Dissipative or just nonextensive hydrodynamics? — Nonextensive/dissipative correspondence

We argue that there is correspondence between the perfect nonextensive hydrodynamics and the usual dissipative hydrodynamics, which we call nonextensive/dissipative correspondence (NexDC). It leads to simple expression for dissipative entropy current and allows for predictions for the ratio of bulk and shear viscosities to entropy density, ζ/s and η/F.     

Statistical Physics on the Space (x, v) for Dissipative Systems and Study of an Ensemble of Harmonic Oscillators in a Weak Linear Dissipative Medium

We use the phase space position-velocity (x, v) to deal with the statistical properties of velocity dependent dynamical systems, like dissipative ones. Within this approach, we study the statistical properties of an ensemble of harmonic oscillators in a linear weak dissipative media. Using the Debye model of a crystal, we calculate at first order in the dissipative parameter the entropy, free energy, internal energy, equation of state and specific heat using the classical and quantum approaches. For the classical approach we found that the entropy, the equation of state, and the free energy depend on the dissipative parameter, but the internal energy and specific heat do not depend of it. For the quantum case, we found that all the thermodynamical quantities depend on this parameter. PACS: 05.20.Gg, 05.30.Ch, 05.20.-y, 05.30.-d     

Lower Bounds for an Integral Involving Fractional Laplacians and the Generalized Navier-Stokes Equations in Besov Spaces

When estimating solutions of dissipative partial differential equations in L^p-related spaces, we often need lower bounds for an integral involving the dissipative term. If the dissipative term is given by the usual Laplacian −Δ, lower bounds can be derived through integration by parts and embedding inequalities. However, when the Laplacian is replaced by the fractional Laplacian (−Δ)^α, the approach of integration by parts no longer applies. In this paper, we obtain lower bounds for the integral involving (−Δ)^α by combining pointwise inequalities for (−Δ)^α with Bernstein's inequalities for fractional derivatives. As an application of these lower bounds, we establish the existence and uniqueness of solutions to the generalized Navier-Stokes equations in Besov spaces. The generalized Navier-Stokes equations are the equations resulting from replacing −Δ in the Navier-Stokes equations by (−Δ)^α.     

Thermal Fields as Causal Fluids

In a previous paper we investigated a divergence-type theory (DDT) describing the dissipative interaction between a field and a fluid. In this paper we compare the macroscopic view of DDT with a microscopic special case, an O(N) scalar field to leading order in the large N approximation and its thermal fluctuations. Our aim is to compare within a simple model the two approaches.     

An imaginary potential with universal normalization for dissipative processes in heavy-ion reactions

In this work we present new coupled channel calculations with the São Paulo potential (SPP) as the bare interaction, and an imaginary potential with system and energy independent normalization that has been developed to take into account dissipative processes in heavy-ion reactions. This imaginary potential is based on high-energy nucleon interaction in nuclear medium. Our theoretical predictions for energies up to ≈100 MeV/nucleon agree very well with the experimental data for the p,n+nucleus, ¹⁶O + ²⁷Al, ¹⁶O + ⁶⁰Ni, ⁵⁸Ni + ¹²⁴Sn, and weakly bound projectile ⁷Li + ¹²⁰Sn systems.     

Nonextensive perfect hydrodynamics — a model of dissipative relativistic hydrodynamics?

We demonstrate that nonextensive perfect relativistic hydrodynamics (q-hydrodynamics) can serve as a model of the usual relativistic dissipative hydrodynamics (d-hydrodynamics) therefore facilitating considerably its applications. As an illustration, we show how using q-hydrodynamics one gets the q-dependent expressions for the dissipative entropy current and the corresponding ratios of the bulk and shear viscosities to entropy density, ζ/s and η/srespectively.      

Quantization and instability of the damped harmonic oscillator subject to a time-dependent force

We consider the one-dimensional motion of a particle immersed in a potential field U(x) under the influence of a frictional (dissipative) force linear in velocity () and a time-dependent external force (K(t)). The dissipative system subject to these forces is discussed by introducing the extended Bateman’s system, which is described by the Lagrangian: which leads to the familiar classical equations of motion for the dissipative (open) system. The equation for a variable y is the time-reversed of the x motion. We discuss the extended Bateman dual Lagrangian and Hamiltonian by setting specifically for a dual extended damped–amplified harmonic oscillator subject to the time-dependent external force. We show the method of quantizing such dissipative systems, namely the canonical quantization of the extended Bateman’s Hamiltonian ?. The Heisenberg equations of motion utilizing the quantized Hamiltonian surely lead to the equations of motion for the dissipative dynamical quantum systems, which are the quantum analog of the corresponding classical systems. To discuss the stability of the quantum dissipative system due to the influence of an external force K(t) and the dissipative force, we derived a formula for transition amplitudes of the dissipative system with the help of the perturbation analysis. The formula is specifically applied for a damped–amplified harmonic oscillator subject to the impulsive force. This formula is used to study the influence of dissipation such as the instability due to the dissipative force and/or the applied impulsive force.     

