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Sample records for quantum unique ergodicity

  1. Ergodicity and mixing in quantum dynamics

    NASA Astrophysics Data System (ADS)

    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.

  2. Quantum ergodicity on graphs.

    PubMed

    Gnutzmann, S; Keating, J P; Piotet, F

    2008-12-31

    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 sigma 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.

  3. Quantum Ergodicity on Graphs

    SciTech Connect

    Gnutzmann, S.; Keating, J. P.; Piotet, F.

    2008-12-31

    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 {sigma} 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.

  4. 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.

  5. Quantum Ergodicity on Regular Graphs

    NASA Astrophysics Data System (ADS)

    Anantharaman, Nalini

    2017-07-01

    We give three different proofs of the main result of Anantharaman and Le Masson (Duke Math J 164(4):723-765, 2015), establishing quantum ergodicity—a form of delocalization—for eigenfunctions of the laplacian on large regular graphs of fixed degree. These three proofs are much shorter than the original one, quite different from one another, and we feel that each of the four proofs sheds a different light on the problem. The goal of this exploration is to find a proof that could be adapted for other models of interest in mathematical physics, such as the Anderson model on large regular graphs, regular graphs with weighted edges, or possibly certain models of non-regular graphs. A source of optimism in this direction is that we are able to extend the last proof to the case of anisotropic random walks on large regular graphs.

  6. Quantum mechanical models with strictly ergodic disorder

    NASA Astrophysics Data System (ADS)

    Mavi, Rajinder

    We study quantum Hamiltonians with potentials defined by strictly ergodic dynamical systems. Our interest here are models where physical properties are understood in some regimes of disorder and the extent to which they vary in alternate regimes of disorder. For Schrodinger operators we show properties known to hold in the case of analytic potentials on the torus hold even for rough potentials only required to be Holder continuous. Specifically in this case we show, assuming a positive Lyapunov exponent, dynamical localization properties hold; as well as continuity of the measure of the spectrum for all rotations. For the quantum Ising model we show for phase structure that occur in the random regime, there are similar conditions for existence under the assumption of strictly ergodic dynamics. That is, moment conditions for random disorder are paralleled by conditions on the sampling functions in deterministic disorder. We obtain conditions for existence of phase transitions given any strictly egodically defined disorder. In addition, a new multiscale analysis method is developed to show the existence of stretched exponential decay in the random cluster model generalization of the quantum Ising model where only slower decay was obainable by previous methods.

  7. Ergodicity in randomly perturbed quantum systems

    NASA Astrophysics Data System (ADS)

    Gherardini, Stefano; Lovecchio, Cosimo; Müller, Matthias M.; Lombardi, Pietro; Caruso, Filippo; Saverio Cataliotti, Francesco

    2017-03-01

    The theoretical cornerstone of statistical mechanics is the ergodic assumption, i.e. the assumption that the time average of an observable equals its ensemble average. Here, we show how such a property is present when an open quantum system is continuously perturbed by an external environment effectively observing the system at random times while the system dynamics approaches the quantum Zeno regime. In this context, by large deviation theory we analytically show how the most probable value of the probability for the system to be in a given state eventually deviates from the non-stochastic case when the Zeno condition is not satisfied. We experimentally test our results with ultra-cold atoms prepared on an atom chip.

  8. Ergodic dynamics and thermalization in an isolated quantum system

    NASA Astrophysics Data System (ADS)

    Neill, C.; Roushan, P.; Fang, M.; Chen, Y.; Kolodrubetz, M.; Chen, Z.; Megrant, A.; Barends, R.; Campbell, B.; Chiaro, B.; Dunsworth, A.; Jeffrey, E.; Kelly, J.; Mutus, J.; O'Malley, P. J. J.; Quintana, C.; Sank, D.; Vainsencher, A.; Wenner, J.; White, T. C.; Polkovnikov, A.; Martinis, J. M.

    2016-11-01

    Statistical mechanics is founded on the assumption that all accessible configurations of a system are equally likely. This requires dynamics that explore all states over time, known as ergodic dynamics. In isolated quantum systems, however, the occurrence of ergodic behaviour has remained an outstanding question. Here, we demonstrate ergodic dynamics in a small quantum system consisting of only three superconducting qubits. The qubits undergo a sequence of rotations and interactions and we measure the evolution of the density matrix. Maps of the entanglement entropy show that the full system can act like a reservoir for individual qubits, increasing their entropy through entanglement. Surprisingly, these maps bear a strong resemblance to the phase space dynamics in the classical limit; classically, chaotic motion coincides with higher entanglement entropy. We further show that in regions of high entropy the full multi-qubit system undergoes ergodic dynamics. Our work illustrates how controllable quantum systems can investigate fundamental questions in non-equilibrium thermodynamics.

  9. Quantum Uniqueness

    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.

  10. A simple condition for uniqueness of the absolutely continuous ergodic measure and its application to economic models

    NASA Astrophysics Data System (ADS)

    Sato, Kenji; Yano, Makoto

    2012-09-01

    Unique existence of the absolutely continuous ergodic measure, or existence of ergodic chaos (in a strong sense), has been considered important in economics since it explains the mechanism underlying economic fluctuations. In the present study, a simple sufficient condition for ergodic chaos is proved and applied to economic models.

  11. Quantum ergodicity of random orthonormal bases of spaces of high dimension

    PubMed Central

    Zelditch, Steve

    2014-01-01

    We consider a sequence of finite-dimensional Hilbert spaces of dimensions . Motivating examples are eigenspaces, or spaces of quasi-modes, for a Laplace or Schrödinger operator on a compact Riemannian manifold. The set of Hermitian orthonormal bases of may be identified with U(dN), and a random orthonormal basis of is a choice of a random sequence UN∈U(dN) from the product of normalized Haar measures. We prove that if and if tends to a unique limit state ω(A), then almost surely an orthonormal basis is quantum ergodic with limit state ω(A). This generalizes an earlier result of the author in the case where is the space of spherical harmonics on S2. In particular, it holds on the flat torus if d≥5 and shows that a highly localized orthonormal basis can be synthesized from quantum ergodic ones and vice versa in relatively small dimensions. PMID:24344341

  12. Quantum ergodicity breaking in semi-classical electron transfer dynamics.

    PubMed

    Goychuk, Igor

    2017-01-25

    Can the statistical properties of single-electron transfer events be correctly predicted within a common equilibrium ensemble description? This fundamental in nanoworld question of ergodic behavior is scrutinized within a very basic semi-classical curve-crossing problem. It is shown that in the limit of non-adiabatic electron transfer (weak tunneling) well-described by the Marcus-Levich-Dogonadze (MLD) rate the answer is yes. However, in the limit of the so-called solvent-controlled adiabatic electron transfer, a profound breaking of ergodicity occurs. Namely, a common description based on the ensemble reduced density matrix with an initial equilibrium distribution of the reaction coordinate is not able to reproduce the statistics of single-trajectory events in this seemingly classical regime. For sufficiently large activation barriers, the ensemble survival probability in a state remains nearly exponential with the inverse rate given by the sum of the adiabatic curve crossing (Kramers) time and the inverse MLD rate. In contrast, near to the adiabatic regime, the single-electron survival probability is clearly non-exponential, even though it possesses an exponential tail which agrees well with the ensemble description. Initially, it is well described by a Mittag-Leffler distribution with a fractional rate. Paradoxically, the mean transfer time in this classical on the ensemble level regime is well described by the inverse of the nonadiabatic quantum tunneling rate on a single particle level. An analytical theory is developed which perfectly agrees with stochastic simulations and explains our findings.

  13. Periodically driven ergodic and many-body localized quantum systems

    SciTech Connect

    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.

  14. On Unique Ergodicity in Nonlinear Stochastic Partial Differential Equations

    NASA Astrophysics Data System (ADS)

    Glatt-Holtz, Nathan; Mattingly, Jonathan C.; Richards, Geordie

    2017-02-01

    We illustrate how the notion of asymptotic coupling provides a flexible and intuitive framework for proving the uniqueness of invariant measures for a variety of stochastic partial differential equations whose deterministic counterpart possesses a finite number of determining modes. Examples exhibiting parabolic and hyperbolic structure are studied in detail. In the later situation we also present a simple framework for establishing the existence of invariant measures when the usual approach relying on the Krylov-Bogolyubov procedure and compactness fails.

  15. Towards a definition of the Quantum Ergodic Hierarchy: Kolmogorov and Bernoulli systems

    NASA Astrophysics Data System (ADS)

    Gomez, Ignacio; Castagnino, Mario

    2014-01-01

    In this paper we translate the two higher levels of the Ergodic Hierarchy [11], the Kolmogorov level and the Bernoulli level, to quantum language. Moreover, this paper can be considered as the second part of [3]. As in [3], we consider the formalism where the states are positive functionals on the algebra of observables and we use the properties of the Wigner transform [12]. We illustrate the physical relevance of the Quantum Ergodic Hierarchy with two emblematic examples of the literature: the Casati-Prosen model [13,14] and the kicked rotator [6-8].

  16. Total correlations of the diagonal ensemble as a generic indicator for ergodicity breaking in quantum systems

    NASA Astrophysics Data System (ADS)

    Pietracaprina, F.; Gogolin, C.; Goold, J.

    2017-03-01

    The diagonal ensemble is the infinite time average of a quantum state following unitary dynamics in systems without degeneracies. In analogy to the time average of a classical phase-space dynamics, it is intimately related to the ergodic properties of the quantum system giving information on the spreading of the initial state in the eigenstates of the Hamiltonian. In this work we apply a concept from quantum information, known as total correlations, to the diagonal ensemble. Forming an upper bound on the multipartite entanglement, it quantifies the combination of both classical and quantum correlations in a mixed state. We generalize the total correlations of the diagonal ensemble to more general α -Renyi entropies and focus on the cases α =1 and α =2 with further numerical extensions in mind. Here we show that the total correlations of the diagonal ensemble is a generic indicator of ergodicity breaking, displaying a subextensive behavior when the system is ergodic. We demonstrate this by investigating its scaling in a range of spin chain models focusing not only on the cases of integrability breaking but also emphasize its role in understanding the transition from an ergodic to a many-body localized phase in systems with disorder or quasiperiodicity.

  17. Classical ergodicity and quantum eigenstate thermalization: Analysis in fully connected Ising ferromagnets

    NASA Astrophysics Data System (ADS)

    Mori, Takashi

    2017-07-01

    We investigate the relation between the classical ergodicity and the quantum eigenstate thermalization in the fully connected Ising ferromagnets. In the case of spin-1/2, an expectation value of an observable in a single-energy eigenstate coincides with the long-time average in the underlying classical dynamics, which is a consequence of the Wentzel-Kramers-Brillouin approximation. In the case of spin-1, the underlying classical dynamics is not necessarily ergodic. In that case, it turns out that, in the thermodynamic limit, the statistics of the expectation values of an observable in the energy eigenstates coincides with the statistics of the long-time averages in the underlying classical dynamics starting from random initial states sampled uniformly from the classical phase space. This feature seems to be a general property in semiclassical systems, and the result presented here is crucial in discussing equilibration, thermalization, and dynamical transitions of such systems.

  18. Stochastic functional differential equations with infinite delay: Existence and uniqueness of solutions, solution maps, Markov properties, and ergodicity

    NASA Astrophysics Data System (ADS)

    Wu, Fuke; Yin, George; Mei, Hongwei

    2017-02-01

    This work is devoted to stochastic functional differential equations (SFDEs) with infinite delay. First, existence and uniqueness of the solutions of such equations are examined. Because the solutions of the delay equations are not Markov, a viable alternative for studying further asymptotic properties is to use solution maps or segment processes. By examining solution maps, this work investigates the Markov properties as well as the strong Markov properties. Also obtained are adaptivity and continuity, mean-square boundedness, and convergence of solution maps from different initial data. This paper then examines the ergodicity of underlying processes and establishes existence of the invariant measure for SFDEs with infinite delay under suitable conditions.

  19. Dynamical control of quantum systems in the context of mean ergodic theorems

    NASA Astrophysics Data System (ADS)

    Bernád, J. Z.

    2017-02-01

    Equidistant and non-equidistant single pulse ‘bang-bang’ dynamical controls are investigated in the context of mean ergodic theorems. We show the requirements in which the limit of infinite pulse control for both the equidistant and the non-equidistant dynamical control converges to the same unitary evolution. It is demonstrated that the generator of this evolution can be obtained by projecting the generator of the free evolution onto the commutant of the unitary operator representing the pulse. Inequalities are derived to prove this statement and in the case of non-equidistant approach these inequalities are optimised as a function of the time intervals.

  20. Slowly changing potential problems in Quantum Mechanics: Adiabatic theorems, ergodic theorems, and scattering

    SciTech Connect

    Fishman, S.; Soffer, A.

    2016-07-15

    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.

  1. Quantum Catastrophes and Ergodicity in the Dynamics of Bosonic Josephson Junctions

    NASA Astrophysics Data System (ADS)

    O'Dell, D. H. J.

    2012-10-01

    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?

  2. Quantum catastrophes and ergodicity in the dynamics of bosonic Josephson junctions

    NASA Astrophysics Data System (ADS)

    O'Dell, Duncan

    2013-05-01

    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: are there circumstances when it is necessary to second-quantize wave theory in order to avoid singularities? NSERC

  3. 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.

  4. Using Quantum Confinement to Uniquely Identify Devices

    PubMed Central

    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

  5. Emergent kinetic constraints, ergodicity breaking, and cooperative dynamics in noisy quantum systems

    NASA Astrophysics Data System (ADS)

    Everest, B.; Marcuzzi, M.; Garrahan, J. P.; Lesanovsky, I.

    2016-11-01

    Kinetically constrained spin systems play an important role in understanding key properties of the dynamics of slowly relaxing materials, such as glasses. Recent experimental studies have revealed that manifest kinetic constraints govern the evolution of strongly interacting gases of highly excited atoms in a noisy environment. Motivated by this development we explore which types of kinetically constrained dynamics can generally emerge in quantum spin systems subject to strong noise and show how, in this framework, constraints are accompanied by conservation laws. We discuss an experimentally realizable case of a lattice gas, where the interplay between those and the geometry of the lattice leads to collective behavior and time-scale separation even at infinite temperature. This is in contrast to models of glass-forming substances which typically rely on low temperatures and the consequent suppression of thermal activation.

  6. Emergent kinetic constraints, ergodicity breaking, and cooperative dynamics in noisy quantum systems.

    PubMed

    Everest, B; Marcuzzi, M; Garrahan, J P; Lesanovsky, I

    2016-11-01

    Kinetically constrained spin systems play an important role in understanding key properties of the dynamics of slowly relaxing materials, such as glasses. Recent experimental studies have revealed that manifest kinetic constraints govern the evolution of strongly interacting gases of highly excited atoms in a noisy environment. Motivated by this development we explore which types of kinetically constrained dynamics can generally emerge in quantum spin systems subject to strong noise and show how, in this framework, constraints are accompanied by conservation laws. We discuss an experimentally realizable case of a lattice gas, where the interplay between those and the geometry of the lattice leads to collective behavior and time-scale separation even at infinite temperature. This is in contrast to models of glass-forming substances which typically rely on low temperatures and the consequent suppression of thermal activation.

  7. Uniqueness of measures in loop quantum cosmology

    SciTech Connect

    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.

  8. Ergodic theorem, ergodic theory, and statistical mechanics

    PubMed Central

    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

  9. Duality Theorems in Ergodic Transport

    NASA Astrophysics Data System (ADS)

    Lopes, Artur O.; Mengue, Jairo K.

    2012-11-01

    We analyze several problems of Optimal Transport Theory in the setting of Ergodic Theory. In a certain class of problems we consider questions in Ergodic Transport which are generalizations of the ones in Ergodic Optimization. Another class of problems is the following: suppose σ is the shift acting on Bernoulli space X={1,2,…, d}ℕ, and, consider a fixed continuous cost function c: X× X→ℝ. Denote by Π the set of all Borel probabilities π on X× X, such that, both its x and y marginals are σ-invariant probabilities. We are interested in the optimal plan π which minimizes ∫ c dπ among the probabilities in Π. We show, among other things, the analogous Kantorovich Duality Theorem. We also analyze uniqueness of the optimal plan under generic assumptions on c. We investigate the existence of a dual pair of Lipschitz functions which realizes the present dual Kantorovich problem under the assumption that the cost is Lipschitz continuous. For continuous costs c the corresponding results in the Classical Transport Theory and in Ergodic Transport Theory can be, eventually, different. We also consider the problem of approximating the optimal plan π by convex combinations of plans such that the support projects in periodic orbits.

  10. Continuously broken ergodicity.

    PubMed

    Mauro, John C; Gupta, Prabhat K; Loucks, Roger J

    2007-05-14

    A system that is initially ergodic can become nonergodic, i.e., display "broken ergodicity," if the relaxation time scale of the system becomes longer than the observation time over which properties are measured. The phenomenon of broken ergodicity is of vital importance to the study of many condensed matter systems. While previous modeling efforts have focused on systems with a sudden, discontinuous loss of ergodicity, they cannot be applied to study a gradual transition between ergodic and nonergodic behavior. This transition range, where the observation time scale is comparable to that of the structural relaxation process, is especially pertinent for the study of glass transition range behavior, as ergodicity breaking is an inherently continuous process for normal laboratory glass formation. In this paper, we present a general statistical mechanical framework for modeling systems with continuously broken ergodicity. Our approach enables the direct computation of entropy loss upon ergodicity breaking, accounting for actual transition rates between microstates and observation over a specified time interval. In contrast to previous modeling efforts for discontinuously broken ergodicity, we make no assumptions about phase space partitioning or confinement. We present a hierarchical master equation technique for implementing our approach and apply it to two simple one-dimensional landscapes. Finally, we demonstrate the compliance of our approach with the second and third laws of thermodynamics.

  11. The equivalence principle of quantum mechanics: Uniqueness theorem

    SciTech Connect

    Faraggi, A.E.; Matone, M.

    1997-10-28

    Recently the authors showed that the postulated diffeomorphic equivalence of states implies quantum mechanics. This approach takes the canonical variables to be dependent by the relation p = {partial_derivative}{sub q}S{sub 0} and exploits a basic GL(2,C)-symmetry which underlies the canonical formalism. In particular, they looked for the special transformations leading to the free system with vanishing energy. Furthermore, they saw that while on the one hand the equivalence principle cannot be consistently implemented in classical mechanics, on the other it naturally led to the quantum analogue of the Hamilton-Jacobi equation, thus implying the Schroedinger equation. In this letter they show that actually the principle uniquely leads to this solution. The authors also express the canonical and Schroedinger equations by means of the brackets recently introduced in the framework of N = 2 SYM. These brackets are the analogue of the Poisson brackets with the canonical variables taken as dependent.

  12. True Limits to Precision via Unique Quantum Probe

    NASA Astrophysics Data System (ADS)

    Durkin, Gabriel

    2014-05-01

    Quantum instruments derived from composite systems allow greater measurement precision than their classical counterparts due to coherences maintained between N components; spins, atoms or photons. Decoherence that plagues real-world devices can be particle loss, or thermal excitation and relaxation, or dephasing due to external noise sources (and also due to prior parameter uncertainty). All these adversely affect precision estimation of time, phase or frequency. We develop a novel technique uncovering the uniquely optimal probe states of the N ``qubits'' alongside new tight bounds on precision under local and collective mechanisms of these noise types above. For large quantum ensembles where numerical techniques fail, the problem reduces by analogy to finding the ground state of a 1-D particle in a potential well; the shape of the well is dictated by the type and strength of decoherence. The formalism is applied to prototypical Mach-Zehnder and Ramsey interferometers to discover the ultimate performance of real-world instruments.

  13. Proof of the ergodic theorem and the H-theorem in quantum mechanics. Translation of: Beweis des Ergodensatzes und des H-Theorems in der neuen Mechanik

    NASA Astrophysics Data System (ADS)

    von Neumann, J.

    2010-11-01

    It is shown how to resolve the apparent contradiction between the macroscopic approach of phase space and the validity of the uncertainty relations. The main notions of statistical mechanics are re-interpreted in a quantum-mechanical way, the ergodic theorem and the H-theorem are formulated and proven (without “assumptions of disorder”), followed by a discussion of the physical meaning of the mathematical conditions characterizing their domain of validity. The German original was published in Zeitschrift für Physik 57, 30-70 (1929) [paper received on May 10th, 1929] and is available as electronic supplementary material at www.epj.org. Translated by Roderich Tumulka, Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019, USA; e-mail: tumulka@math.rutgers.edu. Additions in the text by the translator are put in square brackets. Footnotes are also footnotes in the original unless otherwise marked. Footnotes in the original containing only citations have been moved to the main text. In the original, equations and references are not numbered. The notation agrees essentially with the original, with the following exceptions: h/2π has been replaced with ħ; the notation [a,b] for intervals has been introduced to simplify some sentences. In a few cases, misprints and other mistakes in formulas have been identified by the translator, corrected in the text, and mentioned in a footnote. The translator is grateful to Wolf Beiglböck for suggesting improvements and librarian Mei Ling Lo of Rutgers University for help with the bibliography.

  14. Uniqueness of the equation for quantum state vector collapse.

    PubMed

    Bassi, Angelo; Dürr, Detlef; Hinrichs, Günter

    2013-11-22

    The linearity of quantum mechanics leads, under the assumption that the wave function offers a complete description of reality, to grotesque situations famously known as Schrödinger's cat. Ways out are either adding elements of reality or replacing the linear evolution by a nonlinear one. Models of spontaneous wave function collapses took the latter path. The way such models are constructed leaves the question of whether such models are in some sense unique, i.e., whether the nonlinear equations replacing Schrödinger's equation are uniquely determined as collapse equations. Various people worked on identifying the class of nonlinear modifications of the Schrödinger equation, compatible with general physical requirements. Here we identify the most general class of continuous wave function evolutions under the assumption of no-faster-than-light signaling.

  15. Conditions for uniqueness of product representations for separable quantum channels and separable quantum states

    NASA Astrophysics Data System (ADS)

    Cohen, Scott M.

    2014-06-01

    We give a sufficient condition that an operator sum representation of a separable quantum channel in terms of product operators is the unique product representation for that channel, and then provide examples of such channels for any number of parties. This result has implications for efforts to determine whether or not a given separable channel can be exactly implemented by local operations and classical communication. By the Choi-Jamiolkowski isomorphism, it also translates to a condition for the uniqueness of product state ensembles representing a given quantum state. These ideas follow from considerations concerning whether or not a subspace spanned by a given set of product operators contains at least one additional product operator.

  16. Ergodicity in randomly forced Rayleigh-Bénard convection

    NASA Astrophysics Data System (ADS)

    Földes, J.; Glatt-Holtz, N. E.; Richards, G.; Whitehead, J. P.

    2016-11-01

    We consider the Boussinesq approximation for Rayleigh-Bénard convection perturbed by an additive noise and with boundary conditions corresponding to heating from below. In two space dimensions, with sufficient stochastic forcing in the temperature component and large Prandtl number Pr  >  0, we establish the existence of a unique ergodic invariant measure. In three space dimensions, we prove the existence of a statistically invariant state, and establish unique ergodicity for the infinite Prandtl Boussinesq system. Throughout this work we provide streamlined proofs of unique ergodicity which invoke an asymptotic coupling argument, a delicate usage of the maximum principle, and exponential martingale inequalities. Lastly, we show that the background method of Constantin and Doering (1996 Nonlinearity 9 1049-60) can be applied in our stochastic setting, and prove bounds on the Nusselt number relative to the unique invariant measure.

  17. Stationary and dynamical scattering problems and ergodic-type theorems

    NASA Astrophysics Data System (ADS)

    Sakhnovich, Lev

    2017-09-01

    We prove that for the radial Schrödinger equation with Coulomb-type potential the generalized dynamical scattering operator coincides with the corresponding generalized stationary scattering operator. This fact is a quantum mechanical analogue of the ergodic results in classical mechanics.

  18. The Liouville equation for singular ergodic magnetic Schroedinger operators

    SciTech Connect

    Kang Yang; Klein, Abel

    2010-03-15

    We study the time evolution of a density matrix in a quantum mechanical system described by an ergodic magnetic Schroedinger operator with singular magnetic and electric potentials, the electric field being introduced adiabatically. We construct a unitary propagator that solves weakly the corresponding time-dependent Schroedinger equation and solve a Liouville equation in an appropriate Hilbert space.

  19. The unique world of the Everett version of quantum theory

    NASA Astrophysics Data System (ADS)

    Squires, Euan J.

    1988-03-01

    We ask whether the basic Everett assumption, that there are no changes of the wavefunction other than those given by the Schrödinger equation, is compatible with experience. We conclude that it is, provided we allow the world of observation to be partially a creation of consciousness. The model suggests the possible existence of quantum paranormal effects.

  20. 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.

  1. On the unique mapping relationship between initial and final quantum states

    SciTech Connect

    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.

  2. Geometric perspective on singularity resolution and uniqueness in loop quantum cosmology

    NASA Astrophysics Data System (ADS)

    Corichi, Alejandro; Singh, Parampreet

    2009-08-01

    We reexamine the issue of singularity resolution in homogeneous loop quantum cosmology from the perspective of geometrical entities such as expansion rate and the shear scalar. These quantities are very reliable measures of the properties of spacetime and can be defined not only at the classical and effective level, but also at an operator level in the quantum theory. From their behavior in the effective constraint surface and in the effective loop quantum spacetime, we show that one can severely restrict the ambiguities in regularization of the quantum constraint and rule out unphysical choices. We analyze this in the flat isotropic model and the Bianchi-I spacetimes. In the former case we show that the expansion rate is absolutely bounded only for the so-called improved quantization, a result which synergizes with uniqueness of this quantization as proved earlier. Surprisingly, for the Bianchi-I spacetime, we show that out of the available choices, the expansion rate and shear are bounded for only one regularization of the quantum constraint. It turns out that only for this choice, the theory exhibits quantum gravity corrections at a unique scale, and is physically viable.

  3. Geometric perspective on singularity resolution and uniqueness in loop quantum cosmology

    SciTech Connect

    Corichi, Alejandro; Singh, Parampreet

    2009-08-15

    We reexamine the issue of singularity resolution in homogeneous loop quantum cosmology from the perspective of geometrical entities such as expansion rate and the shear scalar. These quantities are very reliable measures of the properties of spacetime and can be defined not only at the classical and effective level, but also at an operator level in the quantum theory. From their behavior in the effective constraint surface and in the effective loop quantum spacetime, we show that one can severely restrict the ambiguities in regularization of the quantum constraint and rule out unphysical choices. We analyze this in the flat isotropic model and the Bianchi-I spacetimes. In the former case we show that the expansion rate is absolutely bounded only for the so-called improved quantization, a result which synergizes with uniqueness of this quantization as proved earlier. Surprisingly, for the Bianchi-I spacetime, we show that out of the available choices, the expansion rate and shear are bounded for only one regularization of the quantum constraint. It turns out that only for this choice, the theory exhibits quantum gravity corrections at a unique scale, and is physically viable.

  4. Dynamics and ergodicity of the infinite harmonic crystal

    NASA Astrophysics Data System (ADS)

    van Hemmen, J. L.

    1980-10-01

    This is a comprehensive, relatively formal study of the a priori infinite harmonic crystal. A phase space is introduced and the equations of motion of a harmonic crystal, which need not be a primitive one, are explicitly solved by several methods. The crystal is taken infinite right at the beginni ng. Exploiting the fact that the dynamics is known we derive the thermal equilibrium state of the infinite system. In so doing we use the classical Kubo-Martin-Schwinger (KMS) condition. The thermal equilibrium state is a, so-called, gaussian measure on the phase space. The traditional procedure of the thermodynamic limit is considered as well. In both cases we exploit the advantages of the technique of Fourier transforms of measures. This technique is elucidated in a separate section, where the many connections with Euclidean quantum field theory are also indicated. Finally we settle the problem of the existence of a crystalline state in its appropriate setting: the infinite system. The system is a “crystal” only if it is three-dimensional. The three essential ingredients of the ergodic analysis are a phase space, a dynamics, and an invariant state, here the thermal equilibrium state. A system is ergodic when the time average of any observable equals its phase average. There are, however, stronger notions of ergodicity which are classified in an “ergodic hierarchy”. When a system is Bernoulli it is at the top of this hierarchy. A finite harmonic system is never ergodic. Here it is shown that, generally speaking, a perfect, infinite harmonic crystal in thermal equilibrium has to be Bernoulli. A detailed discussion of the physical relevance of this result has been included.

  5. ergodicity and chaos in geomorphology

    NASA Astrophysics Data System (ADS)

    Aadel, S.; Gaiumi, M.

    2009-04-01

    The past three dicades can be considered as a period in which the fundamentals of scientific epistemology have been subjected to drastic revision.The dissemination of the general theory of systems in 1972 , one year after the death of ludwing von Berthalanfi , the proposition of fuzzy logic by Zade, and the foemulation of chaos theory in 1986 by Harison and Biswas allserved to explode the myth that scientific thought was invulnerable. This paper , which has resulted from the theoretical investigation of project based on the paraglicial sediment and glacial evidence on the Zagros-pishkoh to explain the elements of chaos theory and their compatibility with ergodic geomorphology

  6. Ergodic decomposition for measures quasi-invariant under a Borel action of an inductively compact group

    SciTech Connect

    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.

  7. Synthesis and unique photoluminescence properties of nitrogen-rich quantum dots and their applications.

    PubMed

    Chen, Xiuxian; Jin, Qingqing; Wu, Lizhu; Tung, ChenHo; Tang, Xinjing

    2014-11-10

    Nitrogen-rich quantum dots (N-dots) were serendipitously synthesized in methanol or aqueous solution at a reaction temperature as low as 50 °C. These N-dots have a small size (less than 10 nm) and contain a high percentage of the element nitrogen, and are thus a new member of quantum-dot family. These N-dots show unique and distinct photoluminescence properties with an increasing percentage of nitrogen compared to the neighboring carbon dots. The photoluminescence behavior was adjusted from blue to green simply through variation of the reaction temperature. Furthermore, the detailed mechanism of N-dot formation was also proposed with the trapped intermediate. These N-dots have also shown promising applications as fluorescent ink and biocompatible staining in C. elegans. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  8. Unique properties of graphene quantum dots and their applications in photonic/electronic devices

    NASA Astrophysics Data System (ADS)

    Choi, Suk-Ho

    2017-03-01

    In recent years, graphene quantum dots (GQDs) have been recognized as an attractive building block for electronic, photonic, and bio-molecular device applications. This paper reports the current status of studies on the novel properties of GQDs and their hybrids with conventional and low-dimensional materials for device applications. In this review, more emphasis is placed on the structural, electronic, and optical properties of GQDs, and device structures based on the combination of GQDs with various semiconducting/insulating materials such as graphene, silicon dioxide, Si quantum dots, silica nanoparticles, organic materials, and so on. Because of GQDs’ unique properties, their hybrid structures are employed in high-efficiency devices, including photodetectors, solar cells, light-emitting diodes, flash memory, and sensors.

  9. 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.

  10. Ergodicity of the generalized lemon billiards

    SciTech Connect

    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.

  11. 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.

  12. 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

  13. Ergodicity in natural earthquake fault networks

    SciTech Connect

    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

  14. Are atmospheric surface layer flows ergodic?

    NASA Astrophysics Data System (ADS)

    Higgins, Chad W.; Katul, Gabriel G.; Froidevaux, Martin; Simeonov, Valentin; Parlange, Marc B.

    2013-06-01

    The transposition of atmospheric turbulence statistics from the time domain, as conventionally sampled in field experiments, is explained by the so-called ergodic hypothesis. In micrometeorology, this hypothesis assumes that the time average of a measured flow variable represents an ensemble of independent realizations from similar meteorological states and boundary conditions. That is, the averaging duration must be sufficiently long to include a large number of independent realizations of the sampled flow variable so as to represent the ensemble. While the validity of the ergodic hypothesis for turbulence has been confirmed in laboratory experiments, and numerical simulations for idealized conditions, evidence for its validity in the atmospheric surface layer (ASL), especially for nonideal conditions, continues to defy experimental efforts. There is some urgency to make progress on this problem given the proliferation of tall tower scalar concentration networks aimed at constraining climate models yet are impacted by nonideal conditions at the land surface. Recent advancements in water vapor concentration lidar measurements that simultaneously sample spatial and temporal series in the ASL are used to investigate the validity of the ergodic hypothesis for the first time. It is shown that ergodicity is valid in a strict sense above uniform surfaces away from abrupt surface transitions. Surprisingly, ergodicity may be used to infer the ensemble concentration statistics of a composite grass-lake system using only water vapor concentration measurements collected above the sharp transition delineating the lake from the grass surface.

  15. Gapped two-body hamiltonian whose unique ground state is universal for one-way quantum computation.

    PubMed

    Chen, Xie; Zeng, Bei; Gu, Zheng-Cheng; Yoshida, Beni; Chuang, Isaac L

    2009-06-05

    Many-body entangled quantum states studied in condensed matter physics can be primary resources for quantum information, allowing any quantum computation to be realized using measurements alone, on the state. Such a universal state would be remarkably valuable, if only it were thermodynamically stable and experimentally accessible, by virtue of being the unique ground state of a physically reasonable Hamiltonian made of two-body, nearest-neighbor interactions. We introduce such a state, composed of six-state particles on a hexagonal lattice, and describe a general method for analyzing its properties based on its projected entangled pair state representation.

  16. Mixing, ergodicity and slow relaxation phenomena

    NASA Astrophysics Data System (ADS)

    Costa, I. V. L.; Vainstein, M. H.; Lapas, L. C.; Batista, A. A.; Oliveira, F. A.

    2006-11-01

    Investigations on diffusion in systems with memory [I.V.L. Costa, R. Morgado, M.V.B.T. Lima, F.A. Oliveira, Europhys. Lett. 63 (2003) 173] have established a hierarchical connection between mixing, ergodicity, and the fluctuation-dissipation theorem (FDT). This hierarchy means that ergodicity is a necessary condition for the validity of the FDT, and mixing is a necessary condition for ergodicity. In this work, we compare those results with recent investigations using the Lee recurrence relations method [M.H. Lee, Phys. Rev. B 26 (1982) 2547; M.H. Lee, Phys. Rev. Lett. 87 (2001) 250601; M.H. Lee, J. Phys. A: Math. Gen. 39 (2006) 4651]. Lee shows that ergodicity is violated in the dynamics of the electron gas [M.H. Lee, J. Phys. A: Math. Gen. 39 (2006) 4651]. This reinforces both works and implies that the results of [I.V.L. Costa, R. Morgado, M.V.B.T. Lima, F.A. Oliveira, Europhys. Lett. 63 (2003) 173] are more general than the framework in which they were obtained. Some applications to slow relaxation phenomena are discussed.

  17. Ergodicity: How Can It Be Broken?

    NASA Astrophysics Data System (ADS)

    Benettin, Giancarlo; Livi, Roberto; Parisi, Giorgio

    The introduction of the ergodic hypothesis can be traced back to the contributions by Boltzmann to the foundations of Statistical Mechanics. The formulation of this hypothesis was at the origin of a long standing debate between supporters and opponents of the Boltzmann mechanistic formulation of thermodynamics. The great intuition of the Austrian physicist nevertheless inspired the following contributions that aimed at establishing rigorous mathematical basis for ergodicity. The first part of this chapter will be devoted to reconstructing the evolution of the concept of ergodicity, going through the basic contributions by Birkhoff, Khinchin, Kolmogorov, Sinai etc. The second part will be focused on more recent case studies, associated with the phenomenon known as "ergodicity breaking" and its relations with physical systems. In particular, we describe how it can be related to the presence of exceedingly large relaxation time scales that emerge in nonlinear systems (e.g., the Fermi-Pasta-Ulam model and the Discrete Nonlinear Schrödinger Equation) and to the coexistence of more than one equilibrium phase in disordered systems (spins and structural glasses).

  18. Ergodic transitions in continuous-time random walks

    NASA Astrophysics Data System (ADS)

    Saa, Alberto; Venegeroles, Roberto

    2010-09-01

    We consider continuous-time random walk models described by arbitrary sojourn time probability density functions. We find a general expression for the distribution of time-averaged observables for such systems, generalizing some recent results presented in the literature. For the case where sojourn times are identically distributed independent random variables, our results shed some light on the recently proposed transitions between ergodic and weakly nonergodic regimes. On the other hand, for the case of nonidentical trapping time densities over the lattice points, the distribution of time-averaged observables reveals that such systems are typically nonergodic, in agreement with some recent experimental evidences on the statistics of blinking quantum dots. Some explicit examples are considered in detail. Our results are independent of the lattice topology and dimensionality.

  19. 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.

  20. Ergodicity for Nonlinear Stochastic Equations in Variational Formulation

    SciTech Connect

    Barbu, Viorel Da Prato, Giuseppe

    2006-03-15

    This paper is concerned with nonlinear partial differential equations of the calculus of variation (see [13]) perturbed by noise. Well-posedness of the problem was proved by Pardoux in the seventies (see [14]), using monotonicity methods.The aim of the present work is to investigate the asymptotic behaviour of the corresponding transition semigroup P{sub t}. We show existence and, under suitable assumptions, uniqueness of an ergodic invariant measure {nu}. Moreover, we solve the Kolmogorov equation and prove the so-called 'identite du carre du champs'. This will be used to study the Sobolev space W{sup 1,2}(H,{nu}) and to obtain information on the domain of the infinitesimal generator of P{sub t}.

  1. Anomalous Thermalization in Ergodic Systems

    NASA Astrophysics Data System (ADS)

    Luitz, David J.; Bar Lev, Yevgeny

    2016-10-01

    It is commonly believed that quantum isolated systems satisfying the eigenstate thermalization hypothesis (ETH) are diffusive. We show that this assumption is too restrictive since there are systems that are asymptotically in a thermal state yet exhibit anomalous, subdiffusive thermalization. We show that such systems satisfy a modified version of the ETH ansatz and derive a general connection between the scaling of the variance of the off-diagonal matrix elements of local operators, written in the eigenbasis of the Hamiltonian, and the dynamical exponent. We find that for subdiffusively thermalizing systems the variance scales more slowly with system size than expected for diffusive systems. We corroborate our findings by numerically studying the distribution of the coefficients of the eigenfunctions and the off-diagonal matrix elements of local operators of the random field Heisenberg chain, which has anomalous transport in its thermal phase. Surprisingly, this system also has non-Gaussian distributions of the eigenfunctions, thus, directly violating Berry's conjecture.

  2. Anomalous Thermalization in Ergodic Systems.

    PubMed

    Luitz, David J; Bar Lev, Yevgeny

    2016-10-21

    It is commonly believed that quantum isolated systems satisfying the eigenstate thermalization hypothesis (ETH) are diffusive. We show that this assumption is too restrictive since there are systems that are asymptotically in a thermal state yet exhibit anomalous, subdiffusive thermalization. We show that such systems satisfy a modified version of the ETH ansatz and derive a general connection between the scaling of the variance of the off-diagonal matrix elements of local operators, written in the eigenbasis of the Hamiltonian, and the dynamical exponent. We find that for subdiffusively thermalizing systems the variance scales more slowly with system size than expected for diffusive systems. We corroborate our findings by numerically studying the distribution of the coefficients of the eigenfunctions and the off-diagonal matrix elements of local operators of the random field Heisenberg chain, which has anomalous transport in its thermal phase. Surprisingly, this system also has non-Gaussian distributions of the eigenfunctions, thus, directly violating Berry's conjecture.

  3. Ergodicity breaking in geometric Brownian motion.

    PubMed

    Peters, O; Klein, W

    2013-03-08

    Geometric Brownian motion (GBM) is a model for systems as varied as financial instruments and populations. The statistical properties of GBM are complicated by nonergodicity, which can lead to ensemble averages exhibiting exponential growth while any individual trajectory collapses according to its time average. A common tactic for bringing time averages closer to ensemble averages is diversification. In this Letter, we study the effects of diversification using the concept of ergodicity breaking.

  4. Unification of Classical Mechanics and Quantum Mechanics in Unique Conception of Particle Dynamics

    NASA Astrophysics Data System (ADS)

    Rylov, Yuri A.

    2017-08-01

    It is shown that motion of quantum particles and classical particles can be described in the framework of the same formalism. Stochasticity of particle motion depends on the form of the space-time geometry, which is to be described as a physical geometry, i.e. a geometry obtained as a result of deformation of the proper Euclidean geometry. The new method of the particle motion description does not use quantum principles. It admits one to use the structural approach to theory of elementary particles. The structural approach admits one to consider structure and arrangement of elementary particles, that cannot been obtained at conventional approach, using quantum principles.

  5. Are there ergodic limits to evolution? Ergodic exploration of genome space and convergence.

    PubMed

    McLeish, Tom C B

    2015-12-06

    We examine the analogy between evolutionary dynamics and statistical mechanics to include the fundamental question of ergodicity-the representative exploration of the space of possible states (in the case of evolution this is genome space). Several properties of evolutionary dynamics are identified that allow a generalization of the ergodic dynamics, familiar in dynamical systems theory, to evolution. Two classes of evolved biological structure then arise, differentiated by the qualitative duration of their evolutionary time scales. The first class has an ergodicity time scale (the time required for representative genome exploration) longer than available evolutionary time, and has incompletely explored the genotypic and phenotypic space of its possibilities. This case generates no expectation of convergence to an optimal phenotype or possibility of its prediction. The second, more interesting, class exhibits an evolutionary form of ergodicity-essentially all of the structural space within the constraints of slower evolutionary variables have been sampled; the ergodicity time scale for the system evolution is less than the evolutionary time. In this case, some convergence towards similar optima may be expected for equivalent systems in different species where both possess ergodic evolutionary dynamics. When the fitness maximum is set by physical, rather than co-evolved, constraints, it is additionally possible to make predictions of some properties of the evolved structures and systems. We propose four structures that emerge from evolution within genotypes whose fitness is induced from their phenotypes. Together, these result in an exponential speeding up of evolution, when compared with complete exploration of genomic space. We illustrate a possible case of application and a prediction of convergence together with attaining a physical fitness optimum in the case of invertebrate compound eye resolution.

  6. Exponential ergodicity for non-Lipschitz multivalued stochastic differential equations with Lévy jumps

    NASA Astrophysics Data System (ADS)

    Guan, Yue; Wu, Jing

    We study the exponential ergodicity of diffusions generated by a multivalued stochastic differential equation with Lévy jumps when the coefficients are non-Lipschitz continuous by proving that the transition semigroup is strongly Feller and irreducible, and that it admits a unique invariant measure. This is obtained through an L2-convergence result, Girsanov’s theorem, coupling method combined and a stopping argument.

