Showing papers on "Conservation law published in 2013"
TL;DR: It is argued that the many-body localization can be used to protect coherence in the system by suppressing relaxation between eigenstates with different local integrals of motion.
Abstract: We construct a complete set of local integrals of motion that characterize the many-body localized (MBL) phase. Our approach relies on the assumption that local perturbations act locally on the eigenstates in the MBL phase, which is supported by numerical simulations of the random-field $XXZ$ spin chain. We describe the structure of the eigenstates in the MBL phase and discuss the implications of local conservation laws for its nonequilibrium quantum dynamics. We argue that the many-body localization can be used to protect coherence in the system by suppressing relaxation between eigenstates with different local integrals of motion.
804 citations
TL;DR: The dual symmetry between electric and magnetic fields is an important intrinsic property of Maxwell equations in free space as mentioned in this paper, which underlies the conservation of optical helicity and is closely related to the separation of spin and orbital degrees of freedom of light.
Abstract: The dual symmetry between electric and magnetic fields is an important intrinsic property of Maxwell equations in free space. This symmetry underlies the conservation of optical helicity and, as we show here, is closely related to the separation of spin and orbital degrees of freedom of light (the helicity flux coincides with the spin angular momentum). However, in the standard field-theory formulation of electromagnetism, the field Lagrangian is not dual symmetric. This leads to problematic dual-asymmetric forms of the canonical energy–momentum, spin and orbital angular-momentum tensors. Moreover, we show that the components of these tensors conflict with the helicity and energy conservation laws. To resolve this discrepancy between the symmetries of the Lagrangian and Maxwell equations, we put forward a dual-symmetric Lagrangian formulation of classical electromagnetism. This dual electromagnetism preserves the form of Maxwell equations, yields meaningful canonical energy–momentum and angular-momentum tensors, and ensures a self-consistent separation of the spin and orbital degrees of freedom. This provides a rigorous derivation of the results suggested in other recent approaches. We make the Noether analysis of the dual symmetry and all the Poincare symmetries, examine both local and integral conserved quantities and show that only the dual electromagnetism naturally produces a complete self-consistent set of conservation laws. We also discuss the observability of physical quantities distinguishing the standard and dual theories, as well as relations to quantum weak measurements and various optical experiments.
329 citations
TL;DR: A dynamical real space renormalization group approach to describe the time evolution of a random spin-1/2 chain, or interacting fermions, initialized in a state with fixed particle positions identifies a many-body localized state of the chain as a dynamical infinite randomness fixed point, which become asymptotically exact conservation laws at the fixed point.
Abstract: We formulate a dynamical real space renormalization group (RG) approach to describe the time evolution of a random spin-$1/2$ chain, or interacting fermions, initialized in a state with fixed particle positions. Within this approach we identify a many-body localized state of the chain as a dynamical infinite randomness fixed point. Near this fixed point our method becomes asymptotically exact, allowing analytic calculation of time dependent quantities. In particular, we explain the striking universal features in the growth of the entanglement seen in recent numerical simulations: unbounded logarithmic growth delayed by a time inversely proportional to the interaction strength. This is in striking contrast to the much slower entropy growth as $\mathrm{log} \mathrm{log} t$ found for noninteracting fermions with bond disorder. Nonetheless, even the interacting system does not thermalize in the long time limit. We attribute this to an infinite set of approximate integrals of motion revealed in the course of the RG flow, which become asymptotically exact conservation laws at the fixed point. Hence we identify the many-body localized state with an emergent generalized Gibbs ensemble.
317 citations
TL;DR: A comparison technique is used to derive a new Entropy Stable Weighted Essentially Non-Oscillatory (SSWENO) finite difference method, appropriate for simulations of problems with shocks.
286 citations
TL;DR: In this article, a nonlinear version of fluctuating hydrodynamics is developed, in which the Euler currents are kept to second order in the deviations from equilibrium and dissipation plus noise are added.
