG turbulence model, respectively, are compared and contrasted to determine the physical characteristics of the flow. It is concluded that the RNG model is the best suited for describing this problem. The goal of the presented work was to characterize internal flow in an oscillating droplet of liquid metal, and to verify the accuracy of the characterization by comparing calculated surface tension and viscosity.
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.
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.
Charge transfer and coherence dynamics of a tunnelling system coupled to an harmonic oscillator.
Paganelli, S; Ciuchi, S
2008-06-11
We study the transition probability and coherence of a two-site system, interacting with an oscillator. Both properties depend on the initial preparation. The oscillator is prepared in a thermal state and, even though it cannot be considered as an extended bath, it produces decoherence because of the large number of states involved in the dynamics. In the case in which the oscillator is initially displaced, a coherent dynamics of charge entangled with oscillator modes takes place. Coherency is, however, degraded as far as the oscillator mass increases, producing an increasingly large recoherence time. Calculations are carried on by exact diagonalization and compared with two semiclassical approximations. The role of the quantum effects are highlighted in the long time dynamics, where semiclassical approaches give rise to a dissipative behaviour. Moreover, we find that the oscillator dynamics has to be taken into account, even in a semiclassical approximation, in order to reproduce a thermally activated enhancement of the transition probability.
Harmonic and interharmonic distortion modeling in multiconverter systems
Carbone, R.; Morrison, R.E.; Testa, A.; Menniti, D.
1995-07-01
The problem of modeling multiconverter systems in presence of harmonic and interharmonic distortion is considered. Specifically, current source rectifiers are considered as distortion sources some supply d.c. motors and the remaining supplying inverters feeding a.c. machines. The classical analogue, frequency domain and time domain models proposed in the literature to study harmonic distortion in a multiconverter system are considered and for each model suitable extension to include the interharmonic distortion are presented and critically analyzed. The results of several experiments are reported to show the usefulness and to compare the accuracy of the different extensions considered.
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.
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.
Bound electron dynamics: Exact solution for a one-dimensional oscillator-string model
NASA Astrophysics Data System (ADS)
Dekker, H.
1984-11-01
The dynamical problem of a harmonically bound electron with standard dipole model coupling to the electromagnetic field in a finite one-dimensional space is solved exactly in a simple manner. It is easily shown that in this model the coupling between the electron and the field is “rigid”, in the sense of and in complete analogy with a recent treatment of a purely mechanical particle on a string. As a consequence the electron's quantum mechanical momentum fluctuations exhibit a logarithmic ultraviolet divergence. In the limit of infinite spatial extension of the field, and apart from quantal noise, the electron behaves exactly as a simple linearly damped harmonic oscillator.
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.
Decoherence of a quantum harmonic oscillator monitored by a Bose-Einstein condensate
Brouard, S.; Alonso, D.; Sokolovski, D.
2011-07-15
We investigate the dynamics of a quantum oscillator, whose evolution is monitored by a Bose-Einstein condensate (BEC) trapped in a symmetric double-well potential. It is demonstrated that the oscillator may experience various degrees of decoherence depending on the variable being measured and the state in which the BEC is prepared. These range from a ''coherent'' regime in which only the variances of the oscillator position and momentum are affected by measurement, to a slow (power-law) or rapid (Gaussian) decoherence of the mean values themselves.
Draganescu, Gheorghe Eugen
2012-08-17
We used the dicrete variable three-dimmensional Charlier oscillator. For a system of molecules interacting with the coherent radiation field the temporal variation of the refractive index has been established.
Non-Hamiltonian Modeling of Squeezing and Thermal Disorder in Driven Oscillators
NASA Astrophysics Data System (ADS)
Sewran, Sashwin; Zloshchastiev, Konstantin G.; Sergi, Alessandro
2015-04-01
Recently, model systems with quadratic Hamiltonians and time-dependent interactions were studied by Briegel and Popescu (Proc R Soc A 469:20110290, 2013) and by Galve et al. (Phys Rev Lett 105:180501, 2010; Phys Rev Lett 81:062117, 2010) in order to consider the possibility of both quantum refrigeration in enzymes and entanglement in the high temperature limit. Following this line of research, we studied a model comprising two quantum harmonic oscillators driven by a time-dependent harmonic coupling. Such a system was embedded in a thermal bath represented in two different ways. In one case, the bath was composed of a finite but great number of independent harmonic oscillators with an Ohmic spectral density. In the other case, the bath was more efficiently defined in terms of a single oscillator coupled to a non-Hamiltonian thermostat. In both cases, we simulated the effect of the thermal disorder on the generation of the squeezed states in the two-oscillators relevant system. We found that, in our model, the thermal disorder of the bath determines the presence of a threshold temperature, for the generation of squeezed states, equal to K. Such a threshold is estimated to be within temperatures where chemical reactions and biological activity comfortably take place.
3/4-Fractional Superdiffusion in a System of Harmonic Oscillators Perturbed by a Conservative Noise
NASA Astrophysics Data System (ADS)
Bernardin, Cédric; Gonçalves, Patrícia; Jara, Milton
2016-05-01
We consider a harmonic chain perturbed by an energy conserving noise and show that after a space-time rescaling the energy-energy correlation function is given by the solution of a skew-fractional heat equation with exponent 3/4.
NASA Astrophysics Data System (ADS)
Wang, Yang; Song, Hai-Ying; Liu, H. Y.; Liu, Shi-Bing
2017-07-01
We theoretically study high-order harmonic generation (HHG) from relativistically driven overdense plasma targets with rectangularly grating-structured surfaces by femtosecond laser pulses. Our particle-in-cell (PIC) simulations show that, under the conditions of low laser intensity and plasma density, the harmonics emit principally along small angles deviating from the target surface. Further investigation of the surface electron dynamics reveals that the electron bunches are formed by the interaction between the laser field and the target surface, giving rise to the oscillation of equivalent electric-dipole (OEED), which enhances specific harmonic orders. Our work helps understand the mechanism of harmonic emissions from grating targets and the distinction from the planar harmonic scheme.
A Computer Model for Soda Bottle Oscillations: "The Bottelator".
ERIC Educational Resources Information Center
Soltzberg, Leonard J.; And Others
1997-01-01
Presents a model to explain the behavior of oscillatory phenomena found in the soda bottle oscillator. Describes recording the oscillations, and the design of the model based on the qualitative explanation of the oscillations. Illustrates a variety of physiochemical concepts including far-from-equilibrium oscillations, feedback, solubility and…
A Computer Model for Soda Bottle Oscillations: "The Bottelator".
ERIC Educational Resources Information Center
Soltzberg, Leonard J.; And Others
1997-01-01
Presents a model to explain the behavior of oscillatory phenomena found in the soda bottle oscillator. Describes recording the oscillations, and the design of the model based on the qualitative explanation of the oscillations. Illustrates a variety of physiochemical concepts including far-from-equilibrium oscillations, feedback, solubility and…
Physical models for the source of Lascar's harmonic tremor
NASA Astrophysics Data System (ADS)
Hellweg, M.
2000-08-01
Over an 18 h interval in April 1994, the tremor at Lascar volcano, Chile, was characterized by a spectrum with narrow peaks at a fundamental freqency of about 0.63 Hz and more than 25 overtones at exact integer multiples. This harmonic tremor was recorded at four three-component, high-dynamic range stations during the deployment of the Proyecto de Investigación Sismológica de la Cordillera Occidental 94 (PISCO'94). Usually this tremor's source is modeled as the resonance of a fluid-filled crack or organ pipe-like structure in the volcano. The resonance of a real, physical structure, however, can produce neither as many overtones nor such exact multiples as those observed in the harmonic tremor at Lascar. Harmonics also occur in a spectrum if the source signal is repetitive but nonsinusoidal. Fluid dynamics offers at least three realistic source models for harmonic tremor which produce repetitive, nonsinusoidal waveforms: the release of gas through a very small outlet (the soda bottle model), slug flow in a narrow conduit, and von Kármán vortices produced at obstacles. These models represent different flow regimes, each with its own characteristic range of Reynolds numbers. For each model the fundamental frequency of the tremor is related to the Reynolds number for the flow. Combining the Reynolds numbers for each model with typical kinematic viscosities for the possible fluids present in a volcano-magma, water, steam, air or some combination, at appropriate temperatures and pressures-provides limits on such physical parameters of the volcano as the dimensions of the flow conduit and the flow velocity of the fluid generating the tremor. If any single one of these three models is actually the process in the volcano which generates harmonic tremor, then the tremor is caused by movements of water or gases in the hydrothermal system near the volcano's surface.
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.
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.
A Comprehensive and Harmonized Digital Forensic Investigation Process Model.
Valjarevic, Aleksandar; Venter, Hein S
2015-11-01
Performing a digital forensic investigation (DFI) requires a standardized and formalized process. There is currently neither an international standard nor does a global, harmonized DFI process (DFIP) exist. The authors studied existing state-of-the-art DFIP models and concluded that there are significant disparities pertaining to the number of processes, the scope, the hierarchical levels, and concepts applied. This paper proposes a comprehensive model that harmonizes existing models. An effort was made to incorporate all types of processes proposed by the existing models, including those aimed at achieving digital forensic readiness. The authors introduce a novel class of processes called concurrent processes. This is a novel contribution that should, together with the rest of the model, enable more efficient and effective DFI, while ensuring admissibility of digital evidence. Ultimately, the proposed model is intended to be used for different types of DFI and should lead to standardization. © 2015 American Academy of Forensic Sciences.
Harmonic generation in the generalized Sagdeev pseudopotential
NASA Astrophysics Data System (ADS)
Akbari-Moghanjoughi, M.