  7. A unique structure for the multiplexer in quantum-dot cellular automata to create a revolution in design of nanostructures

    NASA Astrophysics Data System (ADS)

    Naji Asfestani, Mazaher; Rasouli Heikalabad, Saeed

    2017-05-01

    Quantum-dot cellular automata (QCA) is the advent of technology and suitable replacement for semiconductor transistor technology. In this paper, a unique structure for the 2:1 multiplexer is presented in QCA. The structure of this component is simple, ultra-efficient and very useful to implement the various logical functions. The proposed structure does not follow any Boolean function. It takes advantage of the inherent characteristics of quantum technology to produce the desired output. Based on these principles, we design the new and efficient structures for the 4:1 multiplexer and 8:1 multiplexer in the QCA technology. These structures are designed with QCADesigner simulator and simulation results are examined. Investigation results indicate the amazing performance of proposed structure compared to existing structures in terms of area, complexity, power consumption and latency.

  8. Ergodic theory and visualization. I. Mesochronic plots for visualization of ergodic partition and invariant sets.

    PubMed

    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)].

  9. Ergodic theory and visualization. I. Mesochronic plots for visualization of ergodic partition and invariant sets

    NASA Astrophysics Data System (ADS)

    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)].

  10. Ergodic properties of fractional Langevin motion with spatial correlated noise

    NASA Astrophysics Data System (ADS)

    Duan, H.-G.; Liang, X.-T.

    2012-06-01

    In this paper, using fractional Langevin equation, we investigate the diffusion behavior of particles in the potential with spatial correlated noise (random disorder). Weak ergodicity breaking is revealed by plotting time averaged mean square displacement and ergodicity breaking parameter. The results are consistent with continuous time random walk (CTRW) and also in agreement with the properties of ones obtained with experiments.

  11. Ergodicity and mixing in four-mode spectral models of two-dimensional turbulence

    NASA Astrophysics Data System (ADS)

    Mosher, M. C.

    1984-08-01

    A system of equations derived by truncating a Fourier representation of the two-dimensional Euler equations which uses four frequencies is investigated. The system has been used by Lorenz, for example, to model atmospheric flow. Also, truncated Fourier representations have been used in many analytic and numerical investigations of turbulence. Since the investigations take a statistical mechanics approach, an important question is whether the truncated systems are ergodic or mixing. The following results have been obtained. If the four frequencies of the truncation form a rectangle, then the system has six constants of motion and these define four disjoint tori. On each torus the solutions of the system are either ergodic with respect to a unique invariant measure or they are all periodic. But, the solutions are never mixing. A computer program has been written which gives a representation of the system's trajectory as it moves on one of the four tori.

  12. Generalized continued fractions and ergodic theory

    NASA Astrophysics Data System (ADS)

    Pustyl'nikov, L. D.

    2003-02-01

    In this paper a new theory of generalized continued fractions is constructed and applied to numbers, multidimensional vectors belonging to a real space, and infinite-dimensional vectors with integral coordinates. The theory is based on a concept generalizing the procedure for constructing the classical continued fractions and substantially using ergodic theory. One of the versions of the theory is related to differential equations. In the finite-dimensional case the constructions thus introduced are used to solve problems posed by Weyl in analysis and number theory concerning estimates of trigonometric sums and of the remainder in the distribution law for the fractional parts of the values of a polynomial, and also the problem of characterizing algebraic and transcendental numbers with the use of generalized continued fractions. Infinite-dimensional generalized continued fractions are applied to estimate sums of Legendre symbols and to obtain new results in the classical problem of the distribution of quadratic residues and non-residues modulo a prime. In the course of constructing these continued fractions, an investigation is carried out of the ergodic properties of a class of infinite-dimensional dynamical systems which are also of independent interest.

  13. Momentum estimates and ergodicity for the 3D stochastic cubic Ginzburg-Landau equation with degenerate noise

    NASA Astrophysics Data System (ADS)

    Pu, Xueke; Guo, Boling

    In this paper, we consider the ergodicity of invariant measures for the stochastic Ginzburg-Landau equation with degenerate random forcing. First, we show the existence and pathwise uniqueness of strong solutions with H-initial data, and then the existence of an invariant measure for the Feller semigroup by the Krylov-Bogoliubov method. Then in the case of degenerate additive noise, using the notion of asymptotically strong Feller property, we prove the uniqueness of invariant measures for the transition semigroup.

  14. Non-uniqueness of quantum transition state theory and general dividing surfaces in the path integral space.

    PubMed

    Jang, Seogjoo; Voth, Gregory A

    2017-05-07

    Despite the fact that quantum mechanical principles do not allow the establishment of an exact quantum analogue of the classical transition state theory (TST), the development of a quantum TST (QTST) with a proper dynamical justification, while recovering the TST in the classical limit, has been a long standing theoretical challenge in chemical physics. One of the most recent efforts of this kind was put forth by Hele and Althorpe (HA) [J. Chem. Phys. 138, 084108 (2013)], which can be specified for any cyclically invariant dividing surface defined in the space of the imaginary time path integral. The present work revisits the issue of the non-uniqueness of QTST and provides a detailed theoretical analysis of HA-QTST for a general class of such path integral dividing surfaces. While we confirm that HA-QTST reproduces the result based on the ring polymer molecular dynamics (RPMD) rate theory for dividing surfaces containing only a quadratic form of low frequency Fourier modes, we find that it produces different results for those containing higher frequency imaginary time paths which accommodate greater quantum fluctuations. This result confirms the assessment made in our previous work [Jang and Voth, J. Chem. Phys. 144, 084110 (2016)] that HA-QTST does not provide a derivation of RPMD-TST in general and points to a new ambiguity of HA-QTST with respect to its justification for general cyclically invariant dividing surfaces defined in the space of imaginary time path integrals. Our analysis also offers new insights into similar path integral based QTST approaches.

  15. On the uniqueness of paths for spin-0 and spin-1 quantum mechanics

    NASA Astrophysics Data System (ADS)

    Struyve, W.; De Baere, W.; De Neve, J.; De Weirdt, S.

    2004-02-01

    The uniqueness of the Bohmian particle interpretation of the Kemmer equation, which describes massive spin-0 and spin-1 particles, is discussed. Recently the same problem for spin-(1/2) was dealt with by Holland. It appears that the uniqueness of boson paths can be enforced under well determined conditions. This in turn fixes the nonrelativistic particle equations of the nonrelativistic Schrödinger equation, which appear to correspond with the original definitions given by de Broglie and Bohm only in the spin-0 case. Similar to the spin-(1/2) case, there appears an additional spin-dependent term in the guidance equation in the spin-1 case. We also discuss the ambiguity associated with the introduction of an electromagnetic coupling in the Kemmer theory. We argue that when the minimal coupling is correctly introduced, then the current constructed from the energy-momentum tensor is no longer conserved. Hence this current cannot serve as a particle probability four-vector.

  16. Resonant magnetic perturbations and edge ergodization on the COMPASS tokamak

    SciTech Connect

    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.

  17. 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.

  18. Nature of base stacking: reference quantum-chemical stacking energies in ten unique B-DNA base-pair steps.

    PubMed

    Sponer, Jirí; Jurecka, Petr; Marchan, Ivan; Luque, F Javier; Orozco, Modesto; Hobza, Pavel

    2006-03-20

    Base-stacking energies in ten unique B-DNA base-pair steps and some other arrangements were evaluated by the second-order Møller-Plesset (MP2) method, complete basis set (CBS) extrapolation, and correction for triple (T) electron-correlation contributions. The CBS(T) calculations were compared with decade-old MP2/6-31G*(0.25) reference data and AMBER force field. The new calculations show modest increases in stacking stabilization compared to the MP2/6-31G*(0.25) data and surprisingly large sequence-dependent variation of stacking energies. The absolute force-field values are in better agreement with the new reference data, while relative discrepancies between quantum-chemical (QM) and force-field values increase modestly. Nevertheless, the force field provides good qualitative description of stacking, and there is no need to introduce additional pair-additive electrostatic terms, such as distributed multipoles or out-of-plane charges. There is a rather surprising difference of about 0.1 A between the vertical separation of base pairs predicted by quantum chemistry and derived from crystal structures. Evaluations of different local arrangements of the 5'-CG-3' step indicate a sensitivity of the relative stacking energies to the level of calculation. Thus, describing quantitative relations between local DNA geometrical variations and stacking may be more complicated than usually assumed. The reference calculations are complemented by continuum-solvent assessment of solvent-screening effects.

  19. A statistical evaluation of non-ergodic variogram estimators

    USGS Publications Warehouse

    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.

  20. 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

  1. Stationary distribution and ergodicity of a stochastic food-chain model with Lévy jumps

    NASA Astrophysics Data System (ADS)

    Yu, Jingyi; Liu, Meng

    2017-09-01

    In this paper, a three-species stochastic food-chain model with Lévy jumps is proposed and analyzed. Sharp sufficient criteria for the existence and uniqueness of an ergodic stationary distribution are established. The effects of Lévy jumps on the existence of the stationary distribution are revealed: in some cases, the Lévy jumps could make the stationary distribution appear, while in some cases, the Lévy jumps could make the stationary distribution disappear. Some numerical simulations are introduced to illustrate the theoretical results.

  2. space and time in ergodic gemorphology

    NASA Astrophysics Data System (ADS)

    Seyed Ebrahimi, S.

    2009-04-01

    Epistemological perspectives rank among the main factors contributing to word coinage in scientific literature. New words come into existence as new epistemological fields evolve (Sack1992). Each field, however, tends to impose its own interpretation on the words associated with it. To illustrate the point, certain words retain formal structure and relate to the same subject area, but can nonetheless be employed in totally different epistemological fields. The semantic content undergoes a drastic change in each case. Granted that numerous theoretical stances can be identified within the discipline of geomorphology, acquaintance with the semantic content of certain words should help toward a more realistic understanding of what the theorists and practitioners in this field have in mind. This paper, which is based on an analysis of these three theoretical positions aims to highlight the importance of the semantic content of the term equilibrium as utilized in ergodic geomorphology, and the ways in which it is construed from different viewpoints. For this purpose, the authors have of necessity availed themselves of dated sources, rather than up-to-date ones. The paper also argues that familiarity with concepts such as these will ensure a better grasp of the paradigms in question.

  3. Ergodic properties of linked-twist maps

    NASA Astrophysics Data System (ADS)

    Springham, James

    2008-12-01

    We study a class of homeomorphisms of surfaces collectively known as linked-twist maps. We introduce an abstract definition which enables us to give a precise characterisation of a property observed by other authors, namely that such maps fall into one of two classes termed co- and counter-twisting. We single out three specific linked-twist maps, one each on the two-torus, in the plane and on the two-sphere and for each prove a theorem concerning its ergodic properties with respect to the invariant Lebesgue measure. For the map on the torus we prove that there is an invariant, zero-measure Cantor set on which the dynamics are topologically conjugate to a full shift on the space of symbol sequences. Such features are commonly known as topological horseshoes. For the map in the plane we prove that there is a set of full measure on which the dynamics are measure-theoretically isomorphic to a full shift on the space of symbol sequences. This is commonly known as the Bernoulli property and verifies, under certain conditions, a conjecture of Wojtkowski's. We introduce the map on the sphere and prove that it too has the Bernoulli property. We conclude with some conjectures, drawn from our experience, concerning how one might extend the results we have for specific linked-twist maps to the abstract linked-twist maps we have defined.

  4. Chaotic synchronization of coupled ergodic maps.

    PubMed

    Sterling, D. G.

    2001-03-01

    With few exceptions, studies of chaotic synchronization have focused on dissipative chaos. Though less well known, chaotic systems that lack dissipation may also synchronize. Motivated by an application in communication systems, we couple a family of ergodic maps on the N-torus and study the global stability of the synchronous state. While most trajectories synchronize at some time, there is a measure zero set that never synchronizes. We give explicit examples of these asynchronous orbits in dimensions two and four. On more typical trajectories, the synchronization error reaches arbitrarily small values and, in practice, converges. In dimension two we derive bounds on the average synchronization time for trajectories resulting from randomly chosen initial conditions. Numerical experiments suggest similar bounds exist in higher dimensions as well. Adding noise to the coupling signal destroys the invariance of the synchronous state and causes typical trajectories to desynchronize. We propose a modification of the standard coupling scheme that corrects this problem resulting in robust synchronization in the presence of noise.

  5. Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes

    NASA Astrophysics Data System (ADS)

    Cherstvy, Andrey G.; Chechkin, Aleksei V.; Metzler, Ralf

    2013-08-01

    We demonstrate the non-ergodicity of a simple Markovian stochastic process with space-dependent diffusion coefficient D(x). For power-law forms D(x) ≃ |x|α, this process yields anomalous diffusion of the form ≃ t2/(2-α). Interestingly, in both the sub- and superdiffusive regimes we observe weak ergodicity breaking: the scaling of the time-averaged mean-squared displacement \\overline{\\delta ^2(\\Delta)} remains linear in the lag time Δ and thus differs from the corresponding ensemble average . We analyse the non-ergodic behaviour of this process in terms of the time-averaged mean-squared displacement \\overline {\\delta ^2} and its random features, i.e. the statistical distribution of \\overline {\\delta ^2} and the ergodicity breaking parameters. The heterogeneous diffusion model represents an alternative approach to non-ergodic, anomalous diffusion that might be particularly relevant for diffusion in heterogeneous media.

  6. The permutation entropy rate equals the metric entropy rate for ergodic information sources and ergodic dynamical systems

    NASA Astrophysics Data System (ADS)

    Amigó, José M.; Kennel, Matthew B.; Kocarev, Ljupco

    2005-10-01

    Permutation entropy quantifies the diversity of possible orderings of the values a random or deterministic system can take, as Shannon entropy quantifies the diversity of values. We show that the metric and permutation entropy rates-measures of new disorder per new observed value-are equal for ergodic finite-alphabet information sources (discrete-time stationary stochastic processes). With this result, we then prove that the same holds for deterministic dynamical systems defined by ergodic maps on n-dimensional intervals. This result generalizes a previous one for piecewise monotone interval maps on the real line [C. Bandt, G. Keller, B. Pompe, Entropy of interval maps via permutations, Nonlinearity 15 (2002) 1595-1602.] at the expense of requiring ergodicity and using a definition of permutation entropy rate differing modestly in the order of two limits. The case of non-ergodic finite-alphabet sources is also studied and an inequality developed. Finally, the equality of permutation and metric entropy rates is extended to ergodic non-discrete information sources when entropy is replaced by differential entropy in the usual way.

  7. Weak ergodicity breaking, irreproducibility, and ageing in anomalous diffusion processes

    SciTech Connect

    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.

  8. 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.

  9. Weak ergodicity breaking, irreproducibility, and ageing in anomalous diffusion processes

    NASA Astrophysics Data System (ADS)

    Metzler, Ralf

    2014-01-01

    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.

  10. No-go theorem for ergodicity and an Einstein relation

    NASA Astrophysics Data System (ADS)

    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.

  11. Fractional kinetics emerging from ergodicity breaking in random media

    NASA Astrophysics Data System (ADS)

    Molina-García, Daniel; Pham, Tuan Minh; Paradisi, Paolo; Manzo, Carlo; Pagnini, Gianni

    2016-11-01

    We present a modeling approach for diffusion in a complex medium characterized by a random length scale. The resulting stochastic process shows subdiffusion with a behavior in qualitative agreement with single-particle tracking experiments in living cells, such as ergodicity breaking, p variation, and aging. In particular, this approach recapitulates characteristic features previously described in part by the fractional Brownian motion and in part by the continuous-time random walk. Moreover, for a proper distribution of the length scale, a single parameter controls the ergodic-to-nonergodic transition and, remarkably, also drives the transition of the diffusion equation of the process from nonfractional to fractional, thus demonstrating that fractional kinetics emerges from ergodicity breaking.

  12. Zeno effect and ergodicity in finite-time quantum measurements

    SciTech Connect

    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.

  13. 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

  14. Non-Ergodicity and Ageing in Anomalous Diffusion

    NASA Astrophysics Data System (ADS)

    Metzler, Ralf

    2015-03-01

    Anomalous diffusion, the deviation from classical Brownian motion with its linear-in-time mean squared displacement, is a widespread phenomenon in a large variety of complex systems, ranging from amorphous semiconductors to biological cells. Anomalous diffusion processes are no longer confined by the central limit theorem, that enforces the convergence of Brownian motion to the Gaussian shape of the probability density function. Instead, anomalous processes have a rich variety of physical origins and non-traditional mathematical properties. We here provide a summary of various anomalous diffusion models, paying special attention to their non-ergodic and ageing behaviour. Whether a process is ergodic or not is of vital importance when measurements are evaluated in terms of time averaged observables such as the mean squared displacement. For non-ergodic processes these can no longer be interpreted by comparison to the typically calculated ensemble averaged observables. Breaking of ergodicity occurs in many anomalous diffusion processes. We also consider their ageing properties, the explicit dependence of observables on the time span between the original system initiation and the start of the measurement.

  15. On the Ergodic Behaviour of Atomic Systems Under the Action of the Zero-Point Radiation Field

    NASA Astrophysics Data System (ADS)

    de La Peña, L.; Cetto, A. M.

    2007-09-01

    We study anew the behaviour of an otherwise classical bound particle immersed in a radiation field that includes the zero-point field component of average energy (1/2)ħω per mode. The presence of this field introduces an essential stochasticity into the dynamics of the particle, characterized by Planck's constant ħ this has been the basis for stochastic electrodynamics. Both the near field and the particle are affected substantially by their continuous interaction. Stationary solutions are in principle possible when a balance is achieved between the mean powers emitted and absorbed by the particle. By demanding that the ensuing approximate stationary solutions satisfy an ergodic principle, we are led to a resonant response that is linear in the Fourier amplitudes of the field; this is the essence of linear stochastic electrodynamics. The connection with the matrix formulation of quantum mechanics can be readily made, with the resonance frequencies of the ergodic solutions corresponding to the quantum mechanical transition frequencies. Some implications of these results for the understanding of quantum phenomena are briefly discussed.

  16. 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.

  17. Notions of the ergodic hierarchy for curved statistical manifolds

    NASA Astrophysics Data System (ADS)

    Gomez, Ignacio S.

    2017-10-01

    We present an extension of the ergodic, mixing, and Bernoulli levels of the ergodic hierarchy for statistical models on curved manifolds, making use of elements of the information geometry. This extension focuses on the notion of statistical independence between the microscopical variables of the system. Moreover, we establish an intimately relationship between statistical models and families of probability distributions belonging to the canonical ensemble, which for the case of the quadratic Hamiltonian systems provides a closed form for the correlations between the microvariables in terms of the temperature of the heat bath as a power law. From this, we obtain an information geometric method for studying Hamiltonian dynamics in the canonical ensemble. We illustrate the results with two examples: a pair of interacting harmonic oscillators presenting phase transitions and the 2 × 2 Gaussian ensembles. In both examples the scalar curvature results a global indicator of the dynamics.

  18. Ergodic chaotic parameter modulation with application to digital image watermarking.

    PubMed

    Chen, Siyue; Leung, Henry

    2005-10-01

    This paper presents a novel technique for image watermarking based on chaos theory. Chaotic parameter modulation (CPM) is employed to modulate the copyright information into the bifurcating parameter of a chaotic system. The system output is a wideband signal and is used as a watermark to be inserted into the host image. In the detection, a novel method based on the ergodic property of chaotic signal is developed to demodulate the embedded copyright information. Compared to previous works on blind watermarking, the proposed technique can effectively remove the interference from the host image and, thus, improve the detection performance dramatically. Simulation results show that the ergodic CPM approach is effective for image watermarking in terms of noise performance, robustness against attacks, and payload. In addition, its implementation is very simple and the computation speed is fast. Compared to holographic transform domain method and the conventional spread spectrum watermarking scheme, the proposed technique is shown to be superior.

  19. 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.

  20. Is Dissociation of Peptide Radical Cations an Ergodic Process?

    SciTech Connect

    Laskin, Julia; Futrell, Jean H.; Chu, Ivan K.

    2007-08-08

    Achieving a fundamental understanding of the mechanism of unimolecular dissociation of internally excited complex molecules is one of the most important challenges in modern mass spectrometry. One of the central questions is whether the dissociation of large molecules is properly described by statistical theories—RRKM/QET or Phase Space Theories —that have proved to be remarkably successful both for small molecules and a number of small and medium size peptides. The concept question is whether the ergodic assumption that the internal excitation of the ion is randomly redistributed among the vibrational degrees of freedom prior to fragmentation is satisfied for large molecules. The validity of the ergodic hypothesis for dissociation of gas-phase biomolecules has been recently reviewed and will be only briefly discussed here.

  1. Ergodicity and Energy Distributions for Some Boundary Driven Integrable Hamiltonian Chains

    NASA Astrophysics Data System (ADS)

    Balint, Peter; Lin, Kevin K.; Young, Lai-Sang

    2010-02-01

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

  2. 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.

  3. Ergodic capacity analysis for DF strategies in cooperative FSO systems.

    PubMed

    Boluda-Ruiz, Rubén; García-Zambrana, Antonio; Castillo-Vázquez, Beatriz; Castillo-Vázquez, Carmen

    2015-08-24

    This paper focuses on the ergodic capacity analysis in the context of cooperative free-space optical (FSO) systems when the line of sight is available. Novel asymptotic closed-form expressions for the ergodic capacity corresponding to two different decode-and-forward (DF) strategies are obtained for a cooperative FSO communication system. Here, the atmospheric turbulence is modeled by a gamma-gamma distribution of parameters α and β which allows to study a wide range of turbulence conditions (moderate-to-strong) as well as the effect of the misalignment with zero boresight. It is demonstrated that cooperative communications are able to achieve not only a better performance in terms of the error rate performance as well as outage probability than direct transmission, but also in terms of the channel capacity in the context of FSO systems without much increase in hardware. In this way, a 3-way FSO communication setup is considered, in which the cooperative protocol can be applied to achieve a greater ergodic capacity compared to a direct transmission. It can be concluded that a greater and robust capacity strongly dependent on the relay location is achieved compared to a direct transmission without cooperative communication when line of sight is available. Here, the line of sight is taken into account in order to achieve a significant robustness under different turbulence conditions and more severe pointing errors regardless of the relay location. Simulation results are further demonstrated to confirm the accuracy and usefulness of the derived results.

  4. The ergodicity bias in the observed galaxy distribution

    NASA Astrophysics Data System (ADS)

    Pan, Jun; Zhang, Pengjie

    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.

  5. Ergodic properties of fractional Brownian-Langevin motion.

    PubMed

    Deng, Weihua; Barkai, Eli

    2009-01-01

    We investigate the time average mean-square displacement delta;{2}[over ](x(t))=integral_{0};{t-Delta}[x(t;{'}+Delta)-x(t;{'})];{2}dt;{'}(t-Delta) for fractional Brownian-Langevin motion where x(t) is the stochastic trajectory and Delta is the lag time. Unlike the previously investigated continuous-time random-walk model, delta;{2}[over ] converges to the ensemble average x;{2} approximately t;{2H} in the long measurement time limit. The convergence to ergodic behavior is slow, however, and surprisingly the Hurst exponent H=3/4 marks the critical point of the speed of convergence. When H<3/4 , the ergodicity breaking parameter E_{B}=[[delta;{2}[over ](x(t))];{2}-delta;{2}[over ](x(t));{2}]/delta;{2}[over ](x(t));{2} approximately k(H)Deltat;{-1} , when H=3/4 , E_{B} approximately (9/16)(lnt)Deltat;{-1} , and when 3/41 ergodicity is broken and E_{B} approximately 2 . The critical point H=3/4 is marked by the divergence of the coefficient k(H) . Fractional Brownian motion as a model for recent experiments of subdiffusion of mRNA in the cell is briefly discussed, and a comparison with the continuous-time random-walk model is made.

  6. Weak ergodicity breaking and ageing in anomalous diffusion

    NASA Astrophysics Data System (ADS)

    Metzler, Ralf

    2015-01-01

    Modern single particle tracking techniques and many large scale simulations produce time series r(t) of the position of a tracer particle. Standardly these are evaluated in terms of the time averaged mean squared displacement. For ergodic processes such as Brownian motion, one can interpret the results of such an analysis in terms of the known theories for the corresponding ensemble averaged mean squared displacement, if only the measurement time is sufficiently long. In anomalous diffusion processes, that are widely observed over many orders of magnitude, the equivalence between (long) time and ensemble averages may be broken (weak ergodicity breaking). In such cases the time averages may no longer be interpreted in terms of ensemble theories. Here we collect some recent results on weakly non-ergodic systems with respect to the time averaged mean squared displacement and the inherent irreproducibility of individual measurements. 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.

  7. Ergodic properties of fractional Brownian-Langevin motion

    NASA Astrophysics Data System (ADS)

    Deng, Weihua; Barkai, Eli

    2009-01-01

    We investigate the time average mean-square displacement δ2¯(x(t))=∫0t-Δ[x(t'+Δ)-x(t')]2dt'/(t-Δ) for fractional Brownian-Langevin motion where x(t) is the stochastic trajectory and Δ is the lag time. Unlike the previously investigated continuous-time random-walk model, δ2¯ converges to the ensemble average ⟨x2⟩˜t2H in the long measurement time limit. The convergence to ergodic behavior is slow, however, and surprisingly the Hurst exponent H=(3)/(4) marks the critical point of the speed of convergence. When H<(3)/(4) , the ergodicity breaking parameter EB=[⟨[δ2¯(x(t))]2⟩-⟨δ2¯(x(t))⟩2]/⟨δ2¯(x(t))⟩2˜k(H)Δt-1 , when H=(3)/(4) , EB˜((9)/(16))(lnt)Δt-1 , and when (3)/(4)ergodicity is broken and EB˜2 . The critical point H=(3)/(4) is marked by the divergence of the coefficient k(H) . Fractional Brownian motion as a model for recent experiments of subdiffusion of mRNA in the cell is briefly discussed, and a comparison with the continuous-time random-walk model is made.

  8. The ergodicity bias in the observed galaxy distribution

    SciTech Connect

    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.

  9. Improving hole injection and carrier distribution in InGaN light-emitting diodes by removing the electron blocking layer and including a unique last quantum barrier

    SciTech Connect

    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.

  10. Revisiting optimal eavesdropping in quantum cryptography: Optimal interaction is unique up to rotation of the underlying basis

    NASA Astrophysics Data System (ADS)

    Acharyya, Atanu; Paul, Goutam

    2017-02-01

    A general framework of optimal eavesdropping on BB84 protocol was provided by Fuchs et al. [Phys. Rev. A 56, 1163 (1997), 10.1103/PhysRevA.56.1163]. An upper bound on mutual information was derived, which could be achieved by a specific type of interaction and the corresponding measurement. However, uniqueness of optimal interaction was posed as an unsolved problem there and it has remained open for almost two decades now. In this paper, we solve this open problem and establish the uniqueness of optimal interaction up to rotation. The specific choice of optimal interaction by Fuchs et al. is shown to be a special case of the form derived in our work.

  11. Ergodicity of Truncated Stochastic Navier Stokes with Deterministic Forcing and Dispersion

    NASA Astrophysics Data System (ADS)

    Majda, Andrew J.; Tong, Xin T.

    2016-10-01

    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.

  12. Fractional Feynman-Kac equation for weak ergodicity breaking.

    PubMed

    Carmi, Shai; Barkai, Eli

    2011-12-01

    The continuous-time random walk (CTRW) is a model of anomalous subdiffusion in which particles are immobilized for random times between successive jumps. A power-law distribution of the waiting times, ψ(τ) ~ τ(-(1+α)), leads to subdiffusion (x(2) ~ t(α)) for 0 < α < 1. In closed systems, the long stagnation periods cause time averages to divert from the corresponding ensemble averages, which is a manifestation of weak ergodicity breaking. The time average of a general observable U(t) = 1/t ∫(0)(t) U[x(τ)]dτ is a functional of the path and is described by the well-known Feynman-Kac equation if the motion is Brownian. Here, we derive forward and backward fractional Feynman-Kac equations for functionals of CTRW in a binding potential. We use our equations to study two specific time averages: the fraction of time spent by a particle in half-box, and the time average of the particle's position in a harmonic field. In both cases, we obtain the probability density function of the time averages for t → ∞ and the first two moments. Our results show that both the occupation fraction and the time-averaged position are random variables even for long times, except for α = 1, when they are identical to their ensemble averages. Using our fractional Feynman-Kac equation, we also study the dynamics leading to weak ergodicity breaking, namely the convergence of the fluctuations to their asymptotic values.

  13. Inhomogeneous diffusion and ergodicity breaking induced by global memory effects

    NASA Astrophysics Data System (ADS)

    Budini, Adrián A.

    2016-11-01

    We introduce a class of discrete random-walk model driven by global memory effects. At any time, the right-left transitions depend on the whole previous history of the walker, being defined by an urnlike memory mechanism. The characteristic function is calculated in an exact way, which allows us to demonstrate that the ensemble of realizations is ballistic. Asymptotically, each realization is equivalent to that of a biased Markovian diffusion process with transition rates that strongly differs from one trajectory to another. Using this "inhomogeneous diffusion" feature, the ergodic properties of the dynamics are analytically studied through the time-averaged moments. Even in the long-time regime, they remain random objects. While their average over realizations recovers the corresponding ensemble averages, departure between time and ensemble averages is explicitly shown through their probability densities. For the density of the second time-averaged moment, an ergodic limit and the limit of infinite lag times do not commutate. All these effects are induced by the memory effects. A generalized Einstein fluctuation-dissipation relation is also obtained for the time-averaged moments.

  14. 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.

  15. 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.

  16. The structural chemistry of metallocorroles: combined X-ray crystallography and quantum chemistry studies afford unique insights.

    PubMed

    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

  17. 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

  18. Room-Temperature Large and Reversible Modulation of Photoluminescence by in Situ Electric Field in Ergodic Relaxor Ferroelectrics.

    PubMed

    Sun, Hailing; Wu, Xiao; Peng, Deng Feng; Kwok, K W

    2017-10-04

    Ferroelectric oxides with luminescent ions hold great promise in future optoelectronic devices because of their unique photoluminescence and inherent ferroelectric properties. Intriguingly, the photoluminescence performance of ferroelectric ceramics could be modulated by an external electric field. However, researchers face a current challenge of the diminutive extent and degree of reversibility of the field-driven modification that hinder their use in room-temperature practical applications. Within the scope of current contribution in rare-earth-doped bismuth sodium titanate relaxors, the most important information to be noted is the shifting of the depolarization temperature toward room temperature and the resulting considerable enhancement in ergodicity, as evidenced by the dielectric properties, polarization, and strain hysteresis, as well as the in situ Raman/X-ray diffraction studies. After the introduction of 1 mol % Eu, the induced composition and charge disorders disrupt the original long-range ferroelectric macrodomains into randomly dynamic and weakly correlated polar nanoregions, which facilitates a reversible transformation between polar nanoregions and unstable ferroelectric state under an electric field, engendering a large strain. By virtue of this, both the extent and degree of reversibility of photoluminescence modulation are enhanced (∼60%) considerably, and room-temperature in situ tunable photoluminescence response is then achieved under electric field. These should be helpful for the realization of regulating the physical couplings (photoluminescent-ferroelectrics) in multifunctional inorganic ferroelectrics with a high ergodic state by reversibly tuning the structural symmetry.

  19. Percolation approach to glassy dynamics with continuously broken ergodicity.

    PubMed

    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 F(12) 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.

  20. Ergodic Transition in a Simple Model of the Continuous Double Auction

    PubMed Central

    Radivojević, Tijana; Anselmi, Jonatha; Scalas, Enrico

    2014-01-01

    We study a phenomenological model for the continuous double auction, whose aggregate order process is equivalent to two independent queues. The continuous double auction defines a continuous-time random walk for trade prices. The conditions for ergodicity of the auction are derived and, as a consequence, three possible regimes in the behavior of prices and logarithmic returns are observed. In the ergodic regime, prices are unstable and one can observe a heteroskedastic behavior in the logarithmic returns. On the contrary, non-ergodicity triggers stability of prices, even if two different regimes can be seen. PMID:24558377

  1. Asymptotic behaviour of time averages for non-ergodic Gaussian processes

    NASA Astrophysics Data System (ADS)

    Ślęzak, Jakub

    2017-08-01

    In this work, we study the behaviour of time-averages for stationary (non-ageing), but ergodicity-breaking Gaussian processes using their representation in Fourier space. We provide explicit formulae for various time-averaged quantities, such as mean square displacement, density, and analyse the behaviour of time-averaged characteristic function, which gives insight into rich memory structure of the studied processes. Moreover, we show applications of the ergodic criteria in Fourier space, determining the ergodicity of the generalised Langevin equation's solutions.

  2. Identifying ergodicity breaking for fractional anomalous diffusion: Criteria for minimal trajectory length

    NASA Astrophysics Data System (ADS)

    Loch-Olszewska, Hanna; Sikora, Grzegorz; Janczura, Joanna; Weron, Aleksander

    2016-11-01

    In this paper, we study ergodic properties of α -stable autoregressive fractionally integrated moving average (ARFIMA) processes which form a large class of anomalous diffusions. A crucial practical question is how long trajectories one needs to observe in an experiment in order to claim that the analyzed data are ergodic or not. This will be solved by checking the asymptotic convergence to 0 of the empirical estimator F (n ) for the dynamical functional D (n ) defined as a Fourier transform of the n -lag increments of the ARFIMA process. Moreover, we introduce more flexible concept of the ɛ -ergodicity.

  3. 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.

  4. Quantum

    NASA Astrophysics Data System (ADS)

    Elbaz, Edgard

    This book gives a new insight into the interpretation of quantum mechanics (stochastic, integral paths, decoherence), a completely new treatment of angular momentum (graphical spin algebra) and an introduction to Fermion fields (Dirac equation) and Boson fields (e.m. and Higgs) as well as an introduction to QED (quantum electrodynamics), supersymmetry and quantum cosmology.

  5. Upper and lower bounds for the ergodic capacity of MIMO Jacobi fading channels.

    PubMed

    Nafkha, Amor; Bonnefoi, Rémi

    2017-05-29

    In multi-(core/mode) optical fiber communication, the transmission channel can be modeled as a complex sub-matrix of the Haar-distributed unitary matrix (complex Jacobi unitary ensemble). In this letter, we present new analytical expressions of the upper and lower bounds for the ergodic capacity of multiple-input multiple-output Jacobi-fading channels. Recent results on the determinant of the Jacobi unitary ensemble are employed to derive a tight lower bound on the ergodic capacity. We use Jensen's inequality to provide an analytical closed-form upper bound to the ergodic capacity at any signal-to-noise ratio (SNR). Closed-form expressions of the ergodic capacity, at low and high SNR regimes, are also derived. Simulation results are presented to validate the accuracy of the derived expressions.

  6. Ergodicity and asymptotic stability of Feller semigroups on Polish metric spaces

    NASA Astrophysics Data System (ADS)

    Gong, FuZhou; Liu, Yuan

    2015-06-01

    We provide some sharp criteria for studying the ergodicity and asymptotic stability of general Feller semigroups on Polish metric spaces. As application, the 2D Navier-Stokes equations with degenerate stochastic forcing will be simply revisited.

  7. Design of weak-donor alkyl-functionalized push-pull pyrene dyes exhibiting enhanced fluorescence quantum yields and unique on/off switching properties.

    PubMed

    Niko, Yosuke; Sasaki, Shunsuke; Kawauchi, Susumu; Tokumaru, Katsumi; Konishi, Gen-Ichi

    2014-07-01

    We designed, synthesized, and evaluated environmentally responsive solvatochromic fluorescent dyes by incorporating weak push-pull moieties. The quantum yields of the push (alkyl)-pull (formyl) pyrene dyes were dramatically enhanced by the introduction of alkyl groups into formylpyrene (1-formylpyrene: Φ(F) =0.10; 3,6,8-tri-n-butyl-1-formylpyrene: Φ(F) =0.90; in MeOH). The new dyes exhibited unique sensitivity to solvent polarity and hydrogen-bond donor ability, and specific fluorescence turn-on/off properties (e.g., 3,6,8-tri-n-butyl-1-formylpyrene: Φ(F) =0.004, 0.80, 0.37, and 0.90 in hexane, chloroform, DMSO, and MeOH, respectively). Here, the alkyl groups act as weak donors to suppress intersystem crossing by destabilizing the HOMOs of 1-formylpyrene while maintaining weak intramolecular charge-transfer properties. By using alkyl groups as weak donors, environmentally responsive, and in particular, pH-responsive fluorescent materials may be developed in the future.

  8. In Vivo Anomalous Diffusion and Weak Ergodicity Breaking of Lipid Granules

    NASA Astrophysics Data System (ADS)

    Jeon, Jae-Hyung; Tejedor, Vincent; Burov, Stas; Barkai, Eli; Selhuber-Unkel, Christine; Berg-Sørensen, Kirstine; Oddershede, Lene; Metzler, Ralf

    2011-01-01

    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.

  9. Ergodicity and Parameter Estimates for Infinite-Dimensional Fractional Ornstein-Uhlenbeck Process

    SciTech Connect

    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.

  10. Ergodic properties of continuous-time random walks: Finite-size effects and ensemble dependences

    NASA Astrophysics Data System (ADS)

    Miyaguchi, Tomoshige; Akimoto, Takuma

    2013-03-01

    The effects of spatial confinements and smooth cutoffs of the waiting time distribution in continuous-time random walks are studied analytically. We also investigate dependences of ergodic properties on initial ensembles (i.e., distributions of the first waiting time). Here, we consider two ensembles: the equilibrium and a typical nonequilibrium ensemble. For both ensembles, it is shown that the time-averaged mean square displacement (TAMSD) exhibits a crossover from normal to anomalous diffusion due to the spatial confinement and this crossover does not vanish even in the long measurement time limit. Moreover, for the nonequilibrium ensemble, we show that the probability density function of the diffusion constant of TAMSD follows the transient Mittag-Leffler distribution, and that scatter in the TAMSD shows a clear transition from weak ergodicity breaking (an irreproducible regime) to ordinary ergodic behavior (a reproducible regime) as the measurement time increases. This convergence to ordinary ergodicity requires a long measurement time compared to common distributions such as the exponential distribution; in other words, the weak ergodicity breaking persists for a long time. In addition, it is shown that, aside from the TAMSD, a class of observables also exhibits this slow convergence to ergodicity. We also point out that, even though the system with the equilibrium initial ensemble shows no aging, its behavior is quite similar to that for the nonequilibrium ensemble.

  11. Around Property (T) for Quantum Groups

    NASA Astrophysics Data System (ADS)

    Daws, Matthew; Skalski, Adam; Viselter, Ami

    2017-07-01

    We study Property (T) for locally compact quantum groups, providing several new characterisations, especially related to operator algebraic ergodic theory. Quantum Property (T) is described in terms of the existence of various Kazhdan type pairs, and some earlier structural results of Kyed, Chen and Ng are strengthened and generalised. For second countable discrete unimodular quantum groups with low duals, Property (T) is shown to be equivalent to Property (T)1,1 of Bekka and Valette. This is used to extend to this class of quantum groups classical theorems on `typical' representations (due to Kerr and Pichot), and on connections of Property (T) with spectral gaps (due to Li and Ng) and with strong ergodicity of weakly mixing actions on a particular von Neumann algebra (due to Connes and Weiss). Finally, we discuss in the Appendix equivalent characterisations of the notion of a quantum group morphism with dense image.

  12. Anderson localization and ergodicity on random regular graphs

    NASA Astrophysics Data System (ADS)

    Tikhonov, K. Â. S.; Mirlin, A. Â. D.; Skvortsov, M. Â. A.

    2016-12-01

    A numerical study of Anderson transition on random regular graphs (RRGs) with diagonal disorder is performed. The problem can be described as a tight-binding model on a lattice with N sites that is locally a tree with constant connectivity. In a certain sense, the RRG ensemble can be seen as an infinite-dimensional (d →∞ ) cousin of the Anderson model in d dimensions. We focus on the delocalized side of the transition and stress the importance of finite-size effects. We show that the data can be interpreted in terms of the finite-size crossover from a small (N ≪Nc ) to a large (N ≫Nc ) system, where Nc is the correlation volume diverging exponentially at the transition. A distinct feature of this crossover is a nonmonotonicity of the spectral and wave-function statistics, which is related to properties of the critical phase in the studied model and renders the finite-size analysis highly nontrivial. Our results support an analytical prediction that states in the delocalized phase (and at N ≫Nc ) are ergodic in the sense that their inverse participation ratio scales as 1 /N .

  13. Ergodicity breaking and particle spreading in noisy heterogeneous diffusion processes

    NASA Astrophysics Data System (ADS)

    Cherstvy, Andrey G.; Metzler, Ralf

    2015-04-01

    We study noisy heterogeneous diffusion processes with a position dependent diffusivity of the form D(x) ˜ D0|x|α0 in the presence of annealed and quenched disorder of the environment, corresponding to an effective variation of the exponent α in time and space. In the case of annealed disorder, for which effectively α0 = α0(t), we show how the long time scaling of the ensemble mean squared displacement (MSD) and the amplitude variation of individual realizations of the time averaged MSD are affected by the disorder strength. For the case of quenched disorder, the long time behavior becomes effectively Brownian after a number of jumps between the domains of a stratified medium. In the latter situation, the averages are taken over both an ensemble of particles and different realizations of the disorder. As physical observables, we analyze in detail the ensemble and time averaged MSDs, the ergodicity breaking parameter, and higher order moments of the time averages.

  14. 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…

  15. 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…

  16. Topics in quantum chaos

    NASA Astrophysics Data System (ADS)

    Jordan, Andrew Noble

    2002-09-01

    In this dissertation, we study the quantum mechanics of classically chaotic dynamical systems. We begin by considering the decoherence effects a quantum chaotic system has on a simple quantum few state system. Typical time evolution of a quantum system whose classical limit is chaotic generates structures in phase space whose size is much smaller than Planck's constant. A naive application of Heisenberg's uncertainty principle indicates that these structures are not physically relevant. However, if we take the quantum chaotic system in question to be an environment which interacts with a simple two state quantum system (qubit), we show that these small phase-space structures cause the qubit to generically lose quantum coherence if and only if the environment has many degrees of freedom, such as a dilute gas. This implies that many-body environments may be crucial for the phenomenon of quantum decoherence. Next, we turn to an analysis of statistical properties of time correlation functions and matrix elements of quantum chaotic systems. A semiclassical evaluation of matrix elements of an operator indicates that the dominant contribution will be related to a classical time correlation function over the energy surface. For a highly chaotic class of dynamics, these correlation functions may be decomposed into sums of Ruelle resonances, which control exponential decay to the ergodic distribution. The theory is illustrated both numerically and theoretically on the Baker map. For this system, we are able to isolate individual Ruelle modes. We further consider dynamical systems whose approach to ergodicity is given by a power law rather than an exponential in time. We propose a billiard with diffusive boundary conditions, whose classical solution may be calculated analytically. We go on to compare the exact solution with an approximation scheme, as well calculate asympotic corrections. Quantum spectral statistics are calculated assuming the validity of the Again, Altshuler

  17. Granular Contact Forces: Proof of "Self-Ergodicity" by Generalizing Boltzmann's Stosszahlansatz and H Theorem

    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.