Abstract: With focus on anharmonic chains, we develop a nonlinear version of fluctuating hydrodynamics, in which the Euler currents are kept to second order in the deviations from equilibrium and dissipation plus noise are added. The required model-dependent parameters are written in such a way that they can be computed numerically within seconds, once the interaction potential, pressure, and temperature are given. In principle the theory is applicable to any one-dimensional system with local conservation laws. The resulting nonlinear stochastic field theory is handled in the one-loop approximation. Some of the large scale predictions can still be worked out analytically. For more details one has to rely on numerical simulations of the corresponding mode-coupling equations. In this way we arrive at detailed predictions for the equilibrium time correlations of the locally conserved fields of an anharmonic chain.
215 citations
TL;DR: It is shown that the electromagnetic duality symmetry can be restored for the macroscopic Maxwell's equations by the presence of charges, and the restoration is shown to be independent of the geometry of the problem.
Abstract: In this Letter, we show that the electromagnetic duality symmetry, broken in the microscopic Maxwell’s equations by the presence of charges, can be restored for the macroscopic Maxwell’s equations. The restoration of this symmetry is shown to be independent of the geometry of the problem. These results provide a tool for the study of light-matter interactions within the framework of symmetries and conservation laws. We illustrate its use by determining the helicity content of the natural modes of structures possessing spatial inversion symmetries and by elucidating the root causes for some surprising effects in the scattering off magnetic spheres.
176 citations
TL;DR: A general procedure for defining a continuous family of quasilocal operators whose time derivative is supported near the two boundary sites only is outlined, resulting in improved rigorous estimates for the high temperature spin Drude weight.
Abstract: For fundamental integrable quantum chains with deformed symmetries we outline a general procedure for defining a continuous family of quasilocal operators whose time derivative is supported near the two boundary sites only. The program is implemented for a spin 1/2 XXZ chain, resulting in improved rigorous estimates for the high temperature spin Drude weight.
175 citations
TL;DR: This work proves an L2(R) maximum principle, in the form of a new “log” conservation law which is satisfied by the equation (1) for the interface, and takes advantage of the fact that the bound ‖∂xf0‖L∞ < 1 is propagated by solutions, which grants strong compactness properties in comparison to the log conservation law.
Abstract: . The Muskat problem models the dynamics of the interface between two incompressible immiscible fluids with different constant densities. In this work we prove three results. First we prove an L2(R) maximum principle, in the form of a new “log” conservation law (3) which is satisfied by the equation (1) for the interface. Our second result is a proof of global existence for unique strong solutions if the initial data is smaller than an explicitly computable constant, for instance ‖f ‖1 ≤ 1/5. Previous results of this sort used a small constant 1 which was not explicit [7, 19, 9, 14]. Lastly, we prove a global existence result for Lipschitz continuous solutions with initial data that satisfy ‖f0‖L∞ < ∞ and ‖∂xf0‖L∞ < 1. We take advantage of the fact that the bound ‖∂xf0‖L∞ < 1 is propagated by solutions, which grants strong compactness properties in comparison to the log conservation law.
167 citations
TL;DR: In this article, the Lax-Wendroff theorem states that conservation law equations that are split into linear combinations of the divergence and product rule form and then discretized using any diagonal-norm skew-symmetric summation-by-parts spatial operator yield discrete operators that are conservative.
154 citations
TL;DR: In this paper, the modification of the cumulants of the net baryon and net proton distributions due to the global conservation of Baryon number in heavy-ion collisions is discussed.
Abstract: We discuss the modification of the cumulants of the net baryon and net proton distributions due to the global conservation of baryon number in heavy-ion collisions. Corresponding probability distributions and their cumulants are derived analytically. We show that the conservation of baryon number results in a substantial decrease of higher order cumulants. Based on our studies, we propose an observable that is insensitive to the modifications due to baryon number conservation.
