Design of a second cyclotron harmonic gyrotron oscillator with photonic band-gap cavity
Liu Gaofeng; Chen Xiaoan; Tang Changjian, E-mail: angelchen765@163.com [College of Physical Science and Technology of Sichuan University, Chengdu 610065 (China)
2011-07-27
A photonic band-gap cavity (PBGC) gyrotron with a frequency of about 98 GHz is designed. Theoretical analyses and numerical calculations are made for the PBGC operating at fundamental and second cyclotron harmonic with a TE{sub 34} waveguide mode to demonstrate the beam-wave interaction. The results show that mode competition is successfully eliminated in the PBGC using mode selectivity and choosing the appropriate operating parameters. As a result, the second harmonic PBGC gyrotron operating at TE{sub 34} mode achieves a higher output efficiency than that of the fundamental. It is also demonstrated that, in the case of the chosen parameters for TE{sub 34} waveguide mode, the use of PBG structure in the second harmonic gyrotron brings about not only a lower operating B-field but also a weaker mode competition. The results show that the high-order electromagnetic mode can be developed to interact with the high cyclotron harmonic using the selectivity of the PBGC, which gives an encouraging outlook for the development of high-harmonic gyrotrons.
High harmonic terahertz confocal gyrotron with nonuniform electron beam
Fu, Wenjie; Guan, Xiaotong; Yan, Yang [THz Research Center, School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054 (China)
2016-01-15
The harmonic confocal gyrotron with nonuniform electron beam is proposed in this paper in order to develop compact and high power terahertz radiation source. A 0.56 THz third harmonic confocal gyrotron with a dual arc section nonuniform electron beam has been designed and investigated. The studies show that confocal cavity has extremely low mode density, and has great advantage to operate at high harmonic. Nonuniform electron beam is an approach to improve output power and interaction efficiency of confocal gyrotron. A dual arc beam magnetron injection gun for designed confocal gyrotron has been developed and presented in this paper.
Gyrotron oscillators for fusion heating
Jory, H.; Evans, S.; Felch, K.; Shively, J.; Spang, S.
1982-01-01
Recent experiments have been performed to determine the ultimate power capability of a 28 GHz 200 kW CW gyrotron design. A power output of 342 kW CW was measured in these tests with an efficiency of 37%. Progress in the development of 60 GHz 200 kW pulsed and CW gyrotrons is discussed. An output of 200 kW with 100 msec pulse length has been achieved with the pulsed design.
Covariant harmonic oscillators and coupled harmonic oscillators
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.
Khutoryan, Eduard M.; Idehara, Toshitaka; Melnikova, Maria M.; Ryskin, Nikita M.; Dumbrajs, Olgierd
2017-07-01
Effect of delayed reflection on operation of a second-harmonic terahertz (THz)-band gyrotron is studied. Theoretical analyses, numerical calculations, and experimental observations for the 0.394-THz Fukui University (FU) and continuous wave (CW) IIB gyrotron are presented. The reflections decrease starting current and expand frequency tunability range owing to excitation of high-order axial modes. They also increase frequency stability, i.e., reduce frequency change due to variation of the magnetic field. In addition, the reflections strongly affect mode competition causing suppress of the second-harmonic mode by the fundamental one and vice versa or, in the case of cooperative mode interaction, mutual power increase.
Observation of harmonic gyro-backward-wave oscillation in a 100 GHz CARM oscillator experiment
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.
On The Harmonic Oscillator Group
Lopez, Raquel M; Vega-Guzman, Jose M
2011-01-01
We discuss the maximum kinematical invariance group of the quantum harmonic oscillator from a view point of the Ermakov-type system. The invariance group of generalized driven harmonic oscillator is shown to be isomorphic to the corresponding Schroedinger group of the free particle.
Design of an electronically tunable millimeter wave Gyrotron Backward Wave Oscillator
Caplan, M.
1987-01-01
A non-linear self-consistent computer simulation code is used to analyze the saturated output of the Gyrotron Backward Wave Oscillator (Gyro BWO) which can be used as a tunable driver for a 250 GHz FEL amplifier. Simulations show that the Gyrotron BWO using a Pierce/Wiggler gun configuration can produce at least 10 kW of microwave power over the range 249 GHz to 265 GHz by varying beam voltage alone.
Design of an electronically tunable millimeter wave Gyrotron Backward Wave Oscillator
Caplan, M.
1987-01-01
A non-linear self-consistent computer simulation code is used to analyze the saturated output of the Gyrotron Backward Wave Oscillator (Gyro BWO) which can be used as a tunable driver for a 250 GHz FEL amplifier. Simulations show that the Gyrotron BWO using a Pierce/Wiggler gun configuration can produce at least 10 kW of microwave power over the range 249 GHz to 265 GHz by varying beam voltage alone.
Long-Term Operating Experience with High-Power Gyrotron Oscillators
Felch, Kevin
2005-10-01
High-power, megawatt-class gyrotron oscillators have now been used in electron cyclotron heating (ECH) experiments for several years. The long periods of sustained operation have provided important information about the design limits that had initially been placed on the key elements of the gyrotron. In particular, observations made on recent 110 GHz, 1 MW gyrotrons used in ECH experiments on DIII-D at General Atomics indicate that several of the important components of the device, including the electron guns, interaction cavities and diamond output windows, have performed quite well, while analyses of the electron beam collectors on some of the devices indicate that design limits have often been exceeded. Observations made on these gyrotrons will be summarized and plans to address problem areas will be discussed.
Study on the Before Cavity Interaction in a Second Harmonic Gyrotron Using 3D CFDTD PIC Simulations
Lin, M. C.; Illy, S.; Thumm, M.; Jelonnek, J.
2016-10-01
A computational study on before cavity interaction (BCI) in a 28 GHz second harmonic (SH) gryotron for industrial applications has been performed using a 3-D conformal finite-difference time-domain (CFDTD) particle-in-cell (PIC) method. On the contrary to the after cavity interaction (ACI), i.e. beam wave interaction in the non-linear uptaper after the cavity, which has been widely investigated, the BCI, i.e. beam wave interaction in the non-linear downtaper before the cavity connected to the beam tunnel with an entrance, is less noticed and discussed. Usually the BCI might be considered easy to be eliminated. However, this is not always the case. As the SH gyrotron had been designed for SH TE12 mode operation, the first harmonic (FH) plays the main competition. In the 3-D CFDTD PIC simulations, a port boundary has been employed for the gyro-beam entrance of the gyrotron cavity instead of a metallic short one which is not reflecting a realistic situation as an FH backward wave oscillation (BWO) is competing with the desired SH generation. A numerical instability has been found and identified as a failure of the entrance port boundary caused by an evanescent wave or mode conversion. This indicates the entrance and downtaper are not fully cut-off for some oscillations. A further study shows that the undesired oscillation is the FH TE11 BWO mode concentrated around the beam tunnel entrance and downtaper. A mitigation strategy has been found to suppress this undesired BCI and avoid possible damage to the gun region.
A 0.33-THz second-harmonic frequency-tunable gyrotron
Zheng-Di, Li; Chao-Hai, Du; Xiang-Bo, Qi; Li, Luo; Pu-Kun, Liu
2016-02-01
Dynamics of the axial mode transition process in a 0.33-THz second-harmonic gyrotron is investigated to reveal the physical mechanism of realizing broadband frequency tuning in an open cavity circuit. A new interaction mechanism about propagating waves, featured by wave competition and wave cooperation, is presented and provides a new insight into the beam-wave interaction. The two different features revealed in the two different operation regions of low-order axial modes (LOAMs) and high-order axial modes (HOAMs) respectively determine the characteristic of the overall performance of the device essentially. The device performance is obtained by the simulation based on the time-domain nonlinear theory and shows that using a 12-kV/150-mA electron beam and TE-3,4 mode, the second harmonic gyrotron can generate terahertz radiations with frequency-tuning ranges of about 0.85 GHz and 0.60 GHz via magnetic field and beam voltage tuning, respectively. Additionally, some non-stationary phenomena in the mode startup process are also analyzed. The investigation in this paper presents guidance for future developing high-performance frequency-tunable gyrotrons toward terahertz applications. Project supported by the National Natural Science Foundation of China (Grant Nos. 61471007, 61531002, 61522101, and 11275206) and the Seeding Grant for Medicine and Information Science of Peking University, China (Grant No. 2014-MI-01).
Design and operation of 140 GHz gyrotron oscillators for power levels up to 1 MW CW
Jory, H.; Bier, R.; Craig, L.J.; Felch, K.; Ives, L.; Lopez, N.; Spang, S.
1986-12-01
Varian has designed and tested 140 GHz gyrotron oscillators that have generated output powers of 100 kW CW and 200 kW for 1 ms pulses. Upcoming tubes will be designed to operate at power levels of 200 kW CW and ultimately up to 1 MW CW. The important design considerations which are addressed in the higher power tubes include the design of the electron gun, interaction circuit, and output window. These issues will be discussed and the results of the earlier 140 GHz gyrotron work at Varian will be summarized.
Nonlinear harmonic oscillators
Calogero, F [Dipartimento di Fisica, Universita di Roma ' La Sapienza' (Italy); Inozemtsev, V I [Joint Institute for Nuclear Research, Dubna (Russian Federation)
2002-12-06
The existence is noted of assemblies of an arbitrary number of complex oscillators, or equivalently, of an arbitrary even number of real oscillators, characterized by Newtonian equations of motion ('acceleration equal force') with one-body velocity-dependent linear forces and many-body velocity-independent cubic forces, all the nonsingular solutions of which are isochronous (completely periodic with the same period). As for the singular solutions, as usual they emerge, in the context of the initial-value problem, from a closed domain in phase space having lower dimensionality.
Harmonic oscillator: an analysis via Fourier series
de Castro, A S
2013-01-01
The Fourier series method is used to solve the homogeneous equation governing the motion of the harmonic oscillator. It is shown that the general solution to the problem can be found in a surprisingly simple way for the case of the simple harmonic oscillator. It is also shown that the damped harmonic oscillator is susceptible to the analysis.
Efficient Low-Voltage Operation of a CW Gyrotron Oscillator at 233 GHz.
Hornstein, Melissa K; Bajaj, Vikram S; Griffin, Robert G; Temkin, Richard J
2007-02-01
The gyrotron oscillator is a source of high average power millimeter-wave through terahertz radiation. In this paper, we report low beam power and high-efficiency operation of a tunable gyrotron oscillator at 233 GHz. The low-voltage operating mode provides a path to further miniaturization of the gyrotron through reduction in the size of the electron gun, power supply, collector, and cooling system, which will benefit industrial and scientific applications requiring portability. Detailed studies of low-voltage operation in the TE(2) (,) (3) (,) (1) mode reveal that the mode can be excited with less than 7 W of beam power at 3.5 kV. During CW operation with 3.5-kV beam voltage and 50-mA beam current, the gyrotron generates 12 W of RF power at 233.2 GHz. The EGUN electron optics code describes the low-voltage operation of the electron gun. Using gun-operating parameters derived from EGUN simulations, we show that a linear theory adequately predicts the low experimental starting currents.
A double-beam magnetron-injection gun for third-harmonic continuous wave 1-THz gyrotron
Glyavin, M. [Faculty of Radiophysics, N. I. Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod 603950 (Russian Federation); Institute of Applied Physics of the Russian Academy of Sciences (IAP RAS), Nizhny Novgorod 603600 (Russian Federation); Research Center for Development of Far Infrared Region, University of Fukui (FIR FU), Fukui-shi 910-8507 (Japan); Manuilov, V. [Faculty of Radiophysics, N. I. Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod 603950 (Russian Federation); Research Center for Development of Far Infrared Region, University of Fukui (FIR FU), Fukui-shi 910-8507 (Japan); Idehara, T. [Research Center for Development of Far Infrared Region, University of Fukui (FIR FU), Fukui-shi 910-8507 (Japan)
2013-12-15
The concept of a continuous wave 1-kW/1-THz gyrotron operated at the third cyclotron harmonic of the transverse electric TE{sub 9,7} operating mode has been developed. To suppress the mode competition effects in a terahertz gyrotron, we propose a scheme with two generating helical electron beams (HEBs) formed in a double-beam triode magnetron-injection gun (MIG), where both emitters of the electron beams are located on a common cathode of the conventional MIG. An optimal geometry of the MIG electrodes is found. It is shown that in a proposed scheme two HEBs having close pitch factors and a moderate velocity spread can be formed. This makes them suitable for high-efficiency single-mode generation in the high frequency gyrotron at high harmonic.
Anomalous Dissipative Quantum Harmonic Oscillator
CHEN Dian-Yong; BAI Zhan-Wu; DONG Yu-Bing
2008-01-01
We investigate the low-temperature statistical properties of a harmonic oscillator coupled to a heat bath, where the low-frequency spectrum vanishes. We obtain the exact result of the zero point energy. Due to the low frequency shortage of environmental oscillators' spectral density, the coordinate and momentum correlation functions decay as r-4and r-6 respectively at zero temperature, where T is the correlation time. The low-temperature behavior of the mean energy does not violate the third law of thermodynamics, but differs largely from the Ohmic spectrum case.
Harmonic Oscillators and Elementary Particles
Sobouti, Y
2016-01-01
Two dynamical systems with same symmetry should have features in common, and as far as their shared symmetry is concerned, one may represent the other. The three light quark constituents of the hadrons, a) have an approximate flavor SU(3) symmetry, b) have an exact color SU(3) symmetry, and c) as spin 1/2 particles, have a Lorentz SO(3,1) symmetry. So does a 3D harmonic oscillator. a) Its Hamiltonian has the SU(3) symmetry, breakable if the 3 fundamental modes of oscillation are not identical. b) The 3 directions of oscillation have the permutation symmetry. This enables one to create three copies of unbreakable SU(3) symmetry for each mode of the oscillation, and mimic the color of the elementary particles. And c) The Lagrangian of the 3D oscillator has the SO(3,1) symmetry. This can be employed to accommodate the spin of the particles. In this paper we draw up a one-to-one correspondence between the eigen modes of the Poisson bracket operator of the 3D oscillator and the flavor multiplets of the particles, ...
Making space for harmonic oscillators
Michelotti, Leo; /Fermilab
2004-11-01
If we restrict the number of harmonic oscillator energy eigenstates to some finite value, N, then the discrete spectrum of the corresponding position operator comprise the roots of the Hermite polynomial H{sub N+1}. Its range is just large enough to accommodate classical motion at high energy. A negative energy term must be added to the Hamiltonian which affects only the last eigenstate, |N>, suggesting it is concentrated at the extrema of this finite ''space''. Calculations support a conjecture that, in the limit of large N, the global distribution of points approaches the differential form for classical action.
Quantizing the damped harmonic oscillator
Latimer, D C [Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235 (United States)
2005-03-04
We consider the Fermi quantization of the classical damped harmonic oscillator (dho). In past work on the subject, authors double the phase space of the dho in order to close the system at each moment in time. For an infinite-dimensional phase space, this method requires one to construct a representation of the CAR algebra for each time. We show that the unitary dilation of the contraction semigroup governing the dynamics of the system is a logical extension of the doubling procedure, and it allows one to avoid the mathematical difficulties encountered with the previous method.
Introduction to classical and quantum harmonic oscillators
Bloch, Sylvan C
2013-01-01
From conch shells to lasers . harmonic oscillators, the timeless scientific phenomenon As intriguing to Galileo as they are to scientists today, harmonic oscillators have provided a simple and compelling paradigm for understanding the complexities that underlie some of nature's and mankind's most fascinating creations. From early string and wind instruments fashioned from bows and seashells to the intense precision of lasers, harmonic oscillators have existed in various forms, as objects of beauty and scientific use. And harmonic oscillation has endured as one of science's most fascinating con
Experimental Study Of A 1.5-mw, 110-ghz Gyrotron Oscillator
Anderson, J P
2005-01-01
This thesis reports the design, construction and testing of a 1.5 MW, 110 GHz gyrotron oscillator. This high power microwave tube has been proposed as the next evolutionary step for gyrotrons used to provide electron cyclotron heating required in fusion devices. A short pulse gyrotron based on the industrial tube design was built at MIT for experimental studies. The experiments are the first demonstration of such high powers at 110 GHz. Using a 96 kV, 40 A electron beam, over 1.4 MW was axially extracted in the design (TE22,6) mode in 3 μs pulses, corresponding to a microwave efficiency of 37%. The beam alpha, the ratio of transverse to axial velocity in the electron beam, was measured with a probe. At the high efficiency operating point the beam alpha was measured as 1.33. This value of alpha is less than the design value of 1.4, possibly accounting for the slightly reduced experimental efficiency. The output power and efficiency, as a function of magnetic field, beam voltage, and beam current, are in...
Singh, Ashutosh, E-mail: asingh.rs.ece@iitbhu.ac.in [Faculty of Physical Sciences, Institute of Natural Sciences and Humanities, Shri Ramswaroop Memorial University, Lucknow-Deva Road, Uttar Pradesh 225003 (India); Center of Research in Microwave Tubes, Department of Electronics Engineering, Indian Institute of Technology (Banaras Hindu University), Varanasi 221005 (India); Jain, P. K. [Center of Research in Microwave Tubes, Department of Electronics Engineering, Indian Institute of Technology (Banaras Hindu University), Varanasi 221005 (India)
2015-09-15
In this paper, the effects of electron beam parameters and velocity spread on the RF behavior of a metallic photonic band gap (PBG) cavity gyrotron operating at 35 GHz with TE{sub 041}–like mode have been theoretically demonstrated. PBG cavity is used here to achieve a single mode operation of the overmoded cavity. The nonlinear time-dependent multimode analysis has been used to observe the beam-wave interaction behavior of the PBG cavity gyrotron, and a commercially available PIC code “CST Particle Studio” has been reconfigured to obtain 3D simulation results in order to validate the analytical values. The output power for this typical PBG gyrotron has been obtained ∼108 kW with ∼15.5% efficiency in a well confined TE{sub 041}–like mode, while all other competing modes have significantly low values of power output. The output power and efficiency of a gyrotron depend highly on the electron beam parameters and velocity spread. The influence of several electron beam parameters, e.g., beam voltage, beam current, beam velocity pitch factor, and DC magnetic field, on the PBG gyrotron operations has been investigated. This study would be helpful in optimising the electron beam parameters and estimating accurate RF output power of the high frequency PBG cavity based gyrotron oscillators.
Quantum dynamics of the damped harmonic oscillator
Philbin, T G
2012-01-01
The quantum theory of the damped harmonic oscillator has been a subject of continual investigation since the 1930s. The obstacle to quantization created by the dissipation of energy is usually dealt with by including a discrete set of additional harmonic oscillators as a reservoir. But a discrete reservoir cannot directly yield dynamics such as Ohmic damping (proportional to velocity) of the oscillator of interest. By using a continuum of oscillators as a reservoir, we canonically quantize the harmonic oscillator with Ohmic damping and also with general damping behaviour. The dynamics of a damped oscillator is determined by an arbitrary effective susceptibility that obeys Kramers-Kronig relations. This approach offers an alternative description of nano-mechanical oscillators and opto-mechanical systems.
三次谐波光子带隙谐振腔回旋管%Third-Harmonic of Photonic-Band-Gap Cavity Gyrotron
夏玉玺; 唐昌建
2011-01-01
Effective coupling of interaction between high-order electromagnetic mode gyrotron oscillator and high-effective electron cyclotron mode is achieved through the analysis of mode selection function of the photonic band gap cavity（PBGC）.After band characteristics of the PBGC are investigated,TE34-mode is set as working mode and the mode competition is suppressed successfully.The concept of equivalent radius of PBGC gyrotron is established,self-consistent nonlinear theory and related computer simulation program are completed.Studies have shown that TE34-mode can interact with third electronic cyclotron harmonics effectively,the coupling frequency of which is 130.5GHz,and meanwhile it reduces the required magnetic field greatly.The parameters are optimized when many physical factors are taken into account,and a third-harmonic PBGC gyrotron oscillator with voltage 430KV,current 35A,output power 1.75MW and interaction efficiency 11.5% are obtained consequently.%分析了光子晶体谐振腔（PBGC）的模式选择功能,实现PBGC回旋管振荡器高阶电磁模与高次电子回旋模的有效耦合。通过对PBGC禁带特性的分析,定出了工作模式TE34模,并成功抑制了模式竞争。文中建立了PBGC回旋管的等效半径的概念,完成了自洽非线性理论和相关的计算机数值模拟程序。研究发现TE34模能有效地与电子的3次回旋谐波相互作用,其耦合频率为130.5GHz,并极大地降低了对工作磁场的要求。在考虑诸多物理因素影响的情况下,对该3次谐波PBGC回旋管振荡器进行了参数优化研究,得到了参数为：电压430kV、
Glyavin, M. Yu.; Zavolskiy, N. A.; Sedov, A. S.; Nusinovich, G. S.
2013-03-01
For a long time, the gyrotrons were primarily developed for electron cyclotron heating and current drive of plasmas in controlled fusion reactors where a multi-megawatt, quasi-continuous millimeter-wave power is required. In addition to this important application, there are other applications (and their number increases with time) which do not require a very high power level, but such issues as the ability to operate at low voltages and have compact devices are very important. For example, gyrotrons are of interest for a dynamic nuclear polarization, which improves the sensitivity of the nuclear magnetic resonance spectroscopy. In this paper, some issues important for operation of gyrotrons driven by low-voltage electron beams are analyzed. An emphasis is made on the efficiency of low-voltage gyrotron operation at the fundamental and higher cyclotron harmonics. These efficiencies calculated with the account for ohmic losses were, first, determined in the framework of the generalized gyrotron theory based on the cold-cavity approximation. Then, more accurate, self-consistent calculations for the fundamental and second harmonic low-voltage sub-THz gyrotron designs were carried out. Results of these calculations are presented and discussed. It is shown that operation of the fundamental and second harmonic gyrotrons with noticeable efficiencies is possible even at voltages as low as 5-10 kV. Even the third harmonic gyrotrons can operate at voltages about 15 kV, albeit with rather low efficiency (1%-2% in the submillimeter wavelength region).
The harmonic oscillator and nuclear physics
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.
Geometric Models of the Relativistic Harmonic Oscillator
Cotaescu, I I
1997-01-01
A family of relativistic geometric models is defined as a generalization of the actual anti-de Sitter (1+1) model of the relativistic harmonic oscillator. It is shown that all these models lead to the usual harmonic oscillator in the non-relativistic limit, even though their relativistic behavior is quite different. Among quantum models we find a set of models with countable energy spectra, and another one having only a finite number of energy levels and in addition a continuous spectrum.
Sobolev Spaces Associated to the Harmonic Oscillator
B Bongioanni; J L Torrea
2006-08-01
We define the Hermite-Sobolev spaces naturally associated to the harmonic oscillator $H= - + |x|^2$. Structural properties, relations with the classical Sobolev spaces, boundedness of operators and almost everywhere convergence of solutions of the Schrödinger equation are also considered.
The Berry Phase for Simple Harmonic Oscillators
Suslov, Sergei K
2011-01-01
We evaluate the Berry phase for a "missing" family of the square integrable wavefunctions for the linear harmonic oscillator, which cannot be derived by the separation of variables. It is obtained by the action of the maximal kinematical invariance group on the standard solutions. An explicit simple formula for the phase is found by integration with the help of a computer algebra system.
A 0.52THz third harmonic little-orbit gyrotron%小回旋三次谐波0.52THz回旋管
袁学松; 马春燕; 韩煜; 鄢扬
2012-01-01
A third harmonic little-orbit gyrotron oscillator is investigated theoretically in order to develop high power and efficiency terahertz (THz) radiation sources. Mode competition with different electron-beam parameters have been investigated in a 0.52 THz third harmonic TE37 mode gyrotron oscillator, which can generate 3.7kW of RF power at resonant magnetic field 6.98T. In addition, a high magnetic compression ratio magnetron injection gun (MIG) with 65 kV/2. 5 A has been developed. PIC simulation results show that the velocity ratio of electron beam is 1.24, the average beam radius in the cavity is 0.35 mm. The spread of perpendicular and parallel velocities are 6.1% and 6.6% , respectively.%为了发展大功率高效率太赫兹辐射源,对小回旋电子注激励三次谐波太赫兹电子回旋脉塞进行了研究,分析了不同参数情况下的模式竞争.研究结果表明,采用近轴小回旋电子注能够实现三次谐波单模振荡.在此基础上设计了一只0.52 THz、TE37模三次谐波回旋管,数值计算表明,该回旋管在工作磁场为6.98 T下输出功率可以达到3.7 kW.对产生近轴小回旋电子注的高磁压缩比磁控注入式电子光学系统进行的粒子模拟研究结果表明,该电子枪能够产生满足实验要求的65 kV/2.5 A,横纵速度比为1.24,引导中心半径0.35 mm的小回旋电子注,其纵向速度离散6.6％,横向速度离散6.1％.
Perturbative Semiclassical Trace Formulae for Harmonic Oscillators
Møller-Andersen, Jakob; Ögren, Magnus
2015-01-01
In this article we extend previous semiclassical studies by including more general perturbative potentials of the harmonic oscillator in arbitrary spatial dimensions. Our starting point is a radial harmonic potential with an arbitrary even monomial perturbation, which we use to study the resulting...... U(D) to O(D) symmetry breaking. We derive the gross structure of the semiclassical spectrum from periodic orbit theory, in the form of a perturbative (ħ → 0) trace formula. We then show how to apply the results to even-order polynomial potentials, possibly including mean-field terms. We have drawn...
Harmonic oscillator model for the helium atom
Carlsen, Martin
2015-01-01
A harmonic oscillator model in four dimensions is presented for the helium atom to estimate the distance to the inner and outer electron from the nucleus, the angle between electrons and the energy levels. The method is algebraic and is not based on the choice of correct trial wave function. Three harmonic oscillators and thus three quantum numbers are sufficient to describe the two-electron system. We derive a simple formula for the energy in the general case and in the special case of the Wannier Ridge. For a set of quantum numbers the distance to the electrons and the angle between the electrons are uniquely determined as the intersection between three surfaces. We show that the excited states converge either towards ionization thresholds or towards extreme parallel or antiparallel states and provide an estimate of the ground state energy.
Quantum Harmonic Oscillator Algebra and Link Invariants
Gómez, C
1991-01-01
The $q$--deformation $U_q (h_4)$ of the harmonic oscillator algebra is defined and proved to be a Ribbon Hopf algebra.Associated with this Hopf algebra we define an infinite dimensional braid group representation on the Hilbert space of the harmonic oscillator, and an extended Yang--Baxter system in the sense of Turaev. The corresponding link invariant is computed in some particular cases and coincides with the inverse of the Alexander--Conway polynomial. The $R$ matrix of $U_q (h_4)$ can be interpreted as defining a baxterization of the intertwiners for semicyclic representations of $SU(2)_q$ at $q=e^{2 \\pi i/N}$ in the $N \\rightarrow \\infty$ limit.Finally we define new multicolored braid group representations and study their relation to the multivariable Alexander--Conway polynomial.
Yeh, Y. S.; Kao, W. J.; Li, L. J.; Guo, Y. W.
2017-01-01
The harmonic multiplying operation in a gyrotron traveling-wave amplifier (gyro-TWA) permits magnetic field reduction and frequency multiplication. This study presents a comparative analysis of fourth-harmonic multiplying gyro-TWAs with three schemes of operation. An improved mode-selective circuit using circular waveguides with various radii provides the rejection points within the range of operating frequencies to suppress the competing modes of gyro-TWAs. The simulated results reveal that gyro-TWAs are the most susceptible to the fundamental-harmonic TE11 competing mode, regardless of the operating scheme, and that the mode-selective circuit can provide an attenuation of more than 20 dB to suppress the competing modes. The amplification of the waves in a gyro-TWA depends on the lengths of the sections, and the simulated results show that the gain increases for all schemes, as the length of the lossy section or the length of the copper section increases. All schemes exhibit nearly the same saturated output powers and bandwidths; however, the saturated gain of the scheme at a high frequency multiplication ratio is less than that of the scheme at a low frequency multiplication ratio. Extensive numerical calculations of power and gain scaling are conducted for all schemes.
Quantum control of harmonic oscillator networks
Genoni, Marco G; Kim, M S; Burgarth, Daniel
2011-01-01
Controllability -- the possibility of performing any target dynamics by applying a set of available operations -- is a fundamental requirement for the practical use of any physical system. For finite-dimensional systems, as for instance spin systems, precise criterions to establish controllability, such as the so called rank criterion, are well known. However most physical systems require a description in terms of an infinite-dimensional Hilbert space whose controllability properties are poorly understood. Here, we investigate infinite-dimensional bosonic quantum systems -- encompassing quantum light, ensembles of bosonic atoms, motional degrees of freedom of ions, and nano-mechanical oscillators -- governed by quadratic Hamiltonians (such that their evolution is analogous to coupled harmonic oscillators). After having highlighted the intimate connection between controllability and recurrence in the Hilbert space, we prove that, for coupled oscillators, a simple extra condition has to be fulfilled to extend t...
Information cloning of harmonic oscillator coherent states
N D Hari Dass; Pradeep Ganesh
2002-08-01
We show that in the case of unknown harmonic oscillator coherent statesit is possible to achieve what we call perfect information cloning. By this we mean that it is still possible to make arbitrary number of copies of a state which has exactly the same information content as the original unknown coherent state. By making use of this perfect information cloning it would be possible to estimate the original state through measurements and make arbitrary number of copies of the estimator. We deﬁne the notion of a measurement ﬁdelity and calculate it for our case as well as for the Gaussian cloners.
Lipschitz spaces and bounded mean oscillation of harmonic mappings
Chen, Sh; Vuorinen, M; Wang, X
2012-01-01
In this paper, we first study the bounded mean oscillation of planar harmonic mappings, then a relationship between Lipschitz-type spaces and equivalent modulus of real harmonic mappings is established. At last, we obtain sharp estimates on Lipschitz number of planar harmonic mappings in terms of bounded mean oscillation norm, which shows that the harmonic Bloch space is isomorphic to $BMO_{2}$ as a Banach space.
Virial Theorem for a Class of Quantum Nonlinear Harmonic Oscillators
王雪红; 郭军义; 李艳
2012-01-01
In this paper,the Virial Theorem based on a class of quantum nonlinear harmonic oscillators is presented.This relationship has to do with parameter λ and ?/?λ,where the λ is a real number.When λ=0,the nonlinear harmonic oscillator naturally reduces to the usual quantum linear harmonic oscillator,and the Virial Theorem also reduces to the usual Virial Theorem.
Effective harmonic oscillator description of anharmonic molecular vibrations
Tapta Kanchan Roy; M Durga Prasad
2009-09-01
The validity of an effective harmonic oscillator approximation for anharmonic molecular vibrations is tested and compared with vibrational self consistent field and vibrational configurational interaction results. The effective harmonic oscillator is constructed variationally, by taking the trial wave function as a harmonic oscillator eigenfunction with the centroid and width parameter as variational paraeters. It is found that the effective harmonic oscillator approximation provides a description of the anharmonic eigenstates very similar to the vibrational self consistent field results. Coriolis coupling is also included in these studies.
The noncommutative harmonic oscillator in more than one dimensions
Hatzinikitas, A; Hatzinikitas, Agapitos; Smyrnakis, Ioannis
2002-01-01
The noncommutative harmonic oscillator in arbitrary dimension is examined. It is shown that the $\\star$-genvalue problem can be decomposed into separate harmonic oscillator equations for each dimension. The noncommutative plane is investigated in greater detail. The constraints for rotationally symmetric solutions and the corresponding two-dimensional harmonic oscillator are solved. The angular momentum operator is derived and its $\\star$-genvalue problem is shown to be equivalent to the usual eigenvalue problem. The $\\star$-genvalues for the angular momentum are found to depend on the energy difference of the oscillations in each dimension. Furthermore two examples of assymetric noncommutative harmonic oscillator are analysed. The first is the noncommutative two-dimensional Landau problem and the second is the three-dimensional harmonic oscillator with symmetrically noncommuting coordinates and momenta.
Spectral inverse problem for q-deformed harmonic oscillator
P K Bera; J Datta
2006-12-01
The supersymmetric quantization condition is used to study the wave functions of SWKB equivalent -deformed harmonic oscillator which are obtained by using only the knowledge of bound-state spectra of -deformed harmonic oscillator. We have also studied the nonuniqueness of the obtained interactions by this spectral inverse method.
A Look at Damped Harmonic Oscillators through the Phase Plane
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…
Harmonic oscillation in a spatially finite array waveguide.
Gordon, R
2004-12-01
A waveguide array is presented that behaves as an oscillator, showing periodic image reconstruction, focusing, and transverse wave-packet oscillation. The oscillator has a finite width, which removes the need for premature truncation. The array waveguide oscillator shows properties analogous to those of a pedagogically important one-dimensional quantum harmonic oscillator, which are fundamentally different from previously demonstrated oscillations in Wannier-Stark waveguide arrays. Calculations of the entire array waveguide oscillator are presented that quantify higher-order corrections to the coupled-mode approach. These results can be extended to waveguide oscillators in other systems, such as electrons in superlattices.
First harmonic injection locking of 24-GHz-oscillators
M. R. Kühn
2003-01-01
Full Text Available An increasing number of applications is proposed for the 24 GHz ISM-band, like automotive radar systems and short-range communication links. These applications demand for oscillators providing moderate output power of a few mW and moderate frequency stability of about 0.5%. The maximum oscillation frequency of low-cost off-theshelf transistors is too low for stable operation of a fundamental 24GHz oscillator. Thus, we designed a 24 GHz first harmonic oscillator, where the power generated at the fundamental frequency (12 GHz is reflected resulting in effective generation of output power at the first harmonic. We measured a radiated power from an integrated planar antenna of more than 1mW. Though this oscillator provides superior frequency stability compared to fundamental oscillators, for some applications additional stabilization is required. As a low-cost measure, injection locking can be used to phase lock oscillators that provide sufficient stability in free running mode. Due to our harmonic oscillator concept injection locking has to be achieved at the first harmonic, since only the antenna is accessible for signal injection. We designed, fabricated and characterized a harmonic oscillator using the antenna as a port for injection locking. The locking range was measured versus various parameters. In addition, phase-noise improvement was investigated. A theoretical approach for the mechanism of first harmonic injection locking is presented.
W波段三次谐波回旋管实验研究%Experimental study on W-band third-harmonic gyrotron
孙迪敏; 胡鹏; 马国武; 陈洪斌; 孟凡宝; 陈怀璧
2013-01-01
It is the first time that the W-band,third harmonic gyrotron radiation is observed in China.The operation mode of the third harmonic gyrotron is TE61.The magnetic field is 1.2 T and the frequency is 94.86 GHz.When beam current changes from 1.6 A to 4.4 A,keeping the anode voltage 45 kV,the third harmonic radiation can be observed.The largest output power is 4.9 kW,and the efficiency is about 3％.%国内首次成功进行W波段三次谐波回旋管实验.回旋管工作模式为TE61,磁场1.2T,采用拍频法测定工作频率为94.86 GHz.电子束电压为45 kV时,电流1.6～4.4A范围内都观测到了三次谐波振荡信号.采用焦热计测定最大输出功率4.9 kW,效率约3％.
Driven damped harmonic oscillator resonance with an Arduino
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.
A harmonic oscillator having “volleyball damping”
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.
Bound states of two-dimensional relativistic harmonic oscillators
Qiang Wen-Chao
2004-01-01
We give the exact normalized bound state wavefunctions and energy expressions of the Klein-Gordon and Dirac equations with equal scalar and vector harmonic oscillator potentials in the two-dimensional space.
Deformed quantum harmonic oscillator with diffusion and dissipation
Isar, A
2002-01-01
A master equation for the deformed quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is derived in the microscopic model by using perturbation theory. The coefficients of the master equation and of equations of motion for observables depend on the deformation function. The steady state solution of the equation for the density matrix in the number representation is obtained and the equilibrium energy of the deformed harmonic oscillator is calculated in the approximation of small deformation.
Deformed quantum harmonic oscillator with diffusion and dissipation
Isar, A.; Scheid, W.
2002-07-01
A master equation for the deformed quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is derived in the microscopic model by using perturbation theory. The coefficients of the master equation and of equations of motion for observables depend on the deformation function. The steady-state solution of the equation for the density matrix in the number representation is obtained and the equilibrium energy of the deformed harmonic oscillator is calculated in the approximation of small deformation.
A new analytical approximation to the Duffing-harmonic oscillator
Fesanghary, M. [Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA 70803 (United States); Pirbodaghi, T. [School of Mechanical Engineering, Sharif University of Technology, Azadi Ave., 11365-9567 Tehran (Iran, Islamic Republic of); Asghari, M. [School of Mechanical Engineering, Sharif University of Technology, Azadi Ave., 11365-9567 Tehran (Iran, Islamic Republic of)], E-mail: asghari@sharif.edu; Sojoudi, H. [Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA 70803 (United States)
2009-10-15
In this paper, a novel analytical approximation to the nonlinear Duffing-harmonic oscillator is presented. The variational iteration method (VIM) is used to obtain some accurate analytical results for frequency. The accuracy of the results is excellent in the whole range of oscillation amplitude variations.
Predicting charmonium and bottomonium spectra with a quark harmonic oscillator
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
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.
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.
Quantum kicked harmonic oscillator in contact with a heat bath
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.
Thermal state of the general time-dependent harmonic oscillator
Jeong-Ryeol Choi
2003-07-01
Taking advantage of dynamical invariant operator, we derived quantum mechanical solution of general time-dependent harmonic oscillator. The uncertainty relation of the system is always larger than ħ=2 not only in number but also in the thermal state as expected. We used the diagonal elements of density operator satisfying Leouville–von Neumann equation to calculate various expectation values in the thermal state. We applied our theory to a special case which is the forced Caldirola–Kanai oscillator.
Hyperchaotic circuit with damped harmonic oscillators
Lindberg, Erik; Murali, K.; Tamasevicius, A.
2001-01-01
capacitors and one nonlinear active conductor. The Lyapunov exponents are presented to confirm the hyperchaotic nature of the oscillations of the circuit. The nonlinear conductor is realized with a diode. A negative impedance converter and a linear resistor. The performance of the circuit is investigated...
Nonlinear analysis of a cross-coupled quadrature harmonic oscillator
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens;
2005-01-01
The dynamic equations governing the cross-coupled quadrature harmonic oscillator are derived assuming quasi-sinusoidal operation. This allows for an investigation of the previously reported tradeoff between close-to-carrier phase noise and quadrature precision. The results explain how nonlinearit...
On a Hidden Symmetry of Quantum Harmonic Oscillators
Lopez, Raquel M; Vega-Guzman, Jose M
2011-01-01
We present a six parameter family of the square integrable wave functions for the linear harmonic oscillator, which cannot be obtained by the standard separation of variables. They are found by the action of corresponding maximal kinematical invariance group on the standard solutions. Some possible applications are briefly discussed.
Simulating Harmonic Oscillator and Electrical Circuits: A Didactical Proposal
Albano, Giovannina; D'Apice, Ciro; Tomasiello, Stefania
2002-01-01
A Mathematica[TM] package is described that uses simulations and animations to illustrate key concepts in harmonic oscillation and electric circuits for students not majoring in physics or mathematics. Students are not required to know the Mathematica[TM] environment: a user-friendly interface with buttons functionalities and on-line help allows…
A Simple Mechanical Model for the Isotropic Harmonic Oscillator
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.)
Exact complex integrals in two dimensions for shifted harmonic oscillators
Jasvinder Singh Virdi; S C Mishra
2012-07-01
We use rationalization method to study two-dimensional complex dynamical systems (shifted harmonic oscillator in complex plane) on the extended comples phase space (ECPS). The role and scope of the derived invatiants in the context of various physical problems are high-lighted.
Maximal Regularity of the Discrete Harmonic Oscillator Equation
Airton Castro
2009-01-01
Full Text Available We give a representation of the solution for the best approximation of the harmonic oscillator equation formulated in a general Banach space setting, and a characterization of lp-maximal regularity—or well posedness—solely in terms of R-boundedness properties of the resolvent operator involved in the equation.
Twisted Conformal Algebra and Quantum Statistics of Harmonic Oscillators
J. Naji
2014-01-01
Full Text Available We consider noncommutative two-dimensional quantum harmonic oscillators and extend them to the case of twisted algebra. We obtained modified raising and lowering operators. Also we study statistical mechanics and thermodynamics and calculated partition function which yields the free energy of the system.
The harmonic oscillator, dimensional analysis and inflationary solutions
San Costa, S
2002-01-01
In this work, focused on the production of exact inflationary solutions using dimensional analysis, it is shown how to explain inflation from a pragmatic and basic point of view, in a step-by-step process, starting from the one-dimensional harmonic oscillator.