2017-09-01
In this paper, we study the nonlinear harmonic generation effect in different oscillator models. For weakly nonlinear systems, we use the generalized forced Korteweg de Vries Burgers (KdVB) and modified KdVB (mKdVB) models in order to classify three fundamentally different harmonic structures in a nonlinear dynamical system. The first is called the internal harmonic structure which exists due to the self oscillation of the system in the absence of dissipation effect and is shown to follow either relations of nf or (2n - 1)f depending on the symmetry of oscillator potential in which n is an integer number and f is the fundamental frequency which is exactly obtained for the Helmholtz oscillator. The second structure is the resonant harmonics which appears in the presence of damping and follows the harmonic structure nf0 in which f0 is the linear resonance frequency. Finally, the last harmonic structure appears in the presence of dissipation and external periodic forcing effects which we call the external harmonic pattern. It is shown that the external harmonic pattern, in which f1 is the driving frequency, always follows the nf1 rule regardless of the potential symmetry. We then extend our analysis to study the harmonic generation in the fully nonlinear generalized Sagdeev potential for real plasmas with isothermal and adiabatic ion fluids and investigate the effects of different plasma parameters such as the fractional ion temperature and normalized ion acoustic speed on all three kinds of harmonic generation.
On su{sub q}(1,1)-models of quantum oscillator
Atakishiyev, M. N.; Atakishiyev, N. M.; Klimyk, A. U.
2006-09-15
Models of the quantum oscillator, based on the discrete series representations of the quantum algebra su{sub q}(1,1), are constructed. The position and momentum operators in these models are twisted generators J{sub 2} and J{sub 1} for such su{sub q}(1,1)-representations, respectively. As in the case of the standard harmonic oscillator in quantum mechanics, the position and momentum operators here have continuous simple spectra. These spectra cover a finite interval on the real line, which depends on a value of q. Eigenfunctions of these operators are explicitly found. It is shown that the Macfarlane-Biedenharn q-oscillator is a limit case of the oscillators under discussion. The q=1 limit case, in which spectra of the position and momentum operators cover the whole real line, is also considered in detail.
A representation of Jacchia's thermospheric models in spherical harmonics
NASA Technical Reports Server (NTRS)
Blum, P.; Harris, I.
1973-01-01
The Jacchia models are represented in terms of spherical harmonic functions. This representation has the advantages of ease of comparison with theoretical and other observational models and data, mathematical analyticity and relative simplicity. The symmetry properties of the models are emphasized by this representation and some physical characteristics like the increase of the amplitude of the diurnal density variation with decreasing solar activity become more apparent.
Bright multi-keV harmonic generation from relativistically oscillating plasma surfaces.
Dromey, B; Kar, S; Bellei, C; Carroll, D C; Clarke, R J; Green, J S; Kneip, S; Markey, K; Nagel, S R; Simpson, P T; Willingale, L; McKenna, P; Neely, D; Najmudin, Z; Krushelnick, K; Norreys, P A; Zepf, M
2007-08-24
The first evidence of x-ray harmonic radiation extending to 3.3 A, 3.8 keV (order n>3200) from petawatt class laser-solid interactions is presented, exhibiting relativistic limit efficiency scaling (eta approximately n{-2.5}-n{-3}) at multi-keV energies. This scaling holds up to a maximum order, n{RO} approximately 8{1/2}gamma;{3}, where gamma is the relativistic Lorentz factor, above which the first evidence of an intensity dependent efficiency rollover is observed. The coherent nature of the generated harmonics is demonstrated by the highly directional beamed emission, which for photon energy hnu>1 keV is found to be into a cone angle approximately 4 degrees , significantly less than that of the incident laser cone (20 degrees ).
NASA Astrophysics Data System (ADS)
Alejo-Molina, Adalberto; Hingerl, Kurt; Hardhienata, Hendradi
2015-04-01
We report for the first time a comprehensive study of the fourth rank tensor describing third harmonic generation (THG) and electric field induced second harmonic (EFISH) in centrosymmetric material from two different viewpoints: Group Theory (GT) and the Simplified Bond Hyperpolarizability Model (SBHM). We show that the fourth rank tensor related to THG and direct current (DC) EFISH can be reduced to two independent elements whereas SBHM always gives only one, reproducing perfectly well EFISH experimental results in Metal Oxyde Semiconductor (MOS). We argue that it is possible to reduce the fourth rank tensor describing EFISH to a third rank tensor and further deliver a classical explanation of EFISH regarding symmetry breaking where the term containing $r^3$ in the potential immediately leads to second harmonic generation (SHG).
Four mass coupled oscillator guitar model.
Popp, John E
2012-01-01
Coupled oscillator models have been used for the low frequency response (50 to 250 Hz) of a guitar. These 2 and 3 mass models correctly predict measured resonance frequency relationships under various laboratory boundary conditions, but did not always represent the true state of a guitar in the players' hands. The model presented has improved these models in three ways, (1) a fourth oscillator includes the guitar body, (2) plate stiffnesses and other fundamental parameters were measured directly and effective areas and masses used to calculate the responses, including resonances and phases, directly, and (3) one of the three resultant resonances varies with neck and side mass and can also be modeled as a bar mode of the neck and body. The calculated and measured resonances and phases agree reasonably well.
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.
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.
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.
Modelling the Madden Julian Oscillation
Slingo, J M; Inness, P M; Sperber, K R
2004-05-21
The MJO has long been an aspect of the global climate that has provided a tough test for the climate modelling community. Since the 1980s there have been numerous studies of the simulation of the MJO in atmospheric general circulation models (GCMs), ranging from Hayashi and Golder (1986, 1988) and Lau and Lau (1986), through to more recent studies such as Wang and Schlesinger (1999) and Wu et al. (2002). Of course, attempts to reproduce the MJO in climate models have proceeded in parallel with developments in our understanding of what the MJO is and what drives it. In fact, many advances in understanding the MJO have come through modeling studies. In particular, failure of climate models to simulate various aspects of the MJO has prompted investigations into the mechanisms that are important to its initiation and maintenance, leading to improvements both in our understanding of, and ability to simulate, the MJO. The initial focus of this chapter will be on modeling the MJO during northern winter, when it is characterized as a predominantly eastward propagating mode and is most readily seen in observations. Aspects of the simulation of the MJO will be discussed in the context of its sensitivity to the formulation of the atmospheric model, and the increasing evidence that it may be a coupled ocean-atmosphere phenomenon. Later, we will discuss the challenges regarding the simulation of boreal summer intraseasonal variability, which is more complex since it is a combination of the eastward propagating MJO and the northward propagation of the tropical convergence zone. Finally some concluding remarks on future directions in modeling the MJO and its relationship with other timescales of variability in the tropics will be made.
Oscillation frequencies of solar models
Cox, A.N.; Guzik, J.A.; Kidman, R.B.
1988-01-01
Two solar models have been constructed, one with no diffusion of the atomic nuclei, and another including diffusive element separation. The opacity at the bottom of the convection zone was increased 15--20 percent (within its theoretical uncertainty) to obtain a few microhertz agreement with observed p-mode frequencies. Original helium mass fractions were 0.291 and 0.289 for the no-diffusion and diffusion models, respectively. The diffusion model evolved to a surface Y = 0.256 at the solar age, and the original Z value of 0.0200 decreased to 0.0179. Agreement of l = 0 and 2 p-mode frequency separations with those observed is good. The g-mode nonadiabatic solutions do not have equal period spacing until high radial order. The lowest order modes are more visible if they all have the same kinetic energy. High central temperatures, produce over 9 SNUs from the B and 1.5 SNUs from the Be reactions. Models with iron condensed-out below the convection zone, and with WIMPs cooling the central regions to reduce the SNUs, agree less well with p-mode frequency separations. 53 refs., 6 figs., 4 tabs.
A three-phase converter model for harmonic analysis of HVDC systems
Xu, W.; Drakos, J.E.; Mansour, Y.; Chang, A. )
1994-07-01
An equivalent circuit model is presented to model bridge converters for three-phase HVDC harmonic power flow analysis. The validity and accuracy of the model are verified by comparing simulation results against field test results. The model is interfaced with a multiphase harmonic load flow program to investigate the generation of non-characteristic harmonics from HVDC links and the flow of HVDC harmonics in a real system.
Local constraints on the oscillating G model
Gonzalez, Jose A.; Quevedo, Hernando; Salgado, Marcelo; Sudarsky, Daniel
2001-08-15
We analyze observational constraints on the effective Brans-Dicke parameter and on the temporal variation of the effective gravitational constant within the context of the oscillating G model, a cosmological model based on a massive scalar field nonminimally coupled to gravity. We show that these local constraints cannot be satisfied simultaneously once the values of the free parameters entering the model become fixed by the global attributes of our Universe. In particular, we show that the lower observational bound for the effective Brans-Dicke parameter and the upper bound of the variation of the effective gravitational constant lead to a specific value of the oscillation amplitude which lies well below the value required to explain the periodicity of 128h{sup -1}Mpc in the galaxy distribution observed in the pencil beam surveys.
Modeling of solar oscillation power spectra
NASA Technical Reports Server (NTRS)
Anderson, Edwin R.; Duvall, Thomas L., Jr.; Jefferies, Stuart M.
1990-01-01
To produce accurate estimates of the line-profile parameters of a model used to represent the spectral features in a solar oscillation power spectrum, it is necessary to (1) select the appropriate probability density function when deriving the maximum-likelihood function to be employed for the parameter estimation and (2) allow for the redistribution of spectral power caused by gaps in the data string. This paper describes a maximum-likelihood method for estimating the model parameters (based on the observed power spectrum statistics) that accounts for redistribution of spectral power caused by gaps in the data string, by convolving the model with the power spectrum of the observed window function. The accuracy and reliability of the method were tested using both artificial and authentic solar oscillation power spectrum data. A comparison of this method with various least-squares techniques is also presented.
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.
A quantum quasi-harmonic nonlinear oscillator with an isotonic term
Rañada, Manuel F.
