Energy of the elastic loading of anharmonic solids

This paper reports on the results of measurements of changes in the temperature of a solid under the adiabatic elastic loading (thermoelastic effect), the coefficient of thermal expansion, and the Young’s modulus of a rigid-chain vitrified polymer, namely, polyimide. It has been found that there are differences in the sign and magnitude of the changes in the energy of thermal origin in samples and the work of the external force. The energy of the thermoelastic effect has been explained in terms of the influence exerted by the anharmonic expansion of a solid, with the separation of the quasi-static potential and dynamic components of the thermal energy of the solid. The loading with an external force causes a redistribution of the thermal energy. A change in the temperature of the solid corresponds to a change in the dynamic component. An energy analysis of the adiabatically loaded anharmonic oscillator has confirmed the conclusion regarding the mechanism of energy transfer and revealed that, under loading, there is a redistribution of the kinetic and potential components of the internal energy of the oscillator.     

Energy of the frequency-elastic effect in solids

A decrease in the frequency of skeletal vibrations (frequency-elastic effect) has been measured using Raman spectroscopy, and the stretching of backbone interatomic bonds in polyethylene molecules under elastic tensile loading of oriented polyethylene fibers has been measured using X-ray diffraction. It has been found that there are differences in the sign and magnitude of the changes in the zero-point energy and the work of the external force. The energy of the frequency-elastic effect has been explained in terms of the influence exerted by the initial (before loading) anharmonic stretching of backbone bonds and the force of anharmonic pressure, with the separation of the anharmonic (potential) component of the zero-point energy of the solid. A change in the frequency of vibrations corresponds to a change in the harmonic component of the zero-point energy. The loading with an external force causes a redistribution of the zero-point energy components. An energy analysis of the loaded quantum anharmonic oscillator has confirmed the conclusion regarding the mechanism of energy transfer and revealed that, under loading, there is a redistribution of the average values of the kinetic and potential components of the internal energy of the oscillator.     

Energy features of an adiabatically loaded anharmonic oscillator

An excited anharmonic oscillator is considered under conditions of adiabatic (i.e., slow, as compared to the oscillation period) loading with an external force tending to a constant value at long times. The energy characteristics of the adiabatically loaded anharmonic oscillator, such as the instantaneous energy of the oscillator, the maximum kinetic (oscillation) energy, and the kinetic and potential energies averaged over the period, are analytically calculated as a function of the steady-state force. The analytical results are confirmed by the data of numerical calculations. It is established that the external force gives rise to a redistribution of the average kinetic and potential components of the initial energy of the anharmonic oscillator and that the transferred energy portions at a small external force considerably exceed the average work done by the external force.     

The dynamical Casimir-Polder force in relativistic atomic motion near the surface of a thick plate

The dynamical Casimir-Polder force between a neutral atom (in the ground state) and a thick plate in relativistic motion of the atom in the direction parallel to the surface has been calculated. The material properties have been considered in the framework of the oscillator model of the atom and the Drude dielectric function for a plate. The limiting cases of the nonrelativistic velocity and perfectly conducting material of the plate have been discussed. A complex dependence of the force on the velocity (energy), the distance, and the material properties of the surface has been found.     

Spectral analysis of a nonlinear oscillator driven by random and periodic forces. I. Linearized theory

We have combined the techniques of statistical and harmonic linearization to develop a linearized approximation theory for the calculation of the second-order statistics (i.e., autocorrelation functions and spectral densities) of nonlinear systems driven by both random and periodic forces. For the special case of a Duffing oscillator (a damped anharmonic oscillator with a cubic nonlinearity) driven by Gaussian white noise and by a sinusoidal force, explicit expressions for the renormalized (linearized) frequency, the autocorrelation function, and the spectral density of the oscillator displacement in terms of all the system parameters have been derived. We have determined the region of the parameter space in which the applied periodic force has a significant influence on the second-order statistics of the oscillator.This research was supported by the Office of Naval Research, by the National Science Foundation under grant No. CHE78-21460 and by a grant from Charles and Reneé Taubman.     

Experimental investigation of the Casimir force beyond the proximity-force approximation

The analysis of all Casimir force experiments using a sphere-plate geometry requires the use of the proximity-force approximation (PFA) to relate the Casimir force between a sphere and a flat plate to the Casimir energy between two parallel plates. Because it has been difficult to assess the PFA's range of applicability theoretically, we have conducted an experimental search for corrections to the PFA by measuring the Casimir force and force gradient between a gold-coated plate and five gold-coated spheres with different radii using a microelectromechanical torsion oscillator. For separations z<300 nm, we find that the magnitude of the fractional deviation from the PFA in the force gradient measurement is, at the 95% confidence level, less than 0.4z/R, where R is the radius of the sphere.     