  18. Density fluctuations at high density in the ergodic divertor configuration of Tore Supra

    NASA Astrophysics Data System (ADS)

    Devynck, P.; Gunn, J.; Ghendrih, Ph.; Garbet, X.; Antar, G.; Beyer, P.; Boucher, C.; Honore, C.; Gervais, F.; Hennequin, P.; Quémeneur, A.; Truc, A.

    2001-03-01

    The effect of the ergodic divertor on the plasma edge in Tore Supra is to enhance the perpendicular transport through ergodization of the magnetic field lines [Ph. Ghendrih et al., Contrib. Plasma Phys. 32 (3&4) (1992) 179]. Nevertheless, the hot spots observed on the divertor plates during ergodic divertor operation indicate that the cross-field transport driven by the fluctuations is still playing an important role, although measurements by CO 2 laser scattering and reflectometry show a decrease of the turbulence level [J. Payan, X. Garbet, J.H. Chatenet et al., Nucl. Fusion 35 (1995) 1357; P. Beyer, X. Garbet, P. Ghendrih, Phys. Plasmas 5 (12) (1998) 4271]. In order to gain more understanding, fluctuation level and poloidal velocity have been measured with a reciprocating Langmuir probe biased to collect the ion saturation current ( jsat) and with a CO 2 laser scattering diagnostic. Though the relative fluctuation level behaves as previously observed at low density, a new interesting result is that this picture is gradually modified when the density is increased. Both diagnostics observe an increase of δn/ n with density in the ergodic region, which is not the usual behavior observed in limiter configuration. This increase is detected on both sides of the Er inversion radius and is therefore also affecting the plasma bulk. Finally, the confinement time is found to follow an L-mode law at all densities indicating that the ergodic divertor does not change the global confinement properties of the plasma.

  19. 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.

  20. 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.

  1. A Characterization of the Existence of Solutions for Hamilton-Jacobi Equations in Ergodic Control Problems with Applications

    SciTech Connect

    Arisawa, M.; Ishii, H.; Lions, P.-L.

    2000-07-01

    We give a characterization of the existence of bounded solutions for Hamilton-Jacobi equations in ergodic control problems with state-constraint. This result is applied to the reexamination of the counterexample concerning the existence of solutions for ergodic control problems in infinite-dimensional Hilbert spaces and also establishing results on effective Hamiltonians in periodic homogenization of Hamilton-Jacobi equations.

  2. Derivation of a true (t → 0+) quantum transition-state theory. I. Uniqueness and equivalence to ring-polymer molecular dynamics transition-state-theory.

    PubMed

    Hele, Timothy J H; Althorpe, Stuart C

    2013-02-28

    Surprisingly, there exists a quantum flux-side time-correlation function which has a non-zero t → 0+ limit and thus yields a rigorous quantum generalization of classical transition-state theory (TST). In this Part I of two articles, we introduce the new time-correlation function and derive its t → 0+ limit. The new ingredient is a generalized Kubo transform which allows the flux and side dividing surfaces to be the same function of path-integral space. Choosing this function to be a single point gives a t → 0+ limit which is identical to an expression introduced on heuristic grounds by Wigner in 1932; however, this expression does not give positive-definite quantum statistics, causing it to fail while still in the shallow-tunnelling regime. Positive-definite quantum statistics is obtained only if the dividing surface is invariant to imaginary-time translation, in which case the t → 0+ limit is identical to ring-polymer molecular dynamics (RPMD) TST. The RPMD-TST rate is not a strict upper bound to the exact quantum rate, but is a good approximation to one if real-time coherence effects are small. Part II will show that the RPMD-TST rate is equal to the exact quantum rate in the absence of recrossing.

  3. Persistence and ergodicity of plant disease model with markov conversion and impulsive toxicant input

    NASA Astrophysics Data System (ADS)

    Zhao, Wencai; Li, Juan; Zhang, Tongqian; Meng, Xinzhu; Zhang, Tonghua

    2017-07-01

    Taking into account of both white and colored noises, a stochastic mathematical model with impulsive toxicant input is formulated. Based on this model, we investigate dynamics, such as the persistence and ergodicity, of plant infectious disease model with Markov conversion in a polluted environment. The thresholds of extinction and persistence in mean are obtained. By using Lyapunov functions, we prove that the system is ergodic and has a stationary distribution under certain sufficient conditions. Finally, numerical simulations are employed to illustrate our theoretical analysis.

  4. Weak Ergodicity Breaking and Aging of Chaotic Transport in Hamiltonian Systems

    NASA Astrophysics Data System (ADS)

    Albers, Tony; Radons, Günter

    2014-10-01

    Momentum diffusion is a widespread phenomenon in generic Hamiltonian systems. We show for the prototypical standard map that this implies weak ergodicity breaking for the superdiffusive transport in coordinate direction with an averaging-dependent quadratic and cubic increase of the mean-squared displacement (MSD), respectively. This is explained via integrated Brownian motion, for which we derive aging time dependent expressions for the ensemble-averaged MSD, the distribution of time-averaged MSDs, and the ergodicity breaking parameter. Generalizations to other systems showing momentum diffusion are pointed out.

  5. 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.

  6. Self-averaging and weak ergodicity breaking of diffusion in heterogeneous media

    NASA Astrophysics Data System (ADS)

    Russian, Anna; Dentz, Marco; Gouze, Philippe

    2017-08-01

    Diffusion in natural and engineered media is quantified in terms of stochastic models for the heterogeneity-induced fluctuations of particle motion. However, fundamental properties such as ergodicity and self-averaging and their dependence on the disorder distribution are often not known. Here, we investigate these questions for diffusion in quenched disordered media characterized by spatially varying retardation properties, which account for particle retention due to physical or chemical interactions with the medium. We link self-averaging and ergodicity to the disorder sampling efficiency Rn, which quantifies the number of disorder realizations a noise ensemble may sample in a single disorder realization. Diffusion for disorder scenarios characterized by a finite mean transition time is ergodic and self-averaging for any dimension. The strength of the sample to sample fluctuations decreases with increasing spatial dimension. For an infinite mean transition time, particle motion is weakly ergodicity breaking in any dimension because single particles cannot sample the heterogeneity spectrum in finite time. However, even though the noise ensemble is not representative of the single-particle time statistics, subdiffusive motion in q ≥2 dimensions is self-averaging, which means that the noise ensemble in a single realization samples a representative part of the heterogeneity spectrum.

  7. Non Ergodic Aging in Lithium-Potassium Tantalate Crystals

    NASA Astrophysics Data System (ADS)

    Alberici, F.; Doussineau, P.; Levelut, A.

    1997-02-01

    Isothermal kinetics of the orientational glasses K{1-x}LixTaO3 (0.001ergodicity breaking. This shows that the phase-space can be pictured as a complicated landscape of mutually inaccessible valleys separated by very high barriers. A further insight is provided by another set of experiments where temperature cycles are performed: they are explained by a temperature dependent hierarchical organization of the phase-space. La cinétique isotherme de verres orientationnels K{1-x}LixTaO3 (0,001

  8. The Spatio-temporal Statistical Structure and Ergodic Behaviour of Scalar Turbulence Within a Rod Canopy

    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

  9. Existence of the thermodynamic limit for disordered quantum Coulomb systems

    NASA Astrophysics Data System (ADS)

    Blanc, Xavier; Lewin, Mathieu

    2012-09-01

    Following a recent method introduced by Hainzl, Solovej, and Lewin, we prove the existence of the thermodynamic limit for a system made of quantum electrons, and classical nuclei whose positions and charges are randomly perturbed in an ergodic fashion. All the particles interact through Coulomb forces.

  10. The Probabilities of Unique Events

    DTIC Science & Technology

    2012-08-30

    probabilities into quantum mechanics, and some psychologists have argued that they have a role to play in accounting for errors in judgment [30]. But, in...Discussion The mechanisms underlying naive estimates of the probabilities of unique events are largely inaccessible to consciousness , but they...Can quantum probability provide a new direc- tion for cognitive modeling? Behavioral and Brain Sciences (in press). 31. Paolacci G, Chandler J

  11. Nonlinear Dynamics and Ergodic Theory Methods in Control

    DTIC Science & Technology

    2005-12-31

    graduate student ( Umesh Vaidya) was working on the problem of control of discrete- time, conservative systems [33, 34] and quantum control [32]. Another...microscale mixing. At the Pr’s group, 1 graduate student ( Umesh Vaidya) was working on the problem of control of discrete-time, conservative systems [35...Dmitri Vainchtein, Partially supported graduate students: Umesh Vaidya, Thomas John, Zoran Levnajic, Andre Valente. 10 3 Interactions/transitions: 3.1

  12. Dynamical typicality of embedded quantum systems

    NASA Astrophysics Data System (ADS)

    Ithier, Grégoire; Benaych-Georges, Florent

    2017-07-01

    We consider the dynamics of an arbitrary quantum system coupled to a large arbitrary and fully quantum-mechanical environment through a random interaction. We establish analytically and check numerically the typicality of this dynamics, in other words, the fact that the reduced density matrix of the system has a self-averaging property. This phenomenon, which lies in a generalized central limit theorem, justifies rigorously averaging procedures over certain classes of random interactions and can explain the absence of sensitivity to microscopic details of irreversible processes, such as thermalization. It provides more generally an ergodic principle for embedded quantum systems.

  13. 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.

  14. Finite-Time Effects and Ultraweak Ergodicity Breaking in Superdiffusive Dynamics

    NASA Astrophysics Data System (ADS)

    Godec, Aljaž; Metzler, Ralf

    2013-01-01

    We study the ergodic properties of superdiffusive, spatiotemporally coupled Lévy walk processes. For trajectories of finite duration, we reveal a distinct scatter of the scaling exponents of the time averaged mean squared displacement δx2¯ around the ensemble value 3-α (1<α<2) ranging from ballistic motion to subdiffusion, in strong contrast to the behavior of subdiffusive processes. In addition we find a significant dependence of the average of δx2¯ over an ensemble of trajectories as a function of the finite measurement time. This so-called finite-time amplitude depression and the scatter of the scaling exponent is vital in the quantitative evaluation of superdiffusive processes. Comparing the long time average of the second moment with the ensemble mean squared displacement, these only differ by a constant factor, an ultraweak ergodicity breaking.

  15. Impact of nonzero boresight pointing error on ergodic capacity of MIMO FSO communication systems.

    PubMed

    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.

  16. Truncated Lévy flights and weak ergodicity breaking in the Hamiltonian mean-field model

    NASA Astrophysics Data System (ADS)

    Figueiredo, A.; Filho, T. M. Rocha; Amato, M. A.; Oliveira, Z. T.; Matsushita, R.

    2014-02-01

    The dynamics of the Hamiltonian mean-field model is studied in the context of continuous-time random walks. We show that the sojourn times in cells in the momentum space are well described by a one-sided truncated Lévy distribution. Consequently, the system is nonergodic for long observation times that diverge with the number of particles. Ergodicity is attained only after very long times both at thermodynamic equilibrium and at quasistationary out-of-equilibrium states.

  17. Truncated Lévy flights and weak ergodicity breaking in the Hamiltonian mean-field model.

    PubMed

    Figueiredo, A; Filho, T M Rocha; Amato, M A; Oliveira, Z T; Matsushita, R

    2014-02-01

    The dynamics of the Hamiltonian mean-field model is studied in the context of continuous-time random walks. We show that the sojourn times in cells in the momentum space are well described by a one-sided truncated Lévy distribution. Consequently, the system is nonergodic for long observation times that diverge with the number of particles. Ergodicity is attained only after very long times both at thermodynamic equilibrium and at quasistationary out-of-equilibrium states.

  18. Ergodic Dynamics by Design: A Route to Predictable Multi-Robot Systems

    DTIC Science & Technology

    2005-03-01

    space ( McQuarrie , 1976, pp. 554). This section has demonstrated that dynamics with a high degree of ergodic- ity are achievable on physical robot...microscopic behavior and macroscopic structures ( McQuarrie , 1976). Typical system sizes for classical work are sig- nificantly larger (∼ 1023) than the...436. McQuarrie , D. A. (1976). Statistical Mechanics. Harper and Row. reprinted by University Sci- ence Books, Sausalito, CA., USA in 2000. Potts, R. B

  19. Exponential Ergodicity of Stochastic Burgers Equations Driven by α-Stable Processes

    NASA Astrophysics Data System (ADS)

    Dong, Zhao; Xu, Lihu; Zhang, Xicheng

    2014-02-01

    In this work, we prove the strong Feller property and the exponential ergodicity of stochastic Burgers equations driven by α/2-subordinated cylindrical Brownian motions with α∈(1,2). To prove the results, we truncate the nonlinearity and use the derivative formula for SDEs driven by α-stable noises established in (Zhang in Stoch. Process. Appl. 123(4):1213-1228, 2013).

  20. The Wave Function and Quantum Reality

    SciTech Connect

    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

  1. Deterministic time-reversible thermostats: chaos, ergodicity, and the zeroth law of thermodynamics

    NASA Astrophysics Data System (ADS)

    Patra, Puneet Kumar; Sprott, Julien Clinton; Hoover, William Graham; Griswold Hoover, Carol

    2015-09-01

    The relative stability and ergodicity of deterministic time-reversible thermostats, both singly and in coupled pairs, are assessed through their Lyapunov spectra. Five types of thermostat are coupled to one another through a single Hooke's-law harmonic spring. The resulting dynamics shows that three specific thermostat types, Hoover-Holian, Ju-Bulgac, and Martyna-Klein-Tuckerman, have very similar Lyapunov spectra in their equilibrium four-dimensional phase spaces and when coupled in equilibrium or nonequilibrium pairs. All three of these oscillator-based thermostats are shown to be ergodic, with smooth analytic Gaussian distributions in their extended phase spaces (coordinate, momentum, and two control variables). Evidently these three ergodic and time-reversible thermostat types are particularly useful as statistical-mechanical thermometers and thermostats. Each of them generates Gibbs' universal canonical distribution internally as well as for systems to which they are coupled. Thus they obey the zeroth law of thermodynamics, as a good heat bath should. They also provide dissipative heat flow with relatively small nonlinearity when two or more such temperature baths interact and provide useful deterministic replacements for the stochastic Langevin equation.

  2. Nonequilibrium entropy, Lyapounov variables, and ergodic properties of classical systems

    PubMed Central

    Misra, B.

    1978-01-01

    We discuss the problem of defining (nonequilibrium) entropy in terms of the concepts of mechanics and of reconciling its monotonic increase with the Hamiltonian evolution of the dynamical system. This leads to investigating necessary and sufficient conditions for the existence of monotonically increasing quantities or the so-called Lyapounov variables of classical systems. It is found that the condition of “mixing” is necessary and the property of being K-flow is sufficient for the existence of a Lyapounov variable. The significance of the study of Lyapounov variables for the elucidation of the fundamental questions of statistical mechanics is briefly discussed. It is seen that every Lyapounov variable must fail to commute with at least some of the operators of multiplication by phase space functions. The uncertainty relations implied by this necessary noncommutativity would then set a limit on the simultaneous determination of entropy and trajectories in phase space. These considerations thus support and sharpen the view that the thermodynamical and the (microscopic) dynamical descriptions of classical systems could be consistently reconciled as being complementary descriptions analogous to the complementary descriptions encountered in quantum mechanics. PMID:16592515

  3. Great-enhanced performance of Pt nanoparticles by the unique carbon quantum dot/reduced graphene oxide hybrid supports towards methanol electrochemical oxidation

    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.

  4. Characterization of microstructure, viscoelasticity, heterogeneity and ergodicity in pectin-laponite-CTAB-calcium nanocomposite hydrogels.

    PubMed

    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.

  5. Hierarchical layered and semantic-based image segmentation using ergodicity map

    NASA Astrophysics Data System (ADS)

    Yadegar, Jacob; Liu, Xiaoqing

    2010-04-01

    Image segmentation plays a foundational role in image understanding and computer vision. Although great strides have been made and progress achieved on automatic/semi-automatic image segmentation algorithms, designing a generic, robust, and efficient image segmentation algorithm is still challenging. Human vision is still far superior compared to computer vision, especially in interpreting semantic meanings/objects in images. We present a hierarchical/layered semantic image segmentation algorithm that can automatically and efficiently segment images into hierarchical layered/multi-scaled semantic regions/objects with contextual topological relationships. The proposed algorithm bridges the gap between high-level semantics and low-level visual features/cues (such as color, intensity, edge, etc.) through utilizing a layered/hierarchical ergodicity map, where ergodicity is computed based on a space filling fractal concept and used as a region dissimilarity measurement. The algorithm applies a highly scalable, efficient, and adaptive Peano- Cesaro triangulation/tiling technique to decompose the given image into a set of similar/homogenous regions based on low-level visual cues in a top-down manner. The layered/hierarchical ergodicity map is built through a bottom-up region dissimilarity analysis. The recursive fractal sweep associated with the Peano-Cesaro triangulation provides efficient local multi-resolution refinement to any level of detail. The generated binary decomposition tree also provides efficient neighbor retrieval mechanisms for contextual topological object/region relationship generation. Experiments have been conducted within the maritime image environment where the segmented layered semantic objects include the basic level objects (i.e. sky/land/water) and deeper level objects in the sky/land/water surfaces. Experimental results demonstrate the proposed algorithm has the capability to robustly and efficiently segment images into layered semantic objects

  6. 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.

  7. Chaos, ergodicity, and the thermodynamics of lower-dimensional time-independent Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Kandrup, Henry E.; Sideris, Ioannis V.; Bohn, Courtlandt L.

    2002-01-01

    This paper uses the assumptions of ergodicity and a microcanonical distribution to compute estimates of the largest Lyapunov exponents in lower-dimensional Hamiltonian systems. That the resulting estimates are in reasonable agreement with the actual values computed numerically corroborates the intuition that chaos in such systems can be understood as arising generically from a parametric instability and that this instability may be modeled by a stochastic-oscillator equation [cf. Casetti, Clementi, and Pettini, Phys. Rev. E 54, 5969 (1996)], linearized perturbations of a chaotic orbit satisfying a harmonic-oscillator equation with a randomly varying frequency.

  8. Non-ergodicity and fluctuations in mesoscopic insulators: The replica cooperon and diffuson

    NASA Astrophysics Data System (ADS)

    Medina, E.; Roman, E.; Rangel, R.

    2001-06-01

    We explore the mesoscopic conductance fluctuations in the insulating regime within the Nguyen, Spivak, and Shklovskii model. We find that fluctuations of the log-conductance are persistent above the decorrelation field Bc in the insulating regime. Using the replica approach, we derive the field coupling and fluctuations in terms of "cooperon"and "diffuson"analogs and determine new corrections to temperature dependencies for small ΔB. We also analyze the ergodicity of fluctuations in the log-conductance and its scaling properties, and discuss the asymptotic validity of the usual criterion involving the commutability of disorder and field fluctuation averages.

  9. Blind Quantum Signature with Blind Quantum Computation

    NASA Astrophysics Data System (ADS)

    Li, Wei; Shi, Ronghua; Guo, Ying

    2017-04-01

    Blind quantum computation allows a client without quantum abilities to interact with a quantum server to perform a unconditional secure computing protocol, while protecting client's privacy. Motivated by confidentiality of blind quantum computation, a blind quantum signature scheme is designed with laconic structure. Different from the traditional signature schemes, the signing and verifying operations are performed through measurement-based quantum computation. Inputs of blind quantum computation are securely controlled with multi-qubit entangled states. The unique signature of the transmitted message is generated by the signer without leaking information in imperfect channels. Whereas, the receiver can verify the validity of the signature using the quantum matching algorithm. The security is guaranteed by entanglement of quantum system for blind quantum computation. It provides a potential practical application for e-commerce in the cloud computing and first-generation quantum computation.

  10. Blind Quantum Signature with Blind Quantum Computation

    NASA Astrophysics Data System (ADS)

    Li, Wei; Shi, Ronghua; Guo, Ying

    2016-12-01

    Blind quantum computation allows a client without quantum abilities to interact with a quantum server to perform a unconditional secure computing protocol, while protecting client's privacy. Motivated by confidentiality of blind quantum computation, a blind quantum signature scheme is designed with laconic structure. Different from the traditional signature schemes, the signing and verifying operations are performed through measurement-based quantum computation. Inputs of blind quantum computation are securely controlled with multi-qubit entangled states. The unique signature of the transmitted message is generated by the signer without leaking information in imperfect channels. Whereas, the receiver can verify the validity of the signature using the quantum matching algorithm. The security is guaranteed by entanglement of quantum system for blind quantum computation. It provides a potential practical application for e-commerce in the cloud computing and first-generation quantum computation.

  11. Thermodynamics of quantum information scrambling.

    PubMed

    Campisi, Michele; Goold, John

    2017-06-01

    Scrambling of quantum information can conveniently be quantified by so-called out-of-time-order correlators (OTOCs), i.e., correlators of the type 〈[W_{τ},V]^{†}[W_{τ},V]〉, whose measurements present a formidable experimental challenge. Here we report on a method for the measurement of OTOCs based on the so-called two-point measurement scheme developed in the field of nonequilibrium quantum thermodynamics. The scheme is of broader applicability than methods employed in current experiments and provides a clear-cut interpretation of quantum information scrambling in terms of nonequilibrium fluctuations of thermodynamic quantities, such as work and heat. Furthermore, we provide a numerical example on a spin chain which highlights the utility of our thermodynamic approach when understanding the differences between integrable and ergodic behaviors. We also discuss how the method can be used to extend the reach of current experiments.

  12. Emergent Quantum Mechanics and the Origin of Quantum Non-local Correlations

    NASA Astrophysics Data System (ADS)

    Torromé, Ricardo Gallego

    2017-10-01

    A geometric interpretation for quantum correlations and entanglement according to a particular framework of emergent quantum mechanics is developed. The mechanism described is based on two ingredients: 1. At an hypothetical sub-quantum level description of physical systems, the dynamics has a regime where it is partially ergodic and 2. A formal projection from a two-dimensional time mathematical formalism of the emergent quantum theory to the usual one-dimensional time formalism of quantum dynamics. Observable consequences of the theory are obtained. Among them we show that quantum correlations must be instantaneous from the point of view of the spacetime description, but the spatial distance up to which they can be observed must be bounded. It is argued how our mechanism avoids Bell theorem and Kochen-Specken theorem. Evidence for non-signaling faster than the speed of light in our proposal is discussed.

  13. Fluctuations around equilibrium laws in ergodic continuous-time random walks.

    PubMed

    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.

  14. 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.

  15. Quantum coherence versus quantum uncertainty

    NASA Astrophysics Data System (ADS)

    Luo, Shunlong; Sun, Yuan

    2017-08-01

    The notion of measurement is of both foundational and instrumental significance in quantum mechanics, and coherence destroyed by measurements (decoherence) lies at the very heart of quantum to classical transition. Qualitative aspects of this spirit have been widely recognized and analyzed ever since the inception of quantum theory. However, axiomatic and quantitative investigations of coherence are attracting great interest only recently with several figures of merit for coherence introduced [Baumgratz, Cramer, and Plenio, Phys. Rev. Lett. 113, 140401 (2014), 10.1103/PhysRevLett.113.140401]. While these resource theoretic approaches have many appealing and intuitive features, they rely crucially on various notions of incoherent operations which are sophisticated, subtle, and not uniquely defined, as have been critically assessed [Chitambar and Gour, Phys. Rev. Lett. 117, 030401 (2016), 10.1103/PhysRevLett.117.030401]. In this paper, we elaborate on the idea that coherence and quantum uncertainty are dual viewpoints of the same quantum substrate, and address coherence quantification by identifying coherence of a state (with respect to a measurement) with quantum uncertainty of a measurement (with respect to a state). Consequently, coherence measures may be set into correspondence with measures of quantum uncertainty. In particular, we take average quantum Fisher information as a measure of quantum uncertainty, and introduce the corresponding measure of coherence, which is demonstrated to exhibit desirable properties. Implications for interpreting quantum purity as maximal coherence, and quantum discord as minimal coherence, are illustrated.

  16. Faithful actions of locally compact quantum groups on classical spaces

    NASA Astrophysics Data System (ADS)

    Goswami, Debashish; Roy, Sutanu

    2017-03-01

    We construct examples of locally compact quantum groups coming from bicrossed product construction, including non-Kac ones, which can faithfully and ergodically act on connected classical (noncompact) smooth manifolds. However, none of these actions can be isometric in the sense of Goswami (Commun Math Phys 285(1):141-160, 2009), leading to the conjecture that the result obtained by Goswami and Joardar (Rigidity of action of compact quantum groups on compact, connected manifolds, 2013. arXiv:1309.1294) about nonexistence of genuine quantum isometry of classical compact connected Riemannian manifolds may hold in the noncompact case as well.

  17. Faithful actions of locally compact quantum groups on classical spaces

    NASA Astrophysics Data System (ADS)

    Goswami, Debashish; Roy, Sutanu

    2017-07-01

    We construct examples of locally compact quantum groups coming from bicrossed product construction, including non-Kac ones, which can faithfully and ergodically act on connected classical (noncompact) smooth manifolds. However, none of these actions can be isometric in the sense of Goswami (Commun Math Phys 285(1):141-160, 2009), leading to the conjecture that the result obtained by Goswami and Joardar (Rigidity of action of compact quantum groups on compact, connected manifolds, 2013. arXiv:1309.1294) about nonexistence of genuine quantum isometry of classical compact connected Riemannian manifolds may hold in the noncompact case as well.

  18. Ergodicity, configurational entropy and free energy in pigment solutions and plant photosystems: influence of excited state lifetime.

    PubMed

    Jennings, Robert C; Zucchelli, Giuseppe

    2014-01-01

    We examine ergodicity and configurational entropy for a dilute pigment solution and for a suspension of plant photosystem particles in which both ground and excited state pigments are present. It is concluded that the pigment solution, due to the extreme brevity of the excited state lifetime, is non-ergodic and the configurational entropy approaches zero. Conversely, due to the rapid energy transfer among pigments, each photosystem is ergodic and the configurational entropy is positive. This decreases the free energy of the single photosystem pigment array by a small amount. On the other hand, the suspension of photosystems is non-ergodic and the configurational entropy approaches zero. The overall configurational entropy which, in principle, includes contributions from both the single excited photosystems and the suspension which contains excited photosystems, also approaches zero. Thus the configurational entropy upon photon absorption by either a pigment solution or a suspension of photosystem particles is approximately zero. Copyright © 2014 Elsevier B.V. All rights reserved.

  19. Quantum coherence and correlations in quantum system

    PubMed Central

    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

  20. 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

  1. On exact statistics and classification of ergodic systems of integer dimension

    SciTech Connect

    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.

  2. Surface-induced dissociation of methanol cations: A non-ergodic process

    DOE PAGES

    Shukla, Anil K.

    2017-09-01

    Here, dissociation of methanol molecular cations, CH3OH+, to CH2OH+ on collision with a self-assembled monolayer surface of fluorinated alkyl thiol on gold 111 crystal has been studied at 12.5 eV collision energy. Two energetically and spatially distinct processes contribute to the dissociation process: one involving loss of very large amount of energy approaching the initial kinetic energy of the primary ions with scattering of fragment ions over a broad angular range between surface normal and surface parallel while the second process results from small amount of energy loss with fragment ions scattered over a narrow angular range close to themore » surface parallel. There is a third process with relatively small contribution to total dissociation whose characteristics are very similar to the low energy loss process. Finally, these results demonstrate that surface-induced dissociation of methanol cations via hydrogen loss is non-ergodic.« less

  3. Transient anomalous diffusion in periodic systems: ergodicity, symmetry breaking and velocity relaxation

    PubMed Central

    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

  4. On the use of stochastic differential games against nature to ergodic control problems with unknown parameters

    NASA Astrophysics Data System (ADS)

    Jasso-Fuentes, Héctor; López-Barrientos, José Daniel

    2015-05-01

    In this paper, we propose an application of the so-called games against nature for giving solution to an ergodic control problem governed by a general class of Markov diffusion processes whose coefficients depend on an unknown and non-observable parameter. To this end, we assume that the values of the parameter are taken by means of 'actions' made by some opposite player of the controller (the nature). Then, the problem reduces to finding optimality for the controller given that the nature has chosen its best strategy. Such a control is also known as the worst case optimal control. Our analysis is based on the use of the dynamic programming technique by showing, among other facts, the existence of classical (twice differentiable) solutions of the so called Hamilton Jacobi Bellman equation. We also provide an example on economic welfare to illustrate our results.

  5. 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.

  6. 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.

  7. The stationary distribution and ergodicity of a stochastic phytoplankton allelopathy model under regime switching

    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.

  8. Diffusive and Subdiffusive Spin Transport in the Ergodic Phase of a Many-Body Localizable System.

    PubMed

    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.

  9. 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.

  10. Ergodic theory and visualization. II. Fourier mesochronic plots visualize (quasi)periodic sets

    SciTech Connect

    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.

  11. Distributional ergodicity in stored-energy-driven Lévy flights

    NASA Astrophysics Data System (ADS)

    Akimoto, Takuma; Miyaguchi, Tomoshige

    2013-06-01

    We study a class of random walk, the stored-energy-driven Lévy flight (SEDLF), whose jump length is determined by a stored energy during a trapped state. The SEDLF is a continuous-time random walk with jump lengths being coupled with the trapping times. It is analytically shown that the ensemble-averaged mean-square displacements exhibit subdiffusion as well as superdiffusion, depending on the coupling parameter. We find that time-averaged mean-square displacements increase linearly with time and the diffusion coefficients are intrinsically random, a manifestation of distributional ergodicity. The diffusion coefficient shows aging in subdiffusive regime, whereas it increases with the measurement time in superdiffusive regime.

  12. Three dimensional cross-correlation dynamic light scattering by non-ergodic turbid media.

    PubMed

    Haro-Pérez, C; Ojeda-Mendoza, G J; Rojas-Ochoa, L F

    2011-06-28

    We investigate dynamic light scattering by non-ergodic turbid media with an adapted version of the method proposed by Pusey and van Megen [Physica A 157, 705 (1989)]. Our formulation follows the derivation of the original method by extending it to the three dimensional cross-correlation scheme (3DDLS). The main finding is an expression to obtain the dynamic structure factor from light scattering that takes into account the system turbidity and the peculiarities of the 3D geometry. From 3DDLS measurements in well-controlled solid-like systems of different turbidity, we confirm that our results can be interpreted reasonably well by the theoretical approach described here. Good agreement is found with earlier reported results on similar systems.

  13. Ergodic theory and visualization. II. Fourier mesochronic plots visualize (quasi)periodic sets

    NASA Astrophysics Data System (ADS)

    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.

  14. 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.

  15. Anti-phase synchronization and ergodicity in arrays of oscillators coupled by an elastic force

    NASA Astrophysics Data System (ADS)

    Dilão, Rui

    2014-04-01

    We have proposed a mechanism of interaction between two non-linear dissipative oscillators, leading to exact and robust anti-phase and in-phase synchronization. The system we have analyzed is a model for the Huygens's two pendulum clocks system, as well as a model for synchronization mediated by an elastic media. Here, we extend these results to arrays, finite or infinite, of conservative pendula coupled by linear elastic forces. We show that, for two interacting pendula, this mechanism leads always to synchronized anti-phase small amplitude oscillations, and it is robust upon variation of the parameters. For three or more interacting pendula, this mechanism leads always to ergodic non-synchronized oscillations. In the continuum limit, the pattern of synchronization is described by a quasi-periodic longitudinal wave.

  16. Outage Probability and Ergodic Capacity of Spectrum-Sharing Systems with MRC Diversity

    NASA Astrophysics Data System (ADS)

    Jarrouj, Jiana; Blagojevic, Vesna; Ivanis, Predrag

    2016-03-01

    The spectrum sharing system employing maximum ratio combining (MRC) is analyzed in Nakagami fading environment, for the case when the interference from the primary user is present at the input of the secondary user receiver. The closed-form expressions for the probability density function of the signal-to-interference-and-noise ratio, the outage probability and the ergodic capacity of the SU link are derived under both peak interference and maximal transmit power constraints. Asymptotical expressions are provided for the important region where peak interference power constraint dominates and the case when the interference from the primary user's is dominant compared to the noise at the secondary user's receiver. The obtained expressions are presented for both cases of outdated and mean-value based power allocation and verified by using Monte Carlo simulation method.

  17. Metabasin approach for computing the master equation dynamics of systems with broken ergodicity.

    PubMed

    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.

  18. Ergodic theory and visualization. II. Fourier mesochronic plots visualize (quasi)periodic sets.

    PubMed

    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.

  19. Ergodicity reflected in macroscopic and microscopic field-dependent behavior of BNT-based relaxors

    SciTech Connect

    Dittmer, Robert; Jo, Wook Rödel, Jürgen; Gobeljic, Danka; Shvartsman, Vladimir V.; Lupascu, Doru C.; Jones, Jacob L.

    2014-02-28

    The effect of heterovalent B-site doping on ergodicity of relaxor ferroelectrics is studied using (1 − y)(0.81Bi{sub 1/2}Na{sub 1/2}TiO{sub 3}-0.19Bi{sub 1/2}K{sub 1/2}TiO{sub 3})-yBiZn{sub 1/2}Ti{sub 1/2}O{sub 3} (BNT-BKT-BZT) with y = (0.02;0.03;0.04) as a model system. Both the large- and small-signal parameters are studied as a function of electric field. The crystal structure is assessed by means of neutron diffraction in the initial state and after exposure to a high electric field. In order to measure ferroelastic domain textures, diffraction patterns of the poled samples are collected as a function of sample rotation angle. Piezoresponse force microscopy (PFM) is employed to probe the microstructure for polar regions at a nanoscopic scale. For low electric fields E < 2 kV·mm{sup −1}, large- and small-signal constitutive behavior do not change with composition. At high electric fields, however, drastic differences are observed due to a field-induced phase transition into a long-range ordered state. It is hypothesized that increasing BZT content decreases the degree of non-ergodicity; thus, the formation of long-range order is impeded. It is suggested that frozen and dynamic polar nano regions exist to a different degree, depending on the BZT content. This image is supported by PFM measurements. Moreover, PFM measurements suggest that the relaxation mechanism after removal of the bias field is influenced by surface charges.

  20. Ergodicity reflected in macroscopic and microscopic field-dependent behavior of BNT-based relaxors

    NASA Astrophysics Data System (ADS)

    Dittmer, Robert; Gobeljic, Danka; Jo, Wook; Shvartsman, Vladimir V.; Lupascu, Doru C.; Jones, Jacob L.; Rödel, Jürgen

    2014-02-01

    The effect of heterovalent B-site doping on ergodicity of relaxor ferroelectrics is studied using (1 - y)(0.81Bi1/2Na1/2TiO3-0.19Bi1/2K1/2TiO3)-yBiZn1/2Ti1/2O3 (BNT-BKT-BZT) with y = {0.02;0.03;0.04} as a model system. Both the large- and small-signal parameters are studied as a function of electric field. The crystal structure is assessed by means of neutron diffraction in the initial state and after exposure to a high electric field. In order to measure ferroelastic domain textures, diffraction patterns of the poled samples are collected as a function of sample rotation angle. Piezoresponse force microscopy (PFM) is employed to probe the microstructure for polar regions at a nanoscopic scale. For low electric fields E < 2 kV.mm-1, large- and small-signal constitutive behavior do not change with composition. At high electric fields, however, drastic differences are observed due to a field-induced phase transition into a long-range ordered state. It is hypothesized that increasing BZT content decreases the degree of non-ergodicity; thus, the formation of long-range order is impeded. It is suggested that frozen and dynamic polar nano regions exist to a different degree, depending on the BZT content. This image is supported by PFM measurements. Moreover, PFM measurements suggest that the relaxation mechanism after removal of the bias field is influenced by surface charges.

  1. 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

  2. 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.

  3. 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.

  4. A Perron-Frobenius Type of Theorem for Quantum Operations

    NASA Astrophysics Data System (ADS)

    Lagro, Matthew; Yang, Wei-Shih; Xiong, Sheng

    2017-08-01

    We define a special class of quantum operations we call Markovian and show that it has the same spectral properties as a corresponding Markov chain. We then consider a convex combination of a quantum operation and a Markovian quantum operation and show that under a norm condition its spectrum has the same properties as in the conclusion of the Perron-Frobenius theorem if its Markovian part does. Moreover, under a compatibility condition of the two operations, we show that its limiting distribution is the same as the corresponding Markov chain. We apply our general results to partially decoherent quantum random walks with decoherence strength 0 ≤ p ≤ 1 . We obtain a quantum ergodic theorem for partially decoherent processes. We show that for 0 < p ≤ 1 , the limiting distribution of a partially decoherent quantum random walk is the same as the limiting distribution for the classical random walk.

  5. A Perron-Frobenius Type of Theorem for Quantum Operations

    NASA Astrophysics Data System (ADS)

    Lagro, Matthew; Yang, Wei-Shih; Xiong, Sheng

    2017-10-01

    We define a special class of quantum operations we call Markovian and show that it has the same spectral properties as a corresponding Markov chain. We then consider a convex combination of a quantum operation and a Markovian quantum operation and show that under a norm condition its spectrum has the same properties as in the conclusion of the Perron-Frobenius theorem if its Markovian part does. Moreover, under a compatibility condition of the two operations, we show that its limiting distribution is the same as the corresponding Markov chain. We apply our general results to partially decoherent quantum random walks with decoherence strength 0 ≤ p ≤ 1. We obtain a quantum ergodic theorem for partially decoherent processes. We show that for 0 < p ≤ 1, the limiting distribution of a partially decoherent quantum random walk is the same as the limiting distribution for the classical random walk.

  6. Dynamic Responses of Tokamak Plasmas Induced by Externally Applied Rotating Helical Magnetic Field in Dynamic Ergodic Divertor

    NASA Astrophysics Data System (ADS)

    Kikuchi, Yusuke; Uesugi, Yoshihiko; Takamura, Shuichi; Budaev, Viatcheslav

    2002-11-01

    Dynamic Ergodic Divertor (DED) is an advanced concept for the control of the tokamak edge plasmas. In contrast to conventional Ergodic Divertor, an externally applied helical magnetic field rotates in the helical direction. This rotating helical field (RHF) may decrease the heat and particle flux onto the local target in the conventional divertor. In the DED experiment, it is also expected that RHF induces the edge plasma rotation due to the shielding current around the resonance surface. Penetration processes into tokamak plasmas and dynamic behavior of RHF have been investigated on HYBTOK-II tokamak. We have confirmed the attenuation of the radial component of RHF from the magnetic probe measurement. When the relative rotation velocity between the plasma and RHF is small around resonance surface, however, the radial component of RHF is amplified by the effect of re-distribution of the plasma current by island formation. We will analyze the penetration process of RHF by linear MHD theory.

  7. Numerical study of long-time dynamics and ergodic-nonergodic transitions in dense simple fluids.

    PubMed

    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 derived from

  8. Beyond the Quantum

    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.].

  9. Diffusion described with quantum Langevin equation in tilted periodic potential

    NASA Astrophysics Data System (ADS)

    Duan, Hong-Guang; Liang, Xian-Ting

    2012-11-01

    In this paper, diffusion behavior of Brownian particles moving in a 1D periodic potential landscape has been theoretically investigated by using the general quantum Langevin equation. At first, in the condition of weak disorder, some anomalous diffusive behaviors have been revealed in the process. Then, two types of mean square displacement, ensemble averaged and time averaged mean square displacement, have been investigated in a long time, and the weak ergodicity breaking phenomenon has been revealed. It is shown that the general quantum Langevin equation can exhibit some novel details of the experimental diffusion process.

  10. Quantum computers.

    PubMed

    Ladd, T D; Jelezko, F; Laflamme, R; Nakamura, Y; Monroe, C; O'Brien, J L

    2010-03-04

    Over the past several decades, quantum information science has emerged to seek answers to the question: can we gain some advantage by storing, transmitting and processing information encoded in systems that exhibit unique quantum properties? Today it is understood that the answer is yes, and many research groups around the world are working towards the highly ambitious technological goal of building a quantum computer, which would dramatically improve computational power for particular tasks. A number of physical systems, spanning much of modern physics, are being developed for quantum computation. However, it remains unclear which technology, if any, will ultimately prove successful. Here we describe the latest developments for each of the leading approaches and explain the major challenges for the future.

  11. Fluorescence molecule counting for single-molecule studies in crowded environment of living cells without and with broken ergodicity.

    PubMed

    Földes-Papp, Zeno; Baumann, Gerd

    2011-05-01

    We present a new approach to distinguish between non-ergodic and ergodic behavior. Performing ensemble averaging in a subpopulation of individual molecules leads to a mean value that can be similar to the mean value obtained in an ergodic system. The averaging is carried out by minimizing the variation between the sum of the temporal averaged mean square deviation of the simulated data with respect to the logarithmic scaling behavior of the subpopulation. For this reason, we first introduce a kind of Continuous Time Random Walks (CTRW), which we call Limited Continuous Time Random Walks (LCTRW) on fractal support. The random waiting time distributions are sampled at points which fulfill the condition N <1, where N is the Poisson probability of finding a single molecule in the femtoliter-sized observation volume ΔV at the single-molecule level. Given a subpopulation of different single molecules of the same kind, the ratio T/ T(m) between the measurement time T and the meaningful time T(m), which is the time for observing just one and the same single molecule, is the experimentally accessible quantity that allows to compare different molecule numbers in the subpopulation. In addition, the mean square displacement traveled by the molecule during the time t is determined by an upper limit of the geometric dimension of the living cell or its nucleus.

  12. Physical properties of quantum field theory measures

    NASA Astrophysics Data System (ADS)

    Mourão, J. M.; Thiemann, T.; Velhinho, J. M.

    1999-05-01

    Well known methods of measure theory on infinite dimensional spaces are used to study physical properties of measures relevant to quantum field theory. The difference of typical configurations of free massive scalar field theories with different masses is studied. We apply the same methods to study the Ashtekar-Lewandowski (AL) measure on spaces of connections. In particular we prove that the diffeomorphism group acts ergodically, with respect to the AL measure, on the Ashtekar-Isham space of quantum connections modulo gauge transformations. We also prove that a typical, with respect to the AL measure, quantum connection restricted to a (piecewise analytic) curve leads to a parallel transport discontinuous at every point of the curve.

  13. 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).

