Local quantum ergodic conjecture
NASA Astrophysics Data System (ADS)
Zambrano, Eduardo; Zapfe, W. P. Karel; Ozorio de Almeida, Alfredo M.
2015-04-01
The quantum ergodic conjecture equates the Wigner function for a typical eigenstate of a classically chaotic Hamiltonian with a δ function on the energy shell. This ensures the evaluation of classical ergodic expectations of simple observables, in agreement with Shnirelman's theorem, but this putative Wigner function violates several important requirements. Consequently, we transfer the conjecture to the Fourier transform of the Wigner function, that is, the chord function. We show that all the relevant consequences of the usual conjecture require only information contained within a small (Planck) volume around the origin of the phase space of chords: translations in ordinary phase space. Loci of complete orthogonality between a given eigenstate and its nearby translation are quite elusive for the Wigner function, but our local conjecture stipulates that their pattern should be universal for ergodic eigenstates of the same Hamiltonian lying within a classically narrow energy range. Our findings are supported by numerical evidence in a Hamiltonian exhibiting soft chaos. Heavily scarred eigenstates are remarkable counter-examples of the ergodic universal pattern.
Ergodicity and mixing in quantum dynamics.
Zhang, Dongliang; Quan, H T; Wu, Biao
2016-08-01
After a brief historical review of ergodicity and mixing in dynamics, particularly in quantum dynamics, we introduce definitions of quantum ergodicity and mixing using the structure of the system's energy levels and spacings. Our definitions are consistent with the usual understanding of ergodicity and mixing. Two parameters concerning the degeneracy in energy levels and spacings are introduced. They are computed for right triangular billiards and the results indicate a very close relation between quantum ergodicity (mixing) and quantum chaos. At the end, we argue that, besides ergodicity and mixing, there may exist a third class of quantum dynamics which is characterized by a maximized entropy. PMID:27627289
NASA Astrophysics Data System (ADS)
Gnutzmann, S.; Keating, J. P.; Piotet, F.
2008-12-01
We investigate the equidistribution of the eigenfunctions on quantum graphs in the high-energy limit. Our main result is an estimate of the deviations from equidistribution for large well-connected graphs. We use an exact field-theoretic expression in terms of a variant of the supersymmetric nonlinear σ model. Our estimate is based on a saddle-point analysis of this expression and leads to a criterion for when equidistribution emerges asymptotically in the limit of large graphs. Our theory predicts a rate of convergence that is a significant refinement of previous estimates, long assumed to be valid for quantum chaotic systems, agreeing with them in some situations but not all. We discuss specific examples for which the theory is tested numerically.
Rate of quantum ergodicity in Euclidean billiards
NASA Astrophysics Data System (ADS)
Bäcker, A.; Schubert, R.; Stifter, P.
1998-05-01
For a large class of quantized ergodic flows the quantum ergodicity theorem states that almost all eigenfunctions become equidistributed in the semiclassical limit. In this work we give a short introduction to the formulation of the quantum ergodicity theorem for general observables in terms of pseudodifferential operators and show that it is equivalent to the semiclassical eigenfunction hypothesis for the Wigner function in the case of ergodic systems. Of great importance is the rate by which the quantum-mechanical expectation values of an observable tend to their mean value. This is studied numerically for three Euclidean billiards (stadium, cosine, and cardioid billiard) using up to 6000 eigenfunctions. We find that in configuration space the rate of quantum ergodicity is strongly influenced by localized eigenfunctions such as bouncing-ball modes or scarred eigenfunctions. We give a detailed discussion and explanation of these effects using a simple but powerful model. For the rate of quantum ergodicity in momentum space we observe a slower decay. We also study the suitably normalized fluctuations of the expectation values around their mean and find good agreement with a Gaussian distribution.
Random Weighted Sobolev Inequalities and Application to Quantum Ergodicity
NASA Astrophysics Data System (ADS)
Robert, Didier; Thomann, Laurent
2015-05-01
This paper is a continuation of Poiret et al. (Ann Henri Poincaré 16:651-689, 2015), where we studied a randomisation method based on the Laplacian with harmonic potential. Here we extend our previous results to the case of any polynomial and confining potential V on . We construct measures, under concentration type assumptions, on the support of which we prove optimal weighted Sobolev estimates on . This construction relies on accurate estimates on the spectral function in a non-compact configuration space. Then we prove random quantum ergodicity results without specific assumption on the classical dynamics. Finally, we prove that almost all bases of Hermite functions are quantum uniquely ergodic.
Quantum Ergodicity for Quantum Graphs without Back-Scattering
NASA Astrophysics Data System (ADS)
Brammall, Matthew; Winn, B.
2016-06-01
We give an estimate of the quantum variance for $d$-regular graphs quantised with boundary scattering matrices that prohibit back-scattering. For families of graphs that are expanders, with few short cycles, our estimate leads to quantum ergodicity for these families of graphs. Our proof is based on a uniform control of an associated random walk on the bonds of the graph. We show that recent constructions of Ramanujan graphs, and asymptotically almost surely, random $d$-regular graphs, satisfy the necessary conditions to conclude that quantum ergodicity holds.
NASA Astrophysics Data System (ADS)
Sych, Denis; Leuchs, Gerd
2015-12-01
Classical physics allows for the existence of pairs of absolutely identical systems. Pairwise application of identical measurements to each of those systems always leads to exactly alike results irrespectively of the choice of measurements. Here we ask a question how the picture looks like in the quantum domain. Surprisingly, we get a counterintuitive outcome. Pairwise application of identical (but a priori unknown) measurements cannot always lead to exactly alike results. We interpret this as quantum uniqueness—a feature that has no classical analog.
Periodically driven ergodic and many-body localized quantum systems
Ponte, Pedro; Chandran, Anushya; Papić, Z.; Abanin, Dmitry A.
2015-02-15
We study dynamics of isolated quantum many-body systems whose Hamiltonian is switched between two different operators periodically in time. The eigenvalue problem of the associated Floquet operator maps onto an effective hopping problem. Using the effective model, we establish conditions on the spectral properties of the two Hamiltonians for the system to localize in energy space. We find that ergodic systems always delocalize in energy space and heat up to infinite temperature, for both local and global driving. In contrast, many-body localized systems with quenched disorder remain localized at finite energy. We support our conclusions by numerical simulations of disordered spin chains. We argue that our results hold for general driving protocols, and discuss their experimental implications.
Open Quantum Random Walks: Ergodicity, Hitting Times, Gambler's Ruin and Potential Theory
NASA Astrophysics Data System (ADS)
Lardizabal, Carlos F.; Souza, Rafael R.
2016-07-01
In this work we study certain aspects of open quantum random walks (OQRWs), a class of quantum channels described by Attal et al. (J Stat Phys 147: 832-852, 2012). As a first objective we consider processes which are nonhomogeneous in time, i.e., at each time step, a possibly distinct evolution kernel. Inspired by a spectral technique described by Saloff-Coste and Zúñiga (Stoch Proc Appl 117: 961-979, 2007), we define a notion of ergodicity for finite nonhomogeneous quantum Markov chains and describe a criterion for ergodicity of such objects in terms of singular values. As a second objective, and based on a quantum trajectory approach, we study a notion of hitting time for OQRWs and we see that many constructions are variations of well-known classical probability results, with the density matrix degree of freedom on each site giving rise to systems which are seen to be nonclassical. In this way we are able to examine open quantum versions of the gambler's ruin, birth-and-death chain and a basic theorem on potential theory.
Open Quantum Random Walks: Ergodicity, Hitting Times, Gambler's Ruin and Potential Theory
NASA Astrophysics Data System (ADS)
Lardizabal, Carlos F.; Souza, Rafael R.
2016-09-01
In this work we study certain aspects of open quantum random walks (OQRWs), a class of quantum channels described by Attal et al. (J Stat Phys 147: 832-852, 2012). As a first objective we consider processes which are nonhomogeneous in time, i.e., at each time step, a possibly distinct evolution kernel. Inspired by a spectral technique described by Saloff-Coste and Zúñiga (Stoch Proc Appl 117: 961-979, 2007), we define a notion of ergodicity for finite nonhomogeneous quantum Markov chains and describe a criterion for ergodicity of such objects in terms of singular values. As a second objective, and based on a quantum trajectory approach, we study a notion of hitting time for OQRWs and we see that many constructions are variations of well-known classical probability results, with the density matrix degree of freedom on each site giving rise to systems which are seen to be nonclassical. In this way we are able to examine open quantum versions of the gambler's ruin, birth-and-death chain and a basic theorem on potential theory.
Quantitative Quantum Ergodicity and the Nodal Domains of Hecke-Maass Cusp Forms
NASA Astrophysics Data System (ADS)
Jung, Junehyuk
2016-07-01
We prove a quantitative statement of the quantum ergodicity for Hecke-Maass cusp forms on the modular surface. As an application of our result, along a density 1 subsequence of even Hecke-Maass cusp forms, we obtain a sharp lower bound for the L 2-norm of the restriction to a fixed compact geodesic segment of {η={iy : y > 0} subset H}. We also obtain an upper bound of {O_ɛ (t_φ^{3/8+ɛ} )} for the {L^∞} norm along a density 1 subsequence of Hecke-Maass cusp forms; for such forms, this is an improvement over the upper bound of {O_ɛ(t_φ^{5/12+ɛ} )} given by Iwaniec and Sarnak. In a recent work of Ghosh, Reznikov, and Sarnak, the authors proved for all even Hecke-Maass forms that the number of nodal domains, which intersect a geodesic segment of {η} , grows faster than {t_φ^{1/12-ɛ}} for any {ɛ > 0} , under the assumption that the Lindelöf Hypothesis is true and that the geodesic segment is long enough. Upon removing a density zero subset of even Hecke-Maass forms, we prove without making any assumptions that the number of nodal domains grows faster than {t_φ^{1/8-ɛ}} for any {ɛ > 0}.
NASA Astrophysics Data System (ADS)
Klein, Abel
2013-11-01
We prove a unique continuation principle for spectral projections of Schrödinger operators. We consider a Schrödinger operator H = - Δ + V on , and let H Λ denote its restriction to a finite box Λ with either Dirichlet or periodic boundary condition. We prove unique continuation estimates of the type χ I ( H Λ ) W χ I ( H Λ ) ≥ κ χ I ( H Λ ) with κ > 0 for appropriate potentials W ≥ 0 and intervals I. As an application, we obtain optimal Wegner estimates at all energies for a class of non-ergodic random Schrödinger operators with alloy-type random potentials (‘crooked’ Anderson Hamiltonians). We also prove optimal Wegner estimates at the bottom of the spectrum with the expected dependence on the disorder (the Wegner estimate improves as the disorder increases), a new result even for the usual (ergodic) Anderson Hamiltonian. These estimates are applied to prove localization at high disorder for Anderson Hamiltonians in a fixed interval at the bottom of the spectrum.
Uniqueness of conserved currents in quantum mechanics
NASA Astrophysics Data System (ADS)
Holland, P.
2003-10-01
It is proved by a functional method that the conventional expression for the Dirac current is the only conserved 4-vector implied by the Dirac equation that is a function of just the quantum state. The demonstration is extended to derive the unique conserved currents implied by the coupled Maxwell-Dirac equations and the Klein-Gordon equation. The uniqueness of the usual Pauli and Schrödinger currents follows by regarding these as the non-relativistic limits of the Dirac and Klein-Gordon currents, respectively. The existence and properties of further conserved vectors that are not functions of just the state is examined.
Using Quantum Confinement to Uniquely Identify Devices
Roberts, J.; Bagci, I. E.; Zawawi, M. A. M.; Sexton, J.; Hulbert, N.; Noori, Y. J.; Young, M. P.; Woodhead, C. S.; Missous, M.; Migliorato, M. A.; Roedig, U.; Young, R. J.
2015-01-01
Modern technology unintentionally provides resources that enable the trust of everyday interactions to be undermined. Some authentication schemes address this issue using devices that give a unique output in response to a challenge. These signatures are generated by hard-to-predict physical responses derived from structural characteristics, which lend themselves to two different architectures, known as unique objects (UNOs) and physically unclonable functions (PUFs). The classical design of UNOs and PUFs limits their size and, in some cases, their security. Here we show that quantum confinement lends itself to the provision of unique identities at the nanoscale, by using fluctuations in tunnelling measurements through quantum wells in resonant tunnelling diodes (RTDs). This provides an uncomplicated measurement of identity without conventional resource limitations whilst providing robust security. The confined energy levels are highly sensitive to the specific nanostructure within each RTD, resulting in a distinct tunnelling spectrum for every device, as they contain a unique and unpredictable structure that is presently impossible to clone. This new class of authentication device operates with minimal resources in simple electronic structures above room temperature. PMID:26553435
Using Quantum Confinement to Uniquely Identify Devices.
Roberts, J; Bagci, I E; Zawawi, M A M; Sexton, J; Hulbert, N; Noori, Y J; Young, M P; Woodhead, C S; Missous, M; Migliorato, M A; Roedig, U; Young, R J
2015-01-01
Modern technology unintentionally provides resources that enable the trust of everyday interactions to be undermined. Some authentication schemes address this issue using devices that give a unique output in response to a challenge. These signatures are generated by hard-to-predict physical responses derived from structural characteristics, which lend themselves to two different architectures, known as unique objects (UNOs) and physically unclonable functions (PUFs). The classical design of UNOs and PUFs limits their size and, in some cases, their security. Here we show that quantum confinement lends itself to the provision of unique identities at the nanoscale, by using fluctuations in tunnelling measurements through quantum wells in resonant tunnelling diodes (RTDs). This provides an uncomplicated measurement of identity without conventional resource limitations whilst providing robust security. The confined energy levels are highly sensitive to the specific nanostructure within each RTD, resulting in a distinct tunnelling spectrum for every device, as they contain a unique and unpredictable structure that is presently impossible to clone. This new class of authentication device operates with minimal resources in simple electronic structures above room temperature. PMID:26553435
Using Quantum Confinement to Uniquely Identify Devices
NASA Astrophysics Data System (ADS)
Roberts, J.; Bagci, I. E.; Zawawi, M. A. M.; Sexton, J.; Hulbert, N.; Noori, Y. J.; Young, M. P.; Woodhead, C. S.; Missous, M.; Migliorato, M. A.; Roedig, U.; Young, R. J.
2015-11-01
Modern technology unintentionally provides resources that enable the trust of everyday interactions to be undermined. Some authentication schemes address this issue using devices that give a unique output in response to a challenge. These signatures are generated by hard-to-predict physical responses derived from structural characteristics, which lend themselves to two different architectures, known as unique objects (UNOs) and physically unclonable functions (PUFs). The classical design of UNOs and PUFs limits their size and, in some cases, their security. Here we show that quantum confinement lends itself to the provision of unique identities at the nanoscale, by using fluctuations in tunnelling measurements through quantum wells in resonant tunnelling diodes (RTDs). This provides an uncomplicated measurement of identity without conventional resource limitations whilst providing robust security. The confined energy levels are highly sensitive to the specific nanostructure within each RTD, resulting in a distinct tunnelling spectrum for every device, as they contain a unique and unpredictable structure that is presently impossible to clone. This new class of authentication device operates with minimal resources in simple electronic structures above room temperature.
NASA Astrophysics Data System (ADS)
Goldstein, S.; Lebowitz, J. L.; Tumulka, R.; Zanghì, N.
2010-11-01
The renewed interest in the foundations of quantum statistical mechanics in recent years has led us to study John von Neumann’s 1929 article on the quantum ergodic theorem. We have found this almost forgotten article, which until now has been available only in German, to be a treasure chest, and to be much misunderstood. In it, von Neumann studied the long-time behavior of macroscopic quantum systems. While one of the two theorems announced in his title, the one he calls the “quantum H-theorem”, is actually a much weaker statement than Boltzmann’s classical H-theorem, the other theorem, which he calls the “quantum ergodic theorem”, is a beautiful and very non-trivial result. It expresses a fact we call “normal typicality” and can be summarized as follows: for a “typical” finite family of commuting macroscopic observables, every initial wave function ψ0 from a micro-canonical energy shell so evolves that for most times t in the long run, the joint probability distribution of these observables obtained from ψt is close to their micro-canonical distribution.
NASA Astrophysics Data System (ADS)
Fishman, S.; Soffer, A.
2016-07-01
We employ the recently developed multi-time scale averaging method to study the large time behavior of slowly changing (in time) Hamiltonians. We treat some known cases in a new way, such as the Zener problem, and we give another proof of the adiabatic theorem in the gapless case. We prove a new uniform ergodic theorem for slowly changing unitary operators. This theorem is then used to derive the adiabatic theorem, do the scattering theory for such Hamiltonians, and prove some classical propagation estimates and asymptotic completeness.
Quantum catastrophes and ergodicity in the dynamics of bosonic Josephson junctions.
O'Dell, D H J
2012-10-12
We study rainbow (fold) and cusp catastrophes that form in Fock space following a quench in a Bose Josephson junction. In the Gross-Pitaevskii mean-field theory, the rainbows are singular caustics, but in the second-quantized theory a Poisson resummation of the wave function shows that they are described by well-behaved Airy functions. The structural stability of these Fock space caustics against variations in the initial conditions and Hamiltonian evolution is guaranteed by catastrophe theory. We also show that the long-time dynamics are ergodic. Our results are relevant to the question posed by Berry [M. V. Berry, Nonlinearity 21, T19 (2008)]: Are there circumstances when it is necessary to second quantize wave theory in order to avoid singularities? PMID:23102282
Uniqueness of measures in loop quantum cosmology
Hanusch, Maximilian
2015-09-15
In Ashtekar and Campiglia [Classical Quantum Gravity 29, 242001 (2012)], residual diffeomorphisms have been used to single out the standard representation of the reduced holonomy-flux algebra in homogeneous loop quantum cosmology (LQC). We show that, in the homogeneous isotropic case, unitarity of the translations with respect to the extended ℝ-action (exponentiated reduced fluxes in the standard approach) singles out the Bohr measure on both the standard quantum configuration space ℝ{sub Bohr} as well as on the Fleischhack one (ℝ⊔ℝ{sub Bohr}). Thus, in both situations, the same condition singles out the standard kinematical Hilbert space of LQC.
Symmetry Breaking and Broken Ergodicity in Full Configuration Interaction Quantum Monte Carlo.
Thomas, Robert E; Overy, Catherine; Booth, George H; Alavi, Ali
2014-05-13
The initiator full configuration interaction quantum Monte Carlo method (i-FCIQMC) is applied to the binding curve of N2 in Slater-determinant Hilbert spaces formed of both canonical restricted Hartree-Fock (RHF) and symmetry-broken unrestricted Hartree-Fock (UHF) orbitals. By explicit calculation, we demonstrate that the technique yields the same total energy for both types of orbital but that as the bond is stretched, FCI expansions expressed in unrestricted orbitals are substantially more compact than their restricted counterparts and more compact than those expressed in split-localized orbitals. These unrestricted Hilbert spaces, however, become nonergodic toward the dissociation limit, and the total wave function may be thought of as the sum of two weakly coupled, spin-impure, functions whose energies are nonetheless very close to the exact energy. In this limit, it is a challenge for i-FCIQMC to resolve a spin-pure wave function. The use of unrestricted natural orbitals is a promising remedy for this problem, as their expansions are more strongly weighted toward lower excitations of the reference, and they provide stronger coupling to higher excitations than do UHF orbitals. PMID:26580521
Ergodic theorem, ergodic theory, and statistical mechanics
Moore, Calvin C.
2015-01-01
This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundamental problem of the subject—namely, the rationale for the hypothesis that time averages can be set equal to phase averages. The evolution of this problem is traced from the origins of statistical mechanics and Boltzman's ergodic hypothesis to the Ehrenfests' quasi-ergodic hypothesis, and then to the ergodic theorems. We discuss communications between von Neumann and Birkhoff in the Fall of 1931 leading up to the publication of these papers and related issues of priority. These ergodic theorems initiated a new field of mathematical-research called ergodic theory that has thrived ever since, and we discuss some of recent developments in ergodic theory that are relevant for statistical mechanics. PMID:25691697
Ergodic theorem, ergodic theory, and statistical mechanics.
Moore, Calvin C
2015-02-17
This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundamental problem of the subject--namely, the rationale for the hypothesis that time averages can be set equal to phase averages. The evolution of this problem is traced from the origins of statistical mechanics and Boltzman's ergodic hypothesis to the Ehrenfests' quasi-ergodic hypothesis, and then to the ergodic theorems. We discuss communications between von Neumann and Birkhoff in the Fall of 1931 leading up to the publication of these papers and related issues of priority. These ergodic theorems initiated a new field of mathematical-research called ergodic theory that has thrived ever since, and we discuss some of recent developments in ergodic theory that are relevant for statistical mechanics. PMID:25691697
Ergodicity breaking and localization.
Geneston, Elvis; Tuladhar, Rohisha; Beig, M T; Bologna, Mauro; Grigolini, Paolo
2016-07-01
We study the joint action of the non-Poisson renewal events (NPR) yielding Continuous-time random walk (CTRW) with index α<1 and two different generators of Hurst coefficient H≠0.5, one generating fractional Brownian motion (FBM) and another scaled Brownian motion (SBM). We discuss the ergodicity breaking emerging from these joint actions and we find that in both cases the adoption of time averages leads to localization. In the case of the joint action of NPR and SBM, localization occurs when SBM would produce subdiffusion. The joint action of NPR and FBM, on the contrary, may lead to localization when FBM is a source of superdiffusion. The joint action of NPR and FBM is equivalent to extending the CTRW to the case where the jumps of the runner are correlated and we argue that the the memory-induced localization requires a refinement of the theoretical perspective about determinism and randomness. PMID:27575105
Ergodicity breaking and localization
NASA Astrophysics Data System (ADS)
Geneston, Elvis; Tuladhar, Rohisha; Beig, M. T.; Bologna, Mauro; Grigolini, Paolo
2016-07-01
We study the joint action of the non-Poisson renewal events (NPR) yielding Continuous-time random walk (CTRW) with index α <1 and two different generators of Hurst coefficient H ≠0.5 , one generating fractional Brownian motion (FBM) and another scaled Brownian motion (SBM). We discuss the ergodicity breaking emerging from these joint actions and we find that in both cases the adoption of time averages leads to localization. In the case of the joint action of NPR and SBM, localization occurs when SBM would produce subdiffusion. The joint action of NPR and FBM, on the contrary, may lead to localization when FBM is a source of superdiffusion. The joint action of NPR and FBM is equivalent to extending the CTRW to the case where the jumps of the runner are correlated and we argue that the the memory-induced localization requires a refinement of the theoretical perspective about determinism and randomness.
A generator for unique quantum random numbers based on vacuum states
NASA Astrophysics Data System (ADS)
Gabriel, Christian; Wittmann, Christoffer; Sych, Denis; Dong, Ruifang; Mauerer, Wolfgang; Andersen, Ulrik L.; Marquardt, Christoph; Leuchs, Gerd
2010-10-01
Random numbers are a valuable component in diverse applications that range from simulations over gambling to cryptography. The quest for true randomness in these applications has engendered a large variety of different proposals for producing random numbers based on the foundational unpredictability of quantum mechanics. However, most approaches do not consider that a potential adversary could have knowledge about the generated numbers, so the numbers are not verifiably random and unique. Here we present a simple experimental setup based on homodyne measurements that uses the purity of a continuous-variable quantum vacuum state to generate unique random numbers. We use the intrinsic randomness in measuring the quadratures of a mode in the lowest energy vacuum state, which cannot be correlated to any other state. The simplicity of our source, combined with its verifiably unique randomness, are important attributes for achieving high-reliability, high-speed and low-cost quantum random number generators.
On the unique mapping relationship between initial and final quantum states
Sanz, A.S.; Miret-Artés, S.
2013-12-15
In its standard formulation, quantum mechanics presents a very serious inconvenience: given a quantum system, there is no possibility at all to unambiguously (causally) connect a particular feature of its final state with some specific section of its initial state. This constitutes a practical limitation, for example, in numerical analyses of quantum systems, which often make necessary the use of some extra assistance from classical methodologies. Here it is shown how the Bohmian formulation of quantum mechanics removes the ambiguity of quantum mechanics, providing a consistent and clear answer to such a question without abandoning the quantum framework. More specifically, this formulation allows to define probability tubes, along which the enclosed probability keeps constant in time all the way through as the system evolves in configuration space. These tubes have the interesting property that once their boundary is defined at a given time, they are uniquely defined at any time. As a consequence, it is possible to determine final restricted (or partial) probabilities directly from localized sets of (Bohmian) initial conditions on the system initial state. Here, these facts are illustrated by means of two simple yet physically insightful numerical examples: tunneling transmission and grating diffraction. -- Highlights: •The concept of quantum probability tube is introduced. •Quantum tubes result from the evolution of a separatrix set of initial Bohmian conditions. •Probabilities inside these sets remain constant along the corresponding quantum tubes. •Particular features of final states are then uniquely linked to specific regions of initial states. •Tunneling and grating diffraction are analyzed.
NASA Astrophysics Data System (ADS)
Gerd, Niestegge
2010-12-01
In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A model involving a clear probabilistic interpretation from the very beginning is provided by the quantum logics with unique conditional probabilities. It includes the projection lattices in von Neumann algebras and here probability conditionalization becomes identical with the state transition of the Lüders-von Neumann measurement process. This motivates the definition of a hierarchy of five compatibility and comeasurability levels in the abstract setting of the quantum logics with unique conditional probabilities. Their meanings are: the absence of quantum interference or influence, the existence of a joint distribution, simultaneous measurability, and the independence of the final state after two successive measurements from the sequential order of these two measurements. A further level means that two elements of the quantum logic (events) belong to the same Boolean subalgebra. In the general case, the five compatibility and comeasurability levels appear to differ, but they all coincide in the common Hilbert space formalism of quantum mechanics, in von Neumann algebras, and in some other cases.
Ergodic theory, randomness, and "chaos".
Ornstein, D S
1989-01-13
Ergodic theory is the theory of the long-term statistical behavior of dynamical systems. The baker's transformation is an object of ergodic theory that provides a paradigm for the possibility of deterministic chaos. It can now be shown that this connection is more than an analogy and that at some level of abstraction a large number of systems governed by Newton's laws are the same as the baker's transformation. Going to this level of abstraction helps to organize the possible kinds of random behavior. The theory also gives new concrete results. For example, one can show that the same process could be produced by a mechanism governed by Newton's laws or by a mechanism governed by coin tossing. It also gives a statistical analog of structural stability. PMID:17747421
Broken Ergodicity in MHD Turbulence
NASA Technical Reports Server (NTRS)
Shebalin, John V.
2010-01-01
Ideal magnetohydrodynamic (MHD) turbulence may be represented by finite Fourier series, where the inherent periodic box serves as a surrogate for a bounded astrophysical plasma. Independent Fourier coefficients form a canonical ensemble described by a Gaussian probability density function containing a Hermitian covariance matrix with positive eigenvalues. The eigenvalues at lowest wave number can be very small, resulting in a large-scale coherent structure: a turbulent dynamo. This is seen in computations and a theoretical explanation in terms of 'broken ergodicity' contains Taylor s theory of force-free states. An important problem for future work is the case of real, i.e., dissipative flows. In real flows, broken ergodicity and coherent structure are still expected to occur in MHD turbulence at the largest scale, as suggested by low resolution simulations. One challenge is to incorporate coherent structure at the largest scale into the theory of turbulent fluctuations at smaller scales.
Bufetov, A I
2014-02-28
The aim of this paper is to prove ergodic decomposition theorems for probability measures which are quasi-invariant under Borel actions of inductively compact groups as well as for σ-finite invariant measures. For infinite measures the ergodic decomposition is not unique, but the measure class of the decomposing measure on the space of projective measures is uniquely defined by the initial invariant measure. Bibliography: 21 titles.
Toward a practical approach for ergodicity analysis
NASA Astrophysics Data System (ADS)
Wang, H.; Wang, C.; Zhao, Y.; Lin, X.; Yu, C.
2015-09-01
It is of importance to perform hydrological forecast using a finite hydrological time series. Most time series analysis approaches presume a data series to be ergodic without justifying this assumption. This paper presents a practical approach to analyze the mean ergodic property of hydrological processes by means of autocorrelation function evaluation and Augmented Dickey Fuller test, a radial basis function neural network, and the definition of mean ergodicity. The mean ergodicity of precipitation processes at the Lanzhou Rain Gauge Station in the Yellow River basin, the Ankang Rain Gauge Station in Han River, both in China, and at Newberry, MI, USA are analyzed using the proposed approach. The results indicate that the precipitations of March, July, and August in Lanzhou, and of May, June, and August in Ankang have mean ergodicity, whereas, the precipitation of any other calendar month in these two rain gauge stations do not have mean ergodicity. The precipitation of February, May, July, and December in Newberry show ergodic property, although the precipitation of each month shows a clear increasing or decreasing trend.
Nonlinear stability and ergodicity of ensemble based Kalman filters
NASA Astrophysics Data System (ADS)
Tong, Xin T.; Majda, Andrew J.; Kelly, David
2016-02-01
The ensemble Kalman filter (EnKF) and ensemble square root filter (ESRF) are data assimilation methods used to combine high dimensional, nonlinear dynamical models with observed data. Despite their widespread usage in climate science and oil reservoir simulation, very little is known about the long-time behavior of these methods and why they are effective when applied with modest ensemble sizes in large dimensional turbulent dynamical systems. By following the basic principles of energy dissipation and controllability of filters, this paper establishes a simple, systematic and rigorous framework for the nonlinear analysis of EnKF and ESRF with arbitrary ensemble size, focusing on the dynamical properties of boundedness and geometric ergodicity. The time uniform boundedness guarantees that the filter estimate will not diverge to machine infinity in finite time, which is a potential threat for EnKF and ESQF known as the catastrophic filter divergence. Geometric ergodicity ensures in addition that the filter has a unique invariant measure and that initialization errors will dissipate exponentially in time. We establish these results by introducing a natural notion of observable energy dissipation. The time uniform bound is achieved through a simple Lyapunov function argument, this result applies to systems with complete observations and strong kinetic energy dissipation, but also to concrete examples with incomplete observations. With the Lyapunov function argument established, the geometric ergodicity is obtained by verifying the controllability of the filter processes; in particular, such analysis for ESQF relies on a careful multivariate perturbation analysis of the covariance eigen-structure.
