Quantization of Underdamped, Critically Damped, and Overdamped Electric Circuits with a Power Source

We have investigated the quantum mechanical effect of the underdamped, critically damped, and overdamped electric circuits with a power source. The charge of the underdamped circuit oscillates while those of the critically damped and overdamped ones don't. The wave function of the system of overdamped circuit represented parabolic cylinder function while underdamped circuit was represented by well-known Hermite polynomial. The eigenvalues of underdamped circuit is discrete while those of the critically damped and overdamped ones are given as continuously.     

Retainability of canonical distributions for a Brownian particle controlled by a time-dependent harmonic potential

The retainability of canonical distributions for a Brownian particle controlled by a time-dependent harmonic potential is investigated in the overdamped and underdamped situations, respectively. Because of different time scales, the overdamped and underdamped Langevin equations (as well as the corresponding Fokker-Planck equations) lead to distinctive restrictions on protocols maintaining canonical distributions. Two special cases are analyzed in details: First, a Brownian particle is controlled by a time-dependent harmonic potential and embedded in medium with constant temperature; Second, a Brownian particle is controlled by a timedependent harmonic potential and embedded in a medium whose temperature is tuned together with the potential stiffness to keep a constant effective temperature of the Brownian particle. We find that the canonical distributions are usually retainable for both the overdamped and underdamped situations in the former case. However, the canonical distributions are retainable merely for the overdamped situation in the latter case. We also investigate general time-dependent potentials beyond the harmonic form and find that the retainability of canonical distributions depends sensitively on the specific form of potentials.     

Phase-charge duality of a josephson junction in a fluctuating electromagnetic environment

We have measured the current-voltage characteristics of a single Josephson junction placed in a high impedance environment. The transfer of Cooper pairs through the junction is governed by overdamped quasicharge dynamics, leading to Coulomb blockade and Bloch oscillations. Exact duality exists to the standard overdamped phase dynamics of a Josephson junction, resulting in a dual shape of the current-voltage characteristic, with current and voltage changing roles. We demonstrate this duality with experiments which allow for a quantitative comparison with a theory that includes the effect of fluctuations due to the finite temperature of the electromagnetic environment.     

Continuum limit of single-electron tunneling

We consider the continuum limit of the standard model for treating single-electron tunneling (SET) of electrons through a one-dimensional array of tunnel junctions. We show that the formalism reduces to the computation of the motion of overdamped particles undergoing potential gradient flow, with the potential being given by the full interacting free energy of the electrons in the system. We show that the tunneling coefficients in the SET model can be re-interpreted in terms of a diffusion coefficient and a temperature and that therefore the SET problem reduces to a fully self-consistent treatment of overdamped particle diffusion.     

Flavoured leptogenesis in the CTP formalism

Within the Closed Time Path (CTP) framework, we derive kinetic equations for particle distribution functions that describe leptogenesis in the presence of several lepton flavours. These flavours have different Standard-Model Yukawa couplings, which induce flavour-sensitive scattering processes and thermal dispersion relations. Kinetic equilibrium, which is rapidly established and maintained via gauge interactions, allows to simplify these equations to kinetic equations for the matrix of lepton charge densities. In performing this simplification, we notice that the rapid flavour-blind gauge interactions damp the flavour oscillations of the leptons. Leptogenesis turns out to be in the parametric regime where the flavour oscillations are overdamped and flavour decoherence is mainly induced by flavour sensitive scatterings. We solve the kinetic equations for the lepton number densities numerically and show that they interpolate between the unflavoured and the fully flavoured regimes within the intermediate parametric region, where neither of these limits is applicable.     

过阻尼谐振子的随机共振

研究了由交叉相关高斯白噪声驱动的过阻尼谐振子的随机共振,其中加法噪声被周期信号所调制,运用平稳关联函数的傅里叶变换,导出了过阻尼谐振子随机模型信噪比的精确表达式.结果揭示:在过阻尼谐振子的随机模型中存在二类随机共振.一类随机共振表现为信噪比随乘法噪声强度Q变化的曲线存在共振峰,另一类随机共振表现为信噪比随振子频率ω变化的曲线存在共振峰.大幅度改变信号频率Ω值的大小,信噪比随乘法噪声强度Q变化的曲线有单峰,一峰一谷和单调变化三种不同的形式.     

