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 and Andreev ansatz. We find singular behavior of the two point spectral correlator in the limit of small spacing. Finally, we analyse the effect that slow decay to ergodicity has on the structure of the quantum propagator, as well as wavefunction localization. We introduce a statistical quantum description of systems that are composed of both an orderly region and a random region. By averaging over the random region only, we find that measures of localization in momentum space semiclassically diverge with the dimension of the Hilbert space. We illustrate this numerically with quantum maps and suggest various other systems where this behavior should be important.

Topological order, entanglement, and quantum memory at finite temperature

NASA Astrophysics Data System (ADS)

Mazáč, Dalimil; Hamma, Alioscia

2012-09-01

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 Z2 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.

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.

Dynamically induced many-body localization

NASA Astrophysics Data System (ADS)

Choi, Soonwon; Abanin, Dmitry A.; Lukin, Mikhail D.

2018-03-01

We show that a quantum phase transition from ergodic to many-body localized (MBL) phases can be induced via periodic pulsed manipulation of spin systems. Such a transition is enabled by the interplay between weak disorder and slow heating rates. Specifically, we demonstrate that the Hamiltonian of a weakly disordered ergodic spin system can be effectively engineered, by using sufficiently fast coherent controls, to yield a stable MBL phase, which in turn completely suppresses the energy absorption from external control field. Our results imply that a broad class of existing many-body systems can be used to probe nonequilibrium phases of matter for a long time, limited only by coupling to external environment.

Quantum phase slips: from condensed matter to ultracold quantum gases.

PubMed

D'Errico, C; Abbate, S Scaffidi; Modugno, G

2017-12-13

Quantum phase slips (QPS) are the primary excitations in one-dimensional superfluids and superconductors at low temperatures. They have been well characterized in most condensed-matter systems, and signatures of their existence have been recently observed in superfluids based on quantum gases too. In this review, we briefly summarize the main results obtained on the investigation of phase slips from superconductors to quantum gases. In particular, we focus our attention on recent experimental results of the dissipation in one-dimensional Bose superfluids flowing along a shallow periodic potential, which show signatures of QPS.This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'. © 2017 The Author(s).

The emergent Copenhagen interpretation of quantum mechanics

NASA Astrophysics Data System (ADS)

Hollowood, Timothy J.

2014-05-01

We introduce a new and conceptually simple interpretation of quantum mechanics based on reduced density matrices of sub-systems from which the standard Copenhagen interpretation emerges as an effective description of macroscopically large systems. This interpretation describes a world in which definite measurement results are obtained with probabilities that reproduce the Born rule. Wave function collapse is seen to be a useful but fundamentally unnecessary piece of prudent book keeping which is only valid for macro-systems. The new interpretation lies in a class of modal interpretations in that it applies to quantum systems that interact with a much larger environment. However, we show that it does not suffer from the problems that have plagued similar modal interpretations like macroscopic superpositions and rapid flipping between macroscopically distinct states. We describe how the interpretation fits neatly together with fully quantum formulations of statistical mechanics and that a measurement process can be viewed as a process of ergodicity breaking analogous to a phase transition. The key feature of the new interpretation is that joint probabilities for the ergodic subsets of states of disjoint macro-systems only arise as emergent quantities. Finally we give an account of the EPR-Bohm thought experiment and show that the interpretation implies the violation of the Bell inequality characteristic of quantum mechanics but in a way that is rather novel. The final conclusion is that the Copenhagen interpretation gives a completely satisfactory phenomenology of macro-systems interacting with micro-systems.

Quantum memories and Landauer's principle

NASA Astrophysics Data System (ADS)

Alicki, Robert

2011-10-01

Two types of arguments concerning (im)possibility of constructing a scalable, exponentially stable quantum memory equipped with Hamiltonian controls are discussed. The first type concerns ergodic properties of open Kitaev models which are considered as promising candidates for such memories. It is shown that, although the 4D Kitaev model provides stable qubit observables, the Hamiltonian control is not possible. The thermodynamical approach leads to the new proposal of the revised version of Landauer's principle and suggests that the existence of quantum memory implies the existence of the perpetuum mobile of the second kind. Finally, a discussion of the stability property of information and its implications is presented.

Chaotic attractors and physical measures for some density dependent Leslie population models

NASA Astrophysics Data System (ADS)

Ugarcovici, Ilie; Weiss, Howard

2007-12-01

Following ecologists' discoveries, mathematicians have begun studying extensions of the ubiquitous age structured Leslie population model that allow some survival probabilities and/or fertility rates to depend on population densities. These nonlinear extensions commonly exhibit very complicated dynamics: through computer studies, some authors have discovered robust Hénon-like strange attractors in several families. Population biologists and demographers frequently wish to average a function over many generations and conclude that the average is independent of the initial population distribution. This type of 'ergodicity' seems to be a fundamental tenet in population biology. In this paper we develop the first rigorous ergodic theoretic framework for density dependent Leslie population models. We study two generation models with Ricker and Hassell (recruitment type) fertility terms. We prove that for some parameter regions these models admit a chaotic (ergodic) attractor which supports a unique physical probability measure. This physical measure, having full Lebesgue measure basin, satisfies in the strongest possible sense the population biologist's requirement for ergodicity in their population models. We use the celebrated work of Wang and Young 2001 Commun. Math. Phys. 218 1-97, and our results are the first applications of their method to biology, ecology or demography.

Quantum Anosov flows: A new family of examples

NASA Astrophysics Data System (ADS)

Peter, Ingo J.; Emch, Gérard G.

1998-09-01

A quantum version is presented for the Anosov system defined by the time evolution implemented by the geodesic coflow on the cotangent bundle of any compact quotient manifold obtained from the Poincaré half-plane. While the canonical Weyl algebra does not close under time evolution, the symplectic structure of these classical systems can be exploited to produce objects akin to the CCR algebras encountered in quantum field theory. This construction allows one to lift both the geodesic and the horocyclic flows to a Weyl algebra describing the quantum dynamics corresponding to the systems under consideration. The Anosov relations as proposed in Ref. Reference 1 are found to be valid for these models. A quantum version of the classical ergodicity of these systems is discussed in the last section.

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.

Quantitative quasiperiodicity

NASA Astrophysics Data System (ADS)

Das, Suddhasattwa; Saiki, Yoshitaka; Sander, Evelyn; Yorke, James A.

2017-11-01

The Birkhoff ergodic theorem concludes that time averages, i.e. Birkhoff averages, B_N( f):=Σn=0N-1 f(x_n)/N of a function f along a length N ergodic trajectory (x_n) of a function T converge to the space average \\int f dμ , where μ is the unique invariant probability measure. Convergence of the time average to the space average is slow. We use a modified average of f(x_n) by giving very small weights to the ‘end’ terms when n is near 0 or N-1 . When (x_n) is a trajectory on a quasiperiodic torus and f and T are C^∞ , our weighted Birkhoff average (denoted \

Multipoint entanglement in disordered systems

NASA Astrophysics Data System (ADS)

Magán, Javier M.; Paganelli, Simone; Oganesyan, Vadim

2017-02-01

We develop an approach to characterize excited states of disordered many-body systems using spatially resolved structures of entanglement. We show that the behavior of the mutual information (MI) between two parties of a many-body system can signal a qualitative difference between thermal and localized phases - MI is finite in insulators while it approaches zero in the thermodynamic limit in the ergodic phase. Related quantities, such as the recently introduced Codification Volume (CV), are shown to be suitable to quantify the correlation length of the system. These ideas are illustrated using prototypical non-interacting wavefunctions of localized and extended particles and then applied to characterize states of strongly excited interacting spin chains. We especially focus on evolution of spatial structure of quantum information between high temperature diffusive and many-body localized (MBL) phases believed to exist in these models. We study MI as a function of disorder strength both averaged over the eigenstates and in time-evolved product states drawn from continuously deformed family of initial states realizable experimentally. As expected, spectral and time-evolved averages coincide inside the ergodic phase and differ significantly outside. We also highlight dispersion among the initial states within the localized phase - some of these show considerable generation and delocalization of quantum information.

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).

Robustness of Many-Body Localization in the Presence of Dissipation

NASA Astrophysics Data System (ADS)

Levi, Emanuele; Heyl, Markus; Lesanovsky, Igor; Garrahan, Juan P.

2016-06-01

Many-body localization (MBL) has emerged as a novel paradigm for robust ergodicity breaking in closed quantum many-body systems. However, it is not yet clear to which extent MBL survives in the presence of dissipative processes induced by the coupling to an environment. Here we study heating and ergodicity for a paradigmatic MBL system—an interacting fermionic chain subject to quenched disorder—in the presence of dephasing. We find that, even though the system is eventually driven into an infinite-temperature state, heating as monitored by the von Neumann entropy can progress logarithmically slowly, implying exponentially large time scales for relaxation. This slow loss of memory of initial conditions makes signatures of nonergodicity visible over a long, but transient, time regime. We point out a potential controlled realization of the considered setup with cold atomic gases held in optical lattices.

BOOK REVIEW:

NASA Astrophysics Data System (ADS)

Berkolaiko, G.

2003-12-01

The book represents the collected lectures given at the Summer School on Mathematical Aspects of Quantum Maps held at Bologna University in September 2001. Quantum maps gained their prominence as a testing ground for mathematical understanding of various concepts in quantum chaos, such as the spectral statistics, quantum ergodicity, scarring of the eigenfunctions and the connection to algebraic number theory. The book is nicely structured. It begins by reviewing the relevant concepts and results from dynamical systems (a contribution by A Knauf) and number theory (by Z Rudnick). A contribution by the editors, M Degli Esposti and S Graffi, explains the quantization procedure for the quantum maps and proceeds to discuss some properties of the quantized maps, such as ergodicity and scarring, and the number theoretical techniques involved in proving these properties. The contribution by A Bäacker discusses the numerical methods used to study quantum chaotic systems. It contains both the mathematical background and a detailed explanation of the numerical techniques, possible pitfalls at the implementation stage and how to avoid them. It even contains a computer program in Python used by the author to compute the eigenvalues of a perturbed cat map. The last contribution, by R Artuso, while very interesting in itself, feels somewhat disconnected from the rest of the book. It deals with deterministic transport in hyperbolic and weakly chaotic systems, where one can observe normal and anomalous diffusion respectively. Although being a collection of contributions from various authors, the book feels very much like a well-coordinated team effort, with frequent cross-contributional references underlying the connections between different facets of the discussed subjects. I consider it an invaluable reference for researchers in the field of quantum chaos and would recommend it as a first read for people just entering the field. It contains both the necessary background information and tasters of the main results and concepts of quantum chaos. The only slight drawback of the book is the misprints in some of the contributions, which can make an understanding more difficult than it should be.

Thermodynamics of quantum information scrambling

NASA Astrophysics Data System (ADS)

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 <[Wτ,V ] †[Wτ,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.

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.

Quantifying nonergodicity in nonautonomous dissipative dynamical systems: An application to climate change

NASA Astrophysics Data System (ADS)

Drótos, Gábor; Bódai, Tamás; Tél, Tamás

2016-08-01

In nonautonomous dynamical systems, like in climate dynamics, an ensemble of trajectories initiated in the remote past defines a unique probability distribution, the natural measure of a snapshot attractor, for any instant of time, but this distribution typically changes in time. In cases with an aperiodic driving, temporal averages taken along a single trajectory would differ from the corresponding ensemble averages even in the infinite-time limit: ergodicity does not hold. It is worth considering this difference, which we call the nonergodic mismatch, by taking time windows of finite length for temporal averaging. We point out that the probability distribution of the nonergodic mismatch is qualitatively different in ergodic and nonergodic cases: its average is zero and typically nonzero, respectively. A main conclusion is that the difference of the average from zero, which we call the bias, is a useful measure of nonergodicity, for any window length. In contrast, the standard deviation of the nonergodic mismatch, which characterizes the spread between different realizations, exhibits a power-law decrease with increasing window length in both ergodic and nonergodic cases, and this implies that temporal and ensemble averages differ in dynamical systems with finite window lengths. It is the average modulus of the nonergodic mismatch, which we call the ergodicity deficit, that represents the expected deviation from fulfilling the equality of temporal and ensemble averages. As an important finding, we demonstrate that the ergodicity deficit cannot be reduced arbitrarily in nonergodic systems. We illustrate via a conceptual climate model that the nonergodic framework may be useful in Earth system dynamics, within which we propose the measure of nonergodicity, i.e., the bias, as an order-parameter-like quantifier of climate change.

The canonical quantization of chaotic maps on the torus

NASA Astrophysics Data System (ADS)

Rubin, Ron Shai

In this thesis, a quantization method for classical maps on the torus is presented. The quantum algebra of observables is defined as the quantization of measurable functions on the torus with generators exp (2/pi ix) and exp (2/pi ip). The Hilbert space we use remains the infinite-dimensional L2/ (/IR, dx). The dynamics is given by a unitary quantum propagator such that as /hbar /to 0, the classical dynamics is returned. We construct such a quantization for the Kronecker map, the cat map, the baker's map, the kick map, and the Harper map. For the cat map, we find the same for the propagator on the plane the same integral kernel conjectured in (HB) using semiclassical methods. We also define a quantum 'integral over phase space' as a trace over the quantum algebra. Using this definition, we proceed to define quantum ergodicity and mixing for maps on the torus. We prove that the quantum cat map and Kronecker map are both ergodic, but only the cat map is mixing, true to its classical origins. For Planck's constant satisfying the integrality condition h = 1/N, with N/in doubz+, we construct an explicit isomorphism between L2/ (/IR, dx) and the Hilbert space of sections of an N-dimensional vector bundle over a θ-torus T2 of boundary conditions. The basis functions are distributions in L2/ (/IR, dx), given by an infinite comb of Dirac δ-functions. In Bargmann space these distributions take on the form of Jacobi ϑ-functions. Transformations from position to momentum representation can be implemented via a finite N-dimensional discrete Fourier transform. With the θ-torus, we provide a connection between the finite-dimensional quantum maps given in the physics literature and the canonical quantization presented here and found in the language of pseudo-differential operators elsewhere in mathematics circles. Specifically, at a fixed point of the dynamics on the θ-torus, we return a finite-dimensional matrix propagator. We present this connection explicitly for several examples.

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.

Quantum Groups, Property (T), and Weak Mixing

NASA Astrophysics Data System (ADS)

Brannan, Michael; Kerr, David

2018-06-01

For second countable discrete quantum groups, and more generally second countable locally compact quantum groups with trivial scaling group, we show that property (T) is equivalent to every weakly mixing unitary representation not having almost invariant vectors. This is a generalization of a theorem of Bekka and Valette from the group setting and was previously established in the case of low dual by Daws, Skalski, and Viselter. Our approach uses spectral techniques and is completely different from those of Bekka-Valette and Daws-Skalski-Viselter. By a separate argument we furthermore extend the result to second countable nonunimodular locally compact quantum groups, which are shown in particular not to have property (T), generalizing a theorem of Fima from the discrete setting. We also obtain quantum group versions of characterizations of property (T) of Kerr and Pichot in terms of the Baire category theory of weak mixing representations and of Connes and Weiss in terms of the prevalence of strongly ergodic actions.

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

Connected components of irreducible maps and 1D quantum phases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Szehr, Oleg, E-mail: oleg.szehr@posteo.de; Wolf, Michael M., E-mail: wolf@ma.tum.de

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 inmore » 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.« less

Nonadditive entropy Sq and nonextensive statistical mechanics: Applications in geophysics and elsewhere

NASA Astrophysics Data System (ADS)

Tsallis, Constantino

2012-06-01

The celebrated Boltzmann-Gibbs (BG) entropy, S BG = -kΣi p i ln p i, and associated statistical mechanics are essentially based on hypotheses such as ergodicity, i.e., when ensemble averages coincide with time averages. This dynamical simplification occurs in classical systems (and quantum counterparts) whose microscopic evolution is governed by a positive largest Lyapunov exponent (LLE). Under such circumstances, relevant microscopic variables behave, from the probabilistic viewpoint, as (nearly) independent. Many phenomena exist, however, in natural, artificial and social systems (geophysics, astrophysics, biophysics, economics, and others) that violate ergodicity. To cover a (possibly) wide class of such systems, a generalization (nonextensive statistical mechanics) of the BG theory was proposed in 1988. This theory is based on nonadditive entropies such as S_q = kfrac{{1 - sumnolimits_i {p_i^q } }} {{q - 1}}left( {S_1 = S_{BG} } right). Here we comment some central aspects of this theory, and briefly review typical predictions, verifications and applications in geophysics and elsewhere, as illustrated through theoretical, experimental, observational, and computational results.

Power-law decay exponents: A dynamical criterion for predicting thermalization

NASA Astrophysics Data System (ADS)

Távora, Marco; Torres-Herrera, E. J.; Santos, Lea F.

2017-01-01

From the analysis of the relaxation process of isolated lattice many-body quantum systems quenched far from equilibrium, we deduce a criterion for predicting when they are certain to thermalize. It is based on the algebraic behavior ∝t-γ of the survival probability at long times. We show that the value of the power-law exponent γ depends on the shape and filling of the weighted energy distribution of the initial state. Two scenarios are explored in detail: γ ≥2 and γ <1 . Exponents γ ≥2 imply that the energy distribution of the initial state is ergodically filled and the eigenstates are uncorrelated, so thermalization is guaranteed to happen. In this case, the power-law behavior is caused by bounds in the energy spectrum. Decays with γ <1 emerge when the energy eigenstates are correlated and signal lack of ergodicity. They are typical of systems undergoing localization due to strong onsite disorder and are found also in clean integrable systems.

Buonomano against Bell: Nonergodicity or nonlocality?

NASA Astrophysics Data System (ADS)

Khrennikov, Andrei

The aim of this note is to attract attention of the quantum foundational community to the fact that in Bell’s arguments, one cannot distinguish two hypotheses: (a) quantum mechanics is nonlocal, (b) quantum mechanics is nonergodic. Therefore, experimental violations of Bell’s inequality can be as well interpreted as supporting the hypothesis that stochastic processes induced by quantum measurements are nonergodic. The latter hypothesis was discussed actively by Buonomano since 1980. However, in contrast to Bell’s hypothesis on nonlocality, it did not attract so much attention. The only experiment testing the hypothesis on nonergodicity was performed in neutron interferometry (by Summhammer, in 1989). This experiment can be considered as rejecting this hypothesis. However, it cannot be considered as a decisive experiment. New experiments are badly needed. We point out that a nonergodic model can be realistic, i.e. the distribution of hidden (local!) variables is well-defined. We also discuss coupling of violation of the Bell inequality with violation of the condition of weak mixing for ergodic dynamical systems.

Emulating Many-Body Localization with a Superconducting Quantum Processor

NASA Astrophysics Data System (ADS)

Xu, Kai; Chen, Jin-Jun; Zeng, Yu; Zhang, Yu-Ran; Song, Chao; Liu, Wuxin; Guo, Qiujiang; Zhang, Pengfei; Xu, Da; Deng, Hui; Huang, Keqiang; Wang, H.; Zhu, Xiaobo; Zheng, Dongning; Fan, Heng

2018-02-01

The law of statistical physics dictates that generic closed quantum many-body systems initialized in nonequilibrium will thermalize under their own dynamics. However, the emergence of many-body localization (MBL) owing to the interplay between interaction and disorder, which is in stark contrast to Anderson localization, which only addresses noninteracting particles in the presence of disorder, greatly challenges this concept, because it prevents the systems from evolving to the ergodic thermalized state. One critical evidence of MBL is the long-time logarithmic growth of entanglement entropy, and a direct observation of it is still elusive due to the experimental challenges in multiqubit single-shot measurement and quantum state tomography. Here we present an experiment fully emulating the MBL dynamics with a 10-qubit superconducting quantum processor, which represents a spin-1 /2 X Y model featuring programmable disorder and long-range spin-spin interactions. We provide essential signatures of MBL, such as the imbalance due to the initial nonequilibrium, the violation of eigenstate thermalization hypothesis, and, more importantly, the direct evidence of the long-time logarithmic growth of entanglement entropy. Our results lay solid foundations for precisely simulating the intriguing physics of quantum many-body systems on the platform of large-scale multiqubit superconducting quantum processors.