Ergodicity of the generalized lemon billiards
Chen, Jingyu; Mohr, Luke; Zhang, Hong-Kun Zhang, Pengfei
2013-12-15
In this paper, we study a two-parameter family of convex billiard tables, by taking the intersection of two round disks (with different radii) in the plane. These tables give a generalization of the one-parameter family of lemon-shaped billiards. Initially, there is only one ergodic table among all lemon tables. In our generalized family, we observe numerically the prevalence of ergodicity among the some perturbations of that table. Moreover, numerical estimates of the mixing rate of the billiard dynamics on some ergodic tables are also provided.
Ergodicity of the generalized lemon billiards
NASA Astrophysics Data System (ADS)
Chen, Jingyu; Mohr, Luke; Zhang, Hong-Kun; Zhang, Pengfei
2013-12-01
In this paper, we study a two-parameter family of convex billiard tables, by taking the intersection of two round disks (with different radii) in the plane. These tables give a generalization of the one-parameter family of lemon-shaped billiards. Initially, there is only one ergodic table among all lemon tables. In our generalized family, we observe numerically the prevalence of ergodicity among the some perturbations of that table. Moreover, numerical estimates of the mixing rate of the billiard dynamics on some ergodic tables are also provided.
Anomalous transport in ergodic lattice systems
NASA Astrophysics Data System (ADS)
Bar Lev, Yevgeny; Reichman, David R.
Many-body localization transition is a peculiar dynamical transition between ergodic and non-ergodic phases, which may occur at any temperature and in any dimension. For temperatures below the transition the system is nonergodic and localized, such that conductivity strictly vanishes at the thermodynamic limit, while for temperatures above the transition the system is thermal and conductive. In this talk I will present a comprehensive study of the dynamical properties of the ergodic phase in one and two dimensional generic disordered and interacting systems, conducted using a combination of nonequilibrium diagrammatic techniques and numerically exact methods. I will show that the ergodic phase, which was expected to be diffusive, exhibits anomalous transport regime for nontrivial times and explain how our findings settle with phenomenological theoretical models. NSF-CHE-1644802.
Ergodicity, ensembles, irreversibility in Boltzmann and beyond
NASA Astrophysics Data System (ADS)
Gallavotti, Giovanni
1995-03-01
The contents of a not too well-known paper by Boltzmann are critically examined. The etymology of the word ergodic and its implications are discussed. A connection with the modern theory of Ruelle is attempted.
Ergodicity in natural earthquake fault networks
Tiampo, K. F.; Rundle, J. B.; Holliday, J.; Klein, W.; Sa Martins, J. S.
2007-06-15
Numerical simulations have shown that certain driven nonlinear systems can be characterized by mean-field statistical properties often associated with ergodic dynamics [C. D. Ferguson, W. Klein, and J. B. Rundle, Phys. Rev. E 60, 1359 (1999); D. Egolf, Science 287, 101 (2000)]. These driven mean-field threshold systems feature long-range interactions and can be treated as equilibriumlike systems with statistically stationary dynamics over long time intervals. Recently the equilibrium property of ergodicity was identified in an earthquake fault system, a natural driven threshold system, by means of the Thirumalai-Mountain (TM) fluctuation metric developed in the study of diffusive systems [K. F. Tiampo, J. B. Rundle, W. Klein, J. S. Sa Martins, and C. D. Ferguson, Phys. Rev. Lett. 91, 238501 (2003)]. We analyze the seismicity of three naturally occurring earthquake fault networks from a variety of tectonic settings in an attempt to investigate the range of applicability of effective ergodicity, using the TM metric and other related statistics. Results suggest that, once variations in the catalog data resulting from technical and network issues are accounted for, all of these natural earthquake systems display stationary periods of metastable equilibrium and effective ergodicity that are disrupted by large events. We conclude that a constant rate of events is an important prerequisite for these periods of punctuated ergodicity and that, while the level of temporal variability in the spatial statistics is the controlling factor in the ergodic behavior of seismic networks, no single statistic is sufficient to ensure quantification of ergodicity. Ergodicity in this application not only requires that the system be stationary for these networks at the applicable spatial and temporal scales, but also implies that they are in a state of metastable equilibrium, one in which the ensemble averages can be substituted for temporal averages in studying their spatiotemporal
Ergodicity in natural earthquake fault networks.
Tiampo, K F; Rundle, J B; Klein, W; Holliday, J; Sá Martins, J S; Ferguson, C D
2007-06-01
Numerical simulations have shown that certain driven nonlinear systems can be characterized by mean-field statistical properties often associated with ergodic dynamics [C. D. Ferguson, W. Klein, and J. B. Rundle, Phys. Rev. E 60, 1359 (1999); D. Egolf, Science 287, 101 (2000)]. These driven mean-field threshold systems feature long-range interactions and can be treated as equilibriumlike systems with statistically stationary dynamics over long time intervals. Recently the equilibrium property of ergodicity was identified in an earthquake fault system, a natural driven threshold system, by means of the Thirumalai-Mountain (TM) fluctuation metric developed in the study of diffusive systems [K. F. Tiampo, J. B. Rundle, W. Klein, J. S. Sá Martins, and C. D. Ferguson, Phys. Rev. Lett. 91, 238501 (2003)]. We analyze the seismicity of three naturally occurring earthquake fault networks from a variety of tectonic settings in an attempt to investigate the range of applicability of effective ergodicity, using the TM metric and other related statistics. Results suggest that, once variations in the catalog data resulting from technical and network issues are accounted for, all of these natural earthquake systems display stationary periods of metastable equilibrium and effective ergodicity that are disrupted by large events. We conclude that a constant rate of events is an important prerequisite for these periods of punctuated ergodicity and that, while the level of temporal variability in the spatial statistics is the controlling factor in the ergodic behavior of seismic networks, no single statistic is sufficient to ensure quantification of ergodicity. Ergodicity in this application not only requires that the system be stationary for these networks at the applicable spatial and temporal scales, but also implies that they are in a state of metastable equilibrium, one in which the ensemble averages can be substituted for temporal averages in studying their spatiotemporal
Ergodicity in natural earthquake fault networks
NASA Astrophysics Data System (ADS)
Tiampo, K. F.; Rundle, J. B.; Klein, W.; Holliday, J.; Sá Martins, J. S.; Ferguson, C. D.
2007-06-01
Numerical simulations have shown that certain driven nonlinear systems can be characterized by mean-field statistical properties often associated with ergodic dynamics [C. D. Ferguson, W. Klein, and J. B. Rundle, Phys. Rev. E 60, 1359 (1999); D. Egolf, Science 287, 101 (2000)]. These driven mean-field threshold systems feature long-range interactions and can be treated as equilibriumlike systems with statistically stationary dynamics over long time intervals. Recently the equilibrium property of ergodicity was identified in an earthquake fault system, a natural driven threshold system, by means of the Thirumalai-Mountain (TM) fluctuation metric developed in the study of diffusive systems [K. F. Tiampo, J. B. Rundle, W. Klein, J. S. Sá Martins, and C. D. Ferguson, Phys. Rev. Lett. 91, 238501 (2003)]. We analyze the seismicity of three naturally occurring earthquake fault networks from a variety of tectonic settings in an attempt to investigate the range of applicability of effective ergodicity, using the TM metric and other related statistics. Results suggest that, once variations in the catalog data resulting from technical and network issues are accounted for, all of these natural earthquake systems display stationary periods of metastable equilibrium and effective ergodicity that are disrupted by large events. We conclude that a constant rate of events is an important prerequisite for these periods of punctuated ergodicity and that, while the level of temporal variability in the spatial statistics is the controlling factor in the ergodic behavior of seismic networks, no single statistic is sufficient to ensure quantification of ergodicity. Ergodicity in this application not only requires that the system be stationary for these networks at the applicable spatial and temporal scales, but also implies that they are in a state of metastable equilibrium, one in which the ensemble averages can be substituted for temporal averages in studying their spatiotemporal
Capturing deviation from ergodicity at different scales
NASA Astrophysics Data System (ADS)
Scott, Sherry E.; Redd, Thomas C.; Kuznetsov, Leonid; Mezić, Igor; Jones, Christopher K. R. T.
2009-08-01
We address here the issue of quantifying the extent to which a given dynamical system falls short of being ergodic and introduce a new multiscale technique which we call the “ergodicity defect”. Our approach is aimed at capturing both deviation from ergodicity and its dependence on scale. The method uses ergodic theory of dynamical systems and applies harmonic analysis, in particular the scaling analysis is motivated by wavelet theory. We base the definition of the ergodicity defect on the Birkhoff characterization. We systematically exploit the role of the observation function by using characteristic functions arising from a dyadic equipartition of the phase space. This allows us to view the dependence of the defect on scale. In order to build intuition, we consider the defect for specific examples with known dynamic properties and we are able to explicitly compute the defect for some of these simple examples. We focus on three distinctive cases of the dependence of the defect on scale: (1) a defect value that increases as the scale becomes finer, (2) a defect value decreasing with scale and (3) a defect value independent of scale, which occurs for instance when a map is ergodic. We explain the information contained in these three scenarios. We see more complicated behavior with an example which has invariant subsets at various scales.
Ergodicity test of the eddy correlation method
NASA Astrophysics Data System (ADS)
Chen, J.; Hu, Y.; Yu, Y.; Lü, S.
2014-07-01
The turbulent flux observation in the near-surface layer is a scientific issue which researchers in the fields of atmospheric science, ecology, geography science, etc. are commonly interested in. For eddy correlation measurement in the atmospheric surface layer, the ergodicity of turbulence is a basic assumption of the Monin-Obukhov (M-O) similarity theory, which is confined to steady turbulent flow and homogenous surface; this conflicts with turbulent flow under the conditions of complex terrain and unsteady, long observational period, which the study of modern turbulent flux tends to focus on. In this paper, two sets of data from the Nagqu Station of Plateau Climate and Environment (NaPlaCE) and the cooperative atmosphere-surface exchange study 1999 (CASE99) were used to analyze and verify the ergodicity of turbulence measured by the eddy covariance system. Through verification by observational data, the vortex of atmospheric turbulence, which is smaller than the scale of the atmospheric boundary layer (i.e., its spatial scale is less than 1000 m and temporal scale is shorter than 10 min) can effectively meet the conditions of the average ergodic theorem, and belong to a wide sense stationary random processes. Meanwhile, the vortex, of which the spatial scale is larger than the scale of the boundary layer, cannot meet the conditions of the average ergodic theorem, and thus it involves non-ergodic stationary random processes. Therefore, if the finite time average is used to substitute for the ensemble average to calculate the average random variable of the atmospheric turbulence, then the stationary random process of the vortex, of which spatial scale was less than 1000 m and thus below the scale of the boundary layer, was possibly captured. However, the non-ergodic random process of the vortex, of which the spatial scale was larger than that of the boundary layer, could not be completely captured. Consequently, when the finite time average was used to substitute
Ergodic to non-ergodic transition monitored by scattered light intensity statistics
NASA Astrophysics Data System (ADS)
Manno, M.; Bulone, D.; Martorana, V.; San Biagio, P. L.
2004-10-01
Many soft materials, such as gels or glasses, exhibit both a fast and a very slow relaxation behavior, often related to thermally activated processes restoring ergodicity. Pusey and Van Megen (Physica A 157 (1989) 705), have elaborated a theory that allows the usage of standard light scattering techniques to treat systems that are dynamically arrested, or non-ergodic, over the experimental time-scale. This theory concerning the distribution of intensity scattered by non-ergodic media is here extended, by taking into account second order temporal coherence of scattered radiation. The time-integrated intensity distribution function so obtained allows to distinguish between fast and slow contributions when the two time scales are not (or not yet) completely separated. Thus, by simple and quick static light scattering measurements one can follow an ergodic-to-non-ergodic transition. We present an experiment on gelation kinetics of sucrose-pectin systems, which illustrates the quality of the method, and show how the gel network is formed out of a homogeneous solution.
Broken Ergodicity in Ideal, Homogeneous, Incompressible Turbulence
NASA Technical Reports Server (NTRS)
Morin, Lee; Shebalin, John; Fu, Terry; Nguyen, Phu; Shum, Victor
2010-01-01
We discuss the statistical mechanics of numerical models of ideal homogeneous, incompressible turbulence and their relevance for dissipative fluids and magnetofluids. These numerical models are based on Fourier series and the relevant statistical theory predicts that Fourier coefficients of fluid velocity and magnetic fields (if present) are zero-mean random variables. However, numerical simulations clearly show that certain coefficients have a non-zero mean value that can be very large compared to the associated standard deviation. We explain this phenomena in terms of broken ergodicity', which is defined to occur when dynamical behavior does not match ensemble predictions on very long time-scales. We review the theoretical basis of broken ergodicity, apply it to 2-D and 3-D fluid and magnetohydrodynamic simulations of homogeneous turbulence, and show new results from simulations using GPU (graphical processing unit) computers.
Chu, M.S.; Jensen, T.H.; La Haye, R.J.; Taylor, T.S.; Evans, T.E.
1991-10-01
A new ergodic divertor is proposed. It utilizes a system of external (n = 3) coils arranged to generate overlapping magnetic islands in the edge region of a diverted tokamak and connect the randomized field lines to the external (cold) divertor plate. The novel feature in the configuration is the placement of the external coils close to the X-point. A realistic design of the external coil set is studied by using the field line tracing method for a low aspect ratio (A {approx equal} 3) tokamak. Two types of effects are observed. First, by placing the coils close to the X-point, where the poloidal magnetic field is weak and the rational surfaces are closely packed only a moderate amount of current in the external coils is needed to ergodize the edge region. This ergodized edge enhances the edge transport in the X-point region and leads to the potential of edge profile control and the avoidance of edge localized modes (ELMs). Furthermore, the trajectories of the field lines close to the X-point are modified by the external coil set, causing the hit points on the external divertor plates to be randomized and spread out in the major radius direction. A time-dependent modulation of the currents in the external (n = 3) coils can potentially spread the heat flux more uniformly on the divertor plate avoiding high concentration of the heat flux. 10 refs., 9 figs.
Special ergodic theorems and dynamical large deviations
NASA Astrophysics Data System (ADS)
Kleptsyn, Victor; Ryzhov, Dmitry; Minkov, Stanislav
2012-11-01
Let f : M → M be a self-map of a compact Riemannian manifold M, admitting a global SRB measure μ. For a continuous test function \\varphi\\colon M\\to R and a constant α > 0, consider the set Kφ,α of the initial points for which the Birkhoff time averages of the function φ differ from its μ-space average by at least α. As the measure μ is a global SRB one, the set Kφ,α should have zero Lebesgue measure. The special ergodic theorem, whenever it holds, claims that, moreover, this set has a Hausdorff dimension less than the dimension of M. We prove that for Lipschitz maps, the special ergodic theorem follows from the dynamical large deviations principle. We also define and prove analogous result for flows. Applying the theorems of Young and of Araújo and Pacifico, we conclude that the special ergodic theorem holds for transitive hyperbolic attractors of C2-diffeomorphisms, as well as for some other known classes of maps (including the one of partially hyperbolic non-uniformly expanding maps) and flows.
Applications of Ergodic Theory to Coverage Analysis
NASA Technical Reports Server (NTRS)
Lo, Martin W.
2003-01-01
The study of differential equations, or dynamical systems in general, has two fundamentally different approaches. We are most familiar with the construction of solutions to differential equations. Another approach is to study the statistical behavior of the solutions. Ergodic Theory is one of the most developed methods to study the statistical behavior of the solutions of differential equations. In the theory of satellite orbits, the statistical behavior of the orbits is used to produce 'Coverage Analysis' or how often a spacecraft is in view of a site on the ground. In this paper, we consider the use of Ergodic Theory for Coverage Analysis. This allows us to greatly simplify the computation of quantities such as the total time for which a ground station can see a satellite without ever integrating the trajectory, see Lo 1,2. More over, for any quantity which is an integrable function of the ground track, its average may be computed similarly without the integration of the trajectory. For example, the data rate for a simple telecom system is a function of the distance between the satellite and the ground station. We show that such a function may be averaged using the Ergodic Theorem.
Ergodic time-reversible chaos for Gibbs' canonical oscillator
NASA Astrophysics Data System (ADS)
Hoover, William Graham; Sprott, Julien Clinton; Patra, Puneet Kumar
2015-12-01
Nosé's pioneering 1984 work inspired a variety of time-reversible deterministic thermostats. Though several groups have developed successful doubly-thermostated models, single-thermostat models have failed to generate Gibbs' canonical distribution for the one-dimensional harmonic oscillator. A 2001 doubly-thermostated model, claimed to be ergodic, has a singly-thermostated version. Though neither of these models is ergodic this work has suggested a successful route toward singly-thermostated ergodicity. We illustrate both ergodicity and its lack for these models using phase-space cross sections and Lyapunov instability as diagnostic tools.
Ergodic mixing for turbulent drift motion
Isichenko, M.B.; Petviashvili, N.V.
1995-02-16
The statistical properties of the long-time chaotic two-dimensional (2D) drift motion of a charged particle in an inhomogeneous magnetic field {beta}(x,y) and a time-dependent electrostatic potential {phi}(x,y,t) are studied by numerical symplectic integration. For a conditionally periodic potential with two or more incommensurate frequencies, an ergodic behavior is demonstrated in which the probability density of the particle position is proportional to the magnetic field {beta}. The accuracy of this prediction is found to be independent of the number N{sub {omega}} of the incommensurate frequencies for N{sub {omega}} {ge}2.
Levnajić, Zoran; Mezić, Igor
2010-09-01
We present a computational study of a visualization method for invariant sets based on ergodic partition theory, first proposed by Mezić (Ph.D. thesis, Caltech, 1994) and Mezić and Wiggins [Chaos 9, 213 (1999)]. The algorithms for computation of the time averages of observables on phase space are developed and used to provide an approximation of the ergodic partition of the phase space. We term the graphical representation of this approximation--based on time averages of observables--a mesochronic plot (from Greek: meso--mean, chronos--time). The method is useful for identifying low-dimensional projections (e.g., two-dimensional slices) of invariant structures in phase spaces of dimensionality bigger than two. We also introduce the concept of the ergodic quotient space, obtained by assigning a point to every ergodic set, and provide an embedding method whose graphical representation we call the mesochronic scatter plot. We use the Chirikov standard map as a well-known and dynamically rich example in order to illustrate the implementation of our methods. In addition, we expose applications to other higher dimensional maps such as the Froéschle map for which we utilize our methods to analyze merging of resonances and, the three-dimensional extended standard map for which we study the conjecture on its ergodicity [I. Mezić, Physica D 154, 51 (2001)]. We extend the study in our next paper [Z. Levnajić and I. Mezić, e-print arXiv:0808.2182] by investigating the visualization of periodic sets using harmonic time averages. Both of these methods are related to eigenspace structure of the Koopman operator [I. Mezić and A. Banaszuk, Physica D 197, 101 (2004)]. PMID:20887054
Ergodicity of perpendicular cosmic ray transport
NASA Astrophysics Data System (ADS)
Tautz, R. C.
2016-06-01
Aims: The random walk of energetic charged particles in turbulent magnetic fields is investigated. Special focus is placed on transport across the mean magnetic field, which had been found to be subdiffusive on many occasions. Therefore, a characterization using the concept of ergodicity is attempted by noting the connection to the time evolution of the mean-square displacement. Methods: Based on the test-particle approach, a numerical Monte Carlo simulation code is used to integrate the equation of motion for particles that are scattered by magnetic turbulence. The turbulent fields are generated by superposing plane waves with a Kolmogorov-type power spectrum. The individual particle trajectories are then used to calculate a variety of statistical quantities. Results: The simulation results clearly demonstrate how the heterogeneity of the particle ensemble causes the system to be weakly non-ergodic. In addition, it is shown how the step length distribution varies with the particle energy. In conclusion, cross-field transport is non-Gaussian but still almost diffusive.
Ergodicity test of the eddy-covariance technique
NASA Astrophysics Data System (ADS)
Chen, J.; Hu, Y.; Yu, Y.; Lü, S.
2015-09-01
The ergodic hypothesis is a basic hypothesis typically invoked in atmospheric surface layer (ASL) experiments. The ergodic theorem of stationary random processes is introduced to analyse and verify the ergodicity of atmospheric turbulence measured using the eddy-covariance technique with two sets of field observational data. The results show that the ergodicity of atmospheric turbulence in atmospheric boundary layer (ABL) is relative not only to the atmospheric stratification but also to the eddy scale of atmospheric turbulence. The eddies of atmospheric turbulence, of which the scale is smaller than the scale of the ABL (i.e. the spatial scale is less than 1000 m and temporal scale is shorter than 10 min), effectively satisfy the ergodic theorems. Under these restrictions, a finite time average can be used as a substitute for the ensemble average of atmospheric turbulence, whereas eddies that are larger than ABL scale dissatisfy the mean ergodic theorem. Consequently, when a finite time average is used to substitute for the ensemble average, the eddy-covariance technique incurs large errors due to the loss of low-frequency information associated with larger eddies. A multi-station observation is compared with a single-station observation, and then the scope that satisfies the ergodic theorem is extended from scales smaller than the ABL, approximately 1000 m to scales greater than about 2000 m. Therefore, substituting the finite time average for the ensemble average of atmospheric turbulence is more faithfully approximate the actual values. Regardless of vertical velocity or temperature, the variance of eddies at different scales follows Monin-Obukhov similarity theory (MOST) better if the ergodic theorem can be satisfied; if not it deviates from MOST. The exploration of ergodicity in atmospheric turbulence is doubtlessly helpful in understanding the issues in atmospheric turbulent observations and provides a theoretical basis for overcoming related difficulties.
Ergodicity, mixing, and time reversibility for atomistic nonequilibrium steady states
Hoover, W.G.; Kum, O.
1997-11-01
Ergodic mixing is prerequisite to any statistical-mechanical calculation of properties derived from atomistic dynamical simulations. Thus the time-reversible thermostats and ergostats used in simulating Gibbsian equilibrium dynamics or nonequilibrium steady-state dynamics should impose ergodicity and mixing. Though it is hard to visualize many-dimensional phase-space distributions, recent developments provide several practical numerical approaches to the problem of ergodic mixing. Here we apply three of these approaches to a useful nonequilibrium test problem, an oscillator in a temperature gradient. {copyright} {ital 1997} {ital The American Physical Society}
The challenge of non-ergodicity in network neuroscience.
Medaglia, John D; Ramanathan, Deepa M; Venkatesan, Umesh M; Hillary, Frank G
2011-01-01
Ergodicity can be assumed when the structure of data is consistent across individuals and time. Neural network approaches do not frequently test for ergodicity in data which holds important consequences for data integration and intepretation. To demonstrate this problem, we present several network models in healthy and clinical samples where there exists considerable heterogeneity across individuals. We offer suggestions for the analysis, interpretation, and reporting of neural network data. The goal is to arrive at an understanding of the sources of non-ergodicity and approaches for valid network modeling in neuroscience. PMID:22149675
Resonant magnetic perturbations and edge ergodization on the COMPASS tokamak
Cahyna, P.; Fuchs, V.; Krlin, L.
2008-09-15
Results of calculations of resonant magnetic perturbation spectra on the COMPASS tokamak are presented. Spectra of the perturbations are calculated from the vacuum field of the perturbation coils. Ergodization is then estimated by applying the criterion of overlap of the resulting islands and verified by field line tracing. Results show that for the chosen configuration of perturbation coils an ergodic layer appears in the pedestal region. The ability to form an ergodic layer is similar to the theoretical results for the ELM suppression experiment at DIII-D; thus, a comparable effect on ELMs can be expected.
An Almost Sure Ergodic Theorem for Quasistatic Dynamical Systems
NASA Astrophysics Data System (ADS)
Stenlund, Mikko
2016-09-01
We prove an almost sure ergodic theorem for abstract quasistatic dynamical systems, as an attempt of taking steps toward an ergodic theory of such systems. The result at issue is meant to serve as a working counterpart of Birkhoff's ergodic theorem which fails in the quasistatic setup. It is formulated so that the conditions, which essentially require sufficiently good memory-loss properties, could be verified in a straightforward way in physical applications. We also introduce the concept of a physical family of measures for a quasistatic dynamical system. These objects manifest themselves, for instance, in numerical experiments. We then illustrate the use of the theorem by examples.
A random matrix model with localization and ergodic transitions
NASA Astrophysics Data System (ADS)
Kravtsov, V. E.; Khaymovich, I. M.; Cuevas, E.; Amini, M.
2015-12-01
Motivated by the problem of many-body localization and the recent numerical results for the level and eigenfunction statistics on the random regular graphs, a generalization of the Rosenzweig-Porter random matrix model is suggested that possesses two transitions. One of them is the Anderson localization transition from the localized to the extended states. The other one is the ergodic transition from the extended non-ergodic (multifractal) states to the extended ergodic states. We confirm the existence of both transitions by computing the two-level spectral correlation function, the spectrum of multifractality f(α ) and the wave function overlap which consistently demonstrate these two transitions.
Anomalous diffusion: Testing ergodicity breaking in experimental data
NASA Astrophysics Data System (ADS)
Magdziarz, Marcin; Weron, Aleksander
2011-11-01
Recent advances in single-molecule experiments show that various complex systems display nonergodic behavior. In this paper, we show how to test ergodicity and ergodicity breaking in experimental data. Exploiting the so-called dynamical functional, we introduce a simple test which allows us to verify ergodic properties of a real-life process. The test can be applied to a large family of stationary infinitely divisible processes. We check the performance of the test for various simulated processes and apply it to experimental data describing the motion of mRNA molecules inside live Escherichia coli cells. We show that the data satisfy necessary conditions for mixing and ergodicity. The detailed analysis is presented in the supplementary material.
Anomalous diffusion: testing ergodicity breaking in experimental data.
Magdziarz, Marcin; Weron, Aleksander
2011-11-01
Recent advances in single-molecule experiments show that various complex systems display nonergodic behavior. In this paper, we show how to test ergodicity and ergodicity breaking in experimental data. Exploiting the so-called dynamical functional, we introduce a simple test which allows us to verify ergodic properties of a real-life process. The test can be applied to a large family of stationary infinitely divisible processes. We check the performance of the test for various simulated processes and apply it to experimental data describing the motion of mRNA molecules inside live Escherichia coli cells. We show that the data satisfy necessary conditions for mixing and ergodicity. The detailed analysis is presented in the supplementary material. PMID:22181399
Numerical Detection of Ergodicity Breaking in a Glass Model
NASA Astrophysics Data System (ADS)
Sasaki, Munetaka; Hukushima, Koji
2016-07-01
We present a numerical method of directly detecting ergodicity breaking in glassy systems. To examine the validity of the proposed method, we applied it to the Biroli-Mézard glass model on a regular random graph. The obtained results clearly indicate that the model exhibits a dynamical transition with ergodicity breaking at an occupation density, that is consistent with the prediction obtained by the cavity method. The present method is applicable to glassy systems in finite dimensions.
Broken Ergodicity in Two-Dimensional Homogeneous Magnetohydrodynamic Turbulence
NASA Technical Reports Server (NTRS)
Shebalin, John V.
2010-01-01
Two-dimensional (2-D) homogeneous magnetohydrodynamic (MHD) turbulence has many of the same qualitative features as three-dimensional (3-D) homogeneous MHD turbulence.The se features include several ideal invariants, along with the phenomenon of broken ergodicity. Broken ergodicity appears when certain modes act like random variables with mean values that are large compared to their standard deviations, indicating a coherent structure or dynamo.Recently, the origin of broken ergodicity in 3-D MHD turbulence that is manifest in the lowest wavenumbers was explained. Here, a detailed description of the origins of broken ergodicity in 2-D MHD turbulence is presented. It will be seen that broken ergodicity in ideal 2-D MHD turbulence can be manifest in the lowest wavenumbers of a finite numerical model for certain initial conditions or in the highest wavenumbers for another set of initial conditions.T he origins of broken ergodicity in ideal 2-D homogeneous MHD turbulence are found through an eigen analysis of the covariance matrices of the modal probability density functions.It will also be shown that when the lowest wavenumber magnetic field becomes quasi-stationary, the higher wavenumber modes can propagate as Alfven waves on these almost static large-scale magnetic structures
A statistical evaluation of non-ergodic variogram estimators
Curriero, F.C.; Hohn, M.E.; Liebhold, A.M.; Lele, S.R.
2002-01-01
Geostatistics is a set of statistical techniques that is increasingly used to characterize spatial dependence in spatially referenced ecological data. A common feature of geostatistics is predicting values at unsampled locations from nearby samples using the kriging algorithm. Modeling spatial dependence in sampled data is necessary before kriging and is usually accomplished with the variogram and its traditional estimator. Other types of estimators, known as non-ergodic estimators, have been used in ecological applications. Non-ergodic estimators were originally suggested as a method of choice when sampled data are preferentially located and exhibit a skewed frequency distribution. Preferentially located samples can occur, for example, when areas with high values are sampled more intensely than other areas. In earlier studies the visual appearance of variograms from traditional and non-ergodic estimators were compared. Here we evaluate the estimators' relative performance in prediction. We also show algebraically that a non-ergodic version of the variogram is equivalent to the traditional variogram estimator. Simulations, designed to investigate the effects of data skewness and preferential sampling on variogram estimation and kriging, showed the traditional variogram estimator outperforms the non-ergodic estimators under these conditions. We also analyzed data on carabid beetle abundance, which exhibited large-scale spatial variability (trend) and a skewed frequency distribution. Detrending data followed by robust estimation of the residual variogram is demonstrated to be a successful alternative to the non-ergodic approach.