147 citations
TL;DR: In this paper, the fundamental scale separations present in plasma turbulence are codified as an asymptotic expansion in the ratio ϵ ǫ = ρ i/a of the gyroradius to the equilibrium scale length.
Abstract: This paper presents a complete theoretical framework for studying turbulence and transport in rapidly rotating tokamak plasmas. The fundamental scale separations present in plasma turbulence are codified as an asymptotic expansion in the ratio ϵ = ρi/a of the gyroradius to the equilibrium scale length. Proceeding order by order in this expansion, a set of coupled multiscale equations is developed. They describe an instantaneous equilibrium, the fluctuations driven by gradients in the equilibrium quantities, and the transport-timescale evolution of mean profiles of these quantities driven by the interplay between the equilibrium and the fluctuations. The equilibrium distribution functions are local Maxwellians with each flux surface rotating toroidally as a rigid body. The magnetic equilibrium is obtained from the generalized Grad–Shafranov equation for a rotating plasma, determining the magnetic flux function from the mean pressure and velocity profiles of the plasma. The slow (resistive-timescale) evolution of the magnetic field is given by an evolution equation for the safety factor q. Large-scale deviations of the distribution function from a Maxwellian are given by neoclassical theory. The fluctuations are determined by the ‘high-flow’ gyrokinetic equation, from which we derive the governing principle for gyrokinetic turbulence in tokamaks: the conservation and local (in space) cascade of the free energy of the fluctuations (i.e. there is no turbulence spreading). Transport equations for the evolution of the mean density, temperature and flow velocity profiles are derived. These transport equations show how the neoclassical and fluctuating corrections to the equilibrium Maxwellian act back upon the mean profiles through fluxes and heating. The energy and entropy conservation laws for the mean profiles are derived from the transport equations. Total energy, thermal, kinetic and magnetic, is conserved and there is no net turbulent heating. Entropy is produced by the action of fluxes flattening gradients, Ohmic heating and the equilibration of interspecies temperature differences. This equilibration is found to include both turbulent and collisional contributions. Finally, this framework is condensed, in the low-Mach-number limit, to a more concise set of equations suitable for numerical implementation.
TL;DR: A class of conservative, discontinuous Galerkin schemes for the Generalized Korteweg–de Vries equation that preserve discrete versions of the first two invariants of the solution, usually identified with the mass, and the L2–norm of the continuous solution.
Abstract: We construct, analyze and numerically validate a class of conservative, discontinuous Galerkin schemes for the Generalized Korteweg–de Vries equation. Up to round-off error, these schemes preserve discrete versions of the first two invariants (the integral of the solution, usually identified with the mass, and the L2–norm) of the continuous solution. Numerical evidence is provided indicating that these conservation properties impart the approximations with beneficial attributes, such as more faithful reproduction of the amplitude and phase of traveling–wave solutions. The numerical simulations also indicate that the discretization errors grow only linearly as a function of time.
TL;DR: In this article, the superhorizon conservation of the curvature perturbation ζ in single-field inflation was shown to hold as an operator statement and all ζ-correlators are time independent at all orders in the loop expansion.
Abstract: In this paper, we prove that the superhorizon conservation of the curvature perturbation ζ in single-field inflation holds as an operator statement. This implies that all ζ-correlators are time independent at all orders in the loop expansion. Our result follows directly from locality and diffeomorphism invariance of the underlying theory. We also explore the relationship between the conservation of ζ, the single-field consistency relation and the renormalization of composite operators.
TL;DR: The equilibrium time correlations for the conserved fields of classical anharmonic chains are studied and it is argued that their dynamic correlator can be predicted on the basis of nonlinear fluctuating hydrodynamics.