Ideas of Flat and Curved Space in History of Physics

NASA Astrophysics Data System (ADS)

Berezin, Alexander A.

2006-04-01

Since ``everything which is not prohibited is compulsory'' (assigned to Gell-Mann) we can postulate infinite flat Cartesian N-dimensional (N: any integer) space-time (ST) as embedding for any curved ST. Ergodicity raises quest of whether total number of inflationary and/or Everett bubbles (mini-verses) is finite, countably infinite (aleph-zero) or uncountably infinite (aleph-one). Are these bubbles form Gaussian distribution or form some non-random subsetting? Perhaps, communication between mini-verses (idea of D.Deutsch) can be facilitated by a kind of minimax non-local dynamics akin to Fermat principle? (Minimax Principle in Bubble Cosmology). Even such classical effects as magnetism and polarization have some non-local features. Can we go below the Planck length to perhaps Compton wavelength of our ``Hubble's bubble'' (h/Mc = 10 to minus 95 m, if M = 10 to 54 kg)? When talking about time loops and ergodicity (eternal return paradigm) is there some hysterisis in the way quantum states are accessed in ``forward'' or ``reverse'' direction? (reverse direction implies backward causality of J.Wheeler and/or Aristotelian final causation).

Floquet Supersymmetry

NASA Astrophysics Data System (ADS)

Iadecola, Thomas; Hsieh, Timothy H.

2018-05-01

We show that time-reflection symmetry in periodically driven (Floquet) quantum systems enables an inherently nonequilibrium phenomenon structurally similar to quantum-mechanical supersymmetry. In particular, we find Floquet analogs of the Witten index that place lower bounds on the degeneracies of states with quasienergies 0 and π . Moreover, we show that in some cases time-reflection symmetry can also interchange fermions and bosons, leading to fermion-boson pairs with opposite quasienergy. We provide a simple class of disordered, interacting, and ergodic Floquet models with an exponentially large number of states at quasienergies 0 and π , which are robust as long as the time-reflection symmetry is preserved. Floquet supersymmetry manifests itself in the evolution of certain local observables as a period-doubling effect with dramatic finite-size scaling, providing a clear signature for experiments.

Dynamical manifestations of quantum chaos

NASA Astrophysics Data System (ADS)

Torres Herrera, Eduardo Jonathan; Santos, Lea

2017-04-01

A main feature of a chaotic quantum system is a rigid spectrum, where the levels do not cross. Dynamical quantities, such as the von Neumann entanglement entropy, Shannon information entropy, and out-of-time correlators can differentiate the ergodic from the nonergodic phase in disordered interacting systems, but not level repulsion from level crossing in the delocalized phase of disordered and clean models. This is in contrast with the long-time evolution of the survival probability of the initial state. The onset of correlated energy levels is manifested by a drop, referred to as correlation hole, below the asymptotic value of the survival probability. The correlation hole is an unambiguous indicator of the presence of level repulsion. EJTH is grateful to VIEP, BUAP for financial support through the VIEP projects program.

A perspective on quantum integrability in many-body-localized and Yang-Baxter systems

NASA Astrophysics Data System (ADS)

Moore, Joel E.

2017-10-01

Two of the most active areas in quantum many-particle dynamics involve systems with an unusually large number of conservation laws. Many-body-localized systems generalize ideas of Anderson localization by disorder to interacting systems. While localization still exists with interactions and inhibits thermalization, the interactions between conserved quantities lead to some dramatic differences from the Anderson case. Quantum integrable models such as the XXZ spin chain or Bose gas with delta-function interactions also have infinite sets of conservation laws, again leading to modifications of conventional thermalization. A practical way to treat the hydrodynamic evolution from local equilibrium to global equilibrium in such models is discussed. This paper expands upon a presentation at a discussion meeting of the Royal Society on 7 February 2017. The work described was carried out with a number of collaborators, including Jens Bardarson, Vir Bulchandani, Roni Ilan, Christoph Karrasch, Siddharth Parameswaran, Frank Pollmann and Romain Vasseur. This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.

Many-Body Quantum Chaos: Analytic Connection to Random Matrix Theory

NASA Astrophysics Data System (ADS)

Kos, Pavel; Ljubotina, Marko; Prosen, Tomaž

2018-04-01

A key goal of quantum chaos is to establish a relationship between widely observed universal spectral fluctuations of clean quantum systems and random matrix theory (RMT). Most prominent features of such RMT behavior with respect to a random spectrum, both encompassed in the spectral pair correlation function, are statistical suppression of small level spacings (correlation hole) and enhanced stiffness of the spectrum at large spectral ranges. For single-particle systems with fully chaotic classical counterparts, the problem has been partly solved by Berry [Proc. R. Soc. A 400, 229 (1985), 10.1098/rspa.1985.0078] within the so-called diagonal approximation of semiclassical periodic-orbit sums, while the derivation of the full RMT spectral form factor K (t ) (Fourier transform of the spectral pair correlation function) from semiclassics has been completed by Müller et al. [Phys. Rev. Lett. 93, 014103 (2004), 10.1103/PhysRevLett.93.014103]. In recent years, the questions of long-time dynamics at high energies, for which the full many-body energy spectrum becomes relevant, are coming to the forefront even for simple many-body quantum systems, such as locally interacting spin chains. Such systems display two universal types of behaviour which are termed the "many-body localized phase" and "ergodic phase." In the ergodic phase, the spectral fluctuations are excellently described by RMT, even for very simple interactions and in the absence of any external source of disorder. Here we provide a clear theoretical explanation for these observations. We compute K (t ) in the leading two orders in t and show its agreement with RMT for nonintegrable, time-reversal invariant many-body systems without classical counterparts, a generic example of which are Ising spin-1 /2 models in a periodically kicking transverse field. In particular, we relate K (t ) to partition functions of a class of twisted classical Ising models on a ring of size t ; hence, the leading-order RMT behavior K (t )≃2 t is a consequence of translation and reflection symmetry of the Ising partition function.

Weak ergodicity of population evolution processes.

PubMed

Inaba, H

1989-10-01

The weak ergodic theorems of mathematical demography state that the age distribution of a closed population is asymptotically independent of the initial distribution. In this paper, we provide a new proof of the weak ergodic theorem of the multistate population model with continuous time. The main tool to attain this purpose is a theory of multiplicative processes, which was mainly developed by Garrett Birkhoff, who showed that ergodic properties generally hold for an appropriate class of multiplicative processes. First, we construct a general theory of multiplicative processes on a Banach lattice. Next, we formulate a dynamical model of a multistate population and show that its evolution operator forms a multiplicative process on the state space of the population. Subsequently, we investigate a sufficient condition that guarantees the weak ergodicity of the multiplicative process. Finally, we prove the weak and strong ergodic theorems for the multistate population and resolve the consistency problem.

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.

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.

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

Scattering General Analysis; ANALISIS GENERAL DE LA DISPERSION

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tixaire, A.G.

1962-01-01

A definition of scattering states is given. It is shown that such states must belong to the absolutely continuous part of the spectrum of the total hamiltonian whenever scattering systems are considered. Such embedding may be proper unless the quantum system is physically admissible. The Moller wave operators are analyzed using Abel- and Cesaro-limit theoretical arguments. Von Neumann s ergodic theorem is partially generalized. A rigorous derivation of the Gell-Mann and Goldberger and Lippmann and Schwinger equations is obtained by making use of results on spectral theory, wave function, and eigendifferential concepts contained. (auth)

Ergodicity of the generalized lemon billiards

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Jingyu; Mohr, Luke; Zhang, Hong-Kun, E-mail: hongkun@math.umass.edu

2013-12-15

In this paper, we study a two-parameter family of convex billiard tables, by taking the intersection of two round disks (with different radii) in the plane. These tables give a generalization of the one-parameter family of lemon-shaped billiards. Initially, there is only one ergodic table among all lemon tables. In our generalized family, we observe numerically the prevalence of ergodicity among the some perturbations of that table. Moreover, numerical estimates of the mixing rate of the billiard dynamics on some ergodic tables are also provided.

Ergodicity 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

2017-12-05

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.

Dynamical manifestations of quantum chaos: correlation hole and bulge

NASA Astrophysics Data System (ADS)

Torres-Herrera, E. J.; Santos, Lea F.

2017-10-01

A main feature of a chaotic quantum system is a rigid spectrum where the levels do not cross. We discuss how the presence of level repulsion in lattice many-body quantum systems can be detected from the analysis of their time evolution instead of their energy spectra. This approach is advantageous to experiments that deal with dynamics, but have limited or no direct access to spectroscopy. Dynamical manifestations of avoided crossings occur at long times. They correspond to a drop, referred to as correlation hole, below the asymptotic value of the survival probability and to a bulge above the saturation point of the von Neumann entanglement entropy and the Shannon information entropy. By contrast, the evolution of these quantities at shorter times reflects the level of delocalization of the initial state, but not necessarily a rigid spectrum. The correlation hole is a general indicator of the integrable-chaos transition in disordered and clean models and as such can be used to detect the transition to the many-body localized phase in disordered interacting systems. This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.

Detection of ɛ-ergodicity breaking in experimental data—A study of the dynamical functional sensibility

NASA Astrophysics Data System (ADS)

Loch-Olszewska, Hanna; Szwabiński, Janusz

2018-05-01

The ergodicity breaking phenomenon has already been in the area of interest of many scientists, who tried to uncover its biological and chemical origins. Unfortunately, testing ergodicity in real-life data can be challenging, as sample paths are often too short for approximating their asymptotic behaviour. In this paper, the authors analyze the minimal lengths of empirical trajectories needed for claiming the ɛ-ergodicity based on two commonly used variants of an autoregressive fractionally integrated moving average model. The dependence of the dynamical functional on the parameters of the process is studied. The problem of choosing proper ɛ for ɛ-ergodicity testing is discussed with respect to especially the variation of the innovation process and the data sample length, with a presentation on two real-life examples.

Detection of ε-ergodicity breaking in experimental data-A study of the dynamical functional sensibility.

PubMed

Loch-Olszewska, Hanna; Szwabiński, Janusz

2018-05-28

The ergodicity breaking phenomenon has already been in the area of interest of many scientists, who tried to uncover its biological and chemical origins. Unfortunately, testing ergodicity in real-life data can be challenging, as sample paths are often too short for approximating their asymptotic behaviour. In this paper, the authors analyze the minimal lengths of empirical trajectories needed for claiming the ε-ergodicity based on two commonly used variants of an autoregressive fractionally integrated moving average model. The dependence of the dynamical functional on the parameters of the process is studied. The problem of choosing proper ε for ε-ergodicity testing is discussed with respect to especially the variation of the innovation process and the data sample length, with a presentation on two real-life examples.

Universality and Thouless energy in the supersymmetric Sachdev-Ye-Kitaev model

NASA Astrophysics Data System (ADS)

García-García, Antonio M.; Jia, Yiyang; Verbaarschot, Jacobus J. M.

2018-05-01

We investigate the supersymmetric Sachdev-Ye-Kitaev (SYK) model, N Majorana fermions with infinite range interactions in 0 +1 dimensions. We have found that, close to the ground state E ≈0 , discrete symmetries alter qualitatively the spectral properties with respect to the non-supersymmetric SYK model. The average spectral density at finite N , which we compute analytically and numerically, grows exponentially with N for E ≈0 . However the chiral condensate, which is normalized with respect the total number of eigenvalues, vanishes in the thermodynamic limit. Slightly above E ≈0 , the spectral density grows exponentially with the energy. Deep in the quantum regime, corresponding to the first O (N ) eigenvalues, the average spectral density is universal and well described by random matrix ensembles with chiral and superconducting discrete symmetries. The dynamics for E ≈0 is investigated by level fluctuations. Also in this case we find excellent agreement with the prediction of chiral and superconducting random matrix ensembles for eigenvalue separations smaller than the Thouless energy, which seems to scale linearly with N . Deviations beyond the Thouless energy, which describes how ergodicity is approached, are universally characterized by a quadratic growth of the number variance. In the time domain, we have found analytically that the spectral form factor g (t ), obtained from the connected two-level correlation function of the unfolded spectrum, decays as 1 /t2 for times shorter but comparable to the Thouless time with g (0 ) related to the coefficient of the quadratic growth of the number variance. Our results provide further support that quantum black holes are ergodic and therefore can be classified by random matrix theory.

Ergodicity in natural earthquake fault networks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tiampo, K. F.; Rundle, J. B.; Holliday, J.

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.more » 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 evolution.« less

Many-body localization-delocalization transition in the quantum Sherrington-Kirkpatrick model

NASA Astrophysics Data System (ADS)

Mukherjee, Sudip; Nag, Sabyasachi; Garg, Arti

2018-04-01

We analyze the many-body localization- (MBL) to-delocalization transition in the Sherrington-Kirkpatrick (SK) model of Ising spin glass in the presence of a transverse field Γ . Based on energy-resolved analysis, which is of relevance for a closed quantum system, we show that the quantum SK model has many-body mobility edges separating the MBL phase, which is nonergodic and nonthermal, from the delocalized phase, which is ergodic and thermal. The range of the delocalized regime increases with an increase in the strength of Γ , and eventually for Γ larger than ΓCP the entire many-body spectrum is delocalized. We show that the Renyi entropy is almost independent of the system size in the MBL phase while the delocalized phase shows extensive Renyi entropy. We further obtain the spin-glass transition curve in the energy density ɛ -Γ plane from the collapse of the eigenstate spin susceptibility. We demonstrate that in most of the parameter regime, the spin-glass transition occurs close to the MBL transition, indicating that the spin-glass phase is nonergodic and nonthermal while the paramagnetic phase is delocalized and thermal.

On the analogues of Szegő's theorem for ergodic operators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kirsch, W; Pastur, L A

2015-01-31

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.

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

Ergodic transition in a simple model of the continuous double auction.

PubMed

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 M/M/1 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.

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.

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.

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.

Quantum and classical behavior in interacting bosonic systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hertzberg, Mark P.

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 differencemore » 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.« less

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.

On the relationship between cell cycle analysis with ergodic principles and age-structured cell population models.

PubMed

Kuritz, K; Stöhr, D; Pollak, N; Allgöwer, F

2017-02-07

Cyclic processes, in particular the cell cycle, are of great importance in cell biology. Continued improvement in cell population analysis methods like fluorescence microscopy, flow cytometry, CyTOF or single-cell omics made mathematical methods based on ergodic principles a powerful tool in studying these processes. In this paper, we establish the relationship between cell cycle analysis with ergodic principles and age structured population models. To this end, we describe the progression of a single cell through the cell cycle by a stochastic differential equation on a one dimensional manifold in the high dimensional dataspace of cell cycle markers. Given the assumption that the cell population is in a steady state, we derive transformation rules which transform the number density on the manifold to the steady state number density of age structured population models. Our theory facilitates the study of cell cycle dependent processes including local molecular events, cell death and cell division from high dimensional "snapshot" data. Ergodic analysis can in general be applied to every process that exhibits a steady state distribution. By combining ergodic analysis with age structured population models we furthermore provide the theoretic basis for extensions of ergodic principles to distribution that deviate from their steady state. Copyright © 2016 Elsevier Ltd. All rights reserved.

Asymptotic behaviors of a cell-to-cell HIV-1 infection model perturbed by white noise

NASA Astrophysics Data System (ADS)

Liu, Qun

2017-02-01

In this paper, we analyze a mathematical model of cell-to-cell HIV-1 infection to CD4+ T cells perturbed by stochastic perturbations. First of all, we investigate that there exists a unique global positive solution of the system for any positive initial value. Then by using Lyapunov analysis methods, we study the asymptotic property of this solution. Moreover, we discuss whether there is a stationary distribution for this system and if it owns the ergodic property. Numerical simulations are presented to illustrate the theoretical results.

Optimal harvesting of a stochastic delay logistic model with Lévy jumps

NASA Astrophysics Data System (ADS)

Qiu, Hong; Deng, Wenmin

2016-10-01

The optimal harvesting problem of a stochastic time delay logistic model with Lévy jumps is considered in this article. We first show that the model has a unique global positive solution and discuss the uniform boundedness of its pth moment with harvesting. Then we prove that the system is globally attractive and asymptotically stable in distribution under our assumptions. Furthermore, we obtain the existence of the optimal harvesting effort by the ergodic method, and then we give the explicit expression of the optimal harvesting policy and maximum yield.

Driven Phases of Quantum Matter

NASA Astrophysics Data System (ADS)

Khemani, Vedika; von Keyserlingk, Curt; Lazarides, Achilleas; Moessner, Roderich; Sondhi, Shivaji

Clean and interacting periodically driven quantum systems are believed to exhibit a single, trivial ``infinite-temperature'' Floquet-ergodic phase. By contrast, I will show that their disordered Floquet many-body localized counterparts can exhibit distinct ordered phases with spontaneously broken symmetries delineated by sharp transitions. Some of these are analogs of equilibrium states, while others are genuinely new to the Floquet setting. I will show that a subset of these novel phases are absolutely stableto all weak local deformations of the underlying Floquet drives, and spontaneously break Hamiltonian dependent emergent symmetries. Strikingly, they simultaneously also break the underlying time-translation symmetry of the Floquet drive and the order parameter exhibits oscillations at multiples of the fundamental period. This ``time-crystallinity'' goes hand in hand with spatial symmetry breaking and, altogether, these phases exhibit a novel form of simultaneous long-range order in space and time. I will describe how this spatiotemporal order can be detected in experiments involving quenches from a broad class of initial states.

Asymptotic Time Decay in Quantum Physics: a Selective Review and Some New Results

NASA Astrophysics Data System (ADS)

Marchetti, Domingos H. U.; Wreszinski, Walter F.

2013-05-01

Decay of various quantities (return or survival probability, correlation functions) in time are the basis of a multitude of important and interesting phenomena in quantum physics, ranging from spectral properties, resonances, return and approach to equilibrium, to dynamical stability properties and irreversibility and the "arrow of time" in [Asymptotic Time Decay in Quantum Physics (World Scientific, 2013)]. In this review, we study several types of decay — decay in the average, decay in the Lp-sense, and pointwise decay — of the Fourier-Stieltjes transform of a measure, usually identified with the spectral measure, which appear naturally in different mathematical and physical settings. In particular, decay in the Lp-sense is related both to pointwise decay and to decay in the average and, from a physical standpoint, relates to a rigorous form of the time-energy uncertainty relation. Both decay on the average and in the Lp-sense are related to spectral properties, in particular, absolute continuity of the spectral measure. The study of pointwise decay for singular continuous measures (Rajchman measures) provides a bridge between ergodic theory, number theory and analysis, including the method of stationary phase. The theory is illustrated by some new results in the theory of sparse models.