Testing ergodicity in dense granular systems
NASA Astrophysics Data System (ADS)
Gao, Guo-Jie; Blawzdziewicz, Jerzy; O'Hern, Corey
2008-03-01
The Edwards' entropy formalism provides a statistical mechanical framework for describing dense granular systems. Experiments on vibrated granular columns and numerical simulations of quasi- static shear flow of dense granular systems have provided indirect evidence that the Edwards' theory may accurately describe certain aspects of these systems. However, a fundamental assumption of the Edwards' description---that all mechanically stable (MS) granular packings at a given packing fraction and externally imposed stress are equally accessible---has not been explicitly tested. We investigate this assumption by generating all mechanically stable hard disk packings in small bidisperse systems using a protocol where we successively compress or decompress the system followed by energy minimization. We then apply quasi-static shear flow at zero pressure to these MS packings and record the MS packings that occur during the shear flow. We generate a complete library of the allowed MS packings at each value of shear strain and determine the frequency with which each MS packing occurs. We find that the MS packings do not occur with equal probability at any value of shear strain. In fact, in small systems we find that the evolution becomes periodic with a period that grows with system-size. Our studies show that ergodicity can be improved by either adding random fluctuations to the system or increasing the system size.
Ergodicity of the recent geomagnetic field
NASA Astrophysics Data System (ADS)
De Santis, A.; Qamili, E.; Cianchini, G.
2011-06-01
The geomagnetic field is a fundamental property of our planet: its study would allow us to understand those processes of Earth's interior, which act in its outer core and produce the main field. Knowledge of whether the field is ergodic, i.e. whether time averages correspond to phase space averages, is an important question since, if this were true, it would point out a strong spatio-temporal coupling amongst the components of the dynamical system behind the present geomagnetic field generation. Another consequence would be that many computations, usually undertaken with many difficulties in the phase space, can be made in the conventional time domain. We analyse the temporal behaviour of the deviation between predictive and definitive geomagnetic global models for successive intervals from 1965 to 2010, finding a similar exponential growth with time. Also going back in time (at around 1600 and 1900 by using the GUFM1 model) confirms the same findings. This result corroborates previous chaotic analyses made in a reconstructed phase space from geomagnetic observatory time series, confirming the chaotic character of the recent geomagnetic field with no reliable prediction after around 6 years from definitive values, and disclosing the potentiality of estimating important entropic quantities of the field by time averages. Although more tests will be necessary, some of our analyses confirm the efforts to improve the representation of the geomagnetic field with more detailed secular variation and acceleration.
Weak ergodicity breaking induced by global memory effects
NASA Astrophysics Data System (ADS)
Budini, Adrián A.
2016-08-01
We study the phenomenon of weak ergodicity breaking for a class of globally correlated random walk dynamics defined over a finite set of states. The persistence in a given state or the transition to another one depends on the whole previous temporal history of the system. A set of waiting time distributions, associated to each state, sets the random times between consecutive steps. Their mean value is finite for all states. The probability density of time-averaged observables is obtained for different memory mechanisms. This statistical object explicitly shows departures between time and ensemble averages. While the residence time in each state may have a divergent mean value, we demonstrate that this condition is in general not necessary for breaking ergodicity. Hence, we conclude that global memory effects are an alternative mechanism able to induce ergodicity breaking without involving power-law statistics. Analytical and numerical calculations support these results.
Weak ergodicity breaking, irreproducibility, and ageing in anomalous diffusion processes
Metzler, Ralf
2014-01-14
Single particle traces are standardly evaluated in terms of time averages of the second moment of the position time series r(t). For ergodic processes, one can interpret such results in terms of the known theories for the corresponding ensemble averaged quantities. In anomalous diffusion processes, that are widely observed in nature over many orders of magnitude, the equivalence between (long) time and ensemble averages may be broken (weak ergodicity breaking), and these time averages may no longer be interpreted in terms of ensemble theories. Here we detail some recent results on weakly non-ergodic systems with respect to the time averaged mean squared displacement, the inherent irreproducibility of individual measurements, and methods to determine the exact underlying stochastic process. We also address the phenomenon of ageing, the dependence of physical observables on the time span between initial preparation of the system and the start of the measurement.
Ergodicity testing for anomalous diffusion: Small sample statistics
NASA Astrophysics Data System (ADS)
Janczura, Joanna; Weron, Aleksander
2015-04-01
The analysis of trajectories recorded in experiments often requires calculating time averages instead of ensemble averages. According to the Boltzmann hypothesis, they are equivalent only under the assumption of ergodicity. In this paper, we implement tools that allow to study ergodic properties. This analysis is conducted in two classes of anomalous diffusion processes: fractional Brownian motion and subordinated Ornstein-Uhlenbeck process. We show that only first of them is ergodic. We demonstrate this by applying rigorous statistical methods: mean square displacement, confidence intervals, and dynamical functional test. Our methodology is universal and can be implemented for analysis of many experimental data not only if a large sample is available but also when there are only few trajectories recorded.
Ergodicity testing for anomalous diffusion: small sample statistics.
Janczura, Joanna; Weron, Aleksander
2015-04-14
The analysis of trajectories recorded in experiments often requires calculating time averages instead of ensemble averages. According to the Boltzmann hypothesis, they are equivalent only under the assumption of ergodicity. In this paper, we implement tools that allow to study ergodic properties. This analysis is conducted in two classes of anomalous diffusion processes: fractional Brownian motion and subordinated Ornstein-Uhlenbeck process. We show that only first of them is ergodic. We demonstrate this by applying rigorous statistical methods: mean square displacement, confidence intervals, and dynamical functional test. Our methodology is universal and can be implemented for analysis of many experimental data not only if a large sample is available but also when there are only few trajectories recorded. PMID:25877558
Weak ergodicity breaking induced by global memory effects.
Budini, Adrián A
2016-08-01
We study the phenomenon of weak ergodicity breaking for a class of globally correlated random walk dynamics defined over a finite set of states. The persistence in a given state or the transition to another one depends on the whole previous temporal history of the system. A set of waiting time distributions, associated to each state, sets the random times between consecutive steps. Their mean value is finite for all states. The probability density of time-averaged observables is obtained for different memory mechanisms. This statistical object explicitly shows departures between time and ensemble averages. While the residence time in each state may have a divergent mean value, we demonstrate that this condition is in general not necessary for breaking ergodicity. Hence, we conclude that global memory effects are an alternative mechanism able to induce ergodicity breaking without involving power-law statistics. Analytical and numerical calculations support these results. PMID:27627247
No-go theorem for ergodicity and an Einstein relation.
Froemberg, D; Barkai, E
2013-08-01
We provide a simple no-go theorem for ergodicity and the generalized Einstein relation for anomalous diffusion processes. The theorem states that either ergodicity in the sense of equal time and ensemble averaged mean squared displacements (MSD) is broken, and/or the generalized Einstein relation for time averaged diffusivity and mobility is invalid, which is in complete contrast to normal diffusion processes. We also give a general relation for the time averages of drift and MSD for ergodic (in the MSD sense) anomalous diffusion processes, showing that the ratio of these quantities depends on the measurement time. The Lévy walk model is used to exemplify the no-go theorem. PMID:24032966
Dielectric relaxation in weakly ergodic dilute dipole systems
NASA Astrophysics Data System (ADS)
Lerner, Shimon E.; Mierzwa, Michal; Paluch, Marian; Feldman, Yuri; Ishai, Paul Ben
2013-05-01
We introduce a method for calculating dipole correlations in systems containing hopping processes exhibiting weak ergodicity breaking. Modeled after the original Kirkwood-Fröhlich theory, the new method provides a bridge extending Fröhlich's insights from the realm of rigid dipoles into weakly non-ergodic fluctuating virtual dipolar entities. Relevant for the investigation of any system containing transport processes, it provides a testable parameter derived primarily from the static dielectric parameters. Three examples of systems including porous silicon, porous glass, and ferroelectric crystals are brought to demonstrate the model's versatility, including direct confirmation of Fröhlich's original idea.
Dielectric relaxation in weakly ergodic dilute dipole systems.
Lerner, Shimon E; Mierzwa, Michal; Paluch, Marian; Feldman, Yuri; Ishai, Paul Ben
2013-05-28
We introduce a method for calculating dipole correlations in systems containing hopping processes exhibiting weak ergodicity breaking. Modeled after the original Kirkwood-Fröhlich theory, the new method provides a bridge extending Fröhlich's insights from the realm of rigid dipoles into weakly non-ergodic fluctuating virtual dipolar entities. Relevant for the investigation of any system containing transport processes, it provides a testable parameter derived primarily from the static dielectric parameters. Three examples of systems including porous silicon, porous glass, and ferroelectric crystals are brought to demonstrate the model's versatility, including direct confirmation of Fröhlich's original idea. PMID:23742487
Zeno effect and ergodicity in finite-time quantum measurements
Sokolovski, D.
2011-12-15
We demonstrate that an attempt to measure a nonlocal in time quantity, such as the time average {sub T} of a dynamical variable A, by separating Feynman paths into ever narrower exclusive classes traps the system in eigensubspaces of the corresponding operator A. Conversely, in a long measurement of {sub T} to a finite accuracy, the system explores its Hilbert space and is driven to a universal steady state in which the von Neumann ensemble average of A coincides with {sub T}. Both effects are conveniently analyzed in terms of singularities and critical points of the corresponding amplitude distribution and the Zeno-like behavior is shown to be a consequence of the conservation of probability.
An ergodic approach to eruption hazard scaling
NASA Astrophysics Data System (ADS)
De la Cruz-Reyna, Servando; Mendoza-Rosas, Ana Teresa
2014-05-01
The complexity and indeterminacy of volcanic processes demand the use of statistical methods to analyze the expectations of the occurrence and size of future eruptions. The probability of a volcano producing potentially destructive eruptions in a given time interval may be estimated analyzing the sequence of past eruptions assuming a physically plausible process. Since the threat posed by eruptions depends on their mass or energy release (magnitude) and on their emission rate (intensity), the Volcanic Explosivity Index is a suitable measure to quantify the eruptive events, particularly considering that the largest available global catalogues use that measure. The definition of volcanic hazard is thus posed here in terms of the expected annual release of energy by eruptions in each VEI category. This concept is based on the ergodic property of a large set of volcanoes to release about the same amount of energy in each VEI category over a sufficiently large time interval. This property is however constrained to the VEI range of eruptions that constitute complete catalogues (VEI >2) in the lower end, and to the extreme eruptions that may destroy or significantly alter a volcanic system, such as the large caldera-forming eruptions (VEI < 7). In such conditions, a simple power law for eruptions at the global level relating the global rate of energy release to the eruption magnitude has been proposed as a statistical basis for eruptive event model development. Following the above mentioned arguments, we assume that a similar scaling law rules the annual rate at which energy is released by eruptions at individual volcanoes as log(EmRm)=bM+a, where Em is the energy released by eruptions in the VEI magnitude class M, and Rm is the occurrence rate of such eruptions over times ranges in which catalogues may be considered complete. The parameters b and a depend on the eruptive history of individual volcanoes, the former determining the preferred mode of the volcano to release
Ergodicity bounds for birth-death processes with particularities
NASA Astrophysics Data System (ADS)
Zeifman, Alexander I.; Satin, Yacov; Korotysheva, Anna; Shilova, Galina; Kiseleva, Ksenia; Korolev, Victor Yu.; Bening, Vladimir E.; Shorgin, Sergey Ya.
2016-06-01
We introduce an inhomogeneous birth-death process with birth rates λk(t), death rates µk(t), and possible transitions to/from zero with rates βk(t), rk(t) respectively, and obtain ergodicity bounds for this process.
Geometry of the ergodic quotient reveals coherent structures in flows
NASA Astrophysics Data System (ADS)
Budišić, Marko; Mezić, Igor
2012-08-01
Dynamical systems that exhibit diverse behaviors can rarely be completely understood using a single approach. However, by identifying coherent structures in their state spaces, i.e., regions of uniform and simpler behavior, we could hope to study each of the structures separately and then form the understanding of the system as a whole. The method we present in this paper uses trajectory averages of scalar functions on the state space to: (a) identify invariant sets in the state space, and (b) to form coherent structures by aggregating invariant sets that are similar across multiple spatial scales. First, we construct the ergodic quotient, the object obtained by mapping trajectories to the space of the trajectory averages of a function basis on the state space. Second, we endow the ergodic quotient with a metric structure that successfully captures how similar the invariant sets are in the state space. Finally, we parametrize the ergodic quotient using intrinsic diffusion modes on it. By segmenting the ergodic quotient based on the diffusion modes, we extract coherent features in the state space of the dynamical system. The algorithm is validated by analyzing the Arnold-Beltrami-Childress flow, which was the test-bed for alternative approaches: the Ulam’s approximation of the transfer operator and the computation of Lagrangian Coherent Structures. Furthermore, we explain how the method extends the Poincaré map analysis for periodic flows. As a demonstration, we apply the method to a periodically-driven three-dimensional Hill’s vortex flow, discovering unknown coherent structures in its state space. Finally, we discuss differences between the ergodic quotient and alternatives, propose a generalization to analysis of (quasi-)periodic structures, and lay out future research directions.
Cheng, Liwen Chen, Haitao; Wu, Shudong
2015-08-28
The effects of removing the AlGaN electron blocking layer (EBL), and using a last quantum barrier (LQB) with a unique design in conventional blue InGaN light-emitting diodes (LEDs), were investigated through simulations. Compared with the conventional LED design that contained a GaN LQB and an AlGaN EBL, the LED that contained an AlGaN LQB with a graded-composition and no EBL exhibited enhanced optical performance and less efficiency droop. This effect was caused by an enhanced electron confinement and hole injection efficiency. Furthermore, when the AlGaN LQB was replaced with a triangular graded-composition, the performance improved further and the efficiency droop was lowered. The simulation results indicated that the enhanced hole injection efficiency and uniform distribution of carriers observed in the quantum wells were caused by the smoothing and thinning of the potential barrier for the holes. This allowed a greater number of holes to tunnel into the quantum wells from the p-type regions in the proposed LED structure.
Ergodic model for the expansion of spherical nanoplasmas
Peano, F.; Silva, L. O.
2007-06-15
Recently, the collisionless expansion of spherical nanoplasmas has been analyzed with a new ergodic model, clarifying the transition from hydrodynamiclike to Coulomb-explosion regimes, and providing accurate laws for the relevant features of the phenomenon. A complete derivation of the model is presented here. The important issue of the self-consistent initial conditions is addressed by analyzing the initial charging transient due to the electron expansion, in the approximation of immobile ions. A comparison among different kinetic models for the expansion is presented, showing that the ergodic model provides a simplified description, which retains the essential information on the electron distribution, in particular, the energy spectrum. Results are presented for a wide range of initial conditions (determined from a single dimensionless parameter), in excellent agreement with calculations from the exact Vlasov-Poisson theory, thus providing a complete and detailed characterization of all the stages of the expansion.
Ergodicity convergence test suggests telomere motion obeys fractional dynamics.
Kepten, E; Bronshtein, I; Garini, Y
2011-04-01
Anomalous diffusion, observed in many biological processes, is a generalized description of a wide variety of processes, all obeying the same law of mean-square displacement. Identifying the basic mechanisms of these observations is important for deducing the nature of the biophysical systems measured. We implement a previously suggested method for distinguishing between fractional Langevin dynamics, fractional Brownian motion, and continuous time random walk based on the ergodic nature of the data. We apply the method together with the recently suggested P-variation test and the displacement correlation to the lately measured dynamics of telomeres in the nucleus of mammalian cells and find strong evidence that the telomeres motion obeys fractional dynamics. The ergodic dynamics are observed experimentally to fit fractional Brownian or Langevin dynamics. PMID:21599212
Ergodicity convergence test suggests telomere motion obeys fractional dynamics
NASA Astrophysics Data System (ADS)
Kepten, E.; Bronshtein, I.; Garini, Y.
2011-04-01
Anomalous diffusion, observed in many biological processes, is a generalized description of a wide variety of processes, all obeying the same law of mean-square displacement. Identifying the basic mechanisms of these observations is important for deducing the nature of the biophysical systems measured. We implement a previously suggested method for distinguishing between fractional Langevin dynamics, fractional Brownian motion, and continuous time random walk based on the ergodic nature of the data. We apply the method together with the recently suggested P-variation test and the displacement correlation to the lately measured dynamics of telomeres in the nucleus of mammalian cells and find strong evidence that the telomeres motion obeys fractional dynamics. The ergodic dynamics are observed experimentally to fit fractional Brownian or Langevin dynamics.
Robust Criterion for the Existence of Nonhyperbolic Ergodic Measures
NASA Astrophysics Data System (ADS)
Bochi, Jairo; Bonatti, Christian; Díaz, Lorenzo J.
2016-06-01
We give explicit C 1-open conditions that ensure that a diffeomorphism possesses a nonhyperbolic ergodic measure with positive entropy. Actually, our criterion provides the existence of a partially hyperbolic compact set with one-dimensional center and positive topological entropy on which the center Lyapunov exponent vanishes uniformly. The conditions of the criterion are met on a C 1-dense and open subset of the set of diffeomorphisms having a robust cycle. As a corollary, there exists a C 1-open and dense subset of the set of non-Anosov robustly transitive diffeomorphisms consisting of systems with nonhyperbolic ergodic measures with positive entropy. The criterion is based on a notion of a blender defined dynamically in terms of strict invariance of a family of discs.
Smoluchowski dynamics and the ergodic-nonergodic transition.
Mazenko, Gene F
2011-04-01
We use the recently introduced theory for the kinetics of systems of classical particles to investigate systems driven by Smoluchowski dynamics. We investigate the existence of ergodic-nonergodic (ENE) transitions near the liquid-glass transition. We develop a self-consistent perturbation theory in terms of an effective two-body potential and work to second order in this potential. At second order, we have an explicit relationship between the static structure factor and the effective potential and choose the static structure factor in the case of hard spheres to be given by the solution of the Percus-Yevick approximation for hard spheres. Then, using the analytically determined ENE equation for the ergodicity function, we find an ENE transition for packing fraction η greater than a critical value η(*)=0.76, which is physically unaccessible. The existence of a linear fluctuation-dissipation theorem in the problem is shown and used to great advantage. PMID:21599133
Ergodicity and Earthquake Catalogs: Forecast Testing and Resulting Implications
NASA Astrophysics Data System (ADS)
Tiampo, K. F.; Klein, W.; Li, H.-C.; Mignan, A.; Toya, Y.; Kohen-Kadosh, S. Z. L.; Rundle, J. B.; Chen, C.-C.
2010-06-01
Recently the equilibrium property of ergodicity was identified in an earthquake fault system (T iampo et al., Phys. Rev. Lett. 91, 238501, 2003; Phys. Rev. E 75, 066107, 2007). Ergodicity in this context not only requires that the system is stationary for these networks at the applicable spatial and temporal scales, but also implies that they are in a state of metastable equilibrium, one in which the ensemble averages can be substituted for temporal averages when studying their behavior in space and time. In this work we show that this property can be used to identify those regions of parameter space which are stationary when applied to the seismicity of two naturally-occurring earthquake fault networks. We apply this measure to one particular seismicity-based forecasting tool, the Pattern Informatics index (T iampo et al., Europhys. Lett. 60, 481-487, 2002; R undle et al., Proc. National Acad. Sci., U.S.A., Suppl. 1, 99, 2463, 2002), in order to test the hypothesis that the identification of ergodic regions can be used to improve and optimize forecasts that rely on historic seismicity catalogs. We also apply the same measure to synthetic catalogs in order to better understand the physical process that affects this accuracy. We show that, in particular, ergodic regions defined by magnitude and time period provide more reliable forecasts of future events in both natural and synthetic catalogs, and that these improvements can be directly related to specific features or properties of the catalogs that impact the behavior of their spatial and temporal statistics.
The ergodic decomposition of stationary discrete random processes
NASA Technical Reports Server (NTRS)
Gray, R. M.; Davisson, L. D.
1974-01-01
The ergodic decomposition is discussed, and a version focusing on the structure of individual sample functions of stationary processes is proved for the special case of discrete-time random processes with discrete alphabets. The result is stronger in this case than the usual theorem, and the proof is both intuitive and simple. Estimation-theoretic and information-theoretic interpretations are developed and applied to prove existence theorems for universal source codes, both noiseless and with a fidelity criterion.
The ergodicity bias in the observed galaxy distribution
Pan, Jun; Zhang, Pengjie E-mail: pjzhang@shao.ac.cn
2010-08-01
The spatial distribution of galaxies we observed is subject to the given condition that we, human beings are sitting right in a galaxy — the Milky Way. Thus the ergodicity assumption is questionable in interpretation of the observed galaxy distribution. The resultant difference between observed statistics (volume average) and the true cosmic value (ensemble average) is termed as the ergodicity bias. We perform explicit numerical investigation of the effect for a set of galaxy survey depths and near-end distance cuts. It is found that the ergodicity bias in observed two- and three-point correlation functions in most cases is insignificant for modern analysis of samples from galaxy surveys and thus close a loophole in precision cosmology. However, it may become non-negligible in certain circumstances, such as those applications involving three-point correlation function at large scales of local galaxy samples. Thus one is reminded to take extra care in galaxy sample construction and interpretation of the statistics of the sample, especially when the characteristic redshift is low.
Ergodic capacity comparison of optical wireless communications using adaptive transmissions.
Hassan, Md Zoheb; Hossain, Md Jahangir; Cheng, Julian
2013-08-26
Ergodic capacity is investigated for the optical wireless communications employing subcarrier intensity modulation with direct detection, and coherent systems with and without polarization multiplexing over the Gamma-Gamma turbulence channels. We consider three different adaptive transmission schemes: (i) variable-power, variable-rate adaptive transmission, (ii) complete channel inversion with fixed rate, and (iii) truncated channel inversion with fixed rate. For the considered systems, highly accurate series expressions for ergodic capacity are derived using a series expansion of the modified Bessel function and the Mellin transformation of the Gamma-Gamma random variable. Our asymptotic analysis reveals that the high SNR ergodic capacities of coherent, subcarrier intensity modulated, and polarization multiplexing systems gain 0.33 bits/s/Hz, 0.66 bits/s/Hz, and 0.66 bits/s/Hz respectively with 1 dB increase of average transmitted optical power. Numerical results indicate that a polarization control error less than 10° has little influence on the capacity performance of polarization multiplexing systems. PMID:24105580
Thomas, Kolle E; Alemayehu, Abraham B; Conradie, Jeanet; Beavers, Christine M; Ghosh, Abhik
2012-08-21
Although they share some superficial structural similarities with porphyrins, corroles, trianionic ligands with contracted cores, give rise to fundamentally different transition metal complexes in comparison with the dianionic porphyrins. Many metallocorroles are formally high-valent, although a good fraction of them are also noninnocent, with significant corrole radical character. These electronic-structural characteristics result in a variety of fascinating spectroscopic behavior, including highly characteristic, paramagnetically shifted NMR spectra and textbook cases of charge-transfer spectra. Although our early research on corroles focused on spectroscopy, we soon learned that the geometric structures of metallocorroles provide a fascinating window into their electronic-structural characteristics. Thus, we used X-ray structure determinations and quantum chemical studies, chiefly using DFT, to obtain a comprehensive understanding of metallocorrole geometric and electronic structures. This Account describes our studies of the structural chemistry of metallocorroles. At first blush, the planar or mildly domed structure of metallocorroles might appear somewhat uninteresting particularly when compared to metalloporphyrins. Metalloporphyrins, especially sterically hindered ones, are routinely ruffled or saddled, but the missing meso carbon apparently makes the corrole skeleton much more resistant to nonplanar distortions. Ruffling, where the pyrrole rings are alternately twisted about the M-N bonds, is energetically impossible for metallocorroles. Saddling is also uncommon; thus, a number of sterically hindered, fully substituted metallocorroles exhibit almost perfectly planar macrocycle cores. Against this backdrop, copper corroles stand out as an important exception. As a result of an energetically favorable Cu(d(x2-y2))-corrole(π) orbital interaction, copper corroles, even sterically unhindered ones, are inherently saddled. Sterically hindered substituents
Ergodicity of Truncated Stochastic Navier Stokes with Deterministic Forcing and Dispersion
NASA Astrophysics Data System (ADS)
Majda, Andrew J.; Tong, Xin T.
2016-05-01
Turbulence in idealized geophysical flows is a very rich and important topic. The anisotropic effects of explicit deterministic forcing, dispersive effects from rotation due to the β -plane and F-plane, and topography together with random forcing all combine to produce a remarkable number of realistic phenomena. These effects have been studied through careful numerical experiments in the truncated geophysical models. These important results include transitions between coherent jets and vortices, and direct and inverse turbulence cascades as parameters are varied, and it is a contemporary challenge to explain these diverse statistical predictions. Here we contribute to these issues by proving with full mathematical rigor that for any values of the deterministic forcing, the β - and F-plane effects and topography, with minimal stochastic forcing, there is geometric ergodicity for any finite Galerkin truncation. This means that there is a unique smooth invariant measure which attracts all statistical initial data at an exponential rate. In particular, this rigorous statistical theory guarantees that there are no bifurcations to multiple stable and unstable statistical steady states as geophysical parameters are varied in contrast to claims in the applied literature. The proof utilizes a new statistical Lyapunov function to account for enstrophy exchanges between the statistical mean and the variance fluctuations due to the deterministic forcing. It also requires careful proofs of hypoellipticity with geophysical effects and uses geometric control theory to establish reachability. To illustrate the necessity of these conditions, a two-dimensional example is developed which has the square of the Euclidean norm as the Lyapunov function and is hypoelliptic with nonzero noise forcing, yet fails to be reachable or ergodic.
Distribution of time-averaged observables for weak ergodicity breaking.
Rebenshtok, A; Barkai, E
2007-11-23
We find a general formula for the distribution of time-averaged observables for systems modeled according to the subdiffusive continuous time random walk. For Gaussian random walks coupled to a thermal bath we recover ergodicity and Boltzmann's statistics, while for the anomalous subdiffusive case a weakly nonergodic statistical mechanical framework is constructed, which is based on Lévy's generalized central limit theorem. As an example we calculate the distribution of X, the time average of the position of the particle, for unbiased and uniformly biased particles, and show that X exhibits large fluctuations compared with the ensemble average
Multifractals, encoded walks and the ergodicity of protein sequences.
Dewey, T G; Strait, B J
1996-01-01
A variety of statistical methods have been developed to explore correlations in protein and nucleic acid sequences. Such correlations have important implications for the evolution and stability of these macromolecules. Recently, a number of fractal analyses of sequence data have been developed. These analyses have considerable appeal as they are extremely sensitive to long range correlations and to hierarchical structures. One such analysis decodes sequence information into a random walk and the statistics of the resulting random walk is investigated. Anomalous scaling of such walks has been interpreted as indicative of a fractal structure. Alternatively, a generalized box counting analysis of decoded sequences can be used to establish multifractal properties. In this work, the connection between these two seemingly disparate approaches is established. This connection is exploited to investigate correlations in protein sequences. An ensemble consisting of a comprehensive data set of representative protein sequences is analyzed to establish the ergodicity of protein sequences. The implications of this ergodicity for information theoretical approaches to protein structure prediction is explored. PMID:9390234
Broken Ergodicity in MHD Turbulence in a Spherical Domain
NASA Technical Reports Server (NTRS)
Shebalin, John V.; wang, Yifan
2011-01-01
Broken ergodicity (BE) occurs in Fourier method numerical simulations of ideal, homogeneous, incompressible magnetohydrodynamic (MHD) turbulence. Although naive statistical theory predicts that Fourier coefficients of fluid velocity and magnetic field are zero-mean random variables, numerical simulations clearly show that low-wave-number coefficients have non-zero mean values that can be very large compared to the associated standard deviation. In other words, large-scale coherent structure (i.e., broken ergodicity) in homogeneous MHD turbulence can spontaneously grow out of random initial conditions. Eigenanalysis of the modal covariance matrices in the probability density functions of ideal statistical theory leads to a theoretical explanation of observed BE in homogeneous MHD turbulence. Since dissipation is minimal at the largest scales, BE is also relevant for resistive magnetofluids, as evidenced in numerical simulations. Here, we move beyond model magnetofluids confined by periodic boxes to examine BE in rotating magnetofluids in spherical domains using spherical harmonic expansions along with suitable boundary conditions. We present theoretical results for 3-D and 2-D spherical models and also present computational results from dynamical simulations of 2-D MHD turbulence on a rotating spherical surface. MHD turbulence on a 2-D sphere is affected by Coriolus forces, while MHD turbulence on a 2-D plane is not, so that 2-D spherical models are a useful (and simpler) intermediate stage on the path to understanding the much more complex 3-D spherical case.
Is ergodicity a reasonable hypothesis for macroscopic systems?
NASA Astrophysics Data System (ADS)
Gaveau, B.; Schulman, L. S.
2015-07-01
In the physics literature "ergodicity" is sometimes taken to mean that a system, including a macroscopic one, visits all microscopic states in a relatively short time. However, many authors have realized that this is impossible and we provide a rigorous bound demonstrating this fact. A related concept is the "thermal distribution." This enters in an understanding of dissipation, comparing the thermal state (the Boltzmann or Gibbs distribution) to its time evolute using relative entropy. The thermal distribution is based on the microcanonical ensemble, whose equal probability assumption is another phrasing of ergodicity in a macroscopic physical context. The puzzle then is why the results of these assumptions are in agreement with experience. We suggest (as others also have) reasons for this limited agreement, but note that the foundations of statistical mechanics make much stronger assumptions, assumptions that do not have the support of either reason or experience. This article is supplemented with comments by P. Gaspard, Y. Pomeau and H. Qian and a final reply by the authors.
