Flavored multiskyrmions

Static properties of multiskyrmions with baryon numbers up to 8 are calculated on the basis of the recently given rational map Ansätze. The spectra of baryonic systems with strangeness, charm, and bottom are considered within a “rigid oscillator” version of the bound state soliton model. It is suggested that the recently observed negatively charged nuclear fragment can be considered as a quantized strange multiskyrmion with B=6 or 7. In agreement with previous observations, baryonic systems with charm or bottom have a better chance of being bound by the strong interactions than do strange baryonic systems.     

Quantum heat engines, the second law and Maxwell's daemon

We introduce a class of quantum heat engines which consists of two-energy-eigenstate systems, the simplest of quantum mechanical systems, undergoing quantum adiabatic processes and energy exchanges with heat baths, respectively, at different stages of a cycle. Armed with this class of heat engines and some interpretation of heat transferred and work performed at the quantum level, we are able to clarify some important aspects of the second law of thermodynamics. In particular, it is not sufficient to have the heat source hotter than the sink, but there must be a minimum temperature difference between the hotter source and the cooler sink before any work can be extracted through the engines. The size of this minimum temperature difference is dictated by that of the energy gaps of the quantum engines involved. Our new quantum heat engines also offer a practical way, as an alternative to Szilard's engine, to physically realise Maxwell's daemon. Inspired and motivated by the Rabi oscillations, we further introduce some modifications to the quantum heat engines with single-mode cavities in order to, while respecting the second law, extract more work from the heat baths than is otherwise possible in thermal equilibria. Some of the results above are also generalisable to quantum heat engines of an infinite number of energy levels including 1-D simple harmonic oscillators and 1-D infinite square wells, or even special cases of continuous spectra.     

Heat Conduction Networks

We study networks of interacting oscillators, driven at the boundary by heat baths at possibly different temperatures. A set of first elementary questions are discussed concerning the uniqueness of a stationary possibly Gibbsian density and the nature of the entropy production and the local heat currents. We also derive a Carnot efficiency relation for the work that can be extracted from the heat engine.     

Step Density Profiles in Localized Chains

We consider two types of strongly disordered one-dimensional Hamiltonian systems coupled to baths (energy or particle reservoirs) at the boundaries: strongly disordered quantum spin chains and disordered classical harmonic oscillators. These systems are believed to exhibit localization, implying in particular that the conductivity decays exponentially in the chain length L. We ask however for the profile of the (very slowly) transported quantity in the steady state. We find that this profile is a step-function, jumping in the middle of the chain from the value set by the left bath to the value set by the right bath. This is confirmed by numerics on a disordered quantum spin chain of 9 spins and on much longer chains of harmonic oscillators. From theoretical arguments, we find that the width of the step grows not faster than \(\sqrt{L}\), and we confirm this numerically for harmonic oscillators. In this case, we also observe a drastic breakdown of local equilibrium at the step, resulting in a heavily oscillating temperature profile.     

Ergodicity and Energy Distributions for Some Boundary Driven Integrable Hamiltonian Chains

We consider systems of moving particles in 1-dimensional space interacting through energy storage sites. The ends of the systems are coupled to heat baths, and resulting steady states are studied. When the two heat baths are equal, an explicit formula for the (unique) equilibrium distribution is given. The bulk of the paper concerns nonequilibrium steady states, i.e., when the chain is coupled to two unequal heat baths. Rigorous results including ergodicity are proved. Numerical studies are carried out for two types of bath distributions. For chains driven by exponential baths, our main finding is that the system does not approach local thermodynamic equilibrium as system size tends to infinity. For bath distributions that are sharply peaked Gaussians, in spite of the near-integrable dynamics, transport properties are found to be more normal than expected.     

Nontrivial properties of heat flow: Analytical study of some anharmonic lattice microscopic models

We address the analytical investigation of nontrivial properties of heat flow, starting from microscopic models of matter. We present an integral representation for the expression of the heat flow, by taking as our crystal model a self-consistent chain of anharmonic oscillators, precisely, a chain of oscillators with harmonic interparticle interactions, anharmonic on-site potentials, thermal reservoirs at the boundaries, and still with some residual inner stochastic baths. We propose an approximative scheme to make the integral formalism analytically treatable: we test the approximations in harmonic models and analyze some anharmonic systems. For the case of graded anharmonic models with weak interparticle interactions, we derive an expression for the thermal conductivity, and show the existence of thermal rectification and also nonnegative differential thermal resistance. The details of our formalism allow us to note the ingredients behind these phenomena, and the generality of our results (i.e., the results will be valid for other interactions and regimes) shows that rectification in graded materials is a ubiquitous property.     