Low Noise Second Harmonic Oscillator Using Mutually Synchronized Gunn Diodes
Kawasaki, Kengo; Tanaka, Takayuki; Aikawa, Masayoshi
This paper represents a low noise second harmonic oscillator using mutually synchronized Gunn diodes. A multi-layer MIC technology is adopted to reduce the circuit size of the oscillator. The oscillator consists of Gunn diodes, slot line resonators and strip lines. By embedding Gunn diodes in the slot line resonators, a harmonic RF signal can be generated very easily. The strip lines are used for the power combining output circuit. The shape of slot line resonator is square in order to achieve the low phase noise and the suppression of undesired harmonics. The second harmonic oscillator is designed and fabricated in K band. The output power is +8.89dBm at the design frequency of 18.75GHz (2f0) with the phase noise of -116.2dBc/Hz at the offset frequency of 1MHz. Excellent suppression of the undesired fundamental frequency signal (f0) of -33dBc is achieved. Also, the circuit size is reduced by three-tenths relative to that of the previously proposed circuit.
Free Fall and Harmonic Oscillations: Analyzing Trampoline Jumps
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…
Wigner Functions for harmonic oscillator in noncommutative phase space
Wang, Jianhua; Li, Kang; Dulat, Sayipjamal
2009-01-01
We study the Wigner Function in non-commutative quantum mechanics. By solving the time independent Schr\\"{o}dinger equation both on a non-commutative (NC) space and a non-commutative phase space, we obtain the Wigner Function for the harmonic oscillator on NC space and NC phase space respectively.
Equity prices as a simple harmonic oscillator with noise
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.
Chou, C H; Yu, T; Chou, Chung-Hsien; Yu, Ting
2007-01-01
In this paper we derive an exact master equation for two coupled quantum harmonic oscillators interacting via bilinear coupling with a common environment made up of many harmonic oscillators at arbitrary temperature for 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 known [Hu, Paz and Zhang, Phys. Rev. D \\textbf{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 evolution operator of the reduced density matrix which are useful for the study of decoherence and disentanglement issues. We ...
Harmonic Oscillators as Bridges between Theories: Einstein, Dirac, and Feynman
Kim, Y S; Noz, Marilyn E.
2004-01-01
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. Coupled oscillators provide clear illustrative examples for some of the current issues in physics, including entanglement, decoherence, and Feynman's rest of the universe. In addition, 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 $SL(2,c)$...
Harmonic balance approach to the periodic solutions of the (an)harmonic relativistic oscillator
Belendez, Augusto [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es; Pascual, Carolina [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2007-11-19
The first-order harmonic balance method via the first Fourier coefficient is used to construct two approximate frequency-amplitude relations for the relativistic oscillator for which the nonlinearity (anharmonicity) is a relativistic effect due to the time line dilation along the world line. Making a change of variable, a new nonlinear differential equation is obtained and two procedures are used to approximately solve this differential equation. In the first the differential equation is rewritten in a form that does not contain a square-root expression, while in the second the differential equation is solved directly. The approximate frequency obtained using the second procedure is more accurate than the frequency obtained with the first due to the fact that, in the second procedure, application of the harmonic balance method produces an infinite set of harmonics, while in the first procedure only two harmonics are produced. Both approximate frequencies are valid for the complete range of oscillation amplitudes, and excellent agreement of the approximate frequencies with the exact one are demonstrated and discussed. The discrepancy between the first-order approximate frequency obtained by means of the second procedure and the exact frequency never exceeds 1.6%. We also obtained the approximate frequency by applying the second-order harmonic balance method and in this case the relative error is as low 0.31% for all the range of values of amplitude of oscillation A.
Rosu, H.C., E-mail: hcr@ipicyt.edu.mx [IPICyT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo Postal 3-74 Tangamanga, 78231 San Luis Potosi, S.L.P. (Mexico); Khmelnytskaya, K.V. [Universidad Autonoma de Queretaro, Centro Universitario, Cerro de las Campanas s/n, C.P. 76010 Santiago de Queretaro, Qro. (Mexico)
2011-09-19
We determine the kind of parametric oscillators that are generated in the usual factorization procedure of second-order linear differential equations when one introduces a constant shift of the Riccati solution of the classical harmonic oscillator. The mathematical results show that some of these oscillators could be of physical nature. We give the solutions of the obtained second-order differential equations and the values of the shift parameter providing strictly periodic and antiperiodic solutions. We also notice that this simple problem presents parity-time (PT) symmetry. Possible applications are mentioned. -- Highlights: → A particular Riccati solution of the classical harmonic oscillator is shifted by a constant. → Such a solution is used in the factorization brackets to get different equations of motion. → The properties of the parametric oscillators obtained in this way are examined.
Application of Hybrid Functions for Solving Duffing-Harmonic Oscillator
Mohammad Heydari
2014-01-01
Full Text Available A numerical method for finding the solution of Duffing-harmonic oscillator is proposed. The approach is based on hybrid functions approximation. The properties of hybrid functions that consist of block-pulse and Chebyshev cardinal functions are discussed. The associated operational matrices of integration and product are then utilized to reduce the solution of a strongly nonlinear oscillator to the solution of a system of algebraic equations. The method is easy to implement and computationally very attractive. The results are compared with the exact solution and results from several recently published methods, and the comparisons showed proper accuracy of this method.
Quantum Harmonic Oscillator State Control in a Squeezed Fock Basis
Kienzler, D.; Lo, H.-Y.; Negnevitsky, V.; Flühmann, C.; Marinelli, M.; Home, J. P.
2017-07-01
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.
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.
Anisotropic Harmonic Oscillator in a Static Electromagnetic Field
LIN Qiong-Gui
2002-01-01
A nonrelativistic charged particle moving in an anisotropic harmonic oscillator potential plus a homogeneousstatic electromagnetic field is studied. Several configurations of the electromagnetic field are considered. The Schrodingerequation is solved analytically in most of the cases. The energy levels and wave functions are obtained explicitly. Insome of the cases, the ground state obtained is not a minimum wave packet, though it is of the Gaussian type. Coherentand squeezed states and their time evolution axe discussed in detail.
An analogue of the Berry phase for simple harmonic oscillators
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.
Harmonic oscillator Floquet states in the Bargmann-Segal space
Palma, A. [Instituto Nacional de Astrofisica, Optica y Electronica (INAOE), Puebla (Mexico)]. E-mail: palma@sirio.ifuap.buap.mx; Leon, V. [Instituto de Fisica, BUAP, Puebla (Mexico); Lefebvre, R. [Laboratoire de Photophysique Moleculaire du CNRS, Universite Paris-Sud, Orsay (France); UFR de Physique Fondamentale et Appliquee, Universite Pierre et Marie Curie, Paris (France)
2002-01-18
The Floquet quasi-energies and eigenfunctions for the harmonic oscillator interacting with a monochromatic electric field are obtained by using the so-called Bargmann-Segal space. The Schroedinger second-order differential equation in configuration space is transformed into a linear first-order equation in such a space, which is easily solved by means of an auxiliary system (called the Lagrange system) of ordinary differential equations. This method compares favourably with others previously used. (author)
Unitary approach to the quantum forced harmonic oscillator
2014-01-01
In this paper we introduce an alternative approach to studying the evolution of a quantum harmonic oscillator subject to an arbitrary time dependent force. With the purpose of finding the evolution operator, certain unitary transformations are applied successively to Schr\\"odinger's equation reducing it to its simplest form. Therefore, instead of solving the original Schr\\"odinger's partial differential equation in time and space the problem is replaced by a system of ordinary differential eq...
A type of perturbation of the harmonic oscillator
López, Jesús A Álvarez
2011-01-01
Consider perturbations of the harmonic oscillator $H$ of the form $P=H-f_1\\frac{d}{dx}+f_2$ for functions $f_1$ and $f_2$. If $f_2$ can be given as certain expression of $f_1$ and a parameter $\\sigma>-1$, then many well known properties of $H$ are generalized to $P$: self-adjointness in the appropriate Hilbert space, description of the spectrum, recurrence formula for the eigenfunctions, eigenfunction estimates and embedding results.
Coherent and squeezed states for the 3D harmonic oscillator
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.
Teaching from a Microgravity Environment: Harmonic Oscillator and Pendulum
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.
Chih-Chun Chang; Guang-Yin Chen; Lee Lin
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 a...
Pisot q-coherent states quantization of the harmonic oscillator
Gazeau, J.P., E-mail: gazeau@apc.univ-paris7.fr [Laboratoire APC, Univ. Paris Diderot, Sorbonne Paris Cite, 75205 Paris (France); Olmo, M.A. del, E-mail: olmo@fta.uva.es [Departamento de Fisica Teorica and IMEVA, Universidad de Valladolid, E-47005, Valladolid (Spain)
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.
A simple harmonic balance method for solving strongly nonlinear oscillators
Md. Abdur Razzak
2016-10-01
Full Text Available In this paper, a simple harmonic balance method (HBM is proposed to obtain higher-order approximate periodic solutions of strongly nonlinear oscillator systems having a rational and an irrational force. With the proposed procedure, the approximate frequencies and the corresponding periodic solutions can be easily determined. It gives high accuracy for both small and large amplitudes of oscillations and better result than those obtained by other existing results. The main advantage of the present method is that its simplicity and the second-order approximate solutions almost coincide with the corresponding numerical solutions (considered to be exact. The method is illustrated by examples. The present method is very effective and convenient method for solving strongly nonlinear oscillator systems arising in nonlinear science and engineering.
Effective field theory in the harmonic oscillator basis
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.
Rosu, H. C.; Khmelnytskaya, K. V.
2011-09-01
We determine the kind of parametric oscillators that are generated in the usual factorization procedure of second-order linear differential equations when one introduces a constant shift of the Riccati solution of the classical harmonic oscillator. The mathematical results show that some of these oscillators could be of physical nature. We give the solutions of the obtained second-order differential equations and the values of the shift parameter providing strictly periodic and antiperiodic solutions. We also notice that this simple problem presents parity-time (PT) symmetry. Possible applications are mentioned.
Rosu, H C
2010-01-01
Previous research made us consider a simple but curious problem related to the kind of oscillators that are produced in the usual supersymmetric scheme when one introduces a constant shift of the Riccati solution R(t)=-omega _0 tan(omega _0t) of the classical harmonic oscillator. The corresponding mathematical scheme is presented in detail showing that at least some of these oscillators could be of physical nature. We give the solutions of the resulting second-order differential equations obtaining the values of the shift parameter providing strictly periodic and antiperiodic solutions. We also notice that this simple problem presents parity-time (PT) symmetry
Rajarshi Chakrabarti
2009-04-01
Based on a Hamiltonian description we present a rigorous derivation of the transient state work fluctuation theorem and the Jarzynski equality for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics dissipative. Since we do not assume anything about the spectral nature of the harmonic bath the derivation is not restricted only to the Ohmic bath, rather it is more general, for a non-Ohmic bath. We also derive expressions of the average work done and the variance of the work done in terms of the two-time correlation function of the fluctuations of the position of the harmonic oscillator. In the case of an Ohmic bath, we use these relations to evaluate the average work done and the variance of the work done analytically and verify the transient state work fluctuation theorem quantitatively. Actually these relations have far-reaching consequences. They can be used to numerically evaluate the average work done and the variance of the work done in the case of a non-Ohmic bath when analytical evaluation is not possible.
Detecting the harmonics of oscillations with time-variable frequencies
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.
Anisotropic Harmonic Oscillator in s Static Electromagnetic Field
LINQiong－Gui
2002-01-01
A nonrelativistic charged particle moving in an anisotropic harmonic oscillator potential plus a homogeneous static electromagnetic field is studied.Several configurations of the electromagnetic field are considered.The Schoedinger equation is solved analytically in most of the cases.The energy levels and wave functions are obtained explicitly.In some of the cases,the ground state obtained is not a minimum wave packet,though it is of the Gaussian type.Coherent and squeezed states and their time evolution are discussed in detail.
Elementary derivation of the quantum propagator for the harmonic oscillator
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.
Harmonic response of a class of finite extensibility nonlinear oscillators
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
Effective field theory in the harmonic-oscillator basis
Binder, S; Hagen, G; Papenbrock, T; Wendt, K A
2015-01-01
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. We derive useful analytical expressions for an exact and efficient calculation of matrix elements. 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 exhibit a fast convergence of ground-state energies and radii in feasible model spaces.
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.
A method of solving simple harmonic oscillator Schroedinger equation
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.
On quantum harmonic oscillator being subjected to absolute potential state
SWAMI NITYAYOGANANDA
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 remainsdormant. 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 greaterwill 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.
On quantum harmonic oscillator being subjected to absolute potential state
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.
The two capacitor problem revisited: simple harmonic oscillator model approach
Lee, Keeyung
2012-01-01
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 \\emph {exactly half} the work done by a constant applied force is dissipated irrespective of the form of dissipation mechanism when the system comes to a new equilibrium after a constant force is abruptly applied. This model is then applied to the energy loss mechanism in the capacitor charging problem or the two-capacitor problem. This approach allows a simple explanation of the energy dissipation mechanism in these problems and shows that the dissipated energy should always be \\emph {exactly half} the supplied energy whether that is caused by the Joule heat or by the radiation. This paper which provides a simple treatment of the energy dissipation mechanism in the two-capacitor problem is suitable for all undergraduate...
Dissipative quantum trajectories in complex space: Damped harmonic oscillator
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.
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.
P. A. Deymier
2016-12-01
Full Text Available 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.
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.
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.
Entanglement dynamics for a conditionally kicked harmonic oscillator
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.
Exact solution of a quantum forced time-dependent harmonic oscillator
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.
CHEN CHANG-YUAN
2000-01-01
In this paper, the general formulas and the recurrence formulas for radial matrix elements of N-dimensional isotropic harmonic oscillator are obtained. The relevant results of 2- dimensional and 3- dimensiona] isotropic harmonic oscillators reported in the reference papers are contained in a more general equations derived in this paper as special cases.
An application of the 3-dimensional q-deformed harmonic oscillator to the nuclear shell model
Raychev, P P; Lo-Iudice, N; Terziev, P A
1998-01-01
An analysis of the construction of a q-deformed version of the 3-dimensional harmonic oscillator, which is based on the application of q-deformed algebras, is presented. The results together with their applicability to the shell model are compared with the predictions of the modified harmonic oscillator.
Relativistic Harmonic Oscillators and Hadronic Structures in the Quantum-Mechanics Curriculum
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)
The Two-Capacitor Problem Revisited: A Mechanical Harmonic Oscillator Model Approach
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…
Ecological optimization of an irreversible harmonic oscillators Carnot heat engine
无
2009-01-01
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.
Phase-space treatment of the driven quantum harmonic oscillator
DIÓGENES CAMPOS
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.
Chiral potential renormalized in harmonic-oscillator space
Yang, C -J
2016-01-01
We renormalize the chiral effective field theory (EFT) potential in harmonic-oscillator (HO) model space. The low energy constants (LECs) are utilized to absorb not just the ultra-violet 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 (NN) 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 $T_{lab}=100$ MeV with number of HO basis $n_{max}$ 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. Our work serves as the input to perform ab-initio calculations.
Symmetries and conservation laws of the damped harmonic oscillator
Amitava Choudhuri; Subrata Ghosh; B Talukdar
2008-04-01
We work with a formulation of Noether-symmetry analysis which uses the properties of infinitesimal point transformations in the space-time variables to establish the association between symmetries and conservation laws of a dynamical system. Here symmetries are expressed in the form of generators. We have studied the variational or Noether symmetries of the damped harmonic oscillator representing it by an explicitly time-dependent Lagrangian and found that a five-parameter group of transformations leaves the action integral invariant. Amongst the associated conserved quantities only two are found to be functionally independent. These two conserved quantities determine the solution of the problem and correspond to a two-parameter Abelian subgroup.
Excitation with quantum light. I. Exciting a harmonic oscillator
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.
Ecolosical optimization of an irreversible harmonic oscillators Carnot heat engine
LIU XiaoWei; CHEN LinGen; WU Feng; SUN FengRui
2009-01-01
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.
Quantum Encoding and Entanglement in Terms of Phase Operators Associated with Harmonic Oscillator
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.
Entangled Harmonic Oscillators and Space-time Entanglement
Baskal, Sibel; Noz, Marilyn E
2016-01-01
The mathematical basis for the Gaussian entanglement is discussed in detail, as well as its implications in the internal space-time structure of relativistic extended particles. It is shown that the Gaussian entanglement shares the same set of mathematical formulas with the harmonic oscillator in the Lorentz-covariant world. It is thus possible to transfer the concept of entanglement to the Lorentz-covariant picture of the bound state which requires both space and time separations between two constituent particles. These space and time variables become entangled as the bound state moves with a relativistic speed. It is shown also that our inability to measure the time-separation variable leads to an entanglement entropy together with a rise in the temperature of the bound state. As was noted by Paul A. M. Dirac in 1963, the system of two oscillators contains the symmetries of O(3,2) de Sitter group containing two O(3,1) Lorentz groups as its subgroups. Dirac noted also that the system contains the symmetry of...
Novel Approach for Solving the Equation of Motion of a Simple Harmonic Oscillator. Classroom Notes
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…
Generalized Harmonic Oscillator and the Schr(o)dinger Equation with Position-Dependent Mass
JU Guo-Xing; CAI Chang-Ying; REN Zhong-Zhou
2009-01-01
We study the generalized harmonic oscillator that has both the position-dependent mass and the potential depending on the form of mass function in a more general framework. The explicit expressions of the eigenvalue and eigenfunction for such a system are given, they have the same forms as those for the usual harmonic oscillator with constant mass. The coherent state and its properties for the system with PDM are also discussed. We give the corresponding effective potentials for several mass functions, the systems with such potentials are isospectral to the usual harmonic oscillator.
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.
Supersymmetry and the constants of motion of the two-dimensional isotropic harmonic oscillator
Torres del Castillo, G.F. [Departamento de Fisica Matematica, Instituto de Ciencias, Universidad Autonoma de Puebla, 72570 Puebla (Mexico); Tepper G, T. [Escuela de Ciencias, Departamento de Fisica y Matematicas, Universidad de Las Americas-Puebla, Santa Catarina Martir, 72820 Cholula, Puebla (Mexico)
2002-07-01
It is shown that the constants of motion of the two-dimensional isotropic harmonic oscillator not related to the rotational invariance of the Hamiltonian can be derived using the ideas of supersymmetric quantum mechanics. (Author)
On the limiting behavior of a harmonic oscillator with random external disturbance
G. L. Kulinich
1995-01-01
Full Text Available This paper deals with the limiting behavior of a harmonic oscillator under the external random disturbance that is a process of the white noise type. Influence of noises is investigated in resonance and non-resonance cases.
Propagator for a Time-Dependent Damped Harmonic Oscillator with a Force Quadratic in Velocity
HUANG Bo-Wen; GU Zhi-Yu; QIAN Shang-Wu
2003-01-01
The propagator for a time-dependent damped harmonic oscillator with a force quadratic in velocity isobtained by making a specific coordinate transformation and by using the method of time-dependent invariant.
The calculating formula for radial matrix elements of a relativistic harmonic oscillator
强稳朝
2003-01-01
A universal practical formula is given for calculating an integral which includes two confluent hypergeometric functions, power and exponential functions; then by means of this formula, the expressions of the radial matrix elements for a relativistic harmonic oscillator are given.
Transformation between harmonic-oscillator wave functions in different coordinate bases
Davies, K.T.R.; Krieger, S.J.
1981-10-01
Coefficients are derived for transformations between harmonic oscillator wave functions in different coordinate representations. Such coefficients have been found especially useful in performing static Hartree-Fock calculations for nuclei of widely varying shapes.
Braid group representations from a deformation of the harmonic oscillator algebra
Tarlini, Marco
2016-01-01
We describe a new technique to obtain representations of the braid group B_n from the R-matrix of a quantum deformed algebra of the one dimensional harmonic oscillator. We consider the action of the R-matrix not on the tensor product of representations of the algebra, that in the harmonic oscillator case are infinite dimensional, but on the subspace of the tensor product corresponding to the lowest weight vectors.
A Fulling-Kuchment theorem for the 1D harmonic oscillator
Guillemin, Victor
2011-01-01
We prove that there exists a pair of "non-isospectral" 1D semiclassical Schr\\"odinger operators whose spectra agree modulo h^\\infty. In particular, all their semiclassical trace invariants are the same. Our proof is based on an idea of Fulling-Kuchment and Hadamard's variational formula applied to suitable perturbations of the harmonic oscillator. Keywords: Inverse spectral problems, semiclassical Schr\\"odinger operators, trace invariants, Hadamard's variational formula, harmonic oscillator, Penrose mushroom, Sturm-Liouville theory.
Exact diagonalization of the D-dimensional spatially confined quantum harmonic oscillator
Kunle Adegoke
2016-01-01
Full Text Available In the existing literature various numerical techniques have been developed to quantize the confined harmonic oscillator in higher dimensions. In obtaining the energy eigenvalues, such methods often involve indirect approaches such as searching for the roots of hypergeometric functions or numerically solving a differential equation. In this paper, however, we derive an explicit matrix representation for the Hamiltonian of a confined quantum harmonic oscillator in higher dimensions, thus facilitating direct diagonalization.
Harmonic oscillator in Snyder space: The classical case and the quantum case
Carlos Leiva
2010-02-01
The harmonic oscillator in Snyder space is investigated in its classical and quantum versions. The classical trajectory is obtained and the semiclassical quantization from the phase space trajectories is discussed. An effective cut-off to high frequencies is found. The quantum version is developed and an equivalent usual harmonic oscillator is obtained through an effective mass and an effective frequency introduced in the model. This modified parameters give us a modified energy spectrum also.
Design cusp electron gun for of 0.6 THz 3rd-harmonic large orbit gyrotron%0.6THz三次谐波大回旋电子枪设计
马春燕; 胡强; 袁学松; 韩煜; 鄢扬
2012-01-01
Large orbit axis-encircling electron beams can provide improved coupling and mode selectivity in a high harmonic terahertz gyrotron. For developing a 0. 6 THz 3rd-harmonic large orbit gyrotron, a cusp gun with a beam voltage of 55 kV and a beam current of 1 A has been designed based on a comparatively simple Pierce-type electron gun and cusp magnetic field. The optimized result shows that the velocity ratio, axial velocity spread and transverse velocity spread are 1. 53, 7. 10% and 3. 39% , respectively.%基于会切磁场的理论模型,采用粒子模拟软件对0.6 THz三次谐波的太赫兹回旋管所需的大回旋电子光学系统进行研究.文中通过大量的模拟计算,分析讨论了不同参数对电子注的横向速度离散、纵向速度离散及横纵速度比的影响,优化了电子光学系统的性能参量,得到符合设计要求且具有工程实际应用的电子枪,该电子枪能够产生55 kV,1A,横向速度离散为3.39％、纵向速度离散为7.10％、横纵速度比为1.53的大回旋电子注.
Hamiltonian of mean force and a damped harmonic oscillator in an anisotropic medium
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.
Innovation on high-power long-pulse gyrotrons
Litvak, Alexander; Sakamoto, Keishi; Thumm, Manfred
2011-12-01
Progress in the worldwide development of high-power gyrotrons for magnetic confinement fusion plasma applications is described. After technology breakthroughs in research on gyrotron components in the 1990s, significant progress has been achieved in the last decade, in particular, in the field of long-pulse and continuous wave (CW) gyrotrons for a wide range of frequencies. At present, the development of 1 MW-class CW gyrotrons has been very successful; these are applicable for self-ignition experiments on fusion plasmas and their confinement in the tokamak ITER, for long-pulse confinement experiments in the stellarator Wendelstein 7-X (W7-X) and for EC H&CD in the future tokamak JT-60SA. For this progress in the field of high-power long-pulse gyrotrons, innovations such as the realization of high-efficiency stable oscillation in very high order cavity modes, the use of single-stage depressed collectors for energy recovery, highly efficient internal quasi-optical mode converters and synthetic diamond windows have essentially contributed. The total tube efficiencies are around 50% and the purity of the fundamental Gaussian output mode is 97% and higher. In addition, activities for advanced gyrotrons, e.g. a 2 MW gyrotron using a coaxial cavity, multi-frequency 1 MW gyrotrons and power modulation technology, have made progress.
Bohá\\{v}cik, J; August\\'\\{i}n, P
2013-01-01
We find the possibility of the non-perturbative an-harmonic correction to Mehler's formula for propagator of the harmonic oscillator. We evaluate the conditional Wiener measure functional integral with a term of the fourth order in the exponent by an alternative method as in the conventional perturbative approach. In contrast to the conventional perturbation theory, we expand into power series the term linear in the integration variable in the exponent. We discuss the case, when the starting point of the propagator is zero. We present the results in analytical form for positive and negative frequency.
Recent result of gyrotron operation in NIFS
Ito Satoshi
2015-01-01
Full Text Available In the last Large Helical Device (LHD experimental campaign, a 154GHz gyrotron which had been conditioned to generate 1 MW/2 s, 0.5 MW/CW was installed for LHD experiments. Four high power gyrotrons (three-77 GHz/1~1.5 MW and one-154 GHz/1 MW and a CW gyrotron (84 GHz/0.2 MW are ready. Our experiment requires high energy and various injection patterns for Electron Cyclotron Resonance Heating (ECRH. Higher individual injection power and various injection patterns, we developed a power enhancement method by stepped anode acceleration voltage control and operated the gyrotron in the hard excitation region. These operations were realized by a remote controlled waveform generator. However the oscillation map of high power or long pulse operation in the hard excitation region were limited because in order to achieve the hard excitation region by the anode voltage control one must pass through the high anode current phase within a time short enough that the anode or the anode power supply is not overloaded. This limitation becomes more critical when the gyrotron beam current is increased in order to increase the output power. In the long pulse operation it was impossible to reach the hard excitation region in a low beam current (<10A.
Recent result of gyrotron operation in NIFS
Ito, Satoshi; Shimozuma, Takashi; Yoshimura, Yasuo; Igami, Hiroe; Takahashi, Hiromi; Nishiura, Masaki; Kobayashi, Sakuji; Mizuno, Yoshinori; Okada, Kota; Kubo, Shin
2015-03-01
In the last Large Helical Device (LHD) experimental campaign, a 154GHz gyrotron which had been conditioned to generate 1 MW/2 s, 0.5 MW/CW was installed for LHD experiments. Four high power gyrotrons (three-77 GHz/1~1.5 MW and one-154 GHz/1 MW) and a CW gyrotron (84 GHz/0.2 MW) are ready. Our experiment requires high energy and various injection patterns for Electron Cyclotron Resonance Heating (ECRH). Higher individual injection power and various injection patterns, we developed a power enhancement method by stepped anode acceleration voltage control and operated the gyrotron in the hard excitation region. These operations were realized by a remote controlled waveform generator. However the oscillation map of high power or long pulse operation in the hard excitation region were limited because in order to achieve the hard excitation region by the anode voltage control one must pass through the high anode current phase within a time short enough that the anode or the anode power supply is not overloaded. This limitation becomes more critical when the gyrotron beam current is increased in order to increase the output power. In the long pulse operation it was impossible to reach the hard excitation region in a low beam current (<10A).
On harmonic oscillators and their Kemmer relativistic forms
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.
Double Fourier Harmonic Balance Method for Nonlinear Oscillators by Means of Bessel Series
2014-10-16
Duffing oscillator . As an example of the results, the predicted period of a simple pendulum swinging between −90° and +90° is found to be only 0.4% larger...Eq. (42). 4.5 The Duffing oscillator with zero linear term For an anharmonic oscillator having restoring force f(x) = αx3, define ω0 = A √ α. Using...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
The 3-Dimensional q-Deformed Harmonic Oscillator and Magic Numbers of Alkali Metal Clusters
Bonatsos, Dennis; Raychev, P P; Roussev, R P; Terziev, P A; Bonatsos, Dennis
1999-01-01
Magic numbers predicted by a 3-dimensional q-deformed harmonic oscillator with Uq(3) > SOq(3) symmetry are compared to experimental data for alkali metal clusters, as well as to theoretical predictions of jellium models, Woods--Saxon and wine bottle potentials, and to the classification scheme using the 3n+l pseudo quantum number. The 3-dimensional q-deformed harmonic oscillator correctly predicts all experimentally observed magic numbers up to 1500 (which is the expected limit of validity for theories based on the filling of electronic shells), thus indicating that Uq(3), which is a nonlinear extension of the U(3) symmetry of the spherical (3-dimensional isotropic) harmonic oscillator, is a good candidate for being the symmetry of systems of alkali metal clusters.
Ground-state isolation and discrete flows in a rationally extended quantum harmonic oscillator
Cariñena, José F
2016-01-01
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 non-physical 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.
Time dependent quantum harmonic oscillator subject to a sudden change of mass: continuous solution
Moya C, H. [INAOE, Coordinacion de Optica, AP 51 y 216, 72000 Puebla (Mexico); Fernandez G, M. [Depto. de Fisica, CBI, Universidad Autonoma Metropolitana - Iztapalapa, 09340, Mexico, D.F. AP 55-534 (Mexico)
2007-07-01
We show that a harmonic oscillator subject to a sudden change of mass produces squeezed states. Our study is based on an approximate analytic solution to the time-dependent harmonic oscillator equation with a sub period function parameter. This continuous treatment differs from former studies that involve the matching of two time-independent solutions at the discontinuity. This formalism requires an ad hoc transformation of the original differential equation and is also applicable for rapid, although not necessarily instantaneous, mass variations. (Author)
Yilun Shang
2012-07-01
Full Text Available In this paper, we investigate the leader-follower synchronization ofcoupled second-order linear harmonic oscillators with the presence ofrandom noises and time delays. The interaction topology is modeledby a weighted directed graph and the weights are perturbed by whitenoise. On the basis of stability theory of stochastic differential delayequations, algebraic graph theory and matrix theory, we show that thecoupled harmonic oscillators can be synchronized almost surely withrandom perturbation and time delays. Numerical examples are presentedto illustrate our theoretical results.
Megawatt, 330 Hz PRF tunable gyrotron experiments
Spark, S. N.; Cross, A. W.; Phelps, A. D. R.; Ronald, K.
1994-12-01
Repetitively pulsed and cw gyrotrons have hitherto used thermionic cathodes, whereas cold cathode gyrotrons have normally operated as ‘single shot’ devices. The novel results presented here show that cold cathode gyrotrons can be successfully pulsed repetitively. A tunable gyrotron with a pulse repetition frequency (PRF) of 150Hz is demonstrated. This system developed >4MW mm-wave output pulses at 100GHz. The gyrotron is based on a two-electrode configuration comprising a field-immersed, field emission, cold cathode and a shaped anode cavity. A superconducting magnet was used to produce the homogeneous intra-cavity magnetic field and a cable pulser was used to drive the electron beam. This pulser produced up to a (200±20)kV pulse with 10ns rise time, a 100ns flat top, a 10ns decay with a characteristic impedance of 200Ω. The energy storage capacity of the cable pulser was 35J. The charging unit limited the maximum PRF to 330Hz. Due to spark gap switching limitations 330Hz was only obtainable in 5 to 10 pulse bursts. For substantial periods of the order of 30 seconds, 100Hz PRF was achieved over an oscillating range of 28 to 100GHz and 150Hz PRF was achieved at 80GHz. No degradation effects on the mm-wave output pulse was evident due to diode recovery time throughout this series of results. A subsequent conclusion is that the diode recovery time in our cold cathode gyrotron is less than 3ms.
Martinez, D [Universidad Autonoma de la Ciudad de Mexico, Plantel Cuautepec, Av. La Corona 320, Col. Loma la Palma, Delegacion Gustavo A. Madero, 07160, Mexico DF (Mexico); Flores-Urbina, J C; Mota, R D [Unidad Profesional Interdisciplinaria de Ingenieria y Tecnologias Avanzadas, IPN. Av. Instituto Politecnico Nacional 2580, Col. La Laguna Ticoman, Delegacion Gustavo A. Madero, 07340 Mexico DF (Mexico); Granados, V D [Escuela Superior de Fisica y Matematicas, Instituto Politecnico Nacional, Ed. 9, Unidad Profesional Adolfo Lopez Mateos, 07738 Mexico DF (Mexico)], E-mail: dmartinezs77@yahoo.com.mx
2010-04-02
We apply the Schroedinger factorization to construct the ladder operators for the hydrogen atom, Mie-type potential, harmonic oscillator and pseudo-harmonic oscillator in arbitrary dimensions. By generalizing these operators we show that the dynamical algebra for these problems is the su(1, 1) Lie algebra.
Deformed Harmonic Oscillators for Metal Clusters and Balian-Bloch Theory
Bonatsos, D; Raychev, P P; Terziev, P A; Bonatsos, Dennis
2003-01-01
The predictions for the shell structure of metal clusters of the three-dimensional q-deformed harmonic oscillator (3D q-HO), utilizing techniques of quantum groups and having the symmetry Uq(3)$\\supset$SOq(3), are compared to the restrictions imposed by the periodic orbit theory of Balian and Bloch, of electrons moving in a spherical cavity. It is shown that agreement between the predictions of the two models is established through the introduction of an additional term to the Hamiltonian of the 3D q-HO, which does not influence the predictions for supershells. This term preserves the Uq(3)$\\supset$SOq(3) symmetry, while in addition it can be derived through a variational procedure, analogous to the one leading from the usual harmonic oscillator to the Morse oscillator by introducing the concept of the Variable Frequency Oscillator (VFO).
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.
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.
刘宇峰; 曾谨言
1997-01-01
The factorization of the radial Schrodinger equation of n-dimensional (n≥2) hydrogen atoms and isotropic harmonic oscillators was investigated and four kinds of raising and lowering operators were derived.The relation between n -dimensional (n≥2) and one-dimensional hydrogen atoms and harmonic oscillators was discussed.
Nonlinear Analysis of a Cross-Coupled Quadrature Harmonic Oscillator
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens;
2004-01-01
We derive the dynamic equations governing the cross-coupled quadrature oscillator leading to an expression for the trade-off between signal quadrature and close-in phase noise. The theory shows that nonlinearity in the coupling transconductance results in AM-PM noise close to the carrier, which...
Exact solutions of N-dimensional harmonic oscillator via Laplace transformation
Chen Gang
2005-01-01
The N-dimensional Schrodinger equation for the harmonic oscillator is reduced to a first-order differential equation in terms of the Laplace transformation and the exact bound state solutions are derived. It is shown that this method of solving Schrodinger equation may serve as a substitute for the standard functional, analytical approach also in lower dimensions.
Continuous vs. discrete models for the quantum harmonic oscillator and the hydrogen atom
Lorente, M
2001-01-01
The Kravchuk and Meixner polynomials of discrete variable are introduced for the discrete models of the harmonic oscillator and hydrogen atom. Starting from Rodrigues formula we construct raising and lowering operators, commutation and anticommutation relations. The physical properties of discrete models are figured out through the equivalence with the continuous models obtained by limit process.
Continuous vs. discrete models for the quantum harmonic oscillator and the hydrogen atom
Lorente, Miguel
2001-07-01
The Kravchuk and Meixner polynomials of discrete variable are introduced for the discrete models of the harmonic oscillator and hydrogen atom. Starting from Rodrigues formula we construct raising and lowering operators, commutation and anticommutation relations. The physical properties of discrete models are figured out through the equivalence with the continuous models obtained by limit process.
su(2) Lie algebra approach for the Feynman propagator of the one-dimensional harmonic oscillator
Martínez, D.; Avendaño, C. G.
2014-04-01
We evaluate the Feynman propagator for the harmonic oscillator in one dimension. Considering the ladder operators for the Hamiltonian of this system, we construct a set of operators which satisfy the su(2) Lie algebra to obtain Mehler’s formula.
Convergence for Fourier Series Solutions of the Forced Harmonic Oscillator II
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…
Coherent presentation of density operator of the harmonic oscillator in thermostat
Avakyan, R.M. [Department of Physics, Yerevan State University, 0025 Yerevan (Armenia); Hayrapetyan, A.G. [Institute of Applied Problems of Physics, National Academy of Sciences of Republic of Armenia, 0014 Yerevan (Armenia)], E-mail: armen@iapp.sci.am; Khachatryan, B.V.; Petrosyan, R.G. [Department of Physics, Yerevan State University, 0025 Yerevan (Armenia)
2007-12-10
Based on basis of the coherent states the density matrix of harmonic oscillator in thermostat is obtained. This method is mathematically refined and physically transparent for the interpretation of quantum phenomena in classical language. Such an approach gives an opportunity to easily find the density matrix in the multi-dimensional case.
Generalized Uncertainty Principle Corrections to the Simple Harmonic Oscillator in Phase Space
Das, Saurya; 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.
Continuous vs. discrete models for the quantum harmonic oscillator and the hydrogen atom
Lorente, M.
2004-01-01
The Kravchuk and Meixner polynomials of discrete variable are introduced for the discrete models of the harmonic oscillator and hydrogen atom. Starting from Rodrigues formula we construct raising and lowering operators, commutation and anticommutation relations. The physical properties of discrete models are figured out through the equivalence with the continuous models obtained by limit process.
Mota, R.D. [Unidad Profesional Interdisciplinaria de Ingenieria y Tecnologias Avanzadas, Mexico DF (Mexico)]. E-mail: mota@gina.esfm.ipn.mx; ravelo@esfm.ipn.mx; Granados, V.D.; Queijeiro, A.; Garcia, J. [Escuela Superior de Fisica y Matematicas, Instituto Politecnico Nacional, Mexico DF (Mexico)
2002-03-29
For the quantum two-dimensional isotropic harmonic oscillator we show that the Infeld-Hull radial operators, as well as those of the supersymmetric approach for the radial equation, are contained in the constants of motion of the problem. (author)
Gauge Invariance of a Time-Dependent Harmonic Oscillator in Magnetic Dipole Approximation
WANG Fei; QIAN Shang-Wu; FU Li-Ping; WANG Jing-Shan; GUO Ke-Tao
2008-01-01
A manifestly gauge-invariant formulation of non-relativistic quantum mechanics is applied to the case of time-dependent harmonic oscillator in the magnetic dipole approximation. A genera/ equation for obtaining gauge-invariant transition probability amplitudes is derived.
Spatial growth of fundamental solutions for certain perturbations of the harmonic oscillator
Jensen, Arne; Yajima, Kenji
2010-01-01
We consider the fundamental solution for the Cauchy problem for perturbations of the harmonic oscillator by time dependent potentials which grow at spatial infinity slower than quadratic but faster than linear functions and whose Hessian matrices have a fixed sign. We prove that the fundamental...
Density Matrix and Squeezed Vacuum State for General Coupling Harmonic Oscillator
SONG Tong-Qiang
2003-01-01
By taking a unitary transformation approach, we study two harmonic oscillators with both kinetic coupling and coordinate coupling terms, and derive the density matrix of the system. The results show that the ground state of the system is a rotated two single-mode squeezed state.
Bonatsos, Dennis; Kolokotronis, P; Lenis, D; Bonatsos, Dennis
1994-01-01
The symmetry algebra of the two-dimensional quantum harmonic oscillator with rational ratio of frequencies is identified as a non-linear extension of the u(2) algebra. The finite dimensional representation modules of this algebra are studied and the energy eigenvalues are determined using algebraic methods of general applicability to quantum superintegrable systems.
Exact Solutions of Two Coupled Harmonic Oscillators Related to the Sp(4, R) Lie Algebra
PAN Feng; DAI LianRong
2001-01-01
Exact solutions of the eigenvalue problem of two coupled harmonic oscillators related to the Sp(4, R) Lie algebra are derived by using an algebraic method. It is found that the energy spectrum of the system is determined by one-boson excitation energies built on a vector coherent state of Sp(4, R) U(2).``
The study of entanglement and teleportation of the harmonic oscillator bipartite coherent states
A Rabeie and
2015-01-01
Full Text Available In this paper, we reproduce the harmonic oscillator bipartite coherent states with imperfect cloning of coherent states. We show that if these entangled coherent states are embedded in a vacuum environment, their entanglement is degraded but not totally lost . Also, the optimal fidelity of these states is worked out for investigating their teleportation
Attainable conditions and exact invariant for the time-dependent harmonic oscillator
Guasti, Manuel Fernandez [Lab. de Optica Cuantica, Dep. de Fisica, Universidad A. Metropolitana, Unidad Iztapalapa, Mexico DF, Ap. Post. 55-534 (Mexico)
2006-09-22
The time-dependent oscillator equation is solved numerically for various trajectories in amplitude and phase variables. The solutions exhibit a finite time-dependent parameter whenever the squared amplitude times the derivative of the phase is invariant. If the invariant relationship does not hold, the time-dependent parameter has divergent singularities. These observations lead to the proposition that the harmonic oscillator equation with finite time-dependent parameter must have amplitude and phase solutions fulfilling the invariant relationship. Since the time-dependent parameter or the potential must be finite for any real oscillator implementation, the invariant must hold for any such physically realizable system.
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.
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
Ehlers, E. F.