2014-08-01
The properties of a nonlinear oscillator with an additional term k{sub g}/x², characterizing the isotonic oscillator, are studied. The nonlinearity affects to both the kinetic term and the potential and combines two nonlinearities associated to two parameters, κ and k{sub g}, in such a way that for κ = 0 all the characteristics of the standard isotonic system are recovered. The first part is devoted to the classical system and the second part to the quantum system. This is a problem of quantization of a system with position-dependent mass of the form m(x) = 1/(1 − κx²), with a κ-dependent non-polynomial rational potential and with an additional isotonic term. The Schrödinger equation is exactly solved and the (κ, k{sub g})-dependent wave functions and bound state energies are explicitly obtained for both κ < 0 and κ > 0.
1988-08-15
could. The criterion for the validity of semiclassical calculation is that, for given initial oscillator and incident energies, the ;% possible...This is an expression of the correspondence principle. As is well known, suitable semiclassical calculations may give rather accurate results even when...follows: I "> - Ikot> + Co +’ VKT >, (6) where ;o,> is the normalized eigen function of Ho and Go is the Green s function, defined by ’,.4 G lim (7) -oE-Ho
Improved harmonic mean estimator for phylogenetic model evidence.
Arima, Serena; Tardella, Luca
2012-04-01
Bayesian phylogenetic methods are generating noticeable enthusiasm in the field of molecular systematics. Many phylogenetic models are often at stake, and different approaches are used to compare them within a Bayesian framework. The Bayes factor, defined as the ratio of the marginal likelihoods of two competing models, plays a key role in Bayesian model selection. We focus on an alternative estimator of the marginal likelihood whose computation is still a challenging problem. Several computational solutions have been proposed, none of which can be considered outperforming the others simultaneously in terms of simplicity of implementation, computational burden and precision of the estimates. Practitioners and researchers, often led by available software, have privileged so far the simplicity of the harmonic mean (HM) estimator. However, it is known that the resulting estimates of the Bayesian evidence in favor of one model are biased and often inaccurate, up to having an infinite variance so that the reliability of the corresponding conclusions is doubtful. We consider possible improvements of the generalized harmonic mean (GHM) idea that recycle Markov Chain Monte Carlo (MCMC) simulations from the posterior, share the computational simplicity of the original HM estimator, but, unlike it, overcome the infinite variance issue. We show reliability and comparative performance of the improved harmonic mean estimators comparing them to approximation techniques relying on improved variants of the thermodynamic integration.
NASA Astrophysics Data System (ADS)
Hegedűs, Ferenc
2016-03-01
The topology of the stable periodic orbits of a harmonically driven bubble oscillator, the Rayleigh-Plesset equation, in the space of the excitation parameters (pressure amplitude and frequency) has been revealed numerically. This topology is governed by a hierarchy of two-sided Farey trees initiated from a unique primary structure defined also by a simple asymmetric Farey tree. The sub-topology of each of these building blocks is driven by a homoclinic tangency of a periodic saddle. This self-similar organisation is a suitable basis for a general description, since it is in good agreement with partial results obtained in other periodically forced oscillators and iterated maps. The applied ambient pressure in the model is near but still below Blake's critical threshold. Therefore, this paper is also a straightforward continuation of the work of Hegedűs [1], who first found numerical evidence for the existence of stable, period 1 solutions beyond Blake's threshold. The present findings are crucial for the extension of the available numerical results from period 1 to arbitrary periodicity.
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.
van Zon, Ramses; Hernández de la Peña, Lisandro; Peslherbe, Gilles H; Schofield, Jeremy
2008-10-01
Nonequilibrium path-integral methods for computing quantum free-energy differences are applied to a quantum particle trapped in a harmonic well of uniformly changing strength with the purpose of establishing the convergence properties of the work distribution and free energy as the number of degrees of freedom M in the regularized path integrals goes to infinity. The work distribution is found to converge when M tends to infinity regardless of the switching speed, leading to finite results for the free-energy difference when the Jarzynski nonequilibrium work relation or the Crooks fluctuation relation are used. The nature of the convergence depends on the regularization method. For the Fourier method, the convergence of the free-energy difference and work distribution go as 1/M , while both quantities converge as 1/M(2) when the bead regularization procedure is used. The implications of these results to more general systems are discussed.
Numerical linearized MHD model of flapping oscillations
NASA Astrophysics Data System (ADS)
Korovinskiy, D. B.; Ivanov, I. B.; Semenov, V. S.; Erkaev, N. V.; Kiehas, S. A.
2016-06-01
Kink-like magnetotail flapping oscillations in a Harris-like current sheet with earthward growing normal magnetic field component Bz are studied by means of time-dependent 2D linearized MHD numerical simulations. The dispersion relation and two-dimensional eigenfunctions are obtained. The results are compared with analytical estimates of the double-gradient model, which are found to be reliable for configurations with small Bz up to values ˜ 0.05 of the lobe magnetic field. Coupled with previous results, present simulations confirm that the earthward/tailward growth direction of the Bz component acts as a switch between stable/unstable regimes of the flapping mode, while the mode dispersion curve is the same in both cases. It is confirmed that flapping oscillations may be triggered by a simple Gaussian initial perturbation of the Vz velocity.
Testing the Model of Oscillating Magnetic Traps
NASA Astrophysics Data System (ADS)
Szaforz, Ż.; Tomczak, M.
2015-01-01
The aim of this paper is to test the model of oscillating magnetic traps (the OMT model), proposed by Jakimiec and Tomczak ( Solar Phys. 261, 233, 2010). This model describes the process of excitation of quasi-periodic pulsations (QPPs) observed during solar flares. In the OMT model energetic electrons are accelerated within a triangular, cusp-like structure situated between the reconnection point and the top of a flare loop as seen in soft X-rays. We analyzed QPPs in hard X-ray light curves for 23 flares as observed by Yohkoh. Three independent methods were used. We also used hard X-ray images to localize magnetic traps and soft X-ray images to diagnose thermal plasmas inside the traps. We found that the majority of the observed pulsation periods correlates with the diameters of oscillating magnetic traps, as was predicted by the OMT model. We also found that the electron number density of plasma inside the magnetic traps in the time of pulsation disappearance is strongly connected with the pulsation period. We conclude that the observations are consistent with the predictions of the OMT model for the analyzed set of flares.
NASA Astrophysics Data System (ADS)
Hu, Xuanyu
2016-06-01
The spherical and ellipsoidal harmonic series of the external gravitational potential for a given mass distribution are equivalent in their mutual region of uniform convergence. In an instructive case, the equality of the two series on the common coordinate surface of an infinitely large sphere reveals the exact correspondence between the spherical and ellipsoidal harmonic coefficients. The transformation between the two sets of coefficients can be accomplished via the numerical methods by Walter (Celest Mech 2:389-397, 1970) and Dechambre and Scheeres (Astron Astrophys 387:1114-1122, 2002), respectively. On the other hand, the harmonic coefficients are defined by the integrals of mass density moments in terms of the respective solid harmonics. This paper presents general algebraic formulas for expressing the solid ellipsoidal harmonics as a linear combination of the corresponding solid spherical harmonics. An exact transformation from spherical to ellipsoidal harmonic coefficients is found by incorporating these connecting expressions into the density integral. A computational procedure is proposed for the transformation. Numerical results based on the nearly ellipsoidal Martian moon, Phobos, are presented for validation of the method.
Modeling flexible flapping wings oscillating at resonance
NASA Astrophysics Data System (ADS)
Alexeev, Alexander; Masoud, Hassan
2010-03-01
Using a hybrid approach for fluid-structure interactions that integrates the lattice Boltzmann and lattice spring models, we study the three-dimensional aerodynamics of flexible flapping wings at hovering. The wings are a pair of flat elastic plates tilted from the horizontal and driven to oscillate according to the sinusoidal law. Our simulations reveal that resonance oscillations of flexible wings dramatically increase aerodynamic lift at low Reynolds number. Comparing to otherwise identical rigid wings, flexible wings at resonance generate up to two orders of magnitude greater lift. Within the resonance band, we identify two operation regimes leading to the maximum lift and the maximum efficiency, respectively. The maximum lift occurs when the wing tip and root move with a phase lag of 90 degrees, whereas the maximum efficiency occurs at the frequency where the wing tip and root oscillate in counterphase. Our results suggest that the resonance regimes would be optimal for the design of microscale flying machines using flexible flapping wings driven by simple kinematic strokes.
A representation of Jacchia's thermospheric models in spherical harmonic functions
NASA Technical Reports Server (NTRS)
Blum, P.; Harris, I.
1974-01-01
The Jacchia models are represented in terms of spherical harmonic functions. This representation has the advantage of ease of comparison with other global theoretical and empirical models that use this mathematical form. Furthermore, it is analytic, continuous, and has continuous derivatives all over the globe. The representation of the exospheric temperatures shows clearly the amplitudes of the various periodic terms and uses relatively few constants. An example of a similar representation for the total mass density at a particular height and level of solar activity is given as well.
Low-noise sub-harmonic injection locked multiloop ring oscillator
NASA Astrophysics Data System (ADS)
Weilin, Xu; Di, Wu; Xueming, Wei; Baolin, Wei; Jihai, Duan; Fadi, Gui
2016-09-01
A three-stage differential voltage-controlled ring oscillator is presented for wide-tuning and low-phase noise requirement of clock and data recovery circuit in ultra wideband (UWB) wireless body area network. To improve the performance of phase noise of delay cell with coarse and fine frequency tuning, injection locked technology together with pseudo differential architecture are adopted. In addition, a multiloop is employed for frequency boosting. Two RVCOs, the standard RVCO without the IL block and the proposed IL RVCO, were fabricated in SMIC 0.18 μm 1P6M Salicide CMOS process. The proposed IL RVCO exhibits a measured phase noise of -112.37 dBc/Hz at 1 MHz offset from the center frequency of 1 GHz, while dissipating a current of 8 mA excluding the buffer from a 1.8-V supply voltage. It shows a 16.07 dB phase noise improvement at 1 MHz offset compared to the standard topology. Project supported by the National Natural Science Foundation of China (No. 61264001), the Guangxi Natural Science Foundation (Nos. 2013GXNSFAA019333, 2015GXNSFAA139301, 2014GXNSFAA118386), the Graduate Education Innovation Program of GUET (No. GDYCSZ201457), the Project of Guangxi Education Department (No. LD14066B) and the High-Level-Innovation Team and Outstanding Scholar Project of Guangxi Higher Education Institutes.