Phenomenological sizes of confinement regions in baryons

Standard order of magnitude estimates from QCD indicate that the radius of the quarkgluon core in the nucléon is Λ _QCD ^?1 ?1 fm. However, in work with the chiral bag model, we have found that the effective confinement size for low energy reactions can be as small as ～ 1/2 fm or smaller. This shrinking of the effective confinement size has been attributed to the pressure of the pion cloud surrounding the quark core. The concept of confinement size is evidently subtle in light-quark systems, due to the chiral vacuum structure. This is indicated by the “Cheshire Cat” phenomenon, in which physical observables tend to be insensitive to the bag radiusR. In four dimensions, no exact Cheshire Cat principle has yet been established but it is likely to involve infinitely many mesons. We suggest that when strange quarks are present, a qualitative change occurs in the Cheshire Cat picture; in particular, we propose that strangeness provides an obstruction to this picture. We present a phenomenological indication that when strange quarks are present, the bag radiusR is frozen at a value substantially larger than 0.5 fm by as much as a factor of two. Roughly speaking, the Cheshire Cat picture emerges from a near cancellation between repulsive quark kinetic and attractive pion-cloud energies in the case of the nucleon. In theΛ andΣ particles, however, replacement of one up or down quark by a strange quark removes ～ 1/N_c of the attraction from the coupling of the quarks to the pion cloud. This upsets the balance needed for the Cheshire Cat phenomenon and makes larger strange baryons more favorable energetically than the 0.5 fm ones appropriate for pureu- andd-systems. Since the above argument is crude, we appeal strongly to phenomenology. We find that magnetic moments of strange baryons favor a bag radius R?1.1 fm. We find that the excited states of theΛ-hyperons favor similarly large bag radii. Somewhat less convincingly, we argue that — due to perturbative effects — the bag radius appropriate to the Δ(1232) lies intermediate between that of the nucleon and of the strange baryons.     

Comment on the low temperature specific heat of ferroelectrics,antiferroelectrics, and related materials

Lawless has reported accurate, low temperature (2–30°K) specific heat measurements (C_Exp) of a large number of ferroelectrics, antiferroelectrics, and related materials. A plot of C_Exp T^?3 vs. T (T is temperature) reveals an “excess’ specific heat in the 10–30K range. Lawless has interpreted and fit this excess heat with an Einstein term determining the number of oscillators and the Einstein frequence for each material. He has related these large number of extra oscillators to modes observed in some Raman experiments. Using a more realistic density of states, we suggest that the experimental data can be understood in terms of straightforward harmonic lattice dynamics and that there are no extra modes. The “extra” heat capacity merely arises from the differences between the more realistic density of states and that of a Debye solid.     

Thermal energy transport in harmonic systems

One and two-dimensional oscillator systems are constructed so that individual oscillators are bound to their home positions and coupled to nearest neighbors by linear forces; both systems are treated for the case of weak coupling. The two-dimensional system has a tensor binding force that does not permit it to be decoupled into two noninteracting systems.Segments and strips are treated as thermodynamic systems in contact with a heat bath and Gaussian initial probability densities are used to compute correlations. Expressions for entropy and “temperature” are computed by relating initial system and bath variances to equilibrium temperature.Asymptotic relations for “temperature” are found that show the degree of coupling between dimensions affects the rate of approach to equilibrium, but only through the coefficient of time and not its power. Both systems approach equilibrium as t^?1 rather than $\text{t}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$ as predicted by continuum theory.     