  14. Polarization fields and phase space densities in storage rings: Stroboscopic averaging and the ergodic theorem

    NASA Astrophysics Data System (ADS)

    Ellison, James A.; Heinemann, Klaus

    2007-10-01

    A class of orbital motions with volume preserving flows and with vector fields periodic in the “time” parameter θ is defined. Spin motion coupled to the orbital dynamics is then defined, resulting in a class of spin-orbit motions which are important for storage rings. Phase space densities and polarization fields are introduced. It is important, in the context of storage rings, to understand the behavior of periodic polarization fields and phase space densities. Due to the 2π time periodicity of the spin-orbit equations of motion the polarization field, taken at a sequence of increasing time values θ,θ+2π,θ+4π,…, gives a sequence of polarization fields, called the stroboscopic sequence. We show, by using the Birkhoff ergodic theorem, that under very general conditions the Cesàro averages of that sequence converge almost everywhere on phase space to a polarization field which is 2π-periodic in time. This fulfills the main aim of this paper in that it demonstrates that the tracking algorithm for stroboscopic averaging, encoded in the program SPRINT and used in the study of spin motion in storage rings, is mathematically well-founded. The machinery developed is also shown to work for the stroboscopic average of phase space densities associated with the orbital dynamics. This yields a large family of periodic phase space densities and, as an example, a quite detailed analysis of the so-called betatron motion in a storage ring is presented.

  15. 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.

  16. Geometric ergodicity of a hybrid sampler for Bayesian inference of phylogenetic branch lengths.

    PubMed

    Spade, David A; Herbei, Radu; Kubatko, Laura S

    2015-10-01

    One of the fundamental goals in phylogenetics is to make inferences about the evolutionary pattern among a group of individuals, such as genes or species, using present-day genetic material. This pattern is represented by a phylogenetic tree, and as computational methods have caught up to the statistical theory, Bayesian methods of making inferences about phylogenetic trees have become increasingly popular. Bayesian inference of phylogenetic trees requires sampling from intractable probability distributions. Common methods of sampling from these distributions include Markov chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC) methods, and one way that both of these methods can proceed is by first simulating a tree topology and then taking a sample from the posterior distribution of the branch lengths given the tree topology and the data set. In many MCMC methods, it is difficult to verify that the underlying Markov chain is geometrically ergodic, and thus, it is necessary to rely on output-based convergence diagnostics in order to assess convergence on an ad hoc basis. These diagnostics suffer from several important limitations, so in an effort to circumvent these limitations, this work establishes geometric convergence for a particular Markov chain that is used to sample branch lengths under a fairly general class of nucleotide substitution models and provides a numerical method for estimating the time this Markov chain takes to converge.

  17. Ergodicity breaking and wave-function statistics in disordered interacting systems

    SciTech Connect

    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.

  18. Channel characterization and empirical model for ergodic capacity of free-space optical communication link

    NASA Astrophysics Data System (ADS)

    Alimi, Isiaka; Shahpari, Ali; Ribeiro, Vítor; Sousa, Artur; Monteiro, Paulo; Teixeira, António

    2017-05-01

    In this paper, we present experimental results on channel characterization of single input single output (SISO) free-space optical (FSO) communication link that is based on channel measurements. The histograms of the FSO channel samples and the log-normal distribution fittings are presented along with the measured scintillation index. Furthermore, we extend our studies to diversity schemes and propose a closed-form expression for determining ergodic channel capacity of multiple input multiple output (MIMO) FSO communication systems over atmospheric turbulence fading channels. The proposed empirical model is based on SISO FSO channel characterization. Also, the scintillation effects on the system performance are analyzed and results for different turbulence conditions are presented. Moreover, we observed that the histograms of the FSO channel samples that we collected from a 1548.51 nm link have good fits with log-normal distributions and the proposed model for MIMO FSO channel capacity is in conformity with the simulation results in terms of normalized mean-square error (NMSE).

  19. Heat capacity, enthalpy fluctuations, and configurational entropy in broken ergodic systems.

    PubMed

    Mauro, John C; Loucks, Roger J; Sen, Sabyasachi

    2010-10-28

    A common assumption in the glass science community is that the entropy of a glass can be calculated by integration of measured heat capacity curves through the glass transition. Such integration assumes that glass is an equilibrium material and that the glass transition is a reversible process. However, as a nonequilibrium and nonergodic material, the equations from equilibrium thermodynamics are not directly applicable to the glassy state. Here we investigate the connection between heat capacity and configurational entropy in broken ergodic systems such as glass. We show that it is not possible, in general, to calculate the entropy of a glass from heat capacity curves alone, since additional information must be known related to the details of microscopic fluctuations. Our analysis demonstrates that a time-average formalism is essential to account correctly for the experimentally observed dependence of thermodynamic properties on observation time, e.g., in specific heat spectroscopy. This result serves as experimental and theoretical proof for the nonexistence of residual glass entropy at absolute zero temperature. Example measurements are shown for Corning code 7059 glass.

  20. Ergodicity breaking, ageing, and confinement in generalized diffusion processes with position and time dependent diffusivity

    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.

  1. Harmonic Analysis on Quantum Tori

    NASA Astrophysics Data System (ADS)

    Chen, Zeqian; Xu, Quanhua; Yin, Zhi

    2013-09-01

    This paper is devoted to the study of harmonic analysis on quantum tori. We consider several summation methods on these tori, including the square Fejér means, square and circular Poisson means, and Bochner-Riesz means. We first establish the maximal inequalities for these means, then obtain the corresponding pointwise convergence theorems. In particular, we prove the noncommutative analogue of the classical Stein theorem on Bochner-Riesz means. The second part of the paper deals with Fourier multipliers on quantum tori. We prove that the completely bounded L p Fourier multipliers on a quantum torus are exactly those on the classical torus of the same dimension. Finally, we present the Littlewood-Paley theory associated with the circular Poisson semigroup on quantum tori. We show that the Hardy spaces in this setting possess the usual properties of Hardy spaces, as one can expect. These include the quantum torus analogue of Fefferman's H1-BMO duality theorem and interpolation theorems. Our analysis is based on the recent developments of noncommutative martingale/ergodic inequalities and Littlewood-Paley-Stein theory.

  2. 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

  3. Ergodicity and model quality in template-restrained canonical and temperature/Hamiltonian replica exchange coarse-grained molecular dynamics simulations of proteins.

    PubMed

    Karczyńska, Agnieszka S; Czaplewski, Cezary; Krupa, Paweł; Mozolewska, Magdalena A; Joo, Keehyoung; Lee, Jooyoung; Liwo, Adam

    2017-09-22

    Molecular simulations restrained to single or multiple templates are commonly used in protein-structure modeling. However, the restraints introduce additional barriers, thus impairing the ergodicity of simulations, which can affect the quality of the resulting models. In this work, the effect of restraint types and simulation schemes on ergodicity and model quality was investigated by performing template-restrained canonical molecular dynamics (MD), multiplexed replica-exchange molecular dynamics, and Hamiltonian replica exchange molecular dynamics (HREMD) simulations with the coarse-grained UNRES force field on nine selected proteins, with pseudo-harmonic log-Gaussian (unbounded) or Lorentzian (bounded) restraint functions. The best ergodicity was exhibited by HREMD. It has been found that non-ergodicity does not affect model quality if good templates are used to generate restraints. However, when poor-quality restraints not covering the entire protein are used, the improved ergodicity of HREMD can lead to significantly improved protein models. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

  4. Analyzing the dynamics of cell cycle processes from fixed samples through ergodic principles.

    PubMed

    Wheeler, Richard John

    2015-11-05

    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. © 2015 Wheeler. This article is distributed by The American Society for Cell Biology under license from the author(s). Two months after publication it is available to the public under an Attribution–Noncommercial–Share Alike 3.0 Unported Creative Commons License (http://creativecommons.org/licenses/by-nc-sa/3.0).

  5. Modeling of neutral pressure and pumping in the Tore Supra ergodic divertor and outboard pump limiter

    NASA Astrophysics Data System (ADS)

    Owen, L. W.; Loarer, T.; Grosman, A.; Meslin, B.; Klepper, C. C.; Mioduszewski, P. K.; Uckan, T.

    1997-02-01

    Active control of the core plasma density and partial depletion of the wall particle content have been achieved in experiments on Tore Supra with the plasma leaning on either the ergodic divertor (ED) or the pump limiters. Measurements of neutral pressures in the ED and outboard pump limiter (OPL) are modeled with 1D parallel transport equations (continuity and momentum balance) for the SOL plasma coupled to 2D neutral particle transport simulations. SOL density and temperature profiles from reciprocating Langmuir probe measurements for a range of volume-averaged densities are renormalized, where necessary, to agree with Langmuir probe measurements in the OPL throat and constitute the upstream boundary conditions for the 1D calculations. Good agreement with measured pressures and exhaust rates are obtained for both the ED and OPL in scans that span a factor of 2-3 in volume-averaged density. The importance of a self-consistent treatment of the plasma and neutral particle transport in the neighborhood of the neutralizer plate is demonstrated, particularly in the stronger recycling regimes characteristic of densities at the high end of the scans. Plasma flow reversal near the plasma/plenum interface is predicted to occur at the higher densities due to the large local ionization source. Predictions of pressure buildup in the plenum behind the prototype vented neutralizer plate agree with experiment if it is assumed that both the tops and partially the sides of the needles comprising the plate are wetted by the plasma. A discharge in which the ED pumps are active is analyzed; the calculated pressure and exhaust rate agree with experiment. The core fueling rate is the same as without pumping, suggesting, as is seen in the experiment, a small density decay rate and significant wall particle depletion.

  6. Bistability, non-ergodicity, and inhibition in pairwise maximum-entropy models.

    PubMed

    Rostami, Vahid; Porta Mana, PierGianLuca; Grün, Sonja; Helias, Moritz

    2017-10-02

    Pairwise maximum-entropy models have been used in neuroscience to predict the activity of neuronal populations, given only the time-averaged correlations of the neuron activities. This paper provides evidence that the pairwise model, applied to experimental recordings, would produce a bimodal distribution for the population-averaged activity, and for some population sizes the second mode would peak at high activities, that experimentally would be equivalent to 90% of the neuron population active within time-windows of few milliseconds. Several problems are connected with this bimodality: 1. The presence of the high-activity mode is unrealistic in view of observed neuronal activity and on neurobiological grounds. 2. Boltzmann learning becomes non-ergodic, hence the pairwise maximum-entropy distribution cannot be found: in fact, Boltzmann learning would produce an incorrect distribution; similarly, common variants of mean-field approximations also produce an incorrect distribution. 3. The Glauber dynamics associated with the model is unrealistically bistable and cannot be used to generate realistic surrogate data. This bimodality problem is first demonstrated for an experimental dataset from 159 neurons in the motor cortex of macaque monkey. Evidence is then provided that this problem affects typical neural recordings of population sizes of a couple of hundreds or more neurons. The cause of the bimodality problem is identified as the inability of standard maximum-entropy distributions with a uniform reference measure to model neuronal inhibition. To eliminate this problem a modified maximum-entropy model is presented, which reflects a basic effect of inhibition in the form of a simple but non-uniform reference measure. This model does not lead to unrealistic bimodalities, can be found with Boltzmann learning, and has an associated Glauber dynamics which incorporates a minimal asymmetric inhibition.

  7. Quantum chaotic dynamics and random polynomials

    SciTech Connect

    Bogomolny, E.; Bohigas, O.; Leboeuf, P.

    1996-12-01

    We investigate the distribution of roots of polynomials of high degree with random coefficients which, among others, appear naturally in the context of {open_quotes}quantum chaotic dynamics.{close_quotes} It is shown that under quite general conditions their roots tend to concentrate near the unit circle in the complex plane. In order to further increase this tendency, we study in detail the particular case of self-inversive random polynomials and show that for them a finite portion of all roots lies exactly on the unit circle. Correlation functions of these roots are also computed analytically, and compared to the correlations of eigenvalues of random matrices. The problem of ergodicity of chaotic wavefunctions is also considered. For that purpose we introduce a family of random polynomials whose roots spread uniformly over phase space. While these results are consistent with random matrix theory predictions, they provide a new and different insight into the problem of quantum ergodicity Special attention is devoted to the role of symmetries in the distribution of roots of random polynomials.

  8. Comment on "Heat capacity, enthalpy fluctuations, and configurational entropy in broken ergodic systems" [J. Chem. Phys. 133, 164503 (2010)].

    PubMed

    Johari, G P

    2011-04-14

    A critical examination shows that the specific heat and shear modulus relaxation spectra do not support the notions of continuously broken ergodicity and loss of configurational contribution on isothermal glass transition, nor does the long-known result that C(p) → 0 as T → 0 K prove that S(conf) → 0. Spectra show variation of the real and imaginary components due to phase lag and not due to loss of configurational degrees of freedom. The high-frequency shear modulus, G(∞), of glass increases with time as its fictive temperature decreases and dG(∞)∕dT decreases when a glass forms.

  9. Response to 'Comment on 'Heat capacity, enthalpy fluctuations, and configurational entropy in broken ergodic systems'' [J. Chem. Phys. 134, 147101 (2011)

    SciTech Connect

    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.

  10. A Parallel Quantum Computer Simulator

    DTIC Science & Technology

    2016-09-01

    The unique principles of quantum mechanics may one day enable computers to perform operations that would be impossible on a classical computer...Although no one knows whether it will be possible to build a large-scale, functional, and stable quantum computer, researchers can study quantum- mechanical

  11. 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.

  12. Multifractality of eigenstates in the delocalized non-ergodic phase of some random matrix models: Wigner-Weisskopf approach

    NASA Astrophysics Data System (ADS)

    Monthus, Cécile

    2017-07-01

    The delocalized non-ergodic phase existing in some random N × N matrix models is analyzed via the Wigner-Weisskopf approximation for the dynamics from an initial site j 0. The main output of this approach is the inverse Γj_0(N) of the characteristic time to leave the state j 0 that provides some broadening Γj_0(N) for the weights of the eigenvectors. In this framework, the localized phase corresponds to the region where the broadening Γj_0(N) is smaller in scaling than the level spacing Δj_0(N) \\propto \\frac{1}{N} , while the delocalized non-ergodic phase corresponds to the region where the broadening Γj_0(N) decays with N but is bigger in scaling than the level spacing Δj_0(N) . Then the number \\fracΓj_0(N)}{Δj_0(N)} of resonances grows only sub-extensively in N. This approach allows to recover the multifractal spectrum of the Generalized-Rosenzweig-Potter (GRP) Matrix model (Kravtsov et al 2015 New. J. Phys. 17 122 002). We then consider the Lévy generalization of the GRP Matrix model, where the off-diagonal matrix elements are drawn with an heavy-tailed distribution of Lévy index 1<μ<2 : the dynamics is then governed by a stretched exponential of exponent β=\\frac{2 (μ-1)}{μ and the multifractal properties of eigenstates are explicitly computed.

  13. The Equivalence of Dissipation from Gibbs’ Entropy Production with Phase-Volume Loss in Ergodic Heat-Conducting Oscillators

    NASA Astrophysics Data System (ADS)

    Patra, Puneet Kumar; Hoover, William Graham; Hoover, Carol Griswold; Sprott, Julien Clinton

    Gibbs’ thermodynamic entropy is given by the logarithm of the phase volume, which itself responds to heat transfer to and from thermal reservoirs. We compare the thermodynamic dissipation described by (i) phase-volume loss with (ii) heat-transfer entropy production. Their equivalence is documented for computer simulations of the response of an ergodic harmonic oscillator to thermostated temperature gradients. In the simulations one or two thermostat variables control the kinetic energy or the kinetic energy and its fluctuation. All of the motion equations are time-reversible. We consider both strong and weak control variables. In every case, the time-averaged dissipative loss of phase-space volume coincides with the entropy produced by heat transfer. Linear-response theory nicely reproduces the small-gradient results obtained by computer simulation. The thermostats considered here are ergodic and provide simple dynamical models, some of them with as few as three ordinary differential equations, while remaining capable of reproducing Gibbs’ canonical phase-space distribution and are precisely consistent with irreversible thermodynamics.

  14. The Shannon's mutual information of a multiple antenna time and frequency dependent channel: An ergodic operator approach

    NASA Astrophysics Data System (ADS)

    Hachem, Walid; Moustakas, Aris; Pastur, Leonid A.

    2015-11-01

    Consider a random non-centered multiple antenna radio transmission channel. Assume that the deterministic part of the channel is itself frequency selective and that the random multipath part is represented by an ergodic stationary vector process. In the Hilbert space l2(ℤ), one can associate to this channel a random ergodic self-adjoint operator having a so-called Integrated Density of States (IDS). Shannon's mutual information per receive antenna of this channel coincides then with the integral of a log function with respect to the IDS. In this paper, it is shown that when the numbers of antennas at the transmitter and at the receiver tend to infinity at the same rate, the mutual information per receive antenna tends to a quantity that can be identified and, in fact, is closely related to that obtained within the random matrix approach [I. Telatar, Eur. Trans. Telecommun. 10, 585 (1999)]. This result can be obtained by analyzing the behavior of the Stieltjes transform of the IDS in the regime of the large numbers of antennas.

  15. Persistent non-ergodic fluctuations in mesoscopic insulators: The NSS model in the unitary and symplectic ensembles

    NASA Astrophysics Data System (ADS)

    Rangel, R.; Medina, E.

    2002-11-01

    We give a detailed picture of the mesoscopic conductance fluctuations in the deep insulating regime (DIR) within the Nguyen, Spivak and Shklovskii model in the unitary and symplectic ensembles. Slutski's theorem is invoked to rigorously state the ergodic problem for conductance fluctuations in the DIR, in contrast with previous studies. A weakly decaying behavior of the log-conductance correlation function, even weaker when spin-orbit scatterers are included, is established on the relevant field scale of the model. Such a slow decay implies that the stochastic process, defined by the fluctuations of the log-conductance, is non-ergodic in the mean square sense in the ensembles with the reported symmetries. The results can be interpreted in terms of the effective number of samples within the available magnetic scale. Using the replica approach, we derive the strong localisation counterparts of the well known `cooperon' and `diffuson' which permit analyzing quantitatively the decaying behavior of the correlation function and reveal its symmetry related properties in agreement with the numerical results.

  16. Unique Access to Learning

    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,…

  17. Akhenaten, a unique pharaoh.

    PubMed

    Retief, François Pieter; Cilliers, Louise

    2011-09-05

    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.

  18. Unique Access to Learning

    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,…

  19. Unique oxide overcoating of CuInS2/ZnS core/shell quantum dots with ZnGa2O4 for fabrication of white light-emitting diode with improved operational stability

    NASA Astrophysics Data System (ADS)

    Song, Woo-Seuk; Jang, Eun-Pyo; Kim, Jong-Hoon; Jang, Ho Seong; Yang, Heesun

    2013-02-01

    CuInS2 quantum dots (QDs) have been recently highlighted as blue-to-yellow color converters for the demonstration of QD-based white light-emitting diodes (LEDs) owing to their advantageous fluorescent attributes including a broadband yellow emission and exceptional quantum yield. Similar to other types of elaborate core/shell structured QDs, however, core/shell QDs of CuInS2/ZnS are also susceptible to the photo-induced degradation, rendering them inappropriate for the practical application to high operational stability white LED. In this study, CuInS2/ZnS QDs are overcoated with the unprecedented oxide phase of ZnGa2O4 to enhance their photostability, and the resulting CuInS2/ZnS/ZnGa2O4 QDs are characterized with X-ray diffraction and transmission electron microscope. The operational stability test of CuInS2/ZnS/ZnGa2O4 QD-based white LED is performed and compared with that of uncoated CuInS2/ZnS QD-based one, and the efficacy of ZnGa2O4 overlayer is proved in mitigating the photodegradation of QDs and thus improving the device stability.

  20. 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.

  1. Uniquely human social cognition.

    PubMed

    Saxe, Rebecca

    2006-04-01

    Recent data identify distinct components of social cognition associated with five brain regions. In posterior temporal cortex, the extrastriate body area is associated with perceiving the form of other human bodies. A nearby region in the posterior superior temporal sulcus is involved in interpreting the motions of a human body in terms of goals. A distinct region at the temporo-parietal junction supports the uniquely human ability to reason about the contents of mental states. Medial prefrontal cortex is divided into at least two subregions. Ventral medial prefrontal cortex is implicated in emotional empathy, whereas dorsal medial prefrontal cortex is implicated in the uniquely human representation of triadic relations between two minds and an object, supporting shared attention and collaborative goals.

  2. Entanglement dynamics in quantum many-body systems

    NASA Astrophysics Data System (ADS)

    Ho, Wen Wei; Abanin, Dmitry A.

    2017-03-01

    The dynamics of entanglement has recently been realized as a useful probe in studying ergodicity and its breakdown in quantum many-body systems. In this paper, we study theoretically the growth of entanglement in quantum many-body systems and propose a method to measure it experimentally. We show that entanglement growth is related to the spreading of local operators in real space. We present a simple toy model for ergodic systems in which linear spreading of operators results in a universal, linear-in-time growth of entanglement for initial product states, in contrast with the logarithmic growth of entanglement in many-body localized (MBL) systems. Furthermore, we show that entanglement growth is directly related to the decay of the Loschmidt echo in a composite system comprised of several copies of the original system, in which connections are controlled by a quantum switch (two-level system). By measuring only the switch's dynamics, the growth of the Rényi entropies can be extracted. Our work provides a way of understanding entanglement dynamics in many-body systems and to directly measure its growth in time via a single local measurement.

  3. Quantum rendering

    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.

  4. Extended quantum U(1)-liquid phase in a three-dimensional quantum dimer model

    SciTech Connect

    Sikora, Olga; Shannon, Nic; Pollmann, Frank; Penc, Karlo; Fulde, Peter

    2011-09-15

    Recently, quantum dimer models have attracted a great deal of interest as a paradigm for the study of exotic quantum phases. Much of this excitement has centered on the claim that a certain class of quantum dimer model can support a quantum U(1)-liquid phase with deconfined fractional excitations in three dimensions. These fractional monomer excitations are quantum analogs of the magnetic monopoles found in spin ice. In this paper, we use extensive quantum Monte Carlo simulations to establish the ground-state phase diagram of the quantum dimer model on the three-dimensional diamond lattice as a function of the ratio {mu} of the potential to kinetic-energy terms in the Hamiltonian. We find that, for {mu}{sub c}=0.75{+-}0.02, the model undergoes a first-order quantum phase transition from an ordered ''R state'' into an extended quantum U(1)-liquid phase, which terminates in a quantum critical Rokhsar-Kivelson (RK) point for {mu}=1. This confirms the published field-theoretical scenario. We present detailed evidence for the existence of the U(1)-liquid phase and indirect evidence for the existence of its photon and monopole excitations. Simulations are benchmarked against a variety of exact and perturbative results, and a comparison is made of different variational wave functions. We also explore the ergodicity of the quantum dimer model on a diamond lattice within a given flux sector, identifying a new conserved quantity related to transition graphs of dimer configurations. These results complete and extend the previous analysis of O. Sikora et al.[Phys. Rev. Lett. 103, 247001 (2009)].

  5. Topological order, entanglement, and quantum memory at finite temperature

    SciTech Connect

    Mazac, Dalimil Hamma, Alioscia

    2012-09-15

    We compute the topological entropy of the toric code models in arbitrary dimension at finite temperature. We find that the critical temperatures for the existence of full quantum (classical) topological entropy correspond to the confinement-deconfinement transitions in the corresponding Z{sub 2} gauge theories. This implies that the thermal stability of topological entropy corresponds to the stability of quantum (classical) memory. The implications for the understanding of ergodicity breaking in topological phases are discussed. - Highlights: Black-Right-Pointing-Pointer We calculate the topological entropy of a general toric code in any dimension. Black-Right-Pointing-Pointer We find phase transitions in the topological entropy. Black-Right-Pointing-Pointer The phase transitions coincide with the appearance of quantum/classical memory.

  6. Quantum Approach to Informatics

    NASA Astrophysics Data System (ADS)

    Stenholm, Stig; Suominen, Kalle-Antti

    2005-08-01

    An essential overview of quantum information Information, whether inscribed as a mark on a stone tablet or encoded as a magnetic domain on a hard drive, must be stored in a physical object and thus made subject to the laws of physics. Traditionally, information processing such as computation occurred in a framework governed by laws of classical physics. However, information can also be stored and processed using the states of matter described by non-classical quantum theory. Understanding this quantum information, a fundamentally different type of information, has been a major project of physicists and information theorists in recent years, and recent experimental research has started to yield promising results. Quantum Approach to Informatics fills the need for a concise introduction to this burgeoning new field, offering an intuitive approach for readers in both the physics and information science communities, as well as in related fields. Only a basic background in quantum theory is required, and the text keeps the focus on bringing this theory to bear on contemporary informatics. Instead of proofs and other highly formal structures, detailed examples present the material, making this a uniquely accessible introduction to quantum informatics. Topics covered include: * An introduction to quantum information and the qubit * Concepts and methods of quantum theory important for informatics * The application of information concepts to quantum physics * Quantum information processing and computing * Quantum gates * Error correction using quantum-based methods * Physical realizations of quantum computing circuits A helpful and economical resource for understanding this exciting new application of quantum theory to informatics, Quantum Approach to Informatics provides students and researchers in physics and information science, as well as other interested readers with some scientific background, with an essential overview of the field.

  7. NASA's unique networking environment

    NASA Technical Reports Server (NTRS)

    Johnson, Marjory J.

    1988-01-01

    Networking is an infrastructure technology; it is a tool for NASA to support its space and aeronautics missions. Some of NASA's networking problems are shared by the commercial and/or military communities, and can be solved by working with these communities. However, some of NASA's networking problems are unique and will not be addressed by these other communities. Individual characteristics of NASA's space-mission networking enviroment are examined, the combination of all these characteristics that distinguish NASA's networking systems from either commercial or military systems is explained, and some research areas that are important for NASA to pursue are outlined.

  8. Symbolic transfer entropy rate is equal to transfer entropy rate for bivariate finite-alphabet stationary ergodic Markov processes

    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.

  9. On the ergodicity of supercooled molecular glass-forming liquids at the dynamical arrest: the o-terphenyl case

    PubMed Central

    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

  10. On the ergodicity of supercooled molecular glass-forming liquids at the dynamical arrest: the o-terphenyl case.

    PubMed

    Mallamace, Francesco; Corsaro, Carmelo; Leone, Nancy; Villari, Valentina; Micali, Norberto; Chen, Sow-Hsin

    2014-01-17

    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.

  11. On the ergodicity of supercooled molecular glass-forming liquids at the dynamical arrest: the o-terphenyl case

    NASA Astrophysics Data System (ADS)

    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.

  12. Moments distributions of single dye molecule spectra in a low-temperature polymer: Analysis of system ergodicity

    NASA Astrophysics Data System (ADS)

    Anikushina, T. A.; Naumov, A. V.

    2013-12-01

    This article demonstrates the principal advantages of the technique for analysis of the long-term spectral evolution of single molecules (SM) in the study of the microscopic nature of the dynamic processes in low-temperature polymers. We performed the detailed analysis of the spectral trail of single tetra-tert-butylterrylene (TBT) molecule in an amorphous polyisobutylene matrix, measured over 5 hours at T = 7K. It has been shown that the slow temporal dynamics is in qualitative agreement with the standard model of two-level systems and stochastic sudden-jump model. At the same time the distributions of the first four moments (cumulants) of the spectra of the selected SM measured at different time points were found not consistent with the standard theory prediction. It was considered as evidence that in a given time interval the system is not ergodic

  13. Production model in the conditions of unstable demand taking into account the influence of trading infrastructure: Ergodicity and its application

    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.

  14. TRIQS/CTHYB: A continuous-time quantum Monte Carlo hybridisation expansion solver for quantum impurity problems

    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.

  15. Equilibrium statistical mechanics for self-gravitating systems: local ergodicity and extended Boltzmann-Gibbs/White-Narayan statistics

    NASA Astrophysics Data System (ADS)

    He, Ping

    2012-01-01

    The long-standing puzzle surrounding the statistical mechanics of self-gravitating systems has not yet been solved successfully. We formulate a systematic theoretical framework of entropy-based statistical mechanics for spherically symmetric collisionless self-gravitating systems. We use an approach that is very different from that of the conventional statistical mechanics of short-range interaction systems. We demonstrate that the equilibrium states of self-gravitating systems consist of both mechanical and statistical equilibria, with the former characterized by a series of velocity-moment equations and the latter by statistical equilibrium equations, which should be derived from the entropy principle. The velocity-moment equations of all orders are derived from the steady-state collisionless Boltzmann equation. We point out that the ergodicity is invalid for the whole self-gravitating system, but it can be re-established locally. Based on the local ergodicity, using Fermi-Dirac-like statistics, with the non-degenerate condition and the spatial independence of the local microstates, we rederive the Boltzmann-Gibbs entropy. This is consistent with the validity of the collisionless Boltzmann equation, and should be the correct entropy form for collisionless self-gravitating systems. Apart from the usual constraints of mass and energy conservation, we demonstrate that the series of moment or virialization equations must be included as additional constraints on the entropy functional when performing the variational calculus; this is an extension to the original prescription by White & Narayan. Any possible velocity distribution can be produced by the statistical-mechanical approach that we have developed with the extended Boltzmann-Gibbs/White-Narayan statistics. Finally, we discuss the questions of negative specific heat and ensemble inequivalence for self-gravitating systems.

  16. Ideal quantum glass transitions: Many-body localization without quenched disorder

    SciTech Connect

    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.

  17. Is Life Unique?

    PubMed Central

    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

  18. Unique stoichiometric representation for computational thermochemistry.

    PubMed

    Fishtik, Ilie

    2012-02-23

    Evaluation of the enthalpy of formation of species via quantum chemical methods, as well as the evaluation of their performance, is mainly based on single reaction schemes, i.e., reaction schemes that involve a minimal number of reference species where minimal means that, if a reference species is omitted, there is no way to write a balanced reaction scheme involving the remaining species. When the number of reference species exceeds the minimal number, the main problem of computational thermochemistry is inevitably becoming an optimization problem. In this communication we present an exact and unique solution of the optimization problem in computational thermochemistry along with a stoichiometric interpretation of the solution. Namely, we prove that the optimization problem may be identically solved by enumerating a finite and unique set of reactions referred to as group additivity (GA) response reactions (RERs). © 2012 American Chemical Society

  19. Quantum stochastic calculus associated with quadratic quantum noises

    SciTech Connect

    Ji, Un Cig; Sinha, Kalyan B.

    2016-02-15

    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.

  20. 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.

  1. 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

  2. Ergodicity of stochastic 2D Navier-Stokes equation with Lévy noise

    NASA Astrophysics Data System (ADS)

    Dong, Zhao; Xie, Yingchao

    In this paper we deal with the 2D Navier-Stokes equation perturbed by a Lévy noise force whose white noise part is non-degenerate and that the intensity measure of Poisson measure is σ-finite. Existence and uniqueness of invariant measure for this equation is obtained, two main properties of the Markov semigroup associated with this equation are proved. In other words, strong Feller property and irreducibility hold in the same space.

  3. Quantum computing

    PubMed Central

    Li, Shu-Shen; Long, Gui-Lu; Bai, Feng-Shan; Feng, Song-Lin; Zheng, Hou-Zhi

    2001-01-01

    Quantum computing is a quickly growing research field. This article introduces the basic concepts of quantum computing, recent developments in quantum searching, and decoherence in a possible quantum dot realization. PMID:11562459

  4. Ergodic capacity and outage capacity analysis for multiple-input single-output free-space optical communications over composite channels

    NASA Astrophysics Data System (ADS)

    Wang, Jin-Yuan; Wang, Jun-Bo; Chen, Ming; Huang, Nuo; Jia, Lin-Qiong; Guan, Rui

    2014-01-01

    Free-space optical (FSO) communications have attracted significant attention recently. The ergodic capacity and outage capacity of a multiple-input single-output FSO communication system are investigated. Initially, a composite channel model including distance-dependant atmospheric loss, pointing error, and atmospheric turbulence is derived. To show different weather conditions, both the weak and strong atmospheric turbulence conditions are taken into account. Moreover, the statistical characteristics of two composite channels (i.e., weak turbulence composite channels and strong turbulence composite channels) are provided. Furthermore, approximated expressions of the ergodic capacity and closed-form expressions of the outage capacity are derived under the two composite channels, respectively. Numerical results finally substantiate that the derived theoretical expressions can provide a very good approximation to the simulation results.

  5. Ergodic channel capacity of spatial correlated multiple-input multiple-output free space optical links using multipulse pulse-position modulation

    NASA Astrophysics Data System (ADS)

    Wang, Huiqin; Wang, Xue; Cao, Minghua

    2017-02-01

    The spatial correlation extensively exists in the multiple-input multiple-output (MIMO) free space optical (FSO) communication systems due to the channel fading and the antenna space limitation. Wilkinson's method was utilized to investigate the impact of spatial correlation on the MIMO FSO communication system employing multipulse pulse-position modulation. Simulation results show that the existence of spatial correlation reduces the ergodic channel capacity, and the reception diversity is more competent to resist this kind of performance degradation.

  6. Jordan Algebraic Quantum Categories

    NASA Astrophysics Data System (ADS)

    Graydon, Matthew; Barnum, Howard; Ududec, Cozmin; Wilce, Alexander

    2015-03-01

    State cones in orthodox quantum theory over finite dimensional complex Hilbert spaces enjoy two particularly essential features: homogeneity and self-duality. Orthodox quantum theory is not, however, unique in that regard. Indeed, all finite dimensional formally real Jordan algebras -- arenas for generalized quantum theories with close algebraic kinship to the orthodox theory -- admit homogeneous self-dual positive cones. We construct categories wherein these theories are unified. The structure of composite systems is cast from universal tensor products of the universal C*-algebras enveloping ambient spaces for the constituent state cones. We develop, in particular, a notion of composition that preserves the local distinction of constituent systems in quaternionic quantum theory. More generally, we explicitly derive the structure of hybrid quantum composites with subsystems of arbitrary Jordan algebraic type.

  7. Is quantum mechanics exact?

    SciTech Connect

    Kapustin, Anton

    2013-06-15

    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.

  8. Transforming quantum operations: Quantum supermaps

    NASA Astrophysics Data System (ADS)

    Chiribella, G.; D'Ariano, G. M.; Perinotti, P.

    2008-08-01

    We introduce the concept of quantum supermap, describing the most general transformation that maps an input quantum operation into an output quantum operation. Since quantum operations include as special cases quantum states, effects, and measurements, quantum supermaps describe all possible transformations between elementary quantum objects (quantum systems as well as quantum devices). After giving the axiomatic definition of supermap, we prove a realization theorem, which shows that any supermap can be physically implemented as a simple quantum circuit. Applications to quantum programming, cloning, discrimination, estimation, information-disturbance trade-off, and tomography of channels are outlined.

  9. Edwards thermodynamics of the jamming transition for frictionless packings: Ergodicity test and role of angoricity and compactivity

    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

  10. Geometrical dependence of quantum decoherence in circular arenas with side-wires

    NASA Astrophysics Data System (ADS)

    Xie, Yuantao; Le Priol, Clément; Heremans, Jean J.

    2016-12-01

    Low-temperature quantum phase coherence lengths were experimentally measured in mesoscopic circular arenas fabricated on InGaAs quantum wells. The arenas are connected to wide sample regions by short side-wires, to investigate the effects of geometry in comparison to intrinsic materials properties on quantum decoherence. Universal conductance fluctuations were used to quantify the phase coherence lengths as a function of temperature and geometry. The experimental data show a dependence of phase coherence lengths on side-wire length and width-to-length ratio, which is accounted for by the competing effects of decoherence by coupling to the classical environment and Nyquist decoherence in ergodic wires. The observed decay of phase coherence lengths with the increasing temperature is consistent with expectations. The work demonstrates that geometrical effects influence the measured mesoscopic quantum decoherence.

  11. Some characterizations of unique extremality

    NASA Astrophysics Data System (ADS)

    Yao, Guowu

    2008-07-01

    In this paper, it is shown that some necessary characteristic conditions for unique extremality obtained by Zhu and Chen are also sufficient and some sufficient ones by them actually imply that the uniquely extremal Beltrami differentials have a constant modulus. In addition, some local properties of uniquely extremal Beltrami differentials are given.

  12. Quantum leaps, bit by bit

    NASA Astrophysics Data System (ADS)

    Trabesinger, Andreas

    2017-03-01

    The promises of quantum computation are unique -- and so are the challenges. Progress in physics, mathematics, computer science and engineering have brought quantum computers to a point where they start to challenge their classical counterparts. By Andreas Trabesinger; illustration by Visual Science.

  13. 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…

  14. 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…

  15. Connected components of irreducible maps and 1D quantum phases

    SciTech Connect

    Szehr, Oleg; Wolf, Michael M.

    2016-08-15

    We investigate elementary topological properties of sets of completely positive (CP) maps that arise in quantum Perron-Frobenius theory. We prove that the set of primitive CP maps of fixed Kraus rank is path-connected and we provide a complete classification of the connected components of irreducible CP maps at given Kraus rank and fixed peripheral spectrum in terms of a multiplicity index. These findings are then applied to analyse 1D quantum phases by studying equivalence classes of translational invariant matrix product states that correspond to the connected components of the respective CP maps. Our results extend the previously obtained picture in that they do not require blocking of physical sites, they lead to analytic paths, and they allow us to decompose into ergodic components and to study the breaking of translational symmetry.

  16. Transition from distributional to ergodic behavior in an inhomogeneous diffusion process: Method revealing an unknown surface diffusivity.

    PubMed

    Akimoto, Takuma; Seki, Kazuhiko

    2015-08-01

    Diffusion of molecules in cells plays an important role in providing a biological reaction on the surface by finding a target on the membrane surface. The water retardation (slow diffusion) near the target assists the searching molecules to recognize the target. Here, we consider effects of the surface diffusivity on the effective diffusivity, where diffusion on the surface is slower than that in bulk. We show that the ensemble-averaged mean-square displacements increase linearly with time when the desorption rate from the surface is finite, which is valid even when the diffusion on the surface is anomalous (subdiffusion). Moreover, this slow diffusion on the surface affects the fluctuations of the time-averaged mean-square displacements (TAMSDs). We find that fluctuations of the TAMSDs remain large when the measurement time is smaller than a characteristic time, and decays according to an increase of the measurement time for a relatively large measurement time. Therefore, we find a transition from nonergodic (distributional) to ergodic diffusivity in a target search process. Moreover, this fluctuation analysis provides a method to estimate an unknown surface diffusivity.

  17. Ergodicity breaking and conformational hysteresis in the dynamics of a polymer tethered at a surface stagnation point.

    PubMed

    Beck, Victor A; Shaqfeh, Eric S G

    2006-03-07

    We study the dynamics of long chain polymer molecules tethered to a plane wall and subjected to a stagnation point flow. Using a combination of theory and numerical techniques, including Brownian dynamics (BD), we demonstrate that a chain conformation hysteresis exists even for freely draining (FD) chains. Hydrodynamic interactions (HI) between the polymer and the wall are included in the BD simulations. We find qualitative agreement between the FD and HI simulations, with both exhibiting simultaneous coiled and stretched states for a wide range of fixed flow strengths. The range of state coexistence is understood by considering an equivalent projected equilibrium problem of a two state reaction. Using this formalism, we construct Kramers rate theory (from the inverse mean first passage time for a Markov process) for the hopping transition from coil to stretch and stretch to coil. The activation energy for this rate is found to scale proportionally to chain length or Kuhn step number. Thus, in the limit of infinite chain size the hopping rates at a fixed value of the suitably defined Deborah number approach zero and the states are "frozen." We present the results that demonstrate this "ergodicity breaking."

  18. Reducing quasi-ergodic behavior in Monte Carlo simulations by J-walking: Applications to atomic clusters

    NASA Astrophysics Data System (ADS)

    Frantz, D. D.; Freeman, D. L.; Doll, J. D.

    1990-08-01

    A method is introduced that is easy to implement and greatly reduces the systematic error resulting from quasi-ergodicity, or incomplete sampling of configuration space, in Monte Carlo simulations of systems containing large potential energy barriers. The method makes possible the jumping over these barriers by coupling the usual Metropolis sampling to the Boltzmann distribution generated by another random walker at a higher temperature. The basic techniques are illustrated on some simple classical systems, beginning for heuristic purposes with a simple one-dimensional double well potential based on a quartic polynomial. The method's suitability for typical multidimensional Monte Carlo systems is demonstrated by extending the double well potential to several dimensions, and then by applying the method to a multiparticle cluster system consisting of argon atoms bound by pairwise Lennard-Jones potentials. Remarkable improvements are demonstrated in the convergence rate for the cluster configuration energy, and especially for the heat capacity, at temperatures near the cluster melting transition region. Moreover, these improvements can be obtained even in the worst-case scenario where the clusters are initialized from random configurations.

  19. Transition from distributional to ergodic behavior in an inhomogeneous diffusion process: Method revealing an unknown surface diffusivity

    NASA Astrophysics Data System (ADS)

    Akimoto, Takuma; Seki, Kazuhiko

    2015-08-01

    Diffusion of molecules in cells plays an important role in providing a biological reaction on the surface by finding a target on the membrane surface. The water retardation (slow diffusion) near the target assists the searching molecules to recognize the target. Here, we consider effects of the surface diffusivity on the effective diffusivity, where diffusion on the surface is slower than that in bulk. We show that the ensemble-averaged mean-square displacements increase linearly with time when the desorption rate from the surface is finite, which is valid even when the diffusion on the surface is anomalous (subdiffusion). Moreover, this slow diffusion on the surface affects the fluctuations of the time-averaged mean-square displacements (TAMSDs). We find that fluctuations of the TAMSDs remain large when the measurement time is smaller than a characteristic time, and decays according to an increase of the measurement time for a relatively large measurement time. Therefore, we find a transition from nonergodic (distributional) to ergodic diffusivity in a target search process. Moreover, this fluctuation analysis provides a method to estimate an unknown surface diffusivity.

  20. Adaptive schemes for incomplete quantum process tomography

    SciTech Connect

    Teo, Yong Siah; Englert, Berthold-Georg; Rehacek, Jaroslav; Hradil, Zdenek

    2011-12-15

    We propose an iterative algorithm for incomplete quantum process tomography with the help of quantum state estimation. The algorithm, which is based on the combined principles of maximum likelihood and maximum entropy, yields a unique estimator for an unknown quantum process when one has less than a complete set of linearly independent measurement data to specify the quantum process uniquely. We apply this iterative algorithm adaptively in various situations and so optimize the amount of resources required to estimate a quantum process with incomplete data.

  1. Equilibrium energy spectrum of point vortex motion with remarks on ensemble choice and ergodicity

    NASA Astrophysics Data System (ADS)

    Esler, J. G.