Thermalization dynamics in a quenched many-body state

NASA Astrophysics Data System (ADS)

Kaufman, Adam; Preiss, Philipp; Tai, Eric; Lukin, Alex; Rispoli, Matthew; Schittko, Robert; Greiner, Markus

2016-05-01

Quantum and classical many-body systems appear to have disparate behavior due to the different mechanisms that govern their evolution. The dynamics of a classical many-body system equilibrate to maximally entropic states and quickly re-thermalize when perturbed. The assumptions of ergodicity and unbiased configurations lead to a successful framework of describing classical systems by a sampling of thermal ensembles that are blind to the system's microscopic details. By contrast, an isolated quantum many-body system is governed by unitary evolution: the system retains memory of past dynamics and constant global entropy. However, even with differing characteristics, the long-term behavior for local observables in quenched, non-integrable quantum systems are often well described by the same thermal framework. We explore the onset of this convergence in a many-body system of bosonic atoms in an optical lattice. Our system's finite size allows us to verify full state purity and measure local observables. We observe rapid growth and saturation of the entanglement entropy with constant global purity. The combination of global purity and thermalized local observables agree with the Eigenstate Thermalization Hypothesis in the presence of a near-volume law in the entanglement entropy.

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.

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.

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.

A new approach to measuring tortuosity

NASA Astrophysics Data System (ADS)

Wert, Amanda; Scott, Sherry E.

2012-03-01

The detection and measurement of the tortuosity - i.e. the bending and winding - of vessels has been shown to be potentially useful in the assessment of cancer progression and treatment response. Although several metrics for tortuosity are used, no single one measure is able to capture all types of tortuosity. This report presents a new multiscale technique for measuring vessel tortuosity. The approach is based on a method - called the ergodicity defect - which gives a scale-dependent measure of deviation from ergodicity. Ergodicity is a concept that captures the manner in which trajectories or signals sample the space; thus, ergodicity and vessel tortuosity both involve the notion of how a signal samples space. Here we begin to explore this connection. We first apply the ergodicity defect tortuosity measure to both 2D and 3D synthetic data in order to demonstrate the response of the method to three types of tortuosity observed in clinical patterns. We then implement the technique on segmented vessels extracted from brain tumor MRA images. Results indicate that the method can be effectively used to detect and measure several types of vessel tortuosity.

Uncountably many maximizing measures for a dense subset of continuous functions

NASA Astrophysics Data System (ADS)

Shinoda, Mao

2018-05-01

Ergodic optimization aims to single out dynamically invariant Borel probability measures which maximize the integral of a given ‘performance’ function. For a continuous self-map of a compact metric space and a dense set of continuous functions, we show the existence of uncountably many ergodic maximizing measures. We also show that, for a topologically mixing subshift of finite type and a dense set of continuous functions there exist uncountably many ergodic maximizing measures with full support and positive entropy.

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.

Response theory of the ergodic many-body delocalized phase: Keldysh Finkel'stein sigma models and the 10-fold way

NASA Astrophysics Data System (ADS)

Liao, Yunxiang; Levchenko, Alex; Foster, Matthew S.

2017-11-01

We derive the finite temperature Keldysh response theory for interacting fermions in the presence of quenched short-ranged disorder, as applicable to any of the 10 Altland-Zirnbauer classes in an Anderson delocalized phase with at least a U(1) continuous symmetry. In this formulation of the interacting Finkel'stein nonlinear sigma model, the statistics of one-body wave functions are encoded by the constrained matrix field, while physical correlations follow from the hydrodynamic density or spin response field, which decouples the interactions. Integrating out the matrix field first, we obtain weak (anti) localization and Altshuler-Aronov quantum conductance corrections from the hydrodynamic response function. This procedure automatically incorporates the correct infrared cutoff physics, and in particular gives the Altshuler-Aronov-Khmelnitsky (AAK) equations for dephasing of weak (anti)localization due to electron-electron collisions. We explicate the method by deriving known quantumcorrections in two dimensions for the symplectic metal class AII, as well as the spin-SU(2) invariant superconductor classes C and CI. We show that quantum conductance corrections due to the special modes at zero energy in nonstandard classes are automatically cut off by temperature, as previously expected, while the Wigner-Dyson class Cooperon modes that persist to all energies are cut by dephasing. We also show that for short-ranged interactions, the standard self-consistent solution for the dephasing rate is equivalent to a particular summation of diagrams via the self-consistent Born approximation. This should be compared to the corresponding AAK solution for long-ranged Coulomb interactions, which exploits the Markovian noise correlations induced by thermal fluctuations of the electromagnetic field. We discuss prospects for exploring the many-body localization transition as a dephasing catastrophe in short-range interacting models, as encountered by approaching from the ergodic side.

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.

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 collapses to a lower-dimensional 'surface'. We explicitly illustrate the situation for accelerating random walks, and a spin system on a constant-conectancy network. We argue that generalized entropies should be relevant for self-organized critical systems such as sand piles, for spin systems which form meta-structures such as vortices, domains, instantons, etc., and for problems associated with anomalous diffusion.

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.

Ergodic Theory, Interpretations of Probability and the Foundations of Statistical Mechanics

NASA Astrophysics Data System (ADS)

van Lith, Janneke

The traditional use of ergodic theory in the foundations of equilibrium statistical mechanics is that it provides a link between thermodynamic observables and microcanonical probabilities. First of all, the ergodic theorem demonstrates the equality of microcanonical phase averages and infinite time averages (albeit for a special class of systems, and up to a measure zero set of exceptions). Secondly, one argues that actual measurements of thermodynamic quantities yield time averaged quantities, since measurements take a long time. The combination of these two points is held to be an explanation why calculating microcanonical phase averages is a successful algorithm for predicting the values of thermodynamic observables. It is also well known that this account is problematic. This survey intends to show that ergodic theory nevertheless may have important roles to play, and it explores three other uses of ergodic theory. Particular attention is paid, firstly, to the relevance of specific interpretations of probability, and secondly, to the way in which the concern with systems in thermal equilibrium is translated into probabilistic language. With respect to the latter point, it is argued that equilibrium should not be represented as a stationary probability distribution as is standardly done; instead, a weaker definition is presented.

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.

Hierarchical relaxation dynamics in a tilted two-band Bose-Hubbard model

NASA Astrophysics Data System (ADS)

Cosme, Jayson G.

2018-04-01

We numerically examine slow and hierarchical relaxation dynamics of interacting bosons described by a tilted two-band Bose-Hubbard model. The system is found to exhibit signatures of quantum chaos within the spectrum and the validity of the eigenstate thermalization hypothesis for relevant physical observables is demonstrated for certain parameter regimes. Using the truncated Wigner representation in the semiclassical limit of the system, dynamics of relevant observables reveal hierarchical relaxation and the appearance of prethermalized states is studied from the perspective of statistics of the underlying mean-field trajectories. The observed prethermalization scenario can be attributed to different stages of glassy dynamics in the mode-time configuration space due to dynamical phase transition between ergodic and nonergodic trajectories.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

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 averagedmore » 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.« less

Phase-space networks of geometrically frustrated systems.

PubMed

Han, Yilong

2009-11-01

We illustrate a network approach to the phase-space study by using two geometrical frustration models: antiferromagnet on triangular lattice and square ice. Their highly degenerated ground states are mapped as discrete networks such that the quantitative network analysis can be applied to phase-space studies. The resulting phase spaces share some comon features and establish a class of complex networks with unique Gaussian spectral densities. Although phase-space networks are heterogeneously connected, the systems are still ergodic due to the random Poisson processes. This network approach can be generalized to phase spaces of some other complex systems.

Dynamical behavior of a stochastic SVIR epidemic model with vaccination

NASA Astrophysics Data System (ADS)

Zhang, Xinhong; Jiang, Daqing; Hayat, Tasawar; Ahmad, Bashir

2017-10-01

In this paper, we investigate the dynamical behavior of SVIR models in random environments. Firstly, we show that if R0s < 1, the disease of stochastic autonomous SVIR model will die out exponentially; if R˜0s > 1, the disease will be prevail. Moreover, this system admits a unique stationary distribution and it is ergodic when R˜0s > 1. Results show that environmental white noise is helpful for disease control. Secondly, we give sufficient conditions for the existence of nontrivial periodic solutions to stochastic SVIR model with periodic parameters. Finally, numerical simulations validate the analytical results.

Ergodicity bounds for birth-death processes with particularities

NASA Astrophysics Data System (ADS)

Zeifman, Alexander I.; Satin, Yacov; Korotysheva, Anna; Shilova, Galina; Kiseleva, Ksenia; Korolev, Victor Yu.; Bening, Vladimir E.; Shorgin, Sergey Ya.

2016-06-01

We introduce an inhomogeneous birth-death process with birth rates λk(t), death rates µk(t), and possible transitions to/from zero with rates βk(t), rk(t) respectively, and obtain ergodicity bounds for this process.

Ergodicity of a singly-thermostated harmonic oscillator

NASA Astrophysics Data System (ADS)

Hoover, William Graham; Sprott, Julien Clinton; Hoover, Carol Griswold

2016-03-01

Although Nosé's thermostated mechanics is formally consistent with Gibbs' canonical ensemble, the thermostated Nosé-Hoover (harmonic) oscillator, with its mean kinetic temperature controlled, is far from ergodic. Much of its phase space is occupied by regular conservative tori. Oscillator ergodicity has previously been achieved by controlling two oscillator moments with two thermostat variables. Here we use computerized searches in conjunction with visualization to find singly-thermostated motion equations for the oscillator which are consistent with Gibbs' canonical distribution. Such models are the simplest able to bridge the gap between Gibbs' statistical ensembles and Newtonian single-particle dynamics.

Ergodicity of two hard balls in integrable polygons

NASA Astrophysics Data System (ADS)

Bálint, Péter; Troubetzkoy, Serge

2004-11-01

We prove the hyperbolicity, ergodicity and thus the Bernoulli property of two hard balls in one of the following four polygons: the square, the equilateral triangle, the 45°-45°-90° triangle or the 30°-60°-90° triangle.

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

PubMed Central

McLeish, Tom C. B.

2015-01-01

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. PMID:26640648

Two-way DF relaying assisted D2D communication: ergodic rate and power allocation

NASA Astrophysics Data System (ADS)

Ni, Yiyang; Wang, Yuxi; Jin, Shi; Wong, Kai-Kit; Zhu, Hongbo

2017-12-01

In this paper, we investigate the ergodic rate for a device-to-device (D2D) communication system aided by a two-way decode-and-forward (DF) relay node. We first derive closed-form expressions for the ergodic rate of the D2D link under asymmetric and symmetric cases, respectively. We subsequently discuss two special scenarios including weak interference case and high signal-to-noise ratio case. Then we derive the tight approximations for each of the considered scenarios. Assuming that each transmitter only has access to its own statistical channel state information (CSI), we further derive closed-form power allocation strategy to improve the system performance according to the analytical results of the ergodic rate. Furthermore, some insights are provided for the power allocation strategy based on the analytical results. The strategies are easy to compute and require to know only the channel statistics. Numerical results show the accuracy of the analysis results under various conditions and test the availability of the power allocation strategy.

Structured Modeling and Analysis of Stochastic Epidemics with Immigration and Demographic Effects

PubMed Central

Baumann, Hendrik; Sandmann, Werner

2016-01-01

Stochastic epidemics with open populations of variable population sizes are considered where due to immigration and demographic effects the epidemic does not eventually die out forever. The underlying stochastic processes are ergodic multi-dimensional continuous-time Markov chains that possess unique equilibrium probability distributions. Modeling these epidemics as level-dependent quasi-birth-and-death processes enables efficient computations of the equilibrium distributions by matrix-analytic methods. Numerical examples for specific parameter sets are provided, which demonstrates that this approach is particularly well-suited for studying the impact of varying rates for immigration, births, deaths, infection, recovery from infection, and loss of immunity. PMID:27010993

Structured Modeling and Analysis of Stochastic Epidemics with Immigration and Demographic Effects.

PubMed

Baumann, Hendrik; Sandmann, Werner

2016-01-01

Stochastic epidemics with open populations of variable population sizes are considered where due to immigration and demographic effects the epidemic does not eventually die out forever. The underlying stochastic processes are ergodic multi-dimensional continuous-time Markov chains that possess unique equilibrium probability distributions. Modeling these epidemics as level-dependent quasi-birth-and-death processes enables efficient computations of the equilibrium distributions by matrix-analytic methods. Numerical examples for specific parameter sets are provided, which demonstrates that this approach is particularly well-suited for studying the impact of varying rates for immigration, births, deaths, infection, recovery from infection, and loss of immunity.

Ordering relations for quantum states

NASA Astrophysics Data System (ADS)

Durham, Ian

2015-03-01

It is often desirable to model physical states in an order-theoretic manner, e.g. as a partially ordered set. Classical states are known to possess a unique ordering relation corresponding to a neo-realist interpretation of these states. No such unique relation exists for quantum states. This lack of a unique ordering relation for quantum states turns out to be a manifestation of quantum contextuality vis-à-vis the Kochen-Specker theorem. It also turns out that this provides a link to certain large-scale thermodynamic processes. The suggestion that the ordering of quantum states leads to macroscopic thermodynamic processes is at least five decades old. The suggestion that the mechanism that drives the ordering is contextuality, is unique to this work. The argument is framed in the language of the theories of domains, categories, and topoi. Financial support provided by FQXi.

Special ergodic theorems and dynamical large deviations

NASA Astrophysics Data System (ADS)

Kleptsyn, Victor; Ryzhov, Dmitry; Minkov, Stanislav

2012-11-01

Let f : M → M be a self-map of a compact Riemannian manifold M, admitting a global SRB measure μ. For a continuous test function \\varphi\\colon M\\to R and a constant α > 0, consider the set Kφ,α of the initial points for which the Birkhoff time averages of the function φ differ from its μ-space average by at least α. As the measure μ is a global SRB one, the set Kφ,α should have zero Lebesgue measure. The special ergodic theorem, whenever it holds, claims that, moreover, this set has a Hausdorff dimension less than the dimension of M. We prove that for Lipschitz maps, the special ergodic theorem follows from the dynamical large deviations principle. We also define and prove analogous result for flows. Applying the theorems of Young and of Araújo and Pacifico, we conclude that the special ergodic theorem holds for transitive hyperbolic attractors of C2-diffeomorphisms, as well as for some other known classes of maps (including the one of partially hyperbolic non-uniformly expanding maps) and flows.

Nanoscale mapping of heterogeneity of the polarization reversal in lead-free relaxor–ferroelectric ceramic composites

DOE PAGES

Gobeljic, D.; Shvartsman, V. V.; Belianinov, A.; ...

2016-01-05

Relaxor/ferroelectric ceramic/ceramic composites have shown to be promising in generating large electromechanical strain at moderate electric fields. However, the mechanisms of polarization and strain coupling between grains of different nature in the composites remain unclear. To rationalize the coupling mechanisms we performed advanced piezoresponse force microscopy (PFM) studies of 0.92BNT-0.06BT-0.02KNN/0.93BNT-0.07BT (ergodic/non-ergodic relaxor) composites. PFM is able to distinguish grains of different phases by characteristic domain patterns. Polarization switching has been probed locally, on a sub-grain scale. k-Means clustering analysis applied to arrays of local hysteresis loops reveals variations of polarization switching characteristics between the ergodic and non-ergodic relaxor grains. Here,more » we report a different set of switching parameters for grains in the composites as opposed to the pure phase samples. These results confirm ceramic/ceramic composites to be a viable approach to tailor the piezoelectric properties and optimize the macroscopic electromechanical characteristics.« less

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.

Giant room-temperature electrostrictive coefficients in lead-free relaxor ferroelectric ceramics by compositional tuning

NASA Astrophysics Data System (ADS)

Ullah, Aman; Gul, Hafiza Bushra; Ullah, Amir; Sheeraz, Muhammad; Bae, Jong-Seong; Jo, Wook; Ahn, Chang Won; Kim, Ill Won; Kim, Tae Heon

2018-01-01

A thermotropic phase boundary between non-ergodic and ergodic relaxor phases is tuned in lead-free Bi1/2Na1/2TiO3-based ceramics through a structural transition driven by compositional modification (usually named as "morphotropic approach"). The substitution of Bi(Ni1/2Ti1/2)O3 for Bi1/2(Na0.78K0.22)1/2TiO3 induces a transition from tetragonal to "metrically" cubic phase and thereby, the ergodic relaxor ferroelectric phase becomes predominant at room temperature. A shift of the transition temperature (denoted as TF-R) in the non-ergodic-to-ergodic phase transition is corroborated via temperature-dependent dielectric permittivity and loss measurements. By monitoring the chemical composition dependence of polarization-electric field and strain-electric field hysteresis loops, it is possible to track the critical concentration of Bi(Ni1/2Ti1/2)O3 where the (1 - x)Bi0.5(Na0.78K0.22)0.5TiO3-xBi(Ni0.5Ti0.5)O3 ceramic undergoes the phase transition around room temperature. At the Bi(Ni0.5Ti0.5)O3 content of x = 0.050, the highest room-temperature electrostrictive coefficient of 0.030 m4/C2 is achieved with no hysteretic characteristic, which can foster the realization of actual electrostrictive devices with high operational efficiency at room temperature.

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.

Competitive agents in a market: Statistical physics of the minority game

NASA Astrophysics Data System (ADS)

Sherrington, David

2007-10-01

A brief review is presented of the minority game, a simple frustrated many-body system stimulated by considerations of a market of competitive speculative agents. Its cooperative behaviour exhibits phase transitions and both ergodic and non-ergodic regimes. It provides novel challenges to statistical physics, reminiscent of those of mean-field spin glasses.

Ergodicity convergence test suggests telomere motion obeys fractional dynamics

NASA Astrophysics Data System (ADS)

Kepten, E.; Bronshtein, I.; Garini, Y.

2011-04-01

Anomalous diffusion, observed in many biological processes, is a generalized description of a wide variety of processes, all obeying the same law of mean-square displacement. Identifying the basic mechanisms of these observations is important for deducing the nature of the biophysical systems measured. We implement a previously suggested method for distinguishing between fractional Langevin dynamics, fractional Brownian motion, and continuous time random walk based on the ergodic nature of the data. We apply the method together with the recently suggested P-variation test and the displacement correlation to the lately measured dynamics of telomeres in the nucleus of mammalian cells and find strong evidence that the telomeres motion obeys fractional dynamics. The ergodic dynamics are observed experimentally to fit fractional Brownian or Langevin dynamics.

Robust Criterion for the Existence of Nonhyperbolic Ergodic Measures

NASA Astrophysics Data System (ADS)

Bochi, Jairo; Bonatti, Christian; Díaz, Lorenzo J.

2016-06-01

We give explicit C 1-open conditions that ensure that a diffeomorphism possesses a nonhyperbolic ergodic measure with positive entropy. Actually, our criterion provides the existence of a partially hyperbolic compact set with one-dimensional center and positive topological entropy on which the center Lyapunov exponent vanishes uniformly. The conditions of the criterion are met on a C 1-dense and open subset of the set of diffeomorphisms having a robust cycle. As a corollary, there exists a C 1-open and dense subset of the set of non-Anosov robustly transitive diffeomorphisms consisting of systems with nonhyperbolic ergodic measures with positive entropy. The criterion is based on a notion of a blender defined dynamically in terms of strict invariance of a family of discs.

Central limit theorem for recurrent random walks on a strip with bounded potential

NASA Astrophysics Data System (ADS)

Dolgopyat, D.; Goldsheid, I.