Abstract: We study the equilibrium time correlations for the conserved fields of classical anharmonic chains and argue that their dynamic correlator can be predicted on the basis of nonlinear fluctuating hydrodynamics. In fact, our scheme is more general and would also cover other one-dimensional Hamiltonian systems, for example, classical and quantum fluids. Fluctuating hydrodynamics is a nonlinear system of conservation laws with noise. For a single mode, it is equivalent to the noisy Burgers equation, for which explicit solutions are available. Our focus is the case of several modes. No exact solution has been found so far, and we rely on a one-loop approximation. The resulting mode-coupling equations have a quadratic memory kernel and describe the time evolving $3\ifmmode\times\else\texttimes\fi{}3$ correlator matrix of the locally conserved fields. Long time asymptotics is computed analytically, and finite time properties are obtained through a numerical simulation of the mode-coupling equations.
TL;DR: In this article, the authors considered the problem of continuous dependence on initial data in the case of degenerate parabolic SPDEs, stochastic hyperbolic conservation laws and SDEs with continues coefficients, and provided a new and fairly elementary proof of Skorkhod's classical theorem on existence of weak solutions.
TL;DR: In this article, an experimental and theoretical analysis of the energy exchanged between two conductors kept at different temperature and coupled by the electric thermal noise is presented. But the system is ruled by the same equations as two Brownian particles.
Abstract: We report an experimental and theoretical analysis of the energy exchanged between two conductors kept at different temperature and coupled by the electric thermal noise. Experimentally we determine, as functions of the temperature difference, the heat flux, the out-of-equilibrium variance, and a conservation law for the fluctuating entropy, which we justify theoretically. The system is ruled by the same equations as two Brownian particles kept at different temperatures and coupled by an elastic force. Our results set strong constraints on the energy exchanged between coupled nanosystems held at different temperatures.
TL;DR: A novel numerical apparatus is employed to reformulate the scalar conservation law as a flow-based partial differential equation (PDE), which is then solved semi-analytically with the Lax–Hopf formula, which allows for an efficient computational scheme for large-scale networks.
Abstract: In this paper we present a continuous-time network loading procedure based on the Lighthill–Whitham–Richards model proposed by Lighthill and Whitham, 1955 , Richards, 1956 . A system of differential algebraic equations (DAEs) is proposed for describing traffic flow propagation, travel delay and route choices. We employ a novel numerical apparatus to reformulate the scalar conservation law as a flow-based partial differential equation (PDE), which is then solved semi-analytically with the Lax–Hopf formula. This approach allows for an efficient computational scheme for large-scale networks. We embed this network loading procedure into the dynamic user equilibrium (DUE) model proposed by Friesz et al. (1993) . The DUE model is solved as a differential variational inequality (DVI) using a fixed-point algorithm. Several numerical examples of DUE on networks of varying sizes are presented, including the Sioux Falls network with a significant number of paths and origin–destination pairs (OD). The DUE model presented in this article can be formulated as a variational inequality (VI) as reported in Friesz et al. (1993) . We will present the Kuhn–Tucker (KT) conditions for that VI, which is a linear system for any given feasible solution, and use them to check whether a DUE solution has been attained. In order to solve for the KT multiplier we present a decomposition of the linear system that allows efficient computation of the dual variables. The numerical solutions of DUE obtained from fixed-point iterations will be tested against the KT conditions and validated as legitimate solutions.
TL;DR: It is proved that under suitable time step restriction for forward Euler time stepping, for general nonlinear convection-diffusion equations, the same scaling limiter coupled with second order DG methods preserves the physical bounds indicated by the initial condition while maintaining uniform second order accuracy.
TL;DR: A new theoretical framework named generalized multi-symplectic integrator for a class of nonlinear wave PDEs with small damping has two remarkable advantages: the excellent long-time numerical behavior and the good conservation property.
TL;DR: It is shown that the global maximum principle can be preserved while the high order accuracy of the underlying scheme is maintained.