1974-01-01
A finite difference method for the solution of the transonic flow about a harmonically oscillating wing is presented. The partial differential equation for the unsteady transonic flow was linearized by dividing the flow into separate steady and unsteady perturbation velocity potentials and by assuming small amplitudes of harmonic oscillation. The resulting linear differential equation is of mixed type, being elliptic or hyperbolic whereever the steady flow equation is elliptic or hyperbolic. Central differences were used for all derivatives except at supersonic points where backward differencing was used for the streamwise direction. Detailed formulas and procedures are described in sufficient detail for programming on high speed computers. To test the method, the problem of the oscillating flap on a NACA 64A006 airfoil was programmed. The numerical procedure was found to be stable and convergent even in regions of local supersonic flow with shocks.
Chang-shui FENG; Wei-qiu ZHU
2009-01-01
We studied the response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control using the stochastic averaging method. First, the time-delayed feedback bang-bang control force is expressed approximately in terms of the system state variables without time delay. Then the averaged Ito stochastic differential equations for the system are derived using the stochastic averaging method. Finally, the response of the system is obtained by solving the Fokker-Plank-Kolmogorov (FPK) equation associated with the averaged Ito equations. A Duffing oscillator with time-delayed feedback bang-bang control under combined harmonic and white noise excitations is taken as an example to illus-trate the proposed method. The analytical results are confirmed by digital simulation. We found that the time delay in feedback bang-bang control will deteriorate the control effectiveness and cause bifurcation of stochastic jump of Duffing oscillator.
Nonclassical phase-space trajectories for the damped harmonic quantum oscillator
Pachon, L.A. [Departamento de Fisica, Universidad Nacional de Colombia, Bogota D.C. (Colombia); Institut fuer Physik, Universitaet Augsburg, Universitaetsstrasse 1, D-86135 Augsburg (Germany); CeiBA - Complejidad, Bogota D.C. (Colombia); Ingold, G.-L., E-mail: gert.ingold@physik.uni-augsburg.de [Institut fuer Physik, Universitaet Augsburg, Universitaetsstrasse 1, D-86135 Augsburg (Germany); Dittrich, T. [Departamento de Fisica, Universidad Nacional de Colombia, Bogota D.C. (Colombia); CeiBA - Complejidad, Bogota D.C. (Colombia)
2010-10-05
Graphical abstract: The phase-space path-integral approach to the damped harmonic oscillator is analyzed beyond the Markovian approximation and the appearance of nonclassical trajectories is discussed. - Abstract: The phase-space path-integral approach to the damped harmonic oscillator is analyzed beyond the Markovian approximation. It is found that pairs of nonclassical trajectories contribute to the path-integral representation of the Wigner propagating function. Due to the linearity of the problem, the sum coordinate of a pair still satisfies the classical equation of motion. Furthermore, it is shown that the broadening of the Wigner propagating function of the damped oscillator arises due to the time-nonlocal interaction mediated by the heat bath.
Wayne Cheng-Wei Huang
2013-01-01
Full Text Available Stochastic electrodynamics (SED predicts a Gaussian probability distribution for a classical harmonic oscillator in the vacuum field. This probability distribution is identical to that of the ground state quantum harmonic oscillator. Thus, the Heisenberg minimum uncertainty relation is recovered in SED. To understand the dynamics that give rise to the uncertainty relation and the Gaussian probability distribution, we perform a numerical simulation and follow the motion of the oscillator. The dynamical information obtained through the simulation provides insight to the connection between the classic double-peak probability distribution and the Gaussian probability distribution. A main objective for SED research is to establish to what extent the results of quantum mechanics can be obtained. The present simulation method can be applied to other physical systems, and it may assist in evaluating the validity range of SED.
Evolution of a quantum harmonic oscillator coupled to a minimal thermal environment
Vidiella-Barranco, A.
2016-10-01
In this paper it is studied the influence of a minimal thermal environment on the dynamics of a quantum harmonic oscillator (labelled A), prepared in a coherent state. The environment itself consists of a second oscillator (labelled B), initially in a thermal state. Two types of interaction Hamiltonians are considered, and the time-evolution of the reduced density operator of oscillator A is compared to the one obtained from the usual master equation approach, i.e., assuming that oscillator A is coupled to a large reservoir. An analysis of the linear entropy evolution of oscillator A shows that simplified models may be able to describe important features related to the phenomenon of decoherence, such as the rapid growth of the linear entropy, as well as its dependence on the effective temperature of the environment.
An easy trick to a periodic solution of relativistic harmonic oscillator
Jafar Biazar
2014-04-01
Full Text Available In this paper, the relativistic harmonic oscillator equation which is a nonlinear ordinary differential equation is investigated by Homotopy perturbation method. Selection of a linear operator, which is a part of the main operator, is one of the main steps in HPM. If the aim is to obtain a periodic solution, this choice does not work here. To overcome this lack, a linear operator is imposed, and Fourier series of sines will be used in solving the linear equations arise in the HPM. Comparison of the results, with those of resulted by Differential Transformation and Harmonic Balance Method, shows an excellent agreement.
López-Ruiz, F. F.; Guerrero, J.; Aldaya, V.; Cossío, F.
2012-08-01
Using a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations (LSODE), including systems with friction linear in velocity such as the damped harmonic oscillator, can be related to the quantum free-particle dynamical system. This implies that symmetries and simple computations in the free particle can be exported to the LSODE-system. The quantum Arnold transformation is given explicitly for the damped harmonic oscillator, and an algebraic connection between the Caldirola-Kanai model for the damped harmonic oscillator and the Bateman system will be sketched out.
Manipulating Fock states of a harmonic oscillator while preserving its linearity
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.
Forced harmonic oscillations of the Euler-Bernoulli beam with resistance forces
Yuriy S. Krutiy
2015-12-01
Full Text Available The important issue in the oscillation theory is the study of resistance impact on oscillatory processes. Unlike the calculations of free oscillations, that reside in determination of natural frequencies and waveshapes and unlike the calculations of forced oscillations far away from resonance, that are performing without reference to friction, the oscillations researches in vicinity of resonance need accounting of friction forces. Special attention is paid to forced transverse fluctuations in beams as an important technical problem for engineering and building. Aim: The aim of the work is constructing of analytical solution of the problem of forced transverse vibrations of a straight rod with constant cross-section, which is under the influence of the harmonic load taking into account external and internal resistances. Materials and Methods: The internal resistance is taken into account using the corrected hypothesis of Kelvin-Voigt which reflects the empirically proven fact about the frequency-independent internal friction in the material. The external friction is also considered as frequency-independent. Results: An analytical solution is built for the differential equation of forced transverse oscillations of a straight rod with constant cross-section which is under the influence of the harmonic load taking into account external and internal resistances. As a result, analytically derived formulae are presented which describe the forced dynamic oscillations and the dynamic internal forces due to the harmonic load applied to the rod thus reducing the problem with any possible fixed ends to the search of unknown integration constants represented in a form of initial parameters.
Quantum entanglement in coupled harmonic oscillator systems: from micro to macro
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.
Coherent states for nonlinear harmonic oscillator and some of its properties
Amir, Naila, E-mail: naila.amir@live.com, E-mail: naila.amir@sns.nust.edu.pk; Iqbal, Shahid, E-mail: sic80@hotmail.com, E-mail: siqbal@sns.nust.edu.pk [School of Natural Sciences, National University of Sciences and Technology, Islamabad (Pakistan)
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.
On the Bandgap quantum coupler and the harmonic oscillator interacting with a reservoir
Quijas, P C G
2007-01-01
In order to be able to study dissipation, the interaction between a single system and their environment was introduced in quantum mechanics. Master and quantum Langeving equations was derived and, also, decoherence was studied using this approach. One of the most used model in this field of research is a single harmonic oscillator interacting with an infinite number of harmonic oscillators. In this work we analytically solve, with the evolution operator method, the Schrodinger equation for this model in the case of resonance. Also we address a different aspect of the quantum computing with linear optics. That is, we propose the linear bandgap quantum coupler, in the cases N=2 and N=3, to generate a new phase operator $U_{dp}^{\\pi} $ working on the two and three qubits basis like an alternative realization of a quantum phase gate.
Non-isospectrality of the generalized Swanson Hamiltonian and harmonic oscillator
Midya, Bikashkali; Dube, P P; Roychoudhury, Rajkumar, E-mail: bikash.midya@gmail.com, E-mail: ppdube1@gmail.com, E-mail: raj@isical.ac.in [Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108 (India)
2011-02-11
The generalized Swanson Hamiltonian H{sub GS}=w(a-tilde a-tilde{sup {dagger}}+1/2)+{alpha}{alpha}-tilde{sup 2}+{beta}a-tilde{sup {dagger}}{sup 2} with a-tilde = A(x) d/dx + B(x) can be transformed into an equivalent Hermitian Hamiltonian with the help of a similarity transformation. It is shown that the equivalent Hermitian Hamiltonian can be further transformed into the harmonic oscillator Hamiltonian so long as [a-ilde,a-tilde{sup {dagger}}]=constant. However, the main objective of this communication is to show that though the commutator of a-tilde and a-tilde{sup {dagger}} is constant, the generalized Swanson Hamiltonian is not necessarily isospectral to the harmonic oscillator. The reason for this anomaly is discussed in the framework of position-dependent mass models by choosing A(x) as the inverse square root of the mass function. (fast track communication)
Non-isospectrality of the generalized Swanson Hamiltonian and harmonic oscillator
Midya, Bikashkali; Roychoudhury, Rajkumar
2011-01-01
The generalized Swanson Hamiltonian $H_{GS} = w (\\tilde{a}\\tilde{a}^\\dag+ 1/2) + \\alpha \\tilde{a}^2 + \\beta \\tilde{a}^{\\dag^2}$ with $\\tilde{a} = A(x)d/dx + B(x)$, can be transformed into an equivalent Hermitian Hamiltonian with the help of a similarity transformation. It is shown that the equivalent Hermitian Hamiltonian can be further transformed into the harmonic oscillator Hamiltonian so long as $[\\tilde{a},\\tilde{a}^\\dag]=$ constant. However, the main objective of this paper is to show that though the commutator of $\\tilde{a}$ and $\\tilde{a}^\\dag$ is constant, the generalized Swanson Hamiltonian is not necessarily isospectral to the harmonic oscillator. Reason for this anomaly is discussed in the frame work of position dependent mass models by choosing $A(x)$ as the inverse square root of the mass function.
Bound States Energies of a Harmonic Oscillator Perturbed by Point Interactions
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
Nonlinear supercoherent states and geometric phases for the supersymmetric harmonic oscillator
Díaz-Bautista, Erik
2016-01-01
Nonlinear supercoherent states, which are eigenstates of nonlinear deformations of the Kornbluth-Zypman annihilation operator for the supersymmetric harmonic oscillator, will be studied. They turn out to be expressed in terms of nonlinear coherent states, associated to the corresponding deformations of the standard annihilation operator. We will discuss as well the Heisenberg uncertainty relation for a special particular case, in order to compare our results with those obtained for the Kornbluth-Zypman linear supercoherent states. As the supersymmetric harmonic oscillator executes an evolution loop, such that the evolution operator becomes the identity at a certain time, thus the linear and nonlinear supercoherent states turn out to be cyclic and the corresponding geometric phases will be evaluated.
Md. Alal Hosen
2015-01-01
Full Text Available In the present paper, a complicated strongly nonlinear oscillator with cubic and harmonic restoring force, has been analysed and solved completely by harmonic balance method (HBM. Investigating analytically such kinds of oscillator is very difficult task and cumbersome. In this study, the offered technique gives desired results and to avoid numerical complexity. An excellent agreement was found between approximate and numerical solutions, which prove that HBM is very efficient and produces high accuracy results. It is remarkably important that, second-order approximate results are almost same with exact solutions. The advantage of this method is its simple procedure and applicable for many other oscillatory problems arising in science and engineering.
Saha, Anirban
2015-01-01
We investigate the quantum mechanical transitions, induced by the combined effect of Gravitational wave (GW) and noncommutative (NC) structure of space, among the states of a 2-dimensional harmonic oscillator. The phonon modes excited by the passing GW within the resonant bar-detector are formally identical to forced harmonic oscillator and they represent a length variation of roughly the same order of magnitude as the characteristic length-scale of spatial noncommutativity estimated from the phenomenological upper bound of the NC parameter. This motivates our present work. We employ a number of different GW wave-forms that are typically expected from possible astronomical sources. We find that the transition probablities are quite sensitive to the nature of polarization of the GW. We further elaborate on the particular type of sources of GW radiation which can induce transitions that can be used as effective probe of the spatial noncommutative structure.
A Novel SIW-Based Planar W-Band GaAs Gunn Harmonic Oscillator
Liu, Yong; Tang, Xiao-Hong; Cao, Zhou
2010-10-01
Based on the substrate integrated waveguide (SIW) technology, a novel W-band low phase noise GaAs Gunn planar harmonic oscillator is developed in this paper. The technique of harmonic extraction from Gunn diodes and SIW resonant cavity structures are discussed in detail. Due to the high quality factor and planar structure of the SIW cavity resonator, the oscillator is characterized by some advantages such as low phase noise, small size, low cost and planar integration. The measured phase noise is -108.56 dBc/Hz at 1 MHz offset and the output power is more than 9 dBm at 94.78 GHz. A 300 MHz of linear tuning range with power fluctuation less than 1.5 dB is observed when the Gunn diode is biased from 4 to 5.3 V.
Sameer M. Ikhdair
2013-01-01
Full Text Available The Klein-Gordon (KG equation for the two-dimensional scalar-vector harmonic oscillator plus Cornell potentials in the presence of external magnetic and Aharonov-Bohm (AB flux fields is solved using the wave function ansatz method. The exact energy eigenvalues and the wave functions are obtained in terms of potential parameters, magnetic field strength, AB flux field, and magnetic quantum number. The results obtained by using different Larmor frequencies are compared with the results in the absence of both magnetic field (ωL = 0 and AB flux field (ξ=0 cases. Effect of external fields on the nonrelativistic energy eigenvalues and wave function solutions is also precisely presented. Some special cases like harmonic oscillator and Coulombic fields are also studied.
Pulsed high harmonic generation of light due to pumped Bloch oscillations in noninteracting metals
Freericks, J K; Kemper, A F; Devereaux, T P; 10.1088/0031-8949/2012/T151/014062
2012-01-01
We derive a simple theory for high-order harmonic generation due to pumping a noninteracting metal with a large amplitude oscillating electric field. The model assumes that the radiated light field arises from the acceleration of electrons due to the time-varying current generated by the pump, and also assumes that the system has a constant density of photoexcited carriers, hence it ignores the dipole excitation between bands (which would create carriers in semiconductors). We examine the circumstances under which odd harmonic frequencies would be expected to dominate the spectrum of radiated light, and we also apply the model to real materials like ZnO, for which high-order harmonic generation has already been demonstrated in experiments.
On anomalous diffusion and the fractional generalized Langevin equation for a harmonic oscillator
Figueiredo Camargo, R.; Capelas de Oliveira, E.; Vaz, J.
2009-12-01
The fractional generalized Langevin equation (FGLE) is proposed to discuss the anomalous diffusive behavior of a harmonic oscillator driven by a two-parameter Mittag-Leffler noise. The solution of this FGLE is discussed by means of the Laplace transform methodology and the kernels are presented in terms of the three-parameter Mittag-Leffler functions. Recent results associated with a generalized Langevin equation are recovered.
An application of the three-dimensional q-deformed harmonic oscillator to the shell model
Raychev, P.P. [Dipartimento di Scienze Fisiche, Universita di Napoli ' Federico II' , Monte S Angelo, via Cintia, I-80125 Napoli (Italy); Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tzarigrad Road, BG-1784 Sofia (Bulgaria); Roussev, R.P.; Terziev, P.A. [Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tzarigrad Road, BG-1784 Sofia (Bulgaria); Lo Iudice, N. [Dipartimento di Scienze Fisiche, Universita di Napoli ' Federico II' , Monte S Angelo, via Cintia, I-80125 Napoli (Italy)
1998-10-01
A procedure for the construction of a q-deformed version of the Hamiltonian of the three-dimensional harmonic oscillator (HO), based on the application of q-deformed algebras, is presented. The spectrum of this Hamiltonian is not degenerated in the quantum number of the q-deformed angular momentum. The results together with their applicability to the shell model are compared with the predictions of the modified HO. (author)
Parallel-path biquad active-RC oscillator with enhanced harmonic rejection
Vosper, J. V.; Heima, M.; Cryan, R. A.
1995-04-01
A biquad active-RC oscillator is described and a linear analysis given which shows that harmonics injected within the feedback loop are multiplied by a factor which is inversely proportional to the effective open-loop Q-factor Q(sub 0). Experimental results show that distortion is low at high Q(sub 0) values even when saturated operation of the main gain-producing opamp is allowed.
(3+1)-Dimensional Quantum Mechanics from Monte Carlo Hamiltonian: Harmonic Oscillator
LUO Xiang-Qian; XU Hao; YANG Jie-Chao; WANG Yu-Li; CHANG Di; LIN Yin; Helmut Kroger
2001-01-01
In Lagrangian formulation, it is extremely difficult to compute the excited spectrum and wavefunctions ora quantum theory via Monte Carlo methods. Recently, we developed a Monte Carlo Hamiltonian method for investigating this hard problem and tested the algorithm in quantum-mechanical systems in 1+1 and 2t1 dimensions. In this paper we apply it to the study of thelow-energy quantum physics of the (3+1)-dimensional harmonic oscillator.``
Solution to the Master Equation of a Free Damped Harmonic Oscillator with Linear Driving
杨洁; 逯怀新; 赵博; 赵梅生; 张永德
2003-01-01
We use the Lie algebra representation theory for superoperators to solve the master equation for a harmonic oscillator with a linear driving term in a squeezed thermal reservoir. By using the quantum displacement transformation and squeeze transformation, we show that the master equation has an su(1, 1) Lie algebra structure,with which we obtain the explicit solution to the master equation. A simple but typical example is given to illustrate our method.
Dynamics of a harmonic oscillator in a finite-dimensional Hilbert space
Kuang Leman (CCAST (World Lab.), Beijing, BJ (China) Dept. of Physics and Inst. of Physics, Hunan Normal Univ. (China)); Wang Fabo (Dept. of Physics, Hunan Normal Univ. (China)); Zhou Yanguo (Dept. of Physics, Hunan Normal Univ. (China))
1993-11-29
Some dynamical properties of a finite-dimensional Hilbert space harmonic oscillator (FDHSHO) are studied. The time evolution of the position and momentum operators and the second-order quadrature squeezing are investigated in detail. It is shown that the coherent states of the FDHSHO are not the minimum uncertainty states of the position and momentum operators of the FDHSHO. It is found that the second-order squeezing of the quadrature operators vanishes and reappears periodically in the time evolution. (orig.)
Spatial growth of fundamental solutions for certain perturbations of the harmonic oscillator
Jensen, Arne; Yajima, Kenji
We consider the fundamental solution for the Cauchy problem for perturbations of the harmonic oscillator by time dependent potentials, which grow at spatial infinity slower than quadratic, but faster than linear functions, and whose Hessian matrices have a fixed sign. We prove that the fundamental...... solution at resonant times grows indefinitely at spatial infinity with the algebraic growth rate, which increases indefinitely, when the growth rate of perturbations at infinity decrease from the near quadratic to the near linear ones....
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.
Das, A; Das, A; Wotzasek, C
1995-01-01
We study a supersymmetric 2-dimensional harmonic oscillator which carries a representation of the general graded Lie algebra GL(2\\vert1) formulate it on the superspace, and discuss its physical spectrum.
WEI Gao-Feng; LONG Chao-Yun; LONG Zheng-Wen; QIN Shui-Jie
2008-01-01
In this paper,the isotropic charged harmonic oscillator in uniform magnetic field is researched in the non-commutative phase space;the corresponding exact energy is obtained,and the analytic eigenfunction is presented in terms of the confluent hypergeometric function.It is shown that in the non-commutative space,the isotropic charged harmonic oscillator in uniform magnetic field has the similar behaviors to the Landau problem.
Wang, Hailing [Institute of Applied Mathematics, Chongqing University of Posts and Telecommunications, Chongqing 400065 (China); Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon (Hong Kong); Chung, Kwok-wai, E-mail: makchung@cityu.edu.hk [Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon (Hong Kong)
2012-02-27
The analytical solutions of nonlinear oscillators obtained from most perturbation or approximate methods usually have poor accuracy near homoclinic/heteroclinic (HH) orbits. In this Letter, we propose a nonlinear time transformation method to overcome such difficulty. In particular, we apply such method with Padé approximation to find analytical solutions of a generalized Duffing-harmonic oscillator having a rational form for the potential energy. For some parametric ranges, HH orbits exist in such an oscillator. For analytical approximation of periodic solution obtained from the present method, it is shown that the relative error of period with respect to the exact period tends to zero when the amplitude of periodic solution tends to either zero or infinity. The relative error is still very small even near to HH orbits. Furthermore, analytical approximate of HH orbits can also be obtained. From the illustrative examples, the phase portraits are in excellent agreement with the exact HH orbits. The results from the present method are compared with the exact solutions and that from the cubication method. -- Highlights: ► A nonlinear transformation is proposed for a generalized Duffing-harmonic oscillator. ► The relative error of period with respect to the exact one is always very small. ► Approximate solution of homoclinic/heteroclinic orbits can be obtained. ► Phase portraits are in excellent agreement even at homoclinic/heteroclinic orbits.
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…
The Harmonic Oscillator in the Classical Limit of a Minimal-Length Scenario
Quintela, T. S.; Fabris, J. C.; Nogueira, J. A.
2016-09-01
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.
The Large-Volume Limit of a Quantum Tetrahedron is a Quantum Harmonic Oscillator
Schliemann, John
2013-01-01
It is shown that the volume operator of a quantum tetrahedron is, in the sector of large eigenvalues, accurately described by a quantum harmonic oscillator. This result relies on the fact that (i) the volume operator couples only neighboring states of its standard basis, and (ii) its matrix elements show a unique maximum as a function of internal angular momentum quantum numbers. These quantum numbers, considered as a continuous variable, are the coordinate of the oscillator describing its quadratic potential, while the corresponding derivative defines a momentum operator. We also analyze the scaling properties of the oscillator parameters as a function of the size of the tetrahedron, and the role of different angular momentum coupling schemes.
Belendez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es; Gimeno, E.; Alvarez, M.L.; Mendez, D.I.; Hernandez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2008-09-22
An analytical approximate technique for conservative nonlinear oscillators is proposed. This method is a modification of the rational harmonic balance method in which analytical approximate solutions have rational form. This approach gives us the frequency of the motion as a function of the amplitude of oscillation. We find that this method works very well for the whole range of parameters, and excellent agreement of the approximate frequencies with the exact one has been demonstrated and discussed. The most significant features of this method are its simplicity and its excellent accuracy for the whole range of oscillation amplitude values and the results reveal that this technique is very effective and convenient for solving conservative truly nonlinear oscillatory systems with complex nonlinearities.
Use of videos for students to see the effect of changing gravity on harmonic oscillators
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.
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.
Effect of ion compensation of the beam space charge on gyrotron operation
Fokin, A. P.; Glyavin, M. Yu. [Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod 603950 (Russian Federation); Nusinovich, G. S. [Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742-3511 (United States)
2015-04-15
In gyrotrons, the coherent radiation of electromagnetic waves takes place when the cyclotron resonance condition between the wave frequency and the electron cyclotron frequency or its harmonic holds. The voltage depression caused by the beam space charge field changes the relativistic cyclotron frequency and, hence, can play an important role in the beam-wave interaction process. In long pulse and continuous-wave regimes, the beam space charge field can be partially compensated by the ions, which appear due to the beam impact ionization of neutral molecules of residual gases in the interaction space. In the present paper, the role of this ion compensation of the beam space charge on the interaction efficiency is analyzed. We also analyze the effect of the electron velocity spread on the limiting currents and discuss some effects restricting the ion-to-beam electron density ratio in the saturation stage. It is shown that the effect of the ion compensation on the voltage depression caused by the beam space charge field can cause significant changes in the efficiency of gyrotron operation and, in some cases, even result in the break of oscillations.
A new method based on the harmonic balance method for nonlinear oscillators
Chen, Y.M. [Department of Mechanics, Zhongshan University, Guangzhou 510275 (China); Liu, J.K. [Department of Mechanics, Zhongshan University, Guangzhou 510275 (China)], E-mail: jikeliu@hotmail.com
2007-08-27
The harmonic balance (HB) method as an analytical approach is widely used for nonlinear oscillators, in which the initial conditions are generally simplified by setting velocity or displacement to be zero. Based on HB, we establish a new theory to address nonlinear conservative systems with arbitrary initial conditions, and deduce a set of over-determined algebraic equations. Since these deduced algebraic equations are not solved directly, a minimization problem is constructed instead and an iterative algorithm is employed to seek the minimization point. Taking Duffing and Duffing-harmonic equations as numerical examples, we find that these attained solutions are not only with high degree of accuracy, but also uniformly valid in the whole solution domain.
Systematic Observation of Time-Dependent Phenomena in the RF Output Spectrum of High Power Gyrotrons
Kern Stefan
2012-09-01
Full Text Available At IHM/KIT, high power gyrotrons with conventional cavity (e.g. 1 MW CW at 140 GHz for the stellarator Wendelstein 7-X and coaxial cavity (2 MW shortpulse at 170 GHz for ITER for fusion applications are being developed and verified experimentally. Especially with respect to the problem of parasitic RF oscillations in the beam tunnel of some W7-X tubes, investigations of the gyrotron RF output spectrum have proved to be a valuable source of diagnostic information. Signs of transient effects in millisecond pulses, like frequency switching or intermittent low-frequency modulation, have indicated that truly time-dependent measurements with high frequency resolution and dynamic range could give deeper insight into these phenomena. In this paper, an improved measurement system is presented, which employs a fast oscilloscope as receiver. Shorttime Fourier transform (STFT is applied to the time-domain signal, yielding time-variant spectra with frequency resolutions only limited by acquisition length and STFT segmentation choice. Typical reasonable resolutions are in the range of 100 kHz to 10 MHz with a currently memory-limited maximum acquisition length of 4 ms. A key feature of the system consists in the unambiguity of frequency measurement: The system receives through two parallel channels, each using a harmonic mixer (h = 9 – 12 to convert the signal from RF millimeter wave frequencies (full D-Band, 110 – 170 GHz to IF (0 – 3 GHz. For each IF output signal of each individual mixer, injection side and receiving harmonic are initially not known. Using accordingly determined LO frequencies, this information is retrieved from the redundancy of the channels, yielding unambiguously reconstructed RF spectra with a total span of twice the usable receiver IF bandwidth, up to ≈ 6 GHz in our case. Using the system, which is still being improved continuously, various transient effects like cavity mode switching, parasitic oscillation frequency variation
Soviet Development of Gyrotrons
1986-05-01
Relationship Type of Device Remarks V, - Vc, anomalous Doppler Capable of 100 percent efficiency, CRM but more cumbersome than Cheren- kov devices V...authors; and discusses inlividual Soviet reseaLc- groups, the basic organizational units responAiLle for the CRM and gyrotron research and development. The...maintained a cCnEistEnt iecord of significant achievements; it has managed to overcome the systenic yeaxness of the Soviet R&C systeg in teimg atle to
Resonant behavior of a harmonic oscillator with fluctuating mass driven by a Mittag-Leffler noise
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.
Pupasov-Maksimov, Andrey M.
2015-12-01
It is shown that fundamental solutions Kσ(x , y ; t) = of the non-stationary Schrödinger equation (Green functions, or propagators) for the rational extensions of the Harmonic oscillator Hσ =Hosc + ΔVσ are expressed in terms of elementary functions only. An algorithm to calculate explicitly Kσ for an arbitrary increasing sequence of positive integers σ is given, and compact expressions for K { 1 , 2 } and K { 2 , 3 } are presented. A generalization of Mehler's formula to the case of exceptional Hermite polynomials is given.
Instrumentation and control of harmonic oscillators via a single-board microprocessor-FPGA device
Picone, Rico A. R.; Davis, Solomon; Devine, Cameron; Garbini, Joseph L.; Sidles, John A.
2017-04-01
We report the development of an instrumentation and control system instantiated on a microprocessor-field programmable gate array (FPGA) device for a harmonic oscillator comprising a portion of a magnetic resonance force microscope. The specific advantages of the system are that it minimizes computation, increases maintainability, and reduces the technical barrier required to enter the experimental field of magnetic resonance force microscopy. Heterodyne digital control and measurement yields computational advantages. A single microprocessor-FPGA device improves system maintainability by using a single programming language. The system presented requires significantly less technical expertise to instantiate than the instrumentation of previous systems, yet integrity of performance is retained and demonstrated with experimental data.
Mota, R D [Departamento de Matematicas, Centro de Investigacion y de Estudios Avenzados del IPN, 07000, Mexico DF (Mexico); Granados, V D [Escuela Superior de Fisica y Matematicas, Instituto Politecnico Nacional, Ed. 9, Unidad Profesional Adolfo Lopez Mateos, 07738 Mexico DF (Mexico); Queijeiro, A [Escuela Superior de Fisica y Matematicas, Instituto Politecnico Nacional, Ed. 9, Unidad Profesional Adolfo Lopez Mateos, 07738 Mexico DF (Mexico); Garcia, J [Escuela Superior de Fisica y Matematicas, Instituto Politecnico Nacional, Ed. 9, Unidad Profesional Adolfo Lopez Mateos, 07738 Mexico DF (Mexico); Guzman, L [Unidad Profesional Interdisciplinaria en Ingenieria y Tecnologias Avanzadas, IPN Av. Instituto Politecnico Nacional No 2580, Col. La Laguna Ticoman, Delegacion Gustavo A Madero, CP 07340 Mexico DF (Mexico)
2003-05-02
We show that the supersymmetric radial ladder operators of the three-dimensional isotropic harmonic oscillator are contained in the spherical components of the creation and annihilation operators of the system. Also, we show that the constants of motion of the problem, written in terms of these spherical components, lead us to second-order radial operators. Further, we show that these operators change the orbital angular momentum quantum number by two units and are equal to those obtained by the Infeld-Hull factorization method.
A hidden non-Abelian monopole in a 16-dimensional isotropic harmonic oscillator
Le, Van-Hoang; Nguyen, Thanh-Son; Phan, Ngoc-Hung [Department of Physics, HCMC University of Pedagogy, 280 An Duong Vuong, Ward 10, Dist. 5, Ho Chi Minh City (Viet Nam)
2009-05-01
We suggest one variant of generalization of the Hurwitz transformation by adding seven extra variables that allow an inverse transformation to be obtained. Using this generalized transformation we establish the connection between the Schroedinger equation of a 16-dimensional isotropic harmonic oscillator and that of a nine-dimensional hydrogen-like atom in the field of a monopole described by a septet of potential vectors in a non-Abelian model of 28 operators. The explicit form of the potential vectors and all the commutation relations of the algebra are given./.
Molecular Solid EOS based on Quasi-Harmonic Oscillator approximation for phonons
Menikoff, Ralph [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
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.
A least squares finite element scheme for transonic flow around harmonically oscillating airfoils
Cox, C. L.; Fix, G. J.; Gunzburger, M. D.
1983-01-01
The present investigation shows that a finite element scheme with a weighted least squares variational principle is applicable to the problem of transonic flow around a harmonically oscillating airfoil. For the flat plate case, numerical results compare favorably with the exact solution. The obtained numerical results for the transonic problem, for which an exact solution is not known, have the characteristics of known experimental results. It is demonstrated that the performance of the employed numerical method is independent of equation type (elliptic or hyperbolic) and frequency. The weighted least squares principle allows the appropriate modeling of singularities, which such a modeling of singularities is not possible with normal least squares.
Two-Variable Hermite Function as Quantum Entanglement of Harmonic Oscillator's Wave Functions
LU Hai-Liang; FAN Hong-Yi
2007-01-01
We reveal that the two-variable Hermite function hm,n, which is the generalized Bargmann representation of the two-mode Fock state, involves quantum entanglement of harmonic oscillator's wave functions.The Schmidt decomposition of hm,n is derived. It also turns out that hm,n can be generated by windowed Fourier transform of the single-variable Hermite functions. As an application, the wave function of the two-variable Hermite polynomial state S(r)Hm,n(μa1+, μa2+)|00〉, which is the minimum uncertainty state for sum squeezing, in 〈η| representation is calculated.
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.
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.
Transient energy excitation in shortcuts to adiabaticity for the time dependent harmonic oscillator
Chen, Xi
2010-01-01
There is recently a surge of interest to cut down the time it takes to change the state of a quantum system adiabatically. We study for the time-dependent harmonic oscillator the transient energy excitation in speed-up processes designed to reproduce the initial populations at some predetermined final frequency and time, providing 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.
Surface second harmonic generation of chiral molecules using three-coupled-oscillator model
Wang Xiao-Ou; Li Chun-Fei; Li Jun-Qing
2006-01-01
Based on the three-coupled-oscillator molecular model we proposed, the relation between the second-order susceptibilities of a chiral film and the molecular hyperpolarizabilities is given. The effect of microscopic parameters on the second-order susceptibilities is simulated numerically and the difference between the efficiencies of s-polarized second-harmonic fields induced by the left- and the right-handed circularly-polarized fundamental beams is discussed. The theoretical basis for studying second-order nonlinear optical properties of the chiral molecular media with a tripod-like structure is provided in this paper.
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.
Fundamental and Subharmonic Resonances of Harmonically Oscillation with Time Delay State Feedback
A.F. EL-Bassiouny
2006-01-01
Full Text Available Time delays occur in many physical systems. In particular, when automatic control is used with structural or mechanical systems, there exists a delay between measurement of the system state and corrective action. The concept of an equivalent damping related to the delay feedback is proposed and the appropriate choice of the feedback gains and the time delay is discussed from the viewpoint of vibration control. We investigate the fundamental resonance and subharmonic resonance of order one-half of a harmonically oscillation under state feedback control with a time delay. By using the multiple scale perturbation technique, the first order approximation of the resonances are derived and the effect of time delay on the resonances is investigated. The fixed points correspond to a periodic motion for the starting system and we show the external excitation-response and frequency-response curves. We analyze the effect of time delay and the other different parameters on these oscillations.
Kurt, Arzu; Eryigit, Resul, E-mail: resul@ibu.edu.tr
2015-12-18
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. - Highlights: • Exact analytical expressions for up to the fourth-order master equation are obtained. • High and low temperature limits of anomalous diffusion coefficients are elucidated. • Convergence range of the oscillator and the bath parameters discussed.
The sojourn time of the inverted harmonic oscillator on the noncommutative plane
Guo Guangjie; Ren Zhongzhou; Ju Guoxing [Department of Physics, Nanjing University, Nanjing 210093 (China); Long Chaoyun, E-mail: woggj@126.com [Department of Physics, Guizhou University, Guiyang 550025 (China)
2011-10-21
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 {omega} of the potential. However, in this paper, we find that the spatial noncommutativity makes the sojourn time a concave function of {omega} with a minimum at an inflection point {omega}{sub 0}. Furthermore, if {omega} 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. (paper)
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.
Harmonic versus subharmonic patterns in a spatially forced oscillating chemical reaction.
Hammele, Martin; Zimmermann, Walter
2006-06-01
The effects of a spatially periodic forcing on an oscillating chemical reaction as described by the Lengyel-Epstein model are investigated. We find a surprising competition between two oscillating patterns, where one is harmonic and the other subharmonic with respect to the spatially periodic forcing. The occurrence of a subharmonic pattern is remarkable as well as its preference up to rather large values of the modulation amplitude. For small modulation amplitudes we derive from the model system a generic equation for the envelope of the oscillating reaction that includes an additional forcing contribution, compared to the amplitude equations known from previous studies in other systems. The analysis of this amplitude equation allows the derivation of analytical expressions even for the forcing corrections to the threshold and to the oscillation frequency, which are in a wide range of parameters in good agreement with the numerical analysis of the complete reaction equations. In the nonlinear regime beyond threshold, the subharmonic solutions exist in a finite range of the control parameter that has been determined by solving the reaction equations numerically for various sets of parameters.
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.
Derivation of exact master equation with stochastic description: Dissipative harmonic oscillator
Li, Haifeng; Wang, Shikuan
2011-01-01
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 comes out. 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...
On the local virial theorems for linear and isotropic harmonic oscillator potentials in d dimensions
Bencheikh, K [Departement de Physique, Laboratoire de physique quantique et systemes dynamiques, Universite de Setif, Setif 19000 (Algeria); Nieto, L M, E-mail: bencheikh.kml@gmail.co [Departamento de Fisica Teorica, Atomica y Optica, Universidad de Valladolid, 47071 Valladolid (Spain)
2010-09-17
For the system of noninteracting fermions in a one-body potential V(r-vector), the local virial theorems (LVT) are relations, at a given point r-vector in space, between this potential, kinetic energy and particle densities. It was recently shown (Brack et al 2010 J. Phys. A: Math. Theor. 43 255204) that for d-dimensional linear and also for isotropic harmonic oscillator potentials these LVTs are exactly satisfied. We present alternative and simple proofs of these theorems, by consideration of the canonical or Bloch density matrix and its relation to the kinetic energy density. The explicit analytical forms of the Bloch density matrix are used for the above-mentioned potentials to achieve the proofs. For the case of linear potential, we obtain a more general result for the so-called semilocal virial theorem, and for the harmonic oscillator potential case we derive a new relationship between the diagonal part of the canonical bloch density and the kinetic energy density.
Haxton, Wick
2007-01-01
Semi-leptonic electroweak interactions in nuclei - such as \\beta decay, \\mu capture, charged- and neutral-current neutrino reactions, and electron scattering - are described by a set of multipole operators carrying definite parity and angular momentum, obtained by projection from the underlying nuclear charge and three-current operators. If these nuclear operators are approximated by their one-body forms and expanded in the nucleon velocity through order |\\vec{p}|/M, where \\vec{p} and M are the nucleon momentum and mass, a set of seven multipole operators is obtained. Nuclear structure calculations are often performed in a basis of Slater determinants formed from harmonic oscillator orbitals, a choice that allows translational invariance to be preserved. Harmonic-oscillator single-particle matrix elements of the multipole operators can be evaluated analytically and expressed in terms of finite polynomials in q^2, where q is the magnitude of the three-momentum transfer. While results for such matrix elements a...
ABC of ladder operators for rationally extended quantum harmonic oscillator systems
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.
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+εV(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.
Reduction of Sub-Harmonic Oscillations in Flyback Converter for High Power Factor
Mr.M.SubbaRao,
2011-03-01
Full Text Available For High power factor (HPFoperation of flyback converter in continuous conduction mode(CCM, a variety of current mode control techniques, such as peak current control, Average current control andcharge control techniques has been analyzed. But these are suffer from stability problem due to presence of sub-harmonic oscillations and noise immunity. This can be overcome by using slope compensationtechnique, but it increases complexity .So the proposed technique in this paper i.e., a Single-Reset Integrator based line current shaping controller is a simple and accurate line current shaping controllerwith reduced sub-harmonic oscillations. In this paper presents the comparison between charge control technique with proposed control i.e., A Single-Reset Integrator based line current shaping controller for a 200 W,140V A.C input and 48V D.C output single phase flyback converter for HPF.MATLAB/Simulink software is used for implementation and simulation results shows the performance of proposed controller.
140 GHz gyrotron development program. Quarterly report No. 4, January-March 1985
Felch, K.L.; Bier, R.E.; Craig, L.J.; Fox, L.J.; Hu, G.; Huey, H.E.; Ives, R.L.; Jory, H.R.; Lopez, N.C.; Reysner, P.I.
1986-01-01
The objective of this program is to develop a gyrotron oscillator capable of producing 100 kW CW at 140 GHz. Further analysis of the electron guns, interaction cavity, and beam tunnel designs for the first two experimental tubes, Experimental Tube 1 and preprototype Tube 1, is presented. A window deflection tester has been built and initial deflection test results are given. The first 140 GHz gyrotron magnet has successfully passed the major points in the acceptance test. The detailed results of the magnet acceptance test are discussed. Progress concerning the fabrication of 149 GHz gyrotron components, diagnostics, and protective devices, as well as the status of Experimental Tube 1, are summarized.
Norrelykke, Simon F
2011-01-01
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) Effects of finite sampling-rate and -time, described exactly here, are similar for other stochastic dynamical systems-e.g. motile micro-organisms and their time-lapse recorded trajectories. (ii) The same statistics is satisfied by any experimental system to the extent 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 effects of finite sampling rate and sampling time for these models as well. Finally, we give a brief discussion of nondimensio...
On a q-extension of the linear harmonic oscillator with the continuous orthogonality property on ℝ
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.
Sameer M.Ikhdair; Majid Hamzavi
2012-01-01
We study the effects of the perpendicular magnetic and Aharonov Bohm (AB) flux fields on the energy levels of a two-dimensional (2D) Klein-Gordon (KG) particle subjected to an equal scalar and vector pseudo-harmonic oscillator (PHO).We calculate the exact energy eigenvalues and normalized wave functions in terms of chemical potential parameter,magnetic field strength,AB flux field,and magnetic quantum number by means of the Nikiforov-Uvarov (NU) method.The non-relativistic limit,PHO,and harmonic oscillator solutions in the existence and absence of external fields are also obtained.