2018-07-01

We prove that the recurrent random walk (RW) in random environment (RE) on a strip in bounded potential satisfies the central limit theorem (CLT). The key ingredients of the proof are the analysis of the invariant measure equation and construction of a linearly growing martingale for walks in bounded potential. Our main result implies a complete classification of recurrent i.i.d. RWRE on the strip. Namely the walk either exhibits the Sinai behaviour in the sense that converges, as , to a (random) limit (the Sinai law) or, it satisfies the CLT. Another application of our main result is the CLT for the quasiperiodic environments with Diophantine frequencies in the recurrent case. We complement this result by proving that in the transient case the CLT holds for all uniquely ergodic environments. We also investigate the algebraic structure of the environments satisfying the CLT. In particular, we show that there exists a collection of proper algebraic subvarieties in the space of transition probabilities, such that: • If RE is stationary and ergodic and the transition probabilities are con-centrated on one of subvarieties from our collection then the CLT holds. • If the environment is i.i.d then the above condition is also necessary forthe CLT. All these results are valid for one-dimensional RWRE with bounded jumps as a particular case of the strip model.

The Wigner distribution and 2D classical maps

NASA Astrophysics Data System (ADS)

Sakhr, Jamal

2017-07-01

The Wigner spacing distribution has a long and illustrious history in nuclear physics and in the quantum mechanics of classically chaotic systems. In this paper, a novel connection between the Wigner distribution and 2D classical mechanics is introduced. Based on a well-known correspondence between the Wigner distribution and the 2D Poisson point process, the hypothesis that typical pseudo-trajectories of a 2D ergodic map have a Wignerian nearest-neighbor spacing distribution (NNSD) is put forward and numerically tested. The standard Euclidean metric is used to compute the interpoint spacings. In all test cases, the hypothesis is upheld, and the range of validity of the hypothesis appears to be robust in the sense that it is not affected by the presence or absence of: (i) mixing; (ii) time-reversal symmetry; and/or (iii) dissipation.

Tunneling with a hydrodynamic pilot-wave model

NASA Astrophysics Data System (ADS)

Nachbin, André; Milewski, Paul A.; Bush, John W. M.

2017-03-01

Eddi et al. [Phys. Rev Lett. 102, 240401 (2009), 10.1103/PhysRevLett.102.240401] presented experimental results demonstrating the unpredictable tunneling of a classical wave-particle association as may arise when a droplet walking across the surface of a vibrating fluid bath approaches a submerged barrier. We here present a theoretical model that captures the influence of bottom topography on this wave-particle association and so enables us to investigate its interaction with barriers. The coupled wave-droplet dynamics results in unpredictable tunneling events. As reported in the experiments by Eddi et al. and as is the case in quantum tunneling [Gamow, Nature (London) 122, 805 (1928), 10.1038/122805b0], the predicted tunneling probability decreases exponentially with increasing barrier width. In the parameter regimes examined, tunneling between two cavities suggests an underlying stationary ergodic process for the droplet's position.

Informational Aspects of Isotopic Diversity in Biology and Medicine

NASA Astrophysics Data System (ADS)

Berezin, Alexander A.

2004-10-01

Use of stable and radioactive isotopes in biology and medicine is intensive, yet informational aspects of isotopes as such are largely neglected (A.A.Berezin, J.Theor.Biol.,1992). Classical distinguishability (``labelability'') of isotopes allows for pattern generation dynamics. Quantum mechanically advantages of isotopicity (diversity of stable isotopes) arise from (almost perfect) degeneracy of various isotopic configurations; this in turn allows for isotopic sweeps (hoppings) by resonance neutron tunneling (Eccles mechanism). Isotopic variations of de Broglie wavelength affect quantum tunneling, diffusivity, magnetic interactions (e.g. by Lorentz force), etc. Ergodicity principle (all isoenergetic states are eventually accessed) implies possibility of fast scanning of library of morphogenetic patterns (cf metaphors of universal ``Platonic'' Library of Patterns: e.g. J.L.Borges, R.Sheldrake) with subsequent Darwinian reinforcement (e.g. by targeted mutations) of evolutionary advantageous patterns and structures. Isotopic shifts in organisms, from viruses and protozoa to mammalians, (e.g. DNA with enriched or depleted C-13) are tools to elucidate possible informational (e.g. Shannon entropy) role of isotopicity in genetic (e.g. evolutionary and morphological), dynamical (e.g. physiological and neurological) as well as medical (e.g. carcinogenesis, aging) aspects of biology and medicine.

Effect of heating on the suppression of tearing modes in tokamaks.

PubMed

Classen, I G J; Westerhof, E; Domier, C W; Donné, A J H; Jaspers, R J E; Luhmann, N C; Park, H K; van de Pol, M J; Spakman, G W; Jakubowski, M W

2007-01-19

The suppression of (neoclassical) tearing modes is of great importance for the success of future fusion reactors like ITER. Electron cyclotron waves can suppress islands, both by driving noninductive current in the island region and by heating the island, causing a perturbation to the Ohmic plasma current. This Letter reports on experiments on the TEXTOR tokamak, investigating the effect of heating, which is usually neglected. The unique set of tools available on TEXTOR, notably the dynamic ergodic divertor to create islands with a fully known driving term, and the electron cyclotron emission imaging diagnostic to provide detailed 2D electron temperature information, enables a detailed study of the suppression process and a comparison with theory.

Beyond the Quantum

NASA Astrophysics Data System (ADS)

Nieuwenhuizen, Theo M.; Mehmani, Bahar; Špička, Václav; Aghdami, Maryam J.; Khrennikov, Andrei Yu

2007-09-01

pt. A. Introductions. The mathematical basis for deterministic quantum mechanics / G.'t Hooft. What did we learn from quantum gravity? / A. Ashtekar. Bose-Einstein condensates and EPR quantum non-locality / F. Laloe. The quantum measurement process: lessons from an exactly solvable model / A.E. Allahverdyan, R. Balian and Th. M. Nieuwenhuizen -- pt. B. Quantum mechanics and quantum information. POVMs: a small but important step beyond standard quantum mechanics / W. M. de Muynck. State reduction by measurements with a null result / G. Nienhuis. Solving open questions in the Bose-Einstein condensation of an ideal gas via a hybrid mixture of laser and statistical physics / M. Kim, A. Svidzinsky and M.O. Scully. Twin-Photon light scattering and causality / G. Puentes, A. Aiello and J. P. Woerdman. Simultaneous measurement of non-commuting observables / G. Aquino and B. Mehmani. Quantum decoherence and gravitational waves / M.T. Jaekel ... [et al.]. Role of various entropies in the black hole information loss problem / Th. M. Nieuwenhuizen and I.V. Volovich. Quantum and super-quantum correlations / G.S. Jaeger -- pt. C. Long distance correlations and bell inequalities. Understanding long-distance quantum correlations / L. Marchildon. Connection of probability models to EPR experiments: probability spaces and Bell's theorem / K. Hess and W. Philipp. Fair sampling vs no-signalling principle in EPR experiments / G. Adenier and A. Yu. Khrennikov -- pt. D. Mathematical foundations. Where the mathematical structure of quantum mechanics comes from / G.M. D'Ariano. Phase space description of quantum mechanics and non-commutative geometry: Wigner-Moyal and Bohm in a wider context / B.J. Hiley. Quantum mechanics as simple algorithm for approximation of classical integrals / A. Yu. Khrennikov. Noncommutative quantum mechanics viewed from Feynman Formalism / J. Lages ... [et al.]. Beyond the quantum in Snyder space / J.F.S. van Huele and M. K. Transtrum -- pt. E. Stochastic 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.].

Applications of Ergodic Theory to Coverage Analysis

NASA Technical Reports Server (NTRS)

Lo, Martin W.

2003-01-01

The study of differential equations, or dynamical systems in general, has two fundamentally different approaches. We are most familiar with the construction of solutions to differential equations. Another approach is to study the statistical behavior of the solutions. Ergodic Theory is one of the most developed methods to study the statistical behavior of the solutions of differential equations. In the theory of satellite orbits, the statistical behavior of the orbits is used to produce 'Coverage Analysis' or how often a spacecraft is in view of a site on the ground. In this paper, we consider the use of Ergodic Theory for Coverage Analysis. This allows us to greatly simplify the computation of quantities such as the total time for which a ground station can see a satellite without ever integrating the trajectory, see Lo 1,2. More over, for any quantity which is an integrable function of the ground track, its average may be computed similarly without the integration of the trajectory. For example, the data rate for a simple telecom system is a function of the distance between the satellite and the ground station. We show that such a function may be averaged using the Ergodic Theorem.

Equilibration of energy in slow–fast systems

PubMed Central

Shah, Kushal; Gelfreich, Vassili; Rom-Kedar, Vered

2017-01-01

Ergodicity is a fundamental requirement for a dynamical system to reach a state of statistical equilibrium. However, in systems with several characteristic timescales, the ergodicity of the fast subsystem impedes the equilibration of the whole system because of the presence of an adiabatic invariant. In this paper, we show that violation of ergodicity in the fast dynamics can drive the whole system to equilibrium. To show this principle, we investigate the dynamics of springy billiards, which are mechanical systems composed of a small particle bouncing elastically in a bounded domain, where one of the boundary walls has finite mass and is attached to a linear spring. Numerical simulations show that the springy billiard systems approach equilibrium at an exponential rate. However, in the limit of vanishing particle-to-wall mass ratio, the equilibration rates remain strictly positive only when the fast particle dynamics reveal two or more ergodic components for a range of wall positions. For this case, we show that the slow dynamics of the moving wall can be modeled by a random process. Numerical simulations of the corresponding springy billiards and their random models show equilibration with similar positive rates. PMID:29183966

Ergodicity, Maximum Entropy Production, and Steepest Entropy Ascent in the Proofs of Onsager's Reciprocal Relations

NASA Astrophysics Data System (ADS)

Benfenati, Francesco; Beretta, Gian Paolo

2018-04-01

We show that to prove the Onsager relations using the microscopic time reversibility one necessarily has to make an ergodic hypothesis, or a hypothesis closely linked to that. This is true in all the proofs of the Onsager relations in the literature: from the original proof by Onsager, to more advanced proofs in the context of linear response theory and the theory of Markov processes, to the proof in the context of the kinetic theory of gases. The only three proofs that do not require any kind of ergodic hypothesis are based on additional hypotheses on the macroscopic evolution: Ziegler's maximum entropy production principle (MEPP), the principle of time reversal invariance of the entropy production, or the steepest entropy ascent principle (SEAP).

Quantum space and quantum completeness

NASA Astrophysics Data System (ADS)

Jurić, Tajron

2018-05-01

Motivated by the question whether quantum gravity can "smear out" the classical singularity we analyze a certain quantum space and its quantum-mechanical completeness. Classical singularity is understood as a geodesic incompleteness, while quantum completeness requires a unique unitary time evolution for test fields propagating on an underlying background. Here the crucial point is that quantum completeness renders the Hamiltonian (or spatial part of the wave operator) to be essentially self-adjoint in order to generate a unique time evolution. We examine a model of quantum space which consists of a noncommutative BTZ black hole probed by a test scalar field. We show that the quantum gravity (noncommutative) effect is to enlarge the domain of BTZ parameters for which the relevant wave operator is essentially self-adjoint. This means that the corresponding quantum space is quantum complete for a larger range of BTZ parameters rendering the conclusion that in the quantum space one observes the effect of "smearing out" the singularity.

Singularities and non-hyperbolic manifolds do not coincide

NASA Astrophysics Data System (ADS)

Simányi, Nándor

2013-06-01

We consider the billiard flow of elastically colliding hard balls on the flat ν-torus (ν ⩾ 2), and prove that no singularity manifold can even locally coincide with a manifold describing future non-hyperbolicity of the trajectories. As a corollary, we obtain the ergodicity (actually the Bernoulli mixing property) of all such systems, i.e. the verification of the Boltzmann-Sinai ergodic hypothesis.

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.

Sandia QIS Capabilities.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Muller, Richard P.

2017-07-01

Sandia National Laboratories has developed a broad set of capabilities in quantum information science (QIS), including elements of quantum computing, quantum communications, and quantum sensing. The Sandia QIS program is built atop unique DOE investments at the laboratories, including the MESA microelectronics fabrication facility, the Center for Integrated Nanotechnologies (CINT) facilities (joint with LANL), the Ion Beam Laboratory, and ASC High Performance Computing (HPC) facilities. Sandia has invested $75 M of LDRD funding over 12 years to develop unique, differentiating capabilities that leverage these DOE infrastructure investments.

Invariant measures in brain dynamics

NASA Astrophysics Data System (ADS)

Boyarsky, Abraham; Góra, Paweł

2006-10-01

This note concerns brain activity at the level of neural ensembles and uses ideas from ergodic dynamical systems to model and characterize chaotic patterns among these ensembles during conscious mental activity. Central to our model is the definition of a space of neural ensembles and the assumption of discrete time ensemble dynamics. We argue that continuous invariant measures draw the attention of deeper brain processes, engendering emergent properties such as consciousness. Invariant measures supported on a finite set of ensembles reflect periodic behavior, whereas the existence of continuous invariant measures reflect the dynamics of nonrepeating ensemble patterns that elicit the interest of deeper mental processes. We shall consider two different ways to achieve continuous invariant measures on the space of neural ensembles: (1) via quantum jitters, and (2) via sensory input accompanied by inner thought processes which engender a “folding” property on the space of ensembles.

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.

Ergodicity Breaking in Geometric Brownian Motion

NASA Astrophysics Data System (ADS)

Peters, O.; Klein, W.

2013-03-01

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.

Occupation times and ergodicity breaking in biased continuous time random walks

NASA Astrophysics Data System (ADS)

Bel, Golan; Barkai, Eli

2005-12-01

Continuous time random walk (CTRW) models are widely used to model diffusion in condensed matter. There are two classes of such models, distinguished by the convergence or divergence of the mean waiting time. Systems with finite average sojourn time are ergodic and thus Boltzmann-Gibbs statistics can be applied. We investigate the statistical properties of CTRW models with infinite average sojourn time; in particular, the occupation time probability density function is obtained. It is shown that in the non-ergodic phase the distribution of the occupation time of the particle on a given lattice point exhibits bimodal U or trimodal W shape, related to the arcsine law. The key points are as follows. (a) In a CTRW with finite or infinite mean waiting time, the distribution of the number of visits on a lattice point is determined by the probability that a member of an ensemble of particles in equilibrium occupies the lattice point. (b) The asymmetry parameter of the probability distribution function of occupation times is related to the Boltzmann probability and to the partition function. (c) The ensemble average is given by Boltzmann-Gibbs statistics for either finite or infinite mean sojourn time, when detailed balance conditions hold. (d) A non-ergodic generalization of the Boltzmann-Gibbs statistical mechanics for systems with infinite mean sojourn time is found.

Stochastic Geometry and Quantum Gravity: Some Rigorous Results

NASA Astrophysics Data System (ADS)

Zessin, H.

The aim of these lectures is a short introduction into some recent developments in stochastic geometry which have one of its origins in simplicial gravity theory (see Regge Nuovo Cimento 19: 558-571, 1961). The aim is to define and construct rigorously point processes on spaces of Euclidean simplices in such a way that the configurations of these simplices are simplicial complexes. The main interest then is concentrated on their curvature properties. We illustrate certain basic ideas from a mathematical point of view. An excellent representation of this area can be found in Schneider and Weil (Stochastic and Integral Geometry, Springer, Berlin, 2008. German edition: Stochastische Geometrie, Teubner, 2000). In Ambjørn et al. (Quantum Geometry Cambridge University Press, Cambridge, 1997) you find a beautiful account from the physical point of view. More recent developments in this direction can be found in Ambjørn et al. ("Quantum gravity as sum over spacetimes", Lect. Notes Phys. 807. Springer, Heidelberg, 2010). After an informal axiomatic introduction into the conceptual foundations of Regge's approach the first lecture recalls the concepts and notations used. It presents the fundamental zero-infinity law of stochastic geometry and the construction of cluster processes based on it. The second lecture presents the main mathematical object, i.e. Poisson-Delaunay surfaces possessing an intrinsic random metric structure. The third and fourth lectures discuss their ergodic behaviour and present the two-dimensional Regge model of pure simplicial quantum gravity. We terminate with the formulation of basic open problems. Proofs are given in detail only in a few cases. In general the main ideas are developed. Sufficiently complete references are given.

Dynamics of a Stochastic Predator-Prey Model with Stage Structure for Predator and Holling Type II Functional Response

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing; Hayat, Tasawar; Alsaedi, Ahmed

2018-01-01

In this paper, we develop and study a stochastic predator-prey model with stage structure for predator and Holling type II functional response. First of all, by constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Then, we obtain sufficient conditions for extinction of the predator populations in two cases, that is, the first case is that the prey population survival and the predator populations extinction; the second case is that all the prey and predator populations extinction. The existence of a stationary distribution implies stochastic weak stability. Numerical simulations are carried out to demonstrate the analytical results.

A performance analysis of ensemble averaging for high fidelity turbulence simulations at the strong scaling limit

DOE Office of Scientific and Technical Information (OSTI.GOV)

Makarashvili, Vakhtang; Merzari, Elia; Obabko, Aleksandr

We analyze the potential performance benefits of estimating expected quantities in large eddy simulations of turbulent flows using true ensembles rather than ergodic time averaging. Multiple realizations of the same flow are simulated in parallel, using slightly perturbed initial conditions to create unique instantaneous evolutions of the flow field. Each realization is then used to calculate statistical quantities. Provided each instance is sufficiently de-correlated, this approach potentially allows considerable reduction in the time to solution beyond the strong scaling limit for a given accuracy. This study focuses on the theory and implementation of the methodology in Nek5000, a massively parallelmore » open-source spectral element code.« less

A performance analysis of ensemble averaging for high fidelity turbulence simulations at the strong scaling limit

DOE PAGES

Makarashvili, Vakhtang; Merzari, Elia; Obabko, Aleksandr; ...

2017-06-07

We analyze the potential performance benefits of estimating expected quantities in large eddy simulations of turbulent flows using true ensembles rather than ergodic time averaging. Multiple realizations of the same flow are simulated in parallel, using slightly perturbed initial conditions to create unique instantaneous evolutions of the flow field. Each realization is then used to calculate statistical quantities. Provided each instance is sufficiently de-correlated, this approach potentially allows considerable reduction in the time to solution beyond the strong scaling limit for a given accuracy. This study focuses on the theory and implementation of the methodology in Nek5000, a massively parallelmore » open-source spectral element code.« less

Dynamics of a Stochastic Predator-Prey Model with Stage Structure for Predator and Holling Type II Functional Response

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing; Hayat, Tasawar; Alsaedi, Ahmed

2018-06-01

In this paper, we develop and study a stochastic predator-prey model with stage structure for predator and Holling type II functional response. First of all, by constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Then, we obtain sufficient conditions for extinction of the predator populations in two cases, that is, the first case is that the prey population survival and the predator populations extinction; the second case is that all the prey and predator populations extinction. The existence of a stationary distribution implies stochastic weak stability. Numerical simulations are carried out to demonstrate the analytical results.

Information, Consistent Estimation and Dynamic System Identification.

DTIC Science & Technology

1976-11-01

Washington,DC 232129 Tj-CUOSITORING AGENCY NAMIE 6 AOORESS(lI dittevmet Itroo CuooottaaII Offics) IS.- SECURITY CLASS. (of this *.part) SCHEDULE ’B...representative model from a given model set, applicable to infinite and even non-compact model sets. S-UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAOrj(*whe...ergodicity. For a thorough development of ergodic theory the reader is referred to, e.g., Doob [1953], Halmos [1956] and Chacon and Ornstein [1959

Dephasing Catastrophe in 4-ε Dimensions: A Possible Instability of the Ergodic (Many-Body-Delocalized) Phase.