Analytical results of the Fokker-Planck equation derived for one superconducting nanowire quantum interference device and for DC SQUIDs-asymmetric devices

We consider an asymmetric two-junction superconducting quantum interference device, whose junctions are assumed to be overdamped, and regard Sin Fourier series for their current-phase relations. We take into account the effects of thermal fluctuations by forming a two-dimensional Fokker-Planck equation for the distribution function. We judge a series expansion of first order with respect to the components of the reduced inductance for distribution function and obtain current-voltage relation. We consider the measured resistance of the superconducting nanowire quantum interference device with mesoscopic leads that Hopkins et al. reported in Hopkins et al. [D.S. Hopkins, D. Pekker, P.M. Goldbart, A. Bezryadin, Science 308 (2005) 1762] and analyzed in Pekker et al. [D. Pekker, A. Bezryadin, D.S. Hopkins, P.M. Goldbart, Phys. Rev. B 72 (2005) 104517], by defining loop inductance, and by considering appropriate relations for resistance of nanowires. In fact we extend Chesca formulation [B. Chesca, J. Low Temp. Phys. 112 (1998) 165] simultaneously in three aspects and give a unified theory for nanowire two-junction devices, low T_c and high T_c DC SQUIDs, in restricted conditions.     

External fluctuations in front dynamics with inertia: The overdamped limit

We study the dynamics of fronts when both inertial effects and external fluctuations are taken into account. Stochastic fluctuations are introduced as multiplicative white noise arising from a control parameter of the system. Contrary to the non-inertial (overdamped) case, we find that important features of the system, such as the velocity selection picture, are not modified by the noise. We then compute the overdamped limit of the underdamped dynamics in a more careful way, finding that it does not exhibit any effect of noise either. Our result poses the question as to whether or not external noise sources can be measured in physical systems of this kind. Received 2 July 1999 and Received in final form 25 November 1999     

Entropy Anomaly in Langevin–Kramers Dynamics with a Temperature Gradient,Matrix Drag,and Magnetic Field

Journal of Statistical Physics - We investigate entropy production in the small-mass (or overdamped) limit of Langevin–Kramers dynamics. The results generalize previous works to provide a...     

Approach to the quantum evolution for underdamped, critically damped, and overdamped driven harmonic oscillators using unitary transformation

Exact solution of the Schrödinger equation is derived for underdamped, critically damped, and overdamped harmonic oscillators with a driving force. A unitary operator transforming Hamiltonian into a simple form is introduced. The transformed Hamiltonian, represented in terms of a modified frequency ω, is identical with the Hamiltonian of the standard harmonic oscillator for the underdamped oscillator, with the Hamiltonian of a free particle for the critically damped oscillator, and with the Hamiltonian of a system with a harmonic parabolic potential for the overdamped oscillator. The eigenvalues of underdamped oscillator are discrete while those of the critically damped and the overdamped oscillators are continuous.     

Gaussian models for the distribution of Brownian particles in tilted periodic potentials The limit of high barriers

We present two Gaussian approximations for the time-dependent probability density function (PDF) of an overdamped Brownian particle moving in a tilted periodic potential. We assume high potential barriers in comparison with the noise intensity. The accuracy of the proposed approximated expressions for the time-dependent PDF is checked with numerical simulations of the Langevin dynamics. We found a quite good agreement between theoretical and numerical results at all times.     