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.
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.
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.
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.
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.
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.
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.
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.
Modeling Very Oscillating Signals. Application to Image Processing
Aubert, Gilles Aujol, Jean-Francois
2005-03-15
This article is a companion paper of a previous work where we have developed the numerical analysis of a variational model first introduced by Rudin et al. and revisited by Meyer for removing the noise and capturing textures in an image. The basic idea in this model is to decompose an image f into two components (u + v) and then to search for (u,v) as a minimizer of an energy functional. The first component u belongs to BV and contains geometrical information, while the second one v is sought in a space G which contains signals with large oscillations, i.e. noise and textures. In Meyer carried out his study in the whole R{sup 2} and his approach is rather built on harmonic analysis tools. We place ourselves in the case of a bounded set{omega} of R{sup 2} which is the proper setting for image processing and our approach is based upon functional analysis arguments. We define in this context the space G, give some of its properties, and then study in this continuous setting the energy functional which allows us to recover the components u and v. We present some numerical experiments to show the relevance of the model for image decomposition and for image denoising.
Core-oscillator model of Caulobacter crescentus
NASA Astrophysics Data System (ADS)
Vandecan, Yves; Biondi, Emanuele; Blossey, Ralf
2016-06-01
The gram-negative bacterium Caulobacter crescentus is a powerful model organism for studies of bacterial cell cycle regulation. Although the major regulators and their connections in Caulobacter have been identified, it still is a challenge to properly understand the dynamics of its circuitry which accounts for both cell cycle progression and arrest. We show that the key decision module in Caulobacter is built from a limit cycle oscillator which controls the DNA replication program. The effect of an induced cell cycle arrest is demonstrated to be a key feature to classify the underlying dynamics.
Nicu, Valentin Paul
2016-08-03
Motivated by the renewed interest in the coupled oscillator (CO) model for VCD, in this work a generalised coupled oscillator (GCO) expression is derived by introducing the concept of a coupled oscillator origin. Unlike the standard CO expression, the GCO expression is exact within the harmonic approximation. Using two illustrative example molecules, the theoretical concepts introduced here are demonstrated by performing a GCO decomposition of the rotational strengths computed using DFT. This analysis shows that: (1) the contributions to the rotational strengths that are normally neglected in the standard CO model can be comparable to or larger than the CO contribution, and (2) the GCO mechanism introduced here can affect the VCD intensities of all types of modes in symmetric and asymmetric molecules.
Saccadic oscillations - membrane, model, and medicine.
Shaikh, Aasef G
2012-10-01
Saccadic oscillations are continuous back-to-back saccades that cause excessive image motion across fovea and threaten clear vision. Acquired processes, related to immune or metabolic mechanisms, are common culprits. Saccadic oscillations are also seen in degenerative cerebellar disease or as a part of a familial syndrome of saccadic oscillations and limb tremor. Some normal individuals have innate ability to voluntarily trigger saccadic oscillations (i.e. voluntary nystagmus). Contemporary theory for the pathogenesis for saccadic oscillations has emphasized hyperexcitable or disinhibited state of the brainstem saccadic burst neuron membrane. This review discusses etiologies and treatment of saccadic oscillations in light of novel cell membrane based theory.
Saccadic oscillations – membrane, model, and medicine
Shaikh, Aasef G.
2015-01-01
Saccadic oscillations are continuous back-to-back saccades that cause excessive image motion across fovea and threaten clear vision. Acquired processes, related to immune or metabolic mechanisms, are common culprits. Saccadic oscillations are also seen in degenerative cerebellar disease or as a part of a familial syndrome of saccadic oscillations and limb tremor. Some normal individuals have innate ability to voluntarily trigger saccadic oscillations (i.e. voluntary nystagmus). Contemporary theory for the pathogenesis for saccadic oscillations has emphasized hyperexcitable or disinhibited state of the brainstem saccadic burst neuron membrane. This review discusses etiologies and treatment of saccadic oscillations in light of novel cell membrane based theory. PMID:25705246
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.
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.
Statistical model of clutter suppression in tissue harmonic imaging
Yan, Xiang; Hamilton, Mark F.
2011-01-01
A statistical model is developed for the suppression of clutter in tissue harmonic imaging (THI). Tissue heterogeneity is modeled as a random phase screen that is characterized by its correlation length and variance. With the autocorrelation function taken to be Gaussian and for small variance, statistical solutions are derived for the mean intensities at the fundamental and second-harmonic frequencies in the field of a focused sound beam that propagates through the phase screen. The statistical solutions are verified by comparison with ensemble averaging of direct numerical simulations. The model demonstrates that THI reduces the aberration clutter appearing in the focal region regardless of the depth of the aberrating layer, with suppression of the clutter most effective when the layer is close to the source. The model is also applied to the reverberation clutter that is transmitted forward along the axis of the beam. As with aberration clutter, suppression of such reverberation clutter by THI is most pronounced when the tissue heterogeneity is located close to the source. PMID:21428483
Statistical model of clutter suppression in tissue harmonic imaging.
Yan, Xiang; Hamilton, Mark F
2011-03-01
A statistical model is developed for the suppression of clutter in tissue harmonic imaging (THI). Tissue heterogeneity is modeled as a random phase screen that is characterized by its correlation length and variance. With the autocorrelation function taken to be Gaussian and for small variance, statistical solutions are derived for the mean intensities at the fundamental and second-harmonic frequencies in the field of a focused sound beam that propagates through the phase screen. The statistical solutions are verified by comparison with ensemble averaging of direct numerical simulations. The model demonstrates that THI reduces the aberration clutter appearing in the focal region regardless of the depth of the aberrating layer, with suppression of the clutter most effective when the layer is close to the source. The model is also applied to the reverberation clutter that is transmitted forward along the axis of the beam. As with aberration clutter, suppression of such reverberation clutter by THI is most pronounced when the tissue heterogeneity is located close to the source.
NASA Astrophysics Data System (ADS)
Chae, Jongchul; Litvinenko, Yuri E.
2017-08-01
The vertical propagation of nonlinear acoustic waves in an isothermal atmosphere is considered. A new analytical solution that describes a finite-amplitude wave of an arbitrary wavelength is obtained. Although the short- and long-wavelength limits were previously considered separately, the new solution describes both limiting cases within a common framework and provides a straightforward way of interpolating between the two limits. Physical features of the nonlinear waves in the chromosphere are described, including the dispersive nature of low-frequency waves, the steepening of the wave profile, and the influence of the gravitational field on wavefront breaking and shock formation. The analytical results suggest that observations of three-minute oscillations in the solar chromosphere may reveal the basic nonlinear effect of oscillations with combination frequencies, superposed on the normal oscillations of the system. Explicit expressions for a second-harmonic signal and the ratio of its amplitude to the fundamental harmonic amplitude are derived. Observational evidence of the second harmonic, obtained with the Fast Imaging Solar Spectrograph, installed at the 1.6 m New Solar Telescope of the Big Bear Observatory, is presented. The presented data are based on the time variations of velocity determined from the Na i D2 and Hα lines.
Modeling spatial oscillations of Min proteins in round bacteria
NASA Astrophysics Data System (ADS)
Huang, Kerwyn; Wingreen, Ned
2004-03-01
In the rod-shaped bacterium phE. coli, the Min proteins oscillate from pole to pole every ˜40 seconds. This internal spatial oscillator plays an essential role in the high accuracy of phE. coli's cell division. Homologs of the Min proteins also exist in round cells (cocci) such as phNeisseria gonorrhoeae. While oscillations have not been directly observed in phN. gonorrhoeae cells because of their small size ( ˜1 micron in diameter), evidence is accumulating that the Min proteins do oscillate in these cells. For example, the Min proteins are observed to oscillate in round mutants of phE. coli, and the phN. gonorrhoeae Min proteins oscillate when expressed in rod-shaped phE. coli. Adding to the evidence for Min-protein oscillations in phN. gonorrhoeae, we report that a numerical model for Min-protein oscillations in rod-shaped cells also produces oscillations in round cells. Our results moreover explain why the rings of MinE protein found in wild-type phE. coli are absent in round phE. coli mutants. Importantly, we find that there is a minimum radius below which oscillations do not occur. Finally, we show that Min-protein oscillations are able to select the longest axis of nearly round cells. This sensitivity of Min-protein oscillations to cell geometry suggests a role for the oscillations in selecting the plane of cell division.
Spherical Harmonics Functions Modelling of Meteorological Parameters in PWV Estimation
NASA Astrophysics Data System (ADS)
Deniz, Ilke; Mekik, Cetin; Gurbuz, Gokhan
2016-08-01
Aim of this study is to derive temperature, pressure and humidity observations using spherical harmonics modelling and to interpolate for the derivation of precipitable water vapor (PWV) of TUSAGA-Active stations in the test area encompassing 38.0°-42.0° northern latitudes and 28.0°-34.0° eastern longitudes of Turkey. In conclusion, the meteorological parameters computed by using GNSS observations for the study area have been modelled with a precision of ±1.74 K in temperature, ±0.95 hPa in pressure and ±14.88 % in humidity. Considering studies on the interpolation of meteorological parameters, the precision of temperature and pressure models provide adequate solutions. This study funded by the Scientific and Technological Research Council of Turkey (TUBITAK) (The Estimation of Atmospheric Water Vapour with GPS Project, Project No: 112Y350).
