SEARCH · Searcharxiv
Search indexed arXiv papers on artificial intelligence, large language models, computer vision and robotics. Read source abstracts and follow links to arXiv.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
We propose a protein model based on a hierarchy of constraints that force the protein to follow certain pathways when changing conformation. The model exhibits a first order phase transition, cooperativity and is exactly solvable. It also shows an unexpected symmetry between folding and unfolding pathways as suggested by a recent experiment.
We propose a scheme for the calculation from the NS equations of the scaling exponents $ζ_n$ of the $n$th order correlators in fully developed hydrodynamic turbulence. The scheme is nonperturbative and constructed to respect the fundamental rescaling symmetry of the Euler equation. It constitutes an infinite hierarchy of coupled equations that are obeyed identically with respect to scaling for any set of $ζ_n$. As a consequence $ζ_n$ are determined by solvability conditions and not from power counting. It is arguedthat in order to achieve such a formulation one must recognize that the many-point space-time correlators are not scale invariant in time arguments. The assumption of full scale invariance leads unavoidably to K41 exponents. It is argued the determination of of $ζ_n$ requires equations for infinitely many renormalized objects. One ca n however proceed in controlled successive approximations by truncations of the infinite hierarchy of equations. Clues as to how to truncate without reintroducing power counting can be obtained from renormalized perturbation theory. To this aim we show that the fully resummed perturbation theory is equivalent in its contents to the exact hierarchy of equations obeyed by the $n$th order correlators and Green's function. In light of this important result we can safely use finite resummations to construct successive closures. This paper presents the conceptual and technical details of the scheme. The analysis of the high-order closure procedures which do not destroy the rescaling symmetry and the actual calculations for truncated models will be presented in a forthcoming paper in collaboration with V. Belinicher.
For ergodic adiabatic quantum systems, we study the evolution of energy distribution as the system evolves in time. Starting from the von Neumann equation for the density operator, we obtain the quantum analogue of the Smoluchowski equation on coarse-graining over the energy spectrum. This result brings out the precise notion of quantum diffusion.
We propose a conjecture for the exact expression of the dynamical zeta function for a family of birational transformations of two variables, depending on two parameters. This conjectured function is a simple rational expression with integer coefficients. This yields an algebraic value for the topological entropy. Furthermore the generating function for the Arnold complexity is also conjectured to be a rational expression with integer coefficients with the same singularities as for the dynamical zeta function. This leads, at least in this example, to an equality between the Arnold complexity and the exponential of the topological entropy. We also give a semi-numerical method to effectively compute the Arnold complexity.
It is argued that the evolution of complex phenomena ought to be described by fractional, differential, stochastic equations whose solutions have scaling properties and are therefore random, fractal functions. To support this argument we demonstrate that the fractional derivative (integral) of a generalized Weierstrass function (GWF) is another fractal function with a greater (lesser) fractal dimension. We also determine that the GWF is a solution to such a fractional differential stochastic equation of motion.
Symbolic sequences with long-range correlations are expected to result in a slow regression to a steady state of entropy increase. However, we prove that also in this case a fast transition to a constant rate of entropy increase can be obtained, provided that the extensive entropy of Tsallis with entropic index q is adopted, thereby resulting in a new form of entropy that we shall refer to as Kolmogorov-Sinai-Tsallis (KST) entropy. We assume that the same symbols, either 1 or -1, are repeated in strings of length l, with the probability distribution p(l) proportional to 1/(l^mu). The numerical evaluation of the KST entropy suggests that at the value mu = 2 a sort of abrupt transition might occur. For the values of mu in the range 1 diverges, thereby breaking the balance between determinism and randomness in favor of determinism. In the region mu > 2 the entropic index q seems to depend on mu through the power law expression q = (mu-2)^(alpha) with alpha approximately 0.13 (q = 1 with mu > 3). It is argued that this phase-transition like property signals the onset of the thermodynamical regime at mu = 2.