Arcos-Olalla, Rafael, E-mail: olalla@fisica.ugto.mx [Departamento de Física, DCI Campus León, Universidad de Guanajuato, Apdo. Postal E143, 37150 León, Gto. (Mexico); Reyes, Marco A., E-mail: marco@fisica.ugto.mx [Departamento de Física, DCI Campus León, Universidad de Guanajuato, Apdo. Postal E143, 37150 León, Gto. (Mexico); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo. Postal 3-74 Tangamanga, 78231 San Luis Potosí, S.L.P. (Mexico)
2012-10-01
We introduce an alternative factorization of the Hamiltonian of the quantum harmonic oscillator which leads to a two-parameter self-adjoint operator from which the standard harmonic oscillator, the one-parameter oscillators introduced by Mielnik, and the Hermite operator are obtained in certain limits of the parameters. In addition, a single Bernoulli-type parameter factorization, which is different from the one introduced by M.A. Reyes, H.C. Rosu, and M.R. Gutiérrez [Phys. Lett. A 375 (2011) 2145], is briefly discussed in the final part of this work. -- Highlights: ► Factorizations with operators which are not mutually adjoint are presented. ► New two-parameter and one-parameter self-adjoint oscillator operators are introduced. ► Their eigenfunctions are two- and one-parameter deformed Hermite functions.
Belendez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es; Fernandez, E. [Departamento de Optica, Farmacologia y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Rodes, J.J. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fuentes, R.; Pascual, I. [Departamento de Optica, Farmacologia y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2009-02-16
The harmonic balance method is used to construct approximate frequency-amplitude relations and periodic solutions to an oscillating charge in the electric field of a ring. By combining linearization of the governing equation with the harmonic balance method, we construct analytical approximations to the oscillation frequencies and periodic solutions for the oscillator. To solve the nonlinear differential equation, firstly we make a change of variable and secondly the differential equation is rewritten in a form that does not contain the square-root expression. The approximate frequencies obtained are valid for the complete range of oscillation amplitudes and excellent agreement of the approximate frequencies and periodic solutions with the exact ones are demonstrated and discussed.
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…
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.
Rong Haiwu
2014-01-01
Full Text Available The erosion of the safe basins and chaotic motions of a nonlinear vibroimpact oscillator under both harmonic and bounded random noise is studied. Using the Melnikov method, the system’s Melnikov integral is computed and the parametric threshold for chaotic motions is obtained. Using the Monte-Carlo and Runge-Kutta methods, the erosion of the safe basins is also discussed. The sudden change in the character of the stochastic safe basins when the bifurcation parameter of the system passes through a critical value may be defined as an alternative stochastic bifurcation. It is founded that random noise may destroy the integrity of the safe basins, bring forward the occurrence of the stochastic bifurcation, and make the parametric threshold for motions vary in a larger region, hence making the system become more unsafely and chaotic motions may occur more easily.
The Klauder-Daubechies Construction of the Phase Space Path Integral and the Harmonic Oscillator
Govaerts, Jan; Mattelaer, Olivier
2009-01-01
The canonical operator quantisation formulation corresponding to the Klauder-Daubechies construction of the phase space path integral is considered. This formulation is explicitly applied and solved in the case of the harmonic oscillator, thereby illustrating in a manner complementary to Klauder and Daubechies' original work some of the promising features offered by their construction of a quantum dynamics. The Klauder-Daubechies functional integral involves a regularisation parameter eventually taken to vanish, which defines a new physical time scale. When extrapolated to the field theory context, besides providing a new regularisation of short distance divergences, keeping a finite value for that time scale offers some tantalising prospects when it comes to strong gravitational quantum systems.
Infrared and ultraviolet cutoffs in variational calculations with a harmonic oscillator basis
Coon, Sidney A
2013-01-01
I abstract from a recent publication [1] the motivations for, analysis in and conclusions of a study of the ultraviolet and infrared momentum regulators induced by the necessary truncation of the model spaces formed by a variational trial wave function. This trial function is built systematically from a complete set of many-body basis states based upon three-dimensional harmonic oscillator (HO) functions. Each model space is defined by a truncation of the expansion characterized by a counting number (N) and by the intrinsic scale ($\\hbar\\omega$) of the HO basis. Extending both the uv cutoff to infinity and the ir cutoff to zero is prescribed for a converged calculation. In [1] we established practical procedures which utilize these regulators to obtain the extrapolated result from sequences of calculations with model spaces. Finally, I update this subject by mentioning recent work on our extrapolation prescriptions which have appeared since the submission of [1]. The numerical example chosen for this contribu...
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.
Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations
Schubert, O; Langer, F; Urbanek, B; Lange, C; Huttner, U; Golde, D; Meier, T; Kira, M; Koch, S W; Huber, R
2016-01-01
Ultrafast charge transport in strongly biased semiconductors is at the heart of highspeed electronics, electro-optics, and fundamental solid-state physics. Intense light pulses in the terahertz (THz) spectral range have opened fascinating vistas: Since THz photon energies are far below typical electronic interband resonances, a stable electromagnetic waveform may serve as a precisely adjustable bias. Novel quantum phenomena have been anticipated for THz amplitudes reaching atomic field strengths. We exploit controlled THz waveforms with peak fields of 72 MV/cm to drive coherent interband polarization combined with dynamical Bloch oscillations in semiconducting gallium selenide. These dynamics entail the emission of phase-stable high-harmonic transients, covering the entire THz-to-visible spectral domain between 0.1 and 675 THz. Quantum interference of different ionization paths of accelerated charge carriers is controlled via the waveform of the driving field and explained by a quantum theory of inter- and in...
Fourth-order master equation for a charged harmonic oscillator coupled to an electromagnetic field
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.
Deformed Relativistic Hartree Theory in Coordinate Space and in Harmonic Oscillator Basis
ZHOU Shan-Gui; MENG Jie; Shuhei YAMAJI; YANG Si-Chun
2000-01-01
The deformed relativistic Hartree theory (DRH) is solved both in coordinate space (DRH-c) and in harmonic oscillator basis (DRH-o). Results obtained from these two methods are compared in details. The DRH-c and DRH-o calculations give similar total binding energies, deformation, level structures and radii for nitrogen iso topes, while their descriptions on the density distributions for drip-line nuclei are very different. The large spatiai istributions of nucleon densities, which is crucial to understand a weakly bound system, can only be obtained by DRH-c calculations. This implies that the DRH theory should be solved in coordinate space in order to describe uclei close to the drip line.
A dynamical systems approach to Bohmian trajectories in a 2D harmonic oscillator
Borondo, F [Departamento de Quimica, and Instituto Mixto de Ciencias Matematicas CSIC-UAM-UC3M-UCM, Universidad Autonoma de Madrid, Cantoblanco-28049 Madrid (Spain); Luque, A; Villanueva, J [Departament de Matematica Aplicada I, Universitat Politecnica de Catalunya, 08028 Barcelona (Spain); Wisniacki, D A [Departamento de Fisica ' J. J. Giambiagi' , FCEN, UBA, Pabellon 1, Ciudad Universitaria, 1428 Buenos Aires (Argentina)], E-mail: f.borondo@uam.es, E-mail: alejandro.luque@upc.edu, E-mail: jordi.villanueva@upc.edu, E-mail: wisniacki@df.uba.ar
2009-12-11
Vortices are known to play a key role in the dynamics of the quantum trajectories defined within the framework of the de Broglie-Bohm formalism of quantum mechanics. It has been rigourously proved that the motion of a vortex in the associated velocity field can induce chaos in these trajectories, and numerical studies have explored the rich variety of behaviors that due to their influence can be observed. In this paper, we go one step further and show how the theory of dynamical systems can be used to construct a general and systematic classification of such dynamical behaviors. This should contribute to establish some firm grounds on which the studies on the intrinsic stochasticity of Bohm's quantum trajectories can be based. An application to the two-dimensional isotropic harmonic oscillator is presented as an illustration.
Gilles Regniers
2009-11-01
Full Text Available In a system of coupled harmonic oscillators, the interaction can be represented by a real, symmetric and positive definite interaction matrix. The quantization of a Hamiltonian describing such a system has been done in the canonical case. In this paper, we take a more general approach and look at the system as a Wigner quantum system. Hereby, one does not assume the canonical commutation relations, but instead one just requires the compatibility between the Hamilton and Heisenberg equations. Solutions of this problem are related to the Lie superalgebras gl(1|n and osp(1|2n. We determine the spectrum of the considered Hamiltonian in specific representations of these Lie superalgebras and discuss the results in detail. We also make the connection with the well-known canonical case.
Harmonic and Dirac oscillators in a (2+1)-dimensional noncommutative space
Vega, F
2013-01-01
We study the Harmonic and Dirac Oscillator problem extended to a three-dimensional noncom- mutative space where the noncommutativity is induced by a shift of the dynamical variables with generators of SL(2;R) in a unitary irreducible representation. The Hilbert space gets the structure of a direct product with the representation space as a factor, where there exist operators which realize the algebra of Lorentz transformations. The spectrum of these models are considered in perturbation theory, both for small and large noncommutativity parameters, ?nding no constraints between coordinates and momenta noncom- mutativity parameters. Since the representation space of the unitary irreducible representations SL(2;R) can be realized in terms of spaces of square-integrable functions, we conclude that these models are equivalent to quantum mechanical models of particles living in a space with an additional compact dimension. PACS: 03.65.-w; 11.30.Cp; 02.40.Gh
Xiaowei Liu, Lingen Chen, Feng Wu, Fengrui Sun
2015-01-01
Full Text Available The optimal performance of an irreversible quantum Carnot refrigerator with working medium consisting of many non-interacting harmonic oscillators is investigated in this paper. The quantum refrigerator cycle is composed of two isothermal processes and two irreversible adiabatic processes, and the irreversibilities of heat resistance, internal friction and bypass heat leakage are considered. By using the quantum master equation, semi-group approach and finite time thermodynamics (FTT, this paper derives the cooling load and coefficient of performance (COP of the quantum refrigeration cycle and provides detailed numerical examples. At high temperature limit, the cooling load versus COP characteristic curves are plotted, and effects of internal friction and bypass heat leakage on the optimal performance of the quantum refrigerator are discussed. Three special cases, i.e., endoreversible, frictionless and without bypass heat leakage, are discussed in brief.
The optimal performance of a quantum refrigeration cycle working with harmonic oscillators
Lin Bi Hong; Hua Ben
2003-01-01
The cycle model of a quantum refrigeration cycle working with many non-interacting harmonic oscillators and consisting of two isothermal and two constant-frequency processes is established. Based on the quantum master equation and semi-group approach, the general performance of the cycle is investigated. Expressions for some important performance parameters, such as the coefficient of performance, cooling rate, power input, and rate of the entropy production, are derived. Several interesting cases are discussed and, especially, the optimal performance of the cycle at high temperatures is discussed in detail. Some important characteristic curves of the cycle, such as the cooling rate versus coefficient of performance curves, the power input versus coefficient of performance curves, the cooling rate versus power input curves, and so on, are presented. The maximum cooling rate and the corresponding coefficient of performance are calculated. Other optimal performances are also analysed. The results obtained here ...
V. Mohammadi
2015-01-01
Full Text Available We study the two-dimensional Klein-Gordon equation with spin symmetry in the presence of the superintegrable potentials. On Euclidean space, the SO(3 group generators of the Schrödinger-like equation with the Kepler-Coulomb potential are represented. In addition, by Levi-Civita transformation, the Schrödinger-like equation with harmonic oscillator which is dual to the Kepler-Coulomb potential and the SU(2 group generators of associated system are studied. Also, we construct the quadratic algebra of the hyperboloid superintegrable system. Then, we obtain the corresponding Casimir operators and the structure functions and the relativistic energy spectra of the corresponding quasi-Hamiltonians by using the quadratic algebra approach.
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.
Bose-Einstein condensation in a two-component Bose gas with harmonic oscillator interaction
Abulseoud, A. A.; Abbas, A. H.; Galal, A. A.; El-Sherbini, Th M.
2016-07-01
In this article a system containing two species of identical bosons interacting via a harmonic oscillator potential is considered. It is assumed that the number of bosons of each species is the same and that bosons belonging to the same species repel each other while those belonging to different species attract. The Hamiltonian is diagonalized and the energy spectrum of the system is written down. The behaviour of the system in the thermodynamic limit is studied within the framework of the grand canonical ensemble, and thermodynamic parameters, such as the internal energy, entropy and specific heat capacity are calculated. It is shown that the system exhibits a single species Bose-Einstein condensation when the coupling strengths are equal and a dual species condensation when they are different.
Dynamical Relation between Quantum Squeezing and Entanglement in Coupled Harmonic Oscillator System
Lock Yue Chew
2014-04-01
Full Text Available In this paper, we investigate into the numerical and analytical relationship between the dynamically generated quadrature squeezing and entanglement within a coupled harmonic oscillator system. The dynamical relation between these two quantum features is observed to vary monotically, such that an enhancement in entanglement is attained at a fixed squeezing for a larger coupling constant. Surprisingly, the maximum attainable values of these two quantum entities are found to consistently equal to the squeezing and entanglement of the system ground state. In addition, we demonstrate that the inclusion of a small anharmonic perturbation has the effect of modifying the squeezing versus entanglement relation into a nonunique form and also extending the maximum squeezing to a value beyond the system ground state.
MAVRI, J; BERENDSEN, HJC
1994-01-01
A density-matrix evolution method [Berendsen and Mavri, J. Phys. Chem. 97, 13464 (1993)] coupled to a classical molecular dynamics simulation was applied to study a quantum harmonic oscillator immersed in a bath of Lennard-Jones particles. Eigenfunctions of the three, lowest levels of the unperturbe
MAVRI, J; BERENDSEN, HJC
1994-01-01
A density-matrix evolution method [Berendsen and Mavri, J. Phys. Chem. 97, 13464 (1993)] coupled to a classical molecular dynamics simulation was applied to study a quantum harmonic oscillator immersed in a bath of Lennard-Jones particles. Eigenfunctions of the three, lowest levels of the unperturbe
侯邦品; 王顺金; 余万伦
2003-01-01
By using the algebraic structure in the operator dual space in the master equation for the driven dissipative harmonic oscillator, we have rewritten the master equation as a Schrodinger-like equation. Then we have used three gauge transformations and obtained an exact solution to the master equation in the particle number representation.
Ita, B. I.; Obong, H. P.; Ehi-Eromosele, C. O.; Edobor-Osoh, A.; Ikeuba, A. I.
2014-11-01
The solutions of the Klein-Gordon equation with equal scalar and vector harmonic oscillator plus inverse quadratic potential for S-waves have been presented using the Nikiforov-Uvarov method. The bound state energy eigenvalues and the corresponding un-normalized eigenfunctions are obtained in terms of the Laguerre polynomials.
Nørrelykke, Simon F; Flyvbjerg, Henrik
2011-01-01
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...
An explicit approximate solution to the Duffing-harmonic oscillator by a cubication method
Belendez, A., E-mail: a.belendez@ua.e [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Mendez, D.I. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, E. [Departamento de Optica, Farmacologia y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Marini, S. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Pascual, I. [Departamento de Optica, Farmacologia y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2009-08-03
The nonlinear oscillations of a Duffing-harmonic oscillator are investigated by an approximated method based on the 'cubication' of the initial nonlinear differential equation. In this cubication method the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain explicit approximate formulas for the frequency and the solution as a function of the complete elliptic integral of the first kind and the Jacobi elliptic function, respectively. These explicit formulas are valid for all values of the initial amplitude and we conclude this cubication method works very well for the whole range of initial amplitudes. Excellent agreement of the approximate frequencies and periodic solutions with the exact ones is demonstrated and discussed and the relative error for the approximate frequency is as low as 0.071%. Unlike other approximate methods applied to this oscillator, which are not capable to reproduce exactly the behaviour of the approximate frequency when A tends to zero, the cubication method used in this Letter predicts exactly the behaviour of the approximate frequency not only when A tends to infinity, but also when A tends to zero. Finally, a closed-form expression for the approximate frequency is obtained in terms of elementary functions. To do this, the relationship between the complete elliptic integral of the first kind and the arithmetic-geometric mean as well as Legendre's formula to approximately obtain this mean are used.
Linear Harmonic Oscillator and Uniform Circular Motion%线性谐振子与匀速圆周运动
岳小萍; 秦鑫
2012-01-01
This article discusses the relationship between uniform circular motion and harmonic vibration of particle by classical mechanics method. The expressions of displacement, velocity and acceleration of linear harmonic oscillator are given, and phase differences among the three are explained by causality and Newton’s second law of motion. This article obtains linear harmonic oscillator force constant k = Gm m / r in-3 1 2 gravitational field, and discusses its physical significance, corrects the mistake of energy of harmonic oscillator is invariably positive for a long time. Electric linear harmonic oscillator concept is introduced. Method of discussing electric linear harmonic oscilators of elliptic orbit and valence electron in different orbital are provided. The method of converting linear harmonic oscillator of real space to quantum mechanics is introduced.% 用经典力学的方法讨论了质点匀速圆周运动与谐振动的关系问题，给出了线性谐振子位移、速度、加速度表达式，用因果律和牛顿第二运动定律，说明了三者之间的位相差关系；得到了万有引力场中二质点系统线性谐振子力常量k = Gm m / r 的结果，讨论了其物理意义，纠正了长期以来认为谐振子能量总是-312大于零的错误认识。引入了线性电谐振子概念；给出了讨论椭圆轨道电线性谐振子、不同轨道上价电子线性电谐振子的方法；介绍了实空间电线性谐振子转化为量子力学线性谐振子的方法
Yen-Yin Lin
2014-11-01
Full Text Available We report a multi-watt broadband continuous-wave multi-harmonic optical comb based on a frequency division-by-three singly-resonant optical parametric oscillator. This cw optical comb is frequency-stabilized with the help of a beat signal derived from the signal and frequency-doubled idler waves. The measured frequency fluctuation in one standard deviation is ~437 kHz. This is comparable to the linewidth of the pump laser which is a master-oscillator seeded Yb:doped fiber amplifier at ~1064 nm. The measured powers of the fundamental wave and the harmonic waves up to the 6th harmonic wave are 1.64 W, 0.77 W, 3.9 W, 0.78 W, 0.17 W, and 0.11 W, respectively. The total spectral width covered by this multi-harmonic comb is ~470 THz. When properly phased, this multi-harmonic optical comb can be expected to produce by Fourier synthesis a light source consisting of periodic optical field waveforms that have an envelope full-width at half-maximum of 1.59 fs in each period.
Plane gyroklinotron at first and third harmonics of cyclotron frequency
Kurayev, A.A.; Lukashonok, D.V.; Sinitsyn, A.K., E-mail: kurayev@bsuir.by, E-mail: timka86@gmail.com [Belarusian State University of Informatics and Radioelectronics, Minsk (Belarus)
2011-07-01
The results of gyroklinotron's parameters optimization for efficiency at f = 100 GHz with interaction on first and third harmonics of the cyclotron frequency are presented. The predicted electron gyroklinotron's efficiency reaches 70% on first harmonic and 40% on third harmonic. This is more than in usual gyrotron. Besides in contrast to usual gyrotron the width electron beam on radius of guiding centers of electron orbits in gyroklinotron may considerable exceed working wave length {lambda}. This allows to use in it considerable more power of electron beams EB then in usual gyrotron. (author)
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.
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.
Teh, Mei-Hui; LeBohec, Stephan
2016-01-01
This article is the first in a series of two presenting the scale relativistic approach to non-differentiability in mechanics and its relation to quantum mechanics. In this first paper, we present the definition of a complex "scale-covariant time-differential operator" and show that mechanics of non-differentiable paths is implemented in the same way as classical mechanics but with the replacement of the time derivative and velocity with the time-differential operator and associated complex velocity. With this, the generalized form of Newton's fundamental relation of dynamics is shown to take the form of a Langevin equation in the case of stationary motion characterized by a null average classical velocity. The numerical integration of the Langevin equation in the case of a harmonic oscillator reveals the same statistics as the stationary solutions of the Schrodinger equation for the same problem. This motivates the second paper which makes the relation to quantum mechanics explicit by discussing the axioms o...
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.
Schröder, Markus; Schreiber, Michael; Kleinekathöfer, Ulrich
2007-03-21
Several techniques to solve a hierarchical set of equations of motion for propagating a reduced density matrix coupled to a thermal bath have been developed in recent years. This is either done using the path integral technique as in the original proposal by Tanimura and Kubo [J. Phys. Soc. Jpn. 58, 101 (1998)] or by the use of stochastic fields as done by Yan et al. [Chem. Phys. Lett. 395, 216 (2004)]. Based on the latter ansatz a compact derivation of the hierarchy using a decomposition of the spectral density function is given in the present contribution. The method is applied to calculate the time evolution of the reduced density matrix describing the motion in a harmonic, an anharmonic, and two coupled oscillators where each system is coupled to a thermal bath. Calculations to several orders in the system-bath coupling with two different truncations of the hierarchy are performed. The respective density matrices are used to calculate the time evolution of various system properties and the results are compared and discussed with a special focus on the convergence with respect to the truncation scheme applied.
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.
Dynamics of ‘quantumness’ measures in the decohering harmonic oscillator
PETER A ROSE; ANDREW C McCLUNG; TYLER E KEATING; ADAM T C STEEGE; ERIC S EGGE; ARJENDU K PATTANAYAK
2016-08-01
We studied the behaviour under decoherence of four different measures of the distance between quantum states and classical states for the harmonic oscillator coupled to a linear Markovian bath. Three of these are relative measures, using different definitions of the distance between the given quantum states and the set of all classical states. The fourth measure is an absolute one, the negative volume of the Wigner function of the state. All four measures are found to agree, in general, with each other. When applied to the eigenstates $|n\\ rangle$, all four measures behave non-trivially as a function of time during dynamical decoherence. First, we find that the first set of classical states to which the set of eigenstate evolves is (by all measures used) closest to the initial set. That is, all the states decohere to classicality along the ‘shortest path’. Finding this closest classical set of states helps improve the behaviour of all the relative distance measures. Second, at each point in time before becoming classical, all measures have a state $n*$ with maximal quantum-classical distance; the value $n*$ decreases as a function of time. Finally, we explore the dynamics of these non-classicality measures for more general states.
A new look at the quantum mechanics of the harmonic oscillator
Kastrup, H.A.
2006-12-15
At first sight it is probably hard to believe that something new can be said about the harmonic oscillator (HO). But that is so indeed: Classically the Harmonic Oscillator (HO) is the generic example for the use of angle and action variables {phi} element of R mod 2{pi} and I>0. However, the transformation q= {radical}(2I)cos {phi}, p=-{radical}(2I)sin {phi} is only locally symplectic and singular for (q,p)=(0,0). Globally the phase space {l_brace}(q,p){r_brace} has the topological structure of the plane R{sup 2}, whereas the phase space {l_brace}({phi},I){r_brace} corresponds globally to the punctured plane R{sup 2}-(0,0) or to a simple cone S{sup 1} x R{sup +} with the tip deleted. This makes a qualitative difference as to the quantum theory of the two phase spaces: The quantizing canonical group for the plane R{sup 2} consists of the (centrally extended) translations generated by the Poisson Lie algebra basis {l_brace}q,p,1{r_brace}, whereas the corresponding canonical group of the phase space {l_brace}({phi},I){r_brace} is the group SO{up_arrow}(1,2)=Sp(2,R)/Z{sub 2}, where Sp(2,R) is the sympletic group of the plane, with the generating Poisson Lie algebra basis {l_brace}h{sub 0}=I,h{sub 1}=Icos{phi},h{sub 2}=-Isin{phi}{r_brace} which provides also the basic ''observables'' on {l_brace}({phi}, I){r_brace}. In the quantum mechanics of the ({phi},I)-model of the HO the three h{sub j} correspond to self-adjoint generators K{sub j}, j=0,1,2, of irreducible unitary representations from the positive discrete series of the group SO{up_arrow}(1,2) or one of its infinitely many covering groups, the representations parametrized by the Bargmann index k>0. This index k determines the ground state energy E{sub k,n=0}={Dirac_h}{omega}k of the ({phi},I)-Hamiltonian H(anti K)={Dirac_h}{omega}K{sub 0}. For an m-fold covering the lowest possible value for k is k=1/m, which can be made arbitrarily small by choosing m accordingly. This is not in contraction to
Davydov, Alexander
2010-01-01
It is accepted wisdom that language and formalism of classical physics are inadequate for description of quantum phenomena. Here I confront this point of view by showing that there exists a surprisingly accurate mapping between representation of some quantum phenomena in one dimension and behavior of a classical time-dependent harmonic oscillator. For the first time, I demonstrate that such quintessentially quantum effect as tunneling through a potential barrier can be described in terms of classical physics without violating the energy conservation law at any time instance. A formula is presented that generates a wide class of one-dimensional potential barrier shapes in analytic form with the desired reflection (transmission) coefficient and transmission phase shift along with the corresponding exact solutions of the time-independent Schr\\"odinger's equation. Based on these results and numerical evidence, I put forward a conjecture that a classical (macroscopic) harmonic oscillator disturbed by a parametric ...
Davydov, Alexander
2010-01-01
It is accepted wisdom that language and formalism of classical physics are inadequate for description of quantum phenomena. Here I confront this point of view by showing that there exists a surprisingly accurate mapping between representation of some quantum phenomena in one dimension and behavior of a classical time-dependent harmonic oscillator. For the first time, I demonstrate that such quintessentially quantum effect as tunneling through a potential barrier can be described in terms of classical physics without violating the energy conservation law at any time instance. A formula is presented that generates a wide class of one-dimensional potential barrier shapes in analytic form with the desired reflection (transmission) coefficient and transmission phase shift along with the corresponding exact solutions of the time-independent Schr\\"odinger's equation. Based on these results and numerical evidence, I put forward a conjecture that a classical (macroscopic) harmonic oscillator disturbed by a parametric ...
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.
Zhu Jiuyun (Department of Physics, Hunan Normal University, Hunan 410006 (China)); Kuang Leman (Theoretical Physics Division, Nankai Institute of Mathematics, Tianjin 300071 (China) Department of Physics and Institute of Physics, Hunan Normal University, Hunan 410081 (China))
1994-10-03
The even and odd coherent states (CSs) of a finite-dimensional Hilbert space harmonic oscillator (FDHSHO) are constructed and some properties of these states are studied. Their quadrature squeezing and amplitude-squared squeezing are investigated in detail. It is shown that, while the squeezing behaviour of the even and odd CSs of the FDHSHO approaches that of the even and odd CSs of the usual harmonic oscillator as the dimension of the Hilbert space tends to infinity, this behaviour is nontrivally different if the dimension of the Hilbert space is finite. In the latter case, it is found that the even and odd CSs exhibit both amplitude-squared squeezing and quadrature squeezing. ((orig.))
Guasti, M Fernandez [Depto de Fisica, CBI, Universidad A Metropolitana - Iztapalapa, 09340 Mexico, DF, Apdo Postal 55-534 (Mexico); Moya-Cessa, H [INAOE, Coordinacion de Optica, Apdo Postal 51 y 216, 72000 Puebla, Pue. (Mexico)
2003-02-28
An extension of the classical orthogonal functions invariant to the quantum domain is presented. This invariant is expressed in terms of the Hamiltonian. Unitary transformations which involve the auxiliary function of this quantum invariant are used to solve the time-dependent Schroedinger equation for a harmonic oscillator with time-dependent parameter. The solution thus obtained is in agreement with the results derived using other methods which invoke the Lewis invariant in their procedures.
Le Yaouanc, A; Morénas, V; Oliver, L; Pène, O; Raynal, J C
2000-01-01
The detailed way in which duality between sum of exclusive states and the free quark model description operates in semileptonic total decay widths, is analysed. It is made very explicit by the use of the non relativistic harmonic oscillator quark model in the SV limit, and a simple interaction current with the lepton pair. In particular, the Voloshin sum rule is found to eliminate the mismatches of order $\\delta m/m_b^2$.
WU Hao; FAN Hong-Yi
2008-01-01
Eigenvalue-solution to those Hamiltonians involving non-commutative coordinates is not easily obtained. In this paper we apply the invariant eigen-operator (IEO) method to solving the energy spectrum of the three-mode harmonic oscillator in non-commutative space with the coordinate operators satisfying cyclic commutative relations, [X1, X2]=[X2, X3]=[X3, X1]=iθ, and this method seems effective and concise.
Mota, R D [Unidad Profesional Interdisciplinaria de IngenierIa y TecnologIas Avanzadas, IPN. Av. Instituto Politecnico Nacional 2580, Col. La Laguna Ticoman, 07340 Mexico DF (Mexico); Xicotencatl, M A [Departamento de Matematicas del Centro de Investigacion y Estudios Avanzados del IPN, Mexico DF, 07000 (Mexico); Granados, V D [Escuela Superior de FIsica y Matematicas, Instituto Politecnico Nacional, Ed. 9, Unidad Profesional Adolfo Lopez Mateos, 07738 Mexico DF (Mexico)
2004-02-20
In this work we introduce a generalization of the Jauch and Rohrlich quantum Stokes operators when the arrival direction from the source is unknown a priori. We define the generalized Stokes operators as the Jordan-Schwinger map of a triplet of harmonic oscillators with the Gell-Mann and Ne'eman matrices of the SU(3) symmetry group. We show that the elements of the Jordan-Schwinger map are the constants of motion of the three-dimensional isotropic harmonic oscillator. Also, we show that the generalized Stokes operators together with the Gell-Mann and Ne'eman matrices may be used to expand the polarization matrix. By taking the expectation value of the Stokes operators in a three-mode coherent state of the electromagnetic field, we obtain the corresponding generalized classical Stokes parameters. Finally, by means of the constants of motion of the classical 3D isotropic harmonic oscillator we describe the geometrical properties of the polarization ellipse.
Bonatsos, Dennis; Lenis, D; Raychev, P P; Roussev, R P; Terziev, P A
2000-01-01
Magic numbers predicted by a 3-dimensional q-deformed harmonic oscillator with Uq(3)>SOq(3) symmetry are compared to experimental data for atomic clusters of alkali metals (Li, Na, K, Rb, Cs), noble metals (Cu, Ag, Au), divalent metals (Zn, Cd), and trivalent metals (Al, In), as well as to theoretical predictions of jellium models, Woods-Saxon and wine bottle potentials, and to the classification scheme using the 3n+l pseudo quantum number. In alkali metal clusters and noble metal clusters the 3-dimensional q-deformed harmonic oscillator correctly predicts all experimentally observed magic numbers up to 1500 (which is the expected limit of validity for theories based on the filling of electronic shells), while in addition it gives satisfactory results for the magic numbers of clusters of divalent metals and trivalent metals, thus indicating that Uq(3), which is a nonlinear extension of the U(3) symmetry of the spherical (3-dimensional isotropic) harmonic oscillator, is a good candidate for being the symmetry ...
Photonic-Band-Gap Traveling-Wave Gyrotron Amplifier
Nanni, E. A.; Lewis, S. M.; Shapiro, M. A.; Griffin, R. G.; Temkin, R. J.
2014-01-01
We report the experimental demonstration of a gyrotron traveling-wave-tube amplifier at 250 GHz that uses a photonic band gap (PBG) interaction circuit. The gyrotron amplifier achieved a peak small signal gain of 38 dB and 45 W output power at 247.7 GHz with an instantaneous −3 dB bandwidth of 0.4 GHz. The amplifier can be tuned for operation from 245–256 GHz. The widest instantaneous −3 dB bandwidth of 4.5 GHz centered at 253.25 GHz was observed with a gain of 24 dB. The PBG circuit provides stability from oscillations by supporting the propagation of transverse electric (TE) modes in a narrow range of frequencies, allowing for the confinement of the operating TE03-like mode while rejecting the excitation of oscillations at nearby frequencies. This experiment achieved the highest frequency of operation for a gyrotron amplifier; at present, there are no other amplifiers in this frequency range that are capable of producing either high gain or high output power. This result represents the highest gain observed above 94 GHz and the highest output power achieved above 140 GHz by any conventional-voltage vacuum electron device based amplifier. PMID:24476286
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.
Thantu, Napoleon; McMorrow, D.; Melinger, J. S.; Kleiman, V.; Lotshaw, W. T.
2001-07-01
The apparently-multicomponent subpicosecond intermolecular dynamics of carbon disulfide liquid are addressed in a unified manner in terms of an inhomogeneously broadened quantum mechanical harmonic oscillator model for a single vibrational coordinate. For an inhomogeneously broadened (Gaussian) distribution of oscillators, the model predicts naturally the bimodal character of the subpicosecond intermolecular dynamics of carbon disulfide liquid, and also the spectral evolution effects (spectral narrowing and saturation) that are observed for solutions of carbon disulfide in weakly interacting alkane solvents. The unique dynamical signature of these low-frequency vibrational coordinates is determined largely by the physical constraints on the coordinates (near equality of oscillator frequency, dephasing frequency, and inhomogeneous bandwidth), such that constructive and destructive interference effects play a dominant role in shaping the experimental observable.
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.
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.
Operation and control of high power Gyrotrons for ECRH systems in SST-1 and Aditya
Shukla, B.K., E-mail: shukla@ipr.res.in; Bora, D.; Jha, R.; Patel, Jatin; Patel, Harshida; Babu, Rajan; Dhorajiya, Pragnesh; Dalakoti, Shefali; Purohit, Dharmesh
2016-11-15
Highlights: • Operation and control of high power Gyrotrons. • Data acquisition and control (DAQ) for Gyrotron system. • Ignitron based crowbar protection. • VME and PXI based systems. - Abstract: The Electron Cyclotron Resonance Heating (ECRH) system is an important heating system for the reliable start-up of tokamak. The 42 GHz and 82.6 GHz ECRH systems are used in tokamaks SST-1 and Aditya to carry out ECRH related experiments. The Gyrotrons are high power microwave tubes used as a source for ECRH systems. The Gyrotron is a delicate microwave tube, which deliver megawatt level power at very high voltage ∼40–50 kV with the current requirement ∼10 A–50 A. The Gyrotrons are associated with the subsystems like: High voltage power supplies (Beam voltage and anode voltage), dedicated crowbar system, magnet, filament and ion pump power supplies, cooling, interlocks and a dedicated data acquisition & control (DAC) system. There are two levels of interlocks used for the protection of Gyrotron: fast interlocks (arcing, beam over current, dI/dt, anode voltage and anode over current etc.) operate within 10 μs and slow interlocks (cooling, filament, silence of Gyrotron, ion pump and magnet currents) operate within 100 ms. Two Gyrotrons (42 GHz/500 kW/500 ms and 82.6 GHz/200 kW/1000 s) have been commissioned on dummy load for full parameters. The 42 GHz ECRH system has been integrated with SST-1 & Aditya tokamak and various experiments have been carried out related to ECRH assisted breakdown and start-up of tokamak at fundamental and second harmonic. These Gyrotrons are operated with VME based data acquisition and control (DAC) system. The DAC system is capable to acquire 64 digital and 32 analog signals. The system is used to monitor & acquire the data and also used for slow interlocks for the protection of Gyrotron. The data acquired from the system are stored online on VME system and after the shot stored in a file in binary format. The MDSPlus, a set of
On Noether's Theorem for the Invariant of the Time-Dependent Harmonic Oscillator
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.
On Noether's theorem for the invariant of the time-dependent harmonic oscillator
Abe, Sumiyoshi; Itto, Yuichi; Matsunaga, Mamoru [Department of Physical Engineering, Mie University, Mie 514-8507 (Japan)
2009-11-15
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.
Development program for a 200 kW, cw gyrotron. Final report
DeHope, W.J.; Ferguson, P.E.; Hart, S.L.; Matranga, V.A.; Sandoval, J.J.; Schmitt, M.J.; Tancredi, J.J.; Wozniak, M.A.
1984-02-01
Development of a millimeter-wave device to produce 200 kW of continuous wave power at 60 GHz is described. The device, a gyrotron oscillator, is intended for electron-cyclotron heating of fusion plasmas. The design philosophy is herein discussed and experimental results, both diagnostic and long pulse, are given.
A model of the two-dimensional quantum harmonic oscillator in an $AdS_3$ background
Frick, Rudolf
2016-01-01
In this paper we study a model of the two-dimensional quantum harmonic oscillator in a 3-dimensional anti-de Sitter background. We use a generalized Schr\\"odinger picture in which the analogs of the Schr\\"odinger 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's uncertainty relations.
Hamerly, Ryan; Jankowski, Marc; Fejer, Martin M; Yamamoto, Yoshihisa; Mabuchi, Hideo
2016-01-01
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 simulton-like 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.
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.
A model of the two-dimensional quantum harmonic oscillator in an AdS{sub 3} background
Frick, R. [Universitaet zu Koeln, Institut fuer Theoretische Physik, Cologne (Germany)
2016-10-15
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 Schroedinger picture in which the analogs of the Schroedinger 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{sub 3} spacetime. In this picture, we have a metamorphosis of the Heisenberg uncertainty relations. (orig.)
The q-DEFORMED SCHRÖDINGER Equation of the Harmonic Oscillator on the Quantum Euclidean Space
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.
Belendez, A [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Pascual, C [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, E [Departamento de Optica, FarmacologIa y AnatomIa, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Neipp, C [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Belendez, T [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2008-02-15
A modified He's homotopy perturbation method is used to calculate higher-order analytical approximate solutions to the relativistic and Duffing-harmonic oscillators. The He's homotopy perturbation method is modified by truncating the infinite series corresponding to the first-order approximate solution before introducing this solution in the second-order linear differential equation, and so on. We find this modified homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. The approximate formulae obtained show excellent agreement with the exact solutions, and are valid for small as well as large amplitudes of oscillation, including the limiting cases of amplitude approaching zero and infinity. For the relativistic oscillator, only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate frequency of less than 1.6% for small and large values of oscillation amplitude, while this relative error is 0.65% for two iterations with two harmonics and as low as 0.18% when three harmonics are considered in the second approximation. For the Duffing-harmonic oscillator the relative error is as low as 0.078% when the second approximation is considered. Comparison of the result obtained using this method with those obtained by the harmonic balance methods reveals that the former is very effective and convenient.
Jory, H.; Felch, K.; Hess, C.; Huey, H.; Jongewaard, E.; Neilson, J.; Pendleton, R.; Tsirulnikov, M. (Varian Associates, Inc., Palo Alto, CA (USA))
1990-09-17
To address the electron cyclotron heating requirements of planned fusion experiments such as the International Thermonuclear Experimental Reactor (ITER) and the Compact Ignition Tokamak (CIT), Varian is developing gyrotrons at frequencies ranging from 100--300 GHz with output power capabilities up to 1 MW CW. Experimental gyrotrons have been built at frequencies between 100--140 GHz, and a study program has addressed the critical elements of designing 280--300 GHz gyrotrons capable of generating CW power levels up to 1 MW. Initial test vehicles at 140 GHz have utilized TE{sub 15,2,1} interaction cavities, and have been designed to generate short-pulse (up to 20 ms) power levels of 1 MW and up to 400 kW CW. Recently, short-pulse power levels of 1040 kW at 38% efficiency have been obtained and average powers of 200 kW have been achieved. Long-pulse operation has been extended to pulse durations of 0.5 seconds at power levels of 400 kW. Gyrotron oscillators capable of generating output powers of 500 kW CW at a frequency of 110 GHz have recently been designed and a prototype is currently being tested. Design work for a 1 MW CW gyrotron at 110 GHz, is in progress. The 1 MW CW tube will employ an output coupling approach where the microwave output is separated from the microwave output. 15 refs., 10 figs., 3 tabs.
An Application of the Harmonic Oscillator Model to Verify Dunning’s Theory of the Economic Growth
Marcin Salamaga
2013-09-01
Full Text Available Analogies with mechanisms ruling the natural world have oft en been sought in the course of economic phenomena.Th is paper is also an attempt to combine the physical phenomenon of a harmonious oscillator withthe theory of economic growth by J. H. Dunning (1981. In his theory, Dunning distinguished stages of economicgrowth of countries that imply the dependency between the investment position of countries and theirGDP per capita, while the graph presenting this dependency reminds a trajectory of oscillating motion of adamped harmonic oscillator. Th is analogy has given inspiration to reinterpret the theory of economy on thegrounds of the mechanism of a physical model. In this paper, the harmonious oscillator motion equation wasadapted to the description of dependencies shown in the theory of economic growth by J. H. Dunning. Th emathematical solution of this equation is properly parameterised and parameters are estimated with the useof the Gauss-Newton algorithm. Th e main objective of this paper is to allocate a specifi c stage in the economicgrowth to each country on the basis of the values of parameter estimations of the proposed cyclical models ofchanges in the net investment indicator.
Application of He’s Energy Balance Method to Duffing-Harmonic Oscillators
Momeni, M.; Jamshidi, j.; Barari, Amin
2011-01-01
In this article, He's energy balance method is applied for calculating angular frequencies of nonlinear Duffing oscillators. This method offers a promising approach by constructing a Hamiltonian for the nonlinear oscillator. We illustrate that the energy balance is very effective and convenient...