    2017-01-01

    The dynamics and statistical mechanics of N chaotically evolving point vortices in the doubly periodic domain are revisited. The selection of the correct microcanonical ensemble for the system is first investigated. The numerical results of Weiss and McWilliams [Phys. Fluids A 3, 835 (1991), 10.1063/1.858014], who argued that the point vortex system with N =6 is nonergodic because of an apparent discrepancy between ensemble averages and dynamical time averages, are shown to be due to an incorrect ensemble definition. When the correct microcanonical ensemble is sampled, accounting for the vortex momentum constraint, time averages obtained from direct numerical simulation agree with ensemble averages within the sampling error of each calculation, i.e., there is no numerical evidence for nonergodicity. Further, in the N →∞ limit it is shown that the vortex momentum no longer constrains the long-time dynamics and therefore that the correct microcanonical ensemble for statistical mechanics is that associated with the entire constant energy hypersurface in phase space. Next, a recently developed technique is used to generate an explicit formula for the density of states function for the system, including for arbitrary distributions of vortex circulations. Exact formulas for the equilibrium energy spectrum, and for the probability density function of the energy in each Fourier mode, are then obtained. Results are compared with a series of direct numerical simulations with N =50 and excellent agreement is found, confirming the relevance of the results for interpretation of quantum and classical two-dimensional turbulence.

  2. Evolution towards ergodic behavior of stationary fractal random processes with memory: application to the study of long-range correlations of nucleotide sequences in DNA

    NASA Astrophysics Data System (ADS)

    Vlad, Marcel Ovidiu; Schönfisch, Birgitt; Mackey, Michael C.

    1996-02-01

    The possible occurrence of ergodic behavior for large times is investigated in the case of stationary random processes with memory. It is shown that for finite times the time average of a state function is generally a random variable and thus two types of cumulants can be introduced: for the time average and for the statistical ensemble, respectively. In the limit of infinite time a transition from the random to the deterministic behavior of the time average may occur, resulting in an ergodic behavior. The conditions of occurrence of this transition are investigated by analyzing the scaling behavior of the cumulants of the time average. A general approach for the computation of these cumulants is developed; explicit computations are presented both for short and long memory in the particular case of separable stationary processes for which the cumulants of a statistical ensemble can be factorized into products of functions depending on binary time differences. In both cases the ergodic behavior emerges for large times provided that the cumulants of a statistical ensemble decrease to zero as the time differences increase to infinity. The analysis leads to the surprising conclusion that the scaling behavior of the cumulants of the time average is relatively insensitive to the type of memory considered: both for short and long memory the cumulants of the time average obey inverse different from zero for large time differences, then the time averaage is random even as the length of the total time interval tends to infinity and the ergodic behavior no longer holds. The theory is applied to the study of long range correlations of nucleotide sequences in DNA; in this case the length t of a sequence of nucleotides plays the role of the time variable. A proportionality relationship is established between the cumulants of the pyrimidine excess in a sequence of length t and the cumulants of the time (length) average of the probability of occurrence of a pyrimidine. It is shown

  3. Is Planck's quantization constant unique?

    NASA Astrophysics Data System (ADS)

    Livadiotis, George

    2016-07-01

    A cornerstone of Quantum Mechanics is the existence of a non-zero least action, the Planck constant. However, the basic concepts and theoretical developments of Quantum Mechanics are independent of its specific numerical value. A different constant h _{*}, similar to the Planck constant h, but ˜12 orders of magnitude larger, characterizes plasmas. The study of >50 different geophysical, space, and laboratory plasmas, provided the first evidence for the universality and the quantum nature of h _{*}, revealing that it is a new quantization constant. The recent results show the diagnostics for determining whether plasmas are characterized by the Planck or the new quantization constant, compounding the challenge to reconcile both quantization constants in quantum mechanics.

  4. 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.

  5. 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. Infact, 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) 2-channel Kondo effect. Except for the relativistic type of phenomena and Kondo effect, the rest depend in a fundamental way on a weak electron correlations that exist in graphene.

  6. 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.

  7. Uniqueness Theorem for Black Objects

    SciTech Connect

    Rogatko, Marek

    2010-06-23

    We shall review the current status of uniqueness theorem for black objects in higher dimensional spacetime. At the beginning we consider static charged asymptotically flat spacelike hypersurface with compact interior with both degenerate and non-degenerate components of the event horizon in n-dimensional spacetime. We gave some remarks concerning partial results in proving uniqueness of stationary axisymmetric multidimensional solutions and winding numbers which can uniquely characterize the topology and symmetry structure of black objects.

  8. Semidirect Products of C*-Quantum Groups: Multiplicative Unitaries Approach

    NASA Astrophysics Data System (ADS)

    Meyer, Ralf; Roy, Sutanu; Woronowicz, Stanisław Lech

    2017-04-01

    C*-quantum groups with projection are the noncommutative analogues of semidirect products of groups. Radford's Theorem about Hopf algebras with projection suggests that any C*-quantum group with projection decomposes uniquely into an ordinary C*-quantum group and a "braided" C*-quantum group. We establish this on the level of manageable multiplicative unitaries.

  9. Weak Ergodicity Breaking of Receptor Motion in Living Cells Stemming from Random Diffusivity

    NASA Astrophysics Data System (ADS)

    Manzo, Carlo; Torreno-Pina, Juan A.; Massignan, Pietro; Lapeyre, Gerald J.; Lewenstein, Maciej; Garcia Parajo, Maria F.

    2015-01-01

    Molecular transport in living systems regulates numerous processes underlying biological function. Although many cellular components exhibit anomalous diffusion, only recently has the subdiffusive motion been associated with nonergodic behavior. These findings have stimulated new questions for their implications in statistical mechanics and cell biology. Is nonergodicity a common strategy shared by living systems? Which physical mechanisms generate it? What are its implications for biological function? Here, we use single-particle tracking to demonstrate that the motion of dendritic cell-specific intercellular adhesion molecule 3-grabbing nonintegrin (DC-SIGN), a receptor with unique pathogen-recognition capabilities, reveals nonergodic subdiffusion on living-cell membranes In contrast to previous studies, this behavior is incompatible with transient immobilization, and, therefore, it cannot be interpreted according to continuous-time random-walk theory. We show that the receptor undergoes changes of diffusivity, consistent with the current view of the cell membrane as a highly dynamic and diverse environment. Simulations based on a model of an ordinary random walk in complex media quantitatively reproduce all our observations, pointing toward diffusion heterogeneity as the cause of DC-SIGN behavior. By studying different receptor mutants, we further correlate receptor motion to its molecular structure, thus establishing a strong link between nonergodicity and biological function. These results underscore the role of disorder in cell membranes and its connection with function regulation. Because of its generality, our approach offers a framework to interpret anomalous transport in other complex media where dynamic heterogeneity might play a major role, such as those found, e.g., in soft condensed matter, geology, and ecology.

  10. Confabulators mistake multiplicity for uniqueness.

    PubMed

    Serra, Mara; La Corte, Valentina; Migliaccio, Raffaella; Brazzarola, Marta; Zannoni, Ilaria; Pradat-Diehl, Pascale; Dalla Barba, Gianfranco

    2014-09-01

    Some patients with organic amnesia show confabulation, the production of statements and actions unintentionally incongruous to the subject's history, present and future situation. It has been shown that confabulators tend to report as unique and specific personal memories, events or actions that belong to their habits and routines (Habits Confabulations). We consider that habits and routines can be characterized by multiplicity, as opposed to uniqueness. This paper examines this phenomenon whereby confabulators mistake multiplicity, i.e., repeated events, for uniqueness, i.e., events that occurred in a unique and specific temporo-spatial context. In order to measure the ability to discriminate unique from repeated events we used four runs of a recognition memory task, in which some items were seen only once at study, whereas others were seen four times. Confabulators, but not non-confabulating amnesiacs (NCA), considered repeated items as unique, thus mistaking multiplicity for uniqueness. This phenomenon has been observed clinically but our study is the first to demonstrate it experimentally. We suggest that a crucial mechanism involved in the production of confabulations is thus the confusion between unique and repeated events.

  11. On the Meaning of Uniqueness

    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…

  12. 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…

  13. On the Meaning of Uniqueness

    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…

  14. Unique Factors Affecting Canadian Education.

    ERIC Educational Resources Information Center

    Farquhar, Robin H.

    In a background statement identifying what is unique about Canada and the issues it currently faces, this paper begins by discussing the concurrent movements toward Canadian nationalism and Quebec nationalism as an illustration of the problems caused by large size and great diversity. It then focuses on unique aspects of Canadian education,…

  15. 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…

  16. Modeling flow and transport in highly heterogeneous three-dimensional aquifers: Ergodicity, Gaussianity, and anomalous behavior—2. Approximate semianalytical solution

    NASA Astrophysics Data System (ADS)

    Fiori, A.; Janković, I.; Dagan, G.

    2006-06-01

    Flow and transport take place in a heterogeneous medium of lognormal distribution of the conductivity K. Flow is uniform in the mean, and the system is defined by U (mean velocity), σY2 (log conductivity variance), and integral scale I. Transport is analyzed in terms of the breakthrough curve of the solute, identical to the traveltime distribution, at control planes at distance x from the source. The "self-consistent" approximation is used, where the traveltime τ is approximated by the sum of τ pertinent to the different separate inclusions, and the neglected interaction between inclusions is accounted for by using the effective conductivity. The pdf f(τ, x), where x is the control plane distance, is derived by a simple convolution. It is found that f(τ, x) has an early arrival time portion that captures most of the mass and a long tail, which is related to the slow solute particles that are trapped in blocks of low K. The macrodispersivity is very large and is independent of x. The tail f(τ, x) is highly skewed, and only for extremely large x/I, depending on σY2, the plume becomes Gaussian. Comparison with numerical simulations shows very good agreement in spite of the absence of parameter fitting. It is found that finite plumes are not ergodic, and a cutoff of f(τ, x) is needed in order to fit the mass flux of a finite plume, depending on σY2 and x/I. The bulk of f(τ, x) can be approximated by a Gaussian shape, with fitted equivalent parameters. The issue of anomalous behavior is examined with the aid of the model.

  17. 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.

  18. 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.

  19. PFPE, A Unique Lubricant for a Unique Application

    DTIC Science & Technology

    1998-01-01

    PFPE , A Unique Lubricant for a Unique Application Mahmoud A. Fowzy Castrol Industrial North America Specialty Products Division 1001 West 31st Street...Downers Grove, Illinois 60148 (630)241-4000 Abstract: PFPE (Perfluoropolyether) is a clear colorless fluorinated synthetic oil that is nonreactive...nonflammable, safe in chemical and oxygen service, and is long lasting. PFPE grease is made by mixing different types of non-soap thickeners with the

  20. Dynamics of symmetry breaking during quantum real-time evolution in a minimal model system.

    PubMed

    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.

  1. Topological order and memory time in marginally-self-correcting quantum memory

    NASA Astrophysics Data System (ADS)

    Siva, Karthik; Yoshida, Beni

    2017-03-01

    We examine two proposals for marginally-self-correcting quantum memory: the cubic code by Haah and the welded code by Michnicki. In particular, we prove explicitly that they are absent of topological order above zero temperature, as their Gibbs ensembles can be prepared via a short-depth quantum circuit from classical ensembles. Our proof technique naturally gives rise to the notion of free energy associated with excitations. Further, we develop a framework for an ergodic decomposition of Davies generators in CSS codes which enables formal reduction to simpler classical memory problems. We then show that memory time in the welded code is doubly exponential in inverse temperature via the Peierls argument. These results introduce further connections between thermal topological order and self-correction from the viewpoint of free energy and quantum circuit depth.

  2. Quantum and classical behavior in interacting bosonic systems

    SciTech Connect

    Hertzberg, Mark P.

    2016-11-21

    It is understood that in free bosonic theories, the classical field theory accurately describes the full quantum theory when the occupancy numbers of systems are very large. However, the situation is less understood in interacting theories, especially on time scales longer than the dynamical relaxation time. Recently there have been claims that the quantum theory deviates spectacularly from the classical theory on this time scale, even if the occupancy numbers are extremely large. Furthermore, it is claimed that the quantum theory quickly thermalizes while the classical theory does not. The evidence for these claims comes from noticing a spectacular difference in the time evolution of expectation values of quantum operators compared to the classical micro-state evolution. If true, this would have dramatic consequences for many important phenomena, including laboratory studies of interacting BECs, dark matter axions, preheating after inflation, etc. In this work we critically examine these claims. We show that in fact the classical theory can describe the quantum behavior in the high occupancy regime, even when interactions are large. The connection is that the expectation values of quantum operators in a single quantum micro-state are approximated by a corresponding classical ensemble average over many classical micro-states. Furthermore, by the ergodic theorem, a classical ensemble average of local fields with statistical translation invariance is the spatial average of a single micro-state. So the correlation functions of the quantum and classical field theories of a single micro-state approximately agree at high occupancy, even in interacting systems. Furthermore, both quantum and classical field theories can thermalize, when appropriate coarse graining is introduced, with the classical case requiring a cutoff on low occupancy UV modes. We discuss applications of our results.

  3. Quantum and classical behavior in interacting bosonic systems

    NASA Astrophysics Data System (ADS)

    Hertzberg, Mark P.

    2016-11-01

    It is understood that in free bosonic theories, the classical field theory accurately describes the full quantum theory when the occupancy numbers of systems are very large. However, the situation is less understood in interacting theories, especially on time scales longer than the dynamical relaxation time. Recently there have been claims that the quantum theory deviates spectacularly from the classical theory on this time scale, even if the occupancy numbers are extremely large. Furthermore, it is claimed that the quantum theory quickly thermalizes while the classical theory does not. The evidence for these claims comes from noticing a spectacular difference in the time evolution of expectation values of quantum operators compared to the classical micro-state evolution. If true, this would have dramatic consequences for many important phenomena, including laboratory studies of interacting BECs, dark matter axions, preheating after inflation, etc. In this work we critically examine these claims. We show that in fact the classical theory can describe the quantum behavior in the high occupancy regime, even when interactions are large. The connection is that the expectation values of quantum operators in a single quantum micro-state are approximated by a corresponding classical ensemble average over many classical micro-states. Furthermore, by the ergodic theorem, a classical ensemble average of local fields with statistical translation invariance is the spatial average of a single micro-state. So the correlation functions of the quantum and classical field theories of a single micro-state approximately agree at high occupancy, even in interacting systems. Furthermore, both quantum and classical field theories can thermalize, when appropriate coarse graining is introduced, with the classical case requiring a cutoff on low occupancy UV modes. We discuss applications of our results.

  4. Diabetes: Unique to Older Adults

    MedlinePlus

    ... Stroke Urinary Incontinence Related Documents PDF Choosing Wisely: Diabetes Tests and Treatments Download Related Video Join our e-newsletter! Aging & Health A to Z Diabetes Unique to Older Adults This section provides information ...

  5. Nutrition: Unique to Older Adults

    MedlinePlus

    ... our e-newsletter! Aging & Health A to Z Nutrition Unique to Older Adults This section provides information ... teeth that are needed for grinding up food, nutrition suffers. If you are unable to chew and ...

  6. Dynamical quantum phase transitions (Review Article)

    NASA Astrophysics Data System (ADS)

    Zvyagin, A. A.

    2016-11-01

    During recent years the interest to dynamics of quantum systems has grown considerably. Quantum many body systems out of equilibrium often manifest behavior, different from the one predicted by standard statistical mechanics and thermodynamics in equilibrium. Since the dynamics of a many-body quantum system typically involve many excited eigenstates, with a non-thermal distribution, the time evolution of such a system provides an unique way for investigation of non-equilibrium quantum statistical mechanics. Last decade such new subjects like quantum quenches, thermalization, pre-thermalization, equilibration, generalized Gibbs ensemble, etc. are among the most attractive topics of investigation in modern quantum physics. One of the most interesting themes in the study of dynamics of quantum many-body systems out of equilibrium is connected with the recently proposed important concept of dynamical quantum phase transitions. During the last few years a great progress has been achieved in studying of those singularities in the time dependence of characteristics of quantum mechanical systems, in particular, in understanding how the quantum critical points of equilibrium thermodynamics affect their dynamical properties. Dynamical quantum phase transitions reveal universality, scaling, connection to the topology, and many other interesting features. Here we review the recent achievements of this quickly developing part of low-temperature quantum physics. The study of dynamical quantum phase transitions is especially important in context of their connection to the problem of the modern theory of quantum information, where namely non-equilibrium dynamics of many-body quantum system plays the major role.

  7. Uniqueness of the Representation in Homogeneous Isotropic LQC

    NASA Astrophysics Data System (ADS)

    Engle, Jonathan; Hanusch, Maximilian; Thiemann, Thomas

    2017-08-01

    We show that the standard representation of homogeneous isotropic loop quantum cosmology (LQC) is the GNS-representation that corresponds to the unique state on the reduced quantum holonomy-flux *-algebra that is invariant under residual diffeomorphisms— both when the standard algebra is used as well as when one uses the extended algebra proposed by Fleischhack. More precisely, we find that in both situations the GNS-Hilbert spaces coincide, and that in the Fleischhack case the additional algebra elements are just mapped to zero operators. In order for the residual diffeomorphisms to have a well-defined action on the quantum algebra, we have let them act on the fiducial cell as well as on the dynamical variables, thereby recovering covariance. Consistency with Ashtekar and Campilgia in the Bianchi case is also shown.

  8. Quantum ontologies

    SciTech Connect

    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.

  9. Quantum computation for quantum chemistry

    NASA Astrophysics Data System (ADS)

    Aspuru-Guzik, Alan

    2010-03-01

    Numerically exact simulation of quantum systems on classical computers is in general, an intractable computational problem. Computational chemists have made progress in the development of approximate methods to tackle complex chemical problems. The downside of these approximate methods is that their failure for certain important cases such as long-range charge transfer states in the case of traditional density functional theory. In 1982, Richard Feynman suggested that a quantum device should be able to simulate quantum systems (in our case, molecules) exactly using quantum computers in a tractable fashion. Our group has been working in the development of quantum chemistry algorithms for quantum devices. In this talk, I will describe how quantum computers can be employed to carry out numerically exact quantum chemistry and chemical reaction dynamics calculations, as well as molecular properties. Finally, I will describe our recent experimental quantum computation of the energy of the hydrogen molecule using an optical quantum computer.

  10. Quantum sensing

    NASA Astrophysics Data System (ADS)

    Degen, C. L.; Reinhard, F.; Cappellaro, P.

    2017-07-01

    "Quantum sensing" describes the use of a quantum system, quantum properties, or quantum phenomena to perform a measurement of a physical quantity. Historical examples of quantum sensors include magnetometers based on superconducting quantum interference devices and atomic vapors or atomic clocks. More recently, quantum sensing has become a distinct and rapidly growing branch of research within the area of quantum science and technology, with the most common platforms being spin qubits, trapped ions, and flux qubits. The field is expected to provide new opportunities—especially with regard to high sensitivity and precision—in applied physics and other areas of science. This review provides an introduction to the basic principles, methods, and concepts of quantum sensing from the viewpoint of the interested experimentalist.

  11. Quantum memristors

    SciTech Connect

    Pfeiffer, P.; Sanz, M.

    2016-07-06

    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. As a result, the proposed quantum memristor is then a building block for neuromorphic quantum computation and quantum simulations of non-Markovian systems.

  12. Quantum memristors

    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.

  13. Quantum memristors

    PubMed Central

    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

  14. Urticarial vasculitis: a unique presentation.

    PubMed

    Stigall, Landon E; Sigmon, Justin R; Leicht, Stuart S

    2009-05-01

    Urticarial vasculitis is a relatively rare diagnosis in a patient presenting with urticaria. The process is classically described as a generalized eruption, painful more so than pruritic, lasting longer than 24 hours. Two forms of urticarial vasculitis have been described: ahypocomplementemic form more commonly associated with systemic disease, and a normocomplementemic form that is generally limited to the skin. We report on a uniquely distributed vasculitic eruption restricted mainly to the anterior belt line area in a patient presenting with urticaria and intense pruritus. Urticarial vasculitis as a unique entity is reviewed along with its clinical and histopathologic presentation and the pharmacologic agents used for treatment.

  15. Static and dynamical quantum correlations in phases of an alternating-field X Y model

    NASA Astrophysics Data System (ADS)

    Chanda, Titas; Das, Tamoghna; Sadhukhan, Debasis; Pal, Amit Kumar; SenDe, Aditi; Sen, Ujjwal

    2016-10-01

    We investigate the static and dynamical patterns of entanglement in an anisotropic X Y model with an alternating transverse magnetic field, which is equivalent to a two-component one-dimensional Fermi gas on a lattice, a system realizable with current technology. Apart from the antiferromagnetic and paramagnetic phases, the model possesses a dimer phase which is not present in the transverse X Y model. At zero temperature, we find that the first derivative of bipartite entanglement can detect all the three phases. We analytically show that the model has a "factorization line" on the plane of system parameters, in which the zero-temperature state is separable. Along with investigating the effect of temperature on entanglement in a phase plane, we also report a nonmonotonic behavior of entanglement with respect to temperature in the antiferromagnetic and paramagnetic phases, which is surprisingly absent in the dimer phase. Since the time dynamics of entanglement in a realizable physical system plays an important role in quantum information processing tasks, the evolutions of entanglement at small as well as large time are examined. Consideration of large-time behavior of entanglement helps us to prove that in this model, entanglement is always ergodic. We observe that other quantum correlation measures can qualitatively show similar features in zero and finite temperatures. However, unlike nearest-neighbor entanglement, the nearest-neighbor information-theoretic measures can be both ergodic as well as nonergodic, depending on the system parameters.

  16. Clustering of Nonergodic Eigenstates in Quantum Spin Glasses.

    PubMed

    Baldwin, C L; Laumann, C R; Pal, A; Scardicchio, A

    2017-03-24

    The two primary categories for eigenstate phases of matter at a finite temperature are many-body localization (MBL) and the eigenstate thermalization hypothesis (ETH). We show that, in the paradigmatic quantum p-spin models of the spin-glass theory, eigenstates violate the ETH yet are not MBL either. A mobility edge, which we locate using the forward-scattering approximation and replica techniques, separates the nonergodic phase at a small transverse field from an ergodic phase at a large transverse field. The nonergodic phase is also bounded from above in temperature, by a transition in configuration-space statistics reminiscent of the clustering transition in the spin-glass theory. We show that the nonergodic eigenstates are organized in clusters which exhibit distinct magnetization patterns, as characterized by an eigenstate variant of the Edwards-Anderson order parameter.

  17. Quantum diffusion with drift and the Einstein relation. I

    SciTech Connect

    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.

  18. Dynamic Nuclear Polarization and the Paradox of Quantum Thermalization.

    PubMed

    De Luca, Andrea; Rosso, Alberto

    2015-08-21

    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.

  19. Clustering of Nonergodic Eigenstates in Quantum Spin Glasses

    NASA Astrophysics Data System (ADS)

    Baldwin, C. L.; Laumann, C. R.; Pal, A.; Scardicchio, A.

    2017-03-01

    The two primary categories for eigenstate phases of matter at a finite temperature are many-body localization (MBL) and the eigenstate thermalization hypothesis (ETH). We show that, in the paradigmatic quantum p -spin models of the spin-glass theory, eigenstates violate the ETH yet are not MBL either. A mobility edge, which we locate using the forward-scattering approximation and replica techniques, separates the nonergodic phase at a small transverse field from an ergodic phase at a large transverse field. The nonergodic phase is also bounded from above in temperature, by a transition in configuration-space statistics reminiscent of the clustering transition in the spin-glass theory. We show that the nonergodic eigenstates are organized in clusters which exhibit distinct magnetization patterns, as characterized by an eigenstate variant of the Edwards-Anderson order parameter.

  20. Subcycle quantum electrodynamics.

    PubMed

    Riek, C; Sulzer, P; Seeger, M; Moskalenko, A S; Burkard, G; Seletskiy, D V; Leitenstorfer, A

    2017-01-18

    Squeezed states of electromagnetic radiation have quantum fluctuations below those of the vacuum field. They offer a unique resource for quantum information systems and precision metrology, including gravitational wave detectors, which require unprecedented sensitivity. Since the first experiments on this non-classical form of light, quantum analysis has been based on homodyning techniques and photon correlation measurements. These methods currently function in the visible to near-infrared and microwave spectral ranges. They require a well-defined carrier frequency, and photons contained in a quantum state need to be absorbed or amplified. Quantum non-demolition experiments may be performed to avoid the influence of a measurement in one quadrature, but this procedure comes at the expense of increased uncertainty in another quadrature. Here we generate mid-infrared time-locked patterns of squeezed vacuum noise. After propagation through free space, the quantum fluctuations of the electric field are studied in the time domain using electro-optic sampling with few-femtosecond laser pulses. We directly compare the local noise amplitude to that of bare (that is, unperturbed) vacuum. Our nonlinear approach operates off resonance and, unlike homodyning or photon correlation techniques, without absorption or amplification of the field that is investigated. We find subcycle intervals with noise levels that are substantially less than the amplitude of the vacuum field. As a consequence, there are enhanced fluctuations in adjacent time intervals, owing to Heisenberg's uncertainty principle, which indicate generation of highly correlated quantum radiation. Together with efforts in the far infrared, this work enables the study of elementary quantum dynamics of light and matter in an energy range at the boundary between vacuum and thermal background conditions.

  1. Subcycle quantum electrodynamics

    NASA Astrophysics Data System (ADS)

    Riek, C.; Sulzer, P.; Seeger, M.; Moskalenko, A. S.; Burkard, G.; Seletskiy, D. V.; Leitenstorfer, A.

    2017-01-01

    Squeezed states of electromagnetic radiation have quantum fluctuations below those of the vacuum field. They offer a unique resource for quantum information systems and precision metrology, including gravitational wave detectors, which require unprecedented sensitivity. Since the first experiments on this non-classical form of light, quantum analysis has been based on homodyning techniques and photon correlation measurements. These methods currently function in the visible to near-infrared and microwave spectral ranges. They require a well-defined carrier frequency, and photons contained in a quantum state need to be absorbed or amplified. Quantum non-demolition experiments may be performed to avoid the influence of a measurement in one quadrature, but this procedure comes at the expense of increased uncertainty in another quadrature. Here we generate mid-infrared time-locked patterns of squeezed vacuum noise. After propagation through free space, the quantum fluctuations of the electric field are studied in the time domain using electro-optic sampling with few-femtosecond laser pulses. We directly compare the local noise amplitude to that of bare (that is, unperturbed) vacuum. Our nonlinear approach operates off resonance and, unlike homodyning or photon correlation techniques, without absorption or amplification of the field that is investigated. We find subcycle intervals with noise levels that are substantially less than the amplitude of the vacuum field. As a consequence, there are enhanced fluctuations in adjacent time intervals, owing to Heisenberg’s uncertainty principle, which indicate generation of highly correlated quantum radiation. Together with efforts in the far infrared, this work enables the study of elementary quantum dynamics of light and matter in an energy range at the boundary between vacuum and thermal background conditions.

  2. Milton: A New, Unique Pallasite

    NASA Technical Reports Server (NTRS)

    Jones, R. H.; Wasson, J. T.; Larson, T.; Sharp, Z. D.

    2003-01-01

    The Milton pallasite was found in Missouri, U.S.A. in October, 2000. It consists of a single stone that originally weighed approximately 2040 g. The chemistry of the olivine and metal phases, plus the oxygen isotope ratios of the olivines, differ significantly from other pallasites, making Milton unique. Unfortunately, the meteorite is heavily fractured and weathered.

  3. Uniqueness theorems in bioluminescence tomography.

    PubMed

    Wang, Ge; Li, Yi; Jiang, Ming

    2004-08-01

    Motivated by bioluminescent imaging needs for studies on gene therapy and other applications in the mouse models, a bioluminescence tomography (BLT) system is being developed in the University of Iowa. While the forward imaging model is described by the well-known diffusion equation, the inverse problem is to recover an internal bioluminescent source distribution subject to Cauchy data. Our primary goal in this paper is to establish the solution uniqueness for BLT under practical constraints despite the ill-posedness of the inverse problem in the general case. After a review on the inverse source literature, we demonstrate that in the general case the BLT solution is not unique by constructing the set of all the solutions to this inverse problem. Then, we show the uniqueness of the solution in the case of impulse sources. Finally, we present our main theorem that solid/hollow ball sources can be uniquely determined up to nonradiating sources. For better readability, the exact conditions for and rigorous proofs of the theorems are given in the Appendices. Further research directions are also discussed.

  4. 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.

  5. 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.

  6. Plasmonic fluorescent quantum dots.

    PubMed

    Jin, Yongdong; Gao, Xiaohu

    2009-09-01

    Combining multiple discrete components into a single multifunctional nanoparticle could be useful in a variety of applications. Retaining the unique optical and electrical properties of each component after nanoscale integration is, however, a long-standing problem. It is particularly difficult when trying to combine fluorophores such as semiconductor quantum dots with plasmonic materials such as gold, because gold and other metals can quench the fluorescence. So far, the combination of quantum dot fluorescence with plasmonically active gold has only been demonstrated on flat surfaces. Here, we combine fluorescent and plasmonic activities in a single nanoparticle by controlling the spacing between a quantum dot core and an ultrathin gold shell with nanometre precision through layer-by-layer assembly. Our wet-chemistry approach provides a general route for the deposition of ultrathin gold layers onto virtually any discrete nanostructure or continuous surface, and should prove useful for multimodal bioimaging, interfacing with biological systems, reducing nanotoxicity, modulating electromagnetic fields and contacting nanostructures.

  7. Quantum cosmology: a review.

    PubMed

    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.

  8. Quantum dynamics and nonintegrability

    NASA Astrophysics Data System (ADS)

    Hogg, T.; Huberman, B. A.

    1983-07-01

    Results of a nonperturbative investigation of the global behavior of quantum systems with time-periodic Hamiltonians are presented. These include the proof of a theorem stating that such systems, if bounded and nonresonant, will reassemble themselves infinitely often in the course of time. In order to illustrate the applicability of this result, an analytic study of a driven harmonic oscillator is presented, together with computer simulations of quantum maps describing the dynamics of a pulsed electron in a well and a periodically kicked rotor. A quantitative study of resonance excitation also shows that in practical situations recurrence is pervasive. Several unique quantum effects are analyzed, and their relevance to the classical limit is discussed. A formula is derived for recurrence times, and computer experiments are performed to test its validity.

  9. Markovian evolution of quantum coherence under symmetric dynamics

    NASA Astrophysics Data System (ADS)

    Lostaglio, Matteo; Korzekwa, Kamil; Milne, Antony

    2017-09-01

    Both conservation laws and practical restrictions impose symmetry constraints on the dynamics of open quantum systems. In the case of time-translation symmetry, which arises naturally in many physically relevant scenarios, the quantum coherence between energy eigenstates becomes a valuable resource for quantum information processing. In this work, we identify the minimum amount of decoherence compatible with this symmetry for a given population dynamics. This yields a generalization to higher-dimensional systems of the relation T2≤2 T1 for qubit decoherence and relaxation times. It also enables us to witness and assess the role of non-Markovianity as a resource for coherence preservation and transfer. Moreover, we discuss the relationship between ergodicity and the ability of Markovian dynamics to indefinitely sustain a superposition of different energy states. Finally, we establish a formal connection between the resource-theoretic and the master equation approaches to thermodynamics, with the former being a non-Markovian generalization of the latter. Our work thus brings the abstract study of quantum coherence as a resource towards the realm of actual physical applications.

  10. Quantum robots and quantum computers

    SciTech Connect

    Benioff, P.

    1998-07-01

    Validation of a presumably universal theory, such as quantum mechanics, requires a quantum mechanical description of systems that carry out theoretical calculations and systems that carry out experiments. The description of quantum computers is under active development. No description of systems to carry out experiments has been given. A small step in this direction is taken here by giving a description of quantum robots as mobile systems with on board quantum computers that interact with different environments. Some properties of these systems are discussed. A specific model based on the literature descriptions of quantum Turing machines is presented.

  11. Quantum Darwinism

    SciTech Connect

    Zurek, Wojciech H

    2008-01-01

    Quantum Darwinism - proliferation, in the environment, of multiple records of selected states of the system (its information-theoretic progeny) - explains how quantum fragility of individual state can lead to classical robustness of their multitude.

  12. Quantum memristors

    DOE PAGES

    Pfeiffer, P.; Egusquiza, I. L.; Di Ventra, M.; ...

    2016-07-06

    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 quantummore » 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. As a result, the proposed quantum memristor is then a building block for neuromorphic quantum computation and quantum simulations of non-Markovian systems.« less

  13. Quantum guidebooks

    NASA Astrophysics Data System (ADS)

    Crease, Robert P.

    2012-06-01

    Fresh from his appearance on the latest Physics World podcast, which examined the enduring popularity of books about quantum mechanics, Robert P Crease surveys the many tour guides to the quantum world.

  14. Application of the Group Algebra of the Problem of the Tail σ-ALGEBRA of a Random Walk on a Group and the Problem of Ergodicity of a Skew-Product Action

    NASA Astrophysics Data System (ADS)

    Ismagilov, R. S.

    1988-02-01

    Two problems in measure theory are considered: that of the tail C*-algebra of a random walk on a group, and that of ergodicity of a skew-product action. These problems are solved in a uniform way by using Banach algebras and harmonic analysis on a group. Bibliography: 22 titles.

  15. Quantum dots: Rethinking the electronics

    SciTech Connect

    Bishnoi, Dimple

    2016-05-06

    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.

  16. 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.

  17. Tight informationally complete quantum measurements

    NASA Astrophysics Data System (ADS)

    Scott, A. J.

    2006-10-01

    We introduce a class of informationally complete positive-operator-valued measures which are, in analogy with a tight frame, 'as close as possible' to orthonormal bases for the space of quantum states. These measures are distinguished by an exceptionally simple state-reconstruction formula which allows 'painless' quantum state tomography. Complete sets of mutually unbiased bases and symmetric informationally complete positive-operator-valued measures are both members of this class, the latter being the unique minimal rank-one members. Recast as ensembles of pure quantum states, the rank-one members are in fact equivalent to weighted 2-designs in complex projective space. These measures are shown to be optimal for quantum cloning and linear quantum state tomography.

  18. Quantum Transport.

    DTIC Science & Technology

    1994-08-15

    Notre Dame was concerned with a variety of quantum transport in mesoscopic structures. This research was funded by the Air Force Office of Scientific...Research under Grant No. AFOSR-91-0211. The major issues examined included quantum transport in high magnetic fields and modulated channels, Coulomb...lifetimes in quasi-1D structures, quantum transport experiments in metals, the mesoscopic photovoltaic effect, and new techniques for fabricating quantum structures in semiconductors.

  19. Optical Fiber Sensing Using Quantum Dots

    PubMed Central

    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.

  20. Uniqueness of large positive solutions

    NASA Astrophysics Data System (ADS)

    López-Gómez, Julián; Maire, Luis

    2017-08-01

    We establish the uniqueness of the positive solution of the singular problem (1.1) through some standard comparison techniques involving the maximum principle. Our proofs do not invoke to the blow-up rates of the solutions, as in most of the specialized literature. We give two different types of results according to the geometrical properties of Ω and the regularity of partial Ω . Even in the autonomous case, our theorems are extremely sharp extensions of all existing results. Precisely, when a(x)≡ 1, it is shown that the monotonicity and superadditivity of f( u) with constant C≥ 0 entail the uniqueness; f is said to be superadditive with constant C≥ 0 if f(a+b) ≥ f(a) + f(b) - C \\quad for all a, b ≥ 0. This condition, introduced by Marcus and Véron (J Evol Equ 3:637-652, 2004), weakens all previous sufficient conditions for uniqueness, as it will become apparent in this paper.

  1. From Dualism to Unity in Quantum Physics

    NASA Astrophysics Data System (ADS)

    Landé, Alfred

    2016-02-01

    Preface; Introduction; 1. Causality, chance, continuity; 2. States, observables, probabilities; 3. The metric law of probabilities; 4. Quantum dynamics; 5. Quantum fact and fiction; Retrospect. From dualism to unity, from positivism to realism; Appendix 1. Survey of elementary postulates; Appendix 2. Two problems of uniqueness; References; Index.

  2. Unique children in unique places: innovative pediatric community clinical.

    PubMed

    Harrison, Suzanne; Laforest, Marie-Eve

    2011-12-01

    Pediatric nursing is a specialization that requires a particular set of skills and abilities. Most nurses seldom get the chance to interact with families who have children living with exceptionalities unless they choose to work in tertiary settings dealing exclusively with children. This article explores how one school of nursing in Canada offers its students two unique learning opportunities where they get the chance to work with children who have special needs in an interdisciplinary community-based setting. Shared statements from parents and students highlight the benefits to all those involved.

  3. Quantum Darwinism

    NASA Astrophysics Data System (ADS)

    Zurek, Wojciech Hubert

    2009-03-01

    Quantum Darwinism describes the proliferation, in the environment, of multiple records of selected states of a quantum system. It explains how the quantum fragility of a state of a single quantum system can lead to the classical robustness of states in their correlated multitude; shows how effective `wave-packet collapse' arises as a result of the proliferation throughout the environment of imprints of the state of the system; and provides a framework for the derivation of Born's rule, which relates the probabilities of detecting states to their amplitudes. Taken together, these three advances mark considerable progress towards settling the quantum measurement problem.

  4. Quantum frames

    NASA Astrophysics Data System (ADS)

    Brown, Matthew J.

    2014-02-01

    The framework of quantum frames can help unravel some of the interpretive difficulties i the foundation of quantum mechanics. In this paper, I begin by tracing the origins of this concept in Bohr's discussion of quantum theory and his theory of complementarity. Engaging with various interpreters and followers of Bohr, I argue that the correct account of quantum frames must be extended beyond literal space-time reference frames to frames defined by relations between a quantum system and the exosystem or external physical frame, of which measurement contexts are a particularly important example. This approach provides superior solutions to key EPR-type measurement and locality paradoxes.

  5. Quantum cheques

    NASA Astrophysics Data System (ADS)

    Moulick, Subhayan Roy; Panigrahi, Prasanta K.

    2016-06-01

    We propose the idea of a quantum cheque scheme, a cryptographic protocol in which any legitimate client of a trusted bank can issue a cheque, that cannot be counterfeited or altered in anyway, and can be verified by a bank or any of its branches. We formally define a quantum cheque and present the first unconditionally secure quantum cheque scheme and show it to be secure against any no-signalling adversary. The proposed quantum cheque scheme can been perceived as the quantum analog of Electronic Data Interchange, as an alternate for current e-Payment Gateways.

  6. Measurement-Based and Universal Blind Quantum Computation

    NASA Astrophysics Data System (ADS)

    Broadbent, Anne; Fitzsimons, Joseph; Kashefi, Elham

    Measurement-based quantum computation (MBQC) is a novel approach to quantum computation where the notion of measurement is the main driving force of computation. This is in contrast with the more traditional circuit model which is based on unitary operation. We review here the mathematical model underlying MBQC and the first quantum cryptographic protocol designed using the unique features of MBQC.

  7. Limited Quantum Helium Transportation through Nano-channels by Quantum Fluctuation.

    PubMed

    Ohba, Tomonori

    2016-07-01

    Helium at low temperatures has unique quantum properties such as superfluidity, which causes it to behave differently from a classical fluid. Despite our deep understanding of quantum mechanics, there are many open questions concerning the properties of quantum fluids in nanoscale systems. Herein, the quantum behavior of helium transportation through one-dimensional nanopores was evaluated by measuring the adsorption of quantum helium in the nanopores of single-walled carbon nanohorns and AlPO4-5 at 2-5 K. Quantum helium was transported unimpeded through nanopores larger than 0.7 nm in diameter, whereas quantum helium transportation was significantly restricted through 0.4-nm and 0.6-nm nanopores. Conversely, nitrogen molecules diffused through the 0.4-nm nanopores at 77 K. Therefore, quantum helium behaved as a fluid comprising atoms larger than 0.4-0.6 nm. This phenomenon was remarkable, considering that helium is the smallest existing element with a (classical) size of approximately 0.27 nm. This finding revealed the presence of significant quantum fluctuations. Quantum fluctuation determined the behaviors of quantum flux and is essential to understanding unique quantum behaviors in nanoscale systems.

  8. Limited Quantum Helium Transportation through Nano-channels by Quantum Fluctuation

    PubMed Central

    Ohba, Tomonori

    2016-01-01

    Helium at low temperatures has unique quantum properties such as superfluidity, which causes it to behave differently from a classical fluid. Despite our deep understanding of quantum mechanics, there are many open questions concerning the properties of quantum fluids in nanoscale systems. Herein, the quantum behavior of helium transportation through one-dimensional nanopores was evaluated by measuring the adsorption of quantum helium in the nanopores of single-walled carbon nanohorns and AlPO4-5 at 2–5 K. Quantum helium was transported unimpeded through nanopores larger than 0.7 nm in diameter, whereas quantum helium transportation was significantly restricted through 0.4-nm and 0.6-nm nanopores. Conversely, nitrogen molecules diffused through the 0.4-nm nanopores at 77 K. Therefore, quantum helium behaved as a fluid comprising atoms larger than 0.4–0.6 nm. This phenomenon was remarkable, considering that helium is the smallest existing element with a (classical) size of approximately 0.27 nm. This finding revealed the presence of significant quantum fluctuations. Quantum fluctuation determined the behaviors of quantum flux and is essential to understanding unique quantum behaviors in nanoscale systems. PMID:27363671

  9. Lithium nephropathy: unique sonographic findings.

    PubMed

    Di Salvo, Donald N; Park, Joseph; Laing, Faye C

    2012-04-01

    This case series describes a unique sonographic appearance consisting of numerous microcysts and punctate echogenic foci seen on renal sonograms of 10 adult patients receiving chronic lithium therapy. Clinically, chronic renal insufficiency was present in 6 and nephrogenic diabetes insipidus in 2. Sonography showed numerous microcysts and punctate echogenic foci. Computed tomography in 5 patients confirmed microcysts and microcalcifications, which were fewer in number than on sonography. Magnetic resonance imaging in 2 patients confirmed microcysts in each case. Renal biopsy in 1 patient showed chronic interstitial nephritis, microcysts, and tubular dilatation. The diagnosis of lithium nephropathy should be considered when sonography shows these findings.

  10. Mucormycosis in India: unique features.

    PubMed

    Chakrabarti, Arunaloke; Singh, Rachna

    2014-12-01

    Mucormycosis remains a devastating invasive fungal infection, with high mortality rates even after active management. The disease is being reported at an alarming frequency over the past decades from India. Indian mucormycosis has certain unique features. Rhino-orbito-cerebral presentation associated with uncontrolled diabetes is the predominant characteristic. Isolated renal mucormycosis has emerged as a new clinical entity. Apophysomyces elegans and Rhizopus homothallicus are emerging species in this region and uncommon agents such as Mucor irregularis and Thamnostylum lucknowense are also being reported. This review focuses on these distinct features of mucormycosis observed in India.

