共查询到20条相似文献,搜索用时 31 毫秒
1.
We show numerical experiments of driven billiards using special relativity. We have the remarkable fact that for the relativistic driven circular and annular concentric billiards, depending on initial conditions and parameters, we observe Fermi Acceleration, absent in the Newtonian case. The velocity for these cases tends to the speed of light very quickly. We find that for the annular eccentric billiard the initial velocity grows for a much longer time than the concentric annular billiard until it asymptotically reach c. 相似文献
2.
Generalized billiards describe nonequilibrium gas, consisting of finitely many particles, that move in a container, whose
walls heat up or cool down. Generalized billiards can be considered both in the framework of the Newtonian mechanics and of
the relativity theory. In the Newtonian case, a generalized billiard may possess an invariant measure; the Gibbs entropy with
respect to this measure is constant. On the contrary, generalized relativistic billiards are always dissipative,and the Gibbs
entropy with respect to the same measure grows under some natural conditions.
In this article, we find the necessary and sufficient conditions for a generalized Newtonian billiard to possess a smooth
invariant measure, which is independent of the boundary action: the corresponding classical billiard should have an additional
first integral of special type. In particular,the generalized Sinai billiards do not possess a smooth invariant measure. We
then consider generalized billiards inside a ball, which is one of the main examples of the Newtonian generalized billiards
which does have an invariant measure. We construct explicitly the invariant measure, and find the conditions for the Gibbs
entropy growth for the corresponding relativistic billiard both formonotone and periodic action of the boundary. 相似文献
3.
4.
S Rajasekar 《Pramana》1995,44(2):121-131
In this paper we investigate numerically the possibility of conversion of a chaotic attractor into a nonchaotic but strange
attractor in both a discrete system (an one dimensional map) and in a continuous dynamical system — Bonhoeffer—van der Pol
oscillator. In these systems we show suppression of chaotic property, namely, the sensitive dependence on initial states,
by adding appropriate i) chaotic signal and ii) Gaussian white noise. The controlled orbit is found to be strange but nonchaotic
with largest Lyapunov exponent negative and noninteger correlation dimension. Return map and power spectrum are also used
to characterize the strange nonchaotic attractor. 相似文献
5.
Einstein’s relation E = Mc 2 between the energy E and the mass M is the cornerstone of the relativity theory. This relation is often derived in a context of the relativistic theory for closed systems which do not accelerate. By contrast, the Newtonian approach to the mass is based on an accelerated motion. We study here a particular neoclassical field model of a particle governed by a nonlinear Klein-Gordon (KG) field equation. We prove that if a solution to the nonlinear KG equation and its energy density concentrate at a trajectory, then this trajectory and the energy must satisfy the relativistic version of Newton’s law with the mass satisfying Einstein’s relation. Therefore the internal energy of a localized wave affects its acceleration in an external field as the inertial mass does in Newtonian mechanics. We demonstrate that the “concentration” assumptions hold for a wide class of rectilinear accelerating motions. 相似文献
6.
We consider the 3-body problem in relativistic lineal [i.e., (1+1)-dimensional] gravity and obtain an exact expression for its Hamiltonian and equations of motion. While general-relativistic effects yield more tightly bound orbits of higher frequency compared to their nonrelativistic counterparts, as energy increases we find in the equal-mass case no evidence for either global chaos or a breakdown from regular to chaotic motion, despite the high degree of nonlinearity in the system. We find numerical evidence for mild chaos and a countably infinite class of nonchaotic orbits, yielding a fractal structure in the outer regions of the Poincaré plot. 相似文献
7.
8.
Evidence is presented for the nonchaotic random behaviour in a
second-order autonomous deterministic system. This behaviour is
different from chaos and strange nonchaotic attractor. The
nonchaotic random behaviour is very sensitive to the initial
conditions. Slight difference of the initial conditions will
generate wholly different phase trajectories. This random behaviour
has a transient random nature and is very similar to the
coin-throwing case in the classical theory of probability. The
existence of the nonchaotic random behaviour not only can be derived
from the theoretical analysis, but also is proved by the results of
the simulated experiments in this paper. 相似文献
9.