A new look at the harmonic oscillator problem in a finite-dimensional Hilbert space
Bagchi, B. [Calcutta Univ. (India). Dept. of Applied Mathematics; Roy, P.K. [Department of Physics, Haldia Government College, Haldia 721 657, West Bengal (India)
1995-05-08
In this Letter some basic properties of a truncated oscillator are studied. By using finite-dimensional representation matrices of the truncated oscillator we construct new parasupersymmetric schemes and remark on their relevance to the transition operators of the non-interacting N-level system endowed with bosonic modes. ((orig.)).
Gyrotron development at KIT: FULGOR test facility and gyrotron concepts for DEMO
Schmid, M., E-mail: martin.schmid@kit.edu [Institute for Pulsed Power and Microwave Technology (IHM), Karlsruhe Institute of Technology, Association EURATOM-KIT, Karlsruhe (Germany); Franck, J.; Kalaria, P.; Avramidis, K.A.; Gantenbein, G.; Illy, S. [Institute for Pulsed Power and Microwave Technology (IHM), Karlsruhe Institute of Technology, Association EURATOM-KIT, Karlsruhe (Germany); Jelonnek, J. [Institute for Pulsed Power and Microwave Technology (IHM), Karlsruhe Institute of Technology, Association EURATOM-KIT, Karlsruhe (Germany); Institute of High Frequency Techniques and Electronics (IHE), Karlsruhe Institute of Technology, Association EURATOM-KIT, Karlsruhe (Germany); Pagonakis, I. Gr.; Rzesnicki, T. [Institute for Pulsed Power and Microwave Technology (IHM), Karlsruhe Institute of Technology, Association EURATOM-KIT, Karlsruhe (Germany); Thumm, M. [Institute for Pulsed Power and Microwave Technology (IHM), Karlsruhe Institute of Technology, Association EURATOM-KIT, Karlsruhe (Germany); Institute of High Frequency Techniques and Electronics (IHE), Karlsruhe Institute of Technology, Association EURATOM-KIT, Karlsruhe (Germany)
2015-10-15
Highlights: • Substantial extension of the KIT gyrotron test facility FULGOR has started. • FULGOR will be able to test gyrotrons with continuous RF output power up to 4 MW. • Design of 240 GHz gyrotrons for efficient electron cyclotron current drive is progressing. • Output power of 240 GHz gyrotrons with conventional cavity up to 830 kW, with coaxial cavity up to 2 MW is feasible. • Multi-frequency operation with gyrotrons is also possible (170–267 GHz). - Abstract: At the Karlsruhe Institute of Technology (KIT), theoretical and experimental foundations for the development of future gyrotrons for fusion applications are being laid down. This includes the construction of the new Fusion Long Pulse Gyrotron Laboratory (FULGOR) test facility as well as physical design studies towards DEMO-compatible gyrotrons. Initially FULGOR will comprise of a 10 MW CW power supply, a 5 MW water cooling system (upgradeable to 10 MW), a superconducting 10 T magnet, one or two 2 MW ECRH test loads and a new control and data acquisition system for all these elements. The test facility will then be equipped to test the conventional 1 MW or coaxial 2 MW gyrotrons for DEMO, currently under design, as well as possible upgraded gyrotrons for W7-X and ITER. The design of the new high voltage DC power supply (HVDCPS) is flexible enough to handle gyrotrons with 4 MW CW output power (conceivably up to 170 GHz), but also test gyrotrons with higher frequencies (>250 GHz) which, due to physical limitations in the gyrotron design, will require less power but have more stringent demands on voltage stability.
Decoherence in a quantum harmonic oscillator monitored by a Bose-Einstein condensate
Brouard, S; Sokolovski, D
2010-01-01
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.
ZHAI Zhi-Yuan; YANG Tao; PAN Xiao-Yin
2012-01-01
The propagator for an anisotropic two-dimension charged harmonic oscillator in the presence of a constant external magnetic field and a time-dependent electric field is exactly evaluated. Various special cases appearing in the literature can be obtained by properly setting the values of the parameters in our results.%The propagator for an anisotropic two-dimension charged harmonic oscillator in the presence of a constant external magnetic field and a time-dependent electric field is exactly evaluated.Various special cases appearing in the literature can be obtained by properly setting the values of the parameters in our results.
High power 303 GHz gyrotron for CTS in LHD
Yamaguchi, Y.; Kasa, J.; Saito, T.; Tatematsu, Y.; Kotera, M.; Kubo, S.; Shimozuma, T.; Tanaka, K.; Nishiura, M.
2015-10-01
A high-power pulsed gyrotron is under development for 300 GHz-band collective Thomson scattering (CTS) diagnostics in the Large Helical Device (LHD). High-density plasmas in the LHD require a probe wave with power exceeding 100 kW in the sub-terahertz region to obtain sufficient signal intensity and large scattering angles. At the same time, the frequency bandwidth should be less than several tens of megahertz to protect the CTS receiver using a notch filter against stray radiations. Moreover, duty cycles of ~ 10% are desired for the time domain analysis of the CTS spectrum. At present, a 77 GHz gyrotron for electron cyclotron heating is used as a CTS wave source in the LHD. However, the use of such a low-frequency wave suffers from refraction, cutoff and absorption at the electron cyclotron resonance layer. Additionally, the signal detection is severely affected by background noise from electron cyclotron emission. To resolve those problems, high-power gyrotrons in the 300 GHz range have been developed. In this frequency range, avoiding mode competition is critical to realizing high-power and stable oscillation. A moderately over-moded cavity was investigated to isolate a desired mode from neighbouring modes. After successful tests with a prototype tube, the practical one was constructed with a cavity for TE22,2 operation mode, a triode electron gun forming intense laminar electron beams, and an internal mode convertor. We have experimentally confirmed single mode oscillation of the TE22,2 mode at the frequency of 303.3 GHz. The spectrum peak is sufficiently narrow. The output power of 290 kW has been obtained at the moment.
Wang, Yang; Song, Hai-Ying; Liu, H.Y.; Liu, Shi-Bing, E-mail: sbliu@bjut.edu.cn
2017-07-12
Highlights: • Proposed a valid mechanism of high harmonic generation by laser grating target interaction: oscillation of equivalent electric dipole (OEED). • Found that there also exist harmonic emission at large emission angle but not just near-surface direction as the former researches had pointed out. • Show the process of the formation and motion of electron bunches at the grating-target surface irradiating with femtosecond laser pulse. - Abstract: 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.
Performance of a quantum heat engine cycle working with harmonic oscillator systems
2007-01-01
A cycle model of an irreversible heat engine working with harmonic systems is established in this paper. Based on the equation of motion of an operator in the Heisenberg picture and semi-group approach, the first law of thermodynamics for a harmonic system and the time evolution of the system are obtained. The general expressions for several important parameters, such as the work, efficiency, power output, and rate of entropy production are derived. By means of numerical analysis, the optimally operating regions and the optimal values of performance parameters of the cycle are determined under the condition of maximum power output. At last, some special cases, such as high temperature limit and frictionless case, are dis-cussed in brief.
Performance of a quantum heat engine cycle working with harmonic oscillator systems
WANG JianHui; HE JiZhou; MAO ZhiYuan
2007-01-01
A cycle model of an irreversible heat engine working with harmonic systems is established in this paper. Based on the equation of motion of an operator in the Heisenberg picture and semi-group approach, the first law of thermodynamics for a harmonic system and the time evolution of the system are obtained. The general expressions for several important parameters, such as the work, efficiency, power output, and rate of entropy production are derived. By means of numerical analysis, the optimally operating regions and the optimal values of performance parameters of the cycle are determined under the condition of maximum power output. At last, some special cases, such as high temperature limit and frictionless case, are discussed in brief.
Katarzyna Kolczyńska
2010-07-01
Full Text Available The HOMA (Harmonic Oscillator Model of Aromaticity index, reformulated in 1993, has been very often applied to describe π-electron delocalization for mono- and polycyclic π-electron systems. However, different measures of π-electron delocalization were employed for the CC, CX, and XY bonds, and this index seems to be inappropriate for compounds containing heteroatoms. In order to describe properly various resonance effects (σ-π hyperconjugation, n-π conjugation, π-π conjugation, and aromaticity possible for heteroatomic π-electron systems, some modifications, based on the original HOMA idea, were proposed and tested for simple DFT structures containing C, N, and O atoms. An abbreviation HOMED was used for the modified index.
Sameer M. Ikhdair
2014-10-01
Full Text Available The two-dimensional solution of the spinless Klein–Gordon (KG equation for scalar–vector harmonic oscillator potentials with and without the presence of constant perpendicular magnetic and Aharonov–Bohm (AB flux fields is studied within the asymptotic function analysis and Nikiforov–Uvarov (NU method. The exact energy eigenvalues and normalized wave functions are analytically obtained in terms of potential parameters, magnetic field strength, AB flux field and magnetic quantum number. The results obtained by using different Larmor frequencies are compared with the results in the absence of both magnetic field (ωL = 0 and AB flux field (ξ = 0 case. Effects of external fields on the non-relativistic energy eigenvalues and wave functions solutions are also precisely presented.
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 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 \\rangle 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.
Robust identification of harmonic oscillator parameters using the adjoint Fokker-Planck equation
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.
AM to PM noise conversion in a cross-coupled quadrature harmonic oscillator
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens
2006-01-01
We derive the dynamic equations governing the cross-coupled quadrature oscillator, perturbed by noise, leading to an expression for the close-in phase noise. The theory shows that a nonlinear coupling transconductance results in AM-PM noise conversion close to the carrier, which increases...
Castro-Palacio, Juan Carlos; Gimenez, Marcos H; Monsoriu, Juan A
2012-01-01
The mobile acceleration sensor has been used to in Physics experiments on free and damped oscillations. Results for the period, frequency, spring constant and damping constant match very well to measurements obtained by other methods. The Accelerometer Monitor application for Android has been used to get the outputs of the sensor. Perspectives for the Physics laboratory have also been discussed.
M. K. Bahar
2013-01-01
Full Text Available Using the asymptotic iteration and wave function ansatz method, we present exact solutions of the Klein-Gordon equation for the quark-antiquark interaction and harmonic oscillator potential in the case of the position-dependent mass.
Liu, Li; Zhang, Liang-Ying; Cao, Li
2009-10-01
The diffusion in a harmonic oscillator driven by coloured noises ζ(t) and η(t) with coloured cross-correlation in which one of the noises is modulated by a biased periodic signal is investigated. The exact expression of diffusion coefficient d as a function of noise parameter, signal parameter, and oscillator frequency is derived. The findings in this paper are as follows. 1) The curves of d versus noise intensity D and d versus noises cross-correlation time τ3 exist as two different phases. The transition between the two phases arises from the change of the cross-correlation coefficient λ of the two Ornstein-Uhlenbeck (O-U) noises. 2) Changing the value of τ3, the curves of d versus Q, the intensity of colored noise that is modulated by the signal, can transform from a phase having a minimum to a monotonic phase. 3) Changing the value of signal amplitude A, d versus Q curves can transform from a phase having a minimum to a monotonic phase. The above-mentioned results demonstrate that a like noise-induced transition appears in the model.
Liu Li; Zhang Liang-Ying; Cao Li
2009-01-01
The diffusion in a harmonic oscillator driven by coloured noises ζ(t) and η(t) with coloured cross-correlation in which one of the noises is modulated by a biased periodic signal is investigated. The exact expression of diffusion coefficient d as a function of noise parameter, signal parameter, and oscillator frequency is derived. The findings in this paper are as follows. 1) The curves of d versus noise intensity D and d versus noises cross-correlation time τ_3 exist as two different phases. The transition between the two phases arises from the change of the cross-correlation coefficient λ of the two Orustein-Uhlenbeck (O-U) noises. 2) Changing the value of τ3, the curves of d versus Q, the intensity of colored noise that is modulated by the signal, can transform from a phase having a minimum to a monotonic phase. 3)Changing the value of signal amplitude A, d versus Q curves can transform from a phase having a minimum to a monotonic phase. The above-mentioned results demonstrate that a like noise-induced transition appears in the model.
A quantum quasi-harmonic nonlinear oscillator with an isotonic term
Rañada, Manuel F., E-mail: mfran@unizar.es [Dep. de Física Teórica and IUMA, Universidad de Zaragoza, 50009 Zaragoza (Spain)
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.
Haxton, Wick; Lunardini, Cecilia
2008-09-01
Semi-leptonic electroweak interactions in nuclei—such as β decay, μ capture, charged- and neutral-current neutrino reactions, and electron scattering—are described by a set of multipole operators carrying definite parity and angular momentum, obtained by projection from the underlying nuclear charge and three-current operators. If these nuclear operators are approximated by their one-body forms and expanded in the nucleon velocity through order |p→|/M, where p→ and M are the nucleon momentum and mass, a set of seven multipole operators is obtained. Nuclear structure calculations are often performed in a basis of Slater determinants formed from harmonic oscillator orbitals, a choice that allows translational invariance to be preserved. Harmonic-oscillator single-particle matrix elements of the multipole operators can be evaluated analytically and expressed in terms of finite polynomials in q, where q is the magnitude of the three-momentum transfer. While results for such matrix elements are available in tabular form, with certain restriction on quantum numbers, the task of determining the analytic form of a response function can still be quite tedious, requiring the folding of the tabulated matrix elements with the nuclear density matrix, and subsequent algebra to evaluate products of operators. Here we provide a Mathematica script for generating these matrix elements, which will allow users to carry out all such calculations by symbolic manipulation. This will eliminate the errors that may accompany hand calculations and speed the calculation of electroweak nuclear cross sections and rates. We illustrate the use of the new script by calculating the cross sections for charged- and neutral-current neutrino scattering in 12C. Program summaryProgram title: SevenOperators Catalogue identifier: AEAY_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAY_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland
Low-noise sub-harmonic injection locked multiloop ring oscillator
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.
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.
StankevičiÅ«tÄ--, K.; PipinytÄ--, I.; Vengelis, J.; MarcinkevičiÅ«tÄ--, A.; Å uminas, R.; Grigonis, R.; Eckardt, R. C.; Sirutkaitis, V.
2013-09-01
We present experimental data obtained during investigation of synchronously pumped optical parametric oscillators (SPOPO's) pumped by fundamental (1030 nm) and second harmonic (515 nm) radiation of mode-locked Yb:KGW laser, providing 105 fs pulses at 76 MHz repetition rate with an average power of 4 W. Different nonlinear crystals such as beta barium borate (BBO), and periodically poled lithium niobate (PPLN) and MgO doped PPLN (MgO:PPLN) were tested to estimate wavelength tuning capabilities and SPOPO's efficiency. Rotation of BBO nonlinear crystal and SPOPO's cavity length variation and, in the case of SPOPO based on PPLN, change of grating period and cavity length allowed signal wavelength tuning in 630 - 1030 nm and 1350 - 1700 nm spectral ranges, respectively. Parametric light conversion from pump power to signal power efficiency was as high as 25 %. Including the idler pulses the tuning ranges were from 630 to 2400 nm and from 1350 to 4000 nm in case of BBO and PPLN crystals, respectively. SPOPO based on BBO wsithout intracavity group velocity dispersion (GVD) compensation generates longer than transform limited pulses, so SPOPO based on BBO with dispersive prisms were investigated.
对称性方法在谐振子模型教学中的应用%Applications of Symmetry Method in Teaching of Harmonic Oscillator Model
夏丽莉
2016-01-01
利用对称性方法探索非线性谐振子的物理特性。给出一种简洁实用的探究系统守恒律的现代数学方法。有利于学生更深入地了解机械振动模型的规律，丰富了教材内容。%The physical properties of the harmonic oscillator are obtained by the symmetry method. The modern mathematical methods of exploring the conserved quantities are proposed. This will help the students to understand the laws of the harmonic oscillator model, and enrich the teaching materials.
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.
A study of a simple gyrotron equation
Goetz, Markus [Max-Planck-Institut fuer Plasmaphysik, EURATOM-Association, D-85748 Garching (Germany); Meyer-Spasche, Rita [Max-Planck-Institut fuer Plasmaphysik, EURATOM-Association, D-85748 Garching (Germany); Weitzner, Harold [New York University, Courant Institute of Mathematical Sciences, New York, NY 10012 (United States)
2007-03-02
A simple standard equation for the evolution of the electrons and electromagnetic fields in a gyrotron cavity is studied. A number of mathematical properties are shown: existence and uniqueness of solutions for a limited axial extent and existence and uniqueness for all axial lengths in one case of particular interest. A Poynting theorem is obtained directly from the model and the Hamiltonian character of the electron motion is demonstrated. The start-up and final state in the gyrotron cavity are also examined. The efficiency of energy flux transfer from the electron beam to the wave is estimated.
Suhufa Alfarisa
2016-03-01
Full Text Available This research aims i to determine the density profile and calculate the ground state energy of a quantum dot in two dimensions (2D with a harmonic oscillator potential using orbital-free density functional theory, and ii to understand the effect of the harmonic oscillator potential strength on the electron density profiles in the quantum dot. This study determines the total energy functional of the quantum dot that is a functional of the density that depends only on spatial variables. The total energy functional consists of three terms. The first term is the kinetic energy functional, which is the Thomas–Fermi approximation in this case. The second term is the external potential. The harmonic oscillator potential is used in this study. The last term is the electron–electron interactions described by the Coulomb interaction. The functional is formally solved to obtain the electron density as a function of spatial variables. This equation cannot be solved analytically, and thus a numerical method is used to determine the profile of the electron density. Using the electron density profiles, the ground state energy of the quantum dot in 2D can be calculated. The ground state energies obtained are 2.464, 22.26, 90.1957, 252.437, and 496.658 au for 2, 6, 12, 20, and 56 electrons, respectively. The highest electron density is localized close to the middle of the quantum dot. The density profiles decrease with the increasing distance, and the lowest density is at the edge of the quantum dot. Generally, increasing the harmonic oscillator potential strength reduces the density profiles around the center of the quantum dot.
Particle simulation of a ka-band gyrotron traveling wave amplifier
Xu Shouxi; Liu Pukun; Zhang Shichang; Du Chaohai; Xue Qianzhong; Geng Zhihui; Su Yinong [Key Laboratory of High Power Microwave Sources and Technologies, Institute of Electronics, Chinese Academy of Sciences, P.O. Box 2652, Beijing 100190 (China)
2011-08-15
The design of a ka-band gyrotron traveling wave (gyro-TWT) amplifier is presented. The gyro-TWT amplifier with a severed structure operates in the fundamental harmonic TE{sub 01} circular electric mode. The beam-wave interaction is studied by using a particle-in-cell (PIC) code. The simulations predict that the amplifier can produce an output peak power of over 155 kW, 22% efficiency, 23 dB gain, and a 3 dB bandwidth of 2 GHz for a 70 kV, 10 A electron beam with an axial velocity spread {Delta}v{sub z}/v{sub z}=5%.
A review on the sub-THz/THz gyrotrons
Kumar, Nitin; Singh, Udaybir; Bera, Anirban; Sinha, A. K.
2016-05-01
A review on the sub-THz/THz gyrotrons is performed in this manuscript. The present development status of gyrotrons can be divided into three streams for the sake of better understanding: 1. low frequency (industrial applications, 2. very high power (1 MW or more), medium frequency (100-200 GHz) gyrotrons for plasma fusion applications, 3. low power (few tens of watt to kW), high frequency (>200 GHz) gyrotrons for various innovative applications. In this manuscript, the third stream of gyrotron development is reviewed. In last few decades several innovative applications are searched in sub-THz/THz band where the gyrotrons could be used as an efficient source of RF radiation. The applications of sub-THz/THz gyrotrons including the futuristic scope of the device are also discussed in this article. Further, several criticalities arise in the design and development when the gyrotron operation shifts toward the high frequency band. Various such design and technological challenges are also discussed here. Finally the development status of sub-THz/THz gyrotrons as per the use in various scientific and technological applications is also discussed.
Theory and Modeling of High-Power Gyrotrons
Nusinovich, Gregory Semeon [Univ. of Maryland, College Park, MD (United States)
2016-04-29
This report summarized results of the work performed at the Institute for Research in Electronics and Applied Physics of the University of Maryland (College Park, MD) in the framework of the DOE Grant “Theory and Modeling of High-Power Gyrotrons”. The report covers the work performed in 2011-2014. The research work was performed in three directions: - possibilities of stable gyrotron operation in very high-order modes offering the output power exceeding 1 MW level in long-pulse/continuous-wave regimes, - effect of small imperfections in gyrotron fabrication and alignment on the gyrotron efficiency and operation, - some issues in physics of beam-wave interaction in gyrotrons.
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.
Bonatsos, Dennis; Kolokotronis, P; Lenis, D; Bonatsos, Dennis
1994-01-01
The symmetry algebra of the two-dimensional anisotropic quantum harmonic oscillator with rational ratio of frequencies, which is characterizing ``pancake'' nuclei, is identified as a non-linear extension of the u(2) algebra. The finite dimensional representation modules of this algebra are studied and the energy eigenvalues are determined using algebraic methods of general applicability to quantum superintegrable systems. For labelling the degenerate states an ``angular momentum'' operator is introduced, the eigenvalues of which are roots of appropriate generalized Hermite polynomials. In the special case with frequency ratio 2:1 the resulting algebra is identified as the finite W algebra W_3^{(2)}.
Damyanova, M.; Sabchevski, S.; Zhelyazkov, I.; Vasileva, E.; Balabanova, E.; Dankov, P.; Malinov, P.
2016-03-01
Gyrotrons are the most powerful sources of coherent CW (continuous wave) radiation in the frequency range situated between the long-wavelength edge of the infrared light (far-infrared region) and the microwaves, i.e., in the region of the electromagnetic spectrum which is usually called the THz-gap (or T-gap), since the output power of other devices (e.g., solid-state oscillators) operating in this interval is by several orders of magnitude lower. In the recent years, the unique capabilities of the sub-THz and THz gyrotrons have opened the road to many novel and future prospective applications in various physical studies and advanced high-power terahertz technologies. In this paper, we present the current status and functionality of the problem-oriented software packages (most notably GYROSIM and GYREOSS) used for numerical studies, computer-aided design (CAD) and optimization of gyrotrons for diverse applications. They consist of a hierarchy of codes specialized to modelling and simulation of different subsystems of the gyrotrons (EOS, resonant cavity, etc.) and are based on adequate physical models, efficient numerical methods and algorithms.
Operation experiences of the super conducting magnet for a gyrotron of the JT-60U ECH system
Igarashi, Koichi; Seki, Masami; Shimono, Mitsugu; Terakado, Masayuki; Ishii, Kazuhiro; Takahashi, Masami [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment
2003-03-01
The JT-60U electron cyclotron heating (ECH) system can heat plasmas locally and drive a plasma current with four 1 MW-5 sec gyrotrons. The super conducting magnets (SCM) are required for oscillation of the gyrotron at a working frequency of 110 GHz. The SCM provides a high magnetic field of 4.5T at the cavity inside the gyrotron. This SCM system is characterized by 1) operation without liquid Helium owing to a 4K-refrigerator applied to the magnetic coils, 2) easy maintenance. Operational experiences about the SCM system through a long term experiment for a high power gyrotron are very valuable. According to those operational experiences, it is clarified the 4K-refrigerator should be renewed in order to keep low temperature of the SCM. It is also found that 200 hours or less are required for the super conducting condition (<5K) after long stopping time of the refrigerator up to 150 hours. This is useful information for making a plan about ECH experiments. (author)
Belendez, A., E-mail: a.belendez@ua.e [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)] [Instituto Universitario de Fisica Aplicada a las Ciencias y las Tecnologias, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, E. [Departamento de Optica, Farmacologia y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Rodes, J.J. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fuentes, R.; Pascual, I. [Instituto Universitario de Fisica Aplicada a las Ciencias y las Tecnologias, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)] [Departamento de Optica, Farmacologia y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2009-11-09
In a previous short communication [A. Belendez, E. Fernandez, 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.
Simon, T. [Bereich Energieverteilung, Schneider Electric GmbH, Ratingen (Germany)
2005-09-01
Single-phase electronic loads in office buildings may cause harmonics that must be considered in busbar design. An analysis of busbars with four conductors of identical cross section showed that the frequently practiced option of doubling the cross section of the neutral conductor is not optimal both from the technical and the economic view. Busbar systems with four identical conductor cross sections are the more advantageous solution if the harmonics effect is taken into account. (orig.)
Scaling Calculations for a Relativistic Gyrotron.
2014-09-26
a relativistic gyrotron. The results of calculations are given in Section 3. The non- linear , slow-time-scale equations of motion used for these...corresponds to a cylindrical resonator and a thin annular electron beam ;, " with the beam radius chosen to coincide with a maximum of the resonator...entering the cavity. A tractable set of non- linear equations based on a slow-time-scale formulation developed previously was used. For this
Continuously tunable, split-cavity gyrotrons
Brand, G. F.; Gross, M.
1985-12-01
Attention is given to a gyrotron cavity configuration which is split in halves longitudinally, to allow any frequency lying between the fixed cavity resonance to be assessed by mechanically changing the separation of the two halves. Experimental results are presented which demonstrate that the rate-of-change in resonant frequency with separation is greatest if the minor axis of the cavity cross section is the one undergoing change. Excellent agreement with theory is noted for these results.
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.
Hegedűs, Ferenc, E-mail: hegedusf@hds.bme.hu
2016-03-06
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. - Highlights: • Spherical gas/vapour bubble in water has been examined numerically. • The bubble model was the Rayleigh–Plesset equation excited harmonically. • Topology of stable periodic solutions has been found near Blake's threshold.
Bennett, Charles L.
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.
Atakishiyev, N.M. [Instituto de Matematicas. Universidad Nacional Autonoma de Mexico. Cuernavaca, Morelos (Mexico); Jafarov, E.I.; Nagiyev, S.M. [Institute of Physics, Azerbaijan Academy of Sciences. Baku, Azerbaijan (Azerbaijan); Wolf, K.B. [Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas. Universidad Nacional Autonoma de Mexico. Cuernavaca, Morelos (Mexico)
1998-10-01
Meixner oscillators have a ground state and an energy spectrum that is equally spaced; they are a two-parameter family of models that satisfy a Hamiltonian equation with a difference operator. Meixner oscillators include as limits and particular cases the Charlier, Kravchuk and Hermite (common quantum-mechanical) harmonic oscillators. By the Sommerfeld-Watson transformation they are also related with a relativistic model of the linear harmonic oscillator, built in terms of the Meixner-Pollaczek polynomials, and their continuous weight function. We construct explicitly the corresponding coherent states with the dynamical symmetry group Sp(2,R). The reproducing kernel for the wavefunctions of these models is also found. (Author)
Maireche Abdelmadjid
2015-01-01
In present search, we have studied the effect of the both non commutativity of three dimensional space and phase on the Schrödinger equation with companied Harmonic oscillator potential and it’s inverse, know by isotopic Harmonic oscillator plus inverse quadratic (h.p.i.) potential, we shown that the Hermitian NC Hamiltonian formed anisotropic operator and described many physics phenomena’s, we have also derived the exact degenerated spectrum for studied potential in the first order of two in...
MAVRI, J; LENSINK, M; BERENDSEN, HJC
1994-01-01
A density matrix evolution (DME) method (Berendsen, H. J. C., and Mavri, J., 1993, J. phys. Chem., 97, 13464) to simulate the dynamics of quantum systems embedded in a classical environment is applied to study the inelastic collisions of a classical particle with a five level quantum harmonic
Zhang Yushan; Liang Jianwen; Hu Yuxian
2005-01-01
Under harmonic wave excitation, the dynamic response of a bilinear SDOF system can be expressed by the Hilbert spectrum. The Hilbert spectrum can be formulated by (1) the inter-wave combination mechanism between the steady response and the transient response when the system behaves linearly, or (2) the intra-wave modulation mechanism embedded in one intrinsic mode function (IMF) component when the system behaves nonlinearly. The temporal variation of the instantaneous frequency of the IMF component is consistent with the system nonlinear behavior of yielding and unloading. As a thorough study of this fundamental structural dynamics problem, this article investigates the influence of the amplitude of the harmonic wave excitation on the Hilbert spectrum and the intrinsic oscillatory mode of the dynamic response of a bilinear SDOF system.
Thumm, M K
2002-01-01
The possible applications of high-power millimeter (mm) and sub-mm waves from free-electron masers (FEMs) and gyro-devices span a wide range of technologies. The plasma physics community has already taken advantage of recent advances in applying high-power mm waves generated by long pulse or continuous wave (CW) gyrotron oscillators and short pulse very high-power FEMs in the areas of RF-plasma production, heating, non-inductive current drive, plasma stabilization and active plasma diagnostics for magnetic confinement thermonuclear fusion research, such as electron cyclotron resonance heating (28-170 GHz), electron cyclotron current drive , collective Thomson scattering , microwave transmission and heat-wave propagation experiments. Continuously frequency tunable FEMs could widen these fields of applications. Another important application of CW gyrotrons is industrial materials processing, e.g. sintering of high-performance functional and structural nanostructured ceramics. Sub-mm wave sources are employed in...
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.
Santos Coelho, Leandro dos [Pontifical Catholic University of Parana, PUCPR Industrial and Systems Engineering Graduate Program, PPGEPS, Imaculada Conceicao, 1155, Zip code 80215-901, Curitiba, PR (Brazil)], E-mail: leandro.coelho@pucpr.br; Mariani, Viviana Cocco [Pontifical Catholic University of Parana, PUCPR Mechanical Engineering Graduate Program, PPGEM, Imaculada Conceicao, 1155, Zip code 80215-901, Curitiba, PR (Brazil)], E-mail: viviana.mariani@pucpr.br
2008-11-15
Particle swarm optimization (PSO) algorithm is population-based heuristic global search algorithm inspired by social behavior patterns of organisms that live and interact within large groups. The PSO is based on researches on swarms such as fish schooling and bird flocking. Inspired by the classical PSO method and quantum mechanics theories, this work presents a quantum-inspired version of the PSO (QPSO) using the harmonic oscillator potential well (HQPSO) to solve economic dispatch problems. A 13-units test system with incremental fuel cost function that takes into account the valve-point loading effects is used to illustrate the effectiveness of the proposed HQPSO method compared with the simulation results based on the classical PSO, the QPSO, and other optimization algorithms reported in the literature.
dos Santos Coelho, Leandro [Pontifical Catholic University of Parana, PUCPR Industrial and Systems Engineering Graduate Program, PPGEPS, Imaculada Conceicao, 1155, Zip code 80215-901, Curitiba, PR (Brazil); Mariani, Viviana Cocco [Pontifical Catholic University of Parana, PUCPR Mechanical Engineering Graduate Program, PPGEM, Imaculada Conceicao, 1155, Zip code 80215-901, Curitiba, PR (Brazil)
2008-11-15
Particle swarm optimization (PSO) algorithm is population-based heuristic global search algorithm inspired by social behavior patterns of organisms that live and interact within large groups. The PSO is based on researches on swarms such as fish schooling and bird flocking. Inspired by the classical PSO method and quantum mechanics theories, this work presents a quantum-inspired version of the PSO (QPSO) using the harmonic oscillator potential well (HQPSO) to solve economic dispatch problems. A 13-units test system with incremental fuel cost function that takes into account the valve-point loading effects is used to illustrate the effectiveness of the proposed HQPSO method compared with the simulation results based on the classical PSO, the QPSO, and other optimization algorithms reported in the literature. (author)
FAN Hong-Yi; TANG Xu-Bing
2007-01-01
We employ the invariant eigen-operator (IEO) method to find the invariant eigen-operators of N-body singular oscillators' Hamiltonians and then derive their energy gaps. The Hamiltonians of parametric amplifiers with singular potential are also discussed in this way.
Bennett, Charles L.
2016-03-22
A reciprocating-piston uniflow engine includes a harmonic oscillator inlet valve capable of oscillating at a resonant frequency for controlling the flow of working fluid into 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. When released, the inlet valve head undergoes a single oscillation past the equilibrium position 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. In other embodiments, the harmonic oscillator arrangement of the inlet valve enables the uniflow engine to be reversibly operated as a uniflow compressor.
Cozzini, M.
2006-01-01
The collective modes of a rotating Bose--Einstein condensate confined in an attractive quadratic plus quartic trap are investigated. Assuming the presence of a large number of vortices we apply the diffused vorticity approach to the system. We then use the sum rule technique for the calculation of collective frequencies, comparing the results with the numerical solution of the linearized hydrodynamic equations. Numerical solutions also show the existence of low-frequency multipole modes which are interpreted as vortex oscillations.
M Cozzini
2006-01-01
The collective modes of a rotating Bose-Einstein condensate confined in an attractive quadratic plus quartic trap are investigated. Assuming the presence of a large number of vortices we apply the diffused vorticity approach to the system. We then use the sum rule technique for the calculation of collective frequencies, comparing the results with the numerical solution of the linearized hydrodynamic equations. Numerical solutions also show the existence of low-frequency multipole modes which are interpreted as vortex oscillations.
Scafetta, Nicola
2013-01-01
Power spectra of global surface temperature (GST) records reveal major periodicities at about 9.1, 10-11, 19-22 and 59-62 years. The Coupled Model Intercomparison Project 5 (CMIP5) general circulation models (GCMs), to be used in the IPCC (2013), are analyzed and found not able to reconstruct this variability. From 2000 to 2013.5 a GST plateau is observed while the GCMs predicted a warming rate of about 2 K/century. In contrast, the hypothesis that the climate is regulated by specific natural oscillations more accurately fits the GST records at multiple time scales. The climate sensitivity to CO2 doubling should be reduced by half, e.g. from the IPCC-2007 2.0-4.5 K range to 1.0-2.3 K with 1.5 C median. Also modern paleoclimatic temperature reconstructions yield the same conclusion. The observed natural oscillations could be driven by astronomical forcings. Herein I propose a semi empirical climate model made of six specific astronomical oscillations as constructors of the natural climate variability spanning ...
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.
Ruderman, M. S.; Petrukhin, N. S.; Pelinovsky, E.
2016-04-01
We study kink oscillations of thin magnetic tubes. We assume that the density inside and outside the tube (and possibly also the cross-section radius) can vary along the tube. This variation is assumed to be of such a form that the kink speed is symmetric with respect to the tube centre and varies monotonically from the tube ends to the tube centre. Then we prove a theorem stating that the ratio of periods of the fundamental mode and first overtone is a monotonically increasing function of the ratio of the kink speed at the tube centre and the tube ends. In particular, it follows from this theorem that the period ratio is lower than two when the kink speed increases from the tube ends to its centre, while it is higher than two when the kink speed decreases from the tube ends to its centre. The first case is typical for non-expanding coronal magnetic loops, and the second for prominence threads. We apply the general results to particular problems. First we consider kink oscillations of coronal magnetic loops. We prove that, under reasonable assumptions, the ratio of the fundamental period to the first overtone is lower than two and decreases when the loop size increases. The second problem concerns kink oscillations of prominence threads. We consider three internal density profiles: generalised parabolic, Gaussian, and Lorentzian. Each of these profiles contain the parameter α that is responsible for its sharpness. We calculate the dependence of the period ratio on the ratio of the mean to the maximum density. For all considered values of α we find that a formula relating the period ratio and the ratio of the mean and maximum density suggested by Soler, Goossens, and Ballester ( Astron. Astrophys. 575, A123, 2015) gives a sufficiently good approximation to the exact dependence.
Gyrotrons for magnetic fusion applications at 110 GHz and 170 GHz
Cahalan P.
2012-09-01
Full Text Available Two megawatt-class gyrotrons at frequencies of 110 GHz and 170 GHz have recently been fabricated at CPI. The 110 GHz gyrotron is designed to produce 1.2 MW of output power for 10-second pulses, and will be used for electron cyclotron heating and current drive on the DIII-D tokamak at General Atomics. This gyrotron has completed factory testing and has been delivered to General Atomics for installation and additional testing. The 170 GHz gyrotron, though specified as a 500 kW CW system, has been designed with the goal of generating up to 1 MW CW. Oak Ridge National Laboratory will use this gyrotron in ITER ECH transmission line testing. This gyrotron has been fabricated and is awaiting factory testing, Design features of each gyrotron are described, and test data for the 110 GHz gyrotron are presented.
Withnall, Robert; Andrews, David L.; Mendham, Andrew P.; Chowdhry, Babur Z.
2001-10-01
A band at ca. 150 cm-1 in the far infrared spectrum of diketopiperazine (DKP) is assigned to a ring puckering vibration. The multiplet structure reported for this band in the low temperature (77 K) far IR spectrum can be interpreted if the vibration is assumed to have quartic character. By means of Rayleigh-Schrodinger perturbation theory, a new vibrational selection rule, (Delta) n equals +/- 1, +/- 3, has been derived for mixed quartic-quadratic vibrations in the near harmonic region for the case of zero electrical anharmonicity. Assignments of the multiplet components have been made in the light of this vibrational selection rule. A two-parameter potential energy function of the ring puckering coordinate has been derived for the DKP molecule. This has enabled a value of ca. 355 cm-1 to be estimated for the energy barrier to interconversion of enantiomeric boat forms of DKP. The 0 - 1 transition has been estimated to have a wavenumber value of 0.033 cm-1 (1 GHz) in excellent agreement with the value of approximately 1 GHz obtained from a gas phase microwave spectroscopic study.
Ibarra-Sierra, V.G.; Sandoval-Santana, J.C. [Departamento de Física, Universidad Autónoma Metropolitana Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, 09340 México D.F. (Mexico); Cardoso, J.L. [Área de Física Teórica y Materia Condensada, Universidad Autónoma Metropolitana Azcapotzalco, Av. San Pablo 180, Col. Reynosa-Tamaulipas, Azcapotzalco, 02200 México D.F. (Mexico); Kunold, A., E-mail: akb@correo.azc.uam.mx [Área de Física Teórica y Materia Condensada, Universidad Autónoma Metropolitana Azcapotzalco, Av. San Pablo 180, Col. Reynosa-Tamaulipas, Azcapotzalco, 02200 México D.F. (Mexico)
2015-11-15
We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra is later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai–Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators. -- Highlights: •We deal with the general quadratic Hamiltonian and a particle in electromagnetic fields. •The evolution operator is worked out through the Lie algebraic approach. •We also obtain the propagator and Heisenberg picture position and momentum operators. •Analytical expressions for a
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.
Marquette, Ian, E-mail: i.marquette@uq.edu.au [School of Mathematics and Physics, The University of Queensland, Brisbane, QLD 4072 (Australia); Quesne, Christiane, E-mail: cquesne@ulb.ac.be [Physique Nucléaire Théorique et Physique Mathématique, Université Libre de Bruxelles, Campus de la Plaine CP229, Boulevard du Triomphe, B-1050 Brussels (Belgium)
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.
Ganeev, Rashid A
2014-01-01
Preface; Why plasma harmonics? A very brief introduction Early stage of plasma harmonic studies - hopes and frustrations New developments in plasma harmonics studies: first successes Improvements of plasma harmonics; Theoretical basics of plasma harmonics; Basics of HHG Harmonic generation in fullerenes using few-cycle pulsesVarious approaches for description of observed peculiarities of resonant enhancement of a single harmonic in laser plasmaTwo-colour pump resonance-induced enhancement of odd and even harmonics from a tin plasmaCalculations of single harmonic generation from Mn plasma;Low-o
Further studies of a simple gyrotron equation: nonlinear theory
Shi Meixuan, E-mail: meixuan@cims.nyu.ed [Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012-1185 (United States)
2010-11-05
A nonlinear version of a standard system of gyrotron model equations is studied using asymptotic analysis and variational methods. The condition for obtaining a high-amplitude wave is achieved in the study. A simple method for obtaining the patterns and amplitude of the wave based on the given free-space wave-number pattern is shown.
Gluck, P.; Krakower, Zeev
2010-01-01
We present a unit comprising theory, simulation and experiment for a body oscillating on a vertical spring, in which the simultaneous use of a force probe and an ultrasonic range finder enables one to explore quantitatively and understand many aspects of simple and damped harmonic motions. (Contains 14 figures.)
A novel vacuum window for megawatt gyrotrons
Haldeman, George Stephenson
2001-08-01
This thesis describes a new microwave output window for megawatt power level, 110 GHz gyrotrons. The window uses two spherically polished sapphire elements separated by a nearly uniform gap of about 1 mm. Pressurized, microwave transparent coolant flows through this gap and across the transmitting aperture, removing absorbed energy at the element face. The design differs from previous face- cooled windows because the sapphire elements have a modestly curved dome, rather than flat shape. This curved shape increases the element's capability to withstand coolant pressures without significantly increasing stresses from differential heating. Consequently, window power can be increased either through enhanced, high pressure cooling or by using thinner elements with reduced microwave absorption. A model was developed to predict window power capability as a function of design geometry. This model predicted an increase from 0.5 to 2.1 MW when flat elements were changed to curved. Both designs used full size, 100mm clear apertures, but the curved elements with 214 mm curvature radii were 1.3 rather than 1.75 mm thick. The model was also used to design a half size prototype experiment. This 50 mm clear aperture system used 60 mm OD x 0.47 mm thick x 107 mm surface radius elements. An initial piece was fabricated and statically tested to a pressure of 1.1 MPa well above the 0.5 MPa analytically predicted to be required for megawatt operation. The complete window structure was then fabricated, including instrumentation to simulate microwave heating and to measure induced temperatures and strains. Test results demonstrated an equivalent continuous Gaussian beam power capability of 700 kW using a coolant flow of 1.1 lps. Scaling from this measurement, fall size boiling limited power is expected to be 1.1 MW for a Gaussian microwave intensity profile, or 2.3 MW for a shaped profile typical of previous flat, face-cooled designs. (Copies available exclusively from MIT Libraries, Rm
Recent Tests on 117.5 GHz and 170 GHz Gyrotrons
Felch K.