Charged Brownian particles: Kramers and Smoluchowski equations and the hydrothermodynamical picture

We consider a charged Brownian gas under the influence of external and non-uniform electric, magnetic and mechanical fields, immersed in a non-uniform bath temperature. With the collision time as an expansion parameter, we study the solution to the associated Kramers equation, including a linear reactive term. To the first order we obtain the asymptotic (overdamped) regime, governed by transport equations, namely: for the particle density, a Smoluchowski-reactive like equation; for the particle’s momentum density, a generalized Ohm’s-like equation; and for the particle’s energy density, a Maxwell-Cattaneo-like equation. Defining a nonequilibrium temperature as the mean kinetic energy density, and introducing Boltzmann’s entropy density via the one particle distribution function, we present a complete thermohydrodynamical picture for a charged Brownian gas. We probe the validity of the local equilibrium approximation, Onsager relations, variational principles associated to the entropy production, and apply our results to: carrier transport in semiconductors, hot carriers and Brownian motors. Finally, we outline a method to incorporate non-linear reactive kinetics and a mean field approach to interacting Brownian particles.     

Novel vibrational resonance in multistable systems

We investigate the role of multistable states on the occurrence of vibrational resonance in a periodic potential system driven by both a low-frequency and a high-frequency periodic force in both underdamped and overdamped limits. In both cases, when the amplitude of the high-frequency force is varied, the response amplitude at the low-frequency exhibits a series of resonance peaks and approaches a limiting value. Using a theoretical approach, we analyse the mechanism of multiresonance in terms of the resonant frequency and the stability of the equilibrium points of the equation of motion of the slow variable. In the overdamped system, the response amplitude is always higher than in the absence of the high-frequency force. However, in the underdamped system, this happens only if the low-frequency is less than 1. In the underdamped system, the response amplitude is maximum when the equilibrium point around which slow oscillations take place is maximally stable and minimum at the transcritical bifurcation. And in the overdamped system, it is maximum at the transcritical bifurcation and minimum when the associated equilibrium point is maximally stable. When the periodicity of the potential is truncated, the system displays only a few resonance peaks.     

Metamagnetic quantum criticality in metals

We present a renormalization group treatment of metamagnetic quantum criticality in metals. We show that for clean systems the universality class is that of the overdamped, conserving (dynamical exponent z = 3) Ising type. We obtain detailed results for the field and temperature dependence of physical quantities including the differential susceptibility, resistivity, and specific heat. Our results are shown to be in quantitative agreement with data on Sr3Ru2O7 except very near to the critical point itself.     

Alternative Simulating Technique for Periodic Motion in the Presence of Multiplicative White Noise

An effective approach for simulating the periodic motion of an overdamped particle subjected to a multiplicative white-noise source is described. The accurate calculations for the velocity of the particle and its correlation function can be realized by introducing an inertial term. The results show that fluctuation around a time-averaged quantity increases with decreasing time step in the overdamped white-noise algorithm, however, a massive white-noise technique greatly reduces this spurious drift. In particular, the present algorithm converges on the correct values of the calculated quantities, while the mass of the particle approaches to zero.     

Thermodynamics of a colloidal particle in a time-dependent nonharmonic potential

We study the motion of an overdamped colloidal particle in a time-dependent nonharmonic potential. We demonstrate the first lawlike balance between applied work, exchanged heat, and internal energy on the level of a single trajectory. The observed distribution of applied work is distinctly non-Gaussian in good agreement with numerical calculations. Both the Jarzynski relation and a detailed fluctuation theorem are verified with good accuracy.     

Limits of the nuclear viscosity coefficient in the liquid-drop model

We estimate the upper and lower limits of the nuclear viscosity coefficient within the framework of the liquid-drop model. In addition, we find that there is a critical fissility parameter above which all quadrupole vibrations are overdamped even at T≈0     

Rectification and phase locking for particles on symmetric two-dimensional periodic substrates

We demonstrate a rectification phenomenon for overdamped particles interacting with a 2D symmetric periodic substrate when driven with a dc and a circular ac drive. As a function of longitudinal dc amplitude, the longitudinal velocity increases in a series of quantized steps distinct from Shapiro steps with transverse rectification occurring near these transitions. The rectification phenomenon is explained using symmetry arguments and a simple model.