  11. A unique solar marking construct.

    PubMed

    Sofaer, A; Zinser, V; Sinclair, R M

    1979-10-19

    An assembly of stone slabs on an isolated butte in New Mexico collimates sunlight onto spiral petroglyphs carved on a cliff face. The light illuminates the spirals in a changing pattern throughout the year and marks the solstices and equinoxes with particular images. The assembly can also be used to observe lunar phenomena. It is unique in archeoastronomy in utilizing the changing height of the midday sun throughout the year rather than its rising and setting points. The construct appears to be the result of deliberate work of the Anasazi Indians, the builders of the great pueblos in the area.

  12. A quantum-implementable neural network model

    NASA Astrophysics Data System (ADS)

    Chen, Jialin; Wang, Lingli; Charbon, Edoardo

    2017-10-01

    A quantum-implementable neural network, namely quantum probability neural network (QPNN) model, is proposed in this paper. QPNN can use quantum parallelism to trace all possible network states to improve the result. Due to its unique quantum nature, this model is robust to several quantum noises under certain conditions, which can be efficiently implemented by the qubus quantum computer. Another advantage is that QPNN can be used as memory to retrieve the most relevant data and even to generate new data. The MATLAB experimental results of Iris data classification and MNIST handwriting recognition show that much less neuron resources are required in QPNN to obtain a good result than the classical feedforward neural network. The proposed QPNN model indicates that quantum effects are useful for real-life classification tasks.

  13. Quantum entanglement, quantum communication and the limits of quantum computing

    NASA Astrophysics Data System (ADS)

    Ambainis, Andris

    Quantum entanglement is a term describing the quantum correlations between different parts of a quantum system. Quantum information theory has developed sophisticated techniques to quantify and study quantum entanglement. In this thesis, we show how to apply those techniques to problems in quantum algorithms, complexity theory, communication and cryptography. The main results are: (1) quantum communication protocols that are exponentially more efficient that conventional (classical) communication protocols, (2) unconditionally secure quantum protocols for cryptographic problems, (3) a new "quantum adversary" method for proving lower bounds on quantum algorithms, (4) a study of "one clean qubit computation", a model related to the experimental implementation of quantum computers using NMR (nucleo-magnetic resonance) technology.

  14. Heisenberg picture approach to the stability of quantum Markov systems

    NASA Astrophysics Data System (ADS)

    Pan, Yu; Amini, Hadis; Miao, Zibo; Gough, John; Ugrinovskii, Valery; James, Matthew R.

    2014-06-01

    Quantum Markovian systems, modeled as unitary dilations in the quantum stochastic calculus of Hudson and Parthasarathy, have become standard in current quantum technological applications. This paper investigates the stability theory of such systems. Lyapunov-type conditions in the Heisenberg picture are derived in order to stabilize the evolution of system operators as well as the underlying dynamics of the quantum states. In particular, using the quantum Markov semigroup associated with this quantum stochastic differential equation, we derive sufficient conditions for the existence and stability of a unique and faithful invariant quantum state. Furthermore, this paper proves the quantum invariance principle, which extends the LaSalle invariance principle to quantum systems in the Heisenberg picture. These results are formulated in terms of algebraic constraints suitable for engineering quantum systems that are used in coherent feedback networks.

  15. Heisenberg picture approach to the stability of quantum Markov systems

    SciTech Connect

    Pan, Yu E-mail: zibo.miao@anu.edu.au; Miao, Zibo E-mail: zibo.miao@anu.edu.au; Amini, Hadis; Gough, John; Ugrinovskii, Valery; James, Matthew R.

    2014-06-15

    Quantum Markovian systems, modeled as unitary dilations in the quantum stochastic calculus of Hudson and Parthasarathy, have become standard in current quantum technological applications. This paper investigates the stability theory of such systems. Lyapunov-type conditions in the Heisenberg picture are derived in order to stabilize the evolution of system operators as well as the underlying dynamics of the quantum states. In particular, using the quantum Markov semigroup associated with this quantum stochastic differential equation, we derive sufficient conditions for the existence and stability of a unique and faithful invariant quantum state. Furthermore, this paper proves the quantum invariance principle, which extends the LaSalle invariance principle to quantum systems in the Heisenberg picture. These results are formulated in terms of algebraic constraints suitable for engineering quantum systems that are used in coherent feedback networks.

  16. Quantum games as quantum types

    NASA Astrophysics Data System (ADS)

    Delbecque, Yannick

    In this thesis, we present a new model for higher-order quantum programming languages. The proposed model is an adaptation of the probabilistic game semantics developed by Danos and Harmer [DH02]: we expand it with quantum strategies which enable one to represent quantum states and quantum operations. Some of the basic properties of these strategies are established and then used to construct denotational semantics for three quantum programming languages. The first of these languages is a formalisation of the measurement calculus proposed by Danos et al. [DKP07]. The other two are new: they are higher-order quantum programming languages. Previous attempts to define a denotational semantics for higher-order quantum programming languages have failed. We identify some of the key reasons for this and base the design of our higher-order languages on these observations. The game semantics proposed in this thesis is the first denotational semantics for a lambda-calculus equipped with quantum types and with extra operations which allow one to program quantum algorithms. The results presented validate the two different approaches used in the design of these two new higher-order languages: a first one where quantum states are used through references and a second one where they are introduced as constants in the language. The quantum strategies presented in this thesis allow one to understand the constraints that must be imposed on quantum type systems with higher-order types. The most significant constraint is the fact that abstraction over part of the tensor product of many unknown quantum states must not be allowed. Quantum strategies are a new mathematical model which describes the interaction between classical and quantum data using system-environment dialogues. The interactions between the different parts of a quantum system are described using the rich structure generated by composition of strategies. This approach has enough generality to be put in relation with other

  17. Contextuality supplies the 'magic' for quantum computation.

    PubMed

    Howard, Mark; Wallman, Joel; Veitch, Victor; Emerson, Joseph

    2014-06-19

    Quantum computers promise dramatic advantages over their classical counterparts, but the source of the power in quantum computing has remained elusive. Here we prove a remarkable equivalence between the onset of contextuality and the possibility of universal quantum computation via 'magic state' distillation, which is the leading model for experimentally realizing a fault-tolerant quantum computer. This is a conceptually satisfying link, because contextuality, which precludes a simple 'hidden variable' model of quantum mechanics, provides one of the fundamental characterizations of uniquely quantum phenomena. Furthermore, this connection suggests a unifying paradigm for the resources of quantum information: the non-locality of quantum theory is a particular kind of contextuality, and non-locality is already known to be a critical resource for achieving advantages with quantum communication. In addition to clarifying these fundamental issues, this work advances the resource framework for quantum computation, which has a number of practical applications, such as characterizing the efficiency and trade-offs between distinct theoretical and experimental schemes for achieving robust quantum computation, and putting bounds on the overhead cost for the classical simulation of quantum algorithms.

  18. Quantum flywheel

    NASA Astrophysics Data System (ADS)

    Levy, Amikam; Diósi, Lajos; Kosloff, Ronnie

    2016-05-01

    In this work we present the concept of a quantum flywheel coupled to a quantum heat engine. The flywheel stores useful work in its energy levels, while additional power is extracted continuously from the device. Generally, the energy exchange between a quantum engine and a quantized work repository is accompanied by heat, which degrades the charging efficiency. Specifically when the quantum harmonic oscillator acts as a work repository, quantum and thermal fluctuations dominate the dynamics. Quantum monitoring and feedback control are applied to the flywheel in order to reach steady state and regulate its operation. To maximize the charging efficiency one needs a balance between the information gained by measuring the system and the information fed back to the system. The dynamics of the flywheel are described by a stochastic master equation that accounts for the engine, the external driving, the measurement, and the feedback operations.

  19. Quantifying Quantumness

    NASA Astrophysics Data System (ADS)

    Braun, Daniel; Giraud, Olivier; Braun, Peter A.

    2010-03-01

    We introduce and study a measure of ``quantumness'' of a quantum state based on its Hilbert-Schmidt distance from the set of classical states. ``Classical states'' were defined earlier as states for which a positive P-function exists, i.e. they are mixtures of coherent states [1]. We study invariance properties of the measure, upper bounds, and its relation to entanglement measures. We evaluate the quantumness of a number of physically interesting states and show that for any physical system in thermal equilibrium there is a finite critical temperature above which quantumness vanishes. We then use the measure for identifying the ``most quantum'' states. Such states are expected to be potentially most useful for quantum information theoretical applications. We find these states explicitly for low-dimensional spin-systems, and show that they possess beautiful, highly symmetric Majorana representations. [4pt] [1] Classicality of spin states, Olivier Giraud, Petr Braun, and Daniel Braun, Phys. Rev. A 78, 042112 (2008)

  20. The Evolution of Human Uniqueness.

    PubMed

    Boyd, Robert

    2017-01-09

    The human species is an outlier in the natural world. Two million years ago our ancestors were a slightly odd apes. Now we occupy the largest ecological and geographical range of any species, have larger biomass, and process more energy. Usually, this transformation is explained in terms of cognitive ability-people are just smarter than all the rest. In this paper I argue that culture, our ability to learn from each other, and cooperation, our ability to make common cause with large groups of unrelated individuals are the real roots of human uniqueness, and sketch an evolutionary account of how these crucial abilities co-evolved with each other and with other features of our life histories.

  1. Unique features of space reactors

    SciTech Connect

    Buden, D.

    1990-01-01

    Space reactors are designed to meet a unique set of requirements; they must be sufficiently compact to be launched in a rocket to their operational location, operate for many years without maintenance and servicing, operate in extreme environments, and reject heat by radiation to space. To meet these restrictions, operating temperatures are much greater than in terrestrial power plants, and the reactors tend to have a fast neutron spectrum. Currently, a new generation of space reactor power plants is being developed. The major effort is in the SP-100 program, where the power plant is being designed for seven years of full power, and no maintenance operation at a reactor outlet operating temperature of 1350 K. 8 refs., 3 figs., 1 tab.

  2. Separable States with Unique Decompositions

    NASA Astrophysics Data System (ADS)

    Ha, Kil-Chan; Kye, Seung-Hyeok

    2014-05-01

    We search for faces of the convex set consisting of all separable states, which are affinely isomorphic to simplices, to get separable states with unique decompositions. In the two-qutrit case, we found that six product vectors spanning a five dimensional space give rise to a face isomorphic to the 5-dimensional simplex with six vertices, under a suitable linear independence assumption. If the partial conjugates of six product vectors also span a 5-dimensional space, then this face is inscribed in the face for PPT states whose boundary shares the fifteen 3-simplices on the boundary of the 5-simplex. The remaining boundary points consist of PPT entangled edge states of rank four. We also show that every edge state of rank four arises in this way. If the partial conjugates of the above six product vectors span a 6-dimensional space then we have a face isomorphic to 5-simplex, whose interior consists of separable states with unique decompositions, but with non-symmetric ranks. We also construct a face isomorphic to the 9-simplex. As applications, we give answers to questions in the literature Chen and Djoković (J Math Phys 54:022201, 2013) and Chen and Djoković (Commun Math Phys 323:241-284, 2013), and construct 3 ⊗ 3PPT states of type (9,5). For the qubit-qudit cases with d ≥ 3, we also show that ( d + 1)-dimensional subspaces give rise to faces isomorphic to the d-simplices, in most cases.

  3. Quantum Dots

    NASA Astrophysics Data System (ADS)

    Tartakovskii, Alexander

    2012-07-01

    Part I. Nanostructure Design and Structural Properties of Epitaxially Grown Quantum Dots and Nanowires: 1. Growth of III/V semiconductor quantum dots C. Schneider, S. Hofling and A. Forchel; 2. Single semiconductor quantum dots in nanowires: growth, optics, and devices M. E. Reimer, N. Akopian, M. Barkelid, G. Bulgarini, R. Heeres, M. Hocevar, B. J. Witek, E. Bakkers and V. Zwiller; 3. Atomic scale analysis of self-assembled quantum dots by cross-sectional scanning tunneling microscopy and atom probe tomography J. G. Keizer and P. M. Koenraad; Part II. Manipulation of Individual Quantum States in Quantum Dots Using Optical Techniques: 4. Studies of the hole spin in self-assembled quantum dots using optical techniques B. D. Gerardot and R. J. Warburton; 5. Resonance fluorescence from a single quantum dot A. N. Vamivakas, C. Matthiesen, Y. Zhao, C.-Y. Lu and M. Atature; 6. Coherent control of quantum dot excitons using ultra-fast optical techniques A. J. Ramsay and A. M. Fox; 7. Optical probing of holes in quantum dot molecules: structure, symmetry, and spin M. F. Doty and J. I. Climente; Part III. Optical Properties of Quantum Dots in Photonic Cavities and Plasmon-Coupled Dots: 8. Deterministic light-matter coupling using single quantum dots P. Senellart; 9. Quantum dots in photonic crystal cavities A. Faraon, D. Englund, I. Fushman, A. Majumdar and J. Vukovic; 10. Photon statistics in quantum dot micropillar emission M. Asmann and M. Bayer; 11. Nanoplasmonics with colloidal quantum dots V. Temnov and U. Woggon; Part IV. Quantum Dot Nano-Laboratory: Magnetic Ions and Nuclear Spins in a Dot: 12. Dynamics and optical control of an individual Mn spin in a quantum dot L. Besombes, C. Le Gall, H. Boukari and H. Mariette; 13. Optical spectroscopy of InAs/GaAs quantum dots doped with a single Mn atom O. Krebs and A. Lemaitre; 14. Nuclear spin effects in quantum dot optics B. Urbaszek, B. Eble, T. Amand and X. Marie; Part V. Electron Transport in Quantum Dots Fabricated by

  4. Experimental simulation of quantum tunneling in small systems.

    PubMed

    Feng, Guan-Ru; Lu, Yao; Hao, Liang; Zhang, Fei-Hao; Long, Gui-Lu

    2013-01-01

    It is well known that quantum computers are superior to classical computers in efficiently simulating quantum systems. Here we report the first experimental simulation of quantum tunneling through potential barriers, a widespread phenomenon of a unique quantum nature, via NMR techniques. Our experiment is based on a digital particle simulation algorithm and requires very few spin-1/2 nuclei without the need of ancillary qubits. The occurrence of quantum tunneling through a barrier, together with the oscillation of the state in potential wells, are clearly observed through the experimental results. This experiment has clearly demonstrated the possibility to observe and study profound physical phenomena within even the reach of small quantum computers.

  5. Dissipative quantum computing with open quantum walks

    SciTech Connect

    Sinayskiy, Ilya; Petruccione, Francesco

    2014-12-04

    An open quantum walk approach to the implementation of a dissipative quantum computing scheme is presented. The formalism is demonstrated for the example of an open quantum walk implementation of a 3 qubit quantum circuit consisting of 10 gates.

  6. Grover's quantum search algorithm and Diophantine approximation

    SciTech Connect

    Dolev, Shahar; Pitowsky, Itamar; Tamir, Boaz

    2006-02-15

    In a fundamental paper [Phys. Rev. Lett. 78, 325 (1997)] Grover showed how a quantum computer can find a single marked object in a database of size N by using only O({radical}(N)) queries of the oracle that identifies the object. His result was generalized to the case of finding one object in a subset of marked elements. We consider the following computational problem: A subset of marked elements is given whose number of elements is either M or K, our task is to determine which is the case. We show how to solve this problem with a high probability of success using iterations of Grover's basic step only, and no other algorithm. Let m be the required number of iterations; we prove that under certain restrictions on the sizes of M and K the estimation m<2{radical}(N)/({radical}(K)-{radical}(M)) obtains. This bound reproduces previous results based on more elaborate algorithms, and is known to be optimal up to a constant factor. Our method involves simultaneous Diophantine approximations, so that Grover's algorithm is conceptualized as an orbit of an ergodic automorphism of the torus. We comment on situations where the algorithm may be slow, and note the similarity between these cases and the problem of small divisors in classical mechanics.

  7. CYP1B1: a unique gene with unique characteristics.

    PubMed

    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.

  8. Delivering quantum dots to cells: bioconjugated quantum dots for targeted and nonspecific extracellular and intracellular imaging.

    PubMed

    Biju, Vasudevanpillai; Itoh, Tamitake; Ishikawa, Mitsuru

    2010-08-01

    Bioconjugated nanomaterials offer endless opportunities to advance both nanobiotechnology and biomedical technology. In this regard, semiconductor nanoparticles, also called quantum dots, are of particular interest for multimodal, multifunctional and multiplexed imaging of biomolecules, cells, tissues and animals. The unique optical properties, such as size-dependent tunable absorption and emission in the visible and NIR regions, narrow emission and broad absorption bands, high photoluminescence quantum yields, large one- and multi-photon absorption cross-sections, and exceptional photostability are the advantages of quantum dots. Multimodal imaging probes are developed by interfacing the unique optical properties of quantum dots with magnetic or radioactive materials. Besides, crystalline structure of quantum dots adds scope for high-contrast X-ray and TEM imaging. Yet another unique feature of a quantum dot is its spacious and flexible surface which is promising to integrate multiple ligands and antibodies and construct multi-functional probes for bioimaging. In this critical review, we will summarize recent advancements in the preparation of biocompatible quantum dots, bioconjugation of quantum dots, and applications of quantum dots and their bioconjugates for targeted and nonspecific imaging of extracellular and intracellular proteins, organelles and functions (181 references).

  9. Quantum microbiology.

    PubMed

    Trevors, J T; Masson, L

    2011-01-01

    During his famous 1943 lecture series at Trinity College Dublin, the reknown physicist Erwin Schrodinger discussed the failure and challenges of interpreting life by classical physics alone and that a new approach, rooted in Quantum principles, must be involved. Quantum events are simply a level of organization below the molecular level. This includes the atomic and subatomic makeup of matter in microbial metabolism and structures, as well as the organic, genetic information code of DNA and RNA. Quantum events at this time do not elucidate, for example, how specific genetic instructions were first encoded in an organic genetic code in microbial cells capable of growth and division, and its subsequent evolution over 3.6 to 4 billion years. However, due to recent technological advances, biologists and physicists are starting to demonstrate linkages between various quantum principles like quantum tunneling, entanglement and coherence in biological processes illustrating that nature has exerted some level quantum control to optimize various processes in living organisms. In this article we explore the role of quantum events in microbial processes and endeavor to show that after nearly 67 years, Schrödinger was prophetic and visionary in his view of quantum theory and its connection with some of the fundamental mechanisms of life.

  10. Quantum Geometry

    NASA Astrophysics Data System (ADS)

    Giesel, Kristina

    The following sections are included: * Canonical Quantization of General Relativity * General Relativity in Connection Variables * Holonomy-Flux Algebra and its Representation(s) * The Ashtekar-Lewandowski Representation and the Kinematical Hilbert Space of LQG * The Quantum Einstein's Equations of Loop Quantum Gravity * Geometric Operators and Their Properties * Summary * References

  11. Quantum metrology

    NASA Technical Reports Server (NTRS)

    Lee, H.; Kok, P.; Dowling, J. P.

    2002-01-01

    This paper addresses the formal equivalence between the Mach-Zehnder interferometer, the Ramsey spectroscope, and a specific quantum logical gate. Based on this equivalence we introduce the quantum Rosetta Stone, and we describe a projective measurement scheme for generating the desired correlations between the interferometric input states in order to achieve Heisenberg-limited sensitivity.

  12. Quantum Algorithms

    NASA Technical Reports Server (NTRS)

    Abrams, D.; Williams, C.

    1999-01-01

    This thesis describes several new quantum algorithms. These include a polynomial time algorithm that uses a quantum fast Fourier transform to find eigenvalues and eigenvectors of a Hamiltonian operator, and that can be applied in cases for which all know classical algorithms require exponential time.

  13. Quantum Finance

    NASA Astrophysics Data System (ADS)

    Baaquie, Belal E.

    2004-11-01

    Financial mathematics is currently almost completely dominated by stochastic calculus. Presenting a completely independent approach, this book applies the mathematical and conceptual formalism of quantum mechanics and quantum field theory (with particular emphasis on the path integral) to the theory of options and to the modeling of interest rates. Many new results, accordingly, emerge from the author's perspective.

  14. Dynamics of hot random quantum spin chains: from anyons to Heisenberg spins

    NASA Astrophysics Data System (ADS)

    Parameswaran, Siddharth; Potter, Andrew; Vasseur, Romain

    2015-03-01

    We argue that the dynamics of the random-bond Heisenberg spin chain are ergodic at infinite temperature, in contrast to the many-body localized behavior seen in its random-field counterpart. First, we show that excited-state real-space renormalization group (RSRG-X) techniques suffer from a fatal breakdown of perturbation theory due to the proliferation of large effective spins that grow without bound. We repair this problem by deforming the SU (2) symmetry of the Heisenberg chain to its `anyonic' version, SU(2)k , where the growth of effective spins is truncated at spin S = k / 2 . This enables us to construct a self-consistent RSRG-X scheme that is particularly simple at infinite temperature. Solving the flow equations, we compute the excited-state entanglement and show that it crosses over from volume-law to logarithmic scaling at a length scale ξk ~eαk3 . This reveals that (a) anyon chains have random-singlet-like excited states for any finite k; and (b) ergodicity is restored in the Heisenberg limit k --> ∞ . We acknowledge support from the Quantum Materials program of LBNL (RV), the Gordon and Betty Moore Foundation (ACP), and UC Irvine startup funds (SAP).

  15. Quantum spin liquids: a review

    NASA Astrophysics Data System (ADS)

    Savary, Lucile; Balents, Leon

    2017-01-01

    Quantum spin liquids may be considered ‘quantum disordered’ ground states of spin systems, in which zero-point fluctuations are so strong that they prevent conventional magnetic long-range order. More interestingly, quantum spin liquids are prototypical examples of ground states with massive many-body entanglement, which is of a degree sufficient to render these states distinct phases of matter. Their highly entangled nature imbues quantum spin liquids with unique physical aspects, such as non-local excitations, topological properties, and more. In this review, we discuss the nature of such phases and their properties based on paradigmatic models and general arguments, and introduce theoretical technology such as gauge theory and partons, which are conveniently used in the study of quantum spin liquids. An overview is given of the different types of quantum spin liquids and the models and theories used to describe them. We also provide a guide to the current status of experiments in relation to study quantum spin liquids, and to the diverse probes used therein.

  16. Quantum Computation Toward Quantum Gravity

    NASA Astrophysics Data System (ADS)

    Zizzi, P. A.

    2001-08-01

    The aim of this paper is to enlighten the emerging relevance of Quantum Information Theory in the field of Quantum Gravity. As it was suggested by J. A. Wheeler, information theory must play a relevant role in understanding the foundations of Quantum Mechanics (the "It from bit" proposal). Here we suggest that quantum information must play a relevant role in Quantum Gravity (the "It from qubit" proposal). The conjecture is that Quantum Gravity, the theory which will reconcile Quantum Mechanics with General Relativity, can be formulated in terms of quantum bits of information (qubits) stored in space at the Planck scale. This conjecture is based on the following arguments: a) The holographic principle, b) The loop quantum gravity approach and spin networks, c) Quantum geometry and black hole entropy. From the above arguments, as they stand in the literature, it follows that the edges of spin networks pierce the black hole horizon and excite curvature degrees of freedom on the surface. These excitations are micro-states of Chern-Simons theory and account of the black hole entropy which turns out to be a quarter of the area of the horizon, (in units of Planck area), in accordance with the holographic principle. Moreover, the states which dominate the counting correspond to punctures of spin j = 1/2 and one can in fact visualize each micro-state as a bit of information. The obvious generalization of this result is to consider open spin networks with edges labeled by the spin -1/ 2 representation of SU(2) in a superposed state of spin "on" and spin "down." The micro-state corresponding to such a puncture will be a pixel of area which is "on" and "off" at the same time, and it will encode a qubit of information. This picture, when applied to quantum cosmology, describes an early inflationary universe which is a discrete version of the de Sitter universe.

  17. Quantum Mechanics and Narratability

    NASA Astrophysics Data System (ADS)

    Myrvold, Wayne C.

    2016-07-01

    As has been noted by several authors, in a relativistic context, there is an interesting difference between classical and quantum state evolution. For a classical system, a state history of a quantum system given along one foliation uniquely determines, without any consideration of the system's dynamics, a state history along any other foliation. This is not true for quantum state evolution; there are cases in which a state history along one foliation is compatible with multiple distinct state histories along some other, a phenomenon that David Albert has dubbed "non-narratability." In this article, we address the question of whether non-narratability is restricted to the sorts of special states that so far have been used to illustrate it. The results of the investigation suggest that there has been a misplaced emphasis on underdetermination of state histories; though this is generic for the special cases that have up until now been considered, involving bipartite systems in pure entangled states, it fails generically in cases in which more component systems are taken into account, and for bipartite systems that have some entanglement with their environment. For such cases, if we impose relativistic causality constraints on the evolution, then, except for very special states, a state history along one foliation uniquely determines a state history along any other. But this in itself is a marked difference between classical and quantum state evolution, because, in a classical setting, no considerations of dynamics at all are needed to go from a state history along one foliation to a state history along another.

  18. Symbols are not uniquely human.

    PubMed

    Ribeiro, Sidarta; Loula, Angelo; de Araújo, Ivan; Gudwin, Ricardo; Queiroz, João

    2007-01-01

    Modern semiotics is a branch of logics that formally defines symbol-based communication. In recent years, the semiotic classification of signs has been invoked to support the notion that symbols are uniquely human. Here we show that alarm-calls such as those used by African vervet monkeys (Cercopithecus aethiops), logically satisfy the semiotic definition of symbol. We also show that the acquisition of vocal symbols in vervet monkeys can be successfully simulated by a computer program based on minimal semiotic and neurobiological constraints. The simulations indicate that learning depends on the tutor-predator ratio, and that apprentice-generated auditory mistakes in vocal symbol interpretation have little effect on the learning rates of apprentices (up to 80% of mistakes are tolerated). In contrast, just 10% of apprentice-generated visual mistakes in predator identification will prevent any vocal symbol to be correctly associated with a predator call in a stable manner. Tutor unreliability was also deleterious to vocal symbol learning: a mere 5% of "lying" tutors were able to completely disrupt symbol learning, invariably leading to the acquisition of incorrect associations by apprentices. Our investigation corroborates the existence of vocal symbols in a non-human species, and indicates that symbolic competence emerges spontaneously from classical associative learning mechanisms when the conditioned stimuli are self-generated, arbitrary and socially efficacious. We propose that more exclusive properties of human language, such as syntax, may derive from the evolution of higher-order domains for neural association, more removed from both the sensory input and the motor output, able to support the gradual complexification of grammatical categories into syntax.

  19. Quantum Chaos

    NASA Astrophysics Data System (ADS)

    Casati, Giulio; Chirikov, Boris

    1995-04-01

    Preface; Acknowledgments; Introduction: 1. The legacy of chaos in quantum mechanics G. Casati and B. V. Chirikov; Part I. Classical Chaos and Quantum Localization: 2. Stochastic behaviour of a quantum pendulum under a periodic perturbation G. Casati, B. V. Chirikov, F. M. Izrailev and J. Ford; 3. Quantum dynamics of a nonintegrable system D. R. Grempel, R. E. Prange and S. E. Fishman; 4. Excitation of molecular rotation by periodic microwave pulses. A testing ground for Anderson localization R. Blümel, S. Fishman and U. Smilansky; 5. Localization of diffusive excitation in multi-level systems D. K. Shepelyansky; 6. Classical and quantum chaos for a kicked top F. Haake, M. Kus and R. Scharf; 7. Self-similarity in quantum dynamics L. E. Reichl and L. Haoming; 8. Time irreversibility of classically chaotic quantum dynamics K. Ikeda; 9. Effect of noise on time-dependent quantum chaos E. Ott, T. M. Antonsen Jr and J. D. Hanson; 10. Dynamical localization, dissipation and noise R. F. Graham; 11. Maximum entropy models and quantum transmission in disordered systems J.-L. Pichard and M. Sanquer; 12. Solid state 'atoms' in intense oscillating fields M. S. Sherwin; Part II. Atoms in Strong Fields: 13. Localization of classically chaotic diffusion for hydrogen atoms in microwave fields J. E. Bayfield, G. Casati, I. Guarneri and D. W. Sokol; 14. Inhibition of quantum transport due to 'scars' of unstable periodic orbits R. V. Jensen, M. M. Sanders, M. Saraceno and B. Sundaram; 15. Rubidium Rydberg atoms in strong fields G. Benson, G. Raithel and H. Walther; 16. Diamagnetic Rydberg atom: confrontation of calculated and observed spectra C.-H. Iu, G. R. Welch, M. M. Kash, D. Kleppner, D. Delande and J. C. Gay; 17. Semiclassical approximation for the quantum states of a hydrogen atom in a magnetic field near the ionization limit M. Y. Kuchiev and O. P. Sushkov; 18. The semiclassical helium atom D. Wintgen, K. Richter and G. Tanner; 19. Stretched helium: a model for quantum chaos

  20. Quantum Chaos

    NASA Astrophysics Data System (ADS)

    Casati, Giulio; Chirikov, Boris

    2006-11-01

    Preface; Acknowledgments; Introduction: 1. The legacy of chaos in quantum mechanics G. Casati and B. V. Chirikov; Part I. Classical Chaos and Quantum Localization: 2. Stochastic behaviour of a quantum pendulum under a periodic perturbation G. Casati, B. V. Chirikov, F. M. Izrailev and J. Ford; 3. Quantum dynamics of a nonintegrable system D. R. Grempel, R. E. Prange and S. E. Fishman; 4. Excitation of molecular rotation by periodic microwave pulses. A testing ground for Anderson localization R. Blümel, S. Fishman and U. Smilansky; 5. Localization of diffusive excitation in multi-level systems D. K. Shepelyansky; 6. Classical and quantum chaos for a kicked top F. Haake, M. Kus and R. Scharf; 7. Self-similarity in quantum dynamics L. E. Reichl and L. Haoming; 8. Time irreversibility of classically chaotic quantum dynamics K. Ikeda; 9. Effect of noise on time-dependent quantum chaos E. Ott, T. M. Antonsen Jr and J. D. Hanson; 10. Dynamical localization, dissipation and noise R. F. Graham; 11. Maximum entropy models and quantum transmission in disordered systems J.-L. Pichard and M. Sanquer; 12. Solid state 'atoms' in intense oscillating fields M. S. Sherwin; Part II. Atoms in Strong Fields: 13. Localization of classically chaotic diffusion for hydrogen atoms in microwave fields J. E. Bayfield, G. Casati, I. Guarneri and D. W. Sokol; 14. Inhibition of quantum transport due to 'scars' of unstable periodic orbits R. V. Jensen, M. M. Sanders, M. Saraceno and B. Sundaram; 15. Rubidium Rydberg atoms in strong fields G. Benson, G. Raithel and H. Walther; 16. Diamagnetic Rydberg atom: confrontation of calculated and observed spectra C.-H. Iu, G. R. Welch, M. M. Kash, D. Kleppner, D. Delande and J. C. Gay; 17. Semiclassical approximation for the quantum states of a hydrogen atom in a magnetic field near the ionization limit M. Y. Kuchiev and O. P. Sushkov; 18. The semiclassical helium atom D. Wintgen, K. Richter and G. Tanner; 19. Stretched helium: a model for quantum chaos

  1. Internal quality control system for non-stationary, non-ergodic analytical processes based upon exponentially weighted estimation of process means and process standard deviation.

    PubMed

    Jansen, Rob T P; Laeven, Mark; Kardol, Wim

    2002-06-01

    The analytical processes in clinical laboratories should be considered to be non-stationary, non-ergodic and probably non-stochastic processes. Both the process mean and the process standard deviation vary. The variation can be different at different levels of concentration. This behavior is shown in five examples of different analytical systems: alkaline phosphatase on the Hitachi 911 analyzer (Roche), vitamin B12 on the Access analyzer (Beckman), prothrombin time and activated partial thromboplastin time on the STA Compact analyzer (Roche) and PO2 on the ABL 520 analyzer (Radiometer). A model is proposed to assess the status of a process. An exponentially weighted moving average and standard deviation was used to estimate process mean and standard deviation. Process means were estimated overall and for each control level. The process standard deviation was estimated in terms of within-run standard deviation. Limits were defined in accordance with state of the art- or biological variance-derived cut-offs. The examples given are real, not simulated, data. Individual control sample results were normalized to a target value and target standard deviation. The normalized values were used in the exponentially weighted algorithm. The weighting factor was based on a process time constant, which was estimated from the period between two calibration or maintenance procedures. The proposed system was compared with Westgard rules. The Westgard rules perform well, despite the underlying presumption of ergodicity. This is mainly caused by the introduction of the starting rule of 12s, which proves essential to prevent a large number of rule violations. The probability of reporting a test result with an analytical error that exceeds the total allowable error was calculated for the proposed system as well as for the Westgard rules. The proposed method performed better. The proposed algorithm was implemented in a computer program running on computers to which the analyzers were

  2. Quantum State Tomography via Reduced Density Matrices

    NASA Astrophysics Data System (ADS)

    Xin, Tao; Lu, Dawei; Klassen, Joel; Yu, Nengkun; Ji, Zhengfeng; Chen, Jianxin; Ma, Xian; Long, Guilu; Zeng, Bei; Laflamme, Raymond

    2017-01-01

    Quantum state tomography via local measurements is an efficient tool for characterizing quantum states. However, it requires that the original global state be uniquely determined (UD) by its local reduced density matrices (RDMs). In this work, we demonstrate for the first time a class of states that are UD by their RDMs under the assumption that the global state is pure, but fail to be UD in the absence of that assumption. This discovery allows us to classify quantum states according to their UD properties, with the requirement that each class be treated distinctly in the practice of simplifying quantum state tomography. Additionally, we experimentally test the feasibility and stability of performing quantum state tomography via the measurement of local RDMs for each class. These theoretical and experimental results demonstrate the advantages and possible pitfalls of quantum state tomography with local measurements.

  3. Quantum Navigation and Ranking in Complex Networks

    NASA Astrophysics Data System (ADS)

    Sánchez-Burillo, Eduardo; Duch, Jordi; Gómez-Gardeñes, Jesús; Zueco, David

    2012-08-01

    Complex networks are formal frameworks capturing the interdependencies between the elements of large systems and databases. This formalism allows to use network navigation methods to rank the importance that each constituent has on the global organization of the system. A key example is Pagerank navigation which is at the core of the most used search engine of the World Wide Web. Inspired in this classical algorithm, we define a quantum navigation method providing a unique ranking of the elements of a network. We analyze the convergence of quantum navigation to the stationary rank of networks and show that quantumness decreases the number of navigation steps before convergence. In addition, we show that quantum navigation allows to solve degeneracies found in classical ranks. By implementing the quantum algorithm in real networks, we confirm these improvements and show that quantum coherence unveils new hierarchical features about the global organization of complex systems.

  4. Quantum Navigation and Ranking in Complex Networks

    PubMed Central

    Sánchez-Burillo, Eduardo; Duch, Jordi; Gómez-Gardeñes, Jesús; Zueco, David

    2012-01-01

    Complex networks are formal frameworks capturing the interdependencies between the elements of large systems and databases. This formalism allows to use network navigation methods to rank the importance that each constituent has on the global organization of the system. A key example is Pagerank navigation which is at the core of the most used search engine of the World Wide Web. Inspired in this classical algorithm, we define a quantum navigation method providing a unique ranking of the elements of a network. We analyze the convergence of quantum navigation to the stationary rank of networks and show that quantumness decreases the number of navigation steps before convergence. In addition, we show that quantum navigation allows to solve degeneracies found in classical ranks. By implementing the quantum algorithm in real networks, we confirm these improvements and show that quantum coherence unveils new hierarchical features about the global organization of complex systems. PMID:22930671

  5. Quantum simulation of classical thermal states.

    PubMed

    Dür, W; Van den Nest, M

    2011-10-21

    We establish a connection between ground states of local quantum Hamiltonians and thermal states of classical spin systems. For any discrete classical statistical mechanical model in any spatial dimension, we find an associated quantum state such that the reduced density operator behaves as the thermal state of the classical system. We show that all these quantum states are unique ground states of a universal 5-body local quantum Hamiltonian acting on a (polynomially enlarged) qubit system on a 2D lattice. The only free parameters of the quantum Hamiltonian are coupling strengths of two-body interactions, which allow one to choose the type and dimension of the classical model as well as the interaction strength and temperature. This opens the possibility to study and simulate classical spin models in arbitrary dimension using a 2D quantum system.

  6. Quantum oscillations in magnetically doped colloidal nanocrystals.

    PubMed

    Ochsenbein, Stefan T; Gamelin, Daniel R

    2011-02-01

    Progress in the synthesis of colloidal quantum dots has recently provided access to entirely new forms of diluted magnetic semiconductors, some of which may find use in quantum computation. The usefulness of a spin qubit is defined by its Rabi frequency, which determines the operation time, and its coherence time, which sets the error correction window. However, the spin dynamics of magnetic impurity ions in colloidal doped quantum dots remain entirely unexplored. Here, we use pulsed electron paramagnetic resonance spectroscopy to demonstrate long spin coherence times of ∼0.9 µs in colloidal ZnO quantum dots containing the paramagnetic dopant Mn(2+), as well as Rabi oscillations with frequencies ranging between 2 and 20 MHz depending on microwave power. We also observe electron spin echo envelope modulations of the Mn(2+) signal due to hyperfine coupling with protons outside the quantum dots, a situation unique to the colloidal form of quantum dots, and not observed to date.

  7. Rhodomentones A and B, novel meroterpenoids with unique NMR characteristics from Rhodomyrtus tomentosa.

    PubMed

    Liu, Hong-Xin; Chen, Kai; Yuan, Yao; Xu, Zhi-Fang; Tan, Hai-Bo; Qiu, Sheng-Xiang

    2016-07-26

    Two novel meroterpenoids, rhodomentones A and B bearing an unprecedented caryophyllene-conjugated oxa-spiro[5.8] tetradecadiene skeleton, were isolated from the leaves of Rhodomyrtus tomentosa. Their structures with unique NMR characteristics were determined by extensive spectroscopic analysis, single-crystal X-ray diffraction, quantum molecular calculation, chemical transformation as well as total synthesis.

  8. Quantum Control Engineering with Trapped Ions

    NASA Astrophysics Data System (ADS)

    Biercuk, Michael

    2015-03-01

    Technologies fundamentally enabled by quantum mechanics are poised to transform a broad range of applications from computation to precision metrology over the coming decades. This talk will introduce a new field of research which is seeing concepts from control engineering translated to the domain of quantum mechanics in an effort to realize the full potential of engineered quantum technologies. We focus on understanding the physics underlying controlled quantum dynamics in the presence of rapidly fluctuating time-dependent Hamiltonians, leveraging the unique capabilities provided by trapped ions as a model quantum system. Our results introduce and experimentally validate generalized filter-transfer functions which cast arbitrary quantum control operations on qubits as noise spectral filters. We demonstrate the utility of these constructs for directly predicting the evolution of a quantum state in a realistic noisy environment, for developing novel robust control and sensing protocols, and for improving the stability of atomic clocks. This work demonstrates how quantum control can be leveraged to overcome some of the most challenging problems in quantum engineering, and even provide totally new functionality to quantum systems.

  9. Quantum Baseball.

    ERIC Educational Resources Information Center

    Peterson, Ivars

    1989-01-01

    An analogy from the game of baseball can be used to examine the philosophy involved in statistics surrounding quantum mechanical events. The "Strong Baseball Principle" is proposed and discussed. (CW)

  10. Quantum Metaphotonics

    DTIC Science & Technology

    2016-03-24

    oxide layer that is between the indium island and gold contacts. This forms a tunnel barrier for electrons. As the temperature is decreased... islands . Low densities of indium islands have been shown to increase the photoluminescence of an ensemble of InAs quantum dots. Indium islands have also...we investigated self-assembled MBE grown indium plasmonic nanostructures, or indium islands . While quantum dots degrade more significantly as they

  11. Quantum Locality?

    NASA Astrophysics Data System (ADS)

    Stapp, Henry P.

    2012-05-01

    Robert Griffiths has recently addressed, within the framework of a `consistent quantum theory' that he has developed, the issue of whether, as is often claimed, quantum mechanics entails a need for faster-than-light transfers of information over long distances. He argues that the putative proofs of this property that involve hidden variables include in their premises some essentially classical-physics-type assumptions that are not entailed by the precepts of quantum mechanics. Thus whatever is proved is not a feature of quantum mechanics, but is a property of a theory that tries to combine quantum theory with quasi-classical features that go beyond what is entailed by quantum theory itself. One cannot logically prove properties of a system by establishing, instead, properties of a system modified by adding properties alien to the original system. Hence Griffiths' rejection of hidden-variable-based proofs is logically warranted. Griffiths mentions the existence of a certain alternative proof that does not involve hidden variables, and that uses only macroscopically described observable properties. He notes that he had examined in his book proofs of this general kind, and concluded that they provide no evidence for nonlocal influences. But he did not examine the particular proof that he cites. An examination of that particular proof by the method specified by his `consistent quantum theory' shows that the cited proof is valid within that restrictive version of quantum theory. An added section responds to Griffiths' reply, which cites general possibilities of ambiguities that might make what is to be proved ill-defined, and hence render the pertinent `consistent framework' ill defined. But the vagaries that he cites do not upset the proof in question, which, both by its physical formulation and by explicit identification, specify the framework to be used. Griffiths confirms the validity of the proof insofar as that pertinent framework is used. The section also shows

  12. Quantum correlations and distinguishability of quantum states

    NASA Astrophysics Data System (ADS)

    Spehner, Dominique

    2014-07-01

    A survey of various concepts in quantum information is given, with a main emphasis on the distinguishability of quantum states and quantum correlations. Covered topics include generalized and least square measurements, state discrimination, quantum relative entropies, the Bures distance on the set of quantum states, the quantum Fisher information, the quantum Chernoff bound, bipartite entanglement, the quantum discord, and geometrical measures of quantum correlations. The article is intended both for physicists interested not only by collections of results but also by the mathematical methods justifying them, and for mathematicians looking for an up-to-date introductory course on these subjects, which are mainly developed in the physics literature.

  13. Quantum technology: the second quantum revolution.

    PubMed

    Dowling, Jonathan P; Milburn, Gerard J

    2003-08-15

    We are currently in the midst of a second quantum revolution. The first quantum revolution gave us new rules that govern physical reality. The second quantum revolution will take these rules and use them to develop new technologies. In this review we discuss the principles upon which quantum technology is based and the tools required to develop it. We discuss a number of examples of research programs that could deliver quantum technologies in coming decades including: quantum information technology, quantum electromechanical systems, coherent quantum electronics, quantum optics and coherent matter technology.

  14. Compatible quantum theory

    NASA Astrophysics Data System (ADS)

    Friedberg, R.; Hohenberg, P. C.