2015-01-01
Full Text Available Two megawatt-class gyrotrons at frequencies of 117.5 GHz and 170 GHz have recently been fabricated and tested at CPI. The 117.5 GHz gyrotron was designed to produce up to 1.8 MW for 10-second pulses, and will be used for electron cyclotron heating and current drive on the DIII-D tokamak at General Atomics. The 170 GHz gyrotron is specified as a 500 kW CW system, but has been designed with the goal of generating up to 1 MW CW. Oak Ridge National Laboratory will use the gyrotron in ITER ECH transmission line testing.
Thumm, Manfred E-mail: manfred.thumm@ihm.fzk.de
2002-05-01
The possible applications of high-power millimeter (mm) and sub-mm waves from free-electron masers (FEMs) and gyro-devices span a wide range of technologies. The plasma physics community has already taken advantage of recent advances in applying high-power mm waves generated by long pulse or continuous wave (CW) gyrotron oscillators and short pulse very high-power FEMs in the areas of RF-plasma production, heating, non-inductive current drive, plasma stabilization and active plasma diagnostics for magnetic confinement thermonuclear fusion research, such as electron cyclotron resonance heating (28-170 GHz), electron cyclotron current drive , collective Thomson scattering , microwave transmission and heat-wave propagation experiments. Continuously frequency tunable FEMs could widen these fields of applications. Another important application of CW gyrotrons is industrial materials processing, e.g. sintering of high-performance functional and structural nanostructured ceramics. Sub-mm wave sources are employed in high-frequency broadband electron paramagnetic resonance and other types of spectroscopy. Future applications which await the development of novel high-power FEM amplifiers and gyro-amplifiers include high-resolution radar ranging and imaging in atmospheric and planetary science as well as deep-space and specialized satellite communications and RF drivers for next-generation high-gradient linear accelerators (supercolliders). The present paper reviews the state-of-the-art and future prospects of these recent applications of gyro-devices and FEMs and compares their specific advantages.
Further studies of a simple gyrotron equation: linear theory
Weitzner, Harold [New York University, Courant Institute of Mathematical Sciences New York, NY 10012 (United States)
2009-07-03
A linearized version of a standard system of gyrotron model equations is studied. The linearization allows the inclusion of some effects of particle bunching. The normal modes of the linearized system are given. It is shown that bunching effects couple incoming and outgoing waves. The waves near resonance duplicate well-known results. Without bunching and with a simple background profile function integral representations of solutions are given and discussed.
Investigations and advanced concepts on gyrotron interaction modeling and simulations
Avramidis, K. A.
2015-12-01
In gyrotron theory, the interaction between the electron beam and the high frequency electromagnetic field is commonly modeled using the slow variables approach. The slow variables are quantities that vary slowly in time in comparison to the electron cyclotron frequency. They represent the electron momentum and the high frequency field of the resonant TE modes in the gyrotron cavity. For their definition, some reference frequencies need to be introduced. These include the so-called averaging frequency, used to define the slow variable corresponding to the electron momentum, and the carrier frequencies, used to define the slow variables corresponding to the field envelopes of the modes. From the mathematical point of view, the choice of the reference frequencies is, to some extent, arbitrary. However, from the numerical point of view, there are arguments that point toward specific choices, in the sense that these choices are advantageous in terms of simulation speed and accuracy. In this paper, the typical monochromatic gyrotron operation is considered, and the numerical integration of the interaction equations is performed by the trajectory approach, since it is the fastest, and therefore it is the one that is most commonly used. The influence of the choice of the reference frequencies on the interaction simulations is studied using theoretical arguments, as well as numerical simulations. From these investigations, appropriate choices for the values of the reference frequencies are identified. In addition, novel, advanced concepts for the definitions of these frequencies are addressed, and their benefits are demonstrated numerically.
Dobaczewski, J.; Olbratowski, P.
2005-05-01
We describe the new version (v2.08k) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock or Skyrme-Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. Similarly as in the previous version (v2.08i), all symmetries can be broken, which allows for calculations with angular frequency and angular momentum tilted with respect to the mass distribution. In the new version, three minor errors have been corrected. New Version Program SummaryTitle of program: HFODD; version: 2.08k Catalogue number: ADVA Catalogue number of previous version: ADTO (Comput. Phys. Comm. 158 (2004) 158) Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVA Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Does the new version supersede the previous one: yes Computers on which this or another recent version has been tested: SG Power Challenge L, Pentium-II, Pentium-III, AMD-Athlon Operating systems under which the program has been tested: UNIX, LINUX, Windows-2000 Programming language used: Fortran Memory required to execute with typical data: 10M words No. of bits in a word: 64 No. of lines in distributed program, including test data, etc.: 52 631 No. of bytes in distributed program, including test data, etc.: 266 885 Distribution format:tar.gz Nature of physical problem: The nuclear mean-field and an analysis of its symmetries in realistic cases are the main ingredients of a description of nuclear states. Within the Local Density Approximation, or for a zero-range velocity-dependent Skyrme interaction, the nuclear mean-field is local and velocity dependent. The locality allows for an effective and fast solution of the self-consistent Hartree-Fock equations, even for heavy nuclei, and for various nucleonic ( n-particle n-hole) configurations, deformations, excitation energies, or angular momenta. Similar Local Density Approximation in the particle-particle channel, which is equivalent to using a zero
李冲; 许立忠; 邢继春
2015-01-01
An electromechanical integrated harmonic piezodrive system was proposed,which had the characteristics of low speed and high torque.The system output torque through oscillating teeth. The principles of the electromechanical integrated harmonic piezodrive system were discussed,the dy-namic models and dynamic equations were set up.Frequency equations of free vibration of oscillating tooth were given and the natural frequencies and vibration modes were solved,and the impacts of pa-rameters on natural frequencies were analyzed.These results provide basis for the improvement and the further research of the electromechanical integrated harmonic piezodrive system.%提出了一种具有低速大转矩特性的机电集成压电谐波传动系统，该传动系统利用活齿传动输出转矩。分析了机电集成压电谐波传动的工作原理，建立了活齿传动动力学模型，推导了其动力学微分方程，给出了活齿传动自由振动特征方程，求出了系统固有频率及振型，并分析了结构参数对固有频率的影响。研究结果为机电集成压电谐波传动系统的进一步优化提供了新的思路和方法。
王德华; 李红艳; 马晓光; 王美山; 杨传路
2007-01-01
Using the periodic orbit theory, we computed the quantum level density of a particle in the two-dimensional harmonic oscillator potential with and without the magnetic flux line for different cases. Especially discuss the influence of the magnetic flux line on the quantum level density. The results show when the frequency ratio of the two-dimensional harmonic potential is a rational number, the quantum level density is discrete. Each peak in the level density corresponds to one energy. However, when the frequency ratio is an irrational number, the level density is oscillating, when the magnetic flux is added, the amplitude of the oscillation decreased. This can be considered as a consequence of Aharonov-Bohm effect.%利用周期轨道理论,我们计算了在不同情况下,一个粒子在二维谐振子势中存在和不存在磁通量时的量子能级密度.重点讨论了磁通量对量子能级密度的影响.计算结果表明:当二维谐振子势的频率比值是有理数时,量子能级是分立的,能级密度中的每一条峰正好对应一个量子能级.然而,当频率比是无理数时,能级密度发生振荡,当加上磁通量后,振荡减小.这可以看作是Aharonov-Bohm效应的结果.
Bratman, V. L.; Savilov, A. V.; Chang, T. H.
2016-02-01
Large ohmic losses in the cavities of terahertz gyrotrons may lead to the overlapping of the axial mode spectra. In a number of gyrotron experiments, this effect has been used to provide a fairly broadband frequency tuning by changing appropriately the operating magnetic field and/or accelerating voltage of the gyrotron. Similar to the systems with nonfixed axial structure of the RF electromagnetic field and low diffraction quality, which are due to weak reflections of the operating wave from the collector end of the electrodynamic system, this changing leads to a monotonic change in the axial index of the operating wave and transition from the gyrotron regime to the gyro-BWO regime. According to a theoretical comparison of these two methods performed on the basis of generalization of self-consistent gyrotron equations with allowance for variations in the axial electron momenta, low-reflection systems can provide a higher efficiency and monotonicity of the frequency tuning.
Deep-UV 236.5 nm laser by fourth-harmonic generation of a single-crystal fiber Nd:YAG oscillator.
Deyra, Loïc; Martial, Igor; Didierjean, Julien; Balembois, François; Georges, Patrick
2014-04-15
We demonstrate a deep-UV laser at 236.5 nm based on extracavity fourth-harmonic generation of a Q-switched Nd:YAG single-crystal fiber laser at 946 nm. We first compare two nonlinear crystals available for second-harmonic generation: LBO and BiBO. The best results at 473 nm are obtained with a BiBO crystal, with an average output power of 3.4 W at 20 kHz, corresponding to a second-harmonic generation efficiency of 38%. This blue laser is frequency-converted to 236.5 nm in a BBO crystal with an overall fourth-harmonic generation yield of 6.5%, corresponding to an average output power of 600 mW at 20 kHz. This represents an order of magnitude increase in average power and energy compared to previously reported pulsed lasers at 236.5 nm. This work opens the possibility of LIDAR detection of dangerous compounds for military or civilian applications.
Farner, Snorre; Vergez, Christophe; Kergomard, Jean; Lizée, Aude
2005-01-01
The harmonic balance method (HBM) was originally developed for finding periodic solutions of electronical and mechanical systems under a periodic force, but has later 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 every periodic solution of the model, whether stable or unstable without care of i...
Rapid frequency step-switching in submillimeter wave gyrotrons (Gyrotrons FU III and FU IV)
Idehara, T.; Shimizu, Y; Ogawa, I.; Tatsukawa, T.; BRAND, G.F.
1999-01-01
The rapid frequency step-switching between two nearby cyclotron fundamental modes achieved by switching beam energy is analyzed by a computer simulation and demonstrated experimentally. More dramatic frequency switching between a fundamental mode and a second harmonic mode is analyzed and demonstrated experimentally.
Effects of electron-cyclotron instabilities on gyrotron beam quality
Jost, G.; Tran, T.M.; Appert, K. [Ecole Polytechnique Federale, Lausanne (Switzerland). Centre de Recherche en Physique des Plasma (CRPP); Wuethrich, S. [CRAY Research, PATP/PSE, EPFL, Lausanne (Switzerland)
1996-02-01
A two-dimensional PIC code aimed at the investigation of electron-cyclotron beam instabilities in gyrotrons and their effects on the beam quality is presented. The code is based on recently developed techniques for handling charge conservation and open boundaries. It has been implemented on the massively parallel computer CRAY T3D. First results show an electromagnetic backward instability periodically growing and decaying to energy levels close to those obtained from the electrostatic Bernstein wave instability. On the average, the resulting beam degradation is 3 to 4 times larger than that predicted by electrostatic models. (author) 8 figs., 14 refs.
Eliazar, Iddo
2017-05-01
The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their 'public relations' for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of this object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford's law, and 1/f noise.
Application of Fusion Gyrotrons to Enhanced Geothermal Systems (EGS)
Woskov, P.; Einstein, H.; Oglesby, K.
2013-10-01
The potential size of geothermal energy resources is second only to fusion energy. Advances are needed in drilling technology and heat reservoir formation to realize this potential. Millimeter-wave (MMW) gyrotrons and related technologies developed for fusion energy research could contribute to enabling EGS. Directed MMW energy can be used to advance rock penetration capabilities, borehole casing, and fracking. MMWs are ideally suited because they can penetrate through small particulate extraction plumes, can be efficiently guided long distances in borehole dimensions, and continuous megawatt sources are commercially available. Laboratory experiments with a 10 kW, 28 GHz CPI gyrotron have shown that granite rock can be fractured and melted with power intensities of about 1 kW/cm2 and minute exposure times. Observed melted rock MMW emissivity and estimated thermodynamics suggest that penetrating hot, hard crystalline rock formations may be economic with fusion research developed MMW sources. Supported by USDOE, Office of Energy Efficiency and Renewable Energy and Impact Technologies, LLC.
A Two Frequency 1.5 MW Gyrotron Experiment
Tax, David; Guss, William; Shapiro, Michael; Temkin, Richard; Rock, Ben; Vernon, Ronald; Neilson, Jeffrey
2012-10-01
Megawatt gyrotrons are an important microwave source for electron cyclotron heating and current drive (ECH/ECCD) in fusion plasmas due to their ability to produce megawatts of power at millimeter wave frequencies. The MIT gyrotron operates nominally at 96 kV and 40 A with 3 μs pulses and has previously demonstrated 1.5 MW of output power with > 50 % efficiency at 110 GHz with a depressed collector. A new cavity has been designed for 1.5 MW operation at two distinct frequencies: 110 GHz in the TE22,6 mode and 124.5 GHz in the TE24,7 mode. A new internal mode converter (IMC) consisting of a dimpled wall launcher and four smooth curved mirrors has also been designed and was optimized for both modes. Simulations of the IMC indicate that > 98 % Gaussian beam content could be achieved for each mode. Cold test results for the components will be presented as well as the current status of the hot test experiment.
Hochman, J. M.; Gilgenbach, R. M.; Jaynes, R. L.; Rintamaki, J. I.; Luginsland, J. W.; Lau, Y. Y.; Spencer, T. A.
1996-11-01
Experiments utilize large and small orbit e-beam gyrotron devices in a rectangular-cross-section (RCS) gyrotron. This device is being explored to examine polarization control. Other research issues include pulse shortening, and mode competition. MELBA generates electron beams with parameters of: -800kV, 1-10kA diode current, and 0.5-1.0 μ sec pulselengths. The small orbit gyrotron device is converted to a large orbit experiment by running MELBA's annular electron beam through a magnetic cusp. Initial experiments showed an increase in beam alpha (V_perp/V_par) of a factor of ~ 4 between small and large orbit devices. Experimental results from the RCS gyrotron will be compared for large-orbit and small-orbit electron beams. Beam transport data and frequency measurements will be presented. Computer modeling utilizing the MAGIC and E-gun codes will be shown.
Ion Compensation for Space Charge in the Helical Electron Beams of Gyrotrons
Manuilov, V. N.; Semenov, V. E.
2016-06-01
We solve analytically the problem about ion compensation for the space charge of a helical electron beam in a gyrotron operated in the long-pulse regime. Elementary processes, which take place during ionization of residual gas in the tube under typical pressures of 10-6-10-7 mm Hg, are considered. It is shown that distribution of the space charge is affected mainly by the electrons of the initial beam and slow-moving ions produced by ionization of the residual gas. Steady-state density of ions in the operating space of the gyrotron after the end of the transitional processes is found, as well as the electron density profile in the channel of electron beam transportation. The results obtained allow us to evaluate the pitch-factor variations caused by partial compensations for the potential "sagging" in the gyrotron cavity, thus being useful for analysis of starting currents, efficiency, and mode competition in high-power gyrotrons.
Cold test of cylindrical open resonator for 42 GHz, 200 kW gyrotron
Vivek Yadav; Sudeep Sharan; Hasina Khatun; Nitin Kumar; M K Alaria; B Jha; S C Deorani; A K Sinha; P K Jain
2013-12-01
This paper presents experimental results for cold testing of a gyrotron open resonator. Experiments were carried out to measure resonant frequency and their particular quality factor for TE mode at the frequency 42 GHz. The perturbation technique was used to determine the axial, radial and azimuthal electric field profile for identification of TE031 mode at operating frequency 42 GHz. The good agreement between experimental results and theoretical studies was found. The results verify the design and fabrication of the specific gyrotron cavity.
Farner, S; Kergomard, J; Lizée, A; Farner, Snorre; Vergez, Christophe; Kergomard, Jean; Liz\\'{e}e, Aude
2005-01-01
The harmonic balance method (HBM) was originally developed for finding periodic solutions of electronical and mechanical systems under a periodic force, but has later 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 every periodic solution of the model, whether stable or unstable without care of initial conditions. 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 continuations facilities are thorougly presented and discussed in the present paper. Application of the method is demonstrated on various problems related to a common model of the clarinet: a reed modelled as a simple spring with and without mass and damping, a nonlinear coupling and a cubic simplification of...
Eliazar, Iddo, E-mail: eliazar@post.tau.ac.il
2017-05-15
The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their ‘public relations’ for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of this object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford’s law, and 1/f noise. - Highlights: • Harmonic statistics are described and reviewed in detail. • Connections to various statistical laws are established. • Connections to perturbation, renormalization and dynamics are established.
Damyanova, M.; Sabchevski, S.; Zhelyazkov, I.; Vasileva, E.; Balabanova, E.; Dankov, P.; Malinov, P.
2016-10-01
As the most powerful CW sources of coherent radiation in the sub-terahertz to terahertz frequency range the gyrotrons have demonstrated a remarkable potential for numerous novel and prospective applications in the fundamental physical research and the technologies. Among them are powerful gyrotrons for electron cyclotron resonance heating (ECRH) and current drive (ECCD) of magnetically confined plasma in various reactors for controlled thermonuclear fusion (e.g., tokamaks and most notably ITER), high-frequency gyrotrons for sub-terahertz spectroscopy (for example NMR-DNP, XDMR, study of the hyperfine structure of positronium, etc.), gyrotrons for thermal processing and so on. Modelling and simulation are indispensable tools for numerical studies, computer-aided design (CAD) and optimization of such sophisticated vacuum tubes (fast-wave devices) operating on a physical principle known as electron cyclotron resonance maser (ECRM) instability. During the recent years, our research team has been involved in the development of physical models and problem-oriented software packages for numerical analysis and CAD of different gyrotrons in the framework of a broad international collaboration. In this paper we present the current status of our simulation tools (GYROSIM and GYREOSS packages) and illustrate their functionality by results of numerical experiments carried out recently. Finally, we provide an outlook on the envisaged further development of the computer codes and the computational modules belonging to these packages and specialized to different subsystems of the gyrotrons.
Paramonov, Guennaddi K; Bandrauk, Andre D
2016-01-01
Non Born-Oppenheimer quantum dynamics of H$_{2}^{+}$ excited by shaped one-cycle laser pulses linearly polarized along the molecular axis have been studied by the numerical solution of the time-dependent Schr\\"odinger equation within a %three-body three-dimensional model, including the internuclear separation, $R$, and the electron coordinates $z$ and $\\rho$. Laser carrier frequencies corresponding to the wavelengths $\\lambda_{l}=25$~nm through $\\lambda_{l}=400$~nm were used and the amplitudes of the pulses were chosen such that the energy of H$_{2}^{+}$ was close to its dissociation threshold at the end of any laser pulse applied. It is shown that there exists a characteristic oscillation frequency $\\omega_{\\rm osc} \\simeq 0.2265$~au (corresponding to the period of $\\tau_{\\rm osc} \\simeq 0.671$~fs and the wavelength of $\\lambda_{\\rm osc} \\simeq 200$~nm) that manifests itself as a "carrier" frequency of temporally shaped oscillations of the time-dependent expectation values $\\langle z \\rangle$ and $\\langle \\p...
Optimization of operation of a three-electrode gyrotron with the use of a flow-type calorimeter
Kharchev, Nikolay K.; Batanov, German M.; Kolik, Leonid V.; Malakhov, Dmitrii V.; Petrov, Aleksandr Ye.; Sarksyan, Karen A.; Skvortsova, Nina N.; Stepakhin, Vladimir D. [Prokhorov General Physics Institute, Vavilova ul. 38, Moscow 119991 (Russian Federation); Belousov, Vladimir I. [Institute of Applied Physics, Ul' yanova ul. 46, Nizhnii Novgorod 603950 (Russian Federation); Malygin, Sergei A.; Tai, Yevgenii M. [GYCOM Company, Ul' yanova ul. 46, Nizhnii Novgorod 603155 (Russian Federation)
2013-01-15
Results are presented for measurements of microwave power of the Borets-75/0.8 gyrotron with recovery of residual electron energy, which were performed by a flow-type calorimeter. This gyrotron is a part of the ECR plasma heating complex put into operation in 2010 at the L-2M stellarator. The new calorimeter is capable of measuring microwave power up to 0.5 MW. Monitoring of the microwave power makes it possible to control the parameters of the gyrotron power supply unit (its voltage and current) and the magnetic field of the cryomagnet in order to optimize the gyrotron operation and arrive at maximum efficiency.
Millimeter-wave gyrotron traveling-wave tube amplifiers
Du, Chao-Hai
2014-01-01
A gyrotron traveling-wave amplifier (gyro-TWT) with the high-power and broad-band capabilities is considered as a turn-on key for next generation high-resolution radar. The book presents comprehensive theory, methods, and physics related to gyro-TWT. The most challenging problem of instability competition has been for the first time addressed in a focused and systematic way, and reported via concise states and vivid pictures. The book is likely to meet the interest of researchers and engineers in radar and microwave technology, who would like to study the gyro-TWTs and to promote its application in millimeter-wave radars. Chao-Hai Du is a research professor, and Pu-Kun Liu is a full professor, at Peking University, Beijing, P. R. China.
Green's Function for the Quartic Oscillator
Anderson, Robert L.
2016-01-01
In this paper, a quantum mechanical Green's function $G_{qo}(y_b,t_b;$ $y_a,t_a)$ for the quartic oscillator is presented. This result is built upon two previous papers: first [1], detailing the linearization of the quartic oscillator $(qo)$ to the harmonic oscillator $(ho)$, second [2], the integration of the classical action function for the quartic oscillator. Here an equivalent form for the quartic oscillator action function $S_{qo}(y_b,t_b;$ $y_a,t_a)$ in terms of harmonic oscillator var...
Glyavin, M. Yu.; Morozkin, M. V.; Tsvetkov, A. I.; Lubyako, L. V.; Golubiatnikov, G. Yu.; Kuftin, A. N.; Zapevalov, V. E.; V. Kholoptsev, V.; Eremeev, A. G.; Sedov, A. S.; Malygin, V. I.; Chirkov, A. V.; Fokin, A. P.; Sokolov, E. V.; Denisov, G. G.
2016-02-01
We study experimentally the automated microwave complex for microwave spectroscopy and diagnostics of various media, which was developed at the Institute of Applied Physics of the Russian Academy of Sciences in cooperation with GYCOM Ltd. on the basis of a gyrotron with a frequency of 263 GHz and operated at the first gyrofrequency harmonic. In the process of the experiments, a controllable output power of 0 .1 -1 kW was achieved with an efficiency of up to 17 % in the continuous-wave generation regime. The measured radiation spectrum with a relative width of about 10 -6 and the frequency values measured at various parameters of the device are presented. The results of measuring the parameters of the wave beam, which was formed by a built-in quasioptical converter, as well as the data obtained by measuring the heat loss in the cavity and the vacuum output window are analyzed.
A Stable 0.2-THz Coaxial-Waveguide Gyrotron Traveling-Wave-Tube Amplifier with Distributed Losses
Hung, C. L.; Yeh, Y. S.; Chang, T. H.; Fang, R. S.
2016-08-01
For high-power operation, a THz gyrotron traveling-wave-tube (gyro-TWT) amplifier must operate in a high-order waveguide mode to enlarge the transverse dimension of an interaction waveguide. However, a gyro-TWT amplifier operating in a high-order waveguide mode is susceptible to spurious oscillations. To improve the device stability, in this study, we investigate the possibility of using a coaxial waveguide with distributed losses as the interaction structure. For the same required attenuation, all threatening oscillating modes can be suppressed using different combinations of losses of inner and outer cylinders. This provides flexibility in designing distributed losses when considering the ohmic loading of the interaction structure. We predict that the 0.2-THz gyro-TWT can stably produce a peak power of 14 kW with an efficiency of 23 %, a 3-dB bandwidth of 3.5 GHz, and a saturated gain of 50 dB for a 20-kV 3-A electron beam with a 5 % velocity spread and 1.0 velocity ratio.
Schunck, N; McDonnell, J; Satula, W; Sheikh, J A; Staszczak, A; Stoitsov, M; Toivanen, P
2011-01-01
We describe the new version (v2.49s) of the code HFODD which solves the nuclear Skyrme Hartree-Fock (HF) or Skyrme Hartree-Fock-Bogolyubov (HFB) problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following physics features: (i) the isospin mixing and projection, (ii) the finite temperature formalism for the HFB and HF+BCS methods, (iii) the Lipkin translational energy correction method, (iv) the calculation of the shell correction. A number of specific numerical methods have also been implemented in order to deal with large-scale multi-constraint calculations and hardware limitations: (i) the two-basis method for the HFB method, (ii) the Augmented Lagrangian Method (ALM) for multi-constraint calculations, (iii) the linear constraint method based on the approximation of the RPA matrix for multi-constraint calculations, (iv) an interface with the axial and parity-conserving Skyrme-HFB code HFBTHO, (v) the mixing of the HF or HFB matrix elements instead...
Schunck, N.; Dobaczewski, J.; Satuła, W.; Bączyk, P.; Dudek, J.; Gao, Y.; Konieczka, M.; Sato, K.; Shi, Y.; Wang, X. B.; Werner, T. R.
2017-07-01
We describe the new version (v2.73y) of the code hfodd which solves the nuclear Skyrme Hartree–Fock or Skyrme Hartree–Fock–Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following new features: (i) full proton–neutron mixing in the particle–hole channel for Skyrme functionals, (ii) the Gogny force in both particle–hole and particle–particle channels, (iii) linear multi-constraint method at finite temperature, (iv) fission toolkit including the constraint on the number of particles in the neck between two fragments, calculation of the interaction energy between fragments, and calculation of the nuclear and Coulomb energy of each fragment, (v) the new version 200d of the code hfbtho, together with an enhanced interface between hfbtho and hfodd, (vi) parallel capabilities, significantly extended by adding several restart options for large-scale jobs, (vii) the Lipkin translational energy correction method with pairing, (viii) higher-order Lipkin particle-number corrections, (ix) interface to a program plotting single-particle energies or Routhians, (x) strong-force isospin-symmetry-breaking terms, and (xi) the Augmented Lagrangian Method for calculations with 3D constraints on angular momentum and isospin. Finally, an important bug related to the calculation of the entropy at finite temperature and several other little significant errors of the previous published version were corrected.
Development of dual frequency gyrotron and high power test of EC components
Sakamoto K.
2012-09-01
Full Text Available In JAEA, development of high-power long-pulse gyrotrons is underway. The output power of the gyrotron was applied for high-power long-pulse tests of the transmission line (TL and the equatorial launcher (EL mock up for ITER. The feature of design in the dual frequency gyrotron is the simultaneously satisfying the matching of both frequencies at a window and the same radiation angle at an internal mode convertor for both frequencies. The dual frequency gyrotron was developed and high power operations at 170 GHz and 137 GHz were carried out. The 170 GHz high power experiment of 40 m length ITER relevant TL was carried out and transmission efficiency and mode purity change caused by long pulse operation were measured. The mock-up model of EL was also tested using 170 GHz gyrotron. The power transmission through the quasi-optical beam line in EL was demonstrated using the full scale mock up model. Furthermore, the high power test results of the transmission components will be summarized.
Plasma scattering measurement using a submillimeter wave gyrotron as a radiation source
Ogawa, I.; Idehara, T.; Itakura, Y.; Myodo, M. [Fukui Univ., Research Center for Development of Far-Infrared Region (Japan); Hori, T. [National Institute of Information and Communications Technology, Basic and Advanced Research Division, Nukui-Kita, Koganei (Japan); Hatae, T. [Japan Atomic Energy Research Institute, Mukoyama, Naka (Japan)
2004-07-01
Plasma scattering measurement is an effective technique to observe low frequency density fluctuations excited in plasma. The spatial and wave number resolutions and the S/N ratio of measurement depend on the wavelength range, the size and the intensity of a probe beam. A well-collimated, submillimeter wave beam is suitable for improving the spatial and wave number resolutions. Application of high frequency gyrotron is effective in improving the S/N ratio of the measurement because of its capacity to deliver high power. Unlike the molecular vapor lasers, the gyrotrons generate diverging beam of radiation with TE{sub mn} mode structure. It is therefore necessary to convert the output radiation into a Gaussian beam. A quasi-optical antenna is a suitable element for the conversion system under consideration since it is applicable to several TE{sub 0n} and TE{sub 1n} modes. In order to apply the gyrotron to plasma scattering measurement, we have stabilized the output (P = 110 W, f = 354 GHz) of gyrotron up to the level ({delta}P/P < 1 %, {delta}f< 10 kHz). The gyrotron output can be stabilized by decreasing the fluctuation of the cathode potential. (authors)
Glyavin, M. Yu., E-mail: glyavin@appl.sci-nnov.ru; Denisov, G. G.; Zapevalov, V. E. [Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod (Russian Federation); Gycom Ltd., Nizhny Novgorod (Russian Federation); Chirkov, A. V.; Fokin, A. P.; Kholoptsev, V. V.; Kuftin, A. N.; Luchinin, A. G.; Golubyatnikov, G. Yu.; Malygin, V. I.; Morozkin, M. V.; Manuilov, V. N.; Proyavin, M. D.; Sedov, A. S.; Tsvetkov, A. I. [Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod (Russian Federation); Sokolov, E. V.; Tai, E. M. [Gycom Ltd., Nizhny Novgorod (Russian Federation)
2015-05-15
A 263 GHz continuous-wave (CW) gyrotron was developed at the IAP RAS for future applications as a microwave power source in Dynamic Nuclear Polarization / Nuclear magnetic resonance (DNP/NMR) spectrometers. A new experimental facility with a computerized control was built to test this and subsequent gyrotrons. We obtained the maximum CW power up to 1 kW in the 15 kV/0.4 A operation regime. The power about 10 W, which is sufficient for many spectroscopic applications, was realized in the low current 14 kV/0.02 A regime. The possibility of frequency tuning by variation of the coolant temperature about 4 MHz/1 °C was demonstrated. The spectral width of the gyrotron radiation was about 10{sup −6}.
60 GHz gyrotron development program. Final report, April 1979-June 1984
Shively, J.F.; Bier, R.E.; Caplan, M.; Cheng, M.K.; Choi, E.; Conner, C.C.; Craig, L.J.; Evans, S.J.; Evers, S.J.; Felch, K.L.
1986-01-01
The original objective of this program was to develop a microwave amplifier or oscillator capable of producing 200 kW CW power output at 110 GHz. The use of cyclotron resonance interaction was pursued, and the design phases of this effort are discussed. Later, however, the program's objective was changed to develop a family of oscillators capable of producing 200 kw of peak output power at 60 GHz. Gyrotron behavior studies were performed at 28 GHz to obtain generic design information as quickly as possible. The first experimental device at 60 GHz produced over 200 kw of peak power at a pulse duration of 20 ..mu..s. Heating problems and mode interference were encountered. The second experimental tube incorporated an optimized gun location but also suffered from mode interference. The third experimental tube included modifications that reduced mode interference. It demonstrated 200 kw of peak output at 100 ms pulse duration. The fourth experimental tube, which used an older rf circuit design but in a CW configuration, produced 71.5 kW CW. The fifth experimental tube incorporated a thinner double-disc output window which improved window bandwidth and reduced window loss. This tube also incorporated modifications to the drift tunnel and cavity coupling, which had proven successful in the third experimental pulse tube tests. It produced 123 kW of CW output power at 60 GHz rf load coolant boiling and tube window failure terminated the tests. A new waterload was designed and constructed, and alternative window designs were explored. A secondary task of developing a 56 GHz CW tube produced in excess of 100 kW CW at this alternate frequency. Testing of the sixth experimental tube resulted in operation at CW output power in the range of 200 to 206 kW for an hour. Output mode purity of the seventh experimental tube was measured at 95% TE/sub 02/. The tube was operated for about forty-five minutes with CW power output over 200 kW.
Harmonic Stability Assessment for Multi-Paralleled, Grid-Connected Inverters
Yoon, Changwoo; Bai, Haofeng; Beres, Remus Narcis;
2016-01-01
This paper investigates the harmonic interactions of current controllers in multi-paralleled grid-connected inverters. Potential harmonic instability phenomenon, which features oscillations above the fundamental frequency are evaluated by the impedance-based stability criterion. The possible reas...
Gyrotrons for High-Power Terahertz Science and Technology at FIR UF
Idehara, Toshitaka
2016-01-01
In this paper, we present the recent progress in the development of a series of gyrotrons at FIR UF that have opened the road to many novel applications in the high-power Terahertz science and technology. The current status of the research in this actively developing field is illustrated by the most representative examples in which the developed gyrotrons are used as powerful and frequency tunable sources of coherent radiation operating in a CW regime. Among them are high-precision spectroscopic techniques (most notably DNP-NMR, ESR, XDMR, and studies of the hyperfine splitting of the energy levels of positronium), treatment and characterization of advanced materials, new medical technologies.
Excited Sessile Drops Perform Harmonically
Chang, Chun-Ti; Steen, Paul H
2013-01-01
In our fluid dynamics video, we demonstrate our method of visualizing and identifying various mode shapes of mechanically oscillated sessile drops. By placing metal mesh under an oscillating drop and projecting light from below, the drop's shape is visualized by the visually deformed mesh pattern seen in the top view. The observed modes are subsequently identified by their number of layers and sectors. An alternative identification associates them with spherical harmonics, as demonstrated in the tutorial. Clips of various observed modes are presented, followed by a 10-second quiz of mode identification.
Stoitsov, M. V.; Schunck, N.; Kortelainen, M.; Michel, N.; Nam, H.; Olsen, E.; Sarich, J.; Wild, S.
2013-06-01
We describe the new version 2.00d of the code HFBTHO that solves the nuclear Skyrme-Hartree-Fock (HF) or Skyrme-Hartree-Fock-Bogoliubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the modified Broyden method for non-linear problems, (ii) optional breaking of reflection symmetry, (iii) calculation of axial multipole moments, (iv) finite temperature formalism for the HFB method, (v) linear constraint method based on the approximation of the Random Phase Approximation (RPA) matrix for multi-constraint calculations, (vi) blocking of quasi-particles in the Equal Filling Approximation (EFA), (vii) framework for generalized energy density with arbitrary density-dependences, and (viii) shared memory parallelism via OpenMP pragmas. Program summaryProgram title: HFBTHO v2.00d Catalog identifier: ADUI_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUI_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License version 3 No. of lines in distributed program, including test data, etc.: 167228 No. of bytes in distributed program, including test data, etc.: 2672156 Distribution format: tar.gz Programming language: FORTRAN-95. Computer: Intel Pentium-III, Intel Xeon, AMD-Athlon, AMD-Opteron, Cray XT5, Cray XE6. Operating system: UNIX, LINUX, WindowsXP. RAM: 200 Mwords Word size: 8 bits Classification: 17.22. Does the new version supercede the previous version?: Yes Catalog identifier of previous version: ADUI_v1_0 Journal reference of previous version: Comput. Phys. Comm. 167 (2005) 43 Nature of problem: The solution of self-consistent mean-field equations for weakly-bound paired nuclei requires a correct description of the asymptotic properties of nuclear quasi-particle wave functions. In the present implementation, this is achieved by using the single-particle wave functions
Scleronomic Holonomic Constraints and Conservative Nonlinear Oscillators
Munoz, R.; Gonzalez-Garcia, G.; Izquierdo-De La Cruz, E.; Fernandez-Anaya, G.
2011-01-01
A bead sliding, under the sole influence of its own weight, on a rigid wire shaped in the fashion of a plane curve, will describe (generally anharmonic) oscillations around a local minimum. For given shapes, the bead will behave as a harmonic oscillator in the whole range, such as an unforced, undamped, Duffing oscillator, etc. We also present…
A Fully-Sealed Carbon-Nanotube Cold-Cathode Terahertz Gyrotron
Yuan, Xuesong; Zhu, Weiwei; Zhang, Yu; Xu, Ningsheng; Yan, Yang; Wu, Jianqiang; Shen, Yan; Chen, Jun; She, Juncong; Deng, Shaozhi
2016-09-01
Gigahertz to terahertz radiation sources based on cold-cathode vacuum electron technology are pursued, because its unique characteristics of instant switch-on and power saving are important to military and space applications. Gigahertz gyrotron was reported using carbon nanotube (CNT) cold-cathode. It is reported here in first time that a fully-sealed CNT cold-cathode 0.22 THz-gyrotron is realized, typically with output power of 500 mW. To achieve this, we have studied mechanisms responsible for CNTs growth on curved shape metal surface, field emission from the sidewall of a CNT, and crystallized interface junction between CNT and substrate material. We have obtained uniform growth of CNTs on and direct growth from cone-cylinder stainless-steel electrode surface, and field emission from both tips and sidewalls of CNTs. It is essential for the success of a CNT terahertz gyrotron to have such high quality, high emitting performance CNTs. Also, we have developed a magnetic injection electron gun using CNT cold-cathode to exploit the advantages of such a conventional gun design, so that a large area emitting surface is utilized to deliver large current for electron beam. The results indicate that higher output power and higher radiation frequency terahertz gyrotron may be made using CNT cold-cathode electron gun.
杨双波; 韦栋
2012-01-01
This paper studies the classical dynamics and quasienergy spectral statistics for a periodically kicked Harmonic oscillator system,under the nonresonance condition.It is found that as we increase the kicking strength Κ ,and the phase space structure starts from tori for integrable system to completely chaotic for nonintegrable system,the nearest neighbor spacing distribution for the quasienergy spectral keeps the Poissonian distribution,and this is similar to that of the peri odically kicked free rotor.The result of spectral rigidities shows that except the case of Κ=30,the rigidities for Κ= 0.13,1.6,2.0,2.6,bunched,increase linearly with L for L 0.1.The number variance∑2 ,skewness γ1,,excess γ2 are not sensitive to the change of Κ.%研究一个周期受击简谐振子系统在非谐振情况下的经典动力学与准能谱统计.研究发现,随着打击强度κ的增加,经典相空间结构从可积(环)到完全混沌时,准能谱按最近邻能级间距分布仍保持Poisson分布不变,这与周期受击转子系统的结果相同.谱刚度的计算表明,除了κ=30的情况外,κ=0.13、1.6、2.0、2.6等的谱刚度在L＜0.1的范围内随L线性变化,呈束状；在L＞0.1以后发散开来,呈非线性变化,且κ=0.13的谱刚度趋于饱和.数方差∑2及高阶矩γ1,γ2随κ的变化不敏感.
Energy Diffusion in Harmonic System with Conservative Noise
Basile, Giada; Olla, Stefano
2014-06-01
We prove diffusive behaviour of the energy fluctuations in a system of harmonic oscillators with a stochastic perturbation of the dynamics that conserves energy and momentum. The results concern pinned systems in any dimension, or unpinned systems in dimension.
Phononic High Harmonic Generation
Ganesan, Adarsh; Seshia, Ashwin A
2016-01-01
This paper reports the first experimental evidence for phononic low-order to high-order harmonic conversion leading to high harmonic generation. Similar to parametric resonance, phononic high harmonic generation is also mediated by a threshold dependent instability of a driven phonon mode. Once the threshold for instability is met, a cascade of harmonic generation processes is triggered. Firstly, the up-conversion of first harmonic phonons into second harmonic phonons is established. Subsequently, the down-conversion of second harmonic phonons into first harmonic phonons and conversion of first and second harmonic phonons into third harmonic phonons occur. On the similar lines, an eventual conversion of third harmonic phonons to high orders is also observed to commence. This surprising physical pathway for phononic low-order to high-order harmonic conversion may find general relevance to other physical systems.
Atakishiyev, Natig M [Centro de Ciencias FIsicas, UNAM, Apartado Postal 48-3, 62251 Cuernavaca, Morelos (Mexico); Klimyk, Anatoliy U [Centro de Ciencias FIsicas, UNAM, Apartado Postal 48-3, 62251 Cuernavaca, Morelos (Mexico); Wolf, Kurt Bernardo [Centro de Ciencias FIsicas, UNAM, Apartado Postal 48-3, 62251 Cuernavaca, Morelos (Mexico)
2004-05-28
The finite q-oscillator is a model that obeys the dynamics of the harmonic oscillator, with the operators of position, momentum and Hamiltonian being functions of elements of the q-algebra su{sub q}(2). The spectrum of position in this discrete system, in a fixed representation j, consists of 2j + 1 'sensor'-points x{sub s} = 1/2 [2s]{sub q}, s element of {l_brace}-j, -j+1, ..., j{r_brace}, and similarly for the momentum observable. The spectrum of energies is finite and equally spaced, so the system supports coherent states. The wavefunctions involve dual q-Kravchuk polynomials, which are solutions to a finite-difference Schroedinger equation. Time evolution (times a phase) defines the fractional Fourier-q-Kravchuk transform. In the classical limit as q {yields} 1 we recover the finite oscillator Lie algebra, the N = 2j {yields} {infinity} limit returns the Macfarlane-Biedenharn q-oscillator and both limits contract the generators to the standard quantum-mechanical harmonic oscillator.