Abstract: In this paper, we present a class of parametrized limiters used to achieve strict maximum principle for high order numerical schemes applied to hyperbolic conservation laws computation. By decoupling a sequence of parameters embedded in a group of explicit inequalities, the numerical fluxes are locally redefined in consistent and conservative formulation. We will show that the global maximum principle can be preserved while the high order accuracy of the underlying scheme is maintained. The parametrized limiters are less restrictive on the CFL number when applied to high order finite volume scheme. The less restrictive limiters allow for the development of the high order finite difference scheme which preserves the maximum principle. Within the proposed parametrized limiters framework, a successive sequence of limiters are designed to allow for significantly large CFL number by relaxing the limits on the intermediate values of the multistage Runge-Kutta method. Numerical results and preliminary analysis for linear and nonlinear scalar problems are presented to support the claim. The parametrized limiters are applied to the numerical fluxes directly. There is no increased complexity to apply the parametrized limiters to different kinds of monotone numerical fluxes.
TL;DR: Prosen et al. as mentioned in this paper considered one-dimensional translationally invariant quantum spin lattices and proved a Mazur-type inequality bounding the time-averaged thermodynamic limit of a finite-temperature expectation of a spatio-temporal autocorrelation function of a local observable in terms of quasi-local conservation laws with open boundary conditions.
Abstract: We consider one-dimensional translationally invariant quantum spin (or fermionic) lattices and prove a Mazur-type inequality bounding the time-averaged thermodynamic limit of a finite-temperature expectation of a spatio-temporal autocorrelation function of a local observable in terms of quasi-local conservation laws with open boundary conditions. Namely, the commutator between the Hamiltonian and the conservation law of a finite chain may result in boundary terms only. No reference to techniques used in Suzuki’s proof of Mazur bound is made (which strictly applies only to finite-size systems with exact conservation laws), but Lieb-Robinson bounds and exponential clustering theorems of quasi-local C* quantum spin algebras are invoked instead. Our result has an important application in the transport theory of quantum spin chains, in particular it provides rigorous non-trivial examples of positive finite-temperature spin Drude weight in the anisotropic Heisenberg XXZ spin 1/2 chain (Prosen, in Phys Rev Lett 106:217206, 2011).
TL;DR: In this article, the Riccati form of the Lax pair is used to construct conservation laws for nonlinear evolution equations with respect to integrability, linearization and constants of motion.
TL;DR: In this paper, a new mixed formulation is presented for the numerical analysis of fast transient dynamics phenomena in large deformations, where the linear momentum, the deformation gradient tensor and the total energy of the system are used as main conservation variables, leading to identical convergence patterns for both displacements and stresses.
TL;DR: In one dimension, the positivity-preserving property is established for both methods under a reasonable assumption, and the performance of the proposed methods, in terms of accuracy, stability andPositivity- Preserving property, is demonstrated through a set of one and two dimensional numerical experiments.
TL;DR: A scattering theory of weakly nonlinear thermoelectric transport through sub-micron scale conductors based on quantum point contacts and resonant tunneling barriers is constructed and sum rules that nonlinear transport coefficients must satisfy are derived to preserve gauge invariance and current conservation.
Abstract: We construct a scattering theory of weakly nonlinear thermoelectric transport through sub-micron scale conductors. The theory incorporates the leading nonlinear contributions in temperature and voltage biases to the charge and heat currents. Because of the finite capacitances of sub-micron scale conducting circuits, fundamental conservation laws such as gauge invariance and current conservation require special care to be preserved. We do this by extending the approach of Christen and Buttiker (1996 Europhys. Lett. 35 523) to coupled charge and heat transport. In this way we write relations connecting nonlinear transport coefficients in a manner similar to Mott’s relation between the linear thermopower and the linear conductance. We derive sum rules that nonlinear transport coefficients must satisfy to preserve gauge invariance and current conservation. We illustrate our theory by calculating the efficiency of heat engines and the coefficient of performance of thermoelectric refrigerators based on quantum point contacts and resonant tunneling barriers. We identify, in particular, rectification effects that increase device performance.