    2014-09-01

    Formulations of quantum mechanics (QM) can be characterized as realistic, operationalist, or a combination of the two. In this paper a realistic theory is defined as describing a closed system entirely by means of entities and concepts pertaining to the system. An operationalist theory, on the other hand, requires in addition entities external to the system. A realistic formulation comprises an ontology, the set of (mathematical) entities that describe the system, and assertions, the set of correct statements (predictions) the theory makes about the objects in the ontology. Classical mechanics is the prime example of a realistic physical theory. A straightforward generalization of classical mechanics to QM is hampered by the inconsistency of quantum properties with classical logic, a circumstance that was noted many years ago by Birkhoff and von Neumann. The present realistic formulation of the histories approach originally introduced by Griffiths, which we call ‘compatible quantum theory (CQT)’, consists of a ‘microscopic’ part (MIQM), which applies to a closed quantum system of any size, and a ‘macroscopic’ part (MAQM), which requires the participation of a large (ideally, an infinite) system. The first (MIQM) can be fully formulated based solely on the assumption of a Hilbert space ontology and the noncontextuality of probability values, relying in an essential way on Gleason's theorem and on an application to dynamics due in large part to Nistico. Thus, the present formulation, in contrast to earlier ones, derives the Born probability formulas and the consistency (decoherence) conditions for frameworks. The microscopic theory does not, however, possess a unique corpus of assertions, but rather a multiplicity of contextual truths (‘c-truths’), each one associated with a different framework. This circumstance leads us to consider the microscopic theory to be physically indeterminate and therefore incomplete, though logically coherent. The

  15. Compatible quantum theory.

    PubMed

    Friedberg, R; Hohenberg, P C

    2014-09-01

    Formulations of quantum mechanics (QM) can be characterized as realistic, operationalist, or a combination of the two. In this paper a realistic theory is defined as describing a closed system entirely by means of entities and concepts pertaining to the system. An operationalist theory, on the other hand, requires in addition entities external to the system. A realistic formulation comprises an ontology, the set of (mathematical) entities that describe the system, and assertions, the set of correct statements (predictions) the theory makes about the objects in the ontology. Classical mechanics is the prime example of a realistic physical theory. A straightforward generalization of classical mechanics to QM is hampered by the inconsistency of quantum properties with classical logic, a circumstance that was noted many years ago by Birkhoff and von Neumann. The present realistic formulation of the histories approach originally introduced by Griffiths, which we call 'compatible quantum theory (CQT)', consists of a 'microscopic' part (MIQM), which applies to a closed quantum system of any size, and a 'macroscopic' part (MAQM), which requires the participation of a large (ideally, an infinite) system. The first (MIQM) can be fully formulated based solely on the assumption of a Hilbert space ontology and the noncontextuality of probability values, relying in an essential way on Gleason's theorem and on an application to dynamics due in large part to Nistico. Thus, the present formulation, in contrast to earlier ones, derives the Born probability formulas and the consistency (decoherence) conditions for frameworks. The microscopic theory does not, however, possess a unique corpus of assertions, but rather a multiplicity of contextual truths ('c-truths'), each one associated with a different framework. This circumstance leads us to consider the microscopic theory to be physically indeterminate and therefore incomplete, though logically coherent. The completion of the theory

  16. Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Commins, Eugene D.

    2014-10-01

    Preface; 1. Introduction; 2. Mathematical preliminaries; 3. The rules of quantum mechanics; 4. The connection between the fundamental rules and wave mechanics; 5. Further illustrations of the rules of quantum mechanics; 6. Further developments in one-dimensional wave mechanics; 7. The theory of angular momentum; 8. Wave mechanics in three dimensions: hydrogenic atoms; 9. Time-independent approximations for bound state problems; 10. Applications of static perturbation theory; 11. Identical particles; 12. Atomic structure; 13. Molecules; 14. The stability of matter; 15. Photons; 16. Interaction of non-relativistic charged particles and radiation; 17. Further topics in perturbation theory; 18. Scattering; 19. Special relativity and quantum mechanics: the Klein-Gordon equation; 20. The Dirac equation; 21. Interaction of a relativistic spin 1/2 particle with an external electromagnetic field; 22. The Dirac field; 23. Interaction between relativistic electrons, positrons, and photons; 24. The quantum mechanics of weak interactions; 25. The quantum measurement problem; Appendix A: useful inequalities for quantum mechanics; Appendix B: Bell's inequality; Appendix C: spin of the photon: vector spherical waves; Works cited; Bibliography; Index.

  17. On the fundamental role of dynamics in quantum physics

    NASA Astrophysics Data System (ADS)

    Hofmann, Holger F.

    2016-05-01

    Quantum theory expresses the observable relations between physical properties in terms of probabilities that depend on the specific context described by the "state" of a system. However, the laws of physics that emerge at the macroscopic level are fully deterministic. Here, it is shown that the relation between quantum statistics and deterministic dynamics can be explained in terms of ergodic averages over complex valued probabilities, where the fundamental causality of motion is expressed by an action that appears as the phase of the complex probability multiplied with the fundamental constant ħ. Importantly, classical physics emerges as an approximation of this more fundamental theory of motion, indicating that the assumption of a classical reality described by differential geometry is merely an artefact of an extrapolation from the observation of macroscopic dynamics to a fictitious level of precision that does not exist within our actual experience of the world around us. It is therefore possible to completely replace the classical concepts of trajectories with the more fundamental concept of action phase probabilities as a universally valid description of the deterministic causality of motion that is observed in the physical world.

  18. Quantum Particles From Quantum Information

    NASA Astrophysics Data System (ADS)

    Görnitz, T.; Schomäcker, U.

    2012-08-01

    Many problems in modern physics demonstrate that for a fundamental entity a more general conception than quantum particles or quantum fields are necessary. These concepts cannot explain the phenomena of dark energy or the mind-body-interaction. Instead of any kind of "small elementary building bricks", the Protyposis, an abstract and absolute quantum information, free of special denotation and open for some purport, gives the solution in the search for a fundamental substance. However, as long as at least relativistic particles are not constructed from the Protyposis, such an idea would remain in the range of natural philosophy. Therefore, the construction of relativistic particles without and with rest mass from quantum information is shown.

  19. Quantum Computing for Quantum Chemistry

    DTIC Science & Technology

    2010-09-01

    random walks as the decoherence became strong. Recent experiments on photosynthetic light -harvesting complexes observed long-lived excitonic coherences...by the light -harvesting complex. In Environment-assisted quantum walks in energy transfer of photosynthetic complexes, J. Chem. Phys. 129 (2008...a decohered quantum walk. Motivated by the experiments on the Fenna-Matthews-Olson (FMO) light -harvesting complex of green sulfur bacteria, we

  20. Plasmonic fluorescent quantum dots

    PubMed Central

    Jin, Yongdong

    2009-01-01

    Combining multiple discrete components into a single multifunctional nanoparticle could be useful in a variety of applications. Retaining the unique optical and electrical properties of each component after nanoscale integration is, however, a long-standing problem1,2. It is particularly difficult when trying to combine fluorophores such as semiconductor quantum dots with plasmonic materials such as gold, because gold and other metals can quench the fluorescence3,4. So far, the combination of quantum dot fluorescence with plasmonically active gold has only been demonstrated on flat surfaces5. Here, we combine fluorescent and plasmonic activities in a single nanoparticle by controlling the spacing between a quantum dot core and an ultrathin gold shell with nanometre precision through layer-by-layer assembly. Our wet-chemistry approach provides a general route for the deposition of ultrathin gold layers onto virtually any discrete nanostructure or continuous surface, and should prove useful for multimodal bioimaging6, interfacing with biological systems7, reducing nanotoxicity8, modulating electromagnetic fields5 and contacting nanostructures9,10. PMID:19734929

  1. Discord as a quantum resource for bi-partite communication

    SciTech Connect

    Chrzanowski, Helen M.; Assad, Syed M.; Symul, Thomas; Lam, Ping Koy; Gu, Mile; Modi, Kavan; Vedral, Vlatko; Ralph, Timothy C.

    2014-12-04

    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’.

  2. Quantum key distribution protocol based on contextuality monogamy

    NASA Astrophysics Data System (ADS)

    Singh, Jaskaran; Bharti, Kishor; Arvind

    2017-06-01

    The security of quantum key distribution (QKD) protocols hinges upon features of physical systems that are uniquely quantum in nature. We explore the role of quantumness, as qualified by quantum contextuality, in a QKD scheme. A QKD protocol based on the Klyachko-Can-Binicioğlu-Shumovsky (KCBS) contextuality scenario using a three-level quantum system is presented. We explicitly show the unconditional security of the protocol by a generalized contextuality monogamy relationship based on the no-disturbance principle. This protocol provides a new framework for QKD which has conceptual and practical advantages over other protocols.

  3. Quantum Transmemetic Intelligence

    NASA Astrophysics Data System (ADS)

    Piotrowski, Edward W.; Sładkowski, Jan

    The following sections are included: * Introduction * A Quantum Model of Free Will * Quantum Acquisition of Knowledge * Thinking as a Quantum Algorithm * Counterfactual Measurement as a Model of Intuition * Quantum Modification of Freud's Model of Consciousness * Conclusion * Acknowledgements * References

  4. Quantum Physics for Beginners.

    ERIC Educational Resources Information Center

    Strand, J.

    1981-01-01

    Suggests a new approach for teaching secondary school quantum physics. Reviews traditional approaches and presents some characteristics of the three-part "Quantum Physics for Beginners" project, including: quantum physics, quantum mechanics, and a short historical survey. (SK)

  5. Quantum Physics for Beginners.

    ERIC Educational Resources Information Center

    Strand, J.

    1981-01-01

    Suggests a new approach for teaching secondary school quantum physics. Reviews traditional approaches and presents some characteristics of the three-part "Quantum Physics for Beginners" project, including: quantum physics, quantum mechanics, and a short historical survey. (SK)

  6. Introduction to Quantum Simulation

    NASA Technical Reports Server (NTRS)

    Williams, Colin P.

    2005-01-01

    This viewgraph presentation addresses the problem of efficiently simulating the evolution of a quantum system. The contents include: 1) Quantum Simulation; 2) Extracting Answers from Quantum Simulations; 3) Quantum Fourier Transform; 4) Eigenvalue Estimation; 5) Fermionic Simulations.

  7. Quantum Communication and Quantum Multivariate Polynomial Interpolation

    NASA Astrophysics Data System (ADS)

    Diep, Do Ngoc; Giang, Do Hoang

    2017-09-01

    The paper is devoted to the problem of multivariate polynomial interpolation and its application to quantum secret sharing. We show that using quantum Fourier transform one can produce the protocol for quantum secret sharing distribution.

  8. Powerlaw Decays and Thermalization in Isolated Many-Body Quantum Systems

    NASA Astrophysics Data System (ADS)

    Tavora, Marco; Torres-Herrera, E. J.; Santos, Lea

    2016-05-01

    We propose a new criterion for thermalization in isolated many-body quantum systems. It is based on the powerlaw behavior of the survival probability at long times. The value of the powerlaw exponent depends on the shape and filling of the energy distribution of the initial state. Exponents larger than or equal to 2 correspond to ergodic filling and consequent thermalization. We show that the algebraic behavior, which occurs in both integrable and chaotic systems, may be caused by bounds in the spectrum or by the presence of correlations between the eigenstates of the Hamiltonian. Numerical and analytical results as well as comparisons with existing rigorous mathematical derivations are presented. Our focus are on initial states that can be prepared experimentally using cold atoms in optical lattices. NSF Grant No. DMR-1147430.

  9. On the Stability of KMS States in Perturbative Algebraic Quantum Field Theories

    NASA Astrophysics Data System (ADS)

    Drago, Nicolò; Faldino, Federico; Pinamonti, Nicola

    2017-08-01

    We analyze the stability properties shown by KMS states for interacting massive scalar fields propagating over Minkowski spacetime, recently constructed in the framework of perturbative algebraic quantum field theories by Fredenhagen and Lindner (Commun Math Phys 332:895, 2014). In particular, we prove the validity of the return to equilibrium property when the interaction Lagrangian has compact spatial support. Surprisingly, this does not hold anymore, if the adiabatic limit is considered, namely when the interaction Lagrangian is invariant under spatial translations. Consequently, an equilibrium state under the adiabatic limit for a perturbative interacting theory evolved with the free dynamics does not converge anymore to the free equilibrium state. Actually, we show that its ergodic mean converges to a non-equilibrium steady state for the free theory.

  10. Experimental quantum channel simulation

    NASA Astrophysics Data System (ADS)

    Lu, He; Liu, Chang; Wang, Dong-Sheng; Chen, Luo-Kan; Li, Zheng-Da; Yao, Xing-Can; Li, Li; Liu, Nai-Le; Peng, Cheng-Zhi; Sanders, Barry C.; Chen, Yu-Ao; Pan, Jian-Wei

    2017-04-01

    Quantum simulation is of great importance in quantum information science. Here, we report an experimental quantum channel simulator imbued with an algorithm for imitating the behavior of a general class of quantum systems. The reported quantum channel simulator consists of four single-qubit gates and one controlled-not gate. All types of quantum channels can be decomposed by the algorithm and implemented on this device. We deploy our system to simulate various quantum channels, such as quantum-noise channels and weak quantum measurement. Our results advance experimental quantum channel simulation, which is integral to the goal of quantum information processing.

  11. Quantum Capacitance in Topological Insulators

    PubMed Central

    Xiu, Faxian; Meyer, Nicholas; Kou, Xufeng; He, Liang; Lang, Murong; Wang, Yong; Yu, Xinxin; Fedorov, Alexei V.; Zou, Jin; Wang, Kang L.

    2012-01-01

    Topological insulators show unique properties resulting from massless, Dirac-like surface states that are protected by time-reversal symmetry. Theory predicts that the surface states exhibit a quantum spin Hall effect with counter-propagating electrons carrying opposite spins in the absence of an external magnetic field. However, to date, the revelation of these states through conventional transport measurements remains a significant challenge owing to the predominance of bulk carriers. Here, we report on an experimental observation of Shubnikov-de Haas oscillations in quantum capacitance measurements, which originate from topological helical states. Unlike the traditional transport approach, the quantum capacitance measurements are remarkably alleviated from bulk interference at high excitation frequencies, thus enabling a distinction between the surface and bulk. We also demonstrate easy access to the surface states at relatively high temperatures up to 60 K. Our approach may eventually facilitate an exciting exploration of exotic topological properties at room temperature. PMID:22993694

  12. A potential application in quantum networks—Deterministic quantum operation sharing schemes with Bell states

    NASA Astrophysics Data System (ADS)

    Zhang, KeJia; Zhang, Long; Song, TingTing; Yang, YingHui

    2016-06-01

    In this paper, we propose certain different design ideas on a novel topic in quantum cryptography — quantum operation sharing (QOS). Following these unique ideas, three QOS schemes, the "HIEC" (The scheme whose messages are hidden in the entanglement correlation), "HIAO" (The scheme whose messages are hidden with the assistant operations) and "HIMB" (The scheme whose messages are hidden in the selected measurement basis), have been presented to share the single-qubit operations determinately on target states in a remote node. These schemes only require Bell states as quantum resources. Therefore, they can be directly applied in quantum networks, since Bell states are considered the basic quantum channels in quantum networks. Furthermore, after analyse on the security and resource consumptions, the task of QOS can be achieved securely and effectively in these schemes.

  13. Localization in the quantum sawtooth map emulated on a quantum-information processor

    SciTech Connect

    Henry, Michael K.; Cory, David G.; Emerson, Joseph; Martinez, Rudy

    2006-12-15

    Quantum computers will be unique tools for understanding complex quantum systems. We report an experimental implementation of a sensitive, quantum coherence-dependent localization phenomenon on a quantum information processor (QIP). The localization effect was studied by emulating the dynamics of the quantum sawtooth map in the perturbative regime on a three-qubit QIP. Our results show that the width of the probability distribution in momentum space remained essentially unchanged with successive iterations of the sawtooth map, a result that is consistent with localization. The height of the peak relative to the baseline of the probability distribution did change, a result that is consistent with our QIP being an ensemble of quantum systems with a distribution of errors over the ensemble. We further show that the previously measured distributions of control errors correctly account for the observed changes in the probability distribution.

  14. Quantum charge pumping through fractional fermions in charge density modulated quantum wires and Rashba nanowires

    NASA Astrophysics Data System (ADS)

    Saha, Arijit; Rainis, Diego; Tiwari, Rakesh P.; Loss, Daniel

    2014-07-01

    We study the phenomenon of adiabatic quantum charge pumping in systems supporting fractionally charged fermionic bound states in two different setups. The first quantum pump setup consists of a charge density modulated quantum wire, and the second one is based on a semiconducting nanowire with Rashba spin-orbit interaction, in the presence of a spatially oscillating magnetic field. In both these quantum pumps transport is investigated in an N-X-N geometry, with the system of interest (X) connected to two normal-metal leads (N), and the two pumping parameters are the strengths of the effective wire-lead barriers. Pumped charge is calculated within the scattering matrix formalism. We show that quantum pumping in both setups provides a unique signature of the presence of the fractional-fermion bound states, in terms of the asymptotically quantized pumped charge. Furthermore, we investigate shot noise arising due to quantum pumping, verifying that the quantized pumped charge corresponds to minimal shot noise.

  15. Quantum hydrodynamics

    NASA Astrophysics Data System (ADS)

    Tsubota, Makoto; Kobayashi, Michikazu; Takeuchi, Hiromitsu

    2013-01-01

    Quantum hydrodynamics in superfluid helium and atomic Bose-Einstein condensates (BECs) has been recently one of the most important topics in low temperature physics. In these systems, a macroscopic wave function (order parameter) appears because of Bose-Einstein condensation, which creates quantized vortices. Turbulence consisting of quantized vortices is called quantum turbulence (QT). The study of quantized vortices and QT has increased in intensity for two reasons. The first is that recent studies of QT are considerably advanced over older studies, which were chiefly limited to thermal counterflow in 4He, which has no analog with classical traditional turbulence, whereas new studies on QT are focused on a comparison between QT and classical turbulence. The second reason is the realization of atomic BECs in 1995, for which modern optical techniques enable the direct control and visualization of the condensate and can even change the interaction; such direct control is impossible in other quantum condensates like superfluid helium and superconductors. Our group has made many important theoretical and numerical contributions to the field of quantum hydrodynamics of both superfluid helium and atomic BECs. In this article, we review some of the important topics in detail. The topics of quantum hydrodynamics are diverse, so we have not attempted to cover all these topics in this article. We also ensure that the scope of this article does not overlap with our recent review article (arXiv:1004.5458), “Quantized vortices in superfluid helium and atomic Bose-Einstein condensates”, and other review articles.

  16. The sensitivity analysis of propagator for path independent quantum finance model

    NASA Astrophysics Data System (ADS)

    Kim, Min Jae; Hwang, Dong Il; Lee, Sun Young; Kim, Soo Yong

    2011-03-01

    Quantum finance successfully implements the imperfectly correlated fluctuation of forward interest rates at different maturities, by replacing the Wiener process with a two-dimensional quantum field. Interest rate derivatives can be priced at a more realistic value under this new framework. The quantum finance model requires three main ingredients for pricing: the initial forward interest rates, the volatility of forward interest rates, and the correlation of forward interest rates at different maturities. However, the hedging strategy only focused on fluctuation of forward interest rates. This hedging method is based on the assumption that the propagator, the covariance of forward interest rates, has an ergodic property. Since inserting the propagator is the main characteristic that distinguishes quantum finance from the Libor market model (LMM) and the Heath, Jarrow and Morton (HJM) model, understanding the impact of propagator dynamics on the price of interest rate derivatives is crucial. This research is the first step in developing a hedge strategy with respect to the evolution of the propagator. We analyze the dynamics of the propagator from Libor futures data and the integrated propagator from zero-coupon bond rate data. Then we study the sensitivity of the implied volatility of caplets and swaptions according to the three dominant dynamics of the propagator, and the change of the zero-coupon bond option price according to the two dominant dynamics of the integrated propagator.

  17. Quantum walk computation

    SciTech Connect

    Kendon, Viv

    2014-12-04

    Quantum versions of random walks have diverse applications that are motivating experimental implementations as well as theoretical studies. Recent results showing quantum walks are “universal for quantum computation” relate to algorithms, to be run on quantum computers. We consider whether an experimental implementation of a quantum walk could provide useful computation before we have a universal quantum computer.

  18. Efficient quantum circuit implementation of quantum walks

    SciTech Connect

    Douglas, B. L.; Wang, J. B.

    2009-05-15

    Quantum walks, being the quantum analog of classical random walks, are expected to provide a fruitful source of quantum algorithms. A few such algorithms have already been developed, including the 'glued trees' algorithm, which provides an exponential speedup over classical methods, relative to a particular quantum oracle. Here, we discuss the possibility of a quantum walk algorithm yielding such an exponential speedup over possible classical algorithms, without the use of an oracle. We provide examples of some highly symmetric graphs on which efficient quantum circuits implementing quantum walks can be constructed and discuss potential applications to quantum search for marked vertices along these graphs.

  19. Numerical characteristics of quantum computer simulation

    NASA Astrophysics Data System (ADS)

    Chernyavskiy, A.; Khamitov, K.; Teplov, A.; Voevodin, V.; Voevodin, Vl.

    2016-12-01

    The simulation of quantum circuits is significantly important for the implementation of quantum information technologies. The main difficulty of such modeling is the exponential growth of dimensionality, thus the usage of modern high-performance parallel computations is relevant. As it is well known, arbitrary quantum computation in circuit model can be done by only single- and two-qubit gates, and we analyze the computational structure and properties of the simulation of such gates. We investigate the fact that the unique properties of quantum nature lead to the computational properties of the considered algorithms: the quantum parallelism make the simulation of quantum gates highly parallel, and on the other hand, quantum entanglement leads to the problem of computational locality during simulation. We use the methodology of the AlgoWiki project (algowiki-project.org) to analyze the algorithm. This methodology consists of theoretical (sequential and parallel complexity, macro structure, and visual informational graph) and experimental (locality and memory access, scalability and more specific dynamic characteristics) parts. Experimental part was made by using the petascale Lomonosov supercomputer (Moscow State University, Russia). We show that the simulation of quantum gates is a good base for the research and testing of the development methods for data intense parallel software, and considered methodology of the analysis can be successfully used for the improvement of the algorithms in quantum information science.

  20. Quantum Security for the Physical Layer

    SciTech Connect

    Humble, Travis S

    2013-01-01

    The physical layer describes how communication signals are encoded and transmitted across a channel. Physical security often requires either restricting access to the channel or performing periodic manual inspections. In this tutorial, we describe how the field of quantum communication offers new techniques for securing the physical layer. We describe the use of quantum seals as a unique way to test the integrity and authenticity of a communication channel and to provide security for the physical layer. We present the theoretical and physical underpinnings of quantum seals including the quantum optical encoding used at the transmitter and the test for non-locality used at the receiver. We describe how the envisioned quantum physical sublayer senses tampering and how coordination with higher protocol layers allow quantum seals to influence secure routing or tailor data management methods. We conclude by discussing challenges in the development of quantum seals, the overlap with existing quantum key distribution cryptographic services, and the relevance of a quantum physical sublayer to the future of communication security.

  1. Circuit quantum electrodynamics

    NASA Astrophysics Data System (ADS)

    Bishop, Lev Samuel

    Circuit Quantum Electrodynamics (cQED), the study of the interaction between superconducting circuits behaving as artificial atoms and 1-dimensional transmission-line resonators, has shown much promise for quantum information processing tasks. For the purposes of quantum computing it is usual to approximate the artificial atoms as 2-level qubits, and much effort has been expended on attempts to isolate these qubits from the environment and to invent ever more sophisticated control and measurement schemes. Rather than focussing on these technological aspects of the field, this thesis investigates the opportunities for using these carefully engineered systems for answering questions of fundamental physics. The low dissipation and small mode volume of the circuits allows easy access to the strong-coupling regime of quantum optics, where one can investigate the interaction of light and matter at the level of single atoms and photons. A signature of strong coupling is the splitting of the cavity transmission peak into a pair of resolvable peaks when a single resonant atom is placed inside the cavity---an effect known as vacuum Rabi splitting. The cQED architecture is ideally suited for going beyond this linear response effect. This thesis shows that increasing the drive power results in two unique nonlinear features in the transmitted heterodyne signal: the supersplitting of each vacuum Rabi peak into a doublet, and the appearance of additional peaks with the characteristic n spacing of the Jaynes-Cummings ladder. These constitute direct evidence for the coupling between the quantized microwave field and the anharmonic spectrum of a superconducting qubit acting as an artificial atom. This thesis also addresses the idea of Bell tests, which are experiments that aim to disprove certain types of classical theories, presenting a proposed method for preparing maximally entangled 3-qubit states via a 'preparation by measurement' scheme using an optimized filter on the time

  2. Constraint algebra for interacting quantum systems

    NASA Astrophysics Data System (ADS)

    Fubini, S.; Roncadelli, M.

    1988-04-01

    We consider relativistic constrained systems interacting with external fields. We provide physical arguments to support the idea that the quantum constraint algebra should be the same as in the free quantum case. For systems with ordering ambiguities this principle is essential to obtain a unique quantization. This is shown explicitly in the case of a relativistic spinning particle, where our assumption about the constraint algebra plus invariance under general coordinate transformations leads to a unique S-matrix. On leave from Dipartimento di Fisica Nucleare e Teorica, Università di Pavia and INFN, I-27100 Pavia, Italy.

  3. Iris Data Classification Using Quantum Neural Networks

    NASA Astrophysics Data System (ADS)

    Sahni, Vishal; Patvardhan, C.

    2006-11-01

    Quantum computing is a novel paradigm that promises to be the future of computing. The performance of quantum algorithms has proved to be stunning. ANN within the context of classical computation has been used for approximation and classification tasks with some success. This paper presents an idea of quantum neural networks along with the training algorithm and its convergence property. It synergizes the unique properties of quantum bits or qubits with the various techniques in vogue in neural networks. An example application of Fisher's Iris data set, a benchmark classification problem has also been presented. The results obtained amply demonstrate the classification capabilities of the quantum neuron and give an idea of their promising capabilities.

  4. Quantum Spring

    NASA Astrophysics Data System (ADS)

    Feng, Chao-Jun; Li, Xin-Zhou

    In this paper, we will give a short review on quantum spring, which is a Casimir effect from the helix boundary condition that proposed in our earlier works. The Casimir force parallel to the axis of the helix behaves very much like the force on a spring that obeys the Hooke's law when the ratio r of the pitch to the circumference of the helix is small, but in this case, the force comes from a quantum effect, so we would like to call it quantum spring. On the other hand, the force perpendicular to the axis decreases monotonously with the increasing of the ratio r. Both forces are attractive and their behaviors are the same in two and three dimensions.

  5. Quantum Cryptography

    NASA Astrophysics Data System (ADS)

    Bruß, D.; Meyer, T.

    The Greek words "kryptos" ≡ "hidden" and "logos" ≡ "word" are the etymological sources for "cryptology," the science of secure communication. Within cryptology, one distinguishes cryptography (or "code-making") and cryptanalysis (or "code-breaking"). The aim of cryptography is to ensure secret or "secure" communication between a sender, traditionally called Alice, and a receiver, called Bob. The encryption and decryption of a so-called plain text into a cipher text and back is achieved using a certain key (not necessarily the same for Alice and Bob), as illustrated in Fig. 1. Here, "secure" means that an eavesdropper, called Eve, has no information on the message. In this chapter we will show that in classical cryptography (using classical signals), security relies on the assumed difficulty to solve certain mathematical tasks, whereas in quantum cryptography (using quantum signals), security arises from the laws of quantum physics.

  6. Quantum turbulence

    NASA Astrophysics Data System (ADS)

    Skrbek, L.

    2011-12-01

    We review physical properties of quantum fluids He II and 3He-B, where quantum turbulence (QT) has been studied experimentally. Basic properties of QT in these working fluids are discussed within the phenomenological two-fluid model introduced by Landau. We consider counterflows in which the normal and superfluid components flow against each other, as well as co-flows in which the direction of the two fluids is the same. We pay special attention to the important case of zero temperature limit, where QT represents an interesting and probably the simplest prototype of three-dimensional turbulence in fluids. Experimental techniques to explore QT such as second sound attenuation, Andreev reflection, NMR, ion propagation are briefly introduced and results of various experiments on so-called Vinen QT and Kolmogorov QT both in He II and 3He are discussed, emphasizing similarities and differences between classical and quantum turbulence.

  7. Quantum dice

    NASA Astrophysics Data System (ADS)

    Sassoli de Bianchi, Massimiliano

    2013-09-01

    In a letter to Born, Einstein wrote [42]: "Quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but does not really bring us any closer to the secret of the 'old one.' I, at any rate, am convinced that He does not throw dice." In this paper we take seriously Einstein's famous metaphor, and show that we can gain considerable insight into quantum mechanics by doing something as simple as rolling dice. More precisely, we show how to perform measurements on a single die, to create typical quantum interference effects, and how to connect (entangle) two identical dice, to maximally violate Bell's inequality.

  8. Non-Markovianity hinders Quantum Darwinism

    NASA Astrophysics Data System (ADS)

    Galve, Fernando; Zambrini, Roberta; Maniscalco, Sabrina

    2016-01-01

    We investigate Quantum Darwinism and the emergence of a classical world from the quantum one in connection with the spectral properties of the environment. We use a microscopic model of quantum environment in which, by changing a simple system parameter, we can modify the information back flow from environment into the system, and therefore its non-Markovian character. We show that the presence of memory effects hinders the emergence of classical objective reality, linking these two apparently unrelated concepts via a unique dynamical feature related to decoherence factors.

  9. Non-Markovianity hinders Quantum Darwinism.

    PubMed

    Galve, Fernando; Zambrini, Roberta; Maniscalco, Sabrina

    2016-01-20

    We investigate Quantum Darwinism and the emergence of a classical world from the quantum one in connection with the spectral properties of the environment. We use a microscopic model of quantum environment in which, by changing a simple system parameter, we can modify the information back flow from environment into the system, and therefore its non-Markovian character. We show that the presence of memory effects hinders the emergence of classical objective reality, linking these two apparently unrelated concepts via a unique dynamical feature related to decoherence factors.

  10. Non-Markovianity hinders Quantum Darwinism

    PubMed Central

    Galve, Fernando; Zambrini, Roberta; Maniscalco, Sabrina

    2016-01-01

    We investigate Quantum Darwinism and the emergence of a classical world from the quantum one in connection with the spectral properties of the environment. We use a microscopic model of quantum environment in which, by changing a simple system parameter, we can modify the information back flow from environment into the system, and therefore its non-Markovian character. We show that the presence of memory effects hinders the emergence of classical objective reality, linking these two apparently unrelated concepts via a unique dynamical feature related to decoherence factors. PMID:26786857

  11. Simple understanding of quantum weak values

    PubMed Central

    Qin, Lupei; Feng, Wei; Li, Xin-Qi

    2016-01-01

    In this work we revisit the important and controversial concept of quantum weak values, aiming to provide a simplified understanding to its associated physics and the origin of anomaly. Taking the Stern-Gerlach setup as a working system, we base our analysis on an exact treatment in terms of quantum Bayesian approach. We also make particular connection with a very recent work, where the anomaly of the weak values was claimed from the pure statistics in association with “disturbance” and “post-selection”, rather than the unique quantum nature. Our analysis resolves the related controversies through a clear and quantitative way. PMID:26838670

  12. Simple understanding of quantum weak values.

    PubMed

    Qin, Lupei; Feng, Wei; Li, Xin-Qi

    2016-02-03

    In this work we revisit the important and controversial concept of quantum weak values, aiming to provide a simplified understanding to its associated physics and the origin of anomaly. Taking the Stern-Gerlach setup as a working system, we base our analysis on an exact treatment in terms of quantum Bayesian approach. We also make particular connection with a very recent work, where the anomaly of the weak values was claimed from the pure statistics in association with "disturbance" and "post-selection", rather than the unique quantum nature. Our analysis resolves the related controversies through a clear and quantitative way.

  13. Detecting the relative localisation of quantum particles

    NASA Astrophysics Data System (ADS)

    Knott, P. A.; Sindt, J.; Dunningham, J. A.

    2013-06-01

    One interpretation of how the classical world emerges from quantum physics involves the build-up of certain robust entangled states between particles due to scattering events [1]. This is intriguing because it links classical behaviour with the uniquely quantum effect of entanglement and differs from other interpretations that say classicality arises when quantum correlations are lost or neglected in measurements. However, the problem with this new interpretation has been finding an experimental way of verifying it. Here we outline a straightforward scheme that enables just that and should, in principle, allow experiments to confirm the theory to any desired degree of accuracy.

  14. Patterned semiconductor inverted quantum dot photonic devices

    NASA Astrophysics Data System (ADS)

    Coleman, J. J.

    2016-03-01

    A novel inverted quantum dot structure is presented, which consists of an InGaAs quantum well that has been periodically perforated and then filled with the higher bandgap GaAs barrier material. This structure exhibits a unique quantized energy structure something like a planar atomic bond structure and formation of allowed and forbidden energy bands instead of highly localized, fully discrete states. We describe the growth, processing and characteristics of inverted quantum dot structures and outline interesting and potentially important effects arising from the introduction of nanoscale features (<50 nm) in the active medium.

  15. Dirac Cellular Automaton from Split-step Quantum Walk.

    PubMed

    Mallick, Arindam; Chandrashekar, C M

    2016-05-17

    Simulations of one quantum system by an other has an implication in realization of quantum machine that can imitate any quantum system and solve problems that are not accessible to classical computers. One of the approach to engineer quantum simulations is to discretize the space-time degree of freedom in quantum dynamics and define the quantum cellular automata (QCA), a local unitary update rule on a lattice. Different models of QCA are constructed using set of conditions which are not unique and are not always in implementable configuration on any other system. Dirac Cellular Automata (DCA) is one such model constructed for Dirac Hamiltonian (DH) in free quantum field theory. Here, starting from a split-step discrete-time quantum walk (QW) which is uniquely defined for experimental implementation, we recover the DCA along with all the fine oscillations in position space and bridge the missing connection between DH-DCA-QW. We will present the contribution of the parameters resulting in the fine oscillations on the Zitterbewegung frequency and entanglement. The tuneability of the evolution parameters demonstrated in experimental implementation of QW will establish it as an efficient tool to design quantum simulator and approach quantum field theory from principles of quantum information theory.

  16. Dirac Cellular Automaton from Split-step Quantum Walk

    NASA Astrophysics Data System (ADS)

    Mallick, Arindam; Chandrashekar, C. M.

    2016-05-01

    Simulations of one quantum system by an other has an implication in realization of quantum machine that can imitate any quantum system and solve problems that are not accessible to classical computers. One of the approach to engineer quantum simulations is to discretize the space-time degree of freedom in quantum dynamics and define the quantum cellular automata (QCA), a local unitary update rule on a lattice. Different models of QCA are constructed using set of conditions which are not unique and are not always in implementable configuration on any other system. Dirac Cellular Automata (DCA) is one such model constructed for Dirac Hamiltonian (DH) in free quantum field theory. Here, starting from a split-step discrete-time quantum walk (QW) which is uniquely defined for experimental implementation, we recover the DCA along with all the fine oscillations in position space and bridge the missing connection between DH-DCA-QW. We will present the contribution of the parameters resulting in the fine oscillations on the Zitterbewegung frequency and entanglement. The tuneability of the evolution parameters demonstrated in experimental implementation of QW will establish it as an efficient tool to design quantum simulator and approach quantum field theory from principles of quantum information theory.

  17. Dirac Cellular Automaton from Split-step Quantum Walk

    PubMed Central

    Mallick, Arindam; Chandrashekar, C. M.

    2016-01-01

    Simulations of one quantum system by an other has an implication in realization of quantum machine that can imitate any quantum system and solve problems that are not accessible to classical computers. One of the approach to engineer quantum simulations is to discretize the space-time degree of freedom in quantum dynamics and define the quantum cellular automata (QCA), a local unitary update rule on a lattice. Different models of QCA are constructed using set of conditions which are not unique and are not always in implementable configuration on any other system. Dirac Cellular Automata (DCA) is one such model constructed for Dirac Hamiltonian (DH) in free quantum field theory. Here, starting from a split-step discrete-time quantum walk (QW) which is uniquely defined for experimental implementation, we recover the DCA along with all the fine oscillations in position space and bridge the missing connection between DH-DCA-QW. We will present the contribution of the parameters resulting in the fine oscillations on the Zitterbewegung frequency and entanglement. The tuneability of the evolution parameters demonstrated in experimental implementation of QW will establish it as an efficient tool to design quantum simulator and approach quantum field theory from principles of quantum information theory. PMID:27184159

  18. Quantum Foam

    SciTech Connect

    Lincoln, Don

    2014-10-24

    The laws of quantum mechanics and relativity are quite perplexing however it is when the two theories are merged that things get really confusing. This combined theory predicts that empty space isn’t empty at all – it’s a seething and bubbling cauldron of matter and antimatter particles springing into existence before disappearing back into nothingness. Scientists call this complicated state of affairs “quantum foam.” In this video, Fermilab’s Dr. Don Lincoln discusses this mind-bending idea and sketches some of the experiments that have convinced scientists that this crazy prediction is actually true.

  19. Quantum Finance

    NASA Astrophysics Data System (ADS)

    Baaquie, Belal E.

    2007-09-01

    Foreword; Preface; Acknowledgements; 1. Synopsis; Part I. Fundamental Concepts of Finance: 2. Introduction to finance; 3. Derivative securities; Part II. Systems with Finite Number of Degrees of Freedom: 4. Hamiltonians and stock options; 5. Path integrals and stock options; 6. Stochastic interest rates' Hamiltonians and path integrals; Part III. Quantum Field Theory of Interest Rates Models: 7. Quantum field theory of forward interest rates; 8. Empirical forward interest rates and field theory models; 9. Field theory of Treasury Bonds' derivatives and hedging; 10. Field theory Hamiltonian of forward interest rates; 11. Conclusions; Appendix A: mathematical background; Brief glossary of financial terms; Brief glossary of physics terms; List of main symbols; References; Index.

  20. Dynamics of quantum entanglement in quantum channels

    NASA Astrophysics Data System (ADS)

    Liang, Shi-Dong

    2017-08-01

    Based on the von Neumann entropy, we give a computational formalism of the quantum entanglement dynamics in quantum channels, which can be applied to a general finite systems coupled with their environments in quantum channels. The quantum entanglement is invariant in the decoupled local unitary quantum channel, but it is variant in the non-local coupled unitary quantum channel. The numerical investigation for two examples, two-qubit and two-qutrit models, indicates that the quantum entanglement evolution in the quantum non-local coupling channel oscillates with the coupling strength and time, and depends on the quantum entanglement of the initial state. It implies that quantum information loses or gains when the state of systems evolves in the quantum non-local coupling channel.

  1. Electron quantum optics as quantum signal processing

    NASA Astrophysics Data System (ADS)

    Roussel, B.; Cabart, C.; Fève, G.; Thibierge, E.; Degiovanni, P.

    2017-03-01

    The recent developments of electron quantum optics in quantum Hall edge channels have given us new ways to probe the behavior of electrons in quantum conductors. It has brought new quantities called electronic coherences under the spotlight. In this paper, we explore the relations between electron quantum optics and signal processing through a global review of the various methods for accessing single- and two-electron coherences in electron quantum optics. We interpret electron quantum optics interference experiments as analog signal processing converting quantum signals into experimentally observable quantities such as current averages and correlations. This point of view also gives us a procedure to obtain quantum information quantities from electron quantum optics coherences. We illustrate these ideas by discussing two mode entanglement in electron quantum optics. We also sketch how signal processing ideas may open new perspectives for representing electronic coherences in quantum conductors and understand the properties of the underlying many-body electronic state.

  2. Quantum memory for images: A quantum hologram

    SciTech Connect

    Vasilyev, Denis V.; Sokolov, Ivan V.; Polzik, Eugene S.

    2008-02-15

    Matter-light quantum interface and quantum memory for light are important ingredients of quantum information protocols, such as quantum networks, distributed quantum computation, etc. [P. Zoller et al., Eur. Phys. J. D 36, 203 (2005)]. In this paper we present a spatially multimode scheme for quantum memory for light, which we call a quantum hologram. Our approach uses a multiatom ensemble which has been shown to be efficient for a single spatial mode quantum memory. Due to the multiatom nature of the ensemble and to the optical parallelism it is capable of storing many spatial modes, a feature critical for the present proposal. A quantum hologram with the fidelity exceeding that of classical hologram will be able to store quantum features of an image, such as multimode superposition and entangled quantum states, something that a standard hologram is unable to achieve.

  3. Quantum interference in an electron-hole graphene ring system

    SciTech Connect

    Smirnov, D.; Schmidt, H.; Haug, R. J.

    2013-12-04

    Quantum interference is observed in a graphene ring system via the Aharonov Bohm effect. As graphene is a gapless semiconductor, this geometry allows to study the unique situation of quantum interference between electrons and holes in addition to the unipolar quantum interference. The period and amplitude of the observed Aharonov-Bohm oscillations are independent of the sign of the applied gate voltage showing the equivalence between unipolar and dipolar interference.

  4. Constructing Dense Graphs with Unique Hamiltonian Cycles

    ERIC Educational Resources Information Center

    Lynch, Mark A. M.

    2012-01-01

    It is not difficult to construct dense graphs containing Hamiltonian cycles, but it is difficult to generate dense graphs that are guaranteed to contain a unique Hamiltonian cycle. This article presents an algorithm for generating arbitrarily large simple graphs containing "unique" Hamiltonian cycles. These graphs can be turned into dense graphs…

  5. 77 FR 69393 - Unique Device Identification System

    Federal Register 2010, 2011, 2012, 2013, 2014

    2012-11-19

    ... HUMAN SERVICES Food and Drug Administration 21 CFR Part 801 RIN 0910-AG31 Unique Device Identification System AGENCY: Food and Drug Administration, HHS. ACTION: Proposed rule; amendment. SUMMARY: The Food and... unique device identification system as required by recent amendments to the Federal Food, Drug, and...

  6. Quantum Speedup by Quantum Annealing

    NASA Astrophysics Data System (ADS)

    Somma, Rolando D.; Nagaj, Daniel; Kieferová, Mária

    2012-08-01

    We study the glued-trees problem from A. M. Childs, R. Cleve, E. Deotto, E. Farhi, S. Gutmann, and D. Spielman, in Proceedings of the 35th Annual ACM Symposium on Theory of Computing (ACM, San Diego, CA, 2003), p. 59. in the adiabatic model of quantum computing and provide an annealing schedule to solve an oracular problem exponentially faster than classically possible. The Hamiltonians involved in the quantum annealing do not suffer from the so-called sign problem. Unlike the typical scenario, our schedule is efficient even though the minimum energy gap of the Hamiltonians is exponentially small in the problem size. We discuss generalizations based on initial-state randomization to avoid some slowdowns in adiabatic quantum computing due to small gaps.