The linear super-Burnett coefficient gives corrections to the diffusion equation in the form of higher derivatives of the density. Like the diffusion coefficient, it can be expressed in terms of integrals of correlation functions, but involving four different times. The power law decay of correlations in real gases (with many moving particles) and the random Lorentz gas (with one moving particle and fixed scatterers) are expected to cause the super-Burnett coefficient to diverge in most cases. Here we show that the expression for the super-Burnett coefficient of the periodic Lorentz gas converges as a result of exponential decay of correlations and a nontrivial cancellation of divergent contributions.
The dynamics of a spheroidal vesicle, bounded by an inextensible membrane, is analyzed in function of the enclosed fluid viscosity, and of the membrane mechanical properties. The two situations in which a bending rigidity and a shear elasticity are the potential energy source in the membrane have been compared, and the stability properties of quasi-spherical vesicle shapes discussed. The transition from tank-treading to flipping motion in an external shear flow, has been studied in function of the vesicle internal viscosity and of the strength of the shear quadratic component. The transverse lift strength has been calculated in both cases of a tank-treading and of a flipping motion regime.
A dynamical systems scenario for developmental cell biology is proposed, based on numerical studies of a system with interacting units with internal dynamics and reproduction. Diversification, formation of discrete and recursive types, and rules for differentiation are found as a natural consequence of such a system. "Stem cells" that either proliferate or differentiate to different types stochastically are found to appear when intra-cellular dynamics are chaotic. Robustness of the developmental process against microscopic and macroscopic perturbations is shown to be a natural consequence of such intra-inter dynamics, while irreversibility in developmental process is discussed in terms of the gain of stability, loss of diversity and chaotic instability.
We discuss recent results obtained for the Hamiltonian Mean Field model. The model describes a system of N fully-coupled particles in one dimension and shows a second-order phase transition from a clustered phase to a homogeneous one when the energy is increased. Strong chaos is found in correspondence to the critical point on top of a weak chaotic regime which characterizes the motion at low energies. For a small region around the critical point, we find anomalous (enhanced) diffusion and Lévy walks in a transient temporal regime before the system relaxes to equilibrium.
A new conformal field theory description of two-dimensional turbulence is proposed. The recently established class of rational logarithmic conformal field theories provides a unique candidate solution which resolves many of the drawbacks of former approaches via minimal models. This new model automatically includes magneto-hydrodynamic turbulence and the Alf'ven effect.
We review the application of random matrix theory (RMT) to chiral symmetry in QCD. Starting from the general philosophy of RMT we introduce a chiral random matrix model with the global symmetries of QCD. Exact results are obtained for universal properties of the Dirac spectrum: i) finite volume corrections to valence quark mass dependence of the chiral condensate, and ii) microscopic fluctuations of Dirac spectra. Comparisons with lattice QCD simulations are made. Most notably, the variance of the number of levels in an interval containing $n$ levels on average is suppressed by a factor $(\log n)/π^2 n$. An extension of the random matrix model model to nonzero temperatures and chemical potential provides us with a schematic model of the chiral phase transition. In particular, this elucidates the nature of the quenched approximation at nonzero chemical potential.
We review the status of the semiclassical trace formula with emphasis on the particular types of singularities that occur in the Gutzwiller-Voros zeta function for bound chaotic systems. To understand the problem better we extend the discussion to include various classical zeta functions and we contrast properties of axiom-A scattering systems with those of typical bound systems. Singularities in classical zeta functions contain topological and dynamical information, concerning e.g. anomalous diffusion, phase transitions among generalized Lyapunov exponents, power law decay of correlations. Singularities in semiclassical zeta functions are artifacts and enters because one neglects some quantum effects when deriving them, typically by making saddle point approximation when the saddle points are not enough separated. The discussion is exemplified by the Sinai billiard where intermittent orbits associated with neutral orbits induce a branch point in the zeta functions. This singularity is responsible for a diverging diffusion constant in Lorentz gases with unbounded horizon. In the semiclassical case there is interference between neutral orbits and intermittent orbits. The Gutzwiller-Voros zeta function exhibit a branch point because it does not take this effect into account. Another consequence is that individual states, high up in the spectrum, cannot be resolved by Berry-Keating technique.