The Entropy of Non-Ergodic Complex Systems — a Derivation from First Principles
NASA Astrophysics Data System (ADS)
Thurner, Stefan; Hanel, Rudolf
In information theory the 4 Shannon-Khinchin1,2 (SK) axioms determine Boltzmann Gibbs entropy, S -∑i pilog pi, as the unique entropy. Physics is different from information in the sense that physical systems can be non-ergodic or non-Markovian. To characterize such strongly interacting, statistical systems - complex systems in particular - within a thermodynamical framework it might be necessary to introduce generalized entropies. A series of such entropies have been proposed in the past decades. Until now the understanding of their fundamental origin and their deeper relations to complex systems remains unclear. To clarify the situation we note that non-ergodicity explicitly violates the fourth SK axiom. We show that by relaxing this axiom the entropy generalizes to, S ∑i Γ(d + 1, 1 - c log pi), where Γ is the incomplete Gamma function, and c and d are scaling exponents. All recently proposed entropies compatible with the first 3 SK axioms appear to be special cases. We prove that each statistical system is uniquely characterized by the pair of the two scaling exponents (c, d), which defines equivalence classes for all systems. The corresponding distribution functions are special forms of Lambert-W exponentials containing, as special cases, Boltzmann, stretched exponential and Tsallis distributions (power-laws) - all widely abundant in nature. This derivation is the first ab initio justification for generalized entropies. We next show how the phasespace volume of a system is related to its generalized entropy, and provide a concise criterion when it is not of Boltzmann-Gibbs type but assumes a generalized form. We show that generalized entropies only become relevant when the dynamically (statistically) relevant fraction of degrees of freedom in a system vanishes in the thermodynamic limit. These are systems where the bulk of the degrees of freedom is frozen. Systems governed by generalized entropies are therefore systems whose phasespace volume effectively
NASA Astrophysics Data System (ADS)
Nakagawa, Masaki; Aizawa, Yoji
2014-10-01
Universal aspects of a certain class of infinite ergodic systems are studied by using the infinite-modal maps with a special interest to their observed measures. It is shown that the ant-lion (AL) property is an important nature to realize the infinite ergodicity in the dissipative dynamics. The AL-property, which seems to be a little bit paradoxical one, is characterized by the monotonical relaxation of mean orbits into a singular stable point, but it causes the divergence of the Lyapunov exponent as well as the emergence of a number of absolutely-continuous invariant measures. Our main concern is to characterize the unique observed measure in those many admissible ergodic measures. To this end, firstly the randomization formulae are developed on the basis of the uniform distribution theorem by Weyl, to derive the stochastic aspects of the AL-property. Actually, it is shown that the statistical natures of the infinite-modal maps are well explained by the randomization formulae. Furthermore, it is shown that the observed measure derived from the randomization formulae is universal, and that the asymptotic form obeys the power law with the exponent -1, in agreement with numerical simulations.
On the analogues of Szegő's theorem for ergodic operators
NASA Astrophysics Data System (ADS)
Kirsch, W.; Pastur, L. A.
2015-01-01
Szegő's theorem on the asymptotic behaviour of the determinants of large Toeplitz matrices is generalized to the class of ergodic operators. The generalization is formulated in terms of a triple consisting of an ergodic operator and two functions, the symbol and the test function. It is shown that in the case of the one-dimensional discrete Schrödinger operator with random ergodic or quasiperiodic potential and various choices of the symbol and the test function this generalization leads to asymptotic formulae which have no analogues in the situation of Toeplitz operators. Bibliography: 22 titles.
Ergodicity and slow diffusion in a supercooled liquid
NASA Astrophysics Data System (ADS)
Bidhoodi, Neeta; Das, Shankar P.
2016-05-01
A model for the slow dynamics of the supercooled liquid is formulated in terms of the standard equations of fluctuating nonlinear hydrodynamics (FNH) with the inclusion of an extra diffusive mode for the collective density fluctuations. If the compressible nature of the liquid is completely ignored, this diffusive mode sets the longest relaxation times in the supercooled state and smooths off a possible sharp ergodicity-nonergodicity (ENE) transition predicted in a mode coupling theory. The scenario changes when the complete dynamics is considered with the inclusion of 1 / ρ nonlinearities in the FNH equations, reflecting the compressible nature of the liquid. The latter primarily determines the extent of slowing down in the supercooled liquid. The presence of slow diffusive modes in the supercooled liquid do not give rise to very long relaxation times unless the role of couplings between density and currents in the compressible liquid is negligible.
Percolation approach to glassy dynamics with continuously broken ergodicity
NASA Astrophysics Data System (ADS)
Arenzon, Jeferson J.; Coniglio, Antonio; Fierro, Annalisa; Sellitto, Mauro
2014-08-01
We show that the relaxation dynamics near a glass transition with continuous ergodicity breaking can be endowed with a geometric interpretation based on percolation theory. At the mean-field level this approach is consistent with the mode-coupling theory (MCT) of type-A liquid-glass transitions and allows one to disentangle the universal and nonuniversal contributions to MCT relaxation exponents. Scaling predictions for the time correlation function are successfully tested in the F12 schematic model and facilitated spin systems on a Bethe lattice. Our approach immediately suggests the extension of MCT scaling laws to finite spatial dimensions and yields predictions for dynamic relaxation exponents below an upper critical dimension of 6.
Individual Pooling for Group-Based Modeling Under the Assumption of Ergodicity.
Gonzales, Joseph E; Ferrer, Emilio
2014-01-01
Psychology principally utilizes nomothetic, interindividual approaches to model phenomena of interest. However, it is the case that these approaches do not always capture the processes for each individual in the sample. If the research is focused on individual processes, confining analysis to the idiographic level may be more appropriate. One way to overcome the nomothetic inability to capture idiographic processes is to identify those participants who meet the criteria of ergodicity and restrict analysis to the resulting sample. Under these conditions it is quantitatively justifiable to create a group model without concern that it may fail to represent each member's idiographic process. In this study we explore the utility of such a method by (a) applying an ergodic pooling test to a sample of dyads (N = 128) who provided daily (T = 50) self-reports of affect, (b) applying an ergodic pooling test to samples (N = 4) of simulated ergodic time series data (T = 50, 250, and 1,000), PMID:26735191
Ergodicity and Parameter Estimates for Infinite-Dimensional Fractional Ornstein-Uhlenbeck Process
Maslowski, Bohdan Pospisil, Jan
2008-06-15
Existence and ergodicity of a strictly stationary solution for linear stochastic evolution equations driven by cylindrical fractional Brownian motion are proved. Ergodic behavior of non-stationary infinite-dimensional fractional Ornstein-Uhlenbeck processes is also studied. Based on these results, strong consistency of suitably defined families of parameter estimators is shown. The general results are applied to linear parabolic and hyperbolic equations perturbed by a fractional noise.
Molecular dynamics ensemble, equation of state, and ergodicity.
Wood, W W; Erpenbeck, J J; Baker, G A; Johnson, J D
2001-01-01
The variant of the NVE ensemble known as the molecular dynamics ensemble was recently redefined by Ray and Zhang [Phys. Rev. E 59, 4781 (1999)] to include the specification of a time invariant G (a function of phase and, explicitly, the time) in addition to the total linear momentum M. We reformulate this ensemble slightly as the NVEMR ensemble, in which R/N is the center-of-mass position, and consider the equation of state of the hard-sphere system in this ensemble through both the virial function and the Boltzmann entropy. We test the quasiergodic hypothesis by a comparison of old molecular dynamics and Monte Carlo results for the compressibility factor of the 12-particle, hard-disk systems. The virial approach, which had previously been found to support the hypothesis in the NVEM ensemble, remains unchanged in the NVEMR ensemble. The entropy S approach depends on whether S is defined through the phase integral over the energy sphere or the energy shell, the parameter straight theta being 0 or 1, respectively. The ergodic hypothesis is found to be supported for straight theta=0 but not for straight theta=1. PMID:11304233
Molecular dynamics ensemble, equation of state, and ergodicity
Wood, William W.; Erpenbeck, Jerome J.; Baker, George A.; Johnson, J. D.
2001-01-01
The variant of the NVE ensemble known as the molecular dynamics ensemble was recently redefined by Ray and Zhang [Phys. Rev. E 59, 4781 (1999)] to include the specification of a time invariant G (a function of phase and, explicitly, the time) in addition to the total linear momentum M. We reformulate this ensemble slightly as the NVEMR ensemble, in which R/N is the center-of-mass position, and consider the equation of state of the hard-sphere system in this ensemble through both the virial function and the Boltzmann entropy. We test the quasiergodic hypothesis by a comparison of old molecular dynamics and Monte Carlo results for the compressibility factor of the 12-particle, hard-disk systems. The virial approach, which had previously been found to support the hypothesis in the NVEM ensemble, remains unchanged in the NVEMR ensemble. The entropy S approach depends on whether S is defined through the phase integral over the energy sphere or the energy shell, the parameter {theta} being 0 or 1, respectively. The ergodic hypothesis is found to be supported for {theta}=0 but not for {theta}=1.
Quantum Computer Games: Quantum Minesweeper
ERIC Educational Resources Information Center
Gordon, Michal; Gordon, Goren
2010-01-01
The computer game of quantum minesweeper is introduced as a quantum extension of the well-known classical minesweeper. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. Quantum minesweeper demonstrates the effects of superposition, entanglement and their non-local characteristics. While in the classical…
Ergodic theory and experimental visualization of chaos in 3D flows
NASA Astrophysics Data System (ADS)
Sotiropoulos, Fotis; Mezic, Igor
2000-11-01
In his motivation for the ergodic hypothesis Gibbs invoked an analogy with fluid mixing: “…Yet no fact is more familiar to us than that stirring tends to bring a liquid to a state of uniform mixture, or uniform densities of its components…”. Although proof of the ergodic hypothesis is possible only for the simplest of systems using methods from ergodic theory, the use of the hypothesis has led to many accurate predictions in statistical mechanics. The problem of fluid mixing, however, turned out to be considerably more complicated than Gibbs envisioned. Chaotic advection can indeed lead to efficient mixing even in non-turbulent flows, but many non-mixed islands are known to persist within well-mixed regions. In numerical studies, Poincaré maps can be used to reveal the structure of such islands but their visualization in the laboratory requires laborious experimental procedures and is possible only for certain types of flows. Here we propose the first non-intrusive, simple to implement, and generally applicable technique for constructing experimental Poincaré maps and apply it to a steady, 3D, vortex breakdown bubble. We employ standard laser-induced fluorescence (LIF) and construct Poincaré maps by time averaging a sufficiently long sequence of instantaneous LIF images. We also show that ergodic theory methods provide a rigorous theoretical justification for this approach whose main objective is to reveal the non-ergodic regions of the flow.
NASA Technical Reports Server (NTRS)
Metzger, Philip T.
2006-01-01
Ergodicity is proved for granular contact forces. To obtain this proof from first principles, this paper generalizes Boltzmann's stosszahlansatz (molecular chaos) so that it maintains the necessary correlations and symmetries of granular packing ensembles. Then it formally counts granular contact force states and thereby defines the proper analog of Boltzmann's H functional. This functional is used to prove that (essentially) all static granular packings must exist at maximum entropy with respect to their contact forces. Therefore, the propagation of granular contact forces through a packing is a truly ergodic process in the Boltzmannian sense, or better, it is self-ergodic. Self-ergodicity refers to the non-dynamic, internal relationships that exist between the layer-by-layer and column-by-column subspaces contained within the phase space locus of any particular granular packing microstate. The generalized H Theorem also produces a recursion equation that may be solved numerically to obtain the density of single particle states and hence the distribution of granular contact forces corresponding to the condition of self-ergodicity. The predictions of the theory are overwhelmingly validated by comparison to empirical data from discrete element modeling.
The non-ergodic nature of internal conversion.
Sølling, Theis I; Kuhlman, Thomas S; Stephansen, Anne B; Klein, Liv B; Møller, Klaus B
2014-02-01
The absorption of light by molecules can induce ultrafast dynamics and coupling of electronic and nuclear vibrational motion. The ultrafast nature in many cases rests on the importance of several potential energy surfaces in guiding the nuclear motion-a concept of central importance in many aspects of chemical reaction dynamics. This Minireview focuses on the non-ergodic nature of internal conversion, that is, on the concept that the nuclear dynamics only sample a reduced phase space, potentially resulting in localization of the dynamics in real space. A series of results that highlight the nonstatistical nature of the excited-state deactivation process is presented. The examples are categorized into four groups. 1) Localization of the energy in one degree of freedom in S2 →S1 transitions, in which the transition is either determined by the time spent in the S2 →S1 coupling region or by the time it takes to reach it. 2) Localization of energy into a single reactive mode, which is dictated by the internal conversion process. 3) Initiation of the internal conversion by activation of a single complex motion, which then specifically couples to a reactive mode. 4) Nonstatistical internal conversion as a tool to accomplish biomolecular stability. Herein, the discussion on nonstatistical internal conversion in DNA as a mechanism to eliminate electronic excitation energy is extended to include molecules with an S-S bond as a model of the disulfide bridge in peptides. All of these examples are summed up in Kasha's rule. For systems with multiple degrees of freedom it will be possible to locate an appropriate motion somewhere in phase space that will take the wavepacket to the coupling region and facilitate an ultrafast transition to S1. Once at S1, the momentum of the wavepacket is lost and the only options left are the statistical processes of reaction or light emission. PMID:24375886
Kinetics of ergodic-to-nonergodic transitions in charged colloidal suspensions: Aging and gelation
NASA Astrophysics Data System (ADS)
Tanaka, Hajime; Jabbari-Farouji, Sara; Meunier, Jacques; Bonn, Daniel
2005-02-01
There are two types of isotropic disordered nonergodic states in colloidal suspensions: colloidal glasses and gels. In a recent paper [H. Tanaka, J. Meunier, and D. Bonn, Phys. Rev. E 69, 031404 (2004)], we discussed the static aspect of the differences and the similarities between the two. In this paper, we focus on the dynamic aspect. The kinetics of the liquid-glass transition is called “aging,” while that of the sol-gel transition is called “gelation.” The former is primarily governed by repulsive interactions between particles, while the latter is dominated by attractive interactions. Slowing down of the dynamics during aging reflects the increasing cooperativity required for the escape of a particle from the cage formed by the surrounding particles, while that during gelation reflects the increase in the size of particle clusters towards the percolation transition. Despite these clear differences in the origin of the slowing down of the kinetics between the two, it is not straightforward experimentally to distinguish them in a clear manner. For an understanding of the universal nature of ergodic-to-nonergodic transitions, it is of fundamental importance to elucidate the differences and the similarities in the kinetics between aging and gelation. We consider this problem, taking Laponite suspension as an explicit example. In particular, we focus on the two types of nonergodic states: (i) an attractive gel formed by van der Waals attractions for high ionic strengths and (ii) a repulsive Wigner glass stabilized by long-range Coulomb repulsions for low ionic strengths. We demonstrate that the aging of colloidal Wigner glass crucially differs not only from gelation, but also from the aging of structural and spin glasses. The aging of the colloidal Wigner glass is characterized by the unique cage-forming regime that does not exist in the aging of spin and structural glasses.
Self-averaging and ergodicity of subdiffusion in quenched random media
NASA Astrophysics Data System (ADS)
Dentz, Marco; Russian, Anna; Gouze, Philippe
2016-01-01
We study the self-averaging properties and ergodicity of the mean square displacement m (t ) of particles diffusing in d dimensional quenched random environments which give rise to subdiffusive average motion. These properties are investigated in terms of the sample to sample fluctuations as measured by the variance of m (t ) . We find that m (t ) is not self-averaging for d <2 due to the inefficient disorder sampling by random motion in a single realization. For d ≥2 in contrast, the efficient sampling of heterogeneity by the space random walk renders m (t ) self-averaging and thus ergodic. This is remarkable because the average particle motion in d >2 obeys a CTRW, which by itself displays weak ergodicity breaking. This paradox is resolved by the observation that the CTRW as an average model does not reflect the disorder sampling by random motion in a single medium realization.
Ergodicity in a two-dimensional self-gravitating many-body system
NASA Astrophysics Data System (ADS)
Silvestre, C. H.; Rocha Filho, T. M.
2016-01-01
We study the ergodic properties of a two-dimensional self-gravitating system using molecular dynamics simulations. We apply three different tests for ergodicity: a direct method comparing the time average of a particle momentum and position to the respective ensemble average, sojourn times statistics and the dynamical functional method. For comparison purposes they are also applied to a short-range interacting system and to the Hamiltonian mean-field model. Our results show that a two-dimensional self-gravitating system takes a very long time to establish ergodicity. If a Kac factor is used in the potential energy, such that the total energy is extensive, then this time is independent of particle number, and diverges with √{ N} without a Kac factor.
The Ergodic Structure of Passive Scalar Turbulence Statistics within Dense Canopies
NASA Astrophysics Data System (ADS)
Ghannam, K.; Poggi, D.; Porporato, A. M.; Katul, G. G.
2014-12-01
The ergodic hypothesis, implicitly used in virtually all atmospheric boundary layer studies, assumes that the time/space average of a measured flow variable converges to an ensemble of independent realizations from similar initial states and boundary conditions and for sufficiently long sampling times. Turbulent flows within roughness elements such as canopies differ from their classical boundary layer counterparts due to the short-circuiting of the energy cascade and the prevalence of von Karman vortex streets in the deeper layers of the canopy (see Figure). Despite recent experimental support for the validity of the ergodic hypothesis on turbulence statistics in the atmospheric surface layer, the impact of the aforementioned phenomena on the ergodicity of passive scalars within dense canopies remains unexplored. Using Laser Induced Florescence (LIF) measurements and flow visualization of scalar concentration within a rod canopy situated in a flume (see Figure), the necessary conditions for ergodicity of passive scalar turbulence statistics at two different depths were considered. The integral time and length scales were first analyzed and their corresponding maximum values were used to construct an ensemble of (weak) independent realizations. To within experimental limitation, a Kolmogorov-Smirnov test on the distributions of temporal and spatial concentration series against the ensembles revealed that the ergodic hypothesis was reasonable, except close to the rods where wake-induced inhomogeneity and damped turbulence prevail. The spatial concentration statistics within a repeated rod-cell configuration appeared less ergodic than their temporal counterpart given the periodicity and persistence of von Karman vortices on the flow field. Using lagged cross-correlations of scalar concentration time series at different spatial locations, the local advection velocity of dominant eddies was inferred. The computed probability density function of the longitudinal
Non-ergodic aging and hierarchical organization in lithium-potassium tantalate crystals
NASA Astrophysics Data System (ADS)
Doussineau, P.; Levelut, A.; Ziolkiewicz, S.
1996-02-01
The dielectric constant of K1 - xLixTaO3, with x = 0.01 and x = 0.025, and specially its value at very long times, measured as a function of time (aging) at 4 K, depends on the cooling rate; this is a non-ergodic behaviour which manifests the lack of self-similarity of the phase space. The response to temperature jumps, similar to that of spin-glasses, is the signature of hierarchical organization of the phase space. For x = 0 (pure KTaO3), the behaviour is ergodic.
Constants in estimates for the rates of convergence in von Neumann's and Birkhoff's ergodic theorems
Kachurovskii, Alexander G; Sedalishchev, Vladimir V
2011-08-31
The paper investigates estimates which relate two equivalent phenomena: the power-type rate of convergence in von Neumann's ergodic theorem and the power-type singularity at zero (with the same exponent) exhibited by the spectral measure of the function being averaged with respect to the corresponding dynamical system. The same rate of convergence is also estimated in terms of the rate of decrease of the correlation coefficients. Also, constants are found in analogous estimates for the power-type convergence in Birkhoff's ergodic theorem. All the results have exact analogues for wide-sense stationary stochastic processes. Bibliography: 15 titles.
Non-ergodic diffusion on quenched, scale-free disorder in two dimensions
NASA Astrophysics Data System (ADS)
Lapeyre, Gerald J., Jr.; Massignan, Pietro; Manzo, Carlo; Torreno-Pina, Juan A.; García-Parajo, Maria F.; Lewenstein, Maciej
2015-03-01
We discuss our recently introduced models of diffsion on media with random diffusivity and their application to transport in cell membranes. We find that the diffusion shows weak ergodicity breaking, and compute the anomalous exponents as a function of model parameters. We also report recent results on criteria for prediciting weak ergodicity breaking in random walks on specific models of quenched, scale-free, random media. This work was supported by ERC AdG Osyris, Spanish Ministry of Science and Innovation (Grants No. FIS2008-00784 and MAT2011-22887).
In vivo anomalous diffusion and weak ergodicity breaking of lipid granules.
Jeon, Jae-Hyung; Tejedor, Vincent; Burov, Stas; Barkai, Eli; Selhuber-Unkel, Christine; Berg-Sørensen, Kirstine; Oddershede, Lene; Metzler, Ralf
2011-01-28
Combining extensive single particle tracking microscopy data of endogenous lipid granules in living fission yeast cells with analytical results we show evidence for anomalous diffusion and weak ergodicity breaking. Namely we demonstrate that at short times the granules perform subdiffusion according to the laws of continuous time random walk theory. The associated violation of ergodicity leads to a characteristic turnover between two scaling regimes of the time averaged mean squared displacement. At longer times the granule motion is consistent with fractional Brownian motion. PMID:21405366
Noisy attractors and ergodic sets in models of gene regulatory networks.
Ribeiro, Andre S; Kauffman, Stuart A
2007-08-21
We investigate the hypothesis that cell types are attractors. This hypothesis was criticized with the fact that real gene networks are noisy systems and, thus, do not have attractors [Kadanoff, L., Coppersmith, S., Aldana, M., 2002. Boolean Dynamics with Random Couplings. http://www.citebase.org/abstract?id=oai:arXiv.org:nlin/0204062]. Given the concept of "ergodic set" as a set of states from which the system, once entering, does not leave when subject to internal noise, first, using the Boolean network model, we show that if all nodes of states on attractors are subject to internal state change with a probability p due to noise, multiple ergodic sets are very unlikely. Thereafter, we show that if a fraction of those nodes are "locked" (not subject to state fluctuations caused by internal noise), multiple ergodic sets emerge. Finally, we present an example of a gene network, modelled with a realistic model of transcription and translation and gene-gene interaction, driven by a stochastic simulation algorithm with multiple time-delayed reactions, which has internal noise and that we also subject to external perturbations. We show that, in this case, two distinct ergodic sets exist and are stable within a wide range of parameters variations and, to some extent, to external perturbations. PMID:17543998
An ergodic configurational thermostat using selective control of higher order temperatures
NASA Astrophysics Data System (ADS)
Patra, Puneet Kumar; Bhattacharya, Baidurya
2015-05-01
The conventional Nosé-Hoover type deterministic thermostat scheme for controlling temperature by configurational variables (Braga-Travis (BT) thermostat) is non-ergodic for systems with a few degrees of freedom. While for the original Nosé-Hoover kinetic thermostat ergodicity has been achieved by controlling the higher order moments of kinetic energy, the issues of nonergodicity of BT thermostat persists. In this paper, we introduce two new measures of configurational temperature (second and third order) based on the generalized temperature-curvature relationship and obtain a family of deterministic thermostatting schemes by selectively (and simultaneously) controlling the different orders of temperatures through pseudo-friction terms. The ergodic characteristics of the proposed thermostats are tested using a single harmonic oscillator through statistical (normality of joint distributions at different Poincare sections) as well as dynamical tests (difference of the minimum and maximum largest Lyapunov exponent). Our results indicate that simultaneously controlling the first and the second order configurational temperatures (C1,2 thermostat) is sufficient to make the dynamics ergodic. A 2000 particle Lennard-Jones system is subjected to (i) equilibrium and (ii) sudden temperature change under BT and C1,2 thermostatting schemes. The C1,2 thermostat is found to be more robust than the BT thermostat without increasing computational costs.
NASA Astrophysics Data System (ADS)
Ghannam, Khaled; Poggi, Davide; Porporato, Amilcare; Katul, Gabriel G.
2015-12-01
Connections between the spatial and temporal statistics of turbulent flow, and their possible convergence to ensemble statistics as assumed by the ergodic hypothesis, are explored for passive scalars within a rod canopy. While complete ergodicity is not expected to apply over all the spatial domain within such heterogeneous flows, the fact that canopy turbulence exhibits self-similar characteristics at a given depth within the canopy encourages a discussion on necessary conditions for an `operational' ergodicity framework. Flows between roughness elements such as within canopies exhibit features that distinguish them from their well-studied classical boundary-layer counterparts. These differences are commonly attributed to short-circuiting of the energy cascade and the prevalence of intermittent von Kármán vortex streets in the deeper layers of the canopy. Using laser-induced fluorescence measurements at two different depths within a rod canopy situated in a large flume, the spatio-temporal statistical properties and concomitant necessary conditions for ergodicity of passive scalar turbulence statistics are evaluated. First, the integral time and length scales are analyzed and their corresponding maximum values are used to guide the construction of an ensemble of independent realizations from repeated spatio-temporal concentration measurements. As a statistical analysis for an operational ergodicity check, a Kolmogorov-Smirnov test on the distributions of temporal and spatial concentration series against the ensemble was conducted. The outcome of this test reveals that ergodicity is reasonably valid over the entire domain except close to the rod elements where wake-induced inhomogeneities and damped turbulence prevail. The spatial concentration statistics within a grid-cell (square domain formed by four corner rods) appear to be less ergodic than their temporal counterparts, which is not surprising given the periodicity and persistence of von Kármán vortices in
NASA Astrophysics Data System (ADS)
Hong, Tian-Zeng; Xue, Qiong; Yang, Zhi-Yong; Dong, Ya-Ping
2016-01-01
The Pt-carbon quantum dot (CQD)/reduced graphene oxide (RGO) catalysts are prepared by one pot reduction method and demonstrate ultraefficient performance towards methanol oxidation reaction (MOR). In the high content CQD products, Pt nanoparticles around 2-3 nm are dispersed uniformly on supporting materials. And the X-ray photoelectron spectroscopy analysis indicates that in the high content CQD products a large part of surface oxygen groups is contributed by CQD. The electrochemical tests reveal that the catalyst with the saturated CQD exhibits best performance in MOR: the mass and specific activity at forward peak position, the potential close to fuel cell operation and 3600 s of chronoamperometric curve are roughly 2-3 folds of the commercial Pt/C. Furthermore, the electrochemical data on the series of catalysts with different quantity of CQD disclose the improving tendency of MOR performance with the increasing content of CQD evidently. Overview the electrochemical and characterization results, we suggest CQD play multiple roles in the enhancement of Pt performance: present abundant nucleating and anchoring points to facilitate the formation of small size and uniform distributed Pt particles; act as spacer to alleviate restacking of RGO sheets; and provide fruitful surface oxygen groups to improve the antipoisonous ability of Pt.
The uncertainty principle and quantum chaos
NASA Technical Reports Server (NTRS)
Chirikov, Boris V.
1993-01-01
The conception of quantum chaos is described in some detail. The most striking feature of this novel phenomenon is that all the properties of classical dynamical chaos persist here but, typically, on the finite and different time scales only. The ultimate origin of such a universal quantum stability is in the fundamental uncertainty principle which makes discrete the phase space and, hence, the spectrum of bounded quantum motion. Reformulation of the ergodic theory, as a part of the general theory of dynamical systems, is briefly discussed.
Impact of nonzero boresight pointing error on ergodic capacity of MIMO FSO communication systems.
Boluda-Ruiz, Rubén; García-Zambrana, Antonio; Castillo-Vázquez, Beatriz; Castillo-Vázquez, Carmen
2016-02-22
A thorough investigation of the impact of nonzero boresight pointing errors on the ergodic capacity of multiple-input/multiple-output (MIMO) free-space optical (FSO) systems with equal gain combining (EGC) reception under different turbulence models, which are modeled as statistically independent, but not necessarily identically distributed (i.n.i.d.) is addressed in this paper. Novel closed-form asymptotic expressions at high signal-to-noise ratio (SNR) for the ergodic capacity of MIMO FSO systems are derived when different geometric arrangements of the receive apertures at the receiver are considered in order to reduce the effect of nonzero inherent boresight displacement, which is inevitably present when more than one receive aperture is considered. As a result, the asymptotic ergodic capacity of MIMO FSO systems is evaluated over log-normal (LN), gamma-gamma (GG) and exponentiated Weibull (EW) atmospheric turbulence in order to study different turbulence conditions, different sizes of receive apertures as well as different aperture averaging conditions. It is concluded that the use of single-input/multiple-output (SIMO) and MIMO techniques can significantly increase the ergodic capacity respect to the direct path link when the inherent boresight displacement takes small values, i.e. when the spacing among receive apertures is not too big. The effect of nonzero additional boresight errors, which is due to the thermal expansion of the building, is evaluated in multiple-input/single-output (MISO) and single-input/single-output (SISO) FSO systems. Simulation results are further included to confirm the analytical results. PMID:26907009
The Wave Function and Quantum Reality
Gao Shan
2011-03-28
We investigate the meaning of the wave function by analyzing the mass and charge density distributions of a quantum system. According to protective measurement, a charged quantum system has effective mass and charge density distributing in space, proportional to the square of the absolute value of its wave function. In a realistic interpretation, the wave function of a quantum system can be taken as a description of either a physical field or the ergodic motion of a particle. The essential difference between a field and the ergodic motion of a particle lies in the property of simultaneity; a field exists throughout space simultaneously, whereas the ergodic motion of a particle exists throughout space in a time-divided way. If the wave function is a physical field, then the mass and charge density will be distributed in space simultaneously for a charged quantum system, and thus there will exist gravitational and electrostatic self-interactions of its wave function. This not only violates the superposition principle of quantum mechanics but also contradicts experimental observations. Thus the wave function cannot be a description of a physical field but be a description of the ergodic motion of a particle. For the later there is only a localized particle with mass and charge at every instant, and thus there will not exist any self-interaction for the wave function. It is further argued that the classical ergodic models, which assume continuous motion of particles, cannot be consistent with quantum mechanics. Based on the negative result, we suggest that the wave function is a description of the quantum motion of particles, which is random and discontinuous in nature. On this interpretation, the square of the absolute value of the wave function not only gives the probability of the particle being found in certain locations, but also gives the probability of the particle being there. The suggested new interpretation of the wave function provides a natural realistic
NASA Astrophysics Data System (ADS)
Faulkner, Michael F.; Bramwell, Steven T.; Holdsworth, Peter C. W.
2015-04-01
The Berezinskii-Kosterlitz-Thouless (BKT) phase transition drives the unbinding of topological defects in many two-dimensional systems. In the two-dimensional Coulomb gas, it corresponds to an insulator-conductor transition driven by charge deconfinement. We investigate the global topological properties of this transition, both analytically and by numerical simulation, using a lattice-field description of the two-dimensional Coulomb gas on a torus. The BKT transition is shown to be an ergodicity breaking between the topological sectors of the electric field, which implies a definition of topological order in terms of broken ergodicity. The breakdown of local topological order at the BKT transition leads to the excitation of global topological defects in the electric field, corresponding to different topological sectors. The quantized nature of these classical excitations, and their strict suppression by ergodicity breaking in the low-temperature phase, afford striking global signatures of topological-sector fluctuations at the BKT transition. We discuss how these signatures could be detected in experiments on, for example, magnetic films and cold-atom systems.