Analysis of energy distribution in a loaded quantum anharmonic oscillator in a wide temperature range

Analysis of the energy distribution in an ensemble of quantum anharmonic oscillators loaded by an external force in a wide temperature range (from T = 0) is carried out using a general approach based on the virial theorem. At T = 0, anharmonic effects are observed: a linear variation of zero-point energy of an oscillator under loading (energy decrease during extension and increase under compression) and a linear variation of the average kinetic and potential energy components. At high temperatures, at which the dynamics of the oscillators becomes classical, the anharmonic effects are manifested in a linear variation in the vibrational energy and a linear variation in the average kinetic and potential energy components upon an increase in force. Mutually compensating variation in the average kinetic and potential energy components of the internal dynamic energy of an oscillator (energy redistribution upon loading) takes place both at low and high temperatures.     

Dynamic drag of dislocations in crystal with structural imperfections

A new mechanism of dynamic drag of dislocations is proposed and analyzed. A pair of dislocations is treated as a linear harmonic oscillator. The dissipation mechanism under investigation involves an irreversible conversion of the kinetic energy of moving dislocations into the vibrational energy of the dislocation oscillator. The proposed mechanism is used for calculating the drag force exerted by stationary trapped dislocations on a moving pair of dislocations and the drag of a solitary dislocation by dislocation dipoles. Radiative drag force acting on a moving pair of dislocations is also calculated.     

Structural and optical characteristics of Ce,Nd, Gd,and Dy-doped $$\hbox {Al}_{2}\hbox {O}_{3}$$ thin films

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.     

Debye屏蔽自洽势下Au50+离子的能级与振子强度

以惯性约束聚变实验中感兴趣的金的类铜离子(Au⁵⁰⁺)为例，讨论了等离子体中自由电子对复杂原子中电子行为的影响.采用受Debye屏蔽的Hartree-Fock-Slater自洽势，计算了Au⁵⁰⁺离子的主量子数n从1到7的28个本征态，得到了对应于一系列Debye长度Λ的能量本征值E_nl，即轨道束缚能，和能级之间的光学振子强度.与类氢情况相似：自由电子的屏蔽作用使所有能级均从无屏蔽时的位置向连续态移动，即电离限下移；对于每个能量本征态(n, 关键词：     

Simulation of thermoelastic properties of solids in the framework of an ensemble of anharmonic oscillators

It has been shown that, in a classical ensemble of anharmonic oscillators, the mean value of the oscillator coordinate is a classical parameter in the sense that the statistical sum of the ensemble satisfies, to the second order in the anharmonicity constant, the stationary condition with respect to this parameter. This stationary condition is equivalent to the classical condition for the balance of external and internal forces acting on the oscillator. This equivalence is justified by the fact that the statistical sum, which is stationary with respect to the mean oscillator coordinate, agrees within this accuracy with the usual statistical sum of independent anharmonic oscillators. After introducing the classical parameter into a large thermodynamic system, the energy balance under the mechanical deformation of the system is realized through the exchange between two scale levels: the energy of oscillations at the microlevel and the macroscopic potential energy of deformation of the sample as a whole.     

Electronic and optical properties of a nanoring in the presence of external magnetic field

Optical properties of a nanoring with Winternitz–Smorodinsky confinement potential in the presence of an external magnetic field have been studied theoretically. Our results demonstrate that energy, oscillator strength and the linear, nonlinear and total absorption are strongly affected by size of the nanoring. Also, we found that magnetic field has little influence on energy difference, oscillator strength and optical absorption of the nanoring.     

On the pressure of gravitational waves

A system of coupled point masses under the influence of gravitational waves is considered. By means of the geodesic deviation equation as the equation of motion it is shown, taking into account the second order small terms, that there exist forces which cause the acceleration of the system in the longitudinal direction. The longitudinal force is due to the fact that simultaneously with energy momentum is also absorbed from waves. It is proved directly on the basis of the equations of motion of the point masses that the energy and momentum absorbed by the test system obey the special relativistic relationship of a zero rest mass particle. The case when the Weber oscillator moves at a relativistic speed with respect to the source of gravitational waves is also examined. In this case, the absorption of energy and momentum by the Weber oscillator is much larger or smaller compared to the stationary situation.     