  7. Quantum learning without quantum memory.

    PubMed

    Sentís, G; Calsamiglia, J; Muñoz-Tapia, R; Bagan, E

    2012-01-01

    A quantum learning machine for binary classification of qubit states that does not require quantum memory is introduced and shown to perform with the minimum error rate allowed by quantum mechanics for any size of the training set. This result is shown to be robust under (an arbitrary amount of) noise and under (statistical) variations in the composition of the training set, provided it is large enough. This machine can be used an arbitrary number of times without retraining. Its required classical memory grows only logarithmically with the number of training qubits, while its excess risk decreases as the inverse of this number, and twice as fast as the excess risk of an "estimate-and-discriminate" machine, which estimates the states of the training qubits and classifies the data qubit with a discrimination protocol tailored to the obtained estimates.

  8. Quantum learning without quantum memory

    NASA Astrophysics Data System (ADS)

    Sentís, G.; Calsamiglia, J.; Muñoz-Tapia, R.; Bagan, E.

    2012-10-01

    A quantum learning machine for binary classification of qubit states that does not require quantum memory is introduced and shown to perform with the minimum error rate allowed by quantum mechanics for any size of the training set. This result is shown to be robust under (an arbitrary amount of) noise and under (statistical) variations in the composition of the training set, provided it is large enough. This machine can be used an arbitrary number of times without retraining. Its required classical memory grows only logarithmically with the number of training qubits, while its excess risk decreases as the inverse of this number, and twice as fast as the excess risk of an ``estimate-and-discriminate'' machine, which estimates the states of the training qubits and classifies the data qubit with a discrimination protocol tailored to the obtained estimates.

  9. A system’s wave function is uniquely determined by its underlying physical state

    NASA Astrophysics Data System (ADS)

    Colbeck, Roger; Renner, Renato

    2017-01-01

    We address the question of whether the quantum-mechanical wave function Ψ of a system is uniquely determined by any complete description Λ of the system’s physical state. We show that this is the case if the latter satisfies a notion of ‘free choice’. This notion requires that certain experimental parameters—those that according to quantum theory can be chosen independently of other variables—retain this property in the presence of Λ. An implication of this result is that, among all possible descriptions Λ of a system’s state compatible with free choice, the wave function {{\\Psi }} is as objective as Λ.

  10. Key distillation in quantum cryptography

    NASA Astrophysics Data System (ADS)

    Slutsky, Boris Aron

    1998-11-01

    Quantum cryptography is a technique which permits two parties to communicate over an open channel and establish a shared sequence of bits known only to themselves. This task, provably impossible in classical cryptography, is accomplished by encoding the data on quantum particles and harnessing their unique properties. It is believed that no eavesdropping attack consistent with the laws of quantum theory can compromise the secret data unknowingly to the legitimate users of the channel. Any attempt by a hostile actor to monitor the data carrying particles while in transit reveals itself through transmission errors it must inevitably introduce. Unfortunately, in practice a communication is not free of errors even when no eavesdropping is present. Key distillation is a technique that permits the parties to overcome this difficulty and establish a secret key despite channel defects, under the assumption that every particle is handled independently from other particles by the enemy. In the present work, key distillation is described and its various aspects are studied. A relationship is derived between the average error rate resulting from an eavesdropping attack and the amount of information obtained by the attacker. Formal definition is developed of the security of the final key. The net throughput of secret bits in a quantum cryptosystem employing key distillation is assessed. An overview of quantum cryptographic protocols and related information theoretical results is also given.

  11. Quantum gravity.

    NASA Astrophysics Data System (ADS)

    Maślanka, K.

    A model of reality based on quantum fields, but with a classical treatment of gravity, is inconsistent. Finding a solution has proved extremely difficult, possibly due to the beauty and conceptual simplicity of general relativity. There is a variety of approaches to a consistent theory of quntum gravity. At present, it seems that superstring theory is the most promising candidate.

  12. Quantum Interferometry

    NASA Technical Reports Server (NTRS)

    Dowling, Jonathan P.

    2000-01-01

    Recently, several researchers, including yours truly, have been able to demonstrate theoretically that quantum photon entanglement has the potential to also revolutionize the entire field of optical interferometry, by providing many orders of magnitude improvement in interferometer sensitivity. The quantum entangled photon interferometer approach is very general and applies to many types of interferometers. In particular, without nonlocal entanglement, a generic classical interferometer has a statistical-sampling shot-noise limited sensitivity that scales like 1/Sqrt[N], where N is the number of particles (photons, electrons, atoms, neutrons) passing through the interferometer per unit time. However, if carefully prepared quantum correlations are engineered between the particles, then the interferometer sensitivity improves by a factor of Sqrt[N] (square root of N) to scale like 1/N, which is the limit imposed by the Heisenberg Uncertainty Principle. For optical (laser) interferometers operating at milliwatts of optical power, this quantum sensitivity boost corresponds to an eight-order-of-magnitude improvement of signal to noise. Applications are to tests of General Relativity such as ground and orbiting optical interferometers for gravity wave detection, Laser Interferometer Gravity Observatory (LIGO) and the European Laser Interferometer Space Antenna (LISA), respectively.

  13. Quantum dice

    SciTech Connect

    Sassoli de Bianchi, Massimiliano

    2013-09-15

    In a letter to Born, Einstein wrote [42]: “Quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but does not really bring us any closer to the secret of the ‘old one.’ I, at any rate, am convinced that He does not throw dice.” In this paper we take seriously Einstein’s famous metaphor, and show that we can gain considerable insight into quantum mechanics by doing something as simple as rolling dice. More precisely, we show how to perform measurements on a single die, to create typical quantum interference effects, and how to connect (entangle) two identical dice, to maximally violate Bell’s inequality. -- Highlights: •Rolling a die is a quantum process admitting a Hilbert space representation. •Rolling experiments with a single die can produce interference effects. •Two connected dice can violate Bell’s inequality. •Correlations need to be created by the measurement, to violate Bell’s inequality.

  14. Quantum Interferometry

    NASA Technical Reports Server (NTRS)

    Dowling, Jonathan P.

    2000-01-01

    Recently, several researchers, including yours truly, have been able to demonstrate theoretically that quantum photon entanglement has the potential to also revolutionize the entire field of optical interferometry, by providing many orders of magnitude improvement in interferometer sensitivity. The quantum entangled photon interferometer approach is very general and applies to many types of interferometers. In particular, without nonlocal entanglement, a generic classical interferometer has a statistical-sampling shot-noise limited sensitivity that scales like 1/Sqrt[N], where N is the number of particles (photons, electrons, atoms, neutrons) passing through the interferometer per unit time. However, if carefully prepared quantum correlations are engineered between the particles, then the interferometer sensitivity improves by a factor of Sqrt[N] (square root of N) to scale like 1/N, which is the limit imposed by the Heisenberg Uncertainty Principle. For optical (laser) interferometers operating at milliwatts of optical power, this quantum sensitivity boost corresponds to an eight-order-of-magnitude improvement of signal to noise. Applications are to tests of General Relativity such as ground and orbiting optical interferometers for gravity wave detection, Laser Interferometer Gravity Observatory (LIGO) and the European Laser Interferometer Space Antenna (LISA), respectively.

  15. Quantum Turbulence

    NASA Astrophysics Data System (ADS)

    Tsubota, Makoto

    2008-11-01

    The present article reviews the recent developments in the physics of quantum turbulence. Quantum turbulence (QT) was discovered in superfluid 4He in the 1950s, and the research has tended toward a new direction since the mid 90s. The similarities and differences between quantum and classical turbulence have become an important area of research. QT is comprised of quantized vortices that are definite topological defects, being expected to yield a model of turbulence that is much simpler than the classical model. The general introduction of the issue and a brief review on classical turbulence are followed by a description of the dynamics of quantized vortices. Then, we discuss the energy spectrum of QT at very low temperatures. At low wavenumbers, the energy is transferred through the Richardson cascade of quantized vortices, and the spectrum obeys the Kolmogorov law, which is the most important statistical law in turbulence; this classical region shows the similarity to conventional turbulence. At higher wavenumbers, the energy is transferred by the Kelvin-wave cascade on each vortex. This quantum regime depends strongly on the nature of each quantized vortex. The possible dissipation mechanism is discussed. Finally, important new experimental studies, which include investigations into temperature-dependent transition to QT, dissipation at very low temperatures, QT created by vibrating structures, and visualization of QT, are reviewed. The present article concludes with a brief look at QT in atomic Bose-Einstein condensates.

  16. Quantum wormholes

    SciTech Connect

    Visser, M. )

    1991-01-15

    This paper presents an application of quantum-mechanical principles to a microscopic variant of the traversable wormholes recently introduced by Morris and Thorne. The analysis, based on the surgical grafting of two Reissner-Nordstroem spacetimes, proceeds by using a minisuperspace model to approximate the geometry of these wormholes. The thin shell'' formalism is applied to this minisuperspace model to extract the effective Lagrangian appropriate to this one-degree-of-freedom system. This effective Lagrangian is then quantized and the wave function for the wormhole is explicitly exhibited. A slightly more general class of wormholes---corresponding to the addition of some dust'' to the wormhole throat---is analyzed by recourse to WKB techniques. In all cases discussed in this paper, the expectation value of the wormhole radius is calculated to be of the order of the Planck length. Accordingly, though these quantum wormholes are of considerable theoretical interest they do not appear to be useful as a means for interstellar travel. The results of this paper may also have a bearing on the question of topological fluctuations in quantum gravity. These calculations serve to suggest that topology-changing effects might in fact be {ital suppressed} by quantum-gravity effects.

  17. Microsensors based on quantum cascade lasers

    NASA Astrophysics Data System (ADS)

    Wu, Sheng; Deev, Andrei; Tang, Yongchun

    2011-06-01

    We present our results on efficient coupling of Quantum Cascade Lasers (QCLs) into Whispering Gallery Resonators, Hollow Waveguide. We also present results of micro sensors using the unique properties of QCLs, e.g. online sensors for Gas Chromatography (GC). We show that because of the unique brightness properties of QCLs, we could improve GC-Infrared sensors' sensitivity to the same level as Mass Spectrometry, and with different dimension of chemical information.

  18. Quantum Search and Beyond

    DTIC Science & Technology

    2008-07-02

    solution of certain problems for which the communication needs do not dominate. A similar situation prevails in the quantum world. Quantum teleportation and...REPORT Quantum Search and Beyond 14. ABSTRACT 16. SECURITY CLASSIFICATION OF: Ten years ago, the quantum search algorithm was designed to provide a way...P.O. Box 12211 Research Triangle Park, NC 27709-2211 15. SUBJECT TERMS quantum searching - partial quantum searching, fixed-point quantum

  19. Quantum channel construction with circuit quantum electrodynamics

    NASA Astrophysics Data System (ADS)

    Shen, Chao; Noh, Kyungjoo; Albert, Victor V.; Krastanov, Stefan; Devoret, M. H.; Schoelkopf, R. J.; Girvin, S. M.; Jiang, Liang

    2017-04-01

    Quantum channels can describe all transformations allowed by quantum mechanics. We adapt two existing works [S. Lloyd and L. Viola, Phys. Rev. A 65, 010101 (2001), 10.1103/PhysRevA.65.010101 and E. Andersson and D. K. L. Oi, Phys. Rev. A 77, 052104 (2008), 10.1103/PhysRevA.77.052104] to superconducting circuits, featuring a single qubit ancilla with quantum nondemolition readout and adaptive control. This construction is efficient in both ancilla dimension and circuit depth. We point out various applications of quantum channel construction, including system stabilization and quantum error correction, Markovian and exotic channel simulation, implementation of generalized quantum measurements, and more general quantum instruments. Efficient construction of arbitrary quantum channels opens up exciting new possibilities for quantum control, quantum sensing, and information processing tasks.

  20. Efficient quantum walk on a quantum processor

    NASA Astrophysics Data System (ADS)

    Qiang, Xiaogang; Loke, Thomas; Montanaro, Ashley; Aungskunsiri, Kanin; Zhou, Xiaoqi; O'Brien, Jeremy L.; Wang, Jingbo B.; Matthews, Jonathan C. F.

    2016-05-01

    The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise, quantum walks have shown much potential as a framework for developing new quantum algorithms. Here we present explicit efficient quantum circuits for implementing continuous-time quantum walks on the circulant class of graphs. These circuits allow us to sample from the output probability distributions of quantum walks on circulant graphs efficiently. We also show that solving the same sampling problem for arbitrary circulant quantum circuits is intractable for a classical computer, assuming conjectures from computational complexity theory. This is a new link between continuous-time quantum walks and computational complexity theory and it indicates a family of tasks that could ultimately demonstrate quantum supremacy over classical computers. As a proof of principle, we experimentally implement the proposed quantum circuit on an example circulant graph using a two-qubit photonics quantum processor.

  1. Efficient quantum walk on a quantum processor.

    PubMed

    Qiang, Xiaogang; Loke, Thomas; Montanaro, Ashley; Aungskunsiri, Kanin; Zhou, Xiaoqi; O'Brien, Jeremy L; Wang, Jingbo B; Matthews, Jonathan C F

    2016-05-05

    The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise, quantum walks have shown much potential as a framework for developing new quantum algorithms. Here we present explicit efficient quantum circuits for implementing continuous-time quantum walks on the circulant class of graphs. These circuits allow us to sample from the output probability distributions of quantum walks on circulant graphs efficiently. We also show that solving the same sampling problem for arbitrary circulant quantum circuits is intractable for a classical computer, assuming conjectures from computational complexity theory. This is a new link between continuous-time quantum walks and computational complexity theory and it indicates a family of tasks that could ultimately demonstrate quantum supremacy over classical computers. As a proof of principle, we experimentally implement the proposed quantum circuit on an example circulant graph using a two-qubit photonics quantum processor.

  2. Efficient quantum walk on a quantum processor

    PubMed Central

    Qiang, Xiaogang; Loke, Thomas; Montanaro, Ashley; Aungskunsiri, Kanin; Zhou, Xiaoqi; O'Brien, Jeremy L.; Wang, Jingbo B.; Matthews, Jonathan C. F.

    2016-01-01

    The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise, quantum walks have shown much potential as a framework for developing new quantum algorithms. Here we present explicit efficient quantum circuits for implementing continuous-time quantum walks on the circulant class of graphs. These circuits allow us to sample from the output probability distributions of quantum walks on circulant graphs efficiently. We also show that solving the same sampling problem for arbitrary circulant quantum circuits is intractable for a classical computer, assuming conjectures from computational complexity theory. This is a new link between continuous-time quantum walks and computational complexity theory and it indicates a family of tasks that could ultimately demonstrate quantum supremacy over classical computers. As a proof of principle, we experimentally implement the proposed quantum circuit on an example circulant graph using a two-qubit photonics quantum processor. PMID:27146471

  3. Quantum Secure Dialogue with Quantum Encryption

    NASA Astrophysics Data System (ADS)

    Ye, Tian-Yu

    2014-09-01

    How to solve the information leakage problem has become the research focus of quantum dialogue. In this paper, in order to overcome the information leakage problem in quantum dialogue, a novel approach for sharing the initial quantum state privately between communicators, i.e., quantum encryption sharing, is proposed by utilizing the idea of quantum encryption. The proposed protocol uses EPR pairs as the private quantum key to encrypt and decrypt the traveling photons, which can be repeatedly used after rotation. Due to quantum encryption sharing, the public announcement on the state of the initial quantum state is omitted, thus the information leakage problem is overcome. The information-theoretical efficiency of the proposed protocol is nearly 100%, much higher than previous information leakage resistant quantum dialogue protocols. Moreover, the proposed protocol only needs single-photon measurements and nearly uses single photons as quantum resource so that it is convenient to implement in practice.

  4. Quantum random walks using quantum accelerator modes

    SciTech Connect

    Ma, Z.-Y.; Burnett, K.; D'Arcy, M. B.; Gardiner, S. A.

    2006-01-15

    We discuss the use of high-order quantum accelerator modes to achieve an atom optical realization of a biased quantum random walk. We first discuss how one can create coexistent quantum accelerator modes, and hence how momentum transfer that depends on the atoms' internal state can be achieved. When combined with microwave driving of the transition between the states, a different type of atomic beam splitter results. This permits the realization of a biased quantum random walk through quantum accelerator modes.

  5. Optical properties of quantum-dot-doped liquid scintillators

    NASA Astrophysics Data System (ADS)

    Aberle, C.; Li, J. J.; Weiss, S.; Winslow, L.

    2013-10-01

    Semiconductor nanoparticles (quantum dots) were studied in the context of liquid scintillator development for upcoming neutrino experiments. The unique optical and chemical properties of quantum dots are particularly promising for the use in neutrinoless double-beta decay experiments. Liquid scintillators for large scale neutrino detectors have to meet specific requirements which are reviewed, highlighting the peculiarities of quantum-dot-doping. In this paper, we report results on laboratory-scale measurements of the attenuation length and the fluorescence properties of three commercial quantum dot samples. The results include absorbance and emission stability measurements, improvement in transparency due to filtering of the quantum dot samples, precipitation tests to isolate the quantum dots from solution and energy transfer studies with quantum dots and the fluorophore PPO.

  6. Optical properties of quantum-dot-doped liquid scintillators.

    PubMed

    Aberle, C; Li, J J; Weiss, S; Winslow, L

    2013-10-14

    Semiconductor nanoparticles (quantum dots) were studied in the context of liquid scintillator development for upcoming neutrino experiments. The unique optical and chemical properties of quantum dots are particularly promising for the use in neutrinoless double-beta decay experiments. Liquid scintillators for large scale neutrino detectors have to meet specific requirements which are reviewed, highlighting the peculiarities of quantum-dot-doping. In this paper, we report results on laboratory-scale measurements of the attenuation length and the fluorescence properties of three commercial quantum dot samples. The results include absorbance and emission stability measurements, improvement in transparency due to filtering of the quantum dot samples, precipitation tests to isolate the quantum dots from solution and energy transfer studies with quantum dots and the fluorophore PPO.

  7. Optical properties of quantum-dot-doped liquid scintillators

    PubMed Central

    Aberle, C.; Li, J.J.; Weiss, S.; Winslow, L.

    2014-01-01

    Semiconductor nanoparticles (quantum dots) were studied in the context of liquid scintillator development for upcoming neutrino experiments. The unique optical and chemical properties of quantum dots are particularly promising for the use in neutrinoless double-beta decay experiments. Liquid scintillators for large scale neutrino detectors have to meet specific requirements which are reviewed, highlighting the peculiarities of quantum-dot-doping. In this paper, we report results on laboratory-scale measurements of the attenuation length and the fluorescence properties of three commercial quantum dot samples. The results include absorbance and emission stability measurements, improvement in transparency due to filtering of the quantum dot samples, precipitation tests to isolate the quantum dots from solution and energy transfer studies with quantum dots and the fluorophore PPO. PMID:25392711

  8. Quantum decision tree classifier

    NASA Astrophysics Data System (ADS)

    Lu, Songfeng; Braunstein, Samuel L.

    2013-11-01

    We study the quantum version of a decision tree classifier to fill the gap between quantum computation and machine learning. The quantum entropy impurity criterion which is used to determine which node should be split is presented in the paper. By using the quantum fidelity measure between two quantum states, we cluster the training data into subclasses so that the quantum decision tree can manipulate quantum states. We also propose algorithms constructing the quantum decision tree and searching for a target class over the tree for a new quantum object.

  9. Tattoos and piercings: bodily expressions of uniqueness?

    PubMed

    Tiggemann, Marika; Hopkins, Louise A

    2011-06-01

    The study aimed to investigate the motivations underlying the body modification practices of tattooing and piercing. There were 80 participants recruited from an Australian music store, who provided descriptions of their tattoos and piercings and completed measures of need for uniqueness, appearance investment and distinctive appearance investment. It was found that tattooed individuals scored significantly higher on need for uniqueness than non-tattooed individuals. Further, individuals with conventional ear piercings scored significantly lower on need for uniqueness than individuals with no piercings or with facial and body piercings. Neither appearance investment nor distinctive appearance investment differed significantly among tattoo or piercing status groups. Strength of identification with music was significantly correlated with number of tattoos, but not number of piercings. It was concluded that tattooing, but not body piercing, represents a bodily expression of uniqueness. Copyright © 2011 Elsevier Ltd. All rights reserved.

  10. Dependence effects in unique signal transmission

    SciTech Connect

    Cooper, J.A.

    1988-04-01

    ''Unique Signals'' are communicated from a source to a ''strong link'' safety device in a weapon by means of one or more digital communication channels. The probability that the expected unique signal pattern could be generated accidentally (e.g., due to an abnormal environment) would be an important measure. A probabilistic assessment of this likelihood is deceptive, because it depends on characteristics of the other traffic on the communication channel. One such characteristic that is frequently neglected in analysis is dependence. This report gives a mathematical model for dependence; cites some of the ways in which dependence can increase the likelihood of inadvertent unique signal pattern generation; and suggests that communicating each unique signal ''event'' at the highest level of protocol in the communication system minimizes dependence effects. 3 refs., 4 figs.

  11. Unique Biosignatures in Caves of All Lithologies

    NASA Astrophysics Data System (ADS)

    Boston, P. J.; Schubert, K. E.; Gomez, E.; Conrad, P. G.

    2015-10-01

    Unique maze-like microbial communities on cave surfaces on all lithologies all over the world are an excellent candidate biosignatures for life detection missions into caves and other extraterrestrial environments.

  12. Unique Ideas in a New Facility

    ERIC Educational Resources Information Center

    Hamby, G. W.

    1977-01-01

    Unique features of a new vocational agriculture department facility in Diamond, Missouri, are described, which include an overhead hoist system, arc welders, storage areas, paint room, and greenhouse. (TA)

  13. Quantum simulated annealing

    NASA Astrophysics Data System (ADS)

    Boixo, Sergio; Somma, Rolando; Barnum, Howard

    2008-03-01

    We develop a quantum algorithm to solve combinatorial optimization problems through quantum simulation of a classical annealing process. Our algorithm combines techniques from quantum walks and quantum phase estimation, and can be viewed as the quantum analogue of the discrete-time Markov Chain Monte Carlo implementation of classical simulated annealing.

  14. Quantum gate decomposition algorithms.

    SciTech Connect

    Slepoy, Alexander

    2006-07-01

    Quantum computing algorithms can be conveniently expressed in a format of a quantum logical circuits. Such circuits consist of sequential coupled operations, termed ''quantum gates'', or quantum analogs of bits called qubits. We review a recently proposed method [1] for constructing general ''quantum gates'' operating on an qubits, as composed of a sequence of generic elementary ''gates''.

  15. Adiabatically implementing quantum gates

    SciTech Connect

    Sun, Jie; Lu, Songfeng Liu, Fang

    2014-06-14

    We show that, through the approach of quantum adiabatic evolution, all of the usual quantum gates can be implemented efficiently, yielding running time of order O(1). This may be considered as a useful alternative to the standard quantum computing approach, which involves quantum gates transforming quantum states during the computing process.

  16. Quantum oligopoly

    NASA Astrophysics Data System (ADS)

    Lo, C. F.; Kiang, D.

    2003-12-01

    Based upon a modification of Li et al.'s "minimal" quantization rules (Phys. Lett. A306(2002) 73), we investigate the quantum version of the Cournot and Bertrand oligopoly. In the Cournot oligopoly, the profit of each of the N firms at the Nash equilibrium point rises monotonically with the measure of the quantum entanglement. Only at maximal entanglement, however, does the Nash equilibrium point coincide with the Pareto optimal point. In the Bertrand case, the Bertrand Paradox remains for finite entanglement (i.e., the perfectly competitive stage is reached for any N>=2), whereas with maximal entanglement each of the N firms will still have a non-zero shared profit. Hence, the Bertrand Paradox is completely resolved. Furthermore, a perfectly competitive market is reached asymptotically for N → ∞ in both the Cournot and Bertrand oligopoly.

  17. Quantum nonlocality

    SciTech Connect

    Stapp, H.P.

    1988-04-01

    It is argued that the validity of the predictions of quantum theory in certain spin-correlation experiments entails a violation of Einstein's locality idea that no causal influence can act outside the forward light cone. First, two preliminary arguments suggesting such a violation are reviewed. They both depend, in intermediate stages, on the idea that the results of certain unperformed experiments are physically determinate. The second argument is entangled also with the problem of the meaning of physical reality. A new argument having neither of these characteristics is constructed. It is based strictly on the orthodox ideas of Bohr and Heisenberg, and has no realistic elements, or other ingredients, that are alien to orthodox quantum thinking.

  18. Quantum Foam

    ScienceCinema

    Lincoln, Don

    2016-07-12

    The laws of quantum mechanics and relativity are quite perplexing however it is when the two theories are merged that things get really confusing. This combined theory predicts that empty space isn’t empty at all – it’s a seething and bubbling cauldron of matter and antimatter particles springing into existence before disappearing back into nothingness. Scientists call this complicated state of affairs “quantum foam.” In this video, Fermilab’s Dr. Don Lincoln discusses this mind-bending idea and sketches some of the experiments that have convinced scientists that this crazy prediction is actually true.

  19. Quantum Design

    SciTech Connect

    Lindgren, W.B.; Cox, D.W.; Simmonds, M.B.; Sager, R.E.

    1988-08-01

    Quantum Design of San Diego, California markets an instrument for measuring magnetic properties of the high-T/sub c/ superconductors. Ironically, their instrument exploits the sensitivity of low-temperature superconducting electronics. Although the company is providing a valuable research tool, their main contribution to superconductivity may turn out to be their pioneering work as a manufacturer of superconducting electronics. Quantum Design is becoming a mature manufacturing company - a supplier of superconducting electronics devices which can be built, tested, installed, operated, maintained, and repaired by people who aren't low temperature physicists. The knowledge this company is gaining now may prove valuable if the promise of ultra-fast, ultra-sensitive superconducting electronics devices becomes a reality.

  20. A neural signature of the unique hues

    PubMed Central

    Forder, Lewis; Bosten, Jenny; He, Xun; Franklin, Anna

    2017-01-01

    Since at least the 17th century there has been the idea that there are four simple and perceptually pure “unique” hues: red, yellow, green, and blue, and that all other hues are perceived as mixtures of these four hues. However, sustained scientific investigation has not yet provided solid evidence for a neural representation that separates the unique hues from other colors. We measured event-related potentials elicited from unique hues and the ‘intermediate’ hues in between them. We find a neural signature of the unique hues 230 ms after stimulus onset at a post-perceptual stage of visual processing. Specifically, the posterior P2 component over the parieto-occipital lobe peaked significantly earlier for the unique than for the intermediate hues (Z = −2.9, p = 0.004). Having identified a neural marker for unique hues, fundamental questions about the contribution of neural hardwiring, language and environment to the unique hues can now be addressed. PMID:28186142

  1. Modularity, comparative cognition and human uniqueness.

    PubMed

    Shettleworth, Sara J

    2012-10-05

    Darwin's claim 'that the difference in mind between man and the higher animals … is certainly one of degree and not of kind' is at the core of the comparative study of cognition. Recent research provides unprecedented support for Darwin's claim as well as new reasons to question it, stimulating new theories of human cognitive uniqueness. This article compares and evaluates approaches to such theories. Some prominent theories propose sweeping domain-general characterizations of the difference in cognitive capabilities and/or mechanisms between adult humans and other animals. Dual-process theories for some cognitive domains propose that adult human cognition shares simple basic processes with that of other animals while additionally including slower-developing and more explicit uniquely human processes. These theories are consistent with a modular account of cognition and the 'core knowledge' account of children's cognitive development. A complementary proposal is that human infants have unique social and/or cognitive adaptations for uniquely human learning. A view of human cognitive architecture as a mosaic of unique and species-general modular and domain-general processes together with a focus on uniquely human developmental mechanisms is consistent with modern evolutionary-developmental biology and suggests new questions for comparative research.

  2. Quantum Computing

    DTIC Science & Technology

    1998-04-01

    information representation and processing technology, although faster than the wheels and gears of the Charles Babbage computation machine, is still in...the same computational complexity class as the Babbage machine, with bits of information represented by entities which obey classical (non-quantum...nuclear double resonances Charles M Bowden and Jonathan P. Dowling Weapons Sciences Directorate, AMSMI-RD-WS-ST Missile Research, Development, and

  3. Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Murdin, P.

    2000-11-01

    A development of quantum theory that was initiated in the 1920s by Werner Heisenberg (1901-76) and Erwin Schrödinger (1887-1961). The theory drew on a proposal made in 1925 Prince Louis de Broglie (1892-1987), that particles have wavelike properties (the wave-particle duality) and that an electron, for example, could in some respects be regarded as a wave with a wavelength that depended on its mo...

  4. Quantum Computers

    DTIC Science & Technology

    2010-03-04

    empty valence-band states ) into a localized poten- tial with discrete energy levels, which is analagous to an electron bound to an atomic nucleus...seminal work, the ideas for implementing quantum computing have diversified, and the DiVincenzo criteria as originally stated are difficult to apply to...many emerging concepts. Here, we rephrase DiVincenzo’s original considerations into three more general criteria; these are stated with the assumption

  5. Quantum Supersymmetric Models in the Causal Approach

    NASA Astrophysics Data System (ADS)

    Grigore, Dan-Radu

    2007-04-01

    We consider the massless supersymmetric vector multiplet in a purely quantum framework. First order gauge invariance determines uniquely the interaction Lagrangian as in the case of Yang-Mills models. Going to the second order of perturbation theory produces an anomaly which cannot be eliminated. We make the analysis of the model working only with the component fields.

  6. Dynamical initial conditions in quantum cosmology.

    PubMed

    Bojowald, M

    2001-09-17

    Loop quantum cosmology is shown to provide both the dynamical law and initial conditions for the wave function of a universe by one discrete evolution equation. Accompanied by the condition that semiclassical behavior is obtained at large volume, a unique wave function is predicted.

  7. Quantum Secure Direct Communication with Quantum Memory

    NASA Astrophysics Data System (ADS)

    Zhang, Wei; Ding, Dong-Sheng; Sheng, Yu-Bo; Zhou, Lan; Shi, Bao-Sen; Guo, Guang-Can

    2017-06-01

    Quantum communication provides an absolute security advantage, and it has been widely developed over the past 30 years. As an important branch of quantum communication, quantum secure direct communication (QSDC) promotes high security and instantaneousness in communication through directly transmitting messages over a quantum channel. The full implementation of a quantum protocol always requires the ability to control the transfer of a message effectively in the time domain; thus, it is essential to combine QSDC with quantum memory to accomplish the communication task. In this Letter, we report the experimental demonstration of QSDC with state-of-the-art atomic quantum memory for the first time in principle. We use the polarization degrees of freedom of photons as the information carrier, and the fidelity of entanglement decoding is verified as approximately 90%. Our work completes a fundamental step toward practical QSDC and demonstrates a potential application for long-distance quantum communication in a quantum network.

  8. Experimental quantum forgery of quantum optical money

    NASA Astrophysics Data System (ADS)

    Bartkiewicz, Karol; Černoch, Antonín; Chimczak, Grzegorz; Lemr, Karel; Miranowicz, Adam; Nori, Franco

    2017-03-01

    Unknown quantum information cannot be perfectly copied (cloned). This statement is the bedrock of quantum technologies and quantum cryptography, including the seminal scheme of Wiesner's quantum money, which was the first quantum-cryptographic proposal. Surprisingly, to our knowledge, quantum money has not been tested experimentally yet. Here, we experimentally revisit the Wiesner idea, assuming a banknote to be an image encoded in the polarization states of single photons. We demonstrate that it is possible to use quantum states to prepare a banknote that cannot be ideally copied without making the owner aware of only unauthorized actions. We provide the security conditions for quantum money by investigating the physically-achievable limits on the fidelity of 1-to-2 copying of arbitrary sequences of qubits. These results can be applied as a security measure in quantum digital right management.

  9. Quantum Secure Direct Communication with Quantum Memory.

    PubMed

    Zhang, Wei; Ding, Dong-Sheng; Sheng, Yu-Bo; Zhou, Lan; Shi, Bao-Sen; Guo, Guang-Can

    2017-06-02

    Quantum communication provides an absolute security advantage, and it has been widely developed over the past 30 years. As an important branch of quantum communication, quantum secure direct communication (QSDC) promotes high security and instantaneousness in communication through directly transmitting messages over a quantum channel. The full implementation of a quantum protocol always requires the ability to control the transfer of a message effectively in the time domain; thus, it is essential to combine QSDC with quantum memory to accomplish the communication task. In this Letter, we report the experimental demonstration of QSDC with state-of-the-art atomic quantum memory for the first time in principle. We use the polarization degrees of freedom of photons as the information carrier, and the fidelity of entanglement decoding is verified as approximately 90%. Our work completes a fundamental step toward practical QSDC and demonstrates a potential application for long-distance quantum communication in a quantum network.

  10. Efficient Quantum Information Processing via Quantum Compressions

    NASA Astrophysics Data System (ADS)

    Deng, Y.; Luo, M. X.; Ma, S. Y.

    2016-01-01

    Our purpose is to improve the quantum transmission efficiency and reduce the resource cost by quantum compressions. The lossless quantum compression is accomplished using invertible quantum transformations and applied to the quantum teleportation and the simultaneous transmission over quantum butterfly networks. New schemes can greatly reduce the entanglement cost, and partially solve transmission conflictions over common links. Moreover, the local compression scheme is useful for approximate entanglement creations from pre-shared entanglements. This special task has not been addressed because of the quantum no-cloning theorem. Our scheme depends on the local quantum compression and the bipartite entanglement transfer. Simulations show the success probability is greatly dependent of the minimal entanglement coefficient. These results may be useful in general quantum network communication.

  11. Multi-bit dark state memory: Double quantum dot as an electronic quantum memory

    NASA Astrophysics Data System (ADS)

    Aharon, Eran; Pozner, Roni; Lifshitz, Efrat; Peskin, Uri

    2016-12-01

    Quantum dot clusters enable the creation of dark states which preserve electrons or holes in a coherent superposition of dot states for a long time. Various quantum logic devices can be envisioned to arise from the possibility of storing such trapped particles for future release on demand. In this work, we consider a double quantum dot memory device, which enables the preservation of a coherent state to be released as multiple classical bits. Our unique device architecture uses an external gating for storing (writing) the coherent state and for retrieving (reading) the classical bits, in addition to exploiting an internal gating effect for the preservation of the coherent state.

  12. New quantum dot sensors

    NASA Astrophysics Data System (ADS)

    Gun'ko, Y. K.; Moloney, M. M.; Gallagher, S.; Govan, J.; Hanley, C.

    2010-04-01

    Quantum dots (QDs) are fluorescent semiconductor (e.g. II-VI) nanocrystals, which have a strong characteristic spectral emission. This emission is tunable to a desired energy by selecting variable particle size, size distribution and composition of the nanocrystals. QDs have recently attracted enormous interest due to their unique photophysical properties and range of potential applications in photonics and biochemistry. The main aim of our work is develop new chiral quantum dots (QDs) and establish fundamental principles influencing their structure, properties and biosensing behaviour. Here we present the synthesis and characterisation of chiral CdSe semiconductor nanoparticles and their utilisation as new chiral biosensors. Penicillamine stabilised CdSe nanoparticles have shown both very strong and very broad luminescence spectra. Circular dichroism (CD) spectroscopy studies have revealed that the D- and Lpenicillamine stabilised CdSe QDs demonstrate circular dichroism and possess almost identical mirror images of CD signals. Studies of photoluminescence and CD spectra have shown that there is a clear relationship between defect emission and CD activity. We have also demonstrated that these new QDs can serve as fluorescent nanosensors for various chiral biomolecules including nucleic acids. These novel nanosensors can be potentially utilized for detection of various chiral biological and chemical species with the broad range of potential applications.

  13. Genuine quantum coherence

    NASA Astrophysics Data System (ADS)

    de Vicente, Julio I.; Streltsov, Alexander

    2017-01-01

    Any quantum resource theory is based on free states and free operations, i.e. states and operations which can be created and performed at no cost. In the resource theory of coherence free states are diagonal in some fixed basis, and free operations are those which cannot create coherence for some particular experimental realization. Recently, some problems of this approach have been discussed, and new sets of operations have been proposed to resolve these problems. We propose here the framework of genuine quantum coherence. This approach is based on a simple principle: we demand that a genuinely incoherent operation preserves all incoherent states. This framework captures coherence under additional constrains such as energy preservation and all genuinely incoherent operations are incoherent regardless of their particular experimental realization. We also introduce the full class of operations with this property, which we call fully incoherent. We analyze in detail the mathematical structure of these classes and also study possible state transformations. We show that deterministic manipulation is severely limited, even in the asymptotic settings. In particular, this framework does not have a unique golden unit, i.e. there is no single state from which all other states can be created deterministically with the free operations. This suggests that any reasonably powerful resource theory of coherence must contain free operations which can potentially create coherence in some experimental realization.

  14. Topological Quantum Double

    NASA Astrophysics Data System (ADS)

    Bonneau, Philippe

    Following a preceding paper showing how the introduction of a t.v.s. topology on quantum groups led to a remarkable unification and rigidification of the different definitions, we adapt here, in the same way, the definition of quantum double. This topological double is dualizable and reflexive (even for infinite dimensional algebras). In a simple case we show, considering the double as the "zero class" of an extension theory, the uniqueness of the double structure as a quasi-Hopf algebra. A la suite d'un précédent article montrant comment l'introduction d'une topologie d'e.v.t. sur les groupes quantiques permet une unification et une rigidification remarquables des différentes définitions, on adapte ici de la même manière la définition du double quantique. Ce double topologique est alors dualisable et reflexif (même pour des algèbres de dimension infinie). Dans un cas simple on montre, en considérant le double comme la "classe zéro" d'une théorie d'extensions, l'unicité de cette structure comme algèbre quasi-Hopf.

  15. Towards new background independent representations for loop quantum gravity

    NASA Astrophysics Data System (ADS)

    Varadarajan, Madhavan

    2008-05-01

    Recently, uniqueness theorems were constructed for the representation used in loop quantum gravity. We explore the existence of alternate representations by weakening the assumptions of the Lewandowski Okolow Sahlmann Thiemann (LOST) uniqueness theorem. The weakened assumptions seem physically reasonable and retain the key requirement of explicit background independence. For simplicity, we restrict attention to the case of gauge group U(1).

  16. Ergodic Relaxor State with High Energy Storage Performance Induced by Doping Sr0.85Bi0.1TiO3 in Bi0.5Na0.5TiO3 Ceramics

    NASA Astrophysics Data System (ADS)

    Li, Qing-Ning; Zhou, Chong-Rong; Xu, Ji-Wen; Yang, Ling; Zhang, Xin; Zeng, Wei-Dong; Yuan, Chang-Lai; Chen, Guo-Hua; Rao, Guang-Hui

    2016-10-01

    The large maximum polarization P max and low remnant polarization P r in relaxor ferroelectrics are key features for the energy storage density ( W) and energy-storage efficiency ( η) in materials selection. In this study, the ergodic relaxor (ER) state with high energy storage performance associated with low P r and large P max, induced by Sr0.85Bi0.1TiO3(SBT) addition in (1 - x)Bi0.5Na0.5TiO3- xSr0.85Bi0.1TiO3 (BNT-SBT x with x = 0.25-0.45, Bi0.5Na0.5TiO3 abbreviated as BNT) ceramics has been observed. In particular, significantly increased energy storage density ( W = 1.5 J/cm3) and energy-storage efficiency ( η = 73%) are obtained for BNT-SBT ergodic relaxor ceramics. These results suggest a new means of designing lead-free energy-storage materials.

  17. Quantum Locality?

    SciTech Connect

    Stapp, Henry

    2011-11-10

    Robert Griffiths has recently addressed, within the framework of a ‘consistent quantum theory’ (CQT) that he has developed, the issue of whether, as is often claimed, quantum mechanics entails a need for faster-than-light transfers of information over long distances. He argues, on the basis of his examination of certain arguments that claim to demonstrate the existence of such nonlocal influences, that such influences do not exist. However, his examination was restricted mainly to hidden-variable-based arguments that include in their premises some essentially classical-physics-type assumptions that are fundamentally incompatible with the precepts of quantum physics. One cannot logically prove properties of a system by attributing to the system properties alien to that system. Hence Griffiths’ rejection of hidden-variable-based proofs is logically warranted. Griffiths mentions the existence of a certain alternative proof that does not involve hidden variables, and that uses only macroscopically described observable properties. He notes that he had examined in his book proofs of this general kind, and concluded that they provide no evidence for nonlocal influences. But he did not examine the particular proof that he cites. An examination of that particular proof by the method specified by his ‘consistent quantum theory’ shows that the cited proof is valid within that restrictive framework. This necessary existence, within the ‘consistent’ framework, of long range essentially instantaneous influences refutes the claim made by Griffiths that his ‘consistent’ framework is superior to the orthodox quantum theory of von Neumann because it does not entail instantaneous influences. An added section responds to Griffiths’ reply, which cites a litany of ambiguities that seem to restrict, devastatingly, the scope of his CQT formalism, apparently to buttress his claim that my use of that formalism to validate the nonlocality theorem is flawed. But the

  18. Decoding the quantum horizon

    NASA Astrophysics Data System (ADS)

    Hayden, Patrick; Myers, Robert

    2017-01-01

    Patrick Hayden and Robert Myers describe how the study of “qubits”, quantum bits of information, may hold the key to uniting quantum theory and general relativity into a unified theory of quantum gravity

  19. Quantum probability and quantum decision-making.

    PubMed

    Yukalov, V I; Sornette, D

    2016-01-13

    A rigorous general definition of quantum probability is given, which is valid not only for elementary events but also for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting observables in addition to commutative observables. Our proposed definition of quantum probability makes it possible to describe quantum measurements and quantum decision-making on the same common mathematical footing. Conditions are formulated for the case when quantum decision theory reduces to its classical counterpart and for the situation where the use of quantum decision theory is necessary.

  20. Quantum Dot Based Chemosensors: Selective Estimation of Cu2+ in Semi-aqueous Medium

    NASA Astrophysics Data System (ADS)

    Sheoran, Vandana; Saluja, Preeti; Singh, Narinder; Kaur, Navneet

    2011-12-01

    Quantum dots are the semiconducting nanocrystals whose exicitons are restricted in all the three dimensions within a range of 2-10 nm. Due to the phenomenon called quantum confinement they have unique optical and photo physical properties which makes them useful as chemosensors. Since quantum dots provide a useful framework for the surface confinement of the receptors thereby resulting in changes in the receptor binding affinity. Therefore capturing this feature of the quantum dots different ligands are synthesized and then attached to the quantum dots. Finally studying the surface modification of the quantum dots helps us to make chemosensorsors.