Implications of lack-of-ergodicity in 2D Potts model
NASA Astrophysics Data System (ADS)
Ota, Smita
2015-03-01
Microcanonical Monte Carlo simulation is used to study two dimensional (2D) q state Potts model. We consider a 2D square lattice having NxN spins with periodic boundary condition and simulated the system with N =15 and q =10. The demon energy distribution is found to be exponential for high system energy and large system size. For smaller system size and above the first order transition the demon energy distribution is found to deviate from exp(- βED) and has the form exp(- βED + γ ED2). Here β = 1/kBT and kB is the Boltzmann constant. It is found that γ is finite at higher temperatures. As the system energy is reduced γ becomes zero near the first order transition. It is found that during cooling γ changes sign from negative to positive and then to negative again near the 1st order transition. Therefore the demon energy distribution becomes exp(- βED) (or ergodic) at two values of system energy near the 1st order transition. Further cooling or at still lower temperatures the system shows lack of ergodicity. However, difference in heating cooling curves are apparent in E vs γ. The system energies for which γ is zero during cooling can represent the 'ergodic' states. This can be related to the two-level systems observed in glasses at low temperatures.
Entanglement dynamics in quantum many-body systems
NASA Astrophysics Data System (ADS)
Ho, Wen Wei; Abanin, Dmitry
The dynamics of quantum entanglement S (t) has proven useful to distinguishing different quantum many-body phases. In particular, the growth of entanglement following a quantum quench can be used to distinguish between many-body localized(S (t) ~ logt) and ergodic(S (t) ~ t) phases. Here, we provide a theoretical description of the growth of entanglement in a quantum many-body system, and propose a method to experimentally measure it. We show that entanglement growth is related to the spreading of local operators. In ergodic systems, the linear spreading of operators results in a universal, linear in time growth of entanglement. Furthermore, we show that entanglement growth is directly related to the decay of the Loschmidt echo in a composite system comprised of many copies of the original system, subject to a perturbation that reconnects different parts of the system. Using this picture, we propose an experimental set-up to measure entanglement growth by using a quantum switch (two-level system) which controls connections in the composite system. Our work provides a way to directly probe dynamical properties of many-body systems, in particular, allowing for a direct observation of many-body localization. This work was partially supported by Sloan Foundation, Ontario Early Researcher Award and NSERC Discovery Grant.
Joshi, Nidhi; Rawat, Kamla; Bohidar, H B
2016-01-20
In order to customize the viscoelastic properties of pectin gels, it is necessary to work on a composite platform. Herein, the gelation kinetics, and viscoelastic characterization of anionic polysaccharide pectin dispersion prepared in presence of nanoclay laponite are reported using dynamic light scattering and rheology measurements. The ratio Rg/Rh (Rg and Rh are radius of gyration and hydrodynamic radius respectively) determined from light scattering data revealed the presence of random coils of pectin chains inside the gel matrix. When nanoclay laponite was added to the pectin chains solution, two-phase separation was noticed instantaneously. Therefore, the surfactant cetyltrimethylammonium bromide [CTAB] was added to exfoliate the clay platelets in the dispersion, and also in its gel phase. The exfoliating agent cetyltrimethylammonium bromide ([CTAB]≈ cmc/10) helped to enhance the homogeneity and stability of the pectin-clay sols and gels. The storage and loss moduli (G' and G") of the composite gel changed significantly as function of nanoclay laponite content for concentration up to 0.03% (w/v) causing the softening of the gels (gel strength reduced by close to 50%) compared to pectin-calcium gel. However, as the concentration of nanoclay laponite was maintained between 0.01% and 0.03% (w/v), the gel rigidity (G') recovered by 30% (35-45 Pa). The transition from ergodic to non-ergodic state occurred during sol-gel transition owing to the presence of the nanoclay laponite. The gelation time was not too different from the ergodicity breaking time. Thus, the presence of nanoclay laponite in such minute concentration is shown to cause considerable change in the thermo-physical property of the composite gels. This material property modulation will facilitate designing of soft gels having storage modulus continuously varying in the wide range of 10-70 Pa while keeping the gelation temperature mostly unaltered. PMID:26572352
The one-dimensional Boltzmann gas: The ergodic hypothesis and the phase portrait of small systems
Rouet, J.L. ); Blasco, F.; Feix, M.R. )
1993-04-01
The concept of ergodicity and its application to microcanonical systems composed of few particles of different masses are clarified. The distribution functions in position and velocity are theoretically derived and numerically verified. Moreover, the authors deal with a one-dimensional Boltzmann gas where the order relation (connected to the one dimensionality) brings constraints depending on the two classes of boundary conditions enforced (reflecting, periodic). The numerical simulations on a one-dimensional Boltzmann gas act as real experiments and allow them to play on the constraints to which the system is subjected. 9 refs., 11 figs.
About ergodicity in the family of limaçon billiards
NASA Astrophysics Data System (ADS)
Dullin, Holger R.; Bäcker, Arnd
2001-11-01
By continuation from the hyperbolic limit of the cardioid billiard we show that there is an abundance of bifurcations in the family of limaçon billiards. The statistics of these bifurcation shows that the size of the stable intervals decreases with approximately the same rate as their number increases with the period. In particular, we give numerical evidence that arbitrarily close to the cardioid there are elliptic islands due to orbits created in saddle-node bifurcations. This shows explicitly that if in this one-parameter family of maps ergodicity occurs for more than one parameter, the set of these parameter values has a complicated structure.
Localization to ergodic transitions: is Rosenzweig-Porter ensemble the hidden skeleton?
NASA Astrophysics Data System (ADS)
Shukla, Pragya
2016-02-01
The presence of local interactions and wave-localization phenomena is quite generic to a wide range of complex systems. Based on the evidence of two transitions similar to those in many body states as well as single particle states, the work by Kravtsov et al (2015 New J. Phys. 17 122002) indicates the strong prospect of Rosenzweig-Porter ensemble to serve as the good model for many particle localization as well as that of single particle. With already well-known statistical universality of ergodic dynamics, this also reveals the next level in the hierarchy of the universality of statistical fluctuations.
NASA Astrophysics Data System (ADS)
Loch, Hanna; Janczura, Joanna; Weron, Aleksander
2016-04-01
In this paper we study asymptotic behavior of a dynamical functional for an α -stable autoregressive fractionally integrated moving average (ARFIMA) process. We find an analytical formula for this important statistics and show its usefulness as a diagnostic tool for ergodic properties. The obtained results point to the very fast convergence of the dynamical functional and show that even for short trajectories one may obtain reliable conclusions on the ergodic properties of the ARFIMA process. Moreover we use the obtained theoretical results to illustrate how the dynamical functional statistics can be used in the verification of the proper model for an analysis of some biophysical experimental data.
Tracking single Kv2.1 channels in live cells reveals anomalous subdiffusion and ergodicity breaking
NASA Astrophysics Data System (ADS)
Weigel, Aubrey; Simon, Blair; Tamkun, Michael; Krapf, Diego
2011-03-01
The dynamic organization of the plasma membrane is responsible for essential cellular processes, such as receptor trafficking and signaling. By studying the dynamics of transmembrane proteins a greater understanding of these processes as a whole can be achieved. It is broadly observed that the diffusion pattern of membrane protein displays anomalous subdiffusion. However, the mechanisms responsible for this behavior are not yet established. We explore the dynamics of the voltage gated potassium channel Kv2.1 by using single-particle tracking. We analyze Kv2.1 channel trajectories in terms of the time and ensemble distributions of square displacements. Our results reveal that all Kv2.1 channels experience anomalous subdiffusion and we observe that the Kv2.1 diffusion pattern is non-ergodic. We further investigated the role of the actin cytoskeleton in these channel dynamics by applying actin depolymerizing drugs. It is seen that with the breakdown of the actin cytoskeleton the Kv2.1 channel trajectories recover ergodicity.
NASA Astrophysics Data System (ADS)
Shyshkin, Oleg A.; Schneider, Ralf; Beidler, Craig D.
2007-11-01
The radial transport of tungsten ions in a fusion plasma of the HELIAS stellarator with five magnetic field periods is studied by means of a new numerical code. The code solves guiding center equations for test particles (tungsten ions) with the use of a Runge-Kutta integrating scheme. Coulomb scattering of the tungsten ions on the background plasma particles (electrons, deuterons and tritons) is simulated by means of a discretized collision operator based on the binomial distribution and presented in terms of pitch-angle scattering and energy slowing down and scattering. The coronal model is used to determine the mean charge state of the tungsten ion ensemble langZ(Te, ne)rang as a function of background electron temperature and density. Two plasma configurations with and without ergodic confinement regions and both with finite plasma pressure of β = 3% are considered. The nonergodic configuration possesses closed nested magnetic surfaces throughout the entire confinement volume. The ergodic magnetic field configuration is represented through additional magnetic field perturbations. Comparative analysis of the radial transport is performed for a time interval greater by a factor of 15 than the energy confinement time τE = 1.62 s required for the HELIAS reactor. In spite of the fact that the tendency of impurities to penetrate towards the plasma core is observed in both cases, the stochastic scenario exhibits reduced inward impurity flux.
Fluctuations around equilibrium laws in ergodic continuous-time random walks.
Schulz, Johannes H P; Barkai, Eli
2015-06-01
We study occupation time statistics in ergodic continuous-time random walks. Under thermal detailed balance conditions, the average occupation time is given by the Boltzmann-Gibbs canonical law. But close to the nonergodic phase, the finite-time fluctuations around this mean are large and nontrivial. They exhibit dual time scaling and distribution laws: the infinite density of large fluctuations complements the Lévy-stable density of bulk fluctuations. Neither of the two should be interpreted as a stand-alone limiting law, as each has its own deficiency: the infinite density has an infinite norm (despite particle conservation), while the stable distribution has an infinite variance (although occupation times are bounded). These unphysical divergences are remedied by consistent use and interpretation of both formulas. Interestingly, while the system's canonical equilibrium laws naturally determine the mean occupation time of the ergodic motion, they also control the infinite and Lévy-stable densities of fluctuations. The duality of stable and infinite densities is in fact ubiquitous for these dynamics, as it concerns the time averages of general physical observables. PMID:26172683
Fluctuations around equilibrium laws in ergodic continuous-time random walks
NASA Astrophysics Data System (ADS)
Schulz, Johannes H. P.; Barkai, Eli
2015-06-01
We study occupation time statistics in ergodic continuous-time random walks. Under thermal detailed balance conditions, the average occupation time is given by the Boltzmann-Gibbs canonical law. But close to the nonergodic phase, the finite-time fluctuations around this mean are large and nontrivial. They exhibit dual time scaling and distribution laws: the infinite density of large fluctuations complements the Lévy-stable density of bulk fluctuations. Neither of the two should be interpreted as a stand-alone limiting law, as each has its own deficiency: the infinite density has an infinite norm (despite particle conservation), while the stable distribution has an infinite variance (although occupation times are bounded). These unphysical divergences are remedied by consistent use and interpretation of both formulas. Interestingly, while the system's canonical equilibrium laws naturally determine the mean occupation time of the ergodic motion, they also control the infinite and Lévy-stable densities of fluctuations. The duality of stable and infinite densities is in fact ubiquitous for these dynamics, as it concerns the time averages of general physical observables.
NASA Astrophysics Data System (ADS)
Hofmann, Holger F.
2014-04-01
Recent results obtained in quantum measurements indicate that the fundamental relations between three physical properties of a system can be represented by complex conditional probabilities. Here, it is shown that these relations provide a fully deterministic and universally valid framework on which all of quantum mechanics can be based. Specifically, quantum mechanics can be derived by combining the rules of Bayesian probability theory with only a single additional law that explains the phases of complex probabilities. This law, which I introduce here as the law of quantum ergodicity, is based on the observation that the reality of physical properties cannot be separated from the dynamics by which they emerge in measurement interactions. The complex phases are an expression of this inseparability and represent the dynamical structure of transformations between the different properties. In its quantitative form, the law of quantum ergodicity describes a fundamental relation between the ergodic probabilities obtained by dynamical averaging and the deterministic relations between three properties expressed by the complex conditional probabilities. The complete formalism of quantum mechanics can be derived from this one relation, without any axiomatic mathematical assumptions about state vectors or superpositions. It is therefore possible to explain all quantum phenomena as the consequence of a single fundamental law of physics.
A review of sigma models for quantum chaotic dynamics
NASA Astrophysics Data System (ADS)
Altland, Alexander; Gnutzmann, Sven; Haake, Fritz; Micklitz, Tobias
2015-07-01
We review the construction of the supersymmetric sigma model for unitary maps, using the color-flavor transformation. We then illustrate applications by three case studies in quantum chaos. In two of these cases, general Floquet maps and quantum graphs, we show that universal spectral fluctuations arise provided the pertinent classical dynamics are fully chaotic (ergodic and with decay rates sufficiently gapped away from zero). In the third case, the kicked rotor, we show how the existence of arbitrarily long-lived modes of excitation (diffusion) precludes universal fluctuations and entails quantum localization.
A review of sigma models for quantum chaotic dynamics.
Altland, Alexander; Gnutzmann, Sven; Haake, Fritz; Micklitz, Tobias
2015-07-01
We review the construction of the supersymmetric sigma model for unitary maps, using the color-flavor transformation. We then illustrate applications by three case studies in quantum chaos. In two of these cases, general Floquet maps and quantum graphs, we show that universal spectral fluctuations arise provided the pertinent classical dynamics are fully chaotic (ergodic and with decay rates sufficiently gapped away from zero). In the third case, the kicked rotor, we show how the existence of arbitrarily long-lived modes of excitation (diffusion) precludes universal fluctuations and entails quantum localization. PMID:26181515
Dong Chunfeng; Wang Erhui; Morita, Shigeru; Kobayashi, Masahiro; Goto, Motoshi; Masuzaki, Suguru; Morisaki, Tomohiro
2011-08-15
Vertical profiles of edge impurity emissions have been measured in upper half region of elliptical plasmas at horizontally elongated plasma cross section in large helical device (LHD). The vertical profiles near upper O-point located just below helical coil are analyzed to study the plasma edge boundary of the ergodic layer consisting of stochastic magnetic field lines with connection lengths of 30 {<=} L{sub c} {<=} 2000 m. As a result, C{sup 3+} ion emitting CIV spectrum is identified as the ion existing in the farthest edge of the ergodic layer. The peak position of CIV (312.4 A: 1s{sup 2}3p {sup 2}P{sub 1/2,3/2}-1s{sup 2}2s {sup 2}S{sub 1/2}) vertical profile does not change at all in a wide temperature range of 150 {<=} T{sub e}({rho} = 1) {<=} 400 eV, whereas it moves inside the ergodic layer when T{sub e}({rho} = 1) is reduced below a threshold temperature, e.g., 130 eV at R{sub ax} = 3.75 m configuration. It is found that the C{sup 3+} ion exists at the boundary between ergodic layer and open magnetic filed layer at which the L{sub c} distributes in lengths of 5 to 30 m. The result indicates that the edge boundary near the O-point in LHD is determined by a starting point of the open filed layer, where a tokamak-like steeper edge temperature gradient is formed, although the edge boundary is quite obscure at the X-point region. Any plasma does not exist between the edge boundary and the vacuum vessel. The CIV profile at the O-point is simulated using a three-dimensional edge transport code of EMC3-EIRENE in which the magnetic field structure in vacuum is used for the ergodic layer. A clear discrepancy of 8 mm is found in the peak positions of CIV between measurement and simulation for magnetic configurations with thick ergodic layer, i.e., R{sub ax}=3.90 m, while only a small discrepancy of 3 mm is observed for those with relatively thin ergodic layer, i.e., R{sub ax} = 3.75 m. It suggests that the discrepancy is caused by a modification of the magnetic filed
Quantum coherence and correlations in quantum system
Xi, Zhengjun; Li, Yongming; Fan, Heng
2015-01-01
Criteria of measure quantifying quantum coherence, a unique property of quantum system, are proposed recently. In this paper, we first give an uncertainty-like expression relating the coherence and the entropy of quantum system. This finding allows us to discuss the relations between the entanglement and the coherence. Further, we discuss in detail the relations among the coherence, the discord and the deficit in the bipartite quantum system. We show that, the one-way quantum deficit is equal to the sum between quantum discord and the relative entropy of coherence of measured subsystem. PMID:26094795
Effective ergodicity breaking in an exclusion process with varying system length
NASA Astrophysics Data System (ADS)
Schultens, Christoph; Schadschneider, Andreas; Arita, Chikashi
2015-09-01
Stochastic processes of interacting particles in systems with varying length are relevant e.g. for several biological applications. We try to explore what kind of new physical effects one can expect in such systems. As an example, we extend the exclusive queueing process that can be viewed as a one-dimensional exclusion process with varying length, by introducing Langmuir kinetics. This process can be interpreted as an effective model for a queue that interacts with other queues by allowing incoming and leaving of customers in the bulk. We find surprising indications for breaking of ergodicity in a certain parameter regime, where the asymptotic growth behavior depends on the initial length. We show that a random walk with site-dependent hopping probabilities exhibits qualitatively the same behavior.
A method for single image restoration based on the principal ergodic.
Molodij, Guillaume; Keil, Steve; Roudier, Thierry; Meunier, Nadège; Rondi, Sylvain
2010-11-01
We present a method to extract from a single image both object and point spread function using low contrast features of an extended field of view. Invoking the principal ergodic on stochastic turbulent phenomena, we show that the aberration parameters, characteristics of the earth's turbulence, can be recovered from multiple features within an isoplanatic patch. The ensemble statistics is replacing the spatial statistics of a single realization to derive an equivalent modulation transfer function and to apply usual deconvolution techniques such as Richardson-Lucy algorithms. The reliability of this postprocessing treatment has been tested on synthetic data, on solar granulation observations performed at La Lunette Jean Rosch du Pic du Midi, and during the event of the Venus transit at La Tour Solaire de Meudon. PMID:21045911
NASA Astrophysics Data System (ADS)
Zhao, Yu; Yuan, Sanling; Zhang, Tonghua
2016-08-01
The effect of toxin-producing phytoplankton and environmental stochasticity are interesting problems in marine plankton ecology. In this paper, we develop and analyze a stochastic phytoplankton allelopathy model, which takes both white and colored noises into account. We first prove the existence of the global positive solution of the model. And then by using the stochastic Lyapunov functions, we investigate the positive recurrence and ergodic property of the model, which implies the existence of a stationary distribution of the solution. Moreover, we obtain the mean and variance of the stationary distribution. Our results show that both the two kinds of environmental noises and toxic substances have great impacts on the evolution of the phytoplankton populations. Finally, numerical simulations are carried out to illustrate our theoretical results.
Ergodic theory and visualization. II. Fourier mesochronic plots visualize (quasi)periodic sets
Levnajić, Zoran; Mezić, Igor
2015-05-15
We present an application and analysis of a visualization method for measure-preserving dynamical systems introduced by I. Mezić and A. Banaszuk [Physica D 197, 101 (2004)], based on frequency analysis and Koopman operator theory. This extends our earlier work on visualization of ergodic partition [Z. Levnajić and I. Mezić, Chaos 20, 033114 (2010)]. Our method employs the concept of Fourier time average [I. Mezić and A. Banaszuk, Physica D 197, 101 (2004)], and is realized as a computational algorithms for visualization of periodic and quasi-periodic sets in the phase space. The complement of periodic phase space partition contains chaotic zone, and we show how to identify it. The range of method's applicability is illustrated using well-known Chirikov standard map, while its potential in illuminating higher-dimensional dynamics is presented by studying the Froeschlé map and the Extended Standard Map.
Diffusive and Subdiffusive Spin Transport in the Ergodic Phase of a Many-Body Localizable System.
Žnidarič, Marko; Scardicchio, Antonello; Varma, Vipin Kerala
2016-07-22
We study high temperature spin transport in a disordered Heisenberg chain in the ergodic regime. By employing a density matrix renormalization group technique for the study of the stationary states of the boundary-driven Lindblad equation we are able to study extremely large systems (400 spins). We find both a diffusive and a subdiffusive phase depending on the strength of the disorder and on the anisotropy parameter of the Heisenberg chain. Studying finite-size effects, we show numerically and theoretically that a very large crossover length exists that controls the passage of a clean-system dominated dynamics to one observed in the thermodynamic limit. Such a large length scale, being larger than the sizes studied before, explains previous conflicting results. We also predict spatial profiles of magnetization in steady states of generic nondiffusive systems. PMID:27494464
Analysis of non-ergodic behaviour in spatio-temporal coherence properties of speckle light
NASA Astrophysics Data System (ADS)
Réfrégier, Philippe
Spatio-temporal coherence properties of light scattered by rough surfaces that leads to speckle fluctuations are analysed. It is demonstrated that the scattered light is non-ergodic with the disorder due to the scattering process. Although the mutual coherence matrix vanishes with isotropic polarization fluctuations, it is shown that spatio-temporal coherence properties can be described with interference experiments that can be obtained between different speckles of the scattered light. For non-singular scattering processes, the maximal value of the modulus of the Wolf degree of coherence is analysed in the spatial time domain. This approach is also applied to totally unpolarized incident light with an isotropic and spatially independent scattering process. The mean value and the standard deviation of the Wolf degree of coherence are then determined from the coherence properties of the incident light.
Time stamping in EPRB experiments: application on the test of non-ergodic theories
NASA Astrophysics Data System (ADS)
Agüero, M. B.; Hnilo, A. A.; Kovalsky, M. G.; Larotonda, M. A.
2009-12-01
In Einstein-Podolsky-Rosen-Bohm (EPRB) experiments, the record of the time of detection of each single photon (“time stamping”) provides much more information than the usual record of coincidence rates. It is a preferable technique for several reasons, and it can be realized with accessible means nowadays. As an illustration of its capacities, we show that a certain class of non-ergodic (local realistic) models that violates the Bell’s inequalities, even in ideally perfect setups, is disproved from the examination of time stamped files. This class of models, which has remained untested until now, exploits the finite size of the time window defining the coincidences, and it cannot be disproved by measuring coincidence rates. We use not only our own experimental data, but also the data obtained in the Innsbruck experiment with random variable analyzers.
From randomly accelerated particles to Lévy walks: non-ergodic behavior and aging
NASA Astrophysics Data System (ADS)
Radons, Guenter; Albers, Tony; Institute of Physics, Complex Systems; Nonlinear Dynamics Team
For randomly accelerated particles we detected, and were able to analyze in detail (PRL 113, 184101 (2014)), the phenomenon of weak-ergodicity breaking (WEB), i.e. the inequivalence of ensemble- and time-averaged mean-squared displacements (MSD). These results, including their aging time dependence, are relevant for anomalous chaotic diffusion in Hamiltonian systems, for passive tracer transport in turbulent flows, and many other systems showing momentum diffusion. There are, however, several related models, such as the integrated random excursion model, or, space-time correlated Lévy walks and flights, with similar statistical behavior. We compare the WEB related properties of these models and find surprising differences although, for equivalent parameters, all of them are supposed to lead to the same ensemble-averaged MSD. Our findings are relevant for distinguishing possible models for the anomalous diffusion occurring in experimental situations.
Spiechowicz, Jakub; Łuczka, Jerzy; Hänggi, Peter
2016-01-01
We study far from equilibrium transport of a periodically driven inertial Brownian particle moving in a periodic potential. As detected for a SQUID ratchet dynamics, the mean square deviation of the particle position from its average may involve three distinct intermediate, although extended diffusive regimes: initially as superdiffusion, followed by subdiffusion and finally, normal diffusion in the asymptotic long time limit. Even though these anomalies are transient effects, their lifetime can be many, many orders of magnitude longer than the characteristic time scale of the setup and turns out to be extraordinarily sensitive to the system parameters like temperature or the potential asymmetry. In the paper we reveal mechanisms of diffusion anomalies related to ergodicity of the system, symmetry breaking of the periodic potential and ultraslow relaxation of the particle velocity towards its steady state. Similar sequences of the diffusive behaviours could be detected in various systems including, among others, colloidal particles in random potentials, glass forming liquids and granular gases. PMID:27492219
On exact statistics and classification of ergodic systems of integer dimension
Guralnik, Zachary Guralnik, Gerald; Pehlevan, Cengiz
2014-06-01
We describe classes of ergodic dynamical systems for which some statistical properties are known exactly. These systems have integer dimension, are not globally dissipative, and are defined by a probability density and a two-form. This definition generalizes the construction of Hamiltonian systems by a Hamiltonian and a symplectic form. Some low dimensional examples are given, as well as a discretized field theory with a large number of degrees of freedom and a local nearest neighbor interaction. We also evaluate unequal-time correlations of these systems without direct numerical simulation, by Padé approximants of a short-time expansion. We briefly speculate on the possibility of constructing chaotic dynamical systems with non-integer dimension and exactly known statistics. In this case there is no probability density, suggesting an alternative construction in terms of a Hopf characteristic function and a two-form.
Natural Divertor Spherical Tokamak Plasmas with bean shape and ergodic limiter
NASA Astrophysics Data System (ADS)
Ribeiro, Celso; Herrera, Julio; Chavez, Esteban; Tritz, Kevin
2013-10-01
The former spherical tokamak (ST) MEDUSA (Madison EDUcation Small Aspect.ratio tokamak, R < 0.14 m, a < 0.10 m, BT < 0.5T, Ip < 40 kA, 3 ms pulse) is being recommissioned in Costa Rica Institute of Technology. The main objectives of the MEDUSA-CR project are training and to clarify several issues in relevant physics for conventional and mainly STs, including beta studies in bean-shaped ST plasmas, transport, heating and current drive via Alfvén wave, and natural divertor STs with ergodic magnetic limiter. We report here improvements in the self-consistency of these equilibrium comparisons and a preliminary study of their MHD stability beta limits. VIE-ITCR, IAEA-CRP contract 17592, National Instruments of Costa Rica.
Extensive numerical investigations on the ergodic properties of two coupled Pomeau-Manneville maps
NASA Astrophysics Data System (ADS)
Sala, Matteo; Manchein, Cesar; Artuso, Roberto
2015-11-01
We present extensive numerical investigations on the ergodic properties of two identical Pomeau-Manneville maps interacting on the unit square through a diffusive linear coupling. The system exhibits anomalous statistics, as expected, but with strong deviations from the single intermittent map: Such differences are characterized by numerical experiments with densities which do not have singularities in the marginal fixed point, escape and Poincaré recurrence time statistics that share a power-law decay exponent modified by a clear dimensional scaling, while the rate of phase-space filling and the convergence of ensembles of Lyapunov exponents show a stretched instead of pure exponential behavior. In spite of the lack of rigorous results about this system, the dependence on both the intermittency and the coupling parameters appears to be smooth, paving the way for further analytical development. We remark that dynamical exponents appear to be independent of the (nonzero) coupling strength.
Metabasin approach for computing the master equation dynamics of systems with broken ergodicity.
Mauro, John C; Loucks, Roger J; Gupta, Prabhat K
2007-08-16
We propose a technique for computing the master equation dynamics of systems with broken ergodicity. The technique involves a partitioning of the system into components, or metabasins, where the relaxation times within a metabasin are short compared to an observation time scale. In this manner, equilibrium statistical mechanics is assumed within each metabasin, and the intermetabasin dynamics are computed using a reduced set of master equations. The number of metabasins depends upon both the temperature of the system and its derivative with respect to time. With this technique, the integration time step of the master equations is governed by the observation time scale rather than the fastest transition time between basins. We illustrate the technique using a simple model landscape with seven basins and show validation against direct Euler integration. Finally, we demonstrate the use of the technique for a realistic glass-forming system (viz., selenium) where direct Euler integration is not computationally feasible. PMID:17649986
Spiechowicz, Jakub; Łuczka, Jerzy; Hänggi, Peter
2016-01-01
We study far from equilibrium transport of a periodically driven inertial Brownian particle moving in a periodic potential. As detected for a SQUID ratchet dynamics, the mean square deviation of the particle position from its average may involve three distinct intermediate, although extended diffusive regimes: initially as superdiffusion, followed by subdiffusion and finally, normal diffusion in the asymptotic long time limit. Even though these anomalies are transient effects, their lifetime can be many, many orders of magnitude longer than the characteristic time scale of the setup and turns out to be extraordinarily sensitive to the system parameters like temperature or the potential asymmetry. In the paper we reveal mechanisms of diffusion anomalies related to ergodicity of the system, symmetry breaking of the periodic potential and ultraslow relaxation of the particle velocity towards its steady state. Similar sequences of the diffusive behaviours could be detected in various systems including, among others, colloidal particles in random potentials, glass forming liquids and granular gases. PMID:27492219
Ergodic theory and Diophantine approximation for translation surfaces and linear forms
NASA Astrophysics Data System (ADS)
Athreya, Jayadev; Parrish, Andrew; Tseng, Jimmy
2016-08-01
We derive results on the distribution of directions of saddle connections on translation surfaces using only the Birkhoff ergodic theorem applied to the geodesic flow on the moduli space of translation surfaces. Our techniques, together with an approximation argument, also give an alternative proof of a weak version of a classical theorem in multi-dimensional Diophantine approximation due to Schmidt (1960 Can. J. Math. 12 619–31, 1964 Trans. Am. Math. Soc. 110 493–518). The approximation argument allows us to deduce the Birkhoff genericity of almost all lattices in a certain submanifold of the space of unimodular lattices from the Birkhoff genericity of almost all lattices in the whole space and similarly for the space of affine unimodular lattices.