TL;DR: In this paper, an approach for linking the power spectra, bispectrum, and trispectrum to the geometric and kinematical features of multifield inflationary Lagrangians is presented.
Abstract: We develop an approach for linking the power spectra, bispectrum, and trispectrum to the geometric and kinematical features of multifield inflationary Lagrangians. Our geometric approach can also be useful in determining when a complicated multifield model can be well approximated by a model with one, two, or a handful of fields. To arrive at these results, we focus on the mode interactions in the kinematical basis, starting with the case of no sourcing and showing that there is a series of mode conservation laws analogous to the conservation law for the adiabatic mode in single-field inflation. We then treat the special case of a quadratic potential with canonical kinetic terms, showing that it produces a series of mode sourcing relations identical in form to that for the adiabatic mode. We build on this result to show that the mode sourcing relations for general multifield inflation are an extension of this special case but contain higher-order covariant derivatives of the potential and corrections from the field metric. In parallel, we show how the mode interactions depend on the geometry of the inflationary Lagrangian and on the kinematics of the associated field trajectory. Finally, we consider how the mode interactions and effective number of fields active during inflation are reflected in the spectra and introduce a multifield consistency relation, as well as a multifield observable ${\ensuremath{\beta}}_{2}$ that can potentially distinguish two-field scenarios from scenarios involving three or more effective fields.
TL;DR: In this article, the influence of melting heat transfer in stagnation point flow of Powell-Eyring fluid toward a linear stretching sheet is investigated, which is characterized by conservation laws of mass, linear momentum, and energy.
Abstract: This paper looks at the influence of melting heat transfer in stagnation point flow of Powell–Eyring fluid toward a linear stretching sheet. The mathematical modeling is characterized by conservation laws of mass, linear momentum, and energy. Appropriate similarity transformations are employed for the reduction of partial differential systems into the ordinary differential systems. Series solutions to the resulting problems are presented. Variations of embedded parameters into the derived problems are graphically illustrated. The skin-friction coefficient and the Nusselt number are computed and examined.
TL;DR: Theory of two-population lattice Boltzmann equations for thermal flow simulations is revisited, and a consistent division of the conservation laws between the two lattices is developed, and the advantage of energy conservation in the model construction is demonstrated in detail.
Abstract: Theory of two-population lattice Boltzmann equations for thermal flow simulations is revisited. The present approach makes use of a consistent division of the conservation laws between the two lattices, where mass and the momentum are conserved quantities on the first lattice, and the energy is conserved quantity of the second lattice. The theory of such a division is developed, and the advantage of energy conservation in the model construction is demonstrated in detail. The present fully local lattice Boltzmann theory is specified on the standard lattices for the simulation of thermal flows. Extension to the subgrid entropic lattice Boltzmann formulation is also given. The theory is validated with a set of standard two-dimensional simulations including planar Couette flow and natural convection in two dimensions.
TL;DR: The notion of entropy viscosity method introduced in Guermond and Pasquetti is extended to the discontinuous Galerkin framework for scalar conservation laws and the compressible Euler equations.
TL;DR: In this article, the authors considered several phenomenological models of variable Λ and G and considered the interaction between fluids with energy densities ρ1 and ρ2 assumed as Q = 3Hb(ρ1+ρ2).
Abstract: In this paper we consider several phenomenological models of variable Λ. Model of a flat Universe with variable Λ and G is accepted. It is well known, that varying G and Λ gives rise to modified field equations and modified conservation laws, which gives rise to many different manipulations and assumptions in literature. We will consider two component fluid, which parameters will enter to Λ. Interaction between fluids with energy densities ρ1 and ρ2 assumed as Q = 3Hb(ρ1+ρ2). We have numerical analyze of important cosmological parameters like EoS parameter of the composed fluid and deceleration parameter q of the model.