共查询到20条相似文献,搜索用时 265 毫秒
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通过正则化变换技巧,寻找到一种对阻尼系数随时间变化的阻尼谐振子直接量子化方案,进而采用高斯型传播子和费曼路径积分方法求出了含时阻尼谐振子的严格波函数,并对波函数的普遍意义,坐标和动量的零点涨落以及两者的不确定关系作了讨论
关键词:
含时阻尼
传播子
费曼路径积分 相似文献
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改进了组态路径积分蒙卡方法,简化采样过程,开发相应程序并对无库伦相互作用谐振子以及均匀电子气进行模拟.谐振子平衡态能量与Fermi-Dirac分布符合较好,均匀电子气平衡态能量和动量基本符合Fermi-Dirac分布规律.对两种费米子系统的研究表明,组态路径积分蒙卡方法对费米子的交换效应具有较好的描述.本文探讨了费米交换符号问题的解决途径,同时对均匀电子气模型进行研究,为后续温热稠密物质的研究奠定基础. 相似文献
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用路径积分的方法计算了二维无限深方势阱中粒子的传播子,并由传播函数推导出二维无限深方势阱中粒子的波函数和能量,进一步体现了路径积分与其他经典量子化方法的等价性,反映了路径积分应用于难以处理的量子力学问题的价值. 相似文献
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用路径积分的分析方法求得了一维无限深势阱中粒子的传播函数,并由传播函数导出了粒子的波函数和能量,展示了路径积分与传统方法的等价性,同时还介绍了一种有用的数学函数——雅可比θ_3函数. 相似文献
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空气中声源激发的浅海水下声场传播实验研究 总被引:1,自引:0,他引:1
为了了解空气中声源激发的水下声场传播特性,对此开展实验研究。2010年在南海北部海域进行了一次空气中声源激发水下声场实验,在水下成功地接收到远至4km处大功率扬声器在空中发射的脉冲声信号。本文通过分析实验数据,研究空气中声源激发的浅海水下声场传播特点。针对接收阵拾取的声传播信号信噪比低的特点,综合利用脉冲压缩以及波束形成方法提高接收信号的信噪比,得到收发距离1~4km、频率200~1000Hz范围内的传播损失实验值。在理论上,采用波数积分方法进行了声场数据模拟,结果表明理论计算的传播损失与实验结果较为一致。 相似文献
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T. Padmanabhan 《Foundations of Physics》1994,24(11):1543-1562
The action for a massive particle in special relativity can be expressed as the invariant proper length between the end points. In principle, one should be able to construct the quantum theory for such a system by the path integral approach using this action. On the other hand, it is well known that the dynamics of a free, relativistic, spinless massive particle is best described by a scalar field which is equivalent to an infinite number of harmonic oscillators. We clarify the connection between these two—apparently dissimilar—approaches by obtaining the Green function for the system of oscillators from that of the relativistic particle. This is achieved through defining the path integral for a relativistic particle rigorously by two separate approaches. This analysis also shows a connection between square root Lagrangians and the system of harmonic oscillators which is likely to be of value in more general context. 相似文献
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Fractional path integration and particles trajectories in fractional dimensional space are motivating issues in quantum mechanics and kinetics. In this paper, a fractional path integral characterized by a fractional propagator is developed based on the framework of the fractional action-like variational approach. A fractional generalization of the free particle problem is found, the corresponding fractional Schrödinger equation is derived and a fractional path integral formulation of harmonic oscillators characterized by a perturbed Lagrangian is constructed after reducing the fractional action to an integral action on fractal. The new fractal-like path integral offers a number of motivating features which are discussed and analyzed. The main outcome is connected to the possibility of constructing on a fractal a path integral for the oscillators characterized by modified ground energy. In particular for low-temperature case, the fractional perturbed oscillator is characterized by a free energy larger than the standard value \( E_{0} = {{\hbar \omega } \mathord{\left/ {\vphantom {{\hbar \omega } 2}} \right. \kern-0pt} 2}.\) Such an increase in the ground energy generalizes the uncertainty principle without involving differentiable paths or even invoking new phenomenological theories based on deformed algebra. 相似文献
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Time dependence of the average charge and current in a dissipative mesoscopic circuit 总被引:4,自引:0,他引:4 下载免费PDF全文
Taking into consideration the interactions between electrons and phonons,we have studied the temporal evolution of the average charge and current in a dissipative mesoscopic RLC circuit.Our results show that a mesoscopic RLC circuit can be treated as an interactive system between an electromagnetic harmonic oscillator and many lattice harmonic oscillators;this is called the bathing of the harmonic oscillators.The results also show that the quantum equation of motion of the linear mesoscopic RLC circuit is identical in form to its classical equation of motion,the only difference between them being their respective meanings.In order to thoroughly study the quantum properties of a dissipative mesoscopic circuit,we have to consider not only the electromagnetic energy of the circuit,but also the crystal lattice vibration energy and the interactive energy between electrons and phonons. 相似文献