PubMed

Liao, Yunxiang; Foster, Matthew S

2018-06-08

In two dimensions, dephasing by a bath cuts off Anderson localization that would otherwise occur at any energy density for fermions with disorder. For an isolated system with short-range interactions, the system can be its own bath, exhibiting diffusive (non-Markovian) thermal density fluctuations. We recast the dephasing of weak localization due to a diffusive bath as a self-interacting polymer loop. We investigate the critical behavior of the loop in d=4-ε dimensions, and find a nontrivial fixed point corresponding to a temperature T^{*}∼ε>0 where the dephasing time diverges. Assuming that this fixed point survives to ε=2, we associate it with a possible instability of the ergodic phase. Our approach may open a new line of attack against the problem of the ergodic to many-body-localized phase transition in d>1 spatial dimensions.

Dephasing Catastrophe in 4 -ɛ Dimensions: A Possible Instability of the Ergodic (Many-Body-Delocalized) Phase

NASA Astrophysics Data System (ADS)

Liao, Yunxiang; Foster, Matthew S.

2018-06-01

In two dimensions, dephasing by a bath cuts off Anderson localization that would otherwise occur at any energy density for fermions with disorder. For an isolated system with short-range interactions, the system can be its own bath, exhibiting diffusive (non-Markovian) thermal density fluctuations. We recast the dephasing of weak localization due to a diffusive bath as a self-interacting polymer loop. We investigate the critical behavior of the loop in d =4 -ɛ dimensions, and find a nontrivial fixed point corresponding to a temperature T*˜ɛ >0 where the dephasing time diverges. Assuming that this fixed point survives to ɛ =2 , we associate it with a possible instability of the ergodic phase. Our approach may open a new line of attack against the problem of the ergodic to many-body-localized phase transition in d >1 spatial dimensions.

Ergodic model for the expansion of spherical nanoplasmas.

PubMed

Peano, F; Coppa, G; Peinetti, F; Mulas, R; Silva, L O

2007-06-01

Recently, the collisionless expansion of spherical nanoplasmas has been analyzed with a new ergodic model, clarifying the transition from hydrodynamiclike to Coulomb-explosion regimes, and providing accurate laws for the relevant features of the phenomenon. A complete derivation of the model is presented here. The important issue of the self-consistent initial conditions is addressed by analyzing the initial charging transient due to the electron expansion, in the approximation of immobile ions. A comparison among different kinetic models for the expansion is presented, showing that the ergodic model provides a simplified description, which retains the essential information on the electron distribution, in particular, the energy spectrum. Results are presented for a wide range of initial conditions (determined from a single dimensionless parameter), in excellent agreement with calculations from the exact Vlasov-Poisson theory, thus providing a complete and detailed characterization of all the stages of the expansion.

Passive runaway electron suppression in tokamak disruptions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, H. M.; Helander, P.; Boozer, A. H.

2013-07-15

Runaway electrons created in disruptions pose a serious problem for tokamaks with large current. It would be desirable to have a runaway electron suppression method which is passive, i.e., a method that does not rely on an uncertain disruption prediction system. One option is to let the large electric field inherent in the disruption drive helical currents in the wall. This would create ergodic regions in the plasma and increase the runaway losses. Whether these regions appear at a suitable time and place to affect the formation of the runaway beam depends on disruption parameters, such as electron temperature andmore » density. We find that it is difficult to ergodize the central plasma before a beam of runaway current has formed. However, the ergodic outer region will make the Ohmic current profile contract, which can lead to instabilities that yield large runaway electron losses.« less

The condition of a finite Markov chain and perturbation bounds for the limiting probabilities

NASA Technical Reports Server (NTRS)

Meyer, C. D., Jr.

1979-01-01

The inequalities bounding the relative error the norm of w- w squiggly/the norm of w are exhibited by a very simple function of E and A. Let T denote the transition matrix of an ergodic chain, C, and let A = I - T. Let E be a perturbation matrix such that T squiggly = T - E is also the transition matrix of an ergodic chain, C squiggly. Let w and w squiggly denote the limiting probability (row) vectors for C and C squiggly. The inequality is the best one possible. This bound can be significant in the numerical determination of the limiting probabilities for an ergodic chain. In addition to presenting a sharp bound for the norm of w-w squiggly/the norm of w an explicit expression for w squiggly will be derived in which w squiggly is given as a function of E, A, w and some other related terms.

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…

Ergodicity-breaking bifurcations and tunneling in hyperbolic transport models

NASA Astrophysics Data System (ADS)

Giona, M.; Brasiello, A.; Crescitelli, S.

2015-11-01

One of the main differences between parabolic transport, associated with Langevin equations driven by Wiener processes, and hyperbolic models related to generalized Kac equations driven by Poisson processes, is the occurrence in the latter of multiple stable invariant densities (Frobenius multiplicity) in certain regions of the parameter space. This phenomenon is associated with the occurrence in linear hyperbolic balance equations of a typical bifurcation, referred to as the ergodicity-breaking bifurcation, the properties of which are thoroughly analyzed.

Quantifying non-ergodic dynamics of force-free granular gases.

PubMed

Bodrova, Anna; Chechkin, Aleksei V; Cherstvy, Andrey G; Metzler, Ralf

2015-09-14

Brownian motion is ergodic in the Boltzmann-Khinchin sense that long time averages of physical observables such as the mean squared displacement provide the same information as the corresponding ensemble average, even at out-of-equilibrium conditions. This property is the fundamental prerequisite for single particle tracking and its analysis in simple liquids. We study analytically and by event-driven molecular dynamics simulations the dynamics of force-free cooling granular gases and reveal a violation of ergodicity in this Boltzmann-Khinchin sense as well as distinct ageing of the system. Such granular gases comprise materials such as dilute gases of stones, sand, various types of powders, or large molecules, and their mixtures are ubiquitous in Nature and technology, in particular in Space. We treat-depending on the physical-chemical properties of the inter-particle interaction upon their pair collisions-both a constant and a velocity-dependent (viscoelastic) restitution coefficient ε. Moreover we compare the granular gas dynamics with an effective single particle stochastic model based on an underdamped Langevin equation with time dependent diffusivity. We find that both models share the same behaviour of the ensemble mean squared displacement (MSD) and the velocity correlations in the limit of weak dissipation. Qualitatively, the reported non-ergodic behaviour is generic for granular gases with any realistic dependence of ε on the impact velocity of particles.

GENERAL A Hierarchy of Compatibility and Comeasurability Levels in Quantum Logics with Unique Conditional Probabilities

NASA Astrophysics Data System (ADS)

Gerd, Niestegge

2010-12-01

In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A model involving a clear probabilistic interpretation from the very beginning is provided by the quantum logics with unique conditional probabilities. It includes the projection lattices in von Neumann algebras and here probability conditionalization becomes identical with the state transition of the Lüders-von Neumann measurement process. This motivates the definition of a hierarchy of five compatibility and comeasurability levels in the abstract setting of the quantum logics with unique conditional probabilities. Their meanings are: the absence of quantum interference or influence, the existence of a joint distribution, simultaneous measurability, and the independence of the final state after two successive measurements from the sequential order of these two measurements. A further level means that two elements of the quantum logic (events) belong to the same Boolean subalgebra. In the general case, the five compatibility and comeasurability levels appear to differ, but they all coincide in the common Hilbert space formalism of quantum mechanics, in von Neumann algebras, and in some other cases.

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

Spectra of random operators with absolutely continuous integrated density of states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rio, Rafael del, E-mail: delrio@iimas.unam.mx, E-mail: delriomagia@gmail.com

2014-04-15

The structure of the spectrum of random operators is studied. It is shown that if the density of states measure of some subsets of the spectrum is zero, then these subsets are empty. In particular follows that absolute continuity of the integrated density of states implies singular spectra of ergodic operators is either empty or of positive measure. Our results apply to Anderson and alloy type models, perturbed Landau Hamiltonians, almost periodic potentials, and models which are not ergodic.

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.

Speckle dynamics under ergodicity breaking

NASA Astrophysics Data System (ADS)

Sdobnov, Anton; Bykov, Alexander; Molodij, Guillaume; Kalchenko, Vyacheslav; Jarvinen, Topias; Popov, Alexey; Kordas, Krisztian; Meglinski, Igor

2018-04-01

Laser speckle contrast imaging (LSCI) is a well-known and versatile approach for the non-invasive visualization of flows and microcirculation localized in turbid scattering media, including biological tissues. In most conventional implementations of LSCI the ergodic regime is typically assumed valid. However, most composite turbid scattering media, especially biological tissues, are non-ergodic, containing a mixture of dynamic and static centers of light scattering. In the current study, we examined the speckle contrast in different dynamic conditions with the aim of assessing limitations in the quantitative interpretation of speckle contrast images. Based on a simple phenomenological approach, we introduced a coefficient of speckle dynamics to quantitatively assess the ratio of the dynamic part of a scattering medium to the static one. The introduced coefficient allows one to distinguish real changes in motion from the mere appearance of static components in the field of view. As examples of systems with static/dynamic transitions, thawing and heating of Intralipid samples were studied by the LSCI approach.

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.

Fisher-Symmetric Informationally Complete Measurements for Pure States.

PubMed

Li, Nan; Ferrie, Christopher; Gross, Jonathan A; Kalev, Amir; Caves, Carlton M

2016-05-06

We introduce a new kind of quantum measurement that is defined to be symmetric in the sense of uniform Fisher information across a set of parameters that uniquely represent pure quantum states in the neighborhood of a fiducial pure state. The measurement is locally informationally complete-i.e., it uniquely determines these parameters, as opposed to distinguishing two arbitrary quantum states-and it is maximal in the sense of a multiparameter quantum Cramér-Rao bound. For a d-dimensional quantum system, requiring only local informational completeness allows us to reduce the number of outcomes of the measurement from a minimum close to but below 4d-3, for the usual notion of global pure-state informational completeness, to 2d-1.

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

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…

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.

One-Time Pad as a nonlinear dynamical system

NASA Astrophysics Data System (ADS)

Nagaraj, Nithin

2012-11-01

The One-Time Pad (OTP) is the only known unbreakable cipher, proved mathematically by Shannon in 1949. In spite of several practical drawbacks of using the OTP, it continues to be used in quantum cryptography, DNA cryptography and even in classical cryptography when the highest form of security is desired (other popular algorithms like RSA, ECC, AES are not even proven to be computationally secure). In this work, we prove that the OTP encryption and decryption is equivalent to finding the initial condition on a pair of binary maps (Bernoulli shift). The binary map belongs to a family of 1D nonlinear chaotic and ergodic dynamical systems known as Generalized Luröth Series (GLS). Having established these interesting connections, we construct other perfect secrecy systems on the GLS that are equivalent to the One-Time Pad, generalizing for larger alphabets. We further show that OTP encryption is related to Randomized Arithmetic Coding - a scheme for joint compression and encryption.

Extended slow dynamical regime close to the many-body localization transition

NASA Astrophysics Data System (ADS)

Luitz, David J.; Laflorencie, Nicolas; Alet, Fabien

2016-02-01

Many-body localization is characterized by a slow logarithmic growth of the entanglement entropy after a global quantum quench while the local memory of an initial density imbalance remains at infinite time. We investigate how much the proximity of a many-body localized phase can influence the dynamics in the delocalized ergodic regime where thermalization is expected. Using an exact Krylov space technique, the out-of-equilibrium dynamics of the random-field Heisenberg chain is studied up to L =28 sites, starting from an initially unentangled high-energy product state. Within most of the delocalized phase, we find a sub-ballistic entanglement growth S (t ) ∝t1 /z with a disorder-dependent exponent z ≥1 , in contrast with the pure ballistic growth z =1 of clean systems. At the same time, anomalous relaxation is also observed for the spin imbalance I (t ) ∝t-ζ with a continuously varying disorder-dependent exponent ζ , vanishing at the transition. This provides a clear experimental signature for detecting this nonconventional regime.

Many-body localization transition: Schmidt gap, entanglement length, and scaling

NASA Astrophysics Data System (ADS)

Gray, Johnnie; Bose, Sougato; Bayat, Abolfazl

2018-05-01

Many-body localization has become an important phenomenon for illuminating a potential rift between nonequilibrium quantum systems and statistical mechanics. However, the nature of the transition between ergodic and localized phases in models displaying many-body localization is not yet well understood. Assuming that this is a continuous transition, analytic results show that the length scale should diverge with a critical exponent ν ≥2 in one-dimensional systems. Interestingly, this is in stark contrast with all exact numerical studies which find ν ˜1 . We introduce the Schmidt gap, new in this context, which scales near the transition with an exponent ν >2 compatible with the analytical bound. We attribute this to an insensitivity to certain finite-size fluctuations, which remain significant in other quantities at the sizes accessible to exact numerical methods. Additionally, we find that a physical manifestation of the diverging length scale is apparent in the entanglement length computed using the logarithmic negativity between disjoint blocks.

Molecular engineering with artificial atoms: designing a material platform for scalable quantum spintronics and photonics

NASA Astrophysics Data System (ADS)

Doty, Matthew F.; Ma, Xiangyu; Zide, Joshua M. O.; Bryant, Garnett W.

2017-09-01

Self-assembled InAs Quantum Dots (QDs) are often called "artificial atoms" and have long been of interest as components of quantum photonic and spintronic devices. Although there has been substantial progress in demonstrating optical control of both single spins confined to a single QD and entanglement between two separated QDs, the path toward scalable quantum photonic devices based on spins remains challenging. Quantum Dot Molecules, which consist of two closely-spaced InAs QDs, have unique properties that can be engineered with the solid state analog of molecular engineering in which the composition, size, and location of both the QDs and the intervening barrier are controlled during growth. Moreover, applied electric, magnetic, and optical fields can be used to modulate, in situ, both the spin and optical properties of the molecular states. We describe how the unique photonic properties of engineered Quantum Dot Molecules can be leveraged to overcome long-standing challenges to the creation of scalable quantum devices that manipulate single spins via photonics.

Thermal inclusions: how one spin can destroy a many-body localized phase

NASA Astrophysics Data System (ADS)

Ponte, Pedro; Laumann, C. R.; Huse, David A.; Chandran, A.

2017-10-01

Many-body localized (MBL) systems lie outside the framework of statistical mechanics, as they fail to equilibrate under their own quantum dynamics. Even basic features of MBL systems, such as their stability to thermal inclusions and the nature of the dynamical transition to thermalizing behaviour, remain poorly understood. We study a simple central spin model to address these questions: a two-level system interacting with strength J with N≫1 localized bits subject to random fields. On increasing J, the system transitions from an MBL to a delocalized phase on the vanishing scale Jc(N)˜1/N, up to logarithmic corrections. In the transition region, the single-site eigenstate entanglement entropies exhibit bimodal distributions, so that localized bits are either `on' (strongly entangled) or `off' (weakly entangled) in eigenstates. The clusters of `on' bits vary significantly between eigenstates of the same sample, which provides evidence for a heterogeneous discontinuous transition out of the localized phase in single-site observables. We obtain these results by perturbative mapping to bond percolation on the hypercube at small J and by numerical exact diagonalization of the full many-body system. Our results support the arguments that the MBL phase is unstable in systems with short-range interactions and quenched randomness in dimensions d that are high but finite. This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.

On base station cooperation using statistical CSI in jointly correlated MIMO downlink channels

NASA Astrophysics Data System (ADS)

Zhang, Jun; Jiang, Bin; Jin, Shi; Gao, Xiqi; Wong, Kai-Kit

2012-12-01

This article studies the transmission of a single cell-edge user's signal using statistical channel state information at cooperative base stations (BSs) with a general jointly correlated multiple-input multiple-output (MIMO) channel model. We first present an optimal scheme to maximize the ergodic sum capacity with per-BS power constraints, revealing that the transmitted signals of all BSs are mutually independent and the optimum transmit directions for each BS align with the eigenvectors of the BS's own transmit correlation matrix of the channel. Then, we employ matrix permanents to derive a closed-form tight upper bound for the ergodic sum capacity. Based on these results, we develop a low-complexity power allocation solution using convex optimization techniques and a simple iterative water-filling algorithm (IWFA) for power allocation. Finally, we derive a necessary and sufficient condition for which a beamforming approach achieves capacity for all BSs. Simulation results demonstrate that the upper bound of ergodic sum capacity is tight and the proposed cooperative transmission scheme increases the downlink system sum capacity considerably.

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.

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.

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.

Evaluating gambles using dynamics

NASA Astrophysics Data System (ADS)

Peters, O.; Gell-Mann, M.

2016-02-01

Gambles are random variables that model possible changes in wealth. Classic decision theory transforms money into utility through a utility function and defines the value of a gamble as the expectation value of utility changes. Utility functions aim to capture individual psychological characteristics, but their generality limits predictive power. Expectation value maximizers are defined as rational in economics, but expectation values are only meaningful in the presence of ensembles or in systems with ergodic properties, whereas decision-makers have no access to ensembles, and the variables representing wealth in the usual growth models do not have the relevant ergodic properties. Simultaneously addressing the shortcomings of utility and those of expectations, we propose to evaluate gambles by averaging wealth growth over time. No utility function is needed, but a dynamic must be specified to compute time averages. Linear and logarithmic "utility functions" appear as transformations that generate ergodic observables for purely additive and purely multiplicative dynamics, respectively. We highlight inconsistencies throughout the development of decision theory, whose correction clarifies that our perspective is legitimate. These invalidate a commonly cited argument for bounded utility functions.

Operator Hydrodynamics, OTOCs, and Entanglement Growth in Systems without Conservation Laws

NASA Astrophysics Data System (ADS)

von Keyserlingk, C. W.; Rakovszky, Tibor; Pollmann, Frank; Sondhi, S. L.

2018-04-01

Thermalization and scrambling are the subject of much recent study from the perspective of many-body quantum systems with locally bounded Hilbert spaces ("spin chains"), quantum field theory, and holography. We tackle this problem in 1D spin chains evolving under random local unitary circuits and prove a number of exact results on the behavior of out-of-time-ordered commutators (OTOCs) and entanglement growth in this setting. These results follow from the observation that the spreading of operators in random circuits is described by a "hydrodynamical" equation of motion, despite the fact that random unitary circuits do not have locally conserved quantities (e.g., no conserved energy). In this hydrodynamic picture, quantum information travels in a front with a "butterfly velocity" vB that is smaller than the light-cone velocity of the system, while the front itself broadens diffusively in time. The OTOC increases sharply after the arrival of the light cone, but we do not observe a prolonged exponential regime of the form ˜eλL(t -x /v ) for a fixed Lyapunov exponent λL. We find that the diffusive broadening of the front has important consequences for entanglement growth, leading to an entanglement velocity that can be significantly smaller than the butterfly velocity. We conjecture that the hydrodynamical description applies to more generic Floquet ergodic systems, and we support this idea by verifying numerically that the diffusive broadening of the operator wavefront also holds in a more traditional nonrandom Floquet spin chain. We also compare our results to Clifford circuits, which have less rich hydrodynamics and consequently trivial OTOC behavior, but which can nevertheless exhibit linear entanglement growth and thermalization.