Understanding synchronization induced by “common noise”

Noise-induced synchronization refers to the phenomenon where two uncoupled, independent nonlinear oscillators can achieve synchronization through a “common” noisy forcing. Here, “common” means identical. However, “common noise” is a construct which does not exist in practice. Noise by nature is unique and two noise signals cannot be exactly the same. How to justify and understand this central concept in noise-induced synchronization? What is the relation between noise-induced synchronization and the usual chaotic synchronization? Here we argue and demonstrate that noise-induced synchronization is closely related to generalized synchronization as characterized by the emergence of a functional relation between distinct dynamical systems through mutual interaction. We show that the same mechanism applies to the phenomenon of noise-induced (or chaos-induced) phase synchronization.     

Fourier's Law confirmed for a class of small quantum systems

Within the Lindblad formalism we consider an interacting spin chain coupled locally to heat baths. We investigate the dependence of the energy transport on the type of interaction in the system as well as on the overall interaction strength. For a large class of couplings we find a normal heat conduction and confirm Fourier's Law. In a fully quantum mechanical approach linear transport behavior appears to be generic even for small quantum systems.Received: 14 May 2003, Published online: 11 August 2003PACS: 05.60.Gg Quantum transport - 05.30.-d Quantum statistical mechanics - 05.70.Ln Nonequilibrium and irreversible thermodynamics     

Low-dimensional models of coherent structures in turbulence

For fluid flow one has a well-accepted mathematical model: the Navier-Stokes equations. Why, then, is the problem of turbulence so intractable? One major difficulty is that the equations appear insoluble in any reasonable sense. (A direct numerical simulation certainly yields a “solution”, but it provides little understanding of the process per se.) However, three developments are beginning to bear fruit: (1) The discovery, by experimental fluid mechanicians, of coherent structures in certain fully developed turbulent flows; (2) the suggestion, by Ruelle, Takens and others, that strange attractors and other ideas from dynamical systems theory might play a role in the analysis of the governing equations, and (3) the introduction of the statistical technique of Karhunen-Loève or proper orthogonal decomposition, by Lumley in the case of turbulence. Drawing on work on modeling the dynamics of coherent structures in turbulent flows done over the past ten years, and concentrating on the near-wall region of the fully developed boundary layer, we describe how these three threads can be drawn together to weave low-dimensional models which yield new qualitative understanding. We focus on low wave number phenomena of turbulence generation, appealing to simple, conventional modeling of inertial range transport and energy dissipation.     

Effect of resonant-frequency mismatch on attractors

Resonant perturbations are effective for harnessing nonlinear oscillators for various applications such as controlling chaos and inducing chaos. Of physical interest is the effect of small frequency mismatch on the attractors of the underlying dynamical systems. By utilizing a prototype of nonlinear oscillators, the periodically forced Duffing oscillator and its variant, we find a phenomenon: resonant-frequency mismatch can result in attractors that are nonchaotic but are apparently strange in the sense that they possess a negative Lyapunov exponent but its information dimension measured using finite numerics assumes a fractional value. We call such attractors pseudo-strange. The transition to pesudo-strange attractors as a system parameter changes can be understood analytically by regarding the system as nonstationary and using the Melnikov function. Our results imply that pseudo-strange attractors are common in nonstationary dynamical systems.     

Fourier's law from closure equations

We sketch a rigorous derivation of Fourier's law from a system of closure equations for a nonequilibrium stationary state of a Hamiltonian system of coupled oscillators subjected to heat baths on the boundary. The local heat flux is proportional to the temperature gradient with a temperature dependent heat conductivity and the stationary temperature exhibits a nonlinear profile.     

Nonequilibrium stationary states of harmonic chains with bulk noises

We consider a chain composed of N coupled harmonic oscillators in contact with heat baths at temperature T _ℓ and T _r at sites 1 and N respectively. The oscillators are also subjected to non-momentum conserving bulk stochastic noises. These make the heat conductivity satisfy Fourier’s law. Here we describe some new results about the hydrodynamical equations for typical macroscopic energy and displacement profiles, as well as their fluctuations and large deviations, in two simple models of this type.     