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M. Rybaczuk 《Physica A》1989,160(3):519-526
The influence of an external noise on two linearly coupled quantum oscillators is investigated. The noise is described by the probability measure corresponding to a symmetric Lévy stable distribution. In calculations the path integral technique is used. This paper is a continuation of investigations started by Bose, Datta and Feinsilver. 相似文献
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C. Grosche 《Physics of Particles and Nuclei》2006,37(3):368-399
In this paper, the Feynman path integral technique is applied to two-dimensional spaces of nonconstant curvature: these spaces are called Darboux spaces D I-D IV. We start each consideration in terms of the metric and then analyze the quantum theory in the separable coordinate systems. The path integral in each case is formulated and then solved in the majority of cases; the exceptions being the quartic oscillators where no closed solution is known. The required ingredients are the path integral solutions of the linear potential, the harmonic oscillator, the radial harmonic oscillator, the modified Pöschl-Teller potential, and the spheroidal wave functions. The basic path integral solutions, which appear here in a complicated way, have been developed in recent work and are known. The final solutions are represented in terms of the corresponding Green’s functions and the expansions into the wave functions. We also sketch some limiting cases of the Darboux spaces, where spaces of constant negative and zero curvature emerge. 相似文献
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Jonathan C. Mattingly Toufic M. Suidan Eric Vanden-Eijnden 《Journal of statistical physics》2007,128(5):1145-1152
We study a system of stochastically forced infinite-dimensional coupled harmonic oscillators. Although this system formally
conserves energy and is not explicitly dissipative, we show that it has a nontrivial invariant probability measure. This phenomenon,
which has no finite dimensional equivalent, is due to the appearance of some anomalous dissipation mechanism which transports
energy to infinity. This prevents the energy from building up locally and allows the system to converge to the invariant measure.
The invariant measure is constructed explicitly and some of its properties are analyzed. 相似文献
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A novel approximate analytical approach for determining the response evolutionary power spectrum (EPS) of nonlinear/hysteretic structural systems subject to stochastic excitation is developed. Specifically, relying on the theory of locally stationary processes and utilizing a recently proposed representation of non-stationary stochastic processes via wavelets, a versatile formula for determining the nonlinear system response EPS is derived; this is done in conjunction with a stochastic averaging treatment of the problem and by resorting to the orthogonality properties of harmonic wavelets. Further, the nonlinear system non-stationary response amplitude probability density function (PDF), which is required as input for the developed approach, is determined either by utilizing a numerical path integral scheme, or by employing a time-dependent Rayleigh PDF approximation technique. A significant advantage of the approach relates to the fact that it is readily applicable for treating not only separable but non-separable in time and frequency EPS as well. The hardening Duffing and the versatile Preisach (hysteretic) oscillators are considered in the numerical examples section. Comparisons with pertinent Monte Carlo simulations demonstrate the reliability of the approach. 相似文献
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Superradiance, the enhanced collective emission of energy from a coherent ensemble of quantum systems, has been typically
studied in atomic ensembles. In this work we study theoretically the enhanced emission of energy from coherent ensembles of
harmonic oscillators. We show that it should be possible to observe harmonic oscillator superradiance for the first time in
waveguide arrays in integrated photonics. Furthermore, we describe how pairwise correlations within the ensemble can be measured
with this architecture. These pairwise correlations are an integral part of the phenomenon of superradiance and have never
been observed in experiments to date. 相似文献
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目前不变量本征算符方法已成功地解决了某些量子系统哈密顿量能级问题.对于二维耦合量子谐振子,利用这一方法可以非常简捷有效地给出其能级信息,而不需要使其哈密顿量对角化.计算结果表明,不同耦合形式的二维耦合量子谐振子的能级间隔是不同的. 相似文献