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

Quantum order, entanglement and localization in many-body systems

NASA Astrophysics Data System (ADS)

Khemani, Vedika

The interplay of disorder and interactions can have remarkable effects on the physics of quantum systems. A striking example is provided by the long conjectured--and recently confirmed--phenomenon of many-body localization. Many-body localized (MBL) phases violate foundational assumptions about ergodicity and thermalization in interacting systems, and represent a new frontier for non-equilibrium quantum statistical mechanics. We start with a study of the dynamical response of MBL phases to time-dependent perturbations. We find that that an asymptotically slow, local perturbation induces a highly non-local response, a surprising result for a localized insulator. A complementary calculation in the linear-response regime elucidates the structure of many-body resonances contributing to the dynamics of this phase. We then turn to a study of quantum order in MBL systems. It was shown that localization can allow novel high-temperature phases and phase transitions that are disallowed in equilibrium. We extend this idea of "localization protected order'' to the case of symmetry-protected topological phases and to the elucidation of phase structure in periodically driven Floquet systems. We show that Floquet systems can display nontrivial phases, some of which show a novel form of correlated spatiotemporal order and are absolutely stable to all generic perturbations. The next part of the thesis addresses the role of quantum entanglement, broadly speaking. Remarkably, it was shown that even highly-excited MBL eigenstates have low area-law entanglement. We exploit this feature to develop tensor-network based algorithms for efficiently computing and representing highly-excited MBL eigenstates. We then switch gears from disordered, localized systems and examine the entanglement Hamiltonian and its low energy spectrum from a statistical mechanical lens, particularly focusing on issues of universality and thermalization. We close with two miscellaneous results on topologically ordered phases. The first studies the nonequilibrium "Kibble-Zurek'' dynamics resulting from driving a system through a phase transition from a topologically ordered phase to a trivial one at a finite rate. The second shows that the four-state Potts model on the pyrochlore lattice exhibits a "Coulomb Phase'' characterized by three emergent gauge fields.

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

Chaos, ergodic convergence, and fractal instability for a thermostated canonical harmonic oscillator

NASA Astrophysics Data System (ADS)

Hoover, Wm. G.; Hoover, Carol G.; Isbister, Dennis J.

2001-02-01

The authors thermostat a qp harmonic oscillator using the two additional control variables ζ and ξ to simulate Gibbs' canonical distribution. In contrast to the motion of purely Hamiltonian systems, the thermostated oscillator motion is completely ergodic, covering the full four-dimensional \\{q,p,ζ,ξ\\} phase space. The local Lyapunov spectrum (instantaneous growth rates of a comoving corotating phase-space hypersphere) exhibits singularities like those found earlier for Hamiltonian chaos, reinforcing the notion that chaos requires kinetic-as opposed to statistical-study, both at and away from equilibrium. The exponent singularities appear to have a fractal character.

Ab initio relaxation times and time-dependent Hamiltonians within the steepest-entropy-ascent quantum thermodynamic framework

NASA Astrophysics Data System (ADS)

Kim, Ilki; von Spakovsky, Michael R.

2017-08-01

Quantum systems driven by time-dependent Hamiltonians are considered here within the framework of steepest-entropy-ascent quantum thermodynamics (SEAQT) and used to study the thermodynamic characteristics of such systems. In doing so, a generalization of the SEAQT framework valid for all such systems is provided, leading to the development of an ab initio physically relevant expression for the intrarelaxation time, an important element of this framework and one that had as of yet not been uniquely determined as an integral part of the theory. The resulting expression for the relaxation time is valid as well for time-independent Hamiltonians as a special case and makes the description provided by the SEAQT framework more robust at the fundamental level. In addition, the SEAQT framework is used to help resolve a fundamental issue of thermodynamics in the quantum domain, namely, that concerning the unique definition of process-dependent work and heat functions. The developments presented lead to the conclusion that this framework is not just an alternative approach to thermodynamics in the quantum domain but instead one that uniquely sheds new light on various fundamental but as of yet not completely resolved questions of thermodynamics.

Quantum entanglement helps in improving economic efficiency

NASA Astrophysics Data System (ADS)

Du, Jiangfeng; Ju, Chenyong; Li, Hui

2005-02-01

We propose an economic regulation approach based on quantum game theory for the government to reduce the abuses of oligopolistic competition. Theoretical analysis shows that this approach can help government improve the economic efficiency of the oligopolistic market, and help prevent monopoly due to incorrect information. These advantages are completely attributed to the quantum entanglement, a unique quantum mechanical character.

Rigidity of the magic pentagram game

NASA Astrophysics Data System (ADS)

Kalev, Amir; Miller, Carl A.

2018-01-01

A game is rigid if a near-optimal score guarantees, under the sole assumption of the validity of quantum mechanics, that the players are using an approximately unique quantum strategy. Rigidity has a vital role in quantum cryptography as it permits a strictly classical user to trust behavior in the quantum realm. This property can be traced back as far as 1998 (Mayers and Yao) and has been proved for multiple classes of games. In this paper we prove ridigity for the magic pentagram game, a simple binary constraint satisfaction game involving two players, five clauses and ten variables. We show that all near-optimal strategies for the pentagram game are approximately equivalent to a unique strategy involving real Pauli measurements on three maximally-entangled qubit pairs.

Rigidity of the magic pentagram game.

PubMed

Kalev, Amir; Miller, Carl A

2018-01-01

A game is rigid if a near-optimal score guarantees, under the sole assumption of the validity of quantum mechanics, that the players are using an approximately unique quantum strategy. Rigidity has a vital role in quantum cryptography as it permits a strictly classical user to trust behavior in the quantum realm. This property can be traced back as far as 1998 (Mayers and Yao) and has been proved for multiple classes of games. In this paper we prove ridigity for the magic pentagram game, a simple binary constraint satisfaction game involving two players, five clauses and ten variables. We show that all near-optimal strategies for the pentagram game are approximately equivalent to a unique strategy involving real Pauli measurements on three maximally-entangled qubit pairs.

Synthesis, properties and biomedical applications of carbon-based quantum dots: An updated review.

PubMed

Namdari, Pooria; Negahdari, Babak; Eatemadi, Ali

2017-03-01

Carbon-based quantum dots (CQDs) are a newly developed class of carbon nano-materials that have attracted much interest and attention as promising competitors to already available semiconductor quantum dots owing to their un-comparable and unique properties. In addition, controllability of CQDs unique physiochemical properties is as a result of their surface passivation and functionalization. This is an update article (between 2013 and 2016) on the recent progress, characteristics and synthesis methods of CQDs and different advantages in varieties of applications. Copyright © 2017 Elsevier Masson SAS. All rights reserved.

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/regions with contextual topological relationships.

Discord as a quantum resource for bi-partite communication

NASA Astrophysics Data System (ADS)

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

2014-12-01

Coherent interactions that generate negligible entanglement can still exhibit unique quantum behaviour. This observation has motivated a search beyond entanglement for a complete description of all quantum correlations. Quantum discord is a promising candidate. Here, we experimentally demonstrate that under certain measurement constraints, discord between bipartite systems can be consumed to encode information that can only be accessed by coherent quantum interactions. The inability to access this information by any other means allows us to use discord to directly quantify this `quantum advantage'.

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.

Quantum Effects of Magnons Confined in Multilayered CoPd Ferromagnets

NASA Astrophysics Data System (ADS)

Nwokoye, Chidubem; Siddique, Abid; Bennett, Lawrence; Della Torre, Edward; IMR Team

Quantum entanglement is a unique quantum mechanical effect that arises from the correlation between two or more quantum systems. The fundamental aspects of magnon entanglement has been theoretical studied and the interest in developing technologies that exploits quantum entanglement is growing. We discuss the results of an experimental study of magnon entanglement in multilayered CoPd ferromagnets. Our findings are interesting and will aid in developing novel magnonic devices. Office of Naval Research.

Image Encryption Algorithm Based on Hyperchaotic Maps and Nucleotide Sequences Database

PubMed Central

2017-01-01

Image encryption technology is one of the main means to ensure the safety of image information. Using the characteristics of chaos, such as randomness, regularity, ergodicity, and initial value sensitiveness, combined with the unique space conformation of DNA molecules and their unique information storage and processing ability, an efficient method for image encryption based on the chaos theory and a DNA sequence database is proposed. In this paper, digital image encryption employs a process of transforming the image pixel gray value by using chaotic sequence scrambling image pixel location and establishing superchaotic mapping, which maps quaternary sequences and DNA sequences, and by combining with the logic of the transformation between DNA sequences. The bases are replaced under the displaced rules by using DNA coding in a certain number of iterations that are based on the enhanced quaternary hyperchaotic sequence; the sequence is generated by Chen chaos. The cipher feedback mode and chaos iteration are employed in the encryption process to enhance the confusion and diffusion properties of the algorithm. Theoretical analysis and experimental results show that the proposed scheme not only demonstrates excellent encryption but also effectively resists chosen-plaintext attack, statistical attack, and differential attack. PMID:28392799

Decomposition of conditional probability for high-order symbolic Markov chains.

PubMed

Melnik, S S; Usatenko, O V

2017-07-01

The main goal of this paper is to develop an estimate for the conditional probability function of random stationary ergodic symbolic sequences with elements belonging to a finite alphabet. We elaborate on a decomposition procedure for the conditional probability function of sequences considered to be high-order Markov chains. We represent the conditional probability function as the sum of multilinear memory function monomials of different orders (from zero up to the chain order). This allows us to introduce a family of Markov chain models and to construct artificial sequences via a method of successive iterations, taking into account at each step increasingly high correlations among random elements. At weak correlations, the memory functions are uniquely expressed in terms of the high-order symbolic correlation functions. The proposed method fills the gap between two approaches, namely the likelihood estimation and the additive Markov chains. The obtained results may have applications for sequential approximation of artificial neural network training.

Decomposition of conditional probability for high-order symbolic Markov chains

NASA Astrophysics Data System (ADS)

Melnik, S. S.; Usatenko, O. V.

2017-07-01

The main goal of this paper is to develop an estimate for the conditional probability function of random stationary ergodic symbolic sequences with elements belonging to a finite alphabet. We elaborate on a decomposition procedure for the conditional probability function of sequences considered to be high-order Markov chains. We represent the conditional probability function as the sum of multilinear memory function monomials of different orders (from zero up to the chain order). This allows us to introduce a family of Markov chain models and to construct artificial sequences via a method of successive iterations, taking into account at each step increasingly high correlations among random elements. At weak correlations, the memory functions are uniquely expressed in terms of the high-order symbolic correlation functions. The proposed method fills the gap between two approaches, namely the likelihood estimation and the additive Markov chains. The obtained results may have applications for sequential approximation of artificial neural network training.

Magnetohydrodynamic Turbulence and the Geodynamo

NASA Technical Reports Server (NTRS)

Shebalin, John V.

2014-01-01

The ARES Directorate at JSC has researched the physical processes that create planetary magnetic fields through dynamo action since 2007. The "dynamo problem" has existed since 1600, when William Gilbert, physician to Queen Elizabeth I, recognized that the Earth was a giant magnet. In 1919, Joseph Larmor proposed that solar (and by implication, planetary) magnetism was due to magnetohydrodynamics (MHD), but full acceptance did not occur until Glatzmaier and Roberts solved the MHD equations numerically and simulated a geomagnetic reversal in 1995. JSC research produced a unique theoretical model in 2012 that provided a novel explanation of these physical observations and computational results as an essential manifestation of broken ergodicity in MHD turbulence. Research is ongoing, and future work is aimed at understanding quantitative details of magnetic dipole alignment in the Earth as well as in Mercury, Jupiter and its moon Ganymede, Saturn, Uranus, Neptune, and the Sun and other stars.

Chaos based video encryption using maps and Ikeda time delay system

NASA Astrophysics Data System (ADS)

Valli, D.; Ganesan, K.

2017-12-01

Chaos based cryptosystems are an efficient method to deal with improved speed and highly secured multimedia encryption because of its elegant features, such as randomness, mixing, ergodicity, sensitivity to initial conditions and control parameters. In this paper, two chaos based cryptosystems are proposed: one is the higher-dimensional 12D chaotic map and the other is based on the Ikeda delay differential equation (DDE) suitable for designing a real-time secure symmetric video encryption scheme. These encryption schemes employ a substitution box (S-box) to diffuse the relationship between pixels of plain video and cipher video along with the diffusion of current input pixel with the previous cipher pixel, called cipher block chaining (CBC). The proposed method enhances the robustness against statistical, differential and chosen/known plain text attacks. Detailed analysis is carried out in this paper to demonstrate the security and uniqueness of the proposed scheme.

Local conditional entropy in measure for covers with respect to a fixed partition

NASA Astrophysics Data System (ADS)

Romagnoli, Pierre-Paul

2018-05-01

In this paper we introduce two measure theoretical notions of conditional entropy for finite measurable covers conditioned to a finite measurable partition and prove that they are equal. Using this we state a local variational principle with respect to the notion of conditional entropy defined by Misiurewicz (1976 Stud. Math. 55 176–200) for the case of open covers. This in particular extends the work done in Romagnoli (2003 Ergod. Theor. Dynam. Syst. 23 1601–10), Glasner and Weiss (2006 Handbook of Dynamical Systems vol 1B (Amsterdam: Elsevier)) and Huang et al (2006 Ergod. Theor. Dynam. Syst. 26 219–45).

A proof of the log-concavity conjecture related to the computation of the ergodic capacity of MIMO channels

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gurvitis, Leonid

2009-01-01

An upper bound on the ergodic capacity of MIMO channels was introduced recently in [1]. This upper bound amounts to the maximization on the simplex of some multilinear polynomial p({lambda}{sub 1}, ..., {lambda}{sub n}) with non-negative coefficients. In general, such maximizations problems are NP-HARD. But if say, the functional log(p) is concave on the simplex and can be efficiently evaluated, then the maximization can also be done efficiently. Such log-concavity was conjectured in [1]. We give in this paper self-contained proof of the conjecture, based on the theory of H-Stable polynomials.

A semigroup approach to the strong ergodic theorem of the multistate stable population process.

PubMed

Inaba, H

1988-01-01

"In this paper we first formulate the dynamics of multistate stable population processes as a partial differential equation. Next, we rewrite this equation as an abstract differential equation in a Banach space, and solve it by using the theory of strongly continuous semigroups of bounded linear operators. Subsequently, we investigate the asymptotic behavior of this semigroup to show the strong ergodic theorem which states that there exists a stable distribution independent of the initial distribution. Finally, we introduce the dual problem in order to obtain a logical definition for the reproductive value and we discuss its applications." (SUMMARY IN FRE) excerpt

Decryption of pure-position permutation algorithms.

PubMed

Zhao, Xiao-Yu; Chen, Gang; Zhang, Dan; Wang, Xiao-Hong; Dong, Guang-Chang

2004-07-01

Pure position permutation image encryption algorithms, commonly used as image encryption investigated in this work are unfortunately frail under known-text attack. In view of the weakness of pure position permutation algorithm, we put forward an effective decryption algorithm for all pure-position permutation algorithms. First, a summary of the pure position permutation image encryption algorithms is given by introducing the concept of ergodic matrices. Then, by using probability theory and algebraic principles, the decryption probability of pure-position permutation algorithms is verified theoretically; and then, by defining the operation system of fuzzy ergodic matrices, we improve a specific decryption algorithm. Finally, some simulation results are shown.

Multi-fractal characterization of bacterial swimming dynamics: a case study on real and simulated Serratia marcescens

PubMed Central

Bogdan, Paul; Wei, Guopeng; Marculescu, Radu; Zhuang, Jiang; Carlsen, Rika Wright; Sitti, Metin

2017-01-01

To add to the current state of knowledge about bacterial swimming dynamics, in this paper, we study the fractal swimming dynamics of populations of Serratia marcescens bacteria both in vitro and in silico, while accounting for realistic conditions like volume exclusion, chemical interactions, obstacles and distribution of chemoattractant in the environment. While previous research has shown that bacterial motion is non-ergodic, we demonstrate that, besides the non-ergodicity, the bacterial swimming dynamics is multi-fractal in nature. Finally, we demonstrate that the multi-fractal characteristic of bacterial dynamics is strongly affected by bacterial density and chemoattractant concentration. PMID:28804259

Electric Field-Induced Large Strain in Ni/Sb-co Doped (Bi0.5Na0.5) TiO3-Based Lead-Free Ceramics

NASA Astrophysics Data System (ADS)

Li, Liangliang; Hao, Jigong; Xu, Zhijun; Li, Wei; Chu, Ruiqing

2018-02-01

Lead-free piezoelectric ceramics (Bi0.5Na0.5)0.935Ba0.065Ti1- x (Ni0.5Sb0.5) x O3 (BNBT6.5- xNS) have been fabricated using conventional solid sintering technique. The effect of (Ni, Sb) doping on the phase structure and electrical properties of BNBT6.5 ceramics were systematically investigated. Results show that the addition of (Ni, Sb) destroyed the ferroelectric long-range order of BNBT6.5 and shifted the ferroelectric-relaxor transition temperature ( T F-R) down to room temperature. Thus, this process induced an ergodic relaxor phase at zero field in samples with x = 0.005. Under the electric field, the ergodic relaxor phase could reversibly transform to ferroelectric phase, which promotes the strain response with peak value of 0.38% (at 80 kV/cm, corresponding to d 33 * = 479 pm/V) at x = 0.005. Temperature-dependent measurements of both polarization and strain confirmed that the large strain originated from a reversible field-induced ergodic relaxor to ferroelectric phase transformation. The proposed material exhibits potential for nonlinear actuators.

Ergodicity, hidden bias and the growth rate gain

NASA Astrophysics Data System (ADS)

Rochman, Nash D.; Popescu, Dan M.; Sun, Sean X.

2018-05-01

Many single-cell observables are highly heterogeneous. A part of this heterogeneity stems from age-related phenomena: the fact that there is a nonuniform distribution of cells with different ages. This has led to a renewed interest in analytic methodologies including use of the ‘von Foerster equation’ for predicting population growth and cell age distributions. Here we discuss how some of the most popular implementations of this machinery assume a strong condition on the ergodicity of the cell cycle duration ensemble. We show that one common definition for the term ergodicity, ‘a single individual observed over many generations recapitulates the behavior of the entire ensemble’ is implied by the other, ‘the probability of observing any state is conserved across time and over all individuals’ in an ensemble with a fixed number of individuals but that this is not true when the ensemble is growing. We further explore the impact of generational correlations between cell cycle durations on the population growth rate. Finally, we explore the ‘growth rate gain’—the phenomenon that variations in the cell cycle duration leads to an improved population-level growth rate—in this context. We highlight that, fundamentally, this effect is due to asymmetric division.

Adaptive multi-node multiple input and multiple output (MIMO) transmission for mobile wireless multimedia sensor networks.

PubMed

Cho, Sunghyun; Choi, Ji-Woong; You, Cheolwoo

2013-10-02

Mobile wireless multimedia sensor networks (WMSNs), which consist of mobile sink or sensor nodes and use rich sensing information, require much faster and more reliable wireless links than static wireless sensor networks (WSNs). This paper proposes an adaptive multi-node (MN) multiple input and multiple output (MIMO) transmission to improve the transmission reliability and capacity of mobile sink nodes when they experience spatial correlation. Unlike conventional single-node (SN) MIMO transmission, the proposed scheme considers the use of transmission antennas from more than two sensor nodes. To find an optimal antenna set and a MIMO transmission scheme, a MN MIMO channel model is introduced first, followed by derivation of closed-form ergodic capacity expressions with different MIMO transmission schemes, such as space-time transmit diversity coding and spatial multiplexing. The capacity varies according to the antenna correlation and the path gain from multiple sensor nodes. Based on these statistical results, we propose an adaptive MIMO mode and antenna set switching algorithm that maximizes the ergodic capacity of mobile sink nodes. The ergodic capacity of the proposed scheme is compared with conventional SN MIMO schemes, where the gain increases as the antenna correlation and path gain ratio increase.