Ergodic protein dynamics underlie the universal shape of protein distribution in populations
NASA Astrophysics Data System (ADS)
Brenner, Naama; Braun, Erez; Rotella, James; Salman, Hanna; Naama Brenner Collaboration; Erez Collaboration; James Rotella; Hanna Salman Collaboration
2015-03-01
We have previously shown that protein fluctuations in cell populations exhibit a universal distribution shape under a broad range of biological realizations. Here we report new results based on continuous measurement in individual bacteria for over ~ 70 generations, which show that single-cell protein trajectories sample the available states with the same distribution shape as the population, i.e. protein fluctuations are ergodic. Analysis of temporal trajectories reveals that one effective random variable, sampled once each cell cycle, suffices to reconstruct the distribution from the trajectory. This in turn implies that cellular microscopic processes are strongly buffered and population-level protein distributions are insensitive to details of the intracellular dynamics. Probing them thus requires searching for novel universality-breaking experimental perturbations.
Ergodic theory and visualization. II. Fourier mesochronic plots visualize (quasi)periodic sets.
Levnajić, Zoran; Mezić, Igor
2015-05-01
We present an application and analysis of a visualization method for measure-preserving dynamical systems introduced by I. Mezić and A. Banaszuk [Physica D 197, 101 (2004)], based on frequency analysis and Koopman operator theory. This extends our earlier work on visualization of ergodic partition [Z. Levnajić and I. Mezić, Chaos 20, 033114 (2010)]. Our method employs the concept of Fourier time average [I. Mezić and A. Banaszuk, Physica D 197, 101 (2004)], and is realized as a computational algorithms for visualization of periodic and quasi-periodic sets in the phase space. The complement of periodic phase space partition contains chaotic zone, and we show how to identify it. The range of method's applicability is illustrated using well-known Chirikov standard map, while its potential in illuminating higher-dimensional dynamics is presented by studying the Froeschlé map and the Extended Standard Map. PMID:26026317
BBQ Modeling of Recycling from the Tore Supra Ergodic Divertor Neutraliser
NASA Astrophysics Data System (ADS)
Giannella, R.; Guirlet, R.; Demichelis, C.; Hogan, J.; Cherigier, L.
1998-11-01
Generation and recycling of carbon and hydrocarbon impurities, and recycling of neon at the Tore Supra pumped ergodic divertor have been analyzed using the BBQ 3-D scrape-off layer transport code. Code results are compared with spectroscopic observations from fibres located on the neutralizer plates, and background plasma conditions used in the code are constrained with data from langmuir probes embedded in the plates. The sensitivity of neon recycling to assumed reflection coefficients has been studied. A detailed 3-D geometry model for the neutralizer, including all 4 plates, and recycling from the notches between plates, has been prepared. A version of the code describing deuterium processes is being developed to study conditions during the onset of detachment at high density
NASA Astrophysics Data System (ADS)
Spiechowicz, Jakub; Łuczka, Jerzy; Hänggi, Peter
2016-08-01
We study far from equilibrium transport of a periodically driven inertial Brownian particle moving in a periodic potential. As detected for a SQUID ratchet dynamics, the mean square deviation of the particle position from its average may involve three distinct intermediate, although extended diffusive regimes: initially as superdiffusion, followed by subdiffusion and finally, normal diffusion in the asymptotic long time limit. Even though these anomalies are transient effects, their lifetime can be many, many orders of magnitude longer than the characteristic time scale of the setup and turns out to be extraordinarily sensitive to the system parameters like temperature or the potential asymmetry. In the paper we reveal mechanisms of diffusion anomalies related to ergodicity of the system, symmetry breaking of the periodic potential and ultraslow relaxation of the particle velocity towards its steady state. Similar sequences of the diffusive behaviours could be detected in various systems including, among others, colloidal particles in random potentials, glass forming liquids and granular gases.
Diffusive and Subdiffusive Spin Transport in the Ergodic Phase of a Many-Body Localizable System
NASA Astrophysics Data System (ADS)
Žnidarič, Marko; Scardicchio, Antonello; Varma, Vipin Kerala
2016-07-01
We study high temperature spin transport in a disordered Heisenberg chain in the ergodic regime. By employing a density matrix renormalization group technique for the study of the stationary states of the boundary-driven Lindblad equation we are able to study extremely large systems (400 spins). We find both a diffusive and a subdiffusive phase depending on the strength of the disorder and on the anisotropy parameter of the Heisenberg chain. Studying finite-size effects, we show numerically and theoretically that a very large crossover length exists that controls the passage of a clean-system dominated dynamics to one observed in the thermodynamic limit. Such a large length scale, being larger than the sizes studied before, explains previous conflicting results. We also predict spatial profiles of magnetization in steady states of generic nondiffusive systems.
Takesue, Shinji )
1989-08-01
This is the first part of a series devoted to the study of thermodynamic behavior of large dynamical systems with the use of a family of full-discrete and conservative models named elementary reversible cellular automata (ERCAs). In this paper, basic properties such as conservation laws and phase space structure are investigated in preparation for the later studies. ERCAs are a family of one-dimensional reversible cellular automata having two Boolean variables on each site. Reflection and Boolean conjugation symmetries divide them into 88 equivalence classes. For each rule, additive conserved quantities written in a certain form are regarded as a kind of energy, if they exist. By the aid of the discreteness of the variables, every ERCA satisfies the Liouville theorem or the preservation of phase space volume. Thus, if an energy exists in the above sense, statistical mechanics of the model can formally be constructed. If a locally defined quantity is conserved, however, it prevents the realization of statistical mechanics. The existence of such a quantity is examined for each class and a number of rules which have at least one energy but no local conservation laws are selected as hopeful candidates for the realization of thermodynamic behavior. In addition, the phase space structure of ERCAs is analyzed by enumerating cycles exactly in the phase space for systems of comparatively small sizes. As a result, it is revealed that a finite ERCA is not ergodic, that is, a large number of orbits coexist on an energy surface. It is argued that this fact does not necessarily mean the failure of thermodynamic behavior on the basis of an analogy with the ergodic nature of infinite systems.
Numerical study of long-time dynamics and ergodic-nonergodic transitions in dense simple fluids
NASA Astrophysics Data System (ADS)
McCowan, David D.
2015-08-01
Since the mid-1980s, mode-coupling theory (MCT) has been the de facto theoretic description of dense fluids and the transition from the fluid state to the glassy state. MCT, however, is limited by the approximations used in its construction and lacks an unambiguous mechanism to institute corrections. We use recent results from a new theoretical framework—developed from first principles via a self-consistent perturbation expansion in terms of an effective two-body potential—to numerically explore the kinetics of systems of classical particles, specifically hard spheres governed by Smoluchowski dynamics. We present here a full solution for such a system to the kinetic equation governing the density-density time correlation function and show that the function exhibits the characteristic two-step decay of supercooled fluids and an ergodic-nonergodic transition to a dynamically arrested state. Unlike many previous numerical studies—and in stark contrast to experiment—we have access to the full time and wave-number range of the correlation function with great precision and are able to track the solution unprecedentedly close to the transition, covering nearly 15 decades in scaled time. Using asymptotic approximation techniques analogous to those developed for MCT, we fit the solution to predicted forms and extract critical parameters. We find complete qualitative agreement with known glassy behavior (e.g. power-law divergence of the α -relaxation time scale in the ergodic phase and square-root growth of the glass form factors in the nonergodic phase), as well as some limited quantitative agreement [e.g. the transition at packing fraction η*=0.60149761 (10 ) ] , consistent with previous static solutions under this theory and with comparable colloidal suspension experiments. However, most importantly, we establish that this new theory is able to reproduce the salient features seen in other theories, experiments, and simulations but has the advantages of being
The emergent Copenhagen interpretation of quantum mechanics
NASA Astrophysics Data System (ADS)
Hollowood, Timothy J.
2014-05-01
We introduce a new and conceptually simple interpretation of quantum mechanics based on reduced density matrices of sub-systems from which the standard Copenhagen interpretation emerges as an effective description of macroscopically large systems. This interpretation describes a world in which definite measurement results are obtained with probabilities that reproduce the Born rule. Wave function collapse is seen to be a useful but fundamentally unnecessary piece of prudent book keeping which is only valid for macro-systems. The new interpretation lies in a class of modal interpretations in that it applies to quantum systems that interact with a much larger environment. However, we show that it does not suffer from the problems that have plagued similar modal interpretations like macroscopic superpositions and rapid flipping between macroscopically distinct states. We describe how the interpretation fits neatly together with fully quantum formulations of statistical mechanics and that a measurement process can be viewed as a process of ergodicity breaking analogous to a phase transition. The key feature of the new interpretation is that joint probabilities for the ergodic subsets of states of disjoint macro-systems only arise as emergent quantities. Finally we give an account of the EPR-Bohm thought experiment and show that the interpretation implies the violation of the Bell inequality characteristic of quantum mechanics but in a way that is rather novel. The final conclusion is that the Copenhagen interpretation gives a completely satisfactory phenomenology of macro-systems interacting with micro-systems.
Quantum computer games: quantum minesweeper
NASA Astrophysics Data System (ADS)
Gordon, Michal; Gordon, Goren
2010-07-01
The computer game of quantum minesweeper is introduced as a quantum extension of the well-known classical minesweeper. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. Quantum minesweeper demonstrates the effects of superposition, entanglement and their non-local characteristics. While in the classical minesweeper the goal of the game is to discover all the mines laid out on a board without triggering them, in the quantum version there are several classical boards in superposition. The goal is to know the exact quantum state, i.e. the precise layout of all the mines in all the superposed classical boards. The player can perform three types of measurement: a classical measurement that probabilistically collapses the superposition; a quantum interaction-free measurement that can detect a mine without triggering it; and an entanglement measurement that provides non-local information. The application of the concepts taught by quantum minesweeper to one-way quantum computing are also presented.
GR uniqueness and deformations
NASA Astrophysics Data System (ADS)
Krasnov, Kirill
2015-10-01
In the metric formulation gravitons are described with the parity symmetric S + 2 ⊗ S - 2 representation of Lorentz group. General Relativity is then the unique theory of interacting gravitons with second order field equations. We show that if a chiral S + 3 ⊗ S - representation is used instead, the uniqueness is lost, and there is an infinite-parametric family of theories of interacting gravitons with second order field equations. We use the language of graviton scattering amplitudes, and show how the uniqueness of GR is avoided using simple dimensional analysis. The resulting distinct from GR gravity theories are all parity asymmetric, but share the GR MHV amplitudes. They have new all same helicity graviton scattering amplitudes at every graviton order. The amplitudes with at least one graviton of opposite helicity continue to be determinable by the BCFW recursion.
Schumpe, Birga Mareen; Erb, Hans-Peter
2015-01-01
A defining force in the shaping of human identity is a person's need to feel special and different from others. Psychologists term this motivation Need for Uniqueness (NfU). There are manifold ways to establish feelings of uniqueness, e.g., by showing unusual consumption behaviour or by not conforming to majority views. The NfU can be seen as a stable personality trait, that is, individuals differ in their dispositional need to feel unique. The NfU is also influenced by situational factors and social environments. The cultural context is one important social setting shaping the NfU. This article aims to illuminate the NfU from a social psychological perspective. PMID:25942772
Retief, François Pieter; Cilliers, Louise
2011-09-01
Akhenaten was a unique pharaoh in more ways than one. He initiated a major socio-religious revolution that had vast consequences for his country, and possessed a strikingly abnormal physiognomy that was of note in his time and has interested historians up to the present era. In this study, we attempt to identify the developmental disorder responsible for his eunuchoid appearance. PMID:21920162
ERIC Educational Resources Information Center
Goble, Don
2009-01-01
This article describes the many learning opportunities that broadcast technology students at Ladue Horton Watkins High School in St. Louis, Missouri, experience because of their unique access to technology and methods of learning. Through scaffolding, stepladder techniques, and trial by fire, students learn to produce multiple television programs,…
NASA Astrophysics Data System (ADS)
Nieuwenhuizen, Theo M.; Mehmani, Bahar; Špička, Václav; Aghdami, Maryam J.; Khrennikov, Andrei Yu
2007-09-01
electrodynamics. Some quantum experiments from the point of view of Stochastic electrodynamics / V. Spicka ... [et al.]. On the ergodic behaviour of atomic systems under the action of the zero-point radiation field / L. De La Peña and A. M. Cetto. Inertia and the vacuum-view on the emergence of the inertia reaction force / A. Rueda and H. Sunahata -- pt. F. Models for the electron. Rotating Hopf-Kinks: oscillators in the sense of de Broglie / U. Enz. Kerr-Newman particles: symmetries and other properties / H.I. Arcos and J.G. Pereira. Kerr geometry beyond the quantum theory / Th. M. Nieuwenhuizen -- pt. G. Philosophical considerations. Probability in non-collapse interpretations of a quantum mechanics / D. Dieks. The Schrödinger-Park paradox about the concept of "State" in quantum statistical mechanics and quantum information theory is still open: one more reason to go beyond? / G.P. Beretta. The conjecture that local realism is possible / E. Santos -- pt. H. The round table. Round table discussion / A.M. Cetto ... [et al.].
Breaking of Ergodicity in Expanding Systems of Globally Coupled Piecewise Affine Circle Maps
NASA Astrophysics Data System (ADS)
Fernandez, Bastien
2014-02-01
To identify and to explain coupling-induced phase transitions in coupled map lattices (CML) has been a lingering enigma for about two decades. In numerical simulations, this phenomenon has always been observed preceded by a lowering of the Lyapunov dimension, suggesting that the transition might require changes of linear stability. Yet, recent proofs of co-existence of several phases in specially designed models work in the expanding regime where all Lyapunov exponents remain positive. In this paper, we consider a family of CML composed by piecewise expanding individual map, global interaction and finite number of sites, in the weak coupling regime where the CML is uniformly expanding. We show, mathematically for and numerically for , that a transition in the asymptotic dynamics occurs as the coupling strength increases. The transition breaks the (Milnor) attractor into several chaotic pieces of positive Lebesgue measure, with distinct empiric averages. It goes along with various symmetry breaking, quantified by means of magnetization-type characteristics. Despite that it only addresses finite-dimensional systems, to some extend, this result reconciles the previous ones as it shows that loss of ergodicity/symmetry breaking can occur in basic CML, independently of any decay in the Lyapunov dimension.
Ergodic mixing for turbulent drift motion in an inhomogeneous magnetic field
Isichenko, M.B.; Petviashvili, N.V.
1995-10-01
The turbulent {bold E}{times}{bold B} drift of a test particle in an inhomogeneous magnetic field is not reducible to a simple diffusion, but rather leads to a biased diffusion producing an inhomogeneous density distribution (pinch effect). The statistical properties of the long-time chaotic two-dimensional drift motion of a charged particle in the magnetic field {ital B}({ital x},{ital y}) and the time-dependent electrostatic potential {phi}({ital x},{ital y},{ital t}) are studied by numerical symplectic integration. For a conditionally periodic potential with two or more incommensurate frequencies, an ergodic behavior is demonstrated in which the probability density of the particle position is proportional to the magnetic field {ital B}. The accuracy of this prediction is found to be independent of the number {ital N}{sub {omega}} of the incommensurate frequencies for {ital N}{sub {omega}}{ge}2. The relation of this result with the Kolmogorov-Arnold-Moser theory is discussed. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.
NASA Astrophysics Data System (ADS)
Cherstvy, Andrey G.; Metzler, Ralf
2015-05-01
We study generalized anomalous diffusion processes whose diffusion coefficient D(x, t) ∼ D0|x|αtβ depends on both the position x of the test particle and the process time t. This process thus combines the features of scaled Brownian motion and heterogeneous diffusion parent processes. We compute the ensemble and time averaged mean squared displacements of this generalized diffusion process. The scaling exponent of the ensemble averaged mean squared displacement is shown to be the product of the critical exponents of the parent processes, and describes both subdiffusive and superdiffusive systems. We quantify the amplitude fluctuations of the time averaged mean squared displacement as function of the length of the time series and the lag time. In particular, we observe a weak ergodicity breaking of this generalized diffusion process: even in the long time limit the ensemble and time averaged mean squared displacements are strictly disparate. When we start to observe this process some time after its initiation we observe distinct features of ageing. We derive a universal ageing factor for the time averaged mean squared displacement containing all information on the ageing time and the measurement time. External confinement is shown to alter the magnitudes and statistics of the ensemble and time averaged mean squared displacements.
Ergodicity breaking and wave-function statistics in disordered interacting systems
De Luca, Andrea
2014-08-20
We present the study of the structure of many-body eigenfunctions in a one-dimensional disordered spin chain. We discuss the choice of an appropriate basis in the Hilbert space, where the problem can be seen as an Anderson model defined on a high-dimensional non-trivial graph, determined by the many-body Hamiltonian. The comparison with the usual behavior of wave-functions in finite dimensional Anderson localization allows us to put in light the main differences of the many-body case. At high disorder, the typical eigenfunctions do not seem to localize though they occupy a infinitesimal portion of the Hilbert space in the thermodynamic limit. We perform a detailed analysis of the distribution of the wave-function coefficients and their peculiar scaling in the small and large disorder phase. We propose a criterion to identify the position of the transition by looking at the long tails of these distributions. The results coming from exact diagonalization show signs of breaking of ergodicity when the disorder reaches a critical value that agrees with the estimation of the many-body localization transition in the same model.
Burov, Stas; Jeon, Jae-Hyung; Metzler, Ralf; Barkai, Eli
2011-02-01
Anomalous diffusion has been widely observed by single particle tracking microscopy in complex systems such as biological cells. The resulting time series are usually evaluated in terms of time averages. Often anomalous diffusion is connected with non-ergodic behaviour. In such cases the time averages remain random variables and hence irreproducible. Here we present a detailed analysis of the time averaged mean squared displacement for systems governed by anomalous diffusion, considering both unconfined and restricted (corralled) motion. We discuss the behaviour of the time averaged mean squared displacement for two prominent stochastic processes, namely, continuous time random walks and fractional Brownian motion. We also study the distribution of the time averaged mean squared displacement around its ensemble mean, and show that this distribution preserves typical process characteristics even for short time series. Recently, velocity correlation functions were suggested to distinguish between these processes. We here present analytical expressions for the velocity correlation functions. The knowledge of the results presented here is expected to be relevant for the correct interpretation of single particle trajectory data in complex systems. PMID:21203639
Ergodicity and spectral cascades in point vortex flows on the sphere
NASA Astrophysics Data System (ADS)
Dritschel, David G.; Lucia, Marcello; Poje, Andrew C.
2015-06-01
We present results for the equilibrium statistics and dynamic evolution of moderately large [n =O (102-103) ] numbers of interacting point vortices on the sphere under the constraint of zero mean angular momentum. For systems with equal numbers of positive and negative identical circulations, the density of rescaled energies, p (E ) , converges rapidly with n to a function with a single maximum with maximum entropy. Ensemble-averaged wave-number spectra of the nonsingular velocity field induced by the vortices exhibit the expected k-1 behavior at small scales for all energies. Spectra at the largest scales vary continuously with the inverse temperature of the system. For positive temperatures, spectra peak at finite intermediate wave numbers; for negative temperatures, spectra decrease everywhere. Comparisons of time and ensemble averages, over a large range of energies, strongly support ergodicity in the dynamics even for highly atypical initial vortex configurations. Crucially, rapid relaxation of spectra toward the microcanonical average implies that the direction of any spectral cascade process depends only on the relative difference between the initial spectrum and the ensemble mean spectrum at that energy, not on the energy, or temperature, of the system.
Calvo, F; Yurtsever, E
2014-06-01
The interplay between thermal relaxation and statistical dissociation in binary Morse clusters (AB)N has been investigated using numerical simulations and simple statistical approaches, for a variety of interaction parameters covering miscible and non-miscible regimes. While all clusters exhibit a core/shell phase separation pattern in their most stable, T = 0 structure, different melting mechanisms are identified depending on the ranges and their mismatch, including two-step melting of the surface and the core or premelting as alloying. The preference for emitting A or B particles upon evaporation has been evaluated assuming that the cluster is either thermally equilibrated or vibrationally excited in its ground state structure, and compared to the predictions of the Weisskopf theory. The variations of the dissociation rate constants with increasing energy and the branching ratio between the two channels show significant differences in both cases, especially when the clusters are miscible and bound by short-range forces, which indicates that the time scale for evaporation is much shorter than the equilibration time. Our results suggest that dissociation properties could be used to test the ergodic hypothesis in such compounds. PMID:24908002
NASA Astrophysics Data System (ADS)
Calvo, F.; Yurtsever, E.
2014-06-01
The interplay between thermal relaxation and statistical dissociation in binary Morse clusters (AB)N has been investigated using numerical simulations and simple statistical approaches, for a variety of interaction parameters covering miscible and non-miscible regimes. While all clusters exhibit a core/shell phase separation pattern in their most stable, T = 0 structure, different melting mechanisms are identified depending on the ranges and their mismatch, including two-step melting of the surface and the core or premelting as alloying. The preference for emitting A or B particles upon evaporation has been evaluated assuming that the cluster is either thermally equilibrated or vibrationally excited in its ground state structure, and compared to the predictions of the Weisskopf theory. The variations of the dissociation rate constants with increasing energy and the branching ratio between the two channels show significant differences in both cases, especially when the clusters are miscible and bound by short-range forces, which indicates that the time scale for evaporation is much shorter than the equilibration time. Our results suggest that dissociation properties could be used to test the ergodic hypothesis in such compounds.
Plasma flow and carbon production and circulation with the ergodic divertor of Tore Supra
NASA Astrophysics Data System (ADS)
Corre, Y.; Gunn, J.; Pégourié, B.; Guirlet, R.; DeMichelis, C.; Giannella, R.; Ghendrih, P.; Hogan, J.; Monier-Garbet, P.; Azéroual, A.; Escarguel, A.; Gauthier, E.
2007-02-01
This paper presents a detailed study of carbon production and transport from the ergodic divertor (ED) target plates to the plasma core in the Tore Supra tokamak. Adapted experimental and numerical modelling techniques have been used to describe each of the main phenomena in play. Edge electron density and temperature are measured with Langmuir probes. The C II, C III and Hα emission is measured with optical fibres and cameras. The background plasma flow is calculated consistently with the observed recycling pattern by the neutral transport code EDCOLL for the two magnetic connection schemes of interest (short or long connection lengths). 3D Monte-Carlo modelling of carbon near the neutralizer plate (BBQ code) shows that the transport of carbon ions is governed by the friction force in addition to the electric field. Finally, a simplified 3D test particle model is used to estimate the core penetration fraction of carbon. A high value is found for the carbon screening efficiency (fraction of particles that does not penetrate in the plasma core), in the range 95-97% depending on the edge plasma conditions. This value, combined with the calculated carbon influxes, yields the first quantitative estimate of the carbon core contamination during ED operation. The paper shows that the screening of carbon and core contamination are mainly dependent on the carbon source (partially controlled with the ED) and the plasma flow distribution in the laminar region (magnetic topology and particle drifts).
Analyzing the dynamics of cell cycle processes from fixed samples through ergodic principles
Wheeler, Richard John
2015-01-01
Tools to analyze cyclical cellular processes, particularly the cell cycle, are of broad value for cell biology. Cell cycle synchronization and live-cell time-lapse observation are widely used to analyze these processes but are not available for many systems. Simple mathematical methods built on the ergodic principle are a well-established, widely applicable, and powerful alternative analysis approach, although they are less widely used. These methods extract data about the dynamics of a cyclical process from a single time-point “snapshot” of a population of cells progressing through the cycle asynchronously. Here, I demonstrate application of these simple mathematical methods to analysis of basic cyclical processes—cycles including a division event, cell populations undergoing unicellular aging, and cell cycles with multiple fission (schizogony)—as well as recent advances that allow detailed mapping of the cell cycle from continuously changing properties of the cell such as size and DNA content. This includes examples using existing data from mammalian, yeast, and unicellular eukaryotic parasite cell biology. Through the ongoing advances in high-throughput cell analysis by light microscopy, electron microscopy, and flow cytometry, these mathematical methods are becoming ever more important and are a powerful complementary method to traditional synchronization and time-lapse cell cycle analysis methods. PMID:26543196
NASA Astrophysics Data System (ADS)
Fried, H. M.; Müller, B.; Gabellini, Y.
2000-11-01
The Table of Contents for the full book PDF is as follows: * Preface * Basic Concepts and Consequences of a Stochastic Vacuum Model * The Role of the QCD Vacuum in the Heavy-Quark Bound State Dynamics * Stochastic Vacuum Model and High Energy Scattering * Variational Approximations for Correlation Functions in Quantum Field Theories * Long-Range Vacuum Correlations? * Unitary Gauge Theories in Singlet Coordinates * SU(2) Gauge Theory in Covariant (Maximal) Abelian Gauges * Dynamics and Topology of the Gauge-Invariant Gauge Field in Two-Color QCD * The Vacuum Wave Function in Supersymmetric Matrix Theory * Analytic Models for the Forward Scattering Amplitude at High Energies * Extending the Frontiers -- Reconciling Accelerator and Cosmic Ray p - p Cross Sections * HERA Results on Elastic Hadronic and Sub-Hadronic Diffraction * Small-x Structure Functions and QCD Pomeron * AdS/CFT Correspondence for QCD and Pomeron Intercept at Strong Coupling * Short Introduction to QGP Dynamics * Effective Theories for Hot Non-Abelian Dynamics * Non-Perturbative Gluodynamics of High Enerry Heavy-Ion Collisions * Deriving Effective Transport Equations for Non-Abelian Plasmas * Ergodic Properties of Non-Abelian Gauge Theories * String from Large Nc Gauge Fields via Graph Summation on a P+ - x+ Lattice * Aspects of Non-Commutativity in ADS/CFT * Eikonal Scattering of Monopoles and Dyons in Dual QED * Gluon Reggeization and Sudakov Suppression via The Fock-Feynman-Schwinger Approach to QCD * Nonperturbative Gluon Radiation and Energy Dependence of Elastic Scattering * Thermal Field Theory in Equilibrium * Puzzling Aspects of Hot Quantum Fields * Color Superconductivity in Cold, Dense Quark Matter * DIS Results from HERA * Electroproduction of Vector Mesons * Probing the QED and QCD Vacua * New Developments in Cosmology * Duality and SU(1,1) coherent states in the Calogero-Moser Model * pp Elastic scattering at LHC and Signature of Chiral Phase Transition at Large |t| * A New Basis
Rankin triple products and quantum chaos
NASA Astrophysics Data System (ADS)
Watson, Thomas Crawford
2002-01-01
In this dissertation we demonstrate the chaotic nature of some archetypical quantum dynamical systems, using machinery from analytic number theory. We consider the quantized geodesic flow on finite-volume hyperbolic surfaces G/H , with G⊂SL2R consisting of the norm-1 units of an Eichler order in an indefinite quaternion algebra B over Q . For G=SL2Z , we prove that high-energy bound eigen-states obey the Random Wave conjecture of Berry/Hejhal for third moments. In fact we show that the third moment of a wave's amplitude distribution decays like E-112+e . In the more general case of maximal orders, we reduce an optimal quantitative version of the Quantum Unique Ergodicity conjecture of Rudnick-Sarnak to the Lindelof Hypothesis for particular families of automorphic L-functions. Furthermore, our analysis shows that any lowering of the exponent in the Phragmen-Lindelof convexity bound implies QUE. In the moment problem as well, the maximum non-trivial exponents precisely agree when translated between physical and arithmetical formulations. We accomplish this translation by proving identities expressing triple-correlation integrals of eigenforms in terms of central values of the corresponding Rankin triple-product L-functions. Very general forms of such identities were proved by Harris-Kudla, and in using their method to prove our own classical identities, we have to solve two main problems. The first is to explicitly compute the adjoint of Shimizu's theta lift, which realizes the Jacquet-Langlands correspondence by transferring automorphic forms from GL2 to GO( B). We accomplish this for oldforms and newforms of square-free level, with (possibly imprimitive) neben-characters. As a byproduct of these calculations, we obtain explicit formulas for all relevant GL2 Whittaker functions. These play an important role in our second main problem: evaluation of Garrett/Rallis-Piatetsky-Shapiro local zeta integrals in terms of the standard functorial triple-product L
Abel, David L.
2011-01-01
Is life physicochemically unique? No. Is life unique? Yes. Life manifests innumerable formalisms that cannot be generated or explained by physicodynamics alone. Life pursues thousands of biofunctional goals, not the least of which is staying alive. Neither physicodynamics, nor evolution, pursue goals. Life is largely directed by linear digital programming and by the Prescriptive Information (PI) instantiated particularly into physicodynamically indeterminate nucleotide sequencing. Epigenomic controls only compound the sophistication of these formalisms. Life employs representationalism through the use of symbol systems. Life manifests autonomy, homeostasis far from equilibrium in the harshest of environments, positive and negative feedback mechanisms, prevention and correction of its own errors, and organization of its components into Sustained Functional Systems (SFS). Chance and necessity—heat agitation and the cause-and-effect determinism of nature’s orderliness—cannot spawn formalisms such as mathematics, language, symbol systems, coding, decoding, logic, organization (not to be confused with mere self-ordering), integration of circuits, computational success, and the pursuit of functionality. All of these characteristics of life are formal, not physical. PMID:25382119
Crowding Induces Complex Ergodic Diffusion and Dynamic Elongation of Large DNA Molecules
Chapman, Cole D.; Gorczyca, Stephanie; Robertson-Anderson, Rae M.