Nonequilibrium steady state in open quantum systems: Influence action,stochastic equation and power balance

The existence and uniqueness of a steady state for nonequilibrium systems (NESS) is a fundamental subject and a main theme of research in statistical mechanics for decades. For Gaussian systems, such as a chain of classical harmonic oscillators connected at each end to a heat bath, and for classical anharmonic oscillators under specified conditions, definitive answers exist in the form of proven theorems. Answering this question for quantum many-body systems poses a challenge for the present. In this work we address this issue by deriving the stochastic equations for the reduced system with self-consistent backaction from the two baths, calculating the energy flow from one bath to the chain to the other bath, and exhibiting a power balance relation in the total (chain + baths) system which testifies to the existence of a NESS in this system at late times. Its insensitivity to the initial conditions of the chain corroborates to its uniqueness. The functional method we adopt here entails the use of the influence functional, the coarse-grained and stochastic effective actions, from which one can derive the stochastic equations and calculate the average values of physical variables in open quantum systems. This involves both taking the expectation values of quantum operators of the system and the distributional averages of stochastic variables stemming from the coarse-grained environment. This method though formal in appearance is compact and complete. It can also easily accommodate perturbative techniques and diagrammatic methods from field theory. Taken all together it provides a solid platform for carrying out systematic investigations into the nonequilibrium dynamics of open quantum systems and quantum thermodynamics.     

Strong interacting probes for quark gluon plasma

We discuss hadronic signals for quark gluon plasma formation in relativistic nuclear collisions utilizing a non-equilibrium model for hadronisation of the plasma state. In particular, we find that several (non-)strange antibaryon to baryon ratios may serve as a signal for a baryon-rich plasma state. The? toη ratio turns out to be not a direct signal for plasma formation due to its dependence on details of the collision dynamics and hadronisation mechanism. Finally we argue that the η′ to η ratio might be useful as a “gluonometer” in measuring the gluonic content of the matter formed in the initial stage of the collision process.     

Thermal rectification and thermal resistive phase cross over in exponential mass graded materials

Concept of the functional graded materials (FGMs) has been explored by consideringexponential mass variation along the chain of anharmonic oscillators in the study of heattransport at low dimensions. This exponential distribution of mass along the space invokesthe diffusion of phonons transport which results to temperature gradient, asymmetric heatflow, thermal rectification and cross over between positive differential thermalresistance (PDTR) and negative differential thermal resistance (NDTR) in one-dimensional(1D) exponential mass graded chain. The temperature dependence thermal rectificationachieved is 4?74% and also predicted that the thermal rectification can be controlled bytuning the higher and lower average temperature limits of two thermal reservoirs. It isalso seen that in FGMs, the thermal conductivity does not change drastically against theaverage temperature of two heat baths. The cross over between PDTR and NDTR can be tunedeither by mass ratio of one dimensional (1D) exponential mass graded anharmonic chainand/or by temperature difference between two heat baths. The figure of merit of the 1Dstructure can also be tuned by mass gradient, the higher mass gradient material will workas the potential candidate for better thermoelectric material.     

Dark Equations

Abstract

Observing the Universe, astronomers have concluded that the motion of stars can not be accounted for unless one assumes that most of the mass in the Universe is carried on by a “dark matter”, so far impervious to all attempts at being detected. There is now a similar concept of “dark energy”. I shall discuss a different subject, “dark equations”. These have never indicated that they influence anything or even exist, but if one supposes that they do exist, one can systematically discover them and study their properties, some of which turn out to be strange and others mysterious. These equations are similar in spirit to what one gets when linearizing a given system, or studies how an external linear wave interacts with a particular solution of a given system. We define and study linear extensions of dynamical systems in general, and integrable and Hamiltonian systems in particular. Systems discussed include the KdV and mKdV equations and the associated Miura maps, the Burgers hierarchy and the associated Hopf–Cole transformations, long wave equations, the Benney hierarchy, and the KP hierarchy.     

Towards information theory for q-nonextensive statistics without q-deformed distributions

In this paper we extend our recent results [P. Jizba, T. Arimitsu Physica A 340 (2004) 110] on q-nonextensive statistics with non-Tsallis entropies. In particular, we combine an axiomatics of Rényi with the q-deformed version of Khinchin axioms to obtain the entropy which accounts both for systems with embedded self-similarity and q-nonextensivity. We find that this entropy can be uniquely solved in terms of a one-parameter family of information measures. The corresponding entropy maximizer is expressible via a special function known under the name of the Lambert W-function. We analyze the corresponding “high” and “low-temperature” asymptotics and make some remarks on the possible applications.