Adaptive Multi-Node Multiple Input and Multiple Output (MIMO) Transmission for Mobile Wireless Multimedia Sensor Networks

PubMed Central

Cho, Sunghyun; Choi, Ji-Woong; You, Cheolwoo

2013-01-01

Mobile wireless multimedia sensor networks (WMSNs), which consist of mobile sink or sensor nodes and use rich sensing information, require much faster and more reliable wireless links than static wireless sensor networks (WSNs). This paper proposes an adaptive multi-node (MN) multiple input and multiple output (MIMO) transmission to improve the transmission reliability and capacity of mobile sink nodes when they experience spatial correlation. Unlike conventional single-node (SN) MIMO transmission, the proposed scheme considers the use of transmission antennas from more than two sensor nodes. To find an optimal antenna set and a MIMO transmission scheme, a MN MIMO channel model is introduced first, followed by derivation of closed-form ergodic capacity expressions with different MIMO transmission schemes, such as space-time transmit diversity coding and spatial multiplexing. The capacity varies according to the antenna correlation and the path gain from multiple sensor nodes. Based on these statistical results, we propose an adaptive MIMO mode and antenna set switching algorithm that maximizes the ergodic capacity of mobile sink nodes. The ergodic capacity of the proposed scheme is compared with conventional SN MIMO schemes, where the gain increases as the antenna correlation and path gain ratio increase. PMID:24152920

Making sense of snapshot data: ergodic principle for clonal cell populations

PubMed Central

2017-01-01

Population growth is often ignored when quantifying gene expression levels across clonal cell populations. We develop a framework for obtaining the molecule number distributions in an exponentially growing cell population taking into account its age structure. In the presence of generation time variability, the average acquired across a population snapshot does not obey the average of a dividing cell over time, apparently contradicting ergodicity between single cells and the population. Instead, we show that the variation observed across snapshots with known cell age is captured by cell histories, a single-cell measure obtained from tracking an arbitrary cell of the population back to the ancestor from which it originated. The correspondence between cells of known age in a population with their histories represents an ergodic principle that provides a new interpretation of population snapshot data. We illustrate the principle using analytical solutions of stochastic gene expression models in cell populations with arbitrary generation time distributions. We further elucidate that the principle breaks down for biochemical reactions that are under selection, such as the expression of genes conveying antibiotic resistance, which gives rise to an experimental criterion with which to probe selection on gene expression fluctuations. PMID:29187636

Making sense of snapshot data: ergodic principle for clonal cell populations.

PubMed

Thomas, Philipp

2017-11-01

Population growth is often ignored when quantifying gene expression levels across clonal cell populations. We develop a framework for obtaining the molecule number distributions in an exponentially growing cell population taking into account its age structure. In the presence of generation time variability, the average acquired across a population snapshot does not obey the average of a dividing cell over time, apparently contradicting ergodicity between single cells and the population. Instead, we show that the variation observed across snapshots with known cell age is captured by cell histories, a single-cell measure obtained from tracking an arbitrary cell of the population back to the ancestor from which it originated. The correspondence between cells of known age in a population with their histories represents an ergodic principle that provides a new interpretation of population snapshot data. We illustrate the principle using analytical solutions of stochastic gene expression models in cell populations with arbitrary generation time distributions. We further elucidate that the principle breaks down for biochemical reactions that are under selection, such as the expression of genes conveying antibiotic resistance, which gives rise to an experimental criterion with which to probe selection on gene expression fluctuations. © 2017 The Author(s).

Statistical characterization of discrete conservative systems: The web map

NASA Astrophysics Data System (ADS)

Ruiz, Guiomar; Tirnakli, Ugur; Borges, Ernesto P.; Tsallis, Constantino

2017-10-01

We numerically study the two-dimensional, area preserving, web map. When the map is governed by ergodic behavior, it is, as expected, correctly described by Boltzmann-Gibbs statistics, based on the additive entropic functional SB G[p (x ) ] =-k ∫d x p (x ) lnp (x ) . In contrast, possible ergodicity breakdown and transitory sticky dynamical behavior drag the map into the realm of generalized q statistics, based on the nonadditive entropic functional Sq[p (x ) ] =k 1/-∫d x [p(x ) ] q q -1 (q ∈R ;S1=SB G ). We statistically describe the system (probability distribution of the sum of successive iterates, sensitivity to the initial condition, and entropy production per unit time) for typical values of the parameter that controls the ergodicity of the map. For small (large) values of the external parameter K , we observe q -Gaussian distributions with q =1.935 ⋯ (Gaussian distributions), like for the standard map. In contrast, for intermediate values of K , we observe a different scenario, due to the fractal structure of the trajectories embedded in the chaotic sea. Long-standing non-Gaussian distributions are characterized in terms of the kurtosis and the box-counting dimension of chaotic sea.

Quantum stochastic calculus associated with quadratic quantum noises

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ji, Un Cig, E-mail: uncigji@chungbuk.ac.kr; Sinha, Kalyan B., E-mail: kbs-jaya@yahoo.co.in

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 calculusmore » extends the Hudson-Parthasarathy quantum stochastic calculus.« less

Introduction

NASA Astrophysics Data System (ADS)

Cohen, E. G. D.

Lecture notes are organized around the key word dissipation, while focusing on a presentation of modern theoretical developments in the study of irreversible phenomena. A broad cross-disciplinary perspective towards non-equilibrium statistical mechanics is backed by the general theory of nonlinear and complex dynamical systems. The classical-quantum intertwine and semiclassical dissipative borderline issue (decoherence, "classical out of quantum") are here included . Special emphasis is put on links between the theory of classical and quantum dynamical systems (temporal disorder, dynamical chaos and transport processes) with central problems of non-equilibrium statistical mechanics like e.g. the connection between dynamics and thermodynamics, relaxation towards equilibrium states and mechanisms capable to drive and next maintain the physical system far from equilibrium, in a non-equilibrium steady (stationary) state. The notion of an equilibrium state - towards which a system naturally evolves if left undisturbed - is a fundamental concept of equilibrium statistical mechanics. Taken as a primitive point of reference that allows to give an unambiguous status to near equilibrium and far from equilibrium systems, together with the dynamical notion of a relaxation (decay) towards a prescribed asymptotic invariant measure or probability distribution (properties of ergodicity and mixing are implicit). A related issue is to keep under control the process of driving a physical system away from an initial state of equilibrium and either keeping it in another (non-equilibrium) steady state or allowing to restore the initial data (return back, relax). To this end various models of environment (heat bath, reservoir, thermostat, measuring instrument etc.), and the environment - system coupling are analyzed. The central theme of the book is the dynamics of dissipation and various mechanisms responsible for the irreversible behaviour (transport properties) of open systems on classical and quantum levels of description. A distinguishing feature of these lecture notes is that microscopic foundations of irreversibility are investigated basically in terms of "small" systems, when the "system" and/or "environment" may have a finite (and small) number of degrees of freedom and may be bounded. This is to be contrasted with the casual understanding of statistical mechanics which is regarded to refer to systems with a very large number of degrees of freedom. In fact, it is commonly accepted that the accumulation of effects due to many (range of the Avogadro number) particles is required for statistical mechanics reasoning. Albeit those large numbers are not at all sufficient for transport properties. A helpful hint towards this conceptual turnover comes from the observation that for chaotic dynamical systems the random time evolution proves to be compatible with the underlying purely deterministic laws of motion. Chaotic features of the classical dynamics already appear in systems with two degrees of freedom and such systems need to be described in statistical terms, if we wish to quantify the dynamics of relaxation towards an invariant ergodic measure. The relaxation towards equilibrium finds a statistical description through an analysis of statistical ensembles. This entails an extension of the range of validity of statistical mechanics to small classical systems. On the other hand, the dynamics of fluctuations in macroscopic dissipative systems (due to their molecular composition and thermal mobility) may render a characterization of such systems as being chaotic. That motivates attempts of understanding the role of microscopic chaos and various "chaotic hypotheses" - dynamical systems approach is being pushed down to the level of atoms, molecules and complex matter constituents, whose natural substitute are low-dimensional model subsystems (encompassing as well the mesoscopic "quantum chaos") - in non-equilibrium transport phenomena. On the way a number of questions is addressed like e.g.: is there, or what is the nature of a connection between chaos (modern theory of dynamical systems) and irreversible thermodynamics; can really quantum chaos explain some peculiar features of quantum transport? The answer in both cases is positive, modulo a careful discrimination between viewing the dynamical chaos as a necessary or sufficient basis for irreversibility. In those dynamical contexts, another key term dynamical semigroups refers to major technical tools appropriate for the "dissipative mathematics", modelling irreversible behaviour on the classical and quantum levels of description. Dynamical systems theory and "quantum chaos" research involve both a high level of mathematical sophistication and heavy computer "experimentation". One of the present volume specific flavors is a tutorial access to quite advanced mathematical tools. They gradually penetrate the classical and quantum dynamical semigroup description, while culminating in the noncommutative Brillouin zone construction as a prerequisite to understand transport in aperiodic solids. Lecture notes are structured into chapters to give a better insight into major conceptual streamlines. Chapter I is devoted to a discussion of non-equilibrium steady states and, through so-called chaotic hypothesis combined with suitable fluctuation theorems, elucidates the role of Sinai-Ruelle-Bowen distribution in both equilibrium and non-equilibrium statistical physics frameworks (E. G. D. Cohen). Links between dynamics and statistics (Boltzmann versus Tsallis) are also discussed. Fluctuation relations and a survey of deterministic thermostats are given in the context of non-equilibrium steady states of fluids (L. Rondoni). Response of systems driven far from equilibrium is analyzed on the basis of a central assertion about the existence of the statistical representation in terms of an ensemble of dynamical realizations of the driving process. Non-equilibrium work relation is deduced for irreversible processes (C. Jarzynski). The survey of non-equilibrium steady states in statistical mechanics of classical and quantum systems employs heat bath models and the random matrix theory input. The quantum heat bath analysis and derivation of fluctuation-dissipation theorems is performed by means of the influence functional technique adopted to solve quantum master equations (D. Kusnezov). Chapter II deals with an issue of relaxation and its dynamical theory in both classical and quantum contexts. Pollicott-Ruelle resonance background for the exponential decay scenario is discussed for irreversible processes of diffusion in the Lorentz gas and multibaker models (P. Gaspard). The Pollicott-Ruelle theory reappears as a major inspiration in the survey of the behaviour of ensembles of chaotic systems, with a focus on model systems for which no rigorous results concerning the exponential decay of correlations in time is available (S. Fishman). The observation, that non-equilibrium transport processes in simple classical chaotic systems can be described in terms of fractal structures developing in the system phase space, links their formation and properties with the entropy production in the course of diffusion processes displaying a low dimensional deterministic (chaotic) origin (J. R. Dorfman). Chapter III offers an introduction to the theory of dynamical semigroups. Asymptotic properties of Markov operators and Markov semigroups acting in the set of probability densities (statistical ensemble notion is implicit) are analyzed. Ergodicity, mixing, strong (complete) mixing and sweeping are discussed in the familiar setting of "noise, chaos and fractals" (R. Rudnicki). The next step comprises a passage to quantum dynamical semigroups and completely positive dynamical maps, with an ultimate goal to introduce a consistent framework for the analysis of irreversible phenomena in open quantum systems, where dissipation and decoherence are crucial concepts (R. Alicki). Friction and damping in classical and quantum mechanics of finite dissipative systems is analyzed by means of Markovian quantum semigroups with special emphasis on the issue of complete positivity (M. Fannes). Specific two-level model systems of elementary particle physics (kaons) and rudiments of neutron interferometry are employed to elucidate a distinction between positivity and complete positivity (F. Benatti). Quantization of dynamics of stochastic models related to equilibrium Gibbs states results in dynamical maps which form quantum stochastic dynamical semigroups (W. A. Majewski). Chapter IV addresses diverse but deeply interrelated features of driven chaotic (mesoscopic) classical and quantum systems, their dissipative properties, notions of quantum irreversibility, entanglement, dephasing and decoherence. A survey of non-perturbative quantum effects for open quantum systems is concluded by outlining the discrepancies between random matrix theory and non-perturbative semiclassical predictions (D. Cohen). As a useful supplement to the subject of bounded open systems, methods of quantum state control in a cavity (coherent versus incoherent dynamics and dissipation) are described for low dimensional quantum systems (A. Buchleitner). The dynamics of open quantum systems can be alternatively described by means of non-Markovian stochastic Schrödinger equation, jointly for an open system and its environment, which moves us beyond the Linblad evolution scenario of Markovian dynamical semigroups. The quantum Brownian motion is considered (W. Strunz) . Chapter V enforces a conceptual transition 'from "small" to "large" systems with emphasis on irreversible thermodynamics of quantum transport. Typical features of the statistical mechanics of infinitely extended systems and the dynamical (small) systems approach are described by means of representative examples of relaxation towards asymptotic steady states: quantum one-dimensional lattice conductor and an open multibaker map (S. Tasaki). Dissipative transport in aperiodic solids is reviewed by invoking methods on noncommutative geometry. The anomalous Drude formula is derived. The occurence of quantum chaos is discussed together with its main consequences (J. Bellissard). The chapter is concluded by a survey of scaling limits of the N-body Schrödinger quantum dynamics, where classical evolution equations of irreversible statistical mechanics (linear Boltzmann, Hartree, Vlasov) emerge "out of quantum". In particular, a scaling limit of one body quantum dynamics with impurities (static random potential) and that of quantum dynamics with weakly coupled phonons are shown to yield the linear Boltzmann equation (L. Erdös). Various interrelations between chapters and individual lectures, plus a detailed fine-tuned information about the subject matter coverage of the volume, can be recovered by examining an extensive index.

Theoretical study of dynamic electron-spin-polarization via the doublet-quartet quantum-mixed state and time-resolved ESR spectra of the quartet high-spin state.

PubMed

Teki, Yoshio; Matsumoto, Takafumi

2011-04-07

The mechanism of the unique dynamic electron polarization of the quartet (S = 3/2) high-spin state via a doublet-quartet quantum-mixed state and detail theoretical calculations of the population transfer are reported. By the photo-induced electron transfer, the quantum-mixed charge-separate state is generated in acceptor-donor-radical triad (A-D-R). This mechanism explains well the unique dynamic electron polarization of the quartet state of A-D-R. The generation of the selectively populated quantum-mixed state and its transfer to the strongly coupled pure quartet and doublet states have been treated both by a perturbation approach and by exact numerical calculations. The analytical solutions show that generation of the quantum-mixed states with the selective populations after de-coherence and/or accompanying the (complete) dephasing during the charge-recombination are essential for the unique dynamic electron polarization. Thus, the elimination of the quantum coherence (loss of the quantum information) is the key process for the population transfer from the quantum-mixed state to the quartet state. The generation of high-field polarization on the strongly coupled quartet state by the charge-recombination process can be explained by a polarization transfer from the quantum-mixed charge-separate state. Typical time-resolved ESR patterns of the quantum-mixed state and of the strongly coupled quartet state are simulated based on the generation mechanism of the dynamic electron polarization. The dependence of the spectral pattern of the quartet high-spin state has been clarified for the fine-structure tensor and the exchange interaction of the quantum-mixed state. The spectral pattern of the quartet state is not sensitive towards the fine-structure tensor of the quantum-mixed state, because this tensor contributes only as a perturbation in the population transfer to the spin-sublevels of the quartet state. Based on the stochastic Liouville equation, it is also discussed why the selective population in the quantum-mixed state is generated for the "finite field" spin-sublevels. The numerical calculations of the elimination of the quantum coherence (de-coherence and/or dephasing) are demonstrated. A new possibility of the enhanced intersystem crossing pathway in solution is also proposed.

Musical Example to Visualize Abstract Quantum Mechanical Ideas

ERIC Educational Resources Information Center

Eagle, Forrest W.; Seaney, Kyser D.; Grubb, Michael P.

2017-01-01

Quantum mechanics is a notoriously difficult subject to learn, due to a lack of real-world analogies that might help provide an intuitive grasp of the underlying ideas. Discrete energy levels and absorption and emission wavelengths in atoms are sometimes described as uniquely quantum phenomena, but are actually general to spatially confined waves…

Quantum dot-decorated semiconductor micro- and nanoparticles: A review of their synthesis, characterization and application in photocatalysis.

PubMed

Bajorowicz, Beata; Kobylański, Marek P; Gołąbiewska, Anna; Nadolna, Joanna; Zaleska-Medynska, Adriana; Malankowska, Anna

2018-06-01

Quantum dot (QD)-decorated semiconductor micro- and nanoparticles are a new class of functional nanomaterials that have attracted considerable interest for their unique structural, optical and electronic properties that result from the large surface-to-volume ratio and the quantum confinement effect. In addition, because of QDs' excellent light-harvesting capacity, unique photoinduced electron transfer, and up-conversion behaviour, semiconductor nanoparticles decorated with quantum dots have been used widely in photocatalytic applications for the degradation of organic pollutants in both the gas and aqueous phases. This review is a comprehensive overview of the recent progress in synthesis methods for quantum dots and quantum dot-decorated semiconductor composites with an emphasis on their composition, morphology and optical behaviour. Furthermore, various approaches used for the preparation of QD-based composites are discussed in detail with respect to visible and UV light-induced photoactivity. Finally, an outlook on future development is proposed with the goal of overcoming challenges and stimulating further research into this promising field. Copyright © 2018 Elsevier B.V. All rights reserved.

Anosov C-systems and random number generators

NASA Astrophysics Data System (ADS)

Savvidy, G. K.

2016-08-01

We further develop our previous proposal to use hyperbolic Anosov C-systems to generate pseudorandom numbers and to use them for efficient Monte Carlo calculations in high energy particle physics. All trajectories of hyperbolic dynamical systems are exponentially unstable, and C-systems therefore have mixing of all orders, a countable Lebesgue spectrum, and a positive Kolmogorov entropy. These exceptional ergodic properties follow from the C-condition introduced by Anosov. This condition defines a rich class of dynamical systems forming an open set in the space of all dynamical systems. An important property of C-systems is that they have a countable set of everywhere dense periodic trajectories and their density increases exponentially with entropy. Of special interest are the C-systems defined on higher-dimensional tori. Such C-systems are excellent candidates for generating pseudorandom numbers that can be used in Monte Carlo calculations. An efficient algorithm was recently constructed that allows generating long C-system trajectories very rapidly. These trajectories have good statistical properties and can be used for calculations in quantum chromodynamics and in high energy particle physics.

Mirror Numbers and Wigner's ``Unreasonable Effectiveness''

NASA Astrophysics Data System (ADS)

Berezin, Alexander

2006-04-01

Wigner's ``unreasonable effectiveness of mathematics in physics'' can be augmented by concept of mirror number (MN). It is defined as digital string infinite in both directions. Example is ()5141327182() where first 5 digits is Pi ``spelled'' backward (``mirrored'') and last 5 digits is the beginning of decimal exp1 string. Let MN be constructed from two different transcendental (or algebraically irrational) numbers, set of such MNs is Cantor-uncountable. Most MNs have contain any finite digital sequence repeated infinitely many times. In spirit of ``Contact'' (C.Sagan) each normal MN contains ``Library of Babel'' of all possible texts and patterns (J.L.Borges). Infinite at both ends, MN do not have any numerical values and, contrary to numbers written in positional systems, all digits in MNs have equal weight -- sort of ``numerological democracy''. In Pythagorean-Platonic models (space-time and physical world originating from pure numbers) idea of MN resolves paradox of ``beginning'' (or ``end'') of time. Because in MNs all digits have equal status, (quantum) randomness leads to more uniform and fully ergodic phase trajectories (cf. F.Dyson, Infinite in All Directions) .

Entropy, a Unifying Concept: from Physics to Cognitive Psychology

NASA Astrophysics Data System (ADS)

Tsallis, Constantino; Tsallis, Alexandra C.