Relating harmonic and projective descriptions of {N}=2 nonlinear sigma models
NASA Astrophysics Data System (ADS)
Butter, Daniel
2012-11-01
Recent papers have established the relationship between projective superspace and a complexified version of harmonic superspace. We extend this construction to the case of general nonlinear sigma models in both frameworks. Using an analogy with Hamiltonian mechanics, we demonstrate how the Hamiltonian structure of the harmonic action and the symplectic structure of the projective action naturally arise from a single unifying action on a complexified version of harmonic superspace. This links the harmonic and projective descriptions of hyperkähler target spaces. For the two examples of Taub-NUT and Eguchi-Hanson, we show how to derive the projective superspace solutions from the harmonic superspace solutions.
Design and Simulation of a 600 GHz RTD Oscillator Using Commercial Harmonic Balance Software
2000-09-29
64 mS at about 1.3 V as reported in Ref. [I]. This model was developed within the context of dI Vh- IR,+ A2R -V 2 (1) Microwave Harmonica [19...simulated successfully to confirm the validity of the conductance required. Therefore, the resonator only has RTD model within Harmonica . Section IV...3 0, Cj= 2.8 fF, LB = I liH, L 1 = 25 pH ... and RL = 12 Q. R, and Ca were obtained from data -.-- Microwave Harmonica -- MATLAB published in [1
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.
A model for premixed combustion oscillations
Janus, M.C.; Richards, G.A.
1996-03-01
Combustion oscillations are receiving renewed research interest due to increasing application of lean premix (LPM) combustion to gas turbines. A simple, nonlinear model for premixed combustion is described; it was developed to explain experimental results and to provide guidance for developing active control schemes based on nonlinear concepts. The model can be used to quickly examine instability trends associated with changes in equivalence ratio, mass flow rate, geometry, ambient conditions, etc. The model represents the relevant processes occurring in a fuel nozzle and combustor analogous to current LPM turbine combustors. Conservation equations for the nozzle and combustor are developed from simple control volume analysis, providing ordinary differential equations that can be solved on a PC. Combustion is modeled as a stirred reactor, with bimolecular reaction between fuel and air. Although focus is on the model, it and experimental results are compared to understand effects of inlet air temperature and open loop control schemes. The model shows that both are related to changes in transport time.
Experimental investigation and model development for a harmonic drive transmission.
Preissner, C.; Shu, D.; Royston, T. J.; Univ. of Illinois at Chicago
2007-01-01
Harmonic drive transmissions (HDTs) are compact, low-backlash, high-ratio, high-resolution rotary motion transmissions. One application to benefit from these attributes is the revolute joint robot. Engineers at the Advanced Photon Source (APS) are investigating the use of this type of robot for the positioning of an x-ray detector; understanding the properties of the robot components is crucial to modeling positioner behavior. The robot bearing elements had been investigated previously, leaving the transmission as the missing component. While the benefits of HDTs are well known, the disadvantages, including fluctuating dissipation characteristics and nonlinear stiffness, are not understood as well. These characteristics can contribute uncontrolled dynamics to the overall robot performance. A dynamometer has been constructed at the APS to experimentally measure the HDT's response. Empirical torque and position data were recorded for multiple transmission load cases and input conditions. In turn, a computer model of the dynamometer HDT system was constructed to approximate the observed response.
Memcapacitor model and its application in chaotic oscillator with memristor
NASA Astrophysics Data System (ADS)
Wang, Guangyi; Zang, Shouchi; Wang, Xiaoyuan; Yuan, Fang; Iu, Herbert Ho-Ching
2017-01-01
Memristors and memcapacitors are two new nonlinear elements with memory. In this paper, we present a Hewlett-Packard memristor model and a charge-controlled memcapacitor model and design a new chaotic oscillator based on the two models for exploring the characteristics of memristors and memcapacitors in nonlinear circuits. Furthermore, many basic dynamical behaviors of the oscillator, including equilibrium sets, Lyapunov exponent spectrums, and bifurcations with various circuit parameters, are investigated theoretically and numerically. Our analysis results show that the proposed oscillator possesses complex dynamics such as an infinite number of equilibria, coexistence oscillation, and multi-stability. Finally, a discrete model of the chaotic oscillator is given and the main statistical properties of this oscillator are verified via Digital Signal Processing chip experiments and National Institute of Standards and Technology tests.
Memcapacitor model and its application in chaotic oscillator with memristor.
Wang, Guangyi; Zang, Shouchi; Wang, Xiaoyuan; Yuan, Fang; Iu, Herbert Ho-Ching
2017-01-01
Memristors and memcapacitors are two new nonlinear elements with memory. In this paper, we present a Hewlett-Packard memristor model and a charge-controlled memcapacitor model and design a new chaotic oscillator based on the two models for exploring the characteristics of memristors and memcapacitors in nonlinear circuits. Furthermore, many basic dynamical behaviors of the oscillator, including equilibrium sets, Lyapunov exponent spectrums, and bifurcations with various circuit parameters, are investigated theoretically and numerically. Our analysis results show that the proposed oscillator possesses complex dynamics such as an infinite number of equilibria, coexistence oscillation, and multi-stability. Finally, a discrete model of the chaotic oscillator is given and the main statistical properties of this oscillator are verified via Digital Signal Processing chip experiments and National Institute of Standards and Technology tests.
Majority orienting model for the oscillation of market price
NASA Astrophysics Data System (ADS)
Takahashi, H.; Itoh, Y.
2004-01-01
The present paper introduces a majority orienting model in which the dealers' behavior changes based on the influence of the price to show the oscillation of stock price in the stock market. We show the oscillation of the price for the model by applying the vanderPol equation which is a deterministic approximation of our model.
Polymerization and oscillation stuttering in a filamentous model of the subcellular Min oscillation
NASA Astrophysics Data System (ADS)
Rutenberg, Andrew; Sengupta, Supratim; Sain, Anirban; Derr, Julien
2011-03-01
We present a computational model of the E. coli Min oscillation that involves polymerization of MinD filaments followed by depolymerization stimulated by filament-end zones of MinE. Our stochastic model is fully three-dimensional, and tracks the diffusion and interactions of every MinD and MinE molecule. We recover self-organized Min oscillations. We investigate the experimental phenomenon of oscillation stuttering, which we relate to the disruption of MinE tip-binding at the filament scale.
Multiple Bifurcations in a Polynomial Model of Bursting Oscillations
NASA Astrophysics Data System (ADS)
de Vries, G.
1998-06-01
Bursting oscillations are commonly seen to be the primary mode of electrical behaviour in a variety of nerve and endocrine cells, and have also been observed in some biochemical and chemical systems. There are many models of bursting. This paper addresses the issue of being able to predict the type of bursting oscillation that can be produced by a model. A simplified model capable of exhibiting a wide variety of bursting oscillations is examined. By considering the codimension-2 bifurcations associated with Hopf, homoclinic, and saddle-node of periodics bifurcations, a bifurcation map in two-dimensional parameter space is created. Each region on the map is characterized by a qualitatively distinct bifurcation diagram and, hence, represents one type of bursting oscillation. The map elucidates the relationship between the various types of bursting oscillations. In addition, the map provides a different and broader view of the current classification scheme of bursting oscillations.
Farner, Snorre; Vergez, Christophe; Kergomard, Jean; Lizée, Aude
2006-03-01
The harmonic balance method (HBM) was originally developed for finding periodic solutions of electronical and mechanical systems under a periodic force, but has been adapted to self-sustained musical instruments. Unlike time-domain methods, this frequency-domain method does not capture transients and so is not adapted for sound synthesis. However, its independence of time makes it very useful for studying any periodic solution, whether stable or unstable, without care of particular initial conditions in time. A computer program for solving general problems involving nonlinearly coupled exciter and resonator, HARMBAL, has been developed based on the HBM. The method as well as convergence improvements and continuation facilities are thoroughly presented and discussed in the present paper. Applications of the method are demonstrated, especially on problems with severe difficulties of convergence: the Helmholtz motion (square signals) of single-reed instruments when no losses are taken into account, the reed being modeled as a simple spring.
Oscillator-interference models of path integration do not require theta oscillations.
Orchard, Jeff
2015-03-01
Navigation and path integration in rodents seems to involve place cells, grid cells, and theta oscillations (4-12 Hz) in the local field potential. Two main theories have been proposed to explain the neurological underpinnings of how these phenomena relate to navigation and to each other. Attractor network (AN) models revolve around the idea that local excitation and long-range inhibition connectivity can spontaneously generate grid-cell-like activity patterns. Oscillator interference (OI) models propose that spatial patterns of activity are caused by the interference patterns between neural oscillators. In rats, these oscillators have a frequency close to the theta frequency. Recent studies have shown that bats do not exhibit a theta cycle when they crawl, and yet they still have grid cells. This has been interpreted as a criticism of OI models. However, OI models do not require theta oscillations. We explain why the absence of theta oscillations does not contradict OI models and discuss how the two families of models might be distinguished experimentally.
An electric-field representation of the harmonic XY model
NASA Astrophysics Data System (ADS)
Faulkner, Michael F.; Bramwell, Steven T.; Holdsworth, Peter C. W.
2017-03-01
The two-dimensional harmonic XY (HXY) model is a spin model in which the classical spins interact via a piecewise parabolic potential. We argue that the HXY model should be regarded as the canonical classical lattice spin model of phase fluctuations in two-dimensional condensates, as it is the simplest model that guarantees the modular symmetry of the experimental systems. Here we formulate a lattice electric-field representation of the HXY model and contrast this with an analogous representation of the Villain model and the two-dimensional Coulomb gas with a purely rotational auxiliary field. We find that the HXY model is a spin-model analogue of a lattice electric-field model of the Coulomb gas with an auxiliary field, but with a temperature-dependent vacuum (electric) permittivity that encodes the coupling of the spin vortices to their background spin-wave medium. The spin vortices map to the Coulomb charges, while the spin-wave fluctuations correspond to auxiliary-field fluctuations. The coupling explains the striking differences in the high-temperature asymptotes of the specific heats of the HXY model and the Coulomb gas with an auxiliary field. Our results elucidate the propagation of effective long-range interactions throughout the HXY model (whose interactions are purely local) by the lattice electric fields. They also imply that global spin-twist excitations (topological-sector fluctuations) generated by local spin dynamics are ergodically excluded in the low-temperature phase. We discuss the relevance of these results to condensate physics.