Influence of Composite Effect from Quantum Channels on Entanglement

The dynamics of entanglement between two qubits in the local damping two-sided channel and singlesided channel are compared through non-Markovian process and Markovian process. The entanglement between two qubits is found to be longer in the single-sided channel case due to the weakening of the dissipative effects. In the two-sided channel, influenced by the entanglement between qubits, the previous independent dissipative channels incline to the composite effect of the Markovian process. This composite effect results in the dissipative effect of one channel affecting the qubits in the other channel, especially inhibiting the backflow effect in the non-Markovian channel, which is disadvantageous to the entanglement maintenance between qubits. In the Markovian channel, the composite effect of the damping two-sided channels is more obvious since there is no backflow effect, thus more disadvantageous to the entanglement maintenance.     

Influence of Composite Effect from Quantum Channels on Entanglement

The dynamics of entanglement between two qubits in the local damping two-sided channel and single-sided channel are compared through non-Markovian process and Markovian process. The entanglement between two qubits is found to be longer in the single-sided channel case due to the weakening of the dissipative effects. In the two-sided channel, influenced by the entanglement between qubits, the previous independent dissipative channels incline to the composite effect of the Markovian process. This composite effect results in the dissipative effect of one channel affecting the qubits in the other channel, especially inhibiting the backflow effect in the non-Markovian channel, which is disadvantageous to the entanglement maintenance between qubits. In the Markovian channel, the composite effect of the damping two-sided channels is more obvious since there is no backflow effect, thus more disadvantageous to the entanglement maintenance.     

Existence and Regularity of Weak Solutions to the Quasi-Geostrophic Equations in the Spaces Lp or $$\dot{H}^{-1/2}$$

In this paper we study the 2D quasi-geostrophic equation with and without dissipation. We give global existence results of weak solutions for an initial data in the space L ^p or . In the dissipative case, when the initial data is in L ^p , p > 2, we give a regularity result of these solutions.     

Fusion-fission dynamics in the superheavy nucleus production

The fusion-fission reaction mechanism leading to the massive nucleus formation is studied. We investigate the superheavy nucleus formation in heavy-ion induced reactions by analysing the evaporation residue (ER) production in order to study the fusion dynamics and the decay properties of nuclei close to the stability island at Z=114. We consider the ⁶¹Ni+²⁰⁸Pb, ⁴⁸Ca+²³⁸U and ⁴⁸Ca+²⁴⁴Pu reactions that lead to the Z=110, 112 and 114 superheavy elements respectively. By using the dinuclear system (DNS) concept of the two interacting nuclei we calculate the quasifission-fusion competition in the entrance channel and the fission-evaporation competition along the de-excitation cascade of the compound nucleus. The dynamics of the entrance channel allows us to determine the beam energy window which is favorable to the fusion, while the dynamic evolution of the compound nucleus on the shell correction to the fission barrier and the dissipative effects influence the fission-evaporation competition in order to obtain the residue nuclei from the superheavy nucleus formation. We also calculate the τ _n /τ_tot ratio at each step of the de-excitation cascade of the compound nucleus and we present a systematics of τ _n /τ_tot (at first step of the cascade) for many reactions that lead to nuclei with Z=102–114.     

p Dissipative Operator

In this paper the authors prove that the generalized positive p selfadjoint (GPpS) operators in Banach space satisfy the generalized Schwarz inequality, solve the maximal dissipative extension representation of pp dissipative operators in Banach space by using the inequality and introducing the generalized indefinite inner product (GIIP) space, and apply the result to a certain type of Schrödinger operator.     

Warm Gauge-Flation with General Dissipative Coefficient

In this work, we study the effects of generalized dissipative coefficient on the slow-roll inflation driven by non-Abelian gauge field minimally coupled to gravity. The dynamics of warm intermediate and logamediate inflationary models during weak and strong dissipative regimes is analyzed. In both cases, we explore effective scalar potential, slow-roll parameters, scalar and tensor power spectra, scalar spectral index and tensor to scalar ratio under slow-roll conditions. We conclude that our gauge-flationary model with generalized dissipative coefficient remains consistent with the recent data for dissipative parameter m = 3 and m = 1 for weak and strong dissipative eras, respectively.     