Angelo Armenti Jr 《International Journal of Theoretical Physics》1977,16(11):813-827
In a previous paper, a class of exact geodesics for the motion of a particle in a gravitational-monopole-prolate-quadrupole field was investigated, both in Newtonian mechanics and in general relativity. This paper consists of both an amplification of the analysis contained in the previous paper and an extension of the analysis to the case for negative quadrupole moment, which was not treated previously. The relativistic results are based on the monopole-quadrupole metric of Erez and Rosen, the Newtonian results on the monopole-quadrupole potential of Laplace. In the limit of vanishing quadrupole parameter (q 0), the relativistic results reduce to those of the familiar Schwarzschild case; in the weak-field limit (r/m ), the relativistic results reduce to those of the Newtonian case. The existence and stability thresholds in the relativistic case yield values that uniquely characterize the Erez-Rosen metric. 相似文献
10.
We study classical and quantum dynamics of a kicked relativistic particle confined in a one dimensional box. It is found that in classical case for chaotic motion the average kinetic energy grows in time, while for mixed regime the growth is suppressed. However, in case of regular motion energy fluctuates around certain value. Quantum dynamics is treated by solving the time-dependent Dirac equation with delta-kicking potential, whose exact solution is obtained for single kicking period. In quantum case, depending on the values of the kicking parameters, the average kinetic energy can be quasi periodic, or fluctuating around some value. Particle transport is studied by considering spatio-temporal evolution of the Gaussian wave packet and by analyzing the trembling motion. 相似文献
11.
In relativistic mechanics the energy-momentum of a free point mass moving without acceleration forms a four-vector. Einstein’s
celebrated energy-mass relation E=mc
2 is commonly derived from that fact. By contrast, in Newtonian mechanics the mass is introduced for an accelerated motion
as a measure of inertia. In this paper we rigorously derive the relativistic point mechanics and Einstein’s energy-mass relation
using our recently introduced neoclassical field theory where a charge is not a point but a distribution. We show that both
the approaches to the definition of mass are complementary within the framework of our field theory. This theory also predicts
a small difference between the electron rest mass relevant to the Penning trap experiments and its mass relevant to spectroscopic
measurements. 相似文献
12.
《Physics letters. A》2006,354(4):298-304
Usually, phase synchronization is studied in chaotic systems driven by either periodic force or chaotic force. In the present work, we consider frequency locking in chaotic Rössler oscillator by a special driving force from a dynamical system with a strange nonchaotic attractor. In this case, a transition from generalized marginal synchronization to frequency locking is observed. We investigate the bifurcation of the dynamical system and explain why generalized marginal synchronization can occur in this model. 相似文献
13.
Donald Greenspan 《International Journal of Theoretical Physics》1982,21(6-7):505-523
Completely arithmetic formulations, which possess exactly the same conservation laws and symmetry as their continuum counterparts,
are given for both Newtonian and special relativistic mechanics. Applications are made to new models of fluid flow, vibration,
diffusion, planetary evolution, biological self-reorganization, and relativistic oscillation. Computer examples are described
and discussed. 相似文献
14.
Dynamical systems with invariant manifolds occur in a variety of situations (e.g., identical coupled oscillators, and systems with a symmetry). We consider the case where there is both a nonchaotic attractor (e.g., a periodic orbit) and a nonattracting chaotic set (or chaotic repeller) in the invariant manifold. We consider the character of the basins for the attracting nonchaotic set in the invariant manifold and another attractor not in the invariant manifold. It is found that the boundary separating these basins has an interesting structure: The basin of the attractor not in the invariant manifold is characterized by thin cusp shaped regions ("stalactites") extending down to touch the nonattracting chaotic set in the invariant manifold. We also develop theoretical scalings applicable to these systems, and compare with numerical experiments. (c) 2000 American Institute of Physics. 相似文献
15.
Andrei N. Soklakov 《Foundations of Physics Letters》2002,15(2):107-135
We introduce the principle of Occam's Razor in a form that can be used as a basis for economical formulations of physics. This allows us to explain the general structure of the Lagrangian for a composite physical system, as well as some other artificial postulates behind the variational formulations of physical laws. As an example, we derive Hamilton's principle of stationary action together with the Lagrangians for the cases of Newtonian mechanics, relativistic mechanics and a relativistic particle in an external gravitational field. 相似文献
16.