Atakishiyev, Natig M.; Klimyk, Anatoliy U.; Wolf, Kurt Bernardo
2004-05-01
The finite q-oscillator is a model that obeys the dynamics of the harmonic oscillator, with the operators of position, momentum and Hamiltonian being functions of elements of the q-algebra suq(2). The spectrum of position in this discrete system, in a fixed representation j, consists of 2j + 1 'sensor'-points x_s={\\case12}[2s]_q, s\\in\\{-j,-j+1,\\ldots,j\\} , and similarly for the momentum observable. The spectrum of energies is finite and equally spaced, so the system supports coherent states. The wavefunctions involve dual q-Kravchuk polynomials, which are solutions to a finite-difference Schrödinger equation. Time evolution (times a phase) defines the fractional Fourier-q-Kravchuk transform. In the classical limit as q rarr 1 we recover the finite oscillator Lie algebra, the N = 2j rarr infin limit returns the Macfarlane-Biedenharn q-oscillator and both limits contract the generators to the standard quantum-mechanical harmonic oscillator.
The Harmonic Oscillator–A Simplified Approach
L. R. Ganesan
2008-01-01
Full Text Available Among the early problems in quantum chemistry, the one dimensional harmonic oscillator problem is an important one, providing a valuable exercise in the study of quantum mechanical methods. There are several approaches to this problem, the time honoured infinite series method, the ladder operator method etc. A method which is much shorter, mathematically simpler is presented here.
Schunck, N.; Dobaczewski, J.; McDonnell, J.; Satuła, W.; Sheikh, J. A.; Staszczak, A.; Stoitsov, M.; Toivanen, P.
2012-01-01
We describe the new version (v2.49t) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock (HF) or Skyrme-Hartree-Fock-Bogolyubov (HFB) problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following physics features: (i) the isospin mixing and projection, (ii) the finite-temperature formalism for the HFB and HF + BCS methods, (iii) the Lipkin translational energy correction method, (iv) the calculation of the shell correction. A number of specific numerical methods have also been implemented in order to deal with large-scale multi-constraint calculations and hardware limitations: (i) the two-basis method for the HFB method, (ii) the Augmented Lagrangian Method (ALM) for multi-constraint calculations, (iii) the linear constraint method based on the approximation of the RPA matrix for multi-constraint calculations, (iv) an interface with the axial and parity-conserving Skyrme-HFB code HFBTHO, (v) the mixing of the HF or HFB matrix elements instead of the HF fields. Special care has been paid to using the code on massively parallel leadership class computers. For this purpose, the following features are now available with this version: (i) the Message Passing Interface (MPI) framework, (ii) scalable input data routines, (iii) multi-threading via OpenMP pragmas, (iv) parallel diagonalization of the HFB matrix in the simplex-breaking case using the ScaLAPACK library. Finally, several little significant errors of the previous published version were corrected. New version program summaryProgram title:HFODD (v2.49t) Catalogue identifier: ADFL_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADFL_v3_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public Licence v3 No. of lines in distributed program, including test data, etc.: 190 614 No. of bytes in distributed program, including test data, etc.: 985 898 Distribution
Status of the development of the EU 170 GHz/1 MW/CW gyrotron
Pagonakis, Ioannis Gr., E-mail: ioannis.pagonakis@kit.edu [Karlsruhe Institute of Technology (KIT), Karlsruhe (Germany); Albajar, Ferran [The European Joint Undertaking for ITER and The Development of Fusion Energy, Barcelona (Spain); Alberti, Stefano [École Polytechnique Fédérale de Lausanne, Centre de Recherches en Physique des Plasmas (CRPP), Lausanne (Switzerland); Avramidis, Konstantinos [Karlsruhe Institute of Technology (KIT), Karlsruhe (Germany); Bonicelli, Tullio [The European Joint Undertaking for ITER and The Development of Fusion Energy, Barcelona (Spain); Braunmueller, Falk [École Polytechnique Fédérale de Lausanne, Centre de Recherches en Physique des Plasmas (CRPP), Lausanne (Switzerland); Bruschi, Alex [Plasma Physics Institute, National Research Council of Italy, Milano (Italy); Chelis, Ioannis [School of Electrical and Computer Engineering, National Technical University of Athens (Greece); Cismondi, Fabio [The European Joint Undertaking for ITER and The Development of Fusion Energy, Barcelona (Spain); Gantenbein, Gerd [Karlsruhe Institute of Technology (KIT), Karlsruhe (Germany); Hermann, Virgile [Thales Electron Devices (TED), Vélizy-Villacoublay (France); Hesch, Klaus [Karlsruhe Institute of Technology (KIT), Karlsruhe (Germany); Hogge, Jean-Philippe [École Polytechnique Fédérale de Lausanne, Centre de Recherches en Physique des Plasmas (CRPP), Lausanne (Switzerland); Jelonnek, John; Jin, Jianbo; Illy, Stefan [Karlsruhe Institute of Technology (KIT), Karlsruhe (Germany); Ioannidis, Zisis C. [Faculty of Physics, National and Kapodistrian University of Athens (Greece); Kobarg, Thorsten [Karlsruhe Institute of Technology (KIT), Karlsruhe (Germany); and others
2015-10-15
The progress in the development of the European 170 GHz, 1 MW/CW gyrotron for electron cyclotron heating & current drive (ECH&CD) on ITER is reported. A continuous wave (CW) prototype is being manufactured by Thales Electron Devices (TED), France, while a short-pulse (SP) prototype gyrotron is in parallel under manufacture at Karlsruhe Institute of Technology (KIT), with the purpose of validating the design of the CW industrial prototype components. The fabrication of most of the sub-assemblies of the SP prototype has been completed. In a first step, an existing magnetron injection gun (MIG) available at KIT was used. Despite this non-ideal configuration, the experiments provided a validation of the design, substantiated by an excellent agreement with numerical simulations. The tube, operated without a depressed collector, is able to produce more than 1 MW of output power with efficiency in excess of 30%, as expected, and compatible with the ITER requirements.
Development and simulation of RF components for high power millimeter wave gyrotrons
Pereyaslavets, M.; Sato, M.; Shimozuma, T.; Takita, Y.; Idei, H.; Kubo, S.; Ohkubo, K.; Hayashi, K.
1996-11-01
To test gyrotron RF components, efficient low-power generators for rotating high-order modes of high purity are necessary. Designs of generators for the TE{sub 15,3} mode at 84 GHz and for the TE{sub 31,8} mode at 168 GHz are presented and some preliminary test results are discussed. In addition, Toshiba gyrotron cavities at 168 GHz were analyzed for leakage of RF power in the beam tunnel. To decrease RF power leakage, the declination angle of the cut-off cavity cross section has to be decreased. A TE{sub 15,3} waveguide nonlinear uptaper is analyzed at 84 GHz as well as 168 GHz uptapers. Since the calculated conversion losses are slightly higher than designed value, an optimization of those uptapers may be required. (author)
太赫兹回旋管研究进展%Development of Terahertz Gyrotrons
鄢扬; 傅文杰
2013-01-01
回旋管是一种基于电子回旋谐振受激辐射的快波器件,是目前太赫兹波段输出功率和效率最高的重要器件,本文给出了目前国内外太赫兹回旋管技术的发展状况,分析了太赫兹回旋管的特点和应用前景.%Gyrotrons are fast-wave vacuum electron devices based on the stimulated radiation, of electron cyclotron resonance. They are able to deliver powerful radiation in terahertz frequency bands with high efficiency. In this paper, the current status and development of terahertz gyrotrons are reviewed, the characteristics and prospective applications are discussed.
Gyrotrons for High-Power Terahertz Science and Technology at FIR UF
Idehara, Toshitaka; Sabchevski, Svilen Petrov
2016-10-01
In this review paper, we present the recent progress in the development of a series of gyrotrons at the Research Center for Development of Far-Infrared Region, University of Fukui, that have opened the road to many novel applications in the high-power terahertz science and technology. The current status of the research in this actively developing field is illustrated by the most representative examples in which the developed gyrotrons are used as powerful and frequency-tunable sources of coherent radiation operating in a continuous-wave regime. Among them are high-precision spectroscopic techniques (most notably dynamic nuclear polarization-nuclear magnetic resonance, electron spin resonance, X-ray detected magnetic resonance, and studies of the hyperfine splitting of the energy levels of positronium), treatment and characterization of advanced materials, and new medical technologies.
Damyanova, M.; Sabchevski, S.; Zhelyazkov, I.; Vasileva, E.; Balabanova, E.; Dankov, P.; Malinov, P.
2016-05-01
Powerful gyrotrons are necessary as sources of strong microwaves for electron cyclotron resonance heating (ECRH) and electron cyclotron current drive (ECCD) of magnetically confined plasmas in various reactors (most notably ITER) for controlled thermonuclear fusion. Adequate physical models and efficient problem-oriented software packages are essential tools for numerical studies, analysis, optimization and computer-aided design (CAD) of such high-performance gyrotrons operating in a CW mode and delivering output power of the order of 1-2 MW. In this report we present the current status of our simulation tools (physical models, numerical codes, pre- and post-processing programs, etc.) as well as the computational infrastructure on which they are being developed, maintained and executed.
Gyrotrons for High-Power Terahertz Science and Technology at FIR UF
Idehara, Toshitaka; Sabchevski, Svilen Petrov
2017-01-01
In this review paper, we present the recent progress in the development of a series of gyrotrons at the Research Center for Development of Far-Infrared Region, University of Fukui, that have opened the road to many novel applications in the high-power terahertz science and technology. The current status of the research in this actively developing field is illustrated by the most representative examples in which the developed gyrotrons are used as powerful and frequency-tunable sources of coherent radiation operating in a continuous-wave regime. Among them are high-precision spectroscopic techniques (most notably dynamic nuclear polarization-nuclear magnetic resonance, electron spin resonance, X-ray detected magnetic resonance, and studies of the hyperfine splitting of the energy levels of positronium), treatment and characterization of advanced materials, and new medical technologies.
Second Harmonic Generation in Scanning Probe Microscopy for Edge Localization
HU Xiao-Gen; LI Yu-He; LIN Hao-Shan; WANG Dong-Sheng; QI Xin
2011-01-01
We present an approach of second harmonic generation for edge localization of nano-scale defects measurement,based on the impact of the oscillating tip on the sample that induces higher harmonics of the excitation frequency.The harmonic signals of tip motion are measured by the heterodyne interferornetry. The edge amplitude ratio for the edge characterization can be calculated by a mechanics model and the threshold of edge localization is experimentally determined by second harmonic profiles. This approach has been successfully utilized to measure the pitch of a standard sample. The results show that the second harmonic is sensitive to locating the edge of nano-scale defects with high accuracy.%@@ We present an approach of second harmonic generation for edge localization of nano-scale defects measurement,based on the impact of the oscillating tip on the sample that induces higher harmonics of the excitation frequency.The harmonic signals of tip motion are measured by the heterodyne interferometry.The edge amplitude ratio for the edge characterization can be calculated by a mechanics model and the threshold of edge localization is experimentally determined by second harmonic profiles.This approach has been successfully utilized to measure the pitch of a standard sample.The results show that the second harmonic is sensitive to locating the edge of nano-scale defects with high accuracy.
Upgrade of a 30 kV/10 mA anode power supply for triode type gyrotron
Siravo, Ugo, E-mail: ugo.siravo@epfl.ch; Alberti, Stefano; Dubray, Jérémie; Fasel, Damien; Hogge, Jean-Philippe; Marlétaz, Blaise; Marmillod, Philippe; Perez, Albert; Silva, Miguel
2015-10-15
Highlights: • Triode type gyrotron is fed by 3 power supplies: the main, an anode PS(APS) and a heater. • This paper presents the upgrade of 3APS, supplied in 1999, that never fulfilled the specs. • The new working principle is very efficient, easy to implement, for a minimal cost. • Upgraded APS provides extended modulation capabilities, no overshoot and lowerripple. • This upgrade will allow exploring new operation regimes for the 3 TCV X3 gyrotrons. - The RF power of a gyrotron with a triode type magnetron-injection-gun (MIG) can be directly controlled via the voltage applied between its anode and its cathode. Hence, the performance of this type of gyrotron relies directly on the possibilities offered by the power supply controlling the anode to cathode voltage. For a system of gyrotrons connected to the same main high-voltage power supply, with a triode MIG one has the additional advantage of independently controlling each individual gyrotron. This paper presents the modifications brought to the three existing 30 kV/10 mA anode power supplies connected to the 500 kW/118 GHz/2s X3 gyrotrons operated on the TCV Tokamak. The new working principle based on phase-shift modulation (PSM) is described in detail. Experimental results obtained on dummy load are compared to simulations performed during the design phase. With respect to the initial working principle, the modulation frequency capability has been increased by a factor 10 reaching more than 5 kHz, whereas the output voltage ripple as well as the overshoot/undershoot have been significantly reduced.
Piotr FOLĘGA
2014-03-01
Full Text Available The variety of types and sizes currently in production harmonic drive is a problem in their rational choice. Properly selected harmonic drive must meet certain requirements during operation, and achieve the anticipated service life. The paper discusses the problems associated with the selection of the harmonic drive. It also presents the algorithm correct choice of harmonic drive. The main objective of this study was to develop a computer program that allows the correct choice of harmonic drive by developed algorithm.
Batanov, German M.; Borzosekov, Valentin D.; Golberg, Dmitri; Iskhakova, Ludmila D.; Kolik, Leonid V.; Konchekov, Evgeny M.; Kharchev, Nikolai K.; Letunov, Alexander A.; Malakhov, Dmitry V.; Milovich, Filipp O.; Obraztsova, Ekaterina A.; Petrov, Alexander E.; Ryabikina, Irina G.; Sarksian, Karen A.; Stepakhin, Vladimir D.; Skvortsova, Nina N.
2016-01-01
We introduce an approach toward the synthesis of micro- and nanostructures under nonequilibrium microwave discharges within metal-dielectric powder mixtures induced by powerful microwave gyrotron radiation. A new plasma-chemical reactor capable of sustaining a discharge regime with an afterglow phase of an order of magnitude longer than the gyrotron pulse duration was constructed for these experiments. In the nonequilibrium conditions of such a discharge, plasma-induced exothermic chemical reactions leading to the synthesis of various compounds were initiated. The synthesized structures were deposited on the reactor walls and on the impurity particles within the reactor. This method was tested under gyrotron-initiated discharges within various metal-dielectric powder mixtures of titanium-boron, molybdenum-boron, titanium-silicon-boron, molybdenum-boron nitride, molybdenum-tungsten-boron nitride, and so on. Depending on the powder mixture composition, reactor atmosphere, and other parameters, micro- and nanosized particles of boron nitride, titanium diboride, molybdenum boride, titanium boride, molybdenum, and molybdenum oxide, were synthesized, detected, and analyzed.
Nonequilibrium quantum fluctuation relations for harmonic systems in nonthermal environments
Pagel, D.; Nalbach, P.; Alvermann, A.; Fehske, H.; Thorwart, M.
2013-10-01
We formulate exact generalized nonequilibrium fluctuation relations for the quantum mechanical harmonic oscillator coupled to multiple harmonic baths. Each of the different baths is prepared in its own individual (in general nonthermal) state. Starting from the exact solution for the oscillator dynamics we study fluctuations of the oscillator position as well as of the energy current through the oscillator under general nonequilibrium conditions. In particular, we formulate a fluctuation-dissipation relation for the oscillator position autocorrelation function that generalizes the standard result for the case of a single bath at thermal equilibrium. Moreover, we show that the generating function for the position operator fulfils a generalized Gallavotti-Cohen-like relation. For the energy transfer through the oscillator, we determine the average energy current together with the current fluctuations. Finally, we discuss the generalization of the cumulant generating function for the energy transfer to nonthermal bath preparations.
Kravchuk functions for the finite oscillator approximation
Atakishiyev, Natig M.; Wolf, Kurt Bernardo
1995-01-01
Kravchuk orthogonal functions - Kravchuk polynomials multiplied by the square root of the weight function - simplify the inversion algorithm for the analysis of discrete, finite signals in harmonic oscillator components. They can be regarded as the best approximation set. As the number of sampling points increases, the Kravchuk expansion becomes the standard oscillator expansion.
Difference oscillator in terms of the Meixner polynomials
Atakishiyev, Natig M.; Jafarov, Elchin I.; Nagiyev, Shakir M.; Wolf, Kurt B.
1998-07-01
We discuss a difference model of the linear harmonic oscillator based on the Meixner polynomials. As limit and special cases, it contains difference oscillator models in terms of the Kravchuk and Charlier polynomials, as well as the wavefunctions of the linear harmonic oscillator in quantum mechanics. We show that the dynamical group is SU(1,1) and construct explicitly the corresponding coherent state. The reproducing kernel for the wavefunctions of the Meixner model is also found.
Arbitrary Spin Galilean Oscillator
Hagen, C R
2014-01-01
The so-called Dirac oscillator was proposed as a modification of the free Dirac equation which reproduces many of the properties of the simple harmonic oscillator but accompanied by a strong spin-orbit coupling term. It has yet to be extended successfully to the arbitrary spin S case primarily because of the unwieldiness of general spin Lorentz invariant wave equations. It is shown here using the formalism of totally symmetric multispinors that the Dirac oscillator can, however, be made to accommodate spin by incorporating it into the framework of Galilean relativity. This is done explicitly for spin zero and spin one as special cases of the arbitrary spin result. For the general case it is shown that the coefficient of the spin-orbit term has a 1/S behavior by techniques which are virtually identical to those employed in the derivation of the g-factor carried out over four decades ago.
Wang, He, E-mail: wangh@swip.ac.cn; Rao, Jun; Huang, Mei; Zhou, Jun; Wang, Chao; Kang, Zihua; Wang, Mingwei; Feng, Kun; Chen, Gangyu; Lu, Bo; Wang, Jieqiong
2015-12-15
Highlights: • A test stand for the test of gyrotron is introduced. • Test results show that the output power of gyrotron has a close relation to the high voltage, magnet current and heater power. • The measurement method of operation frequency and output power of gyrotron is introduced. - Abstract: To obtain the optimum operation status of gyrotrons, it is necessary to commissioning the gyrotrons before EC wave injected into plasma for ECRH system on HL-2A tokamak. A test stand has been set up for conditioning the 0.5 MW/68 GHz/1.0 s gyrotrons. The specific test results of gyrotrons are described and discussed in this paper, which include measuring the beam profile by using burn paper at the outlet of MOU and calorimetric dummy load, testing the maximum output power and pulse width on dummy load and getting the dependence between output power and magnetic field current, filament power and high voltage powers. Meanwhile, the operation frequency of gyrotron is also measured in the test.
Analysing harmonic motions with an iPhone’s magnetometer
Yavuz, Ahmet; Kağan Temiz, Burak
2016-05-01
In this paper, we propose an experiment for analysing harmonic motion using an iPhone’s (or iPad’s) magnetometer. This experiment consists of the detection of magnetic field variations obtained from an iPhone’s magnetometer sensor. A graph of harmonic motion is directly displayed on the iPhone’s screen using the Sensor Kinetics application. Data from this application was analysed with Eureqa software to establish the equation of the harmonic motion. Analyses show that the use of an iPhone’s magnetometer to analyse harmonic motion is a practical and effective method for small oscillations and frequencies less than 15-20 Hz.
Experimental Research on a 1.5 MW, 110 GHz Gyrotron with a Smooth Mirror Internal Mode Converter
Tax, D. S.; Mastovsky, I.; Shapiro, M. A.; Temkin, R. J.; Torrezan, A. C.
2010-11-01
Megawatt gyrotrons are important for electron cyclotron heating (ECH) of fusion plasmas, including ITER. These gyrotrons should operate with high efficiency to reduce the prime power required and to ensure good reliability. The gyrotron efficiency is affected both by the physical principles that govern the device and the performance of components like the internal mode converter (IMC), which must convert the electromagnetic cavity mode into a Gaussian beam. An IMC consisting of a helically-cut launcher and three smooth curved mirrors, which is less susceptible to alignment errors than an IMC using mirrors with phase correcting surfaces, was recently tested on a 1.5 MW, 110 GHz, 3μs pulsed gyrotron operating in the TE22,6 mode, and an output beam with 95.8 ± 0.5 % Gaussian beam content was measured in both hot and cold tests. We are also examining the issue of mode competition in the gyrotron, which can limit the achievable output power and efficiency. The sequence of competing modes excited during the rise time of the voltage pulse has been measured and results are compared with the numerical simulation code MAGY. These results should provide a good test of the accuracy of the code.
Sum rules in the oscillator radiation processes
Casana, R. [Instituto de Fisica Teorica-IFT/UNESP, Rua Pamplona 145, 01405-900 Sao Paulo, SP (Brazil)]. E-mail: casana@ift.unesp.br; Flores-Hidalgo, G. [Instituto de Fisica Teorica-IFT/UNESP, Rua Pamplona 145, 01405-900 Sao Paulo, SP (Brazil)]. E-mail: gflores@ift.unesp.br; Pimentel, B.M. [Instituto de Fisica Teorica-IFT/UNESP, Rua Pamplona 145, 01405-900 Sao Paulo, SP (Brazil)]. E-mail: pimentel@ift.unesp.br
2005-03-28
We consider the problem of a harmonic oscillator coupled to a scalar field in the framework of recently introduced dressed coordinates. We compute all the probabilities associated with the decay process of an excited level of the oscillator. Instead of doing direct quantum mechanical calculations we establish some sum rules from which we infer the probabilities associated to the different decay processes of the oscillator. Thus, the sum rules allows to show that the transition probabilities between excited levels follow a binomial distribution.
Sum rules in the oscillator radiation processes
Casana, R.; Flores-Hidalgo, G.; Pimentel, B. M.
2005-03-01
We consider the problem of a harmonic oscillator coupled to a scalar field in the framework of recently introduced dressed coordinates. We compute all the probabilities associated with the decay process of an excited level of the oscillator. Instead of doing direct quantum mechanical calculations we establish some sum rules from which we infer the probabilities associated to the different decay processes of the oscillator. Thus, the sum rules allows to show that the transition probabilities between excited levels follow a binomial distribution.
Linearization of the Relativistic Oscillator Hierarchy
Anderson, Robert L
2016-01-01
This paper is based on MacColl's [1] solution of the equation of motion for a linear (harmonic) oscillator subject to the laws of special relativity in the rest frame of the center of attraction. MacColl's result can be extended to the quartic oscillator in this frame with one extremely simple adjustment of the linearization map given in Anderson [2]. In fact, it can be extended to all the attractive oscillators in this frame.
Crane, Edward; Volkov, Stanislav; Wade, Andrew; Waters, Robert
2009-01-01
We study a generalized Polya urn model with two types of ball. If the drawn ball is red it is replaced together with a black ball, but if the drawn ball is black it is replaced and a red ball is thrown out of the urn. When only black balls remain, the roles of the colours are swapped and the process restarts. We prove that the resulting Markov chain is transient but that if we throw out a ball every time the colours swap, the process is positive-recurrent. We show that the embedded process obtained by observing the number of balls in the urn at the swapping times has a scaling limit that is essentially the square of a Bessel diffusion. We consider an oriented percolation model naturally associated with the urn process, and obtain detailed information about its structure, showing that the open subgraph is an infinite tree with a single end. We also study a natural continuous-time embedding of the urn process that demonstrates the relation to the simple harmonic oscillator; in this setting our transience result...
Harmonics of circadian gene transcription in mammals.
Michael E Hughes
2009-04-01
Full Text Available The circadian clock is a molecular and cellular oscillator found in most mammalian tissues that regulates rhythmic physiology and behavior. Numerous investigations have addressed the contribution of circadian rhythmicity to cellular, organ, and organismal physiology. We recently developed a method to look at transcriptional oscillations with unprecedented precision and accuracy using high-density time sampling. Here, we report a comparison of oscillating transcription from mouse liver, NIH3T3, and U2OS cells. Several surprising observations resulted from this study, including a 100-fold difference in the number of cycling transcripts in autonomous cellular models of the oscillator versus tissues harvested from intact mice. Strikingly, we found two clusters of genes that cycle at the second and third harmonic of circadian rhythmicity in liver, but not cultured cells. Validation experiments show that 12-hour oscillatory transcripts occur in several other peripheral tissues as well including heart, kidney, and lungs. These harmonics are lost ex vivo, as well as under restricted feeding conditions. Taken in sum, these studies illustrate the importance of time sampling with respect to multiple testing, suggest caution in use of autonomous cellular models to study clock output, and demonstrate the existence of harmonics of circadian gene expression in the mouse.
Harmonics of circadian gene transcription in mammals.
Hughes, Michael E; DiTacchio, Luciano; Hayes, Kevin R; Vollmers, Christopher; Pulivarthy, S; Baggs, Julie E; Panda, Satchidananda; Hogenesch, John B
2009-04-01
The circadian clock is a molecular and cellular oscillator found in most mammalian tissues that regulates rhythmic physiology and behavior. Numerous investigations have addressed the contribution of circadian rhythmicity to cellular, organ, and organismal physiology. We recently developed a method to look at transcriptional oscillations with unprecedented precision and accuracy using high-density time sampling. Here, we report a comparison of oscillating transcription from mouse liver, NIH3T3, and U2OS cells. Several surprising observations resulted from this study, including a 100-fold difference in the number of cycling transcripts in autonomous cellular models of the oscillator versus tissues harvested from intact mice. Strikingly, we found two clusters of genes that cycle at the second and third harmonic of circadian rhythmicity in liver, but not cultured cells. Validation experiments show that 12-hour oscillatory transcripts occur in several other peripheral tissues as well including heart, kidney, and lungs. These harmonics are lost ex vivo, as well as under restricted feeding conditions. Taken in sum, these studies illustrate the importance of time sampling with respect to multiple testing, suggest caution in use of autonomous cellular models to study clock output, and demonstrate the existence of harmonics of circadian gene expression in the mouse.
500-fold enhancement of in situ 13C liquid state NMR using gyrotron-driven temperature-jump DNP
Yoon, Dongyoung; Soundararajan, Murari; Caspers, Christian; Braunmueller, Falk; Genoud, Jérémy; Alberti, Stefano; Ansermet, Jean-Philippe
2016-09-01
A 550-fold increase in the liquid state 13C NMR signal of a 50 μL sample was obtained by first hyperpolarizing the sample at 20 K using a gyrotron (260 GHz), then, switching its frequency in order to apply 100 W for 1.5 s so as to melt the sample, finally, turning off the gyrotron to acquire the 13C NMR signal. The sample stays in its NMR resonator, so the sequence can be repeated with rapid cooling as the entire cryostat stays cold. DNP and thawing of the sample are performed only by the switchable and tunable gyrotron without external devices. Rapid transition from DNP to thawing in one second time scale was necessary especially in order to enhance liquid 1H NMR signal.
General -Harmonic Blaschke Bodies
Yibin Feng; Weidong Wang
2014-02-01
Lutwak introduced the harmonic Blaschke combination and the harmonic Blaschke body of a star body. Further, Feng and Wang introduced the concept of the -harmonic Blaschke body of a star body. In this paper, we define the notion of general -harmonic Blaschke bodies and establish some of its properties. In particular, we obtain the extreme values concerning the volume and the -dual geominimal surface area of this new notion.
Gain of harmonic generation in high gain free electron laser
DENG Hai-Xiao; DAI Zhi-Min
2008-01-01
In a planar undulator employed free electron laser(FEL),each harmonic radiation starts from linear amplification and ends with nonlinear harmonic interactions of the lower nonlinear harmonics and the fundamental radiation.In this paper,we investigate the harmonic generation based on the dispersion relation driven from the coupled Maxwell-Vlasov equations,taking into account the effects due to energy spread,emittance,betatron oscillation of electron beam as well as diffraction guiding of the radiation field.A 3D universal scaling function for gain of the linear harmonic generation and a 1D universal scaling function for gain of the nonlinear harmonic generation are presented,which promise rapid computation in FEL design and optimization.The analytical approaches have been validated by 3D simulation results in large range.
Dynamics in the Kuramoto model with a bi-harmonic coupling function
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.
170 GHz回旋管电子枪的设计%Design of the magnetron injection gun for 170 GHz gyrotron
曾旭; 王峨锋; 刘本田; 李志良; 冯进军
2013-01-01
A 170 GHz gryotron is an ideal power source for the Electron Cyclotron Resonance Heating (ECRH) in the plasma fusion. The required output power from a single gyrotron tube at 170 GHz operating frequency for ECRH application is 1 MW or more. For generating the high output power,a Magnetron Injection Gun(MIG) which can provide the electron beam with large enough transverse energy for interacting with the transverse filed of the electromagnetic wave is designed. Ideal parameters of the double-anode MIG are obtained according to the adiabatic compression theory and the correlative simulation software. The designed MIG can provide the necessary beams for the 170 GHz fundamental harmonic gyrotron under 80 kV of voltage and 40 A of current with the guidance center radius of 8.27 mm and the pitch factor of 1.5.% 170 GHz回旋管是等离子体核聚变中电子回旋谐振加热的理想功率源，在功率上要求具有1 MW以上的输出功率。要产生这么大的输出功率，就需要具有足够大横向能量的电子注与高频场的横向电场进行互作用，因此要对电子枪进行专门的设计。利用绝热压缩理论及相关的仿真软件对双阳极磁控注入电子枪进行了设计，得到了较好的电子注参数。所设计的电子枪能在工作电压80 kV、工作电流40 A 的条件下为170 GHz 基波回旋管提供所需的回旋电子注，其引导中心半径为8.27 mm，横纵速度比1.5。
Primer on coupling collective electronic oscillations to nuclei
Solem, J.C.; Biedenharn, L.C. Jr.
1987-07-01
On the basis of simple heuristic models, we show that atomic electrons can amplify fields observed at the nucleus, generate harmonics, and drive higher multipolarities. Considered is a model with the nucleus at the focus of a uniformly charged ellipsoid. It amplifies an oscillating external electric field and produces an oscillating electric-field gradient but no higher derivatives. The electric field has only odd harmonics and the electric-field gradient has only even harmonics. There is an optimum intensity for driving each harmonic. Commented on is the relevance of these results to the U/sup 235/ experiment and to the gamma-ray laser.
PT-symmetric quantum oscillator in an optical cavity
Longhi, Stefano
2016-01-01
The quantum harmonic oscillator with parity-time ($\\mathcal{PT}$) symmetry, obtained from the ordinary (Hermitian) quantum harmonic oscillator by an imaginary displacement of the spatial coordinate, provides an important and exactly-solvable model to investigate non-Hermitian extension of the Ehrenfest theorem. Here it is shown that transverse light dynamics in an optical resonator with off-axis longitudinal pumping can emulate a $\\mathcal{PT}$-symmetric quantum harmonic oscillator, providing an experimentally accessible system to investigate non-Hermitian coherent state propagation.
Design of the all solid high-voltage power supply for a gyrotron body
Rao, Yihua [School of Mathematics and Physics, University of South China, Hengyang, 421001 (China); Chen, Wenguang, E-mail: 430000485393@usc.edu.cn [School of Electrical Engineering, University of South China, Hengyang, 421001 (China); Hu, Bo [School of Electrical Engineering, University of South China, Hengyang, 421001 (China); Rao, Jun; Huang, Mei; Kang, Zihua; Feng, Kun [Southwestern Institute of Physics, Chengdu, 610041 (China); Huang, Jiaqi [School of Electrical Engineering, University of South China, Hengyang, 421001 (China)
2017-04-15
Highlights: • Completed design of all solid-state high-voltage power supply for gyrotron body on HL-2M ECRH. • Consist of 58 PSM modules and one BUCK module, controlled by DSP system. • Fabricated full voltage 35 kV, 200 mA BPS and tested in dummy load. • The BPS can operate in three modes: single pulse mode, multi-pulse modulation mode and the six-level preset mode. - Abstract: Gyrotron plays an important role in the research of electron cyclotron resonance heating (ECRH) on Tokomak. The high-frequency switched power supply technology and pulse step modulation (PSM) technology are used in the development of the all solid high-voltage body power supply (BPS) for 1 MW/105 GHz Gyrotron on ECRH system. Firstly, the basic structure of the BPS and its control system are introduced. Secondly, the software control algorithm of voltage stabilization and modulate method are developed. Finally, the design is verified by the experiments. The experimental results of the single pulse mode, the multi-pulse modulation mode and the six-level preset mode, are shown. The output voltage of the power supply can reach 35 kV and the current at about 200 mA, which are adjustable in the full range. The maximum modulation frequency can reach 1 kHz and the front edge of the pulse can be adjust from 0 to 3 ms and the accuracy of the output voltage is less than 100 V. The results show that the control method is feasible and can be applied to other high power microwave sources.
Schulze-Halberg, Axel, E-mail: axgeschu@iun.edu, E-mail: xbataxel@gmail.com [Department of Mathematics and Actuarial Science and Department of Physics, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States); Wang, Jie, E-mail: wangjie@iun.edu [Department of Computer Information Systems, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States)
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.
Axler, Sheldon; Ramey, Wade
2013-01-01
This is a book about harmonic functions in Euclidean space. Readers with a background in real and complex analysis at the beginning graduate level will feel comfortable with the material presented here. The authors have taken unusual care to motivate concepts and simplify proofs. Topics include: basic properties of harmonic functions, Poisson integrals, the Kelvin transform, spherical harmonics, harmonic Hardy spaces, harmonic Bergman spaces, the decomposition theorem, Laurent expansions, isolated singularities, and the Dirichlet problem. The new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bocher's Theorem, new exercises and proofs, as well as revisions throughout to improve the text. A unique software package-designed by the authors and available by e-mail - supplements the text for readers who wish to explore harmonic function theory on a computer.
The sheath effect on the floating harmonic method
Lee, Jaewon; Kim, Kyung-Hyun; Chung, Chin-Wook, E-mail: joykang@hanyang.ac.kr [Department of Electrical Engineering, Hanyang University, 17 Haengdang-dong, Seongdong-gu, Seoul 133-791 (Korea, Republic of)
2015-12-15
The floating harmonic method biases sinusoidal voltage to a probe sheath, and as its response, harmonic currents can be obtained. These currents can be used to determine the plasma parameters. However, different shapes of probes have different shapes of sheaths that can affect the diagnostic results. However, no research has been done on the sheath effect on the floating harmonic method. Therefore, we investigate the effect of the sheath during floating harmonic diagnostics by comparing cylindrical and planar probes. While the sinusoidal voltages were applied to a probe, because the sheath oscillated, the time variant ion current and their harmonic currents were added to the electron harmonic currents. In the floating harmonic method, the harmonic currents are composed of only the electron harmonic currents. Therefore, the ion harmonic currents affect the diagnostic results. In particular, the electron temperature obtained by the small probe tip was higher than that of the large probe tip. This effect was exacerbated when the ratio of the probe tip radius to the sheath length was smaller.
Design of a system for conversion of gyrotron output into a gaussian beam
Ogawa, I. [Faculty of Engineering, Fukui Univ., Fukui (Japan); Idehara, T.; Sabchevski, S.; Glyavin, M.; Mitsudo, S. [Research Center for Development of Far-Infrared Region, Fukui Univ., Fukui (Japan); Sato, M.; Kawahata, K. [National Inst. for Fusion Science, Toki, Gifu (Japan); Brand, G.F. [School of Physics, Univ. of Sydney, NSW (Australia)
2000-03-01
A quasi-optical system consisting of a quasi-optical antenna, two ellipsoidal mirrors and a filter to block sidelobes can convert four TE{sub 1n} mode outputs of the Gyrotron FU IVA into gaussian-like beams with waist size of 16.3 mm. This system can convert three TE{sub 0n} mode outputs into bigaussian-like beams with waist size of 23.5 mm in width and 16.4 mm in length. (author)
Test of a two-dimensionally focusing quasi-optical antenna using a gyrotron
Idehara, T.; Tatsukawa, T.; Brand, G.F.; Fekete, P.W.; Moore, K.J.
1989-05-01
A quasi-optical antenna having one elliptical reflector and one parabolic reflector has been built for millimeter wave scattering measurements on the TORTUS tokamak plasma at the University of Sydney. This letter reports the first demonstration of the properties of such an antenna using a gyrotron millimeter wave source. Its advantages are (1) good two-dimensional focusing (along the major radius and the toroidal directions) and (2) easy movement of the focus across the diameter of the plasma by changing the orientation of the parabolic reflector.
Coupler for coupling gyrotron whispering gallery mode RF into HE11 waveguide
Neilson, Jeffrey M
2015-02-24
A cylindrical waveguide with a mode converter transforms a whispering gallery mode from a gyrotron cylindrical waveguide with a helical cut launch edge to a quasi-Gaussian beam suitable for conveyance through a corrugated waveguide. This quasi-Gaussian beam is radiated away from the waveguide using a spiral cut launch edge, which is in close proximity to a first mode converting reflector. The first mode converting reflector is coupled to a second mode converting reflector which provides an output free-space HE11 mode wave suitable for direct coupling into a corrugated waveguide. The radiated beam produced at the output of the second mode converting reflector is substantially circular.
High harmonic phase in molecular nitrogen
McFarland, Brian K.
2009-10-17
Electronic structure in atoms and molecules modulates the amplitude and phase of high harmonic generation (HHG). We report measurements of the high harmonic spectral amplitude and phase in N{sub 2}. The phase is measured interferometrically by beating the N{sub 2} harmonics with those of an Ar reference oscillator in a gas mixture. A rapid phase shift of 0.2{pi} is observed in the vicinity of the HHG spectral minimum, where a shift of {pi} had been presumed [J. Itatani et al., Nature 432, 867 (2004)]. We compare the phase measurements to a simulation of the HHG recombination step in N{sub 2} that is based on a simple interference model. The results of the simulation suggest that modifications beyond the simple interference model are needed to explain HHG spectra in molecules.
Microscopic optical buffering in a harmonic potential
Sumetsky, M
2015-01-01
In the early days of quantum mechanics, Schr\\"odinger noticed that oscillations of a wave packet in a one-dimensional harmonic potential well are periodic and, in contrast to those in anharmonic potential wells, do not experience distortion over time. This original idea did not find applications up to now since an exact one-dimensional harmonic resonator does not exist in nature and has not been created artificially. However, an optical pulse propagating in a bottle microresonator (a dielectric cylinder with a nanoscale-high bump of the effective radius) can exactly imitate a quantum wave packet in the harmonic potential. Here, we propose a tuneable microresonator that can trap an optical pulse completely, hold it as long as the material losses permit, and release it without distortion. This result suggests the solution of the long standing problem of creating a microscopic optical buffer, the key element of the future optical signal processing devices.
Theory of harmonic dissipation in disordered solids
Damart, T.; Tanguy, A.; Rodney, D.
2017-02-01
Mechanical spectroscopy, i.e., cyclic deformations at varying frequencies, is used theoretically and numerically to compute dissipation in model glasses. From a normal mode analysis, we show that in the high-frequency terahertz regime where dissipation is harmonic, the quality factor (or loss angle) can be expressed analytically. This expression is validated through nonequilibrium molecular dynamics simulations applied to a model of amorphous silica (SiO2). Dissipation is shown to arise from nonaffine relaxations triggered by the applied strain through the excitation of vibrational eigenmodes that act as damped harmonic oscillators. We discuss an asymmetry vector field, which encodes the information about the structural origin of dissipation computed by mechanical spectroscopy. In the particular case of silica, we find that the motion of oxygen atoms, which induce a deformation of the Si-O-Si bonds, is the main contributor to harmonic energy dissipation.
Atakishiyeva, Mesuma K.; Atakishiyev, Natig M.; Wolf, Kurt Bernardo
2014-05-01
The study of irreducible representations of Lie algebras and groups has traditionally considered their action on functions of a continuous manifold (e.g. the 'rotation' Lie algebra so(3) on functions on the sphere). Here we argue that functions of a discrete variable -Kravchuk functions- are on equal footing for that study in the case of so(3). They lead to a discrete quantum model of the harmonic oscillator, and offer a corresponding set of special function relations. The technique is applicable to other special function families of a discrete variable, which stem from low-dimensional Lie algebras and are stationary solutions for the corresponding discrete quantum models.
Quantum entanglement of Pais-Uhlenbeck oscillators
Dimov, Hristo; Rashkov, Radoslav C; Vetsov, Tsvetan
2016-01-01
We study the quantum entanglement of coupled Pais-Uhlenbeck oscillators using the formalism of thermo-field dynamics. The entanglement entropy is computed for the specific cases of two and a ring of $N$ coupled Pais-Uhlenbeck oscillators of fourth order. It is shown that the entanglement entropy depends on the temperatures, frequencies and coupling parameters of the different degrees of freedom corresponding to harmonic oscillators. Finally, we advert to the information geometry theory by calculating the Fisher information metric for the considered system of coupled oscillators.