In pseudo integrable systems diffractive scattering caused by wedges and impurities can be described within the framework of Geometric Theory of Diffraction (GDT) in a way similar to the one used in the Periodic Orbit Theory of Diffraction (POTD). We derive formulas expressing the reflection and transition matrix elements for one and many diffractive points and apply it for impurity and wedge diffraction. Diffraction can cause backscattering in situations, where usual semiclassical backscattering is absent causing an erodation of ideal conductance steps. The length of diffractive periodic orbits and diffractive loops can be detected in the power spectrum of the reflection matrix elements. The tail of the power spectrum shows $\sim 1/l^{1/2}$ decay due to impurity scattering and $\sim 1/l^{3/2}$ decay due to wedge scattering. We think this is a universal sign of the presence of diffractive scattering in pseudo integrable waveguides.
The microscopic origin of dissipation of a driven quantum many body system is addressed in the framework of a parametric banded random matrix approach. We find noticeable violations of the fluctuation-dissipation theorem and we observe also that the energy diffusion has a markedly non-Gaussian character. Within the Feynman-Vernon path integral formalism and in the Markovian limit, we further consider the time evolution of a slow subsystem coupled to such a ``bath'' of intrinsic degrees of freedom. We show that dissipation leads to qualitative modifications of the time evolution of the density matrix of the slow subsystem. In either the spatial, momentum or energy representation the density distribution acquires very long tails and tunneling is greatly enhanced.
We consider a quasi one-dimensional chain of N chaotic scattering elements with periodic boundary conditions. The classical dynamics of this system is dominated by diffusion. The quantum theory, on the other hand, depends crucially on whether the chain is disordered or invariant under lattice translations. In the disordered case, the spectrum is dominated by Anderson localization whereas in the periodic case, the spectrum is arranged in bands. We investigate the special features in the spectral statistics for a periodic chain. For finite N, we define spectral form factors involving correlations both for identical and non-identical Bloch numbers. The short-time regime is treated within the semiclassical approximation, where the spectral form factor can be expressed in terms of a coarse-grained classical propagator which obeys a diffusion equation with periodic boundary conditions. In the long-time regime, the form factor decays algebraically towards an asymptotic constant. In the limit $N\to\infty$, we derive a universal scaling function for the form factor. The theory is supported by numerical results for quasi one-dimensional periodic chains of coupled Sinai billiards.
We discuss a connection (and a proper place in this framework) of the unforced and deterministically forced Burgers equation for local velocity fields of certain flows, with probabilistic solutions of the so-called Schrödinger interpolation problem. The latter allows to reconstruct the microscopic dynamics of the system from the available probability density data, or the input-output statistics in the phenomenological situations. An issue of deducing the most likely dynamics (and matter transport) scenario from the given initial and terminal probability density data, appropriate e.g. for studying chaos in terms of densities, is here exemplified in conjunction with Born's statistical interpretation postulate in quantum theory, that yields stochastic processes which are compatible with the Schrödinger picture free quantum evolution.
In our previous paper: K. Kowalski and J. Rembieliński, Groups and nonlinear dynamical systems. Dynamics on the SU(2) group, Physica D 99, 237 (1996), we introduced an abstract Newton-like equation on a general Lie algebra such that submanifolds fixed by the second-order Casimir operator are attracting set. The corresponding group parameters satisfy the nonlinear dynamical system having an attractor coinciding with the submanifold. In this work we discuss the case with the $SU(2)\times SU(2)$ group. The resulting second-order system in $R^6$ is demonstrated to exhibit chaotic behaviour.