2015-01-01
Despite the ubiquity of molecular crowding in living cells, the effects of crowding on the dynamics of genome-sized DNA are poorly understood. Here, we track single, fluorescent-labeled large DNA molecules (11, 115 kbp) diffusing in dextran solutions that mimic intracellular crowding conditions (0–40%), and determine the effects of crowding on both DNA mobility and conformation. Both DNAs exhibit ergodic Brownian motion and comparable mobility reduction in all conditions; however, crowder size (10 vs. 500 kDa) plays a critical role in the underlying diffusive mechanisms and dependence on crowder concentration. Surprisingly, in 10-kDa dextran, crowder influence saturates at ∼20% with an ∼5× drop in DNA diffusion, in stark contrast to exponentially retarded mobility, coupled to weak anomalous subdiffusion, with increasing concentration of 500-kDa dextran. Both DNAs elongate into lower-entropy states (compared to random coil conformations) when crowded, with elongation states that are gamma distributed and fluctuate in time. However, the broadness of the distribution of states and the time-dependence and length scale of elongation length fluctuations depend on both DNA and crowder size with concentration having surprisingly little impact. Results collectively show that mobility reduction and coil elongation of large crowded DNAs are due to a complex interplay between entropic effects and crowder mobility. Although elongation and initial mobility retardation are driven by depletion interactions, subdiffusive dynamics, and the drastic exponential slowing of DNA, up to ∼300×, arise from the reduced mobility of larger crowders. Our results elucidate the highly important and widely debated effects of cellular crowding on genome-sized DNA. PMID:25762333
Abdoul-Carime, Hassan; Berthias, Francis; Feketeová, Linda; Marciante, Mathieu; Calvo, Florent; Forquet, Valérian; Chermette, Henry; Farizon, Bernadette; Farizon, Michel; Märk, Tilmann D
2015-12-01
The velocity of a molecule evaporated from a mass-selected protonated water nanodroplet is measured by velocity map imaging in combination with a recently developed mass spectrometry technique. The measured velocity distributions allow probing statistical energy redistribution in ultimately small water nanodroplets after ultrafast electronic excitation. As the droplet size increases, the velocity distribution rapidly approaches the behavior expected for macroscopic droplets. However, a distinct high-velocity contribution provides evidence of molecular evaporation before complete energy redistribution, corresponding to non-ergodic events. PMID:26473406
Abdoul-Carime, Hassan; Berthias, Francis; Feketeová, Linda; Marciante, Mathieu; Calvo, Florent; Forquet, Valérian; Chermette, Henry; Farizon, Bernadette; Farizon, Michel; Märk, Tilmann D
2015-01-01
The velocity of a molecule evaporated from a mass-selected protonated water nanodroplet is measured by velocity map imaging in combination with a recently developed mass spectrometry technique. The measured velocity distributions allow probing statistical energy redistribution in ultimately small water nanodroplets after ultrafast electronic excitation. As the droplet size increases, the velocity distribution rapidly approaches the behavior expected for macroscopic droplets. However, a distinct high-velocity contribution provides evidence of molecular evaporation before complete energy redistribution, corresponding to non-ergodic events. PMID:26473406
Mauro, John C.; Loucks, Roger J.; Sen, Sabyasachi
2011-04-14
We show that Johari's critique of our work is based on a misunderstanding of ergodic theory and a disregard for the broken ergodic nature of glass. His analysis is in contradiction with well established experimental results in specific heat spectroscopy, shear-mechanical spectroscopy, and the vanishing of heat capacity in the limit of zero temperature. Based on these misinterpretations, Johari arrives at the erroneous conclusion that the residual entropy of glass is real. However, we show that Johari's result is an artifact in direct contradiction with both rigorous theory and experimental measurements.
Ergodicity and nonergodicity in La-doped Bi1/2(Na0.82K0.18)1/2TiO3 relaxors
NASA Astrophysics Data System (ADS)
Dinh, Thi Hinh; Han, Hyoung-Su; Lee, Jae-Shin; Ahn, Chang-Won; Kim, Ill-Won; Bafandeh, Mohammad Reza
2015-04-01
The phase transition of La-doped [Bi1/2(Na0.82K0.18)1/2]TiO3 (BNKT) ceramics was investigated by using high-temperature X-ray diffraction and temperature-dependent dielectric measurements. Undoped BNKT was found to be a nonergodic relaxor, which was evidenced by the presence of a depolarization temperature below which polar nanoregions were frozen. However, La-doped BNKT ceramics are believed to be composites consisting of ergodic and nonergodic relaxors. The results suggest that a nonergodic relaxor with tetragonal symmetry might be distributed in an ergodic relaxor matrix with pseudocubic symmetry.
NASA Astrophysics Data System (ADS)
Puelma Touzel, Maximilian; Monteforte, Michael; Wolf, Fred
2015-03-01
The stability of a dynamics constrains its ability to process information, a notion intended to be captured by the ergodic theory of chaos and one likely to be important for neuroscience. Asynchronous, irregular network activity can be produced by models in which excitatory and inhibitory inputs are balanced. For negative and sharply pulsed interactions, these networks turn out to be stable. The coexistence of aperiodic activity and stability is called stable chaos. This stability to perturbations only exists up to some finite average strength beyond which they are unstable. This finite-size instability produces entropy not captured by conventional ergodic theory. We derive and use the probability of divergence as a function of perturbation strength to give an expression for a finite-sized analogue of the Kolmolgorov-Sinai (KS) entropy that scales with the perturbation strength, and thus deviates from the conventional KS entropy value of 0. This work provides a foundation for understanding the information processing capacity of networks in the fast synapse, fast action potential onset, and inhibition-dominated regime.
NASA Astrophysics Data System (ADS)
Houdayer, Cyril; Isono, Yusuke
2016-05-01
We investigate the asymptotic structure of (possibly type III) crossed product von Neumann algebras {M = B rtimes Γ} arising from arbitrary actions {Γ &ucedil;rvearrowright B} of bi-exact discrete groups (e.g. free groups) on amenable von Neumann algebras. We prove a spectral gap rigidity result for the central sequence algebra {N' \\cap M^ω} of any nonamenable von Neumann subalgebra with normal expectation {N subset M} . We use this result to show that for any strongly ergodic essentially free nonsingular action {Γ &ucedil;rvearrowright (X, μ)} of any bi-exact countable discrete group on a standard probability space, the corresponding group measure space factor {L^∞(X) rtimes Γ} has no nontrivial central sequence. Using recent results of Boutonnet et al. (Local spectral gap in simple Lie groups and applications, 2015), we construct, for every {0 < λ ≤ 1} , a type {III_λ} strongly ergodic essentially free nonsingular action F_∞ &ucedil;rvearrowright (X_λ, μ_λ) of the free group F_∞ on a standard probability space so that the corresponding group measure space type {III_λ} factor {L^∞(X_λ, μ_λ) rtimes F_∞ has no nontrivial central sequence by our main result. In particular, we obtain the first examples of group measure space type {III} factors with no nontrivial central sequence.
NASA Astrophysics Data System (ADS)
Kalinin, S. V.; Rodriguez, B.; Nikiforov, M. P.; Balke, N.; Jesse, S.; Ovchinnikov, O. S.; Bokov, A. A.; Ye, Z.-G.
2009-03-01
Mesoscopic domain structure and dynamics in PMN-PT solis solutions is studied using spatially resolved time- and voltage spectroscopic imaging modes. For compositions close to the MPB, we observe the formation of classical ferroelectric domains with rough self-affine boundaries. In the ergodic phase (PMN and PMN-10PT), the formation of non-classical labyrinthine domain patterns characterized by a single characteristic length scale is observed. The (a) persistence of these patterns well above Tc and (b) the fact that cannot be switched by tip bias suggest that they can be attributed to the frozen polarization component. Spatial variability of polarization relaxation dynamics in PMN-10PT is studied. Local relaxation attributed to the reorientation of polar nanoregions was found to follow stretched exponential dependence, with β 0.4, much larger than the macroscopic value determined from dielectric spectra (β 0.09). The spatial inhomogeneity of relaxation time distribution with the presence of 100-200 nm ``fast'' and ``slow'' regions is observed. The results are analyzed to map the Vogel-Fulcher temperatures on the nanoscale. The applicability of this technique to map ``ergodic gap'' distribution on the surface is discussed. Research supported by the Division of Materials Science and Engineering, Basic Energy Sciences, U.S. Department of Energy at Oak Ridge National Laboratory, which is managed by UT-Battelle, LLC.
Quantum Computation and Quantum Information
NASA Astrophysics Data System (ADS)
Nielsen, Michael A.; Chuang, Isaac L.
2010-12-01
Part I. Fundamental Concepts: 1. Introduction and overview; 2. Introduction to quantum mechanics; 3. Introduction to computer science; Part II. Quantum Computation: 4. Quantum circuits; 5. The quantum Fourier transform and its application; 6. Quantum search algorithms; 7. Quantum computers: physical realization; Part III. Quantum Information: 8. Quantum noise and quantum operations; 9. Distance measures for quantum information; 10. Quantum error-correction; 11. Entropy and information; 12. Quantum information theory; Appendices; References; Index.
Quantum-Behaved Particle Swarm Optimization with Chaotic Search
NASA Astrophysics Data System (ADS)
Yang, Kaiqiao; Nomura, Hirosato
The chaotic search is introduced into Quantum-behaved Particle Swarm Optimization (QPSO) to increase the diversity of the swarm in the latter period of the search, so as to help the system escape from local optima. Taking full advantages of the characteristics of ergodicity and randomicity of chaotic variables, the chaotic search is carried out in the neighborhoods of the particles which are trapped into local optima. The experimental results on test functions show that QPSO with chaotic search outperforms the Particle Swarm Optimization (PSO) and QPSO.
How periodic driving heats a disordered quantum spin chain
NASA Astrophysics Data System (ADS)
Rehn, Jorge; Lazarides, Achilleas; Pollmann, Frank; Moessner, Roderich
2016-07-01
We study the energy absorption in real time of a disordered quantum spin chain subjected to coherent monochromatic periodic driving. We determine characteristic fingerprints of the well-known ergodic (Floquet-Eigenstate thermalization hypothesis for slow driving/weak disorder) and many-body localized (Floquet-many-body localization for fast driving/strong disorder) phases. In addition, we identify an intermediate regime, where the energy density of the system—unlike the entanglement entropy a local and bounded observable—grows logarithmically slowly over a very large time window.
NASA Astrophysics Data System (ADS)
Lanzagorta, Marco O.; Gomez, Richard B.; Uhlmann, Jeffrey K.
2003-08-01
In recent years, computer graphics has emerged as a critical component of the scientific and engineering process, and it is recognized as an important computer science research area. Computer graphics are extensively used for a variety of aerospace and defense training systems and by Hollywood's special effects companies. All these applications require the computer graphics systems to produce high quality renderings of extremely large data sets in short periods of time. Much research has been done in "classical computing" toward the development of efficient methods and techniques to reduce the rendering time required for large datasets. Quantum Computing's unique algorithmic features offer the possibility of speeding up some of the known rendering algorithms currently used in computer graphics. In this paper we discuss possible implementations of quantum rendering algorithms. In particular, we concentrate on the implementation of Grover's quantum search algorithm for Z-buffering, ray-tracing, radiosity, and scene management techniques. We also compare the theoretical performance between the classical and quantum versions of the algorithms.
NASA Astrophysics Data System (ADS)
Haruna, Taichi; Nakajima, Kohei
2013-05-01
Transfer entropy is a measure of the magnitude and the direction of information flow between jointly distributed stochastic processes. In recent years, its permutation analogues are considered in the literature to estimate the transfer entropy by counting the number of occurrences of orderings of values, not the values themselves. It has been suggested that the method of permutation is easy to implement, computationally low cost and robust to noise when applying to real world time series data. In this paper, we initiate a theoretical treatment of the corresponding rates. In particular, we consider the transfer entropy rate and its permutation analogue, the symbolic transfer entropy rate, and show that they are equal for any bivariate finite-alphabet stationary ergodic Markov process. This result is an illustration of the duality method introduced in [T. Haruna, K. Nakajima, Physica D 240, 1370 (2011)]. We also discuss the relationship among the transfer entropy rate, the time-delayed mutual information rate and their permutation analogues.
NASA Astrophysics Data System (ADS)
Zhang, Shengfeng; Wu, Zhongliang; Jiang, Changsheng
2016-01-01
Instrumentally recorded seismicity from 1970/01/01 to 2014/01/01 of the central China north-south seismic belt (21.0°-41.5°N, 97.5°-107.5°E) was analyzed, emphasizing the applicability of the predictive algorithms based on the assumptions of meta-stable equilibrium. The seismicity in this region was shown to exhibit ergodicity from 1980 to the present, with sub-region dependence, and interrupted by the 2008 Wenchuan earthquake. pattern informatics algorithm, a statistical physics-based predictive model for five-year time scale, is put to forward forecast test for the period 2014/01/01 to 2019/01/01.
Mallamace, Francesco; Corsaro, Carmelo; Leone, Nancy; Villari, Valentina; Micali, Norberto; Chen, Sow-Hsin
2014-01-01
The dynamics of supercooled ortho-terphenyl has been studied using photon-correlation spectroscopy (PCS) in the depolarized scattering geometry. The obtained relaxation curves are analyzed according to the mode-coupling theory (MCT) for supercooled liquids. The main results are: i) the observation of the secondary Johari-Goldstein relaxation (β) that has its onset just at the dynamical crossover temperature TB (TM > TB > Tg); ii) the confirmation, of the suggestion of a recent statistical mechanical study, that such a molecular system remains ergodic also below the calorimetric glass-transition temperature Tg. Our experimental data give evidence that the time scales of the primary (α) and this secondary relaxations are correlated. Finally a comparison with recent PCS experiments in a colloidal system confirms the primary role of the dynamical crossover in the physics of the dynamical arrest. PMID:24434872
NASA Astrophysics Data System (ADS)
Obrosova, N. K.; Shananin, A. A.
2015-04-01
A production model with allowance for a working capital deficit and a restricted maximum possible sales volume is proposed and analyzed. The study is motivated by an attempt to analyze the problems of functioning of low competitive macroeconomic structures. The model is formalized in the form of a Bellman equation, for which a closed-form solution is found. The stochastic process of product stock variations is proved to be ergodic and its final probability distribution is found. Expressions for the average production load and the average product stock are found by analyzing the stochastic process. A system of model equations relating the model variables to official statistical parameters is derived. The model is identified using data from the Fiat and KAMAZ companies. The influence of the credit interest rate on the firm market value assessment and the production load level are analyzed using comparative statics methods.
Wang, Kun; Song, Chaoming; Wang, Ping; Makse, Hernán A
2012-07-01
This paper illustrates how the tools of equilibrium statistical mechanics can help to describe a far-from-equilibrium problem: the jamming transition in frictionless granular materials. Edwards ideas consist of proposing a statistical ensemble of volume and stress fluctuations through the thermodynamic notion of entropy, compactivity, X, and angoricity, A (two temperature-like variables). We find that Edwards thermodynamics is able to describe the jamming transition (J point) in frictionless packings. Using the ensemble formalism we elucidate the following: (i) We test the combined volume-stress ensemble by comparing the statistical properties of jammed configurations obtained by dynamics with those averaged over the ensemble of minima in the potential energy landscape as a test of ergodicity. Agreement between both methods supports the idea of ergodicity and "thermalization" at a given angoricity and compactivity. (ii) A microcanonical ensemble analysis supports the maximum entropy principle for grains. (iii) The intensive variables A and X describe the approach to jamming through a series of scaling relations as A → 0+ and X → 0-. Due to the force-strain coupling in the interparticle forces, the jamming transition is probed thermodynamically by a "jamming temperature" T(J) composed of contributions from A and X. (iv) The thermodynamic framework reveals the order of the jamming phase transition by showing the absence of critical fluctuations at jamming in static observables like pressure and volume, and we discuss other critical scenarios for the jamming transition. (v) Finally, we elaborate on a comparison with relevant studies by Gao, Blawzdziewicz, and O'Hern [Phys. Rev. E 74, 061304 (2006)], showing a breakdown of equiprobability of microstates obtained via fast quenches. A network analysis of the energy landscape reveals the origin of the inhomogeneities in the uneven distribution of the areas of the basins. Such inhomogeneities are also found in other
NASA Astrophysics Data System (ADS)
Dolinšek, J.; Slanovec, J.; Jagličić, Z.; Heggen, M.; Balanetskyy, S.; Feuerbacher, M.; Urban, K.
2008-02-01
The Taylor-phase complex intermetallic compound T-Al3Mn , its solid solutions with Pd and Fe, T-Al3(Mn,Pd) and T-Al3(Mn,Fe) , and the related decagonal d-Al-Mn-Fe quasicrystal belong to the class of magnetically frustrated spin systems that exhibit rich out-of-equilibrium spin dynamics in the nonergodic phase below the spin-freezing temperature Tf . Performing large variety of magnetic experiments as a function of temperature, magnetic field, aging time tw , and different thermal histories, we investigated broken-ergodicity phenomena of (i) a difference in the field-cooled and zero-field-cooled susceptibilities, (ii) the frequency-dependent freezing temperature, Tf(ν) , (iii) hysteresis and remanence, (iv) ultraslow decay of the thermoremanent magnetization, (v) the memory effect (a state of the spin system reached upon isothermal aging can be retrieved after a negative temperature cycle), and (vi) “rejuvenation” (small positive temperature cycle within the nonergodic phase erases the effect of previous aging). We show that the phenomena involving isothermal aging periods (the memory effect, rejuvenation, and the ultraslow decay of the thermoremanent magnetization) get simple explanation by considering that during aging under steady external conditions, localized spin regions quasiequilibrate into more stable configurations, so that higher thermal energy is needed to destroy these regions by spin flipping, as compared to the thermal energy required to reverse a frustrated spin in a disordered spin-glass configuration that forms in the case of no aging. Common to all the investigated broken-ergodicity phenomena is the slow approach of a magnetically frustrated spin system toward a global equilibrium, which can never be reached on accessible experimental time scales due to macroscopic equilibration times.
Exploring Unique Roles for Psychologists
ERIC Educational Resources Information Center
Ahmed, Mohiuddin; Boisvert, Charles M.
2005-01-01
This paper presents comments on "Psychological Treatments" by D. H. Barlow. Barlow highlighted unique roles that psychologists can play in mental health service delivery by providing psychological treatments--treatments that psychologists would be uniquely qualified to design and deliver. In support of Barlow's position, the authors draw from…
ERIC Educational Resources Information Center
Shipman, Barbara A.
2013-01-01
This article analyzes four questions on the meaning of uniqueness that have contrasting answers in common language versus mathematical language. The investigations stem from a scenario in which students interpreted uniqueness according to a definition from standard English, that is, different from the mathematical meaning, in defining an injective…
NASA Astrophysics Data System (ADS)
Seth, Priyanka; Krivenko, Igor; Ferrero, Michel; Parcollet, Olivier
2016-03-01
We present TRIQS/CTHYB, a state-of-the art open-source implementation of the continuous-time hybridisation expansion quantum impurity solver of the TRIQS package. This code is mainly designed to be used with the TRIQS library in order to solve the self-consistent quantum impurity problem in a multi-orbital dynamical mean field theory approach to strongly-correlated electrons, in particular in the context of realistic electronic structure calculations. It is implemented in C++ for efficiency and is provided with a high-level Python interface. The code ships with a new partitioning algorithm that divides the local Hilbert space without any user knowledge of the symmetries and quantum numbers of the Hamiltonian. Furthermore, we implement higher-order configuration moves and show that such moves are necessary to ensure ergodicity of the Monte Carlo in common Hamiltonians even without symmetry-breaking.
Ideal quantum glass transitions: Many-body localization without quenched disorder
Schiulaz, M.; Müller, M.
2014-08-20
We explore the possibility for translationally invariant quantum many-body systems to undergo a dynamical glass transition, at which ergodicity and translational invariance break down spontaneously, driven entirely by quantum effects. In contrast to analogous classical systems, where the existence of such an ideal glass transition remains a controversial issue, a genuine phase transition is predicted in the quantum regime. This ideal quantum glass transition can be regarded as a many-body localization transition due to self-generated disorder. Despite their lack of thermalization, these disorder-free quantum glasses do not possess an extensive set of local conserved operators, unlike what is conjectured for many-body localized systems with strong quenched disorder.
Uniqueness of the momentum map
NASA Astrophysics Data System (ADS)
Esposito, Chiara; Nest, Ryszard
2016-08-01
We give a detailed discussion of existence and uniqueness of the momentum map associated to Poisson Lie actions, which was defined by Lu. We introduce a weaker notion of momentum map, called infinitesimal momentum map, which is defined on one-forms and we analyze its integrability to the Lu's momentum map. Finally, the uniqueness of the Lu's momentum map is studied by describing, explicitly, the tangent space to the space of momentum maps.
Quantum stochastic calculus associated with quadratic quantum noises
NASA Astrophysics Data System (ADS)
Ji, Un Cig; Sinha, Kalyan B.
2016-02-01
We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie †-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Itô formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculus extends the Hudson-Parthasarathy quantum stochastic calculus.
Uniqueness of place: uniqueness of models. The FLEX modelling approach
NASA Astrophysics Data System (ADS)
Fenicia, F.; Savenije, H. H. G.; Wrede, S.; Schoups, G.; Pfister, L.
2009-04-01
The current practice in hydrological modelling is to make use of model structures that are fixed and a-priori defined. However, for a model to reflect uniqueness of place while maintaining parsimony, it is necessary to be flexible in its architecture. We have developed a new approach for the development and testing of hydrological models, named the FLEX approach. This approach allows the formulation of alternative model structures that vary in configuration and complexity, and uses an objective method for testing and comparing model performance. We have tested this approach on three headwater catchments in Luxembourg with marked differences in hydrological response, where we have generated 15 alternative model structures. Each of the three catchments is best represented by a different model architecture. Our results clearly show that uniqueness of place necessarily leads to uniqueness of models.
Quantum Information and Computing
NASA Astrophysics Data System (ADS)
Accardi, L.; Ohya, Masanori; Watanabe, N.
2006-03-01
Preface -- Coherent quantum control of [symbol]-atoms through the stochastic limit / L. Accardi, S. V. Kozyrev and A. N. Pechen -- Recent advances in quantum white noise calculus / L. Accardi and A. Boukas -- Control of quantum states by decoherence / L. Accardi and K. Imafuku -- Logical operations realized on the Ising chain of N qubits / M. Asano, N. Tateda and C. Ishii -- Joint extension of states of fermion subsystems / H. Araki -- Quantum filtering and optimal feedback control of a Gaussian quantum free particle / S. C. Edwards and V. P. Belavkin -- On existence of quantum zeno dynamics / P. Exner and T. Ichinose -- Invariant subspaces and control of decoherence / P. Facchi, V. L. Lepore and S. Pascazio -- Clauser-Horner inequality for electron counting statistics in multiterminal mesoscopic conductors / L. Faoro, F. Taddei and R. Fazio -- Fidelity of quantum teleportation model using beam splittings / K.-H. Fichtner, T. Miyadera and M. Ohya -- Quantum logical gates realized by beam splittings / W. Freudenberg ... [et al.] -- Information divergence for quantum channels / S. J. Hammersley and V. P. Belavkin -- On the uniqueness theorem in quantum information geometry / H. Hasegawa -- Noncanonical representations of a multi-dimensional Brownian motion / Y. Hibino -- Some of future directions of white noise theory / T. Hida -- Information, innovation and elemental random field / T. Hida -- Generalized quantum turing machine and its application to the SAT chaos algorithm / S. Iriyama, M. Ohya and I. Volovich -- A Stroboscopic approach to quantum tomography / A. Jamiolkowski -- Positive maps and separable states in matrix algebras / A. Kossakowski -- Simulating open quantum systems with trapped ions / S. Maniscalco -- A purification scheme and entanglement distillations / H. Nakazato, M. Unoki and K. Yuasa -- Generalized sectors and adjunctions to control micro-macro transitions / I. Ojima -- Saturation of an entropy bound and quantum Markov states / D. Petz -- An
NASA Astrophysics Data System (ADS)
Kapustin, Anton
2013-06-01
We formulate physically motivated axioms for a physical theory which for systems with a finite number of degrees of freedom uniquely lead to quantum mechanics as the only nontrivial consistent theory. Complex numbers and the existence of the Planck constant common to all systems arise naturally in this approach. The axioms are divided into two groups covering kinematics and basic measurement theory, respectively. We show that even if the second group of axioms is dropped, there are no deformations of quantum mechanics which preserve the kinematic axioms. Thus, any theory going beyond quantum mechanics must represent a radical departure from the usual a priori assumptions about the laws of nature.
NASA Astrophysics Data System (ADS)
Wang, Kun; Song, Chaoming; Wang, Ping; Makse, Hernán A.
2012-07-01
This paper illustrates how the tools of equilibrium statistical mechanics can help to describe a far-from-equilibrium problem: the jamming transition in frictionless granular materials. Edwards ideas consist of proposing a statistical ensemble of volume and stress fluctuations through the thermodynamic notion of entropy, compactivity, X, and angoricity, A (two temperature-like variables). We find that Edwards thermodynamics is able to describe the jamming transition (J point) in frictionless packings. Using the ensemble formalism we elucidate the following: (i) We test the combined volume-stress ensemble by comparing the statistical properties of jammed configurations obtained by dynamics with those averaged over the ensemble of minima in the potential energy landscape as a test of ergodicity. Agreement between both methods supports the idea of ergodicity and “thermalization” at a given angoricity and compactivity. (ii) A microcanonical ensemble analysis supports the maximum entropy principle for grains. (iii) The intensive variables A and X describe the approach to jamming through a series of scaling relations as A→0+ and X→0-. Due to the force-strain coupling in the interparticle forces, the jamming transition is probed thermodynamically by a “jamming temperature” TJ composed of contributions from A and X. (iv) The thermodynamic framework reveals the order of the jamming phase transition by showing the absence of critical fluctuations at jamming in static observables like pressure and volume, and we discuss other critical scenarios for the jamming transition. (v) Finally, we elaborate on a comparison with relevant studies by Gao, Blawzdziewicz, and O’Hern [Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.74.061304 74, 061304 (2006)], showing a breakdown of equiprobability of microstates obtained via fast quenches. A network analysis of the energy landscape reveals the origin of the inhomogeneities in the uneven distribution of the areas of the basins
The liberal illusion of uniqueness.
Stern, Chadly; West, Tessa V; Schmitt, Peter G
2014-01-01
In two studies, we demonstrated that liberals underestimate their similarity to other liberals (i.e., display truly false uniqueness), whereas moderates and conservatives overestimate their similarity to other moderates and conservatives (i.e., display truly false consensus; Studies 1 and 2). We further demonstrated that a fundamental difference between liberals and conservatives in the motivation to feel unique explains this ideological distinction in the accuracy of estimating similarity (Study 2). Implications of the accuracy of consensus estimates for mobilizing liberal and conservative political movements are discussed. PMID:24247730
Quantum Computer Games: Schrodinger Cat and Hounds
ERIC Educational Resources Information Center
Gordon, Michal; Gordon, Goren
2012-01-01
The quantum computer game "Schrodinger cat and hounds" is the quantum extension of the well-known classical game fox and hounds. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. "Schrodinger cat and hounds" demonstrates the effects of superposition, destructive and constructive interference, measurements and…
... Multiple Health Problems Prevention Join our e-newsletter! Aging & Health A to Z COPD Unique to Older Adults This section provides information ... not a weakness or a normal part of aging. Most people feel better with ... help you can, so that your COPD does not prevent you from living your life ...
Uniquely identifying wheat plant structures
Technology Transfer Automated Retrieval System (TEKTRAN)
Uniquely naming wheat (Triticum aestivum L. em Thell) plant parts is useful for communicating plant development research and the effects of environmental stresses on normal wheat development. Over the past 30+ years, several naming systems have been proposed for wheat shoot, leaf, spike, spikelet, ...
Identity Foreclosure: A Unique Challenge
ERIC Educational Resources Information Center
Petitpas, Al
1978-01-01
Foreclosure occurs when individuals prematurely make a firm commitment to an occupation or an ideology. If the pressure of having an occupational identity can be eased, then it may be possible to establish an environment in which foreclosed students could move toward the consolidation of their unique identities. (Author)
NASA Astrophysics Data System (ADS)
Eckmann, Jean-Pierre; Procaccia, Itamar
2008-07-01
The aim of this paper is to discuss some basic notions regarding generic glass-forming systems composed of particles interacting via soft potentials. Excluding explicitly hard-core interaction, we discuss the so-called glass transition in which a supercooled amorphous state is formed, accompanied by a spectacular slowing down of relaxation to equilibrium, when the temperature is changed over a relatively small interval. Using the classical example of a 50-50 binary liquid of N particles with different interaction length scales, we show the following. (i) The system remains ergodic at all temperatures. (ii) The number of topologically distinct configurations can be computed, is temperature independent, and is exponential in N . (iii) Any two configurations in phase space can be connected using elementary moves whose number is polynomially bounded in N , showing that the graph of configurations has the small world property. (iv) The entropy of the system can be estimated at any temperature (or energy), and there is no Kauzmann crisis at any positive temperature. (v) The mechanism for the super-Arrhenius temperature dependence of the relaxation time is explained, connecting it to an entropic squeeze at the glass transition. (vi) There is no Vogel-Fulcher crisis at any finite temperature T>0 .
NASA Astrophysics Data System (ADS)
Jazayeri, S. M.; Sohrabi, A. R.
2014-06-01
We use a method based on the conservation of energy, the mean-energy error criterion, to approximately locate the place of a cantorus by locating the series of its convergents. The mean-energy error curve has nearly stationary parts in the vicinity of elliptic (minimax) orbits, the so-called magnetic islands. Stable minimax orbits converge to orbits homoclinic to a cantorus. By tracing the island series, we limit the cantorus to a narrow region. A near-critical perturbation parameter is used so that, while the cantorus may be destabilized, its high-order minimax orbits remain intact. As illustrations, we consider two symplectic maps, systematically derived from the Hamilton-Jacobi equation and Jacobi's theorem, in the context of the magnetically confined plasmas in a tokamak: a symmetric tokamap realistically reproduces the main features of a tokamak, and a symmetric ergodic magnetic limiter (EML) map is defined to describe the action of EML rings on the magnetic field lines in the tokamak.
Hilbert-space localization in closed quantum systems
NASA Astrophysics Data System (ADS)
Cohen, Doron; Yukalov, Vyacheslav I.; Ziegler, Klaus
2016-04-01
Quantum localization within an energy shell of a closed quantum system stands in contrast to the ergodic assumption of Boltzmann, and to the corresponding eigenstate thermalization hypothesis. The familiar case is the real-space Anderson localization and its many-body Fock-space version. We use the term Hilbert-space localization in order to emphasize the more general phase-space context. Specifically, we introduce a unifying picture that extends the semiclassical perspective of Heller, which relates the localization measure to the probability of return. We illustrate our approach by considering several systems of experimental interest, referring in particular to the bosonic Josephson tunneling junction. We explore the dependence of the localization measure on the initial state and on the strength of the many-body interactions using a recursive projection method.
