Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userDecay of the Sinai Well in D dimensions
44
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We study the decay law of the Sinai Well in $D$ dimensions and relate the behavior of the decay law to internal distributions that characterize the dynamics of the system. We show that the long time tail of the decay is algebraic ($1/t$), irrespective of the dimension $D$.
rate research
Read More
We use the kinetic theory of gases to compute the Kolmogorov-Sinai entropy per particle for a dilute gas in equilibrium. For an equilibrium system, the KS entropy, h_KS is the sum of all of the positive Lyapunov exponents characterizing the chaotic behavior of the gas. We compute h_KS/N, where N is the number of particles in the gas. This quantity has a density expansion of the form h_KS/N = a u[-ln{tilde{n}} + b + O(tilde{n})], where u is the single-particle collision frequency and tilde{n} is the reduced number density of the gas. The theoretical values for the coefficients a and b are compared with the results of computer simulations, with excellent agreement for a, and less than satisfactory agreement for b. Possible reasons for this difference in b are discussed.
We investigate numerically parametrically driven coupled nonlinear Schrodinger equations modelling the dynamics of coupled wavefields in a periodically oscillating double-well potential. The equations describe among other things two coupled periodically-curved optical waveguides with Kerr nonlinearity or horizontally shaken Bose-Einstein condensates in a double-well magnetic trap. In particular, we study the persistence of equilibrium states of the undriven system due to the presence of the parametric drive. Using numerical continuations of periodic orbits and calculating the corresponding Floquet multipliers, we find that the drive can (de)stabilize a continuation of an equilibrium state indicated by the change of the (in)stability of the orbit. Hence, we show that parametric drives can provide a powerful control to nonlinear (optical or matter wave) field tunneling. Analytical approximations based on an averaging method are presented. Using perturbation theory the influence of the drive on the symmetry breaking bifurcation point is discussed.
We study the decay rate of the Loschmidt echo or fidelity in a chaotic system under a time-dependent perturbation $V(q,t)$ with typical strength $hbar/tau_{V}$. The perturbation represents the action of an uncontrolled environment interacting with the system, and is characterized by a correlation length $xi_0$ and a correlation time $tau_0$. For small perturbation strengths or rapid fluctuating perturbations, the Loschmidt echo decays exponentially with a rate predicted by the Fermi Golden Rule, $1/tilde{tau}= tau_{c}/tau_{V}^2$, where typically $tau_{c} sim min[tau_{0},xi_0/v]$ with $v$ the particle velocity. Whenever the rate $1/tilde{tau}$ is larger than the Lyapunov exponent of the system, a perturbation independent Lyapunov decay regime arises. We also find that by speeding up the fluctuations (while keeping the perturbation strength fixed) the fidelity decay becomes slower, and hence, one can protect the system against decoherence.
In this paper we present the equations of the evolution of the universe in $D$ spatial dimensions, as a generalization of the work of Lima citep{lima}. We discuss the Friedmann-Robertson-Walker cosmological equations in $D$ spatial dimensions for a simple fluid with equation of state $p=omega_{D}rho$. It is possible to reduce the multidimensional equations to the equation of a point particle system subject to a linear force. This force can be expressed as an oscillator equation, anti-oscillator or a free particle equation, depending on the $k$ parameter of the spatial curvature. An interesting result is the independence on the dimension $D$ in a de Sitter evolution. We also stress the generality of this procedure with a cosmological $Lambda$ term. A more interesting result is that the reduction of the dimensionality leads naturally to an accelerated expansion of the scale factor in the plane case.
We report a search for CP-violating asymmetry in B0 -> D*+- D-+ decays. The analysis employs two methods of B0 reconstruction: full and partial. In the full reconstruction method all daughter particles of the B0 are required to be detected; the partial reconstruction technique requires a fully reconstructed D- and only a slow pion from the D*+ -> D0 pi_slow+ decay. From a fit to the distribution of the time interval corresponding to the distance between two B meson decay points we calculate the CP-violating parameters and find the significance of nonzero CP asymmetry to be 2.7 standard deviations.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
