Elimination of Fast Chaotic Degrees of Freedom: On the Accuracy of the Born Approximation

We apply standard projection operator techniques known from nonequilibrium statistical mechanics to eliminate fast chaotic degrees of freedom in a low-dimensional dynamical system. Through the usual perturbative approach we end up in second order with a stochastic system where the fast chaotic degrees of freedom are modelled by Gaussian white noise. The accuracy of the perturbation expansion is analysed in detail by the discussion of an exactly solvable model.     

Spatial Degrees of Freedom in Everett Quantum Mechanics

Stapp claims that, when spatial degrees of freedom are taken into account, Everett quantum mechanics is ambiguous due to a “core basis problem.” To examine an aspect of this claim I generalize the ideal measurement model to include translational degrees of freedom for both the measured system and the measuring apparatus. Analysis of this generalized model using the Everett interpretation in the Heisenberg picture shows that it makes unambiguous predictions for the possible results of measurements and their respective probabilities. The presence of translational degrees of freedom for the measuring apparatus affects the probabilities of measurement outcomes in the same way that a mixed state for the measured system would. Examination of a measurement scenario involving several observers illustrates the consistency of the model with perceived spatial localization of the measuring apparatus.This work was sponsored by the Air Force under Air Force Contract FA8721-05-C-0002. Opinions, interpretations, conclusions, and recommendations are those of the author and are not necessarily endorsed by the U.S. Government.     

Degrees of Freedom of a Time Series

We give a formal proof that if f is a smooth dynamics on a d-dimensional smooth manifold and is an ergodic and exact dimensional measure with Hausdorff dimension dim >d–1, then the number d of degrees of freedom of the dynamics can be recovered from the observation of an orbit. We implement, with this purpose, an algorithm based on the analysis of the microstructure of . We show how a correct estimation of d permits the computation of the Liapunov spectrum with a high accuracy avoiding the issue of the spurious exponents.     

Vibrational Dissipative Systems with Two Degrees of Freedom

Doklady Physics - Forced linear oscillations of dissipative mechanical systems with two degrees of freedom under the action of time-periodic forces are considered. The Lagrange equations are...     

Are There Thermodynamical Degrees of Freedom of Gravitation?

In discussing fundamentals of general-relativistic irreversible continuum thermodynamics, this theory is shown to be characterized by the feature that no thermodynamical degrees of freedom are ascribed to gravitation. However, accepting that black hole thermodynamics seems to oppose this harmlessness of gravitation one is called on to consider other approaches. Therefore, in brief some gravitational and thermodynamical alternatives are reviewed.     

Second Law of Thermodynamics for Macroscopic Mechanics Coupled to Thermodynamic Degrees of Freedom

Starting from and only using classical Hamiltonian dynamics, we prove the maximum work principle in a system where macroscopic dynamical degrees of freedom are intrinsically coupled to microscopic degrees of freedom. Unlike in many of the standard and recent works on the second law, the macroscopic dynamics is not governed by an external action but undergoes the back reaction of the microscopic degrees of freedom. Our theorems cover such physical situations as impact between macroscopic bodies, thermodynamic machines, and molecular motors. Our work identifies and quantifies the physical limitations on the applicability of the second law for small systems.      

On the Landau–Lifschitz Degrees of Freedom in 2-D Turbulence

We show that if the Kraichnan theory of fully developed turbulence holds, then the Landau–Lifschitz degrees of freedom is bounded (up to a logarithmic term) by G ^1/2, where G is the Grashof number.     

Quantum Nonlinear Oscillator with Two Degrees of Freedom in a Laser Field

The semiclassical dynamics of a quantum nonlinear oscillator with two degrees of freedom and anharmonicity of the fourth order in a periodic laser field is studied both analytically and numerically. In the absence of external excitation and dissipation, the equations of motion for the mean values of the coordinate and momentum operators of both degrees of freedom reduce to the equation of a onedimensional nonlinear pendulum. The general solution of this equation is written in terms of the Jacobian elliptic functions. As can be expected, the energy of the free oscillator is redistributed periodically between degrees of freedom. The periodic excitation of the nonlinear oscillator may substantially change its motion pattern. Using as an example an oscillator with two coupled vibrational degrees of freedom, it is numerically shown that the amount of laser photons absorbed depending on the parameter values and initial conditions may vary with time in a rather complex manner, including chaotic oscillations. A nonlinear oscillator is capable of manifesting bistable behavior with allowance for dissipation. The analytical condition for the origination of bistability is found. Examples of the bistable dependence of the number of quanta in the oscillator vibrational mode on the level of laser excitation are presented.     

Sound Propagation in a Particle Suspension with a Rotational Degree of Freedom

Acoustical Physics - Suspensions are often found in nature and in technological processes. Suspension particles can differ in density and compressibility from the parent medium and affect the speed...     

偏振控制器完成任意偏振态变化的最小自由度研究

偏振控制器(PC)是处理光纤中信号偏振态(SOP)的重要器件,它是偏振模色散(PMD)自适应补偿器的重要组成部分.以两种类型的商用偏振控制器为例,理论和实验证明了转变任意输入态到庞加莱(Poincaré)球上其他任何状态至少需要调整三个自由度而不是两个自由度.因此至少需要控制每一阶段的PMD补偿器中偏振控制器上的三个自由度而不是两个白由度,才能够实现完全的PMD补偿.     

Δ Degrees of Freedom in Trinuclei with the Argonne V28Q Model

The effects of explicit Δ degrees of freedom on trinuclear binding energy and structure are investigated using the Argonne V28Q Δ model. Separate dispersive effects, one- and two-Δ three-body force effects, and one- and two-Δ probabilities are determined for the triton. Some new results are also given for the Hannover and Argonne V28 Δ models, and V28Q trinuclear Δ effects are compared with those of these other models. Considerable consistency among the models is found, suggesting a coherent qualitative picture of trinuclear Δ effects. Received June 8, 1994; accepted for publication September 27, 1994     

Quantum Mechanics of Systems with a Nonenumerable Number of Degrees of Freedom

Is has been shown that the quantum theory of systems with an infinite nonenumerable number of degrees of freedom is incompatible with the assumption about the continuity of the space of indices of degrees of freedom: in this case, a discrete topology on the space of indices is required. This is illustrated by the example of field systems.     

Relational Evolution of the Degrees of Freedom of Generally Covariant Quantum Theories

We study the classical and quantum dynamics of generally covariant theories with vanishing Hamiltonian and with a finite number of degrees of freedom. In particular, the geometric meaning of the full solution of the relational evolution of the degrees of freedom is displayed, which means the determination of the total number of evolving constants of motion required. Also a method to find evolving constants is proposed. The generalized Heisenberg picture needs M time variables, as opposed to the Heisenberg picture of standard quantum mechanics where one time variable t is enough. As an application, we study the parametrized harmonic oscillator and the SL(2, R) model with one physical degree of freedom that mimics the constraint structure of general relativity where a Schrödinger equation emerges in its quantum dynamics.     

Towards the Evaluation of the Relevant Degrees of Freedom in Nonlinear Partial Differential Equations

We investigate an operator renormalization group method to extract and describe the relevant degrees of freedom in the evolution of partial differential equations. The proposed renormalization group approach is formulated as an analytical method providing the fundamental concepts of a numerical algorithm applicable to various dynamical systems. We examine dynamical scaling characteristics in the short-time and the long-time evolution regime providing only a reduced number of degrees of freedom to the evolution process.