Investigation of Decoherence of Superconducting Charge Qubit Entangled with the Environment

In the Born-Markov approximation, a method that calculates the energy relaxation time T ₁ and the decoherence time T ₂ of superconducting qubits is given by solving the set of Bloch-Redfield equations and considering the results of decoherence of a superconducting charge qubit. Compared to the spin-boson model, it not only contains the decoherence being caused by the dissipative environment, but also includes the decoherence being generated by the dissipative elements in a superconducting electronic circuit. Hence, it is good for studying the decoherence of superconducting qubits comprehensively.     

Bistability,autowaves and dissipative structures in semiconductor fibers with anomalous resistivity properties

This work provides a discussion of bistability conditions, switching autowave properties and emergence of dissipative structures in semiconducting fibers with anomalous positive dependence of electrical resistivity on temperature of sigmoid type, (1?+?e ^?T )^?1. An open system thermodynamics approach is utilized for the analysis of this dissipative solid-state system. The approach aims to represent the structure of the solution space of its governing equation in the form of physical phase diagrams, known as non-equilibrium phase diagrams, and two specific binary diagrams have been obtained here. One of the diagrams, where the electrical power density and ambient temperature represent external parameters, shows a wide region with dissipative structures as non-uniform steady-state temperature profiles on the fiber. The possibility of efficient external control over the dissipative structure geometry is also demonstrated.     

Fractional Dynamics of Relativistic Particle

Fractional dynamics of relativistic particle is discussed. Derivatives of fractional orders with respect to proper time describe long-term memory effects that correspond to intrinsic dissipative processes. Relativistic particle subjected to a non-potential four-force is considered as a nonholonomic system. The nonholonomic constraint in four-dimensional space-time represents the relativistic invariance by the equation for four-velocity u _μ u ^μ +c ²=0, where c is a speed of light in vacuum. In the general case, the fractional dynamics of relativistic particle is described as non-Hamiltonian and dissipative. Conditions for fractional relativistic particle to be a Hamiltonian system are considered.     

Aging phenomena in nonlinear dissipative chains

We study the energy relaxation in a one-dimensional nonlinear lattice with dissipative couplings. After thermalisation of this system, the extremities of the chain are put in contact with a zero-temperature reservoir, showing the existence of surprising quasi-stationary states with non zero energy, tough the dissipative coupling is high. This strange behavior, due to long-lived nonlinear localized modes, induces stretched exponential relaxation laws. Furthermore, we observe a strong dependence on the waiting time t_w after the quench of the two-time intermediate correlation function C(t_w+t, t_w). This function can be scaled onto a master curve, similar to the case of spin or Lennard-Jones glasses.Received: 11 February 2003, Published online: 4 August 2003PACS: 05.20.-y Classical statistical mechanics - 05.45.-a Nonlinear dynamics and nonlinear dynamical systems     

Jet spaces in modern Hamiltonian biomechanics

In this paper we propose the time-dependent Hamiltonian form of human biomechanics, as a sequel to our previous work in time-dependent Lagrangian biomechanics [1]. This is the time-dependent generalization of an ‘ordinary’ autonomous human biomechanics, in which total mechanical + biochemical energy is not conserved. In our view, this time-dependent energetic approach is much more realistic than the autonomous one. Starting with the Covariant Force Law, we first develop autonomous Hamiltonian biomechanics. Then we extend it using a powerful geometrical machinery consisting of fibre bundles and jet manifolds associated to the biomechanical configuration manifold. We derive time-dependent, dissipative, Hamiltonian equations and the fitness evolution equation for the general time-dependent human biomechanical system.     

Dissipation of a two-mode squeezed vacuum state in the single-mode amplitude damping channel

We explore how a two-mode squeezed vacuum state sechθ e^{a+b+ tanh θ} |00> evolves when it undergoes a singlemode amplitude dissipative channel with rate of decay κ. We find that in this process not only the squeezing parameter decreases, tanh θ → e^-κt tanh θ, but also the second-mode vacuum state evolves into a chaotic state exp{b⁺bln[1 - e^-2κt tanh² θ]}. The outcome state is no more a pure state, but an entangled mixed state.     

A Geometric Criterion for Positive Topological Entropy¶II: Homoclinic Tangencies

In a series of important papers [GS1,GS2] Gavrilov and Shilnikov established a topological conjugacy between a surface diffeomorphism having a dissipative hyperbolic periodic point with certain types of quadratic homoclinic tangencies and the full shift on two symbols, thus exhibiting horseshoes near a tangential homoclinic point. In this note, which should be viewed of as an addendum to [BW] we extend this result by showing that such a diffeomorphism with a one-sided isolated homoclinic tangency having any order contact, possible with infinite order contact, possesses a horseshoe near the homoclinic point. Received: 2 March 1999 / Accepted: 14 May 1999