Together with classical, relativistic and quantum mechanics, as well as Maxwell electromagnetism, Boltzmann-Gibbs (BG) statistical mechanics constitutes one of the main theories of contemporary physics. This theory primarily concerns inanimate matter, and at its generic foundation we find nonlinear dynamical systems satisfying the ergodic hypothesis. This hypothesis is typically guaranteed for systems whose maximal Lyapunov exponent is positive. What happens when this crucial quantity is zero instead? We suggest here that, in what concerns thermostatistical properties, we typically enter what in some sense may be considered as a new world — the world of living systems — . The need emerges, at least for many systems, for generalizing the basis of BG statistical mechanics, namely the Boltzmann-Gibbs-von Neumann-Shannon en-tropic functional form, which connects the oscopic, thermodynamic quantity, with the occurrence probabilities of microscopic configurations. This unifying approach is briefly reviewed here, and its widespread applications — from physics to cognitive psychology — are overviewed. Special attention is dedicated to the learning/memorizing process in humans and computers. The present observations might be related to the gestalt theory of visual perceptions and the actor-network theory.

Fuzzy fractals, chaos, and noise

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zardecki, A.

1997-05-01

To distinguish between chaotic and noisy processes, the authors analyze one- and two-dimensional chaotic mappings, supplemented by the additive noise terms. The predictive power of a fuzzy rule-based system allows one to distinguish ergodic and chaotic time series: in an ergodic series the likelihood of finding large numbers is small compared to the likelihood of finding them in a chaotic series. In the case of two dimensions, they consider the fractal fuzzy sets whose {alpha}-cuts are fractals, arising in the context of a quadratic mapping in the extended complex plane. In an example provided by the Julia set, the conceptmore » of Hausdorff dimension enables one to decide in favor of chaotic or noisy evolution.« less

Conductance fluctuations in high mobility monolayer graphene: Nonergodicity, lack of determinism and chaotic behavior

PubMed Central

da Cunha, C. R.; Mineharu, M.; Matsunaga, M.; Matsumoto, N.; Chuang, C.; Ochiai, Y.; Kim, G.-H.; Watanabe, K.; Taniguchi, T.; Ferry, D. K.; Aoki, N.

2016-01-01

We have fabricated a high mobility device, composed of a monolayer graphene flake sandwiched between two sheets of hexagonal boron nitride. Conductance fluctuations as functions of a back gate voltage and magnetic field were obtained to check for ergodicity. Non-linear dynamics concepts were used to study the nature of these fluctuations. The distribution of eigenvalues was estimated from the conductance fluctuations with Gaussian kernels and it indicates that the carrier motion is chaotic at low temperatures. We argue that a two-phase dynamical fluid model best describes the transport in this system and can be used to explain the violation of the so-called ergodic hypothesis found in graphene. PMID:27609184

Conductance fluctuations in high mobility monolayer graphene: Nonergodicity, lack of determinism and chaotic behavior.

PubMed

da Cunha, C R; Mineharu, M; Matsunaga, M; Matsumoto, N; Chuang, C; Ochiai, Y; Kim, G-H; Watanabe, K; Taniguchi, T; Ferry, D K; Aoki, N

2016-09-09

We have fabricated a high mobility device, composed of a monolayer graphene flake sandwiched between two sheets of hexagonal boron nitride. Conductance fluctuations as functions of a back gate voltage and magnetic field were obtained to check for ergodicity. Non-linear dynamics concepts were used to study the nature of these fluctuations. The distribution of eigenvalues was estimated from the conductance fluctuations with Gaussian kernels and it indicates that the carrier motion is chaotic at low temperatures. We argue that a two-phase dynamical fluid model best describes the transport in this system and can be used to explain the violation of the so-called ergodic hypothesis found in graphene.

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.

Quantum Confined Semiconductors for High Efficiency Photovoltaics

NASA Astrophysics Data System (ADS)

Beard, Matthew

2014-03-01

Semiconductor nanostructures, where at least one dimension is small enough to produce quantum confinement effects, provide new pathways for controlling energy flow and therefore have the potential to increase the efficiency of the primary photon-to-free energy conversion step. In this discussion, I will present the current status of research efforts towards utilizing the unique properties of colloidal quantum dots (NCs confined in three dimensions) in prototype solar cells and demonstrate that these unique systems have the potential to bypass the Shockley-Queisser single-junction limit for solar photon conversion. The solar cells are constructed using a low temperature solution based deposition of PbS or PbSe QDs as the absorber layer. Different chemical treatments of the QD layer are employed in order to obtain good electrical communication while maintaining the quantum-confined properties of the QDs. We have characterized the transport and carrier dynamics using a transient absorption, time-resolved THz, and temperature-dependent photoluminescence. I will discuss the interplay between carrier generation, recombination, and mobility within the QD layers. A unique aspect of our devices is that the QDs exhibit multiple exciton generation with an efficiency that is ~ 2 to 3 times greater than the parental bulk semiconductor.

Convexity of quantum χ2-divergence.

PubMed

Hansen, Frank

2011-06-21

The general quantum χ(2)-divergence has recently been introduced by Temme et al. [Temme K, Kastoryano M, Ruskai M, Wolf M, Verstrate F (2010) J Math Phys 51:122201] and applied to quantum channels (quantum Markov processes). The quantum χ(2)-divergence is not unique, as opposed to the classical χ(2)-divergence, but depends on the choice of quantum statistics. It was noticed that the elements in a particular one-parameter family of quantum χ(2)-divergences are convex functions in the density matrices (ρ,σ), thus mirroring the convexity of the classical χ(2)(p,q)-divergence in probability distributions (p,q). We prove that any quantum χ(2)-divergence is a convex function in its two arguments.

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.

Preserving the Boltzmann ensemble in replica-exchange molecular dynamics.

PubMed

Cooke, Ben; Schmidler, Scott C

2008-10-28

We consider the convergence behavior of replica-exchange molecular dynamics (REMD) [Sugita and Okamoto, Chem. Phys. Lett. 314, 141 (1999)] based on properties of the numerical integrators in the underlying isothermal molecular dynamics (MD) simulations. We show that a variety of deterministic algorithms favored by molecular dynamics practitioners for constant-temperature simulation of biomolecules fail either to be measure invariant or irreducible, and are therefore not ergodic. We then show that REMD using these algorithms also fails to be ergodic. As a result, the entire configuration space may not be explored even in an infinitely long simulation, and the simulation may not converge to the desired equilibrium Boltzmann ensemble. Moreover, our analysis shows that for initial configurations with unfavorable energy, it may be impossible for the system to reach a region surrounding the minimum energy configuration. We demonstrate these failures of REMD algorithms for three small systems: a Gaussian distribution (simple harmonic oscillator dynamics), a bimodal mixture of Gaussians distribution, and the alanine dipeptide. Examination of the resulting phase plots and equilibrium configuration densities indicates significant errors in the ensemble generated by REMD simulation. We describe a simple modification to address these failures based on a stochastic hybrid Monte Carlo correction, and prove that this is ergodic.

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. Copyright © 2015 Elsevier Ltd. All rights reserved.

Principle of Parsimony, Fake Science, and Scales

NASA Astrophysics Data System (ADS)

Yeh, T. C. J.; Wan, L.; Wang, X. S.

2017-12-01

Considering difficulties in predicting exact motions of water molecules, and the scale of our interests (bulk behaviors of many molecules), Fick's law (diffusion concept) has been created to predict solute diffusion process in space and time. G.I. Taylor (1921) demonstrated that random motion of the molecules reach the Fickian regime in less a second if our sampling scale is large enough to reach ergodic condition. Fick's law is widely accepted for describing molecular diffusion as such. This fits the definition of the parsimony principle at the scale of our concern. Similarly, advection-dispersion or convection-dispersion equation (ADE or CDE) has been found quite satisfactory for analysis of concentration breakthroughs of solute transport in uniformly packed soil columns. This is attributed to the solute is often released over the entire cross-section of the column, which has sampled many pore-scale heterogeneities and met the ergodicity assumption. Further, the uniformly packed column contains a large number of stationary pore-size heterogeneity. The solute thus reaches the Fickian regime after traveling a short distance along the column. Moreover, breakthrough curves are concentrations integrated over the column cross-section (the scale of our interest), and they meet the ergodicity assumption embedded in the ADE and CDE. To the contrary, scales of heterogeneity in most groundwater pollution problems evolve as contaminants travel. They are much larger than the scale of our observations and our interests so that the ergodic and the Fickian conditions are difficult. Upscaling the Fick's law for solution dispersion, and deriving universal rules of the dispersion to the field- or basin-scale pollution migrations are merely misuse of the parsimony principle and lead to a fake science ( i.e., the development of theories for predicting processes that can not be observed.) The appropriate principle of parsimony for these situations dictates mapping of large-scale heterogeneities as detailed as possible and adapting the Fick's law for effects of small-scale heterogeneity resulting from our inability to characterize them in detail.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pan, Yu, E-mail: yu.pan@anu.edu.au, E-mail: zibo.miao@anu.edu.au; Miao, Zibo, E-mail: yu.pan@anu.edu.au, E-mail: zibo.miao@anu.edu.au; Amini, Hadis, E-mail: nhamini@stanford.edu

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, whichmore » 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.« less

Quantum walks of correlated photon pairs in two-dimensional waveguide arrays.

PubMed

Poulios, Konstantinos; Keil, Robert; Fry, Daniel; Meinecke, Jasmin D A; Matthews, Jonathan C F; Politi, Alberto; Lobino, Mirko; Gräfe, Markus; Heinrich, Matthias; Nolte, Stefan; Szameit, Alexander; O'Brien, Jeremy L

2014-04-11

We demonstrate quantum walks of correlated photons in a two-dimensional network of directly laser written waveguides coupled in a "swiss cross" arrangement. The correlated detection events show high-visibility quantum interference and unique composite behavior: strong correlation and independence of the quantum walkers, between and within the planes of the cross. Violations of a classically defined inequality, for photons injected in the same plane and in orthogonal planes, reveal nonclassical behavior in a nonplanar structure.

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. PMID:28903308

The hopf algebra of vector fields on complex quantum groups

NASA Astrophysics Data System (ADS)

Drabant, Bernhard; Jurčo, Branislav; Schlieker, Michael; Weich, Wolfgang; Zumino, Bruno

1992-10-01

We derive the equivalence of the complex quantum enveloping algebra and the algebra of complex quantum vector fields for the Lie algebra types A n , B n , C n , and D n by factorizing the vector fields uniquely into a triangular and a unitary part and identifying them with the corresponding elements of the algebra of regular functionals.

Quantum Communications Systems

DTIC Science & Technology

2012-09-21

metrology practical. The strategy was to develop robust photonic quantum states and sensors serving as an archetype for loss-tolerant information...communications and metrology. Our strategy consisted of developing robust photonic quantum states and sensors serving as an archetype for loss-tolerant...developed atomic memories in caesium vapour, based on a stimulated Raman transition, that have demonstrated a TBP greater than 1000 and are uniquely suited

Dirac fields in flat FLRW cosmology: Uniqueness of the Fock quantization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cortez, Jerónimo, E-mail: jacq@ciencias.unam.mx; Elizaga Navascués, Beatriz, E-mail: beatriz.elizaga@iem.cfmac.csic.es; Martín-Benito, Mercedes, E-mail: m.martin@hef.ru.nl

We address the issue of the infinite ambiguity that affects the construction of a Fock quantization of a Dirac field propagating in a cosmological spacetime with flat compact sections. In particular, we discuss a physical criterion that restricts to a unique possibility (up to unitary equivalence) the infinite set of available vacua. We prove that this desired uniqueness is guaranteed, for any possible choice of spin structure on the spatial sections, if we impose two conditions. The first one is that the symmetries of the classical system must be implemented quantum mechanically, so that the vacuum is invariant under themore » symmetry transformations. The second and more important condition is that the constructed theory must have a quantum dynamics that is implementable as a (non-trivial) unitary operator in Fock space. Actually, this unitarity of the quantum dynamics leads us to identify as explicitly time dependent some very specific contributions of the Dirac field. In doing that, we essentially characterize the part of the dynamics governed by the Dirac equation that is unitarily implementable. The uniqueness of the Fock vacuum is attained then once a physically motivated convention for the concepts of particles and antiparticles is fixed.« less

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.

The New Quantum Logic

NASA Astrophysics Data System (ADS)

Griffiths, Robert B.

2014-06-01

It is shown how all the major conceptual difficulties of standard (textbook) quantum mechanics, including the two measurement problems and the (supposed) nonlocality that conflicts with special relativity, are resolved in the consistent or decoherent histories interpretation of quantum mechanics by using a modified form of quantum logic to discuss quantum properties (subspaces of the quantum Hilbert space), and treating quantum time development as a stochastic process. The histories approach in turn gives rise to some conceptual difficulties, in particular the correct choice of a framework (probabilistic sample space) or family of histories, and these are discussed. The central issue is that the principle of unicity, the idea that there is a unique single true description of the world, is incompatible with our current understanding of quantum mechanics.

Condensed Matter Theories: Volume 25

NASA Astrophysics Data System (ADS)

Ludeña, Eduardo V.; Bishop, Raymond F.; Iza, Peter

2011-03-01

pt. A. Fermi and Bose fluids, exotic systems. Reemergence of the collective mode in [symbol]He and electron layers / H. M. Bohm ... [et al.]. Dissecting and testing collective and topological scenarios for the quantum critical point / J. W. Clark, V. A. Khodel and M. V. Zverev. Helium on nanopatterned surfaces at finite temperature / E. S. Hernandez ... [et al.]. Towards DFT calculations of metal clusters in quantum fluid matrices / S. A. Chin ... [et al.]. Acoustic band gap formation in metamaterials / D. P. Elford ... [et al.]. Dissipative processes in low density strongly interacting 2D electron systems / D. Neilson. Dynamical spatially resolved response function of finite 1-D nano plasmas / T. Raitza, H. Reinholz and G. Ropke. Renormalized bosons and fermions / K. A. Gernoth and M. L. Ristig. Light clusters in nuclear matter / G. Ropke -- pt. B. Quantum magnets, quantum dynamics and phase transitions. Magnetic ordering of antiferromagnets on a spatially anisotropic triangular lattice / R. F. Bishop ... [et al.]. Thermodynamic detection of quantum phase transitions / M. K. G. Kruse ... [et al.]. The SU(2) semi quantum systems dynamics and thermodynamics / C. M. Sarris and A. N. Proto -- pt. C. Physics of nanosystems and nanotechnology. Quasi-one dimensional fluids that exhibit higher dimensional behavior / S. M. Gatica ... [et al.]. Spectral properties of molecular oligomers. A non-Markovian quantum state diffusion approach / J. Roden, W. T. Strunz and A. Eisfeld. Quantum properties in transport through nanoscopic rings: Charge-spin separation and interference effects / K. Hallberg, J. Rincon and S. Ramasesha. Cooperative localization-delocalization in the high T[symbol] cuprates / J. Ranninger. Thermodynamically stable vortex states in superconducting nanowires / W. M. Wu, M. B. Sobnack and F. V. Kusmartsev.pt. D. Quantum information. Quantum information in optical lattices / A. M. Guzman and M. A. Duenas E. -- pt. E. Theory and applications of molecular dynamics and density functional theory. Exchange-correlation functionals from the identical-particle Ornstein-Zernike equation: Basic formulation and numerical algorithms / R. Cuevas-Saavedra and P. W. Ayers. Features and catalytic properties of RhCu: A review / S. Gonzalez, C. Sousa and F. Illas. Kinetic energy functionals: Exact ones from analytic model wave functions and approximate ones in orbital-free molecular dynamics / V. V. Karasiev ... [et al.]. Numerical analysis of hydrogen storage in carbon nanopores / C. Wexler ... [et al.] -- pt. F. Superconductivity. Generalized Bose-Einstein condensation in superconductivity / M. de Llano. Kohn anomaly energy in conventional superconductors equals twice the energy of the superconducting gap: How and why? / R. Chaudhury and M. P. Das. Collective excitations in superconductors and semiconductors in the presence of a condensed phase / Z. Koinov. Thermal expansion of ferromagnetic superconductors: Possible application to UGe[symbol] / N. Hatayama and R. Konno. Generalized superconducting gap in a Boson-Fermion model / T. A. Mamedov and M. de Llano. Influence of domain walls in the superconductor/ferromagnet proximity effect / E. J. Patino. Spin singlet and triplet superconductivity induced by correlated hopping interactions / L. A. Perez, J. S. Millan and C. Wang -- pt. G. Statistical mechanics, relativistic quantum mechanics. Boltzmann's ergodic hypothesis: A meeting place for two cultures / M. H. Lee. Electron-electron interaction in the non-relativistic limit / F. B. Malik.

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.

Unusual strain glassy phase in Fe doped Ni2Mn1.5In0.5

NASA Astrophysics Data System (ADS)

Nevgi, R.; Priolkar, K. R.

2018-01-01

Fe doped Ni2Mn1.5In0.5, particularly, Ni2Mn1.4Fe0.1In0.5, despite having an incommensurate, modulated 7M martensitic structure at room temperature exhibits frequency dependent behavior of storage modulus and loss which obeys the Vogel-Fulcher law as well as shows ergodicity breaking between zero field cooled and field cooled strain measurements just above the transition temperature. Both frequency dependence and ergodicity breaking are characteristics of a strain glassy phase and occur due to the presence of strain domains which are large enough to present signatures of long range martensitic order in diffraction but are non-interacting with other strain domains due to the presence of Fe impurities.

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.

Ergodicity breaking and ageing of underdamped Brownian dynamics with quenched disorder

NASA Astrophysics Data System (ADS)

Guo, Wei; Li, Yong; Song, Wen-Hua; Du, Lu-Chun

2018-03-01

The dynamics of an underdamped Brownian particle moving in one-dimensional quenched disorder under the action of an external force is investigated. Within the tailored parameter regime, the transiently anomalous diffusion and ergodicity breaking, spanning several orders of magnitude in time, have been obtained. The ageing nature of the system weakens as the dissipation of the system increases for other given parameters. Its origin is ascribed to the highly local heterogeneity of the disorder. Two kinds of approximations (in the stationary state), respectively, for large bias and large damping are derived. These results may be helpful in further understanding the nontrivial response of nonlinear dynamics, and also have potential applications to experiments and activities of biological processes.

Minimal evolution time and quantum speed limit of non-Markovian open systems

PubMed Central

Meng, Xiangyi; Wu, Chengjun; Guo, Hong

2015-01-01

We derive a sharp bound as the quantum speed limit (QSL) for the minimal evolution time of quantum open systems in the non-Markovian strong-coupling regime with initial mixed states by considering the effects of both renormalized Hamiltonian and dissipator. For a non-Markovian quantum open system, the possible evolution time between two arbitrary states is not unique, among the set of which we find that the minimal one and its QSL can decrease more steeply by adjusting the coupling strength of the dissipator, which thus provides potential improvements of efficiency in many quantum physics and quantum information areas. PMID:26565062

The photosensitivity of carbon quantum dots/CuAlO2 films composites.

PubMed

Pan, Jiaqi; Sheng, Yingzhuo; Zhang, Jingxiang; Wei, Jumeng; Huang, Peng; Zhang, Xin; Feng, Boxue

2015-07-31

Carbon quantum dots/CuAlO2 films were prepared by a simple route through which CuAlO2 films prepared by sol-gel on crystal quartz substrates were composited with carbon quantum dots on their surface. The characterization results indicated that CuAlO2 films were well combined with carbon quantum dots. The photoconductivity of carbon quantum dots/CuAlO2 films was investigated under illumination and darkness switching, and was demonstrated to be significantly enhanced compared with CuAlO2 films. Through analysis, this enhancement of photoconductivity was attributed to the carbon quantum dots with unique up-converted photoluminescence behavior.

The photosensitivity of carbon quantum dots/CuAlO2 films composites

NASA Astrophysics Data System (ADS)

Pan, Jiaqi; Sheng