Investigation of self-oscillation using particle balance model
Bae, Inshik; Na, Byungkeun Chang, Hongyoung
2015-08-15
Self-oscillation obtained using a DC-only power supply under specific anode voltage conditions is investigated in a cylindrical system with thermal electrons using tungsten filaments. Analysis of the obtained oscillation profiles reveals that the experimental data are consistent with a model derived from the particle balance model. The self-oscillation period characteristics with respect to the pressure and gas species are also analyzed. As the physics and particle motion of self-oscillation near the plasma transition region are analyzed from different perspectives, this paper may advance the study of this phenomenon.
Modeling and analysis of aircraft non-linear components for harmonics analysis
Karimi, K.J.; Voss, J.
1995-12-31
Modern commercial aircraft Electric Power Systems (EPS) include many nonlinear components which produce harmonics. The addition of all the current harmonics could result in a power system with unacceptable levels of voltage distortion. It is important to be able to predict the levels of voltage distortion at early program stages to correct any potential problems and avoid costly redesigns. In this paper the nature and sources of harmonic producing equipment are described. These sources of harmonics and their effect on aircraft power system operation are described. Models for various aircraft non-linear components are developed in this paper. These component models are used in a model of the Boeing 777 EPS which is used to calculate voltage harmonics for various airplane configurations and flight conditions. A description of this model and the models used for various components are given. Tests performed to validate these models are described. Comparison of experimental results with analytical model predictions are given.
Analytical modelling and x-ray imaging of oscillations of a single magnetic domain wall
Bocklage, Lars; Kruger, Benjamin; Fischer, Peter; Meier, Guido
2009-07-10
Domain-wall oscillation in a pinnig potential is described analytically in a one dimensional model for the feld-driven case. For a proper description the pinning potential has to be extended by nonharmonic contributions. Oscillations of a domain wall are observed on its genuine time scale by magnetic X-ray microscopy. It is shown that the nonharmonic terms are present in real samples with a strong restoring potential. In the framework of our model we gain deep insight into the domain-wall motion by looking at different phase spaces. The corrections of the harmonic potential can change the motion of the domain wall significantly. The damping parameter of permalloy is determined via the direct imaging technique.
A three-pulse model of d. c. side harmonic flow in HVDC systems
Shore, N.L.; Andersson, G.; Canelhas, A.P.; Asplund, G.
1989-07-01
A new model for analysis of d.c. side harmonics in HVDC systems is proposed. The model includes the stray capacitances of converter transformers and bushings and represents the 12-pulse converter as four three-pulse harmonic voltage sources. The appearance of ground mode triplen harmonics of troublesome magnitude in pole and electrode lines, as noted in recent site measurements, is explained, as is the increase in magnitude of the characteristic 12-pulse harmonics. The consequences for d.c. filter design and the specification of telephone interference criteria are also discussed.
Harmonizing Social and Environmental Dynamics in Earth Systems Modeling
NASA Astrophysics Data System (ADS)
Evans, T. P.; Estes, L. D.; Caylor, K. K.; McCord, P. F.; Gower, D.; Konar, M.; Baylis, K.; Waldman, K.; Blekking, J.; Schlachter, T.
2016-12-01
The promotion of the Anthropocene has led to new awareness of the role of complex natural-human interactions in environmental change processes. This includes efforts to find causal relationships in empirical studies as well as science to understand how best to incorporate both human and environmental dynamics in models of earth systems spanning fine scale forest ecology models to GCMs. This presentation will discuss challenges and opportunities in integrating social and environmental dynamics in models and recent advances in coupled natural-human systems modeling. The core of this presentation will focus on whether it is possible to harmonize social and environmental dynamics by considering disparities in spatial scale, spatial extent, temporal scale and temporal extent. In the process this presentation will address fundamental questions such as whether social data necessarily entail greater uncertainty than environmental data and the implications for data uncertainty and model design as they relate to the ability to make forecasts and predictions from coupled natural-human systems models. It is imperative that social scientists and environmental scientists collaborate in the development of the data and models needed to understand how environmental systems may change in the future and how human decisions result in or avert environmental degradation. This presentation will argue that the limitations do not lie with data constraints or computational constraints but rather in the tendency for models to be developed without addressing the criticality of environmental vs. social dynamics. This can lead to the somewhat tired conclusion that social scientists and environmental scientists need to collaborate more… But this has been recognized for the last 20-30 years (and arguably longer…). But this is an unsatisfying conclusion. Thus this presentation will discuss new developments in data resources and computational infrastructure that raise the potential for new
Finite element modeling of the higher harmonic controlled OH-6A helicopter airframe
NASA Technical Reports Server (NTRS)
Ferg, Douglas; Toossi, Mostafa
1990-01-01
An MSC/NASTRAN finite element model of the higher harmonic control configured OH-6A helicopter fuselage was developed. This finite element model was verified by performing various model checkouts and correlation with results from a ground vibration test.
Phase computations and phase models for discrete molecular oscillators
2012-01-01
Background Biochemical oscillators perform crucial functions in cells, e.g., they set up circadian clocks. The dynamical behavior of oscillators is best described and analyzed in terms of the scalar quantity, phase. A rigorous and useful definition for phase is based on the so-called isochrons of oscillators. Phase computation techniques for continuous oscillators that are based on isochrons have been used for characterizing the behavior of various types of oscillators under the influence of perturbations such as noise. Results In this article, we extend the applicability of these phase computation methods to biochemical oscillators as discrete molecular systems, upon the information obtained from a continuous-state approximation of such oscillators. In particular, we describe techniques for computing the instantaneous phase of discrete, molecular oscillators for stochastic simulation algorithm generated sample paths. We comment on the accuracies and derive certain measures for assessing the feasibilities of the proposed phase computation methods. Phase computation experiments on the sample paths of well-known biological oscillators validate our analyses. Conclusions The impact of noise that arises from the discrete and random nature of the mechanisms that make up molecular oscillators can be characterized based on the phase computation techniques proposed in this article. The concept of isochrons is the natural choice upon which the phase notion of oscillators can be founded. The isochron-theoretic phase computation methods that we propose can be applied to discrete molecular oscillators of any dimension, provided that the oscillatory behavior observed in discrete-state does not vanish in a continuous-state approximation. Analysis of the full versatility of phase noise phenomena in molecular oscillators will be possible if a proper phase model theory is developed, without resorting to such approximations. PMID:22687330
TDH solution of the Suzuki model of nuclear monopole oscillation
NASA Astrophysics Data System (ADS)
Skalski, J.
1987-09-01
The exact time-dependent Hartree solution of the schematic model describing nuclear monopole oscillation — the Suzuki model — is presented. The energies of vibrational states are quantized according to the gauge-invariant periodic quantization prescription.
Ingold, Kirk A; Marandi, Alireza; Digonnet, Michel J F; Byer, Robert L
2015-09-15
We demonstrate a femtosecond fiber-feedback optical parametric oscillator (OPO) at degeneracy. The OPO cavity comprises an 80-cm-long fiber composed of a combination of normal and anomalous dispersion sections that provide a net intracavity group delay dispersion close to zero. By using a mode-locked, Yb-doped fiber laser as the pump, we achieved half-harmonic generation of 250-MHz, 1.2-nJ nearly transform-limited 97-fs pulses centered at 2090 nm with a total conversion efficiency of 36%.
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.
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.
Simakov, David S. A.; Pérez-Mercader, Juan
2013-01-01
Oscillating chemical reactions are common in biological systems and they also occur in artificial non-biological systems. Generally, these reactions are subject to random fluctuations in environmental conditions which translate into fluctuations in the values of physical variables, for example, temperature. We formulate a mathematical model for a nonisothermal minimal chemical oscillator containing a single negative feedback loop and study numerically the effects of stochastic fluctuations in temperature in the absence of any deterministic limit cycle or periodic forcing. We show that noise in temperature can induce sustained limit cycle oscillations with a relatively narrow frequency distribution and some characteristic frequency. These properties differ significantly depending on the noise correlation. Here, we have explored white and colored (correlated) noise. A plot of the characteristic frequency of the noise induced oscillations as a function of the correlation exponent shows a maximum, therefore indicating the existence of autonomous stochastic resonance, i.e. coherence resonance. PMID:23929212
The analysis of solar models: Neutrinos and oscillations
NASA Technical Reports Server (NTRS)
Ulrich, R. K.; Rhodes, E. J., Jr.; Tomczyk, S.; Dumont, P. J.; Brunish, W. M.
1983-01-01
Tests of solar neutrino flux and solar oscillation frequencies were used to assess standard stellar structure theory. Standard and non-standard solar models are enumerated and discussed. The field of solar seismology, wherein the solar interior is studied from the measurement of solar oscillations, is introduced.
Development of Motor Model of Rotor Slot Harmonics for Speed Sensorless Control of Induction Motor
NASA Astrophysics Data System (ADS)
Okubo, Tatsuya; Ishida, Muneaki; Doki, Shinji
This paper proposes a novel mathematical dynamic model to represent steady-state and transient-state characteristics of rotor slot harmonics of an induction motor for sensorless control. Although it is well known that the rotor slot harmonics originate from the mechanical structure of the induction motor, a mathematical model that describes the relationship between stator/rotor currents of the induction motor and the slot harmonics has not yet been proposed. Therefore, in this paper, a three-phase model of the induction motor that depicts the rotor slot harmonics is developed by taking into consideration the magnetomotive force harmonics and the change in the magnetic air gap caused by the rotor slots. Moreover, the validity of the proposed model is verified by comparing the experimental results and the calculated values.
NASA Astrophysics Data System (ADS)
Beléndez, A.; Fernández, E.; Rodes, J. J.; Fuentes, R.; Pascual, I.
2009-11-01
In a previous short communication [A. Beléndez, E. Fernández, J.J. Rodes, R. Fuentes, I. Pascual, Phys. Lett. A 373 (2009) 735] the nonlinear oscillations of a punctual charge in the electric field of a charged ring were analyzed. Approximate frequency-amplitude relations and periodic solutions were obtained using the harmonic balance method. Now we clarify an important aspect about of this oscillation charge. Taking into account Earnshaw's theorem, this punctual charge cannot be a free charge and so it must be confined, for example, on a finite conducting wire placed along the axis of the ring. Then, the oscillatory system may consist of a punctual charge on a conducting wire placed along the axis of the uniformly charged ring.
Third Harmonic Mechanism in Complex Plasmonic Fano Structures.
Metzger, Bernd; Schumacher, Thorsten; Hentschel, Mario; Lippitz, Markus; Giessen, Harald
2014-06-18
We perform third harmonic spectroscopy of dolmen-type nanostructures, which exhibit plasmonic Fano resonances in the near-infrared. Strong third harmonic emission is predominantly radiated close to the low energy peak of the Fano resonance. Furthermore, we find that the third harmonic polarization of the subradiant mode interferes destructively and diminishes the nonlinear signal in the far-field. By comparing the experimental third harmonic spectra with finite element simulations and an anharmonic oscillator model, we find strong indications that the source of the third harmonic is the optical nonlinearity of the bare gold enhanced by the resonant plasmonic polarization.
Bierbach, Jana; Yeung, Mark; Eckner, Erich; Roedel, Christian; Kuschel, Stephan; Zepf, Matt; Paulus, Gerhard G.
2015-05-01
Surface high-harmonic generation in the relativistic regime is demonstrated as a source of extreme ultra-violet (XUV) pulses with extended operation time. Relativistic high-harmonic generation is driven by a frequency-doubled high-power Ti:Sapphire laser focused to a peak intensity of 3·1019 W/cm2 onto spooling tapes. We demonstrate continuous operation over up to one hour runtime at a repetition rate of 1 Hz. Harmonic spectra ranging from 20 eV to 70 eV (62 nm to 18 nm) were consecutively recorded by an XUV spectrometer. An average XUV pulse energy in the µJ range is measured. With the presented setup, relativistic surface high-harmonic generation becomes a powerful source of coherent XUV pulses that might enable applications in, e.g. attosecond laser physics and the seeding of free-electron lasers, when the laser issues causing 80-% pulse energy fluctuations are overcome.
Oscillation valence electron model of superconducting cuprates
NASA Astrophysics Data System (ADS)
Netesova, Nadezhda P.
2017-03-01
For the first time, Neel, the winner of the Nobel Prize, has applied sublattice theory to explain the magnetism of multicomponent systems. Within the bioscillation electron model a superconducting phase transition in the crystal AB is accomplished by break valence ties, the formation of paired electrons or molecule sublattices of A2 and B2: 2AB=A2+B2. Energy Φ balance equations are 2Φ2[AB]≤Φ2[A2]+Φ2[B2], Φ2[AB]≤Φ2[A2], Φ2[AB]≤Φ2[B2]. The mechanism of the superconducting phase transition in the yttrium-barium YBaCuO or other cuprates under poly oscillation electron model is examined. In the first stage there are formed yttrium, barium (or other elements) and copper oxides, in the second stage the oxides are dissociated. The molecules are formed, provided that the atom association energy is more gap energy of valence bonds in oxides. Calculations of quadratic energies for the oxides and cuprates to room temperature and 90K are performed. To superconducting phase transition has been occurred, the quadratic energy must be greater than the criterion. The cuprate with a stoichiometric composition is not a superconductor according to experimental data. The balance equations at 90K are consistent with the experimental data 406.4256*2 - (328.482+400.6432) = 83.726 eV2. The total quadratic energy required for education Y2 and Ba2 molecules is equal to 812.8512 eV2. Cuprates with the introduction of additional oxygen typeYBa2Cu3O6.5 + 0.5 are superconductors. The energies of the valence bonds are reduced the introduction of oxygen above stoichiometric values by expanding crystal lattice.
Modeling the entrainment of self-oscillating gels to periodic mechanical deformation
NASA Astrophysics Data System (ADS)
Yashin, Victor V.; Levitan, Steven P.; Balazs, Anna C.
2015-06-01
Polymer gels undergoing the oscillatory Belousov-Zhabotinsky (BZ) reaction are one of the few synthetic materials that exhibit biomimetic mechano-chemical transduction, converting mechanical input into chemical energy. Here, we consider self-oscillating BZ gels that are subjected to periodic mechanical forcing, and model the entrainment of the oscillatory gel dynamics to this external stimulus. The gel size is assumed to be sufficiently small that the chemo-mechanical oscillations are spatially uniform. The behavior of the system is captured by equations describing the kinetics of the oscillatory BZ reaction in the gel coupled to equations for the variations in gel size due to the inherent reaction and imposed force. We employ the phase dynamics approach for analyzing the entrainment of the BZ gel to force- and strain-controlled compressive deformations. The phase response curves are obtained using Malkin's method, and time-averaging is applied to extract the slow phase dynamics caused by the periodic forcing. We demonstrate that the entrainment of the self-oscillating BZ gel is sensitive to the chemo-mechanical coupling in gel, the mode of deformation, and the level of static compression. Kuramoto's model of phase oscillators is shown to be applicable if the external forcing is purely harmonic.
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.
Transonic limit cycle oscillation analysis using reduced order aerodynamic models
NASA Astrophysics Data System (ADS)
Dowell, E. H.; Thomas, J. P.; Hall, K. C.
2004-01-01
Limit cycle oscillations have been observed in flight operations of modern aircraft, wind tunnel experiments and mathematical models. Both fluid and structural nonlinearities are thought to contribute to these phenomena. With recent advances in reduced order aerodynamic modeling, it is now feasible to analyze limit cycle oscillations that may occur in transonic flow including the effects of structural and fluid nonlinearities. In this paper an airfoil with control surface freeplay (a common structural nonlinearity) is used to investigate transonic flutter and limit cycle oscillations. The reduced order aerodynamic model used in this paper assumes the shock motion is small and in proportion to the structural motions.
Simple model for temperature control of glycolytic oscillations
NASA Astrophysics Data System (ADS)
Postnikov, E. B.; Verveyko, D. V.; Verisokin, A. Yu.
2011-06-01
We introduce the temperature-dependent autocatalytic coefficient into the Merkin-Needham-Scott version of the Selkov system and consider the resulting equations as a model for temperature-controlled, self-sustained glycolytic oscillations in a closed reactor. It has been shown that this simple model reproduces key features observed in the experiments with temperature growth: (i) exponentially decreasing period of oscillations; (ii) reversal of relative duration leading and tail fronts. The applied model also reproduces the modulations of oscillations induced by the periodic temperature change.
Emergence of coherent oscillations in stochastic models for circadian rhythms
NASA Astrophysics Data System (ADS)
Gonze, Didier; Halloy, José; Goldbeter, Albert
2004-10-01
Most living organisms have developed the capability of generating autonomously sustained oscillations with a period close to 24 h. The mechanism responsible for these circadian rhythms relies on the negative regulation exerted by a protein on the expression of its own gene. Deterministic models for circadian rhythms account for the occurrence of autonomous oscillations of the limit cycle type, for their entrainment by light-dark cycles, and for their phase shifting by light pulses. Such models, however, do not take into consideration the molecular fluctuations which arise when the number of molecules involved in the regulatory mechanism is low. Here we resort to a stochastic description of a core model for circadian rhythms to study the emergence of coherent oscillations in gene expression in the presence of molecular noise. We show that despite the “bar code” pattern of gene activation, robust circadian oscillations can be observed. Simulations of the deterministic, fully developed version of the circadian model indicate, however, that sustained oscillations only emerge above a critical value of the rate constants characterizing the reversible binding of repressor to the gene, while below this value the system evolves towards an excitable steady state. This explains why, depending on whether or not the critical value of these rate constants is exceeded, stochastic simulations of the model produce coherent oscillations or very noisy oscillations with a highly variable period.
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.
Modeling Wave Driven Non-linear Flow Oscillations: The Terrestrial QBO and a Solar Analog
NASA Technical Reports Server (NTRS)
Mayr, Hans G.; Bhartia, P. K. (Technical Monitor)
2001-01-01
The Quasi Biennial Oscillation (QBO) of the zonal circulation observed in the terrestrial atmosphere at low latitudes is driven by wave mean flow interaction as was demonstrated first by Lindzen and Holton (1968), shown in a laboratory experiment by Plumb and McEwan (1978), and modeled by others (e.g., Plumb, Dunkerton). Although influenced by the seasonal cycle of solar forcing, the QBO, in principle, represents a nonlinear flow oscillation that can be maintained by a steady source of upward propagating waves. The wave driven non-linearity is of third or odd order in the flow velocity, which regenerates the fundamental harmonic itself to keep the oscillation going - the fluid dynamical analog of the displacement mechanism in the mechanical clock. Applying Hines' Doppler Spread Parameterization (DSP) for gravity waves (GW), we discuss with a global-scale spectral model numerical experiments that elucidate some properties of the QBO and its possible effects on the climatology of the atmosphere. Depending on the period of the QBO, wave filtering can cause interaction with the seasonal variations to produce pronounced oscillations with beat periods around 10 years. Since the seasonal cycle and its variability influence the period of the QBO, it may also be a potent conduit of solar activity variations to lower altitudes. Analogous to the terrestrial QBO, we propose that a flow oscillation may account for the 22-year periodicity of the solar magnetic cycle, potentially answering Dicke (1978) who asked, "Is there a chronometer hidden deep inside the Sun?" The oscillation would occur below the convection region, where gravity waves can propagate. Employing a simplified, analytic model, Hines' DSP is applied to estimate the flow oscillation. Depending on the adopted horizontal wavelengths of GW's, wave amplitudes less than 10 m/s can be made to produce oscillating zonal flows of about 20 m/s that should be large enough to generate a significant oscillation in the magnetic
Modeling Wave Driven Non-linear Flow Oscillations: The Terrestrial QBO and a Solar Analog
NASA Technical Reports Server (NTRS)
Mayr, Hans G.; Bhartia, P. K. (Technical Monitor)
2001-01-01
The Quasi Biennial Oscillation (QBO) of the zonal circulation observed in the terrestrial atmosphere at low latitudes is driven by wave mean flow interaction as was demonstrated first by Lindzen and Holton (1968), shown in a laboratory experiment by Plumb and McEwan (1978), and modeled by others (e.g., Plumb, Dunkerton). Although influenced by the seasonal cycle of solar forcing, the QBO, in principle, represents a nonlinear flow oscillation that can be maintained by a steady source of upward propagating waves. The wave driven non-linearity is of third or odd order in the flow velocity, which regenerates the fundamental harmonic itself to keep the oscillation going - the fluid dynamical analog of the displacement mechanism in the mechanical clock. Applying Hines' Doppler Spread Parameterization (DSP) for gravity waves (GW), we discuss with a global-scale spectral model numerical experiments that elucidate some properties of the QBO and its possible effects on the climatology of the atmosphere. Depending on the period of the QBO, wave filtering can cause interaction with the seasonal variations to produce pronounced oscillations with beat periods around 10 years. Since the seasonal cycle and its variability influence the period of the QBO, it may also be a potent conduit of solar activity variations to lower altitudes. Analogous to the terrestrial QBO, we propose that a flow oscillation may account for the 22-year periodicity of the solar magnetic cycle, potentially answering Dicke (1978) who asked, "Is there a chronometer hidden deep inside the Sun?" The oscillation would occur below the convection region, where gravity waves can propagate. Employing a simplified, analytic model, Hines' DSP is applied to estimate the flow oscillation. Depending on the adopted horizontal wavelengths of GW's, wave amplitudes less than 10 m/s can be made to produce oscillating zonal flows of about 20 m/s that should be large enough to generate a significant oscillation in the magnetic
Excitable Oscillators as Models for Central Pattern Generators
NASA Astrophysics Data System (ADS)
Taylor, David; Holmes, Philip; Cohen, Avis H.
Chains of coupled oscillators have been used to model the central pattern generator for locomotion in lamprey1,2,3, as well as electrical waves in the mammalian small intestine4. In this paper we examine a variation on the equations for the coupled oscillators used in a number of these papers. In particular, we investigate the effect of modeling the uncoupled oscillators as excitable. The motivation behind this is that it may provide some insight into the electrical activity of the lamprey spinal cord with brainstem attached5
An Intracellular Calcium Oscillations Model Including Mitochondrial Calcium Cycling
NASA Astrophysics Data System (ADS)
Shi, Xiao-Min; Liu, Zeng-Rong
2005-12-01
Calcium is a ubiquitous second messenger. Mitochondria contributes significantly to intracellular Ca2+ dynamics. The experiment of Kaftan et al. [J. Biol. Chem. 275(2000) 25465] demonstrated that inhibiting mitochondrial Ca2+ uptake can reduce the frequency of cytosolic Ca2+ concentration oscillations of gonadotropes. By considering the mitochondrial Ca2+ cycling we develop a three-variable model of intracellular Ca2+ oscillations based on the models of Atri et al. [Biophys. J. 65 (1993) 1727] and Falcke et al. [Biophys. J. 77 (1999) 37]. The model reproduces the fact that mitochondrial Ca2+ cycling increases the frequency of cytosolic Ca2+ oscillations, which accords with Kaftan's results. Moreover the model predicts that when the mitochondria overload with Ca2+, the cytosolic Ca2+ oscillations vanish, which may trigger apoptosis.
Bennett, Charles L.; Sewall, Noel; Boroa, Carl
2014-08-19
An engine based on a reciprocating piston engine that extracts work from pressurized working fluid. The engine includes a harmonic oscillator inlet valve capable of oscillating at a resonant frequency for controlling the flow of working fluid into of the engine. In particular, the inlet valve includes an inlet valve head and a spring arranged together as a harmonic oscillator so that the inlet valve head is moveable from an unbiased equilibrium position to a biased closed position occluding an inlet. Upon releasing the inlet valve the inlet valve head undergoes a single oscillation past the equilibrium positio to a maximum open position and returns to a biased return position close to the closed position to choke the flow and produce a pressure drop across the inlet valve causing the inlet valve to close. Protrusions carried either by the inlet valve head or piston head are used to bump open the inlet valve from the closed position and initiate the single oscillation of the inlet valve head, and protrusions carried either by the outlet valve head or piston head are used to close the outlet valve ahead of the bump opening of the inlet valve.
Oscillating Quintom Model with Time Periodic Varying Deceleration Parameter
NASA Astrophysics Data System (ADS)
Shen, Ming; Zhao, Liang
2014-01-01
We propose a new law for the deceleration parameter that varies periodically with time. According to the law, we give a model of the oscillating universe with quintom matter in the framework of a 4-dimensional Friedmann—Robertson—Walker background. We find that, in the model, the Hubble parameter oscillates and keeps positive. The universe undergoes decelerating expansion and accelerating expansion alternately without singularity
Evaluation of Turbulence Models for Unsteady Flows of an Oscillating Airfoil
NASA Technical Reports Server (NTRS)
Srinivasan, G. R.; Ekaterinaris, J. A.; McCroskey, W. J.
1995-01-01
Unsteady flowfields of a two-dimensional oscillating airfoil are calculated using an implicit, finite-difference, Navier Stokes numerical scheme. Five widely used turbulence models are used with the numerical scheme to assess the accuracy and suitability of the models for simulating the retreating blade stall of helicopter rotor in forward flight. Three unsteady flow conditions corresponding to an essentially attached flow, light-stall, and deep-stall cases of an oscillating NACA 0015 wing experiment were chosen as test cases for computations. Results of unsteady airloads hysteresis curves, harmonics of unsteady pressures, and instantaneous flowfield patterns are presented. Some effects of grid density, time-step size, and numerical dissipation on the unsteady solutions relevant to the evaluation of turbulence models are examined. Comparison of unsteady airloads with experimental data show that all models tested are deficient in some sense and no single model predicts airloads consistently and in agreement with experiment for the three flow regimes. The chief findings are that the simple algebraic model based on the renormalization group theory (RNG) offers some improvement over the Baldwin Lomax model in all flow regimes with nearly same computational cost. The one-equation models provide significant improvement over the algebraic and the half-equation models but have their own limitations. The Baldwin-Barth model overpredicts separation and underpredicts reattachment. In contrast, the Spalart-Allmaras model underpredicts separation and overpredicts reattachment.
Nonlinear propagation in ultrasonic fields: measurements, modelling and harmonic imaging.
Humphrey, V F
2000-03-01
In high amplitude ultrasonic fields, such as those used in medical ultrasound, nonlinear propagation can result in waveform distortion and the generation of harmonics of the initial frequency. In the nearfield of a transducer this process is complicated by diffraction effects associated with the source. The results of a programme to study the nonlinear propagation in the fields of circular, focused and rectangular transducers are described, and comparisons made with numerical predictions obtained using a finite difference solution to the Khokhlov-Zabolotskaya-Kuznetsov (or KZK) equation. These results are extended to consider nonlinear propagation in tissue-like media and the implications for ultrasonic measurements and ultrasonic heating are discussed. The narrower beamwidths and reduced side-lobe levels of the harmonic beams are illustrated and the use of harmonics to form diagnostic images with improved resolution is described.
Bennett, Charles L [Livermore, CA
2009-10-20
A high efficiency harmonic engine based on a resonantly reciprocating piston expander that extracts work from heat and pressurizes working fluid in a reciprocating piston compressor. The engine preferably includes harmonic oscillator valves capable of oscillating at a resonant frequency for controlling the flow of working fluid into and out of the expander, and also preferably includes a shunt line connecting an expansion chamber of the expander to a buffer chamber of the expander for minimizing pressure variations in the fluidic circuit of the engine. The engine is especially designed to operate with very high temperature input to the expander and very low temperature input to the compressor, to produce very high thermal conversion efficiency.
Modelling of photo-thermal control of biological cellular oscillators.
Assanov, Gani S; Zhanabaev, Zeinulla Zh; Govorov, Alexander O; Neiman, Alexander B
2013-10-01
We study the transient dynamics of biological oscillators subjected to brief heat pulses. A prospective well-defined experimental system for thermal control of oscillators is the peripheral electroreceptors in paddlefish. Epithelial cells in these receptors show spontaneous voltage oscillations which are known to be temperature sensitive. We use a computational model to predict the effect of brief thermal pulses in this system. In our model thermal stimulation is realized through the light excitation of gold nanoparticles delivered in close proximity to epithelial cells and generating heat due to plasmon resonance. We use an ensemble of modified Morris-Lecar systems to model oscillatory epithelial cells. First, we validate that the model quantitatively reproduces the dynamics of epithelial oscillations in paddlefish electroreceptors, including responses to static and slow temperature changes. Second, we use the model to predict transient responses to short heat pulses generated by the light actuated gold nanoparticles. The model predicts that the epithelial oscillators can be partially synchronized by brief 5 - 15 ms light stimuli resulting in a large-amplitude oscillations of the mean field potential.