摩擦微观能量耗散机理的复合振子模型研究

提出无磨损界面摩擦微观能量耗散机理的复合振子模型，指出滑动摩擦过程同时存在整体做低频弹性振动的宏观振子和界面原子受激励产生热振动的微观振子，并在此基础上分析了宏观振子和微观振子对摩擦能量耗散的不同影响. 通过对界面原子的动力学分析，指出摩擦过程界面激励力的频率是能量转换的关键:在平衡力作用阶段，界面作用力的频率趋于零，因而可以直接作用到每个原子，力的作用效果是整体和均匀的；在失稳跳跃阶段,由于界面激励力的频率极高，造成摩擦界面原子获得的能量分布很不均匀，从而产生不可逆的能量耗散过程. 与目前通用的独立振子模型比较，复合振子模型能够更准确描述摩擦能量耗散过程，可为摩擦控制提供理论指导. 关键词： 摩擦 能量耗散机理 复合振子模型 独立振子模型     

High repetition rate pulsed laser of twin wavelengths from KTiOPO4 optical parametric oscillation

In this paper, some key techniques of KTiOPO_4 optical parametric oscillation (OPO) laser with repetitive frequencies and twin wavelengths output have been analysed theoretically and studied experimentally in detail. An intracavity optical parametric oscillator (IOPO) has been applied. Operating under 20Hz, laser output energy of more than 38mJ with twin wavelengths 1.57μm and 1.06μm has been achieved. Results of the experiments agree well with the theoretical discussion.     

Energy dissipation prediction in a line of colliding oscillators

In this paper the impact of a line of adjacent structures, or oscillators, is studied using an energy formulation. The energy exchange and dissipation from a collision of a pair of oscillators is studied by creating an equivalent oscillator pair, one has the energy of the in-phase motion and the other has the out-of-phase energy. It is found that the energy exchange between colliding oscillators is proportional to the initial kinetic energy difference of the oscillators and that work in the collision is proportional to the out-of-phase energy or difference energy. The kinetic energy at contact is then related to the mean oscillator energy, permitting a power balance equation to be written for each oscillator in line. The power balance equations have three independent variables for each pair of oscillators: the oscillator time averaged energies and the phase difference. This equation is run in a time-stepping procedure, with steps at the mean collision rate. The work in the collisions and internal oscillator dissipation is output as a function of time. A parameter study is conducted to see how the work changes with oscillator: separation, contact stiffness and contact damping.     

Generation of high energy and good beam quality pulses with a master oscillator power amplifier

A high efficiency and high peak power laser system with short-pulse and good beam quality has been demonstrated by using a master oscillator power amplifier with two-pass amplification configuration. The master oscillator, end-pumped with a fiber-coupled laser diode array, provides low power but excellent beam quality pulses, and the amplifier boosts the pulse energy by orders without significant beam quality degradation. Short pulses of 8.5 ns with energy up to 130 mJ and approximately diffraction limited beam quality have been demonstrated.     

Quantum statistical effects of the motion of an oscillator interacting with a radiation field

The motion of a quantum oscillator interacting with a quantized radiation field is studied. The exact solution shows that the motion of the oscillator is described by a Langevin-type equation in which the friction and the effective frequency depend on time. The physical conditions under which these properties become constant are studied. The stochastic force becomes a gaussian process and in the limit of long times and weak coupling, has an autocorrelation function with the usual delta behavior.     

Quantum theory of a dissipative oscillator

The nonlinear equation of dissipative quantum mechanics is considered in the relaxation-time approximation. It is shown that the steady current-free state does not change when dissipation is taken into account; in particular, there is no ground-state damping, and the zero energy is conserved. A solution is obtained to the problem of the excitation of a harmonic oscillator, serving as a model of single-mode radiation in an open resonator; the solution obtained describes the evolution of the oscillator from an arbitrary steady state under the action of a constraining force. Transition probabilities between the oscillator steady states are calculated. The results are found to be in agreement with the classical theory of damping oscillations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 99–105, September, 1978.     

Generalized classical mechanics

Generalized classical mechanics has been introduced and developed as a classical counterpart of the fractional quantum mechanics. The Lagrangian of generalized classical mechanics has been introduced, and equation of motion has been obtained. Lagrange, Hamilton and Hamilton-Jacobi frameworks have been implemented. Oscillator model has been launched and solved in 1D case. A new equation for the period of oscillations of generalized classical oscillator has been found. The interplay between the energy dependency of the period of classical oscillations and the non-equidistant distribution of the energy levels for fractional quantum oscillator has been discussed. We discuss as well, the relationships between new equations of generalized classical mechanics and the well-known fundamental equations of classical mechanics.