Timothy J. Hollowood 《Contemporary Physics》2016,57(3):289-308
In our quantum mechanics courses, measurement is usually taught in passing, as an ad-hoc procedure involving the ugly collapse of the wave function. No wonder we search for more satisfying alternatives to the Copenhagen interpretation. But this overlooks the fact that the approach fits very well with modern measurement theory with its notions of the conditioned state and quantum trajectory. In addition, what we know of as the Copenhagen interpretation is a later 1950s development and some of the earlier pioneers like Bohr did not talk of wave function collapse. In fact, if one takes these earlier ideas and mixes them with later insights of decoherence, a much more satisfying version of Copenhagen quantum mechanics emerges, one for which the collapse of the wave function is seen to be a harmless book keeping device. Along the way, we explain why chaotic systems lead to wave functions that spread out quickly on macroscopic scales implying that Schrödinger cat states are the norm rather than curiosities generated in physicists’ laboratories. We then describe how the conditioned state of a quantum system depends crucially on how the system is monitored illustrating this with the example of a decaying atom monitored with a time of arrival photon detector, leading to Bohr’s quantum jumps. On the other hand, other kinds of detection lead to much smoother behaviour, providing yet another example of complementarity. Finally we explain how classical behaviour emerges, including classical mechanics but also thermodynamics. 相似文献
17.
We consider situations where, in a continuous-time dynamical system, a nonchaotic attractor coexists with a nonattracting chaotic saddle, as in a periodic window. Under the influence of noise, chaos can arise. We investigate the fundamental dynamical mechanism responsible for the transition and obtain a general scaling law for the largest Lyapunov exponent. A striking finding is that the topology of the flow is fundamentally disturbed after the onset of noisy chaos, and we point out that such a disturbance is due to changes in the number of unstable eigendirections along a continuous trajectory under the influence of noise. 相似文献
18.
We establish rigorous results about the Newtonian limit of general relativity by applying to it the theory of different time scales for non-linear partial differential equations as developed in [4, 1, 8]. Roughly speaking, we obtain a priori estimates for solutions to the Einstein's equations, an intermediate, but fundamental, step to show that given a Newtonian solution there exist continuous one-parameter families of solutions to the full Einstein's equations — the parameter being the inverse of the speed of light — which for a finite amount of time are close to the Newtonian solution. These one-parameter families are chosen via aninitialization procedure applied to the initial data for the general relativistic solutions. This procedure allows one to choose the initial data in such a way as to obtain a relativistic solution close to the Newtonian solution in any a priori given Sobolev norm. In some intuitive sense these relativistic solutions, by being close to the Newtonian one, have little extra radiation content (although, actually, this should be so only in the case of the characteristic initial data formulation along future directed light cones).Our results are local, in the sense that they do not include the treatment of asymptotic regions; global results are admittedly very important — in particular they would say how differentiable the solutions are with respect to the parameter — but their treatment would involve the handling of tools even more technical than the ones used here. On the other hand, this local theory is all that is needed for most problems of practical numerical computation. 相似文献
19.
Solomon L. Schwebel 《International Journal of Theoretical Physics》1970,3(2):145-152
The union of Mach's principle and Newtonian mechanics gives rise to Relational Mechanics. We find that the characteristics
of the revised mechanics are: (1) freedom from any reference to absolute space; (2) the identity of inertial and gravitational
mass; (3) the relative acceleration of a body in a gravitational field dependent on the mass of the body. All these results
are valid in the context of a Newtonian mechanics which is being developed in the center-of-mass system of all the particles.
The conservation of linear momentum, energy, angular momentum are expressed in relational terms, i.e., no reference is made
to absolute space. Relational Mechanics is a classical relativistic theory which can be formulated to satisfy Einsteinian
relativistic requirements. The Hamiltonian formalism for Relational Mechanics is discussed.
Preliminary report Bull. Am. Phys. Soc.14, 15 (1969) 相似文献
20.
William C. Davidon 《Foundations of Physics》1975,5(3):525-542
The usual macroscopic theory of relativistic mechanics and electromagnetism is formulated so that all assumptions but one are consistent with both special relativity and Newtonian mechanics, the distinguishing assumption being that to any energyE, whatever its form, there corresponds an inertial massE/c
2
. The speed of light enters this formulation only as a consequence of the inertial equivalent of energy1/c
2
. While, for1/c
2
>0 the resulting theory has symmetry under the Poincaré group, including Lorentz transformations, all its physical consequences can be derived and tested in any one inertial frame. In particular, an account is given in one inertial frame for the dynamic causes of relativistic effects for simple accelerated clocks and roads. 相似文献