Quantum quenches, thermalization, and many-body localization
NASA Astrophysics Data System (ADS)
Canovi, Elena; Rossini, Davide; Fazio, Rosario; Santoro, Giuseppe E.; Silva, Alessandro
2011-03-01
We conjecture that thermalization following a quantum quench in a strongly correlated quantum system is closely connected to many-body delocalization in the space of quasi-particles. This scenario is tested in the anisotropic Heisenberg spin chain with different types of integrability-breaking terms. We first quantify the deviations from integrability by analyzing the level spacing statistics and the inverse participation ratio of the system’s eigenstates. We then focus on thermalization, by studying the dynamics after a sudden quench of the anisotropy parameter. Our numerical simulations clearly support the conjecture, as long as the integrability-breaking term acts homogeneously on the quasiparticle space, in such a way as to induce ergodicity over all the relevant Hilbert space.
On the approach to thermal equilibrium of macroscopic quantum systems
Goldstein, Sheldon; Tumulka, Roderich
2011-03-24
In joint work with J. L. Lebowitz, C. Mastrodonato, and N. Zanghi[2, 3, 4], we considered an isolated, macroscopic quantum system. Let H be a micro-canonical 'energy shell', i.e., a subspace of the system's Hilbert space spanned by the (finitely) many energy eigenstates with energies between E and E+{delta}E. The thermal equilibrium macro-state at energy E corresponds to a subspace H{sub eq} of H such that dimHeq/dimH is close to 1. We say that a system with state vector {psi}{epsilon}H is in thermal equilibrium if {psi} is 'close' to H{sub eq}. We argue that for 'typical' Hamiltonians, all initial state vectors {psi}{sub 0} evolve in such a way that {psi}{sub t} is in thermal equilibrium for most times t. This is closely related to von Neumann's quantum ergodic theorem of 1929.
A note on the Landauer principle in quantum statistical mechanics
Jakšić, Vojkan; Pillet, Claude-Alain
2014-07-01
The Landauer principle asserts that the energy cost of erasure of one bit of information by the action of a thermal reservoir in equilibrium at temperature T is never less than k_{B}T log 2. We discuss Landauer's principle for quantum statistical models describing a finite level quantum system S coupled to an infinitely extended thermal reservoir R. Using Araki's perturbation theory of KMS states and the Avron-Elgart adiabatic theorem we prove, under a natural ergodicity assumption on the joint system S+R, that Landauer's bound saturates for adiabatically switched interactions. The recent work [Reeb, D. and Wolf M. M., “(Im-)proving Landauer's principle,” preprint http://arxiv.org/abs/arXiv:1306.4352v2 (2013)] on the subject is discussed and compared.
On Milne's quantum number function
NASA Astrophysics Data System (ADS)
Korsch, H. Jürgen
1985-06-01
The quantum number function N( E) introduced by Milne is studied in detail. It is shown that N( E) is not uniquely defined for energies different from the bound state values. The density of states {dN }/{dE } is nowhere unique and not necessarily positive.
Quantum Complexity in Graphene
NASA Astrophysics Data System (ADS)
Baskaran, G.
Carbon has a unique position among elements in the periodic table. It produces an allotrope, graphene, a mechanically robust two dimensional semimetal. The multifarious properties that graphene exhibits has few parallels among elemental metals. From simplicity, namely carbon atoms connected by pure sp2 bonds, a wealth of novel quantum properties emerge. In classical complex systems such as a spin glass or a finance market, several competing agents or elements are responsible for unanticipated and difficult to predict emergent properties. The complex (sic) structure of quantum mechanics is responsbile for an unanticipated set of emergent properties in graphene. We call this quantum complexity. In fact, most quantum systems, phenomena and modern quantum field theory could be viewed as examples of quantum complexity. After giving a brief introduction to the quantum complexity we focus on our own work, which indicates the breadth in the type of quantum phenomena that graphene could support. We review our theoretical suggestions of, (i) spin-1 collective mode in netural graphene, (ii) relativistic type of phenomena in crossed electric and magnetic fields, (iii) room temperature superconductivity in doped graphene and (iv) composite Fermi sea in neutral graphene in uniform magnetic field and (v) two-channel Kondo effect. Except for the relativistic type of phenomena, the rest depend in a fundamental way on a weak electron correlation that exists in the broad two-dimensional band of graphene.
Not Available
1985-06-01
Consafe is now using a computer-aided design and drafting system adapting its multipurpose support vessels (MSVS) to specific user requirements. The vessels are based on the concept of standard container modules adapted into living quarters, workshops, service units, offices with each application for a specific project demanding a unique mix. There is also the need for constant refurbishment program as service conditions take their toll on the modules. The computer-aided design system is described.
Kozyreva, O V; Popov, K V
2000-10-31
The theoretical and practical uniqueness of the results obtained by the method of nonlinear laser fluorimetry is considered. The theoretical uniqueness of measuring three basic photophysical parameters (the absorption cross section, the excited-state lifetime, and the quantum yield of intersystem crossing) from fluorescence saturation curves is proved rigorously mathematically. The practical uniqueness of the results obtained by this method is proved by the measurements of the absorption cross section and the excited-state lifetime from the calculated curves of fluorescence saturation simulating fluorescence saturation of aqueous solutions of rhodamine 6G, eosin, and Bengal rose dyes. (laser applications and other topics in quantum electronics)
Bound states in continuum: Quantum dots in a quantum well
NASA Astrophysics Data System (ADS)
Prodanović, Nikola; Milanović, Vitomir; Ikonić, Zoran; Indjin, Dragan; Harrison, Paul
2013-11-01
We report on the existence of a bound state in the continuum (BIC) of quantum rods (QR). QRs are novel elongated InGaAs quantum dot nanostructures embedded in the shallower InGaAs quantum well. BIC appears as an excited confined dot state and energetically above the bottom of a well subband continuum. We prove that high height-to-diameter QR aspect ratio and the presence of a quantum well are indispensable conditions for accommodating the BIC. QRs are unique semiconductor nanostructures, exhibiting this mathematical curiosity predicted 83 years ago by Wigner and von Neumann.
Quantum correlation via quantum coherence
NASA Astrophysics Data System (ADS)
Yu, Chang-shui; Zhang, Yang; Zhao, Haiqing
2014-06-01
Quantum correlation includes quantum entanglement and quantum discord. Both entanglement and discord have a common necessary condition—quantum coherence or quantum superposition. In this paper, we attempt to give an alternative understanding of how quantum correlation is related to quantum coherence. We divide the coherence of a quantum state into several classes and find the complete coincidence between geometric (symmetric and asymmetric) quantum discords and some particular classes of quantum coherence. We propose a revised measure for total coherence and find that this measure can lead to a symmetric version of geometric quantum correlation, which is analytic for two qubits. In particular, this measure can also arrive at a monogamy equality on the distribution of quantum coherence. Finally, we also quantify a remaining type of quantum coherence and find that for two qubits, it is directly connected with quantum nonlocality.
Roadmap on quantum optical systems
NASA Astrophysics Data System (ADS)
Dumke, Rainer; Lu, Zehuang; Close, John; Robins, Nick; Weis, Antoine; Mukherjee, Manas; Birkl, Gerhard; Hufnagel, Christoph; Amico, Luigi; Boshier, Malcolm G.; Dieckmann, Kai; Li, Wenhui; Killian, Thomas C.
2016-09-01
This roadmap bundles fast developing topics in experimental optical quantum sciences, addressing current challenges as well as potential advances in future research. We have focused on three main areas: quantum assisted high precision measurements, quantum information/simulation, and quantum gases. Quantum assisted high precision measurements are discussed in the first three sections, which review optical clocks, atom interferometry, and optical magnetometry. These fields are already successfully utilized in various applied areas. We will discuss approaches to extend this impact even further. In the quantum information/simulation section, we start with the traditionally successful employed systems based on neutral atoms and ions. In addition the marvelous demonstrations of systems suitable for quantum information is not progressing, unsolved challenges remain and will be discussed. We will also review, as an alternative approach, the utilization of hybrid quantum systems based on superconducting quantum devices and ultracold atoms. Novel developments in atomtronics promise unique access in exploring solid-state systems with ultracold gases and are investigated in depth. The sections discussing the continuously fast-developing quantum gases include a review on dipolar heteronuclear diatomic gases, Rydberg gases, and ultracold plasma. Overall, we have accomplished a roadmap of selected areas undergoing rapid progress in quantum optics, highlighting current advances and future challenges. These exciting developments and vast advances will shape the field of quantum optics in the future.
Uniqueness of photon spheres in electro-vacuum spacetimes
NASA Astrophysics Data System (ADS)
Cederbaum, Carla; Galloway, Gregory J.
2016-04-01
In a recent paper (Cederbaum C and Galloway G J 2015 Commun. Analysis Geom. at press), the authors established the uniqueness of photon spheres in static vacuum asymptotically flat spacetimes by adapting Bunting and Masood-ul-Alam’s proof of static vacuum black hole uniqueness. Here, we establish uniqueness of suitably defined sub-extremal photon spheres in static electro-vacuum asymptotically flat spacetimes by adapting the argument of Masood-ul-Alam (1992 Class. Quantum Grav. 9 L53-5). As a consequence of our result, we can rule out the existence of electrostatic configurations involving multiple ‘very compact’ electrically charged bodies and sub-extremal black holes.
Quantum Opportunities and Challenges for Fundamental Sciences in Space
NASA Technical Reports Server (NTRS)
Yu, Nan
2012-01-01
Space platforms offer unique environment for and measurements of quantum world and fundamental physics. Quantum technology and measurements enhance measurement capabilities in space and result in greater science returns.
NASA Astrophysics Data System (ADS)
Le Gouët, Jean-Louis; Moiseev, Sergey
2012-06-01
Interaction of quantum radiation with multi-particle ensembles has sparked off intense research efforts during the past decade. Emblematic of this field is the quantum memory scheme, where a quantum state of light is mapped onto an ensemble of atoms and then recovered in its original shape. While opening new access to the basics of light-atom interaction, quantum memory also appears as a key element for information processing applications, such as linear optics quantum computation and long-distance quantum communication via quantum repeaters. Not surprisingly, it is far from trivial to practically recover a stored quantum state of light and, although impressive progress has already been accomplished, researchers are still struggling to reach this ambitious objective. This special issue provides an account of the state-of-the-art in a fast-moving research area that makes physicists, engineers and chemists work together at the forefront of their discipline, involving quantum fields and atoms in different media, magnetic resonance techniques and material science. Various strategies have been considered to store and retrieve quantum light. The explored designs belong to three main—while still overlapping—classes. In architectures derived from photon echo, information is mapped over the spectral components of inhomogeneously broadened absorption bands, such as those encountered in rare earth ion doped crystals and atomic gases in external gradient magnetic field. Protocols based on electromagnetic induced transparency also rely on resonant excitation and are ideally suited to the homogeneous absorption lines offered by laser cooled atomic clouds or ion Coulomb crystals. Finally off-resonance approaches are illustrated by Faraday and Raman processes. Coupling with an optical cavity may enhance the storage process, even for negligibly small atom number. Multiple scattering is also proposed as a way to enlarge the quantum interaction distance of light with matter. The
Quantum control in spintronics.
Ardavan, A; Briggs, G A D
2011-08-13
Superposition and entanglement are uniquely quantum phenomena. Superposition incorporates a phase that contains information surpassing any classical mixture. Entanglement offers correlations between measurements in quantum systems that are stronger than any that would be possible classically. These give quantum computing its spectacular potential, but the implications extend far beyond quantum information processing. Early applications may be found in entanglement-enhanced sensing and metrology. Quantum spins in condensed matter offer promising candidates for investigating and exploiting superposition and entanglement, and enormous progress is being made in quantum control of such systems. In gallium arsenide (GaAs), individual electron spins can be manipulated and measured, and singlet-triplet states can be controlled in double-dot structures. In silicon, individual electron spins can be detected by ionization of phosphorus donors, and information can be transferred from electron spins to nuclear spins to provide long memory times. Electron and nuclear spins can be manipulated in nitrogen atoms incarcerated in fullerene molecules, which in turn can be assembled in ordered arrays. Spin states of charged nitrogen vacancy centres in diamond can be manipulated and read optically. Collective spin states in a range of materials systems offer scope for holographic storage of information. Conditions are now excellent for implementing superposition and entanglement in spintronic devices, thereby opening up a new era of quantum technologies. PMID:21727123
Dynamics of symmetry breaking during quantum real-time evolution in a minimal model system.
Heyl, Markus; Vojta, Matthias
2014-10-31
One necessary criterion for the thermalization of a nonequilibrium quantum many-particle system is ergodicity. It is, however, not sufficient in cases where the asymptotic long-time state lies in a symmetry-broken phase but the initial state of nonequilibrium time evolution is fully symmetric with respect to this symmetry. In equilibrium, one particular symmetry-broken state is chosen as a result of an infinitesimal symmetry-breaking perturbation. From a dynamical point of view the question is: Can such an infinitesimal perturbation be sufficient for the system to establish a nonvanishing order during quantum real-time evolution? We study this question analytically for a minimal model system that can be associated with symmetry breaking, the ferromagnetic Kondo model. We show that after a quantum quench from a completely symmetric state the system is able to break its symmetry dynamically and discuss how these features can be observed experimentally. PMID:25396355
The probabilities of unique events.
Khemlani, Sangeet S; Lotstein, Max; Johnson-Laird, Phil
2012-01-01
Many theorists argue that the probabilities of unique events, even real possibilities such as President Obama's re-election, are meaningless. As a consequence, psychologists have seldom investigated them. We propose a new theory (implemented in a computer program) in which such estimates depend on an intuitive non-numerical system capable only of simple procedures, and a deliberative system that maps intuitions into numbers. The theory predicts that estimates of the probabilities of conjunctions should often tend to split the difference between the probabilities of the two conjuncts. We report two experiments showing that individuals commit such violations of the probability calculus, and corroborating other predictions of the theory, e.g., individuals err in the same way even when they make non-numerical verbal estimates, such as that an event is highly improbable. PMID:23056224
The Probabilities of Unique Events
Khemlani, Sangeet S.; Lotstein, Max; Johnson-Laird, Phil
2012-01-01
Many theorists argue that the probabilities of unique events, even real possibilities such as President Obama's re-election, are meaningless. As a consequence, psychologists have seldom investigated them. We propose a new theory (implemented in a computer program) in which such estimates depend on an intuitive non-numerical system capable only of simple procedures, and a deliberative system that maps intuitions into numbers. The theory predicts that estimates of the probabilities of conjunctions should often tend to split the difference between the probabilities of the two conjuncts. We report two experiments showing that individuals commit such violations of the probability calculus, and corroborating other predictions of the theory, e.g., individuals err in the same way even when they make non-numerical verbal estimates, such as that an event is highly improbable. PMID:23056224
NASA Astrophysics Data System (ADS)
Georgescu, I. M.; Ashhab, S.; Nori, Franco
2014-01-01
Simulating quantum mechanics is known to be a difficult computational problem, especially when dealing with large systems. However, this difficulty may be overcome by using some controllable quantum system to study another less controllable or accessible quantum system, i.e., quantum simulation. Quantum simulation promises to have applications in the study of many problems in, e.g., condensed-matter physics, high-energy physics, atomic physics, quantum chemistry, and cosmology. Quantum simulation could be implemented using quantum computers, but also with simpler, analog devices that would require less control, and therefore, would be easier to construct. A number of quantum systems such as neutral atoms, ions, polar molecules, electrons in semiconductors, superconducting circuits, nuclear spins, and photons have been proposed as quantum simulators. This review outlines the main theoretical and experimental aspects of quantum simulation and emphasizes some of the challenges and promises of this fast-growing field.
Some Uniqueness Results for PARAFAC2.
ERIC Educational Resources Information Center
ten Berge, Jos M. F.; Kiers, Henk A. L.
1996-01-01
Some uniqueness properties are presented for the PARAFAC2 model for covariance matrices, focusing on uniqueness in the rank two case of PARAFAC2. PARAFAC2 is shown to be usually unique with four matrices, but not unique with three unless a certain additional assumption is introduced. (SLD)
Uniqueness of the gauge invariant action for cosmological perturbations
Prokopec, Tomislav; Weenink, Jan E-mail: j.g.weenink@uu.nl
2012-12-01
In second order perturbation theory different definitions are known of gauge invariant perturbations in single field inflationary models. Consequently the corresponding gauge invariant cubic actions do not have the same form. Here we show that the cubic action for one choice of gauge invariant variables is unique in the following sense: the action for any other, non-linearly related variable can be brought to the same bulk action, plus additional boundary terms. These boundary terms correspond to the choice of hypersurface and generate extra, disconnected contributions to the bispectrum. We also discuss uniqueness of the action with respect to conformal frames. When expressed in terms of the gauge invariant curvature perturbation on uniform field hypersurfaces the action for cosmological perturbations has a unique form, independent of the original Einstein or Jordan frame. Crucial is that the gauge invariant comoving curvature perturbation is frame independent, which makes it extremely helpful in showing the quantum equivalence of the two frames, and therefore in calculating quantum effects in nonminimally coupled theories such as Higgs inflation.
CYP1B1: a unique gene with unique characteristics.
Faiq, Muneeb A; Dada, Rima; Sharma, Reetika; Saluja, Daman; Dada, Tanuj
2014-01-01
CYP1B1, a recently described dioxin inducible oxidoreductase, is a member of the cytochrome P450 superfamily involved in the metabolism of estradiol, retinol, benzo[a]pyrene, tamoxifen, melatonin, sterols etc. It plays important roles in numerous physiological processes and is expressed at mRNA level in many tissues and anatomical compartments. CYP1B1 has been implicated in scores of disorders. Analyses of the recent studies suggest that CYP1B1 can serve as a universal/ideal cancer marker and a candidate gene for predictive diagnosis. There is plethora of literature available about certain aspects of CYP1B1 that have not been interpreted, discussed and philosophized upon. The present analysis examines CYP1B1 as a peculiar gene with certain distinctive characteristics like the uniqueness in its chromosomal location, gene structure and organization, involvement in developmentally important disorders, tissue specific, not only expression, but splicing, potential as a universal cancer marker due to its involvement in key aspects of cellular metabolism, use in diagnosis and predictive diagnosis of various diseases and the importance and function of CYP1B1 mRNA in addition to the regular translation. Also CYP1B1 is very difficult to express in heterologous expression systems, thereby, halting its functional studies. Here we review and analyze these exceptional and startling characteristics of CYP1B1 with inputs from our own experiences in order to get a better insight into its molecular biology in health and disease. This may help to further understand the etiopathomechanistic aspects of CYP1B1 mediated diseases paving way for better research strategies and improved clinical management. PMID:25658124
Quantum networks reveal quantum nonlocality.
Cavalcanti, Daniel; Almeida, Mafalda L; Scarani, Valerio; Acín, Antonio
2011-01-01
The results of local measurements on some composite quantum systems cannot be reproduced classically. This impossibility, known as quantum nonlocality, represents a milestone in the foundations of quantum theory. Quantum nonlocality is also a valuable resource for information-processing tasks, for example, quantum communication, quantum key distribution, quantum state estimation or randomness extraction. Still, deciding whether a quantum state is nonlocal remains a challenging problem. Here, we introduce a novel approach to this question: we study the nonlocal properties of quantum states when distributed and measured in networks. We show, using our framework, how any one-way entanglement distillable state leads to nonlocal correlations and prove that quantum nonlocality is a non-additive resource, which can be activated. There exist states, local at the single-copy level, that become nonlocal when taking several copies of them. Our results imply that the nonlocality of quantum states strongly depends on the measurement context. PMID:21304513
Discord as a quantum resource for bi-partite communication
NASA Astrophysics Data System (ADS)
Chrzanowski, Helen M.; Gu, Mile; Assad, Syed M.; Symul, Thomas; Modi, Kavan; Ralph, Timothy C.; Vedral, Vlatko; Lam, Ping Koy
2014-12-01
Coherent interactions that generate negligible entanglement can still exhibit unique quantum behaviour. This observation has motivated a search beyond entanglement for a complete description of all quantum correlations. Quantum discord is a promising candidate. Here, we experimentally demonstrate that under certain measurement constraints, discord between bipartite systems can be consumed to encode information that can only be accessed by coherent quantum interactions. The inability to access this information by any other means allows us to use discord to directly quantify this `quantum advantage'.
Respiratory infections unique to Asia.
Tsang, Kenneth W; File, Thomas M
2008-11-01
Asia is a highly heterogeneous region with vastly different cultures, social constitutions and populations affected by a wide spectrum of respiratory diseases caused by tropical pathogens. Asian patients with community-acquired pneumonia differ from their Western counterparts in microbiological aetiology, in particular the prominence of Gram-negative organisms, Mycobacterium tuberculosis, Burkholderia pseudomallei and Staphylococcus aureus. In addition, the differences in socioeconomic and health-care infrastructures limit the usefulness of Western management guidelines for pneumonia in Asia. The importance of emerging infectious diseases such as severe acute respiratory syndrome and avian influenza infection remain as close concerns for practising respirologists in Asia. Specific infections such as melioidosis, dengue haemorrhagic fever, scrub typhus, leptospirosis, salmonellosis, penicilliosis marneffei, malaria, amoebiasis, paragonimiasis, strongyloidiasis, gnathostomiasis, trinchinellosis, schistosomiasis and echinococcosis occur commonly in Asia and manifest with a prominent respiratory component. Pulmonary eosinophilia, endemic in parts of Asia, could occur with a wide range of tropical infections. Tropical eosinophilia is believed to be a hyper-sensitivity reaction to degenerating microfilariae trapped in the lungs. This article attempts to address the key respiratory issues in these respiratory infections unique to Asia and highlight the important diagnostic and management issues faced by practising respirologists. PMID:18945321
Stapp, H.P.
1988-12-01
Quantum ontologies are conceptions of the constitution of the universe that are compatible with quantum theory. The ontological orientation is contrasted to the pragmatic orientation of science, and reasons are given for considering quantum ontologies both within science, and in broader contexts. The principal quantum ontologies are described and evaluated. Invited paper at conference: Bell's Theorem, Quantum Theory, and Conceptions of the Universe, George Mason University, October 20-21, 1988. 16 refs.
NASA Astrophysics Data System (ADS)
Pfeiffer, P.; Egusquiza, I. L.; di Ventra, M.; Sanz, M.; Solano, E.
2016-07-01
Technology based on memristors, resistors with memory whose resistance depends on the history of the crossing charges, has lately enhanced the classical paradigm of computation with neuromorphic architectures. However, in contrast to the known quantized models of passive circuit elements, such as inductors, capacitors or resistors, the design and realization of a quantum memristor is still missing. Here, we introduce the concept of a quantum memristor as a quantum dissipative device, whose decoherence mechanism is controlled by a continuous-measurement feedback scheme, which accounts for the memory. Indeed, we provide numerical simulations showing that memory effects actually persist in the quantum regime. Our quantization method, specifically designed for superconducting circuits, may be extended to other quantum platforms, allowing for memristor-type constructions in different quantum technologies. The proposed quantum memristor is then a building block for neuromorphic quantum computation and quantum simulations of non-Markovian systems.
Pfeiffer, P; Egusquiza, I L; Di Ventra, M; Sanz, M; Solano, E
2016-01-01
Technology based on memristors, resistors with memory whose resistance depends on the history of the crossing charges, has lately enhanced the classical paradigm of computation with neuromorphic architectures. However, in contrast to the known quantized models of passive circuit elements, such as inductors, capacitors or resistors, the design and realization of a quantum memristor is still missing. Here, we introduce the concept of a quantum memristor as a quantum dissipative device, whose decoherence mechanism is controlled by a continuous-measurement feedback scheme, which accounts for the memory. Indeed, we provide numerical simulations showing that memory effects actually persist in the quantum regime. Our quantization method, specifically designed for superconducting circuits, may be extended to other quantum platforms, allowing for memristor-type constructions in different quantum technologies. The proposed quantum memristor is then a building block for neuromorphic quantum computation and quantum simulations of non-Markovian systems. PMID:27381511
Pfeiffer, P.; Egusquiza, I. L.; Di Ventra, M.; Sanz, M.; Solano, E.
2016-01-01
Technology based on memristors, resistors with memory whose resistance depends on the history of the crossing charges, has lately enhanced the classical paradigm of computation with neuromorphic architectures. However, in contrast to the known quantized models of passive circuit elements, such as inductors, capacitors or resistors, the design and realization of a quantum memristor is still missing. Here, we introduce the concept of a quantum memristor as a quantum dissipative device, whose decoherence mechanism is controlled by a continuous-measurement feedback scheme, which accounts for the memory. Indeed, we provide numerical simulations showing that memory effects actually persist in the quantum regime. Our quantization method, specifically designed for superconducting circuits, may be extended to other quantum platforms, allowing for memristor-type constructions in different quantum technologies. The proposed quantum memristor is then a building block for neuromorphic quantum computation and quantum simulations of non-Markovian systems. PMID:27381511
Dynamic Nuclear Polarization and the Paradox of Quantum Thermalization
NASA Astrophysics Data System (ADS)
De Luca, Andrea; Rosso, Alberto
2015-08-01
Dynamic nuclear polarization (DNP) is to date the most effective technique to increase the nuclear polarization opening disruptive perspectives for medical applications. In a DNP setting, the interacting spin system is quasi-isolated and brought out of equilibrium by microwave irradiation. Here we show that the resulting stationary state strongly depends on the ergodicity properties of the spin many-body eigenstates. In particular, the dipolar interactions compete with the disorder induced by local magnetic fields resulting in two distinct dynamical phases: while for weak interaction, only a small enhancement of polarization is observed, for strong interactions the spins collectively equilibrate to an extremely low effective temperature that boosts DNP efficiency. We argue that these two phases are intimately related to the problem of thermalization in closed quantum systems where a many-body localization transition can occur varying the strength of the interactions.
Quantum diffusion with drift and the Einstein relation. I
De Roeck, Wojciech; Fröhlich, Jürg; Schnelli, Kevin
2014-07-15
We study the dynamics of a quantum particle hopping on a simple cubic lattice and driven by a constant external force. It is coupled to an array of identical, independent thermal reservoirs consisting of free, massless Bose fields, one at each site of the lattice. When the particle visits a site x of the lattice it can emit or absorb field quanta of the reservoir at x. Under the assumption that the coupling between the particle and the reservoirs and the driving force are sufficiently small, we establish the following results: The ergodic average over time of the state of the particle approaches a non-equilibrium steady state describing a non-zero mean drift of the particle. Its motion around the mean drift is diffusive, and the diffusion constant and the drift velocity are related to one another by the Einstein relation.
Quantum pump in quantum spin Hall edge states
NASA Astrophysics Data System (ADS)
Cheng, Fang
2016-09-01
We present a theory for quantum pump in a quantum spin Hall bar with two quantum point contacts (QPCs). The pump currents can be generated by applying harmonically modulating gate voltages at QPCs. The phase difference between the gate voltages introduces an effective gauge field, which breaks the time-reversal symmetry and generates pump currents. The pump currents display very different pump frequency dependence for weak and strong e-e interaction. These unique properties are induced by the helical feature of the edge states, and therefore can be used to detect and control edge state transport.
Consistent quantum measurements
NASA Astrophysics Data System (ADS)
Griffiths, Robert B.
2015-11-01
In response to recent criticisms by Okon and Sudarsky, various aspects of the consistent histories (CH) resolution of the quantum measurement problem(s) are discussed using a simple Stern-Gerlach device, and compared with the alternative approaches to the measurement problem provided by spontaneous localization (GRW), Bohmian mechanics, many worlds, and standard (textbook) quantum mechanics. Among these CH is unique in solving the second measurement problem: inferring from the measurement outcome a property of the measured system at a time before the measurement took place, as is done routinely by experimental physicists. The main respect in which CH differs from other quantum interpretations is in allowing multiple stochastic descriptions of a given measurement situation, from which one (or more) can be selected on the basis of its utility. This requires abandoning a principle (termed unicity), central to classical physics, that at any instant of time there is only a single correct description of the world.
Bojowald, Martin
2015-02-01
In quantum cosmology, one applies quantum physics to the whole universe. While no unique version and no completely well-defined theory is available yet, the framework gives rise to interesting conceptual, mathematical and physical questions. This review presents quantum cosmology in a new picture that tries to incorporate the importance of inhomogeneity. De-emphasizing the traditional minisuperspace view, the dynamics is rather formulated in terms of the interplay of many interacting 'microscopic' degrees of freedom that describe the space-time geometry. There is thus a close relationship with more-established systems in condensed-matter and particle physics even while the large set of space-time symmetries (general covariance) requires some adaptations and new developments. These extensions of standard methods are needed both at the fundamental level and at the stage of evaluating the theory by effective descriptions. PMID:25582917
Quantum dots: Rethinking the electronics
NASA Astrophysics Data System (ADS)
Bishnoi, Dimple
2016-05-01
In this paper, we demonstrate theoretically that the Quantum dots are quite interesting for the electronics industry. Semiconductor quantum dots (QDs) are nanometer-scale crystals, which have unique photo physical, quantum electrical properties, size-dependent optical properties, There small size means that electrons do not have to travel as far as with larger particles, thus electronic devices can operate faster. Cheaper than modern commercial solar cells while making use of a wider variety of photon energies, including "waste heat" from the sun's energy. Quantum dots can be used in tandem cells, which are multi junction photovoltaic cells or in the intermediate band setup. PbSe (lead selenide) is commonly used in quantum dot solar cells.
Optical Fiber Sensing Using Quantum Dots
Jorge, Pedro; Martins, Manuel António; Trindade, Tito; Santos, José Luís; Farahi, Faramarz
2007-01-01
Recent advances in the application of semiconductor nanocrystals, or quantum dots, as biochemical sensors are reviewed. Quantum dots have unique optical properties that make them promising alternatives to traditional dyes in many luminescence based bioanalytical techniques. An overview of the more relevant progresses in the application of quantum dots as biochemical probes is addressed. Special focus will be given to configurations where the sensing dots are incorporated in solid membranes and immobilized in optical fibers or planar waveguide platforms.