Gluon spectrum in the glasma from JIMWLK evolution

The JIMWLK equation with a “daughter dipole” running coupling is solved numerically, starting from an initial condition given by the McLerran-Venugopalan model. The resulting Wilson line configurations are then used to compute the spectrum of gluons comprising the glasma initial state of a high energy heavy ion collision. The development of a geometrical scaling region makes the spectrum of produced gluons harder. Thus the ratio of the mean gluon transverse momentum to the saturation scale grows with energy. Also the total gluon multiplicity increases with energy slightly faster than the saturation scale squared.     

Langevin particle in Gaussian noise

The problem of memory of past is discussed for a Langevin particle subject to Gaussian noise of a general type. The most probable trajectories of a particle are found and a generalisation of the Girsanov formula is proposed.     

Langevin equation in field theory

A new approach to quantum field theory is developed based on the Langevin equation (stochastic quantization). Applications to conventional and gauge theories are discussed, as well as various extensions; the Langevin difference equation, the complex Langevin equation in Minkowski space, etc.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 66–76, March, 1986.     

Quantum Langevin systems

It is shown that the canonical quantization of dissipative systems, following a Langevin equation, reduce the physical applicability to particular approximations.     

On the variational form of evolution equations

In this paper a new definition is given for representability in the form of a variational derivative; a particular case of this definition yields the classical expression for the variational derivative. A close connection will be demonstrated between the variational derivative and the exterior differentiation operator d. For the case of functions of one variable one obtains effective computational criteria which solve the “hidden variability” problem. The rigorous mathematical theory is illustrated as applied to the study of a few nonlinear equations of mathematical physics.     

Langevin and generalized Langevin types of spontaneous emission of quantum particles

In the effective Hamiltonian representation, we have obtained a quantum stochastic differential equation of a generalized Langevin type for the evolution operator of an atomic ensemble in a microcavity in an external broadband quantized field and in a nonresonant field of the microcavity. We show that, depending on the number of particles in the atomic ensemble, its dynamics demonstrates both the Langevin and the generalized Langevin types of the two-photon spontaneous decay. In this case, one photon is emitted into the cavity mode, whereas the other photon is emitted into the external broadband electromagnetic field. The Langevin type is determined by a considerable Stark interaction of the atomic ensemble with the broadband photon-free quantized field. We show that, here, the Stark interaction is represented by a quantized Poisson process and, depending on its magnitude (at certain numbers of atoms in the ensemble), the two-photon collective spontaneous emission of microcavity atoms can be completely suppressed. In this case, the two-photon spontaneous emission of the singly excited atomic ensemble is described by the two-level model, while the atom-photon cluster of the microcavity under the described conditions is an artificial two-level quantum particle with a strong Stark interaction.     

Non-linear QCD evolution with improved triple-pomeron vertices

In a previous publication, we have constructed a set of non-linear evolution equations for dipole scattering amplitudes in QCD at high energy, which extends the Balitsky–JIMWLK hierarchy by including the effects of fluctuations in the gluon number. In doing so, we have relied on the color dipole picture, and we have neglected the non-locality of the two-gluon exchanges in the relation between scattering amplitudes and dipole densities. In this Letter, we relax the latter approximation, and thus restore the correct structure of the ‘triple-pomeron vertex’ which describes the splitting of one BFKL pomeron into two in the terms responsible for fluctuations. The ensuing triple-pomeron vertex coincides with the one previously derived by Braun and Vacca within perturbative QCD. The evolution equations can be recast in a Langevin form, but with a multivariable noise term with off-diagonal correlations. Our equations are shown to be equivalent with the modified version of the JIMWLK equation recently proposed by Mueller, Shoshi, and Wong.     

聚苯硫醚材料复合棒型换能器

本文选择了高聚物中杨氏模量较大、损耗较小的聚苯硫醚作为复合棒型换能器的前盖板。计算了聚苯硫醚棒中的纵波传播速度,研究了基于聚苯硫醚材料的复合棒型换能器的等效电路设计方法。利用有限元方法计算了换能器谐振频率、轴向应变分布、平均耗散功率等性能参数。对本文研制的前盖板为聚苯硫醚、后盖板为钢(1#)和前后盖板均为聚苯硫醚(2#)的两个换能器进行了测试。结果表明,理论计算的谐振频率与实验测试相吻合;两个换能器的振幅均与所施加的电压成正比,且1#换能器的振幅电压比更大;两个换能器的耗散功率与外加电压平方成正比,在应变较大处耗散功率较高,导致局部升温明显,测得两个换能器温度最高处均位于应变最大位置处。1#换能器的前后振幅比为26,与同频率的金属组件换能器相比,若后盖板为尺寸相同的钢材,前盖板采用聚苯硫醚材料能够显著提高换能器的前后振幅比,且带宽也较大。     

Nonlinear generalized Langevin equations

Exact generalized Langevin equations are derived for arbitrarily nonlinear systems interacting with specially chosen heat baths. An example is displayed in which the Langevin equation is nonlinear but approximately Markovian.Research supported by NSF grant GP-29534.     

Injected Power Fluctuations in Langevin Equation

In this paper, we consider the Langevin equation from an unusual point of view, that is as an archetype for a dissipative system driven out of equilibrium by an external excitation. Using path integral method, we compute exactly the probability density function of the power (averaged over a time interval of length ) injected (and dissipated) by the random force into a Brownian particle driven by a Langevin equation. The resulting distribution, as well as the associated large deviation function, display strong asymmetry, whose origin is explained. Connections with the so-called Fluctuation Theorem are thereafter discussed. Finally, considering Langevin equations with a pinning potential, we show that the large deviation function associated with the injected power is completely insensitive to the presence of a potential.     

Steady-state thermodynamics of Langevin systems

We study Langevin dynamics describing nonequilibirum steady states. Employing the phenomenological framework of steady-state thermodynamics constructed by Oono and Paniconi [Prog. Theor. Phys. Suppl. 130, 29 (1998)], we find that the extended form of the second law which they proposed holds for transitions between steady states and that the Shannon entropy difference is related to the excess heat produced in an infinitely slow operation. A generalized version of the Jarzynski work relation plays an important role in our theory.     

基于改进差分进化算法的相机标定研究

目前相机标定多采用Tsai和Weng的基于非线性成像模型的分步标定法。在研究标定算法的过程中发现,待优化的目标函数具有多个局部极值点,采用传统的局部优化算法会导致迅速收敛到局部极值点,而非全局最优解,影响了标定精度。差分进化是一种收敛速度很快的进化算法,但当初始种群分布不够理想时,它可能快速收敛到局部极值点。将其改进后用于相机标定,提出了分步法与改进的差分进化算法相结合的相机标定方法。数据实验表明:标定精度比直接采用分步法有所提高。     

On the complex Langevin equation

We discuss the Langevin equation for a complex Boltzmann distribution, allowing for modifications of the process. The relation between the two different time development operators involved is analyzed, with emphasis on their spectra.     

Langevin trajectories between fixed concentrations

We consider the trajectories of particles diffusing between two infinite baths of fixed concentrations connected by a channel, e.g., a protein channel of a biological membrane. The steady state influx and efflux of Langevin trajectories at the boundaries of a finite volume containing the channel and parts of the two baths is replicated by termination of outgoing trajectories and injection according to a residual phase space density. We present a simulation scheme that maintains averaged fixed concentrations without creating spurious boundary layers, consistent with the assumed physics.