Scleronomic holonomic constraints and conservative nonlinear oscillators
Munoz, R; Gonzalez-Garcia, G; Izquierdo-De La Cruz, E Izquierdo-De La [Universidad Autonoma de la Ciudad de Mexico, Centro Historico, Fray Servando Teresa de Mier 92, Col Centro, Del Cuauhtemoc, Mexico DF, CP 06080 (Mexico); Fernandez-Anaya, G, E-mail: rodrigo.munoz@uacm.edu.mx, E-mail: gggharper@gmail.com, E-mail: erickidc@gmail.com, E-mail: guillermo.fernandez@uia.mx [Universidad Iberoamericana, Departamento de Fisica y Matematicas, Prolongacon Paseo de de la Reforma 880, Col Lomas de Santa Fe, Del Alvaro Obregn, Mexico DF, CP 01219 (Mexico)
2011-05-15
A bead sliding, under the sole influence of its own weight, on a rigid wire shaped in the fashion of a plane curve, will describe (generally anharmonic) oscillations around a local minimum. For given shapes, the bead will behave as a harmonic oscillator in the whole range, such as an unforced, undamped, Duffing oscillator, etc. We also present cases in which the effective potential acting on the bead is not analytical around a minimum. The small oscillation approximation cannot be applied to such pathological cases. Nonetheless, these latter instances are studied with other standard techniques.
Coherent harmonic production using a two-section undulator FEL
Jaroszynski, D.A. [Commissariat a l`Energie, Bruyeres-le-Chatel (France); Prazeres, R.; Glotin, F. [Centre Universitaire Paris-Sud (France)] [and others
1995-12-31
We present measurements and a theoretical analysis of a new method of generating harmonic radiation in a free-electron laser oscillator with a two section undulator in a single optical cavity. To produce coherent harmonic radiation the undulator is arranged so that the downstream undulator section resonance frequency matches a harmonic of the upstream undulator. Both the fundamental and the harmonic optical fields evolve in the same optical cavity and are coupled out with different extraction fractions using a hole in one of the cavity mirrors. We present measurements that show that the optical power at the second and third harmonic can be enhanced by more than an order of magnitude in this fundamental/harmonic configuration. We compare the production of harmonic radiation of a two sectioned fundamental/harmonic undulator with that produced from a FEL operating at its highest efficiency with a step-tapered undulator, where the bunching at the end of the first section is very large. We examine, the dependence of the harmonic power on the intracavity power by adjusting the optical cavity desynchronism, {delta}L. We also examine the evolution of the fundamental and harmonic powers as a function of cavity roundtrip number to evaluate the importance of the small signal gain at the harmonic. We compare our measurements with predictions of a multi-electron numerical model that follows the evolution of fundamental and harmonic power to saturation. This fundamental/harmonic mode, of operation of the FEL may have useful applications in the production of coherent X-ray and VUV radiation, a spectral range where high reflectivity optical cavity mirrors are difficult or impossible to manufacture.
Design of the Collective Thomson scattering (CTS) system by using 170-GHz gyrotron in the KSTAR
Park, Min; Kim, Sun-Ho; Kim, Sung-Kyu; Lee, Kyu-Dong; Wang, Son-Jong
2014-10-01
The physics of energetic ions is one of the primary subjects to be understood toward the realization of a nuclear fusion power plant. Collective Thomson scattering (CTS) offers the possibility to diagnose the fast ions and the alpha particles in burning plasmas. Spatially- and temporally-resolved one-dimensional velocity distributions of the fast ions can be obtained from the scattered radiation with fewer geometric constraints by utilizing millimeter waves from a high-power gyrotron as a probe beam. We studied the feasibility of CTS fast-ion measurements in the KSTAR by calculating the spectral density functions. Based on that, we suggest a design for the CTS system that uses the currently-operating 170-GHz gyrotron for electron cyclotron heating (ECH) and electron cyclotron current drive (ECCD) in the KSTAR. The CTS system is presented as two subsystems: the antenna system and the heterodyne receiver system. The design procedure for an off-axis ellipsoidal mirror is described, and the CTS system requirements are discussed.
High current multicharged metal ion source using high power gyrotron heating of vacuum arc plasma.
Vodopyanov, A V; Golubev, S V; Khizhnyak, V I; Mansfeld, D A; Nikolaev, A G; Oks, E M; Savkin, K P; Vizir, A V; Yushkov, G Yu
2008-02-01
A high current, multi charged, metal ion source using electron heating of vacuum arc plasma by high power gyrotron radiation has been developed. The plasma is confined in a simple mirror trap with peak magnetic field in the plug up to 2.5 T, mirror ratio of 3-5, and length variable from 15 to 20 cm. Plasma formed by a cathodic vacuum arc is injected into the trap either (i) axially using a compact vacuum arc plasma gun located on axis outside the mirror trap region or (ii) radially using four plasma guns surrounding the trap at midplane. Microwave heating of the mirror-confined, vacuum arc plasma is accomplished by gyrotron microwave radiation of frequency 75 GHz, power up to 200 kW, and pulse duration up to 150 micros, leading to additional stripping of metal ions by electron impact. Pulsed beams of platinum ions with charge state up to 10+, a mean charge state over 6+, and total (all charge states) beam current of a few hundred milliamperes have been formed.
Beam-wave interaction behavior of a 35 GHz metal PBG cavity gyrotron
Singh, Ashutosh, E-mail: asingh.rs.ece@iitbhu.ac.in [Faculty of Physical Sciences, Institute of Natural Sciences and Humanities Shri Ramswaroop Memorial University, Lucknow-Deva Road, Uttar Pradesh-225003 (India); Center of Research in Microwave Tubes, Department of Electronics Engineering, Indian Institute of Technology (Banaras Hindu University), Varanasi-221005 (India); Jain, P. K. [Center of Research in Microwave Tubes, Department of Electronics Engineering, Indian Institute of Technology (Banaras Hindu University), Varanasi-221005 (India)
2014-09-15
The RF behavior of a 35 GHz photonic band gap (PBG) cavity gyrotron operating in TE{sub 041}-like mode has been presented to demonstrate its single mode operation capability. In this PBG cavity gyrotron, the conventional tapered cylindrical cavity is replaced by a metal PBG cavity as its RF interaction structure. The beam-wave interaction behavior has been explored using time dependent multimode nonlinear analysis as well as through 3D PIC simulation. Metal PBG cavity is treated here similar to that of a conventional cylindrical cavity for the desired mode confinement. The applied DC magnetic field profile has been considered uniform along the PBG cavity length both in analysis as well as in simulation. Electrons energy and phase along the interaction length of the PBG cavity facilitates bunching mechanism as well as energy transfer phenomena from the electron beam to the RF field. The RF output power for the TE{sub 041}-like design mode as well as nearby competing modes have been estimated and found above to 100 kW in TE{sub 041}-like mode with ∼15% efficiency. Results obtained from the analysis and the PIC simulation are found in agreement within 8% variation, and also it supports the single mode operation, as the PBG cavity does not switch into other parasitic modes in considerably large range of varying DC magnetic field, contrary to the conventional cylindrical cavity interaction structure.
Conceptual designs of E × B multistage depressed collectors for gyrotrons
Wu, Chuanren; Pagonakis, Ioannis Gr.; Gantenbein, Gerd; Illy, Stefan; Thumm, Manfred; Jelonnek, John
2017-04-01
Multistage depressed collectors are challenges for high-power, high-frequency fusion gyrotrons. Two concepts exist in the literature: (1) unwinding the spent electron beam cyclotron motion utilizing non-adiabatic transitions of magnetic fields and (2) sorting and collecting the electrons using the E × B drift. To facilitate the collection by the drift, the hollow electron beam can be transformed to one or more thin beams before applying the sorting. There are many approaches, which can transform the hollow electron beam to thin beams; among them, two approaches similar to the tilted electric field collectors of traveling wave tubes are conceptually studied in this paper: the first one transforms the hollow circular electron beam to an elongated elliptic beam, and then the thin elliptic beam is collected by the E × B drift; the second one splits an elliptic or a circular electron beam into two arc-shaped sheet beams; these two parts are collected individually. The functionality of these concepts is proven by CST simulations. A model of a three-stage collector for a 170 GHz, 1 MW gyrotron using the latter approach shows 76% collector efficiency while taking secondary electrons and realistic electron beam characteristics into account.
The 5.8 T Cryogen-Free Gyrotron Superconducting Magnet System on HL-2A
Xia, Donghui; Huang, Mei; Zhou, Jun; Bai, Xingyu; Zheng, Tieliu; Rao, Jun; Zhuang, Ge
2014-04-01
A 5.8 T cryogen-free superconducting magnet (SCM) system with a warm bore hole of 160 mm in diameter, used for gyrotrons operating in the frequency range from 68 GHz to 140 GHz, is installed on the site of the HL-2A tokamak. The SCM consists of two separate solenoidal magnetic coils connected in series, a 4.2 K Gifford-McMahon (GM) refrigerator, a compressor, a coil power supply and two temperature monitors. The performance, test and preliminary experimental results of this SCM system are described in this paper. The magnetic field distribution was measured along the axis, and a dummy tube was used for adjusting the magnet system. Finally, the magnet was used for the operation of a 68 GHz/500 kW gyrotron, which is part of an electron cyclotron resonance heating (ECRH) system. With an additional auxiliary coil and after adjusting the magnet system, a maximum output power for the ECRH system of up to 400 kW was achieved.
Soft X-ray harmonic comb from relativistic electron spikes
Pirozhkov, A S; Esirkepov, T Zh; Gallegos, P; Ahmed, H; Ragozin, E N; Faenov, A Ya; Pikuz, T A; Kawachi, T; Sagisaka, A; Koga, J K; Coury, M; Green, J; Foster, P; Brenner, C; Dromey, B; Symes, D R; Mori, M; Kawase, K; Kameshima, T; Fukuda, Y; Chen, L; Daito, I; Ogura, K; Hayashi, Y; Kotaki, H; Kiriyama, H; Okada, H; Nishimori, N; Imazono, T; Kondo, K; Kimura, T; Tajima, T; Daido, H; Rajeev, P; McKenna, P; Borghesi, M; Neely, D; Kato, Y; Bulanov, S V
2012-01-01
We demonstrate a new high-order harmonic generation mechanism reaching the `water window' spectral region in experiments with multi-terawatt femtosecond lasers irradiating gas jets. A few hundred harmonic orders are resolved, giving uJ/sr pulses. Harmonics are collectively emitted by an oscillating electron spike formed at the joint of the boundaries of a cavity and bow wave created by a relativistically self-focusing laser in underdense plasma. The spike sharpness and stability are explained by catastrophe theory. The mechanism is corroborated by particle-in-cell simulations.
Maccari, A. [Istituto Tecnico `G. Cardano`, Monterotondo, Rome (Italy)
1996-08-01
The most important characteristics of the non-local oscillator, an oscillator subjected to an additional non-local force, are extensively studied by means of a new asymptotic perturbation method that is able to furnish an approximate solution of weakly non-linear differential equations. The resulting motion is doubly periodic, because a second little frequency appears, in addition to the fundamental harmonic frequency. Comparison with the numerical solution obtained by the Runge-Kitta method confirms the validity of the asymptotic perturbation method and its importance for the study of non-linear dynamical systems.
Discretized representations of harmonic variables by bilateral Jacobi operators
Andreas Ruffing
2000-01-01
Full Text Available Starting from a discrete Heisenberg algebra we solve several representation problems for a discretized quantum oscillator in a weighted sequence space. The Schrödinger operator for a discrete harmonic oscillator is derived. The representation problem for a q-oscillator algebra is studied in detail. The main result of the article is the fact that the energy representation for the discretized momentum operator can be interpreted as follows: It allows to calculate quantum properties of a large number of non-interacting harmonic oscillators at the same time. The results can be directly related to current research on squeezed laser states in quantum optics. They reveal and confirm the observation that discrete versions of continuum Schrodinger operators allow more structural freedom than their continuum analogs do.
Tuset-Sanchis, Luis; Castro-Palacio, Juan C.; Gómez-Tejedor, José A.; Manjón, Francisco J.; Monsoriu, Juan A.
2015-01-01
A smartphone acceleration sensor is used to study two-dimensional harmonic oscillations. The data recorded by the free android application, Accelerometer Toy, is used to determine the periods of oscillation by graphical analysis. Different patterns of the Lissajous curves resulting from the superposition of harmonic motions are illustrated for…
The time-dependent forced anisotropic oscillator in noncommutative phase space
Liang Mailin; Chen Qian, E-mail: mailinliang@yahoo.com.cn, E-mail: mailinliang@tju.edu.cn [Physics Department, School of Science, Tianjin University, Tianjin 300072 (China)
2011-07-01
Wave functions of the time-dependent forced anisotropic harmonic oscillator in noncommutative phase space are derived using the linear transformation and unitary transformation methods. The energy spectrum is given for the stationary system. Further, quantum fluctuations and the squeezing effect are investigated. It is found that the anisotropic property of the harmonic oscillator in noncommutative space has the squeezing effect.
Espinosa, Ismael; Gonzalez, Hortensia; Quiza, Jorge; Gonazalez, J. Jesus; Arroyo, Ruben; Lara, Ritaluz
1995-01-01
Oscillation of electrical activity has been found in many nervous systems, from invertebrates to vertebrates including man. There exists experimental evidence of very simple circuits with the capability of oscillation. Neurons with intrinsic oscillation have been found and also neural circuits where oscillation is a property of the network. These two types of oscillations coexist in many instances. It is nowadays hypothesized that behind synchronization and oscillation there is a system of coupled oscillators responsible for activities that range from locomotion and feature binding in vision to control of sleep and circadian rhythms. The huge knowledge that has been acquired on oscillators from the times of Lord Rayleigh has made the simulation of neural oscillators a very active endeavor. This has been enhanced with more recent physiological findings about small neural circuits by means of intracellular and extracellular recordings as well as imaging methods. The future of this interdisciplinary field looks very promising; some researchers are going into quantum mechanics with the idea of trying to provide a quantum description of the brain. In this work we describe some simulations using neuron models by means of which we form simple neural networks that have the capability of oscillation. We analyze the oscillatory activity with root locus method, cross-correlation histograms, and phase planes. In the more complicated neural network models there is the possibility of chaotic oscillatory activity and we study that by means of Lyapunov exponents. The companion paper shows an example of that kind.
DFIG Harmonic Current Controlling with the Grid Low Harmonic Voltage
Huan Wang
2014-01-01
Full Text Available This study presents a vector control strategy based on stator harmonic current closed-loop, it adds individually the control loop about of each stator harmonic current to restrain the stator harmonic current, in order to meet the THD criteria. The control strategy of restraining the harmonic current presents the design of the stator harmonic current restrains the current controller. It influences the rotor voltage of the stator harmonic current restraining strategies.
G. Yu. YUSHKOV; K. P. SAVKIN; A. G. NIKOLAEV; E. M. OKS; A.V. VODOPYANOV; I. V. IZOTOV; D. A. MANSFELD
2011-01-01
A new method for the generation of high charged state metal ion beams is developed. This method is based on microwave heating of vacuum arc plasma in a magnetic trap under electron cyclotron resonance （ECR） conditions. Two gyrotrons for plasma heating were used, which were with the following parameters. The first is with a wave frequency of 37.5 GHz, a pulse duration of 1 ms and power of 100 kW, another is with 75 GHz, 0.15 ms and 400 kW. Two different magnetic traps were considered for vacuum arc plasma confinement. The first one is a simple mirror trap. Such system was already investigated and could provide high charge state ions. The second trap was with a cusp magnetic field configuration with native ＂minimum-B＂ field structure. Two different ways of metal plasma injection into the magnetic trap were used. The first one is an axial injection from an arc source located out of the trap, and the second is a radial injection from four arc sources mounted at the center of the trap. Both traps provide up to 200 eMA of ion beam current for platinum ions with highest charge state 10＋. Ion beams were successfully extracted from the plasma and accelerated by a voltage of up to 20 kV.
HARMONIC COMPONENT EXTRACTION FROM A CHAOTIC SIGNAL BASED ON EMPIRICAL MODE DECOMPOSITION METHOD
LI Hong-guang; MENG Guang
2006-01-01
A novel approach of signal extraction of a harmonic component from a chaotic signal generated by a Duffing oscillator was proposed. Based on empirical mode decomposition (EMD) and concept that any signal is composed of a series of the simple intrinsic modes, the harmonic components were extracted from the chaotic signals. Simulation results show the approach is satisfactory.
Velocity-space tomography of fusion plasmas by collective Thomson scattering of gyrotron radiation
Salewski, Mirko; Jacobsen, A.S.; Jensen, Thomas;
2016-01-01
We propose a diagnostic capable of measuring 2D fast-ion velocity distribution functions 푓2퐷푣 in the MeV-range in magnetized fusion plasmas. Today velocity-space tomography based on fast-ion D훼 spectroscopy is regularly used to measure 푓2퐷푣 for ion energies below 100 keV. Unfortunately, the signal......-tonoise ratio becomes fairly low for MeV-range ions. Ions at any energy can be detected well by collective Thomson scattering of mm-wave radiation from a high-power gyrotron. We demonstrate how collective Thomson scattering can be used to measure 푓2퐷푣 in the MeV-range in reactor relevant plasmas...
Li, Fenfang; Nguyen, Dang Minh; Ohl, Claus-Dieter
2016-01-01
We report about an intriguing boiling regime occurring for small heaters embedded on the boundary in subcooled water. The microheater is realized by focusing a continuous wave laser beam to about $10\\,\\mu$m in diameter onto a 165\\,nm-thick layer of gold, which is submerged in water. After an initial vaporous explosion a single bubble oscillates continuously and repeatably at several $100\\,$kHz. The microbubble's oscillations are accompanied with bubble pinch-off leading to a stream of gaseous bubbles into the subcooled water. The self-driven bubble oscillation is explained with a thermally kicked oscillator caused by the non-spherical collapses and by surface pinning. Additionally, Marangoni stresses induce a recirculating streaming flow which transports cold liquid towards the microheater reducing diffusion of heat along the substrate and therefore stabilizing the phenomenon to many million cycles. We speculate that this oscillate boiling regime may allow to overcome the heat transfer thresholds observed dur...
Manipulating single enzymes by an external harmonic force
Lomholt, Michael A; Urbakh, Michael; Metzler, Ralf
2007-01-01
We study a Michaelis-Menten reaction for a single two-state enzyme molecule, whose transition rates between the two conformations are modulated by an harmonically oscillating external force. In particular, we obtain a range of optimal driving frequencies for changing the conformation of the enzyme...
Second and Third Harmonic Generation in Metal-Based Nanostructures
2010-01-01
free and bound charges that give rise to second and third harmonic generation in metallic nanostructures. Eqs.(29) are also applicable to dielectrics...arbitrary frequencies", Rev. Mexicana de Fisica 49, 231 (2003). [53] E. L. Linder, "Effect of electron pressure on plasma electron oscillations", Phys
Quantum Energy Teleportation with a Linear Harmonic Chain
Nambu, Yasusada
2010-01-01
A protocol of quantum energy teleportation is proposed for a one-dimensional harmonic chain. A coherent-state POVM measurement is performed to coupled oscillators of the chain in the ground state accompanied by energy infusion to the system. This measurement consumes a part of ground state entanglement. Depending on the measurement result, a displacement operation is performed on a distant oscillator accompanied by energy extraction from the zero-point fluctuation of the oscillator. We find that the amount of consumed entanglement is bounded from below by a positive value that is proportional to the amount of teleported energy.
An Eigenvalue Study of a Double Integrator Oscillator
Lindberg, Erik; Murali, K.; Tamasevicius, A.;
2009-01-01
A tutorial study of an oscillator built from a loop of two active RC integrators and an ideal inverter. As a reference the linear harmonic oscillator is modeled as a LC circuit and as an ideal two integrator loop. The nonlinear amplifiers of the active RC integrator circuits are assumed...
Geometric models of (d+1)-dimensional relativistic rotating oscillators
Cotaescu, I I
2000-01-01
Geometric models of quantum relativistic rotating oscillators in arbitrary dimensions are defined on backgrounds with deformed anti-de Sitter metrics. It is shown that these models are analytically solvable, deriving the formulas of the energy levels and corresponding normalized energy eigenfunctions. An important property is that all these models have the same nonrelativistic limit, namely the usual harmonic oscillator.
High-frequency thermal processes in harmonic crystals
Kuzkin, Vitaly A
2016-01-01
We consider two high-frequency thermal processes in uniformly heated harmonic crystals relaxing towards equilibrium: (i) equilibration of kinetic and potential energies and (ii) redistribution of energy among spatial directions. Equation describing these processes with deterministic initial conditions is derived. Solution of the equation shows that characteristic time of these processes is of the order of ten periods of atomic vibrations. After that time the system practically reaches the stationary state. It is shown analytically that in harmonic crystals temperature tensor is not isotropic even in the stationary state. As an example, harmonic triangular lattice is considered. Simple formula relating the stationary value of the temperature tensor and initial conditions is derived. The function describing equilibration of kinetic and potential energies is obtained. It is shown that the difference between the energies (Lagrangian) oscillates around zero. Amplitude of these oscillations decays inversely proport...
朱思峰; 刘芳; 柴争义; 戚玉涛; 吴建设
2012-01-01
In heterogeneous wireless network environment, wireless local area network （WLAN） are usually deployed within the coverage of a cellular network to provide users with the convenience of seamless roaming among heterogeneous wireless access networks. Vertical handoffs between the WLAN and the cellular network could occur frequently, with regard to vertical handoff performance, there is a critical need for developing algorithms for connection management and optimal resource allocation for seamless mobility. In this paper, we develop a mathematical model for vertical handoff decision problem, propose an artificial simple harmonic oscillator immune algorithm-based vertical handoff decision scheme, and perform the simulation experiments to validate proposed solution. Experimental result shows that the proposed solution, compared with literature solutions, can not only balance the overall load among all networks but also increase the collective battery lifetime of mobile terminals, and has the advantage of good application value.%本文设计了垂直切换判决方案问题的数学模型,给出了一种基于简谐振子免疫优化算法的垂直切换判决方案.并与文献方案进行了对比实验实验结果表明,本文方案能够有效地平衡网络负载、增加终端电池的生存时间,具有较好的应用价值.
Kalaria, P. C.; Avramidis, K. A.; Franck, J.; Gantenbein, G.; Illy, S.; Pagonakis, I. Gr.; Thumm, M.; Jelonnek, J.
2016-09-01
High frequency (>230 GHz) megawatt-class gyrotrons are planned as RF sources for electron cyclotron resonance heating and current drive in DEMOnstration fusion power plants (DEMOs). In this paper, for the first time, a feasibility study of a 236 GHz DEMO gyrotron is presented by considering all relevant design goals and the possible technical limitations. A mode-selection procedure is proposed in order to satisfy the multi-frequency and frequency-step tunability requirements. An effective systematic design approach for the optimal design of a gradually tapered cavity is presented. The RF-behavior of the proposed cavity is verified rigorously, supporting 920 kW of stable output power with an interaction efficiency of 36% including the considerations of realistic beam parameters.
Kumar, Anil; Kumar, Nitin; Singh, Udaybir; Khatun, Hasina; Vyas, V.; Sinha, A. K.
2012-04-01
In this paper thermal and structural analysis for 170 GHz, 1 MW gyrotron interaction cavity and the effect of structural deformation on beam wave interaction is presented. Finite element analysis codes ANSYS has been used for the thermal and structural analysis. Electromagnetic simulator-MAGIC, a Particle-in-Cell (PIC) code, has been used to carry out the effect of the radial expansion of the interaction cavity on beam wave interaction. The change in output power and resonant frequency for operating mode TE34,10 due to thermal expansion is 10 kW and 0.07 GHz, respectively. These values are under the tolerance limit of power and frequency of the gyrotron. The major variation is found in the power growth stability time.
Hohmann, Manuel [Physikalisches Institut, Universitaet Tartu (Estonia)
2016-07-01
Tensor harmonics are a useful mathematical tool for finding solutions to differential equations which transform under a particular representation of the rotation group SO(3). In order to make use of this tool also in the setting of Finsler geometry, where the objects of relevance are d-tensors instead of tensors, we construct a set of d-tensor harmonics for both SO(3) and SO(4) symmetries and show how these can be used for calculations in Finsler geometry and gravity.
170 GHz兆瓦级同轴回旋振荡管的分析计算%Analysis and calculation of a 170 GHz megawatt-level coaxial gyrotron
覃觅觅; 罗勇; 杨阔; 黄勇
2014-01-01
回旋管是最有希望应用于正在实施的国际热核实验反应堆计划的微波源器件,然而研究设计符合要求的回旋管还存在很多困难需要解决.对170 GHz兆瓦级光滑同轴回旋管的注-波互作用进行了研究.选取模式谱相对稀疏的TE31,12作为工作模式,利用Matlab编制源程序,计算了同轴回旋管的注-波耦合系数、起振电流.在考虑电子速度零散、腔壁电阻率和单模近似的基础上,对光滑同轴谐振腔的优化设计和注-波互作用进行了仿真,给出了磁场、电压、电流和内导体倾角等参量与回旋管效率的关系.结果表明,电压和磁场对回旋管效率影响较大,电子速度零散对回旋管效率影响较小,因而可降低电子枪的设计要求.此外,优化内导体倾角和同轴谐振腔结构参数可提高注-波互作用效率,降低电子速度零散对互作用效率的影响,获得了约50%的电子效率及1.7 MW输出功率.%Gyrotrons are the most promising microwave source devices that can be used in the International Thermonuclear Experimental Reactor, but there are many diffculties to be solved in study and design of gyrotrons to meet the require-ments. In this paper, the beam-wave interactions of a 170 GHz megawatt-level smooth-wall coaxial gyrotron are studied numerically. In order to attain high effciency and stable radiation, TE31,12 mode that lies in a relative sparse spectrum is selected as the operating mode, and the beam-wave coupling coeffcient and start oscillation current are calculated by a set of source codes developed by Matlab. Taking into account the electronic velocity spread and cavity wall resistivity, and based on a single-mode approximation, the optimization design and simulation of beam-wave interaction of a 170 GHz megawatt smooth-wall coaxial gyrotron have been fulfilled. The relationships between effciency and magnetic field, and the voltage, current, taper angle of insert, and other parameters are
Reconsidering harmonic and anharmonic coherent states: Partial differential equations approach
Toutounji, Mohamad, E-mail: Mtoutounji@uaeu.ac.ae
2015-02-15
This article presents a new approach to dealing with time dependent quantities such as autocorrelation function of harmonic and anharmonic systems using coherent states and partial differential equations. The approach that is normally used to evaluate dynamical quantities involves formidable operator algebra. That operator algebra becomes insurmountable when employing Morse oscillator coherent states. This problem becomes even more complicated in case of Morse oscillator as it tends to exhibit divergent dynamics. This approach employs linear partial differential equations, some of which may be solved exactly and analytically, thereby avoiding the cumbersome noncommutative algebra required to manipulate coherent states of Morse oscillator. Additionally, the arising integrals while using the herein presented method feature stability and high numerical efficiency. The correctness, applicability, and utility of the above approach are tested by reproducing the partition and optical autocorrelation function of the harmonic oscillator. A closed-form expression for the equilibrium canonical partition function of the Morse oscillator is derived using its coherent states and partial differential equations. Also, a nonequilibrium autocorrelation function expression for weak electron–phonon coupling in condensed systems is derived for displaced Morse oscillator in electronic state. Finally, the utility of the method is demonstrated through further simplifying the Morse oscillator partition function or autocorrelation function expressions reported by other researchers in unevaluated form of second-order derivative exponential. Comparison with exact dynamics shows identical results.
Reconsidering harmonic and anharmonic coherent states: Partial differential equations approach
Toutounji, Mohamad
2015-02-01
This article presents a new approach to dealing with time dependent quantities such as autocorrelation function of harmonic and anharmonic systems using coherent states and partial differential equations. The approach that is normally used to evaluate dynamical quantities involves formidable operator algebra. That operator algebra becomes insurmountable when employing Morse oscillator coherent states. This problem becomes even more complicated in case of Morse oscillator as it tends to exhibit divergent dynamics. This approach employs linear partial differential equations, some of which may be solved exactly and analytically, thereby avoiding the cumbersome noncommutative algebra required to manipulate coherent states of Morse oscillator. Additionally, the arising integrals while using the herein presented method feature stability and high numerical efficiency. The correctness, applicability, and utility of the above approach are tested by reproducing the partition and optical autocorrelation function of the harmonic oscillator. A closed-form expression for the equilibrium canonical partition function of the Morse oscillator is derived using its coherent states and partial differential equations. Also, a nonequilibrium autocorrelation function expression for weak electron-phonon coupling in condensed systems is derived for displaced Morse oscillator in electronic state. Finally, the utility of the method is demonstrated through further simplifying the Morse oscillator partition function or autocorrelation function expressions reported by other researchers in unevaluated form of second-order derivative exponential. Comparison with exact dynamics shows identical results.
Replicate periodic windows in the parameter space of driven oscillators
Medeiros, E.S., E-mail: esm@if.usp.br [Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo (Brazil); Souza, S.L.T. de [Universidade Federal de Sao Joao del-Rei, Campus Alto Paraopeba, Minas Gerais (Brazil); Medrano-T, R.O. [Departamento de Ciencias Exatas e da Terra, Universidade Federal de Sao Paulo, Diadema, Sao Paulo (Brazil); Caldas, I.L. [Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo (Brazil)
2011-11-15
Highlights: > We apply a weak harmonic perturbation to control chaos in two driven oscillators. > We find replicate periodic windows in the driven oscillator parameter space. > We find that the periodic window replication is associated with the chaos control. - Abstract: In the bi-dimensional parameter space of driven oscillators, shrimp-shaped periodic windows are immersed in chaotic regions. For two of these oscillators, namely, Duffing and Josephson junction, we show that a weak harmonic perturbation replicates these periodic windows giving rise to parameter regions correspondent to periodic orbits. The new windows are composed of parameters whose periodic orbits have the same periodicity and pattern of stable and unstable periodic orbits already existent for the unperturbed oscillator. Moreover, these unstable periodic orbits are embedded in chaotic attractors in phase space regions where the new stable orbits are identified. Thus, the observed periodic window replication is an effective oscillator control process, once chaotic orbits are replaced by regular ones.
Entanglement of higher-derivative oscillators in holographic systems
Dimov, Hristo; Mladenov, Stefan; Rashkov, Radoslav C.; Vetsov, Tsvetan
2017-05-01
We study the quantum entanglement of coupled Pais-Uhlenbeck oscillators using the formalism of thermo-field dynamics. The entanglement entropy is computed for the specific cases of two and a ring of N coupled Pais-Uhlenbeck oscillators of fourth order. It is shown that the entanglement entropy depends on the temperatures, frequencies and coupling parameters of the different degrees of freedom corresponding to harmonic oscillators. We also make remarks on the appearance of instabilities of higher-derivative oscillators in the context of AdS/CFT correspondence. Finally, we advert to the information geometry theory by calculating the Fisher information metric for the considered system of coupled oscillators.
Entanglement of higher-derivative oscillators in holographic systems
Dimov, Hristo, E-mail: h_dimov@phys.uni-sofia.bg [Department of Physics, Sofia University, 5 J. Bourchier Blvd., 1164 Sofia (Bulgaria); Mladenov, Stefan, E-mail: smladenov@phys.uni-sofia.bg [Department of Physics, Sofia University, 5 J. Bourchier Blvd., 1164 Sofia (Bulgaria); Rashkov, Radoslav C., E-mail: rash@phys.uni-sofia.bg [Department of Physics, Sofia University, 5 J. Bourchier Blvd., 1164 Sofia (Bulgaria); Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstr. 8–10, 1040 Vienna (Austria); Vetsov, Tsvetan, E-mail: vetsov@phys.uni-sofia.bg [Department of Physics, Sofia University, 5 J. Bourchier Blvd., 1164 Sofia (Bulgaria)
2017-05-15
We study the quantum entanglement of coupled Pais–Uhlenbeck oscillators using the formalism of thermo-field dynamics. The entanglement entropy is computed for the specific cases of two and a ring of N coupled Pais–Uhlenbeck oscillators of fourth order. It is shown that the entanglement entropy depends on the temperatures, frequencies and coupling parameters of the different degrees of freedom corresponding to harmonic oscillators. We also make remarks on the appearance of instabilities of higher-derivative oscillators in the context of AdS/CFT correspondence. Finally, we advert to the information geometry theory by calculating the Fisher information metric for the considered system of coupled oscillators.
Nonlinear Oscillations of Microscale Piezoelectric Resonators and Resonator Arrays
2006-06-30
linear characteristics [2-5]. These characteristics include DUffing oscillator like response during resonance excitations [6], temporal harmonics in the...model is used with a single-mode approximation to produce a forced Duffing oscillator . Nonlinear analysis is used to obtain the frequency-response...backward this procedure, the simplified model takes the form of a forced frequency sweeps, only the forward sweep data are used in Duffing oscillator , shown
Surpassing Fundamental Limits of Oscillators Using Nonlinear Resonators
Villanueva, L. G.; Kenig, E.; Karabalin, R. B.; Matheny, M. H.; Lifshitz, R; Cross, M. C.; Roukes, M. L.
2013-01-01
Self-sustained oscillators are ubiquitous and essential for metrology, communications, time reference, and geolocation. In its most basic form an oscillator consists of a resonator driven on-resonance, through feedback, to create a periodic signal sustained by a static energy source. The generation of a stable frequency, the basic function of oscillators, is typically achieved by increasing the amplitude of motion of the resonator while remaining within its linear, harmonic, regime. Contrary ...
Human brain networks function in connectome-specific harmonic waves.
Atasoy, Selen; Donnelly, Isaac; Pearson, Joel
2016-01-21
A key characteristic of human brain activity is coherent, spatially distributed oscillations forming behaviour-dependent brain networks. However, a fundamental principle underlying these networks remains unknown. Here we report that functional networks of the human brain are predicted by harmonic patterns, ubiquitous throughout nature, steered by the anatomy of the human cerebral cortex, the human connectome. We introduce a new technique extending the Fourier basis to the human connectome. In this new frequency-specific representation of cortical activity, that we call 'connectome harmonics', oscillatory networks of the human brain at rest match harmonic wave patterns of certain frequencies. We demonstrate a neural mechanism behind the self-organization of connectome harmonics with a continuous neural field model of excitatory-inhibitory interactions on the connectome. Remarkably, the critical relation between the neural field patterns and the delicate excitation-inhibition balance fits the neurophysiological changes observed during the loss and recovery of consciousness.
Synthesizing Virtual Oscillators to Control Islanded Inverters
Johnson, Brian B.; Sinha, Mohit; Ainsworth, Nathan G.; Dorfler, Florian; Dhople, Sairaj V.
2016-08-01
Virtual oscillator control (VOC) is a decentralized control strategy for islanded microgrids where inverters are regulated to emulate the dynamics of weakly nonlinear oscillators. Compared to droop control, which is only well defined in sinusoidal steady state, VOC is a time-domain controller that enables interconnected inverters to stabilize arbitrary initial conditions to a synchronized sinusoidal limit cycle. However, the nonlinear oscillators that are elemental to VOC cannot be designed with conventional linear-control design methods. We address this challenge by applying averaging- and perturbation-based nonlinear analysis methods to extract the sinusoidal steady-state and harmonic behavior of such oscillators. The averaged models reveal conclusive links between real- and reactive-power outputs and the terminal-voltage dynamics. Similarly, the perturbation methods aid in quantifying higher order harmonics. The resultant models are then leveraged to formulate a design procedure for VOC such that the inverter satisfies standard ac performance specifications related to voltage regulation, frequency regulation, dynamic response, and harmonic content. Experimental results for a single-phase 750 VA, 120 V laboratory prototype demonstrate the validity of the design approach. They also demonstrate that droop laws are, in fact, embedded within the equilibria of the nonlinear-oscillator dynamics. This establishes the backward compatibility of VOC in that, while acting on time-domain waveforms, it subsumes droop control in sinusoidal steady state.
Water Oscillation in an Open Tube
Doh Hoon Chung
2008-01-01
Full Text Available When an open tube is placed in a tank of water, covered on top, raised, and then uncovered, the water inside the tube will oscillate. The characteristics of the oscillation of the water inside the tube were studied. It was shown that, for large oscillations, the top half-period was longer than the bottom half period due to the increased mass of the water column. For small oscillations, it approached simple harmonic motion, with the square of the period varying with mean length, as predicted by theory. An end correction was also shown to exist, due to the motion of the water outside the bottom of the tube during the oscillation. The end correction was shown to be independent of the mean length of the water column, as predicted.
Analysis of a free oscillation atom interferometer
Kafle, Rudra P; Zozulya, Alex A
2011-01-01
We analyze a Bose-Einstein condensate (BEC) - based free oscillation atom Michelson interferometer in a weakly confining harmonic magnetic trap. A BEC at the center of the trap is split into two harmonics by a laser standing wave. The harmonics move in opposite directions with equal speeds and turn back under the influence of the trapping potential at their classical turning points. The harmonics are allowed to pass through each other and a recombination pulse is applied when they overlap at the end of a cycle after they return for the second time. We derive an expression for the contrast of the interferometric fringes and obtain the fundamental limit of performance of the interferometer in the parameter space.
Oscillation death in coupled oscillators
Wei ZOU; Xin-gang WANG; Qi ZHAO; Meng ZHAN
2009-01-01
We study dynamical behaviors in coupled nonlinear oscillators and find that under certain condi- tions, a whole coupled oscillator system can cease oscil- lation and transfer to a globally nonuniform stationary state [I.e., the so-called oscillation death (OD) state], and this phenomenon can be generally observed. This OD state depends on coupling strengths and is clearly differ- ent from previously studied amplitude death (AD) state, which refers to the phenomenon where the whole system is trapped into homogeneously steady state of a fixed point, which already exists but is unstable in the ab- sence of coupling. For larger systems, very rich pattern structures of global death states are observed. These Turing-like patterns may share some essential features with the classical Turing pattern.
Detection of harmonic signals from chaotic interference by empirical mode decomposition
Li, H.G. [State Key Laboratory of Vibration, Shock and Noise, Shanghai Jiao Tong University, Shanghai 200030 (China)]. E-mail: hgli@sjtu.edu.cn; Meng, G. [State Key Laboratory of Vibration, Shock and Noise, Shanghai Jiao Tong University, Shanghai 200030 (China)]. E-mail: gmeng@sjtu.edu.cn
2006-11-15
An empirical mode decomposition (EMD) approach to the harmonic signal extraction from chaotic interference is proposed. Based on the EMD and the concept that any signal is composed of a series of simple intrinsic modes, the chaotic interference signal is decomposed to a series of intrinsic mode functions (IMFs), among which one IMF is the recovered harmonic signal. In this study, harmonic signals are contaminated with a chaotic interference signal which is generated by a Duffing oscillator, and the simulation results show that the harmonic signals can be effectively recovered from the contaminated signals by the EMD approach.
Tunable Soft X-Ray Oscillators
Wurtele, Jonathan; Gandhi, Punut; Gu, X-W; Fawley, William M; Reinsch, Matthia; Penn, Gregory; Kim, K-J; Lindberg, Ryan; Zholents, Alexander
2010-09-17
A concept for a tunable soft x-ray free electron laser (FEL) photon source is presented and studied numerically. The concept is based on echo-enabled harmonic generation (EEHG), wherein two modulator-chicane sections impose high harmonic structure with much greater efficacy as compared to conventional high harmonic FELs that use only one modulator-chicane section. The idea proposed here is to replace the external laser power sources in the EEHG modulators with FEL oscillators, and to combine the bunching of the beam with the production of radiation. Tunability is accomplished by adjusting the magnetic chicanes while the two oscillators remain at a fixed frequency. This scheme eliminates the need to develop coherent sources with the requisite power, pulse length, and stability requirements by exploiting the MHz bunch repetition rates of FEL continuous wave (CW) sources driven by superconducting (SC) linacs. We present time-dependent GINGER simulation results for an EEHG scheme with an oscillator modulator at 43 nm employing 50percent reflective dielectric mirrors and a second modulator employing an external, 215-nm drive laser. Peak output of order 300 MW is obtained at 2.7 nm, corresponding to the 80th harmonic of 215 nm. An alternative single-cavity echo-oscillator scheme based on a 13.4 nm oscillator is investigated with time-independent simulations that a 180-MW peak power at final wavelength of 1.12 nm. Three alternate configurations that use separate bunches to produce the radiation for EEHG microbunching are also presented. Our results show that oscillator-based soft x-ray FELs driven by CWSC linacs are extremely attractive because of their potential to produce tunable radiation at high average power together with excellent longitudinal coherence and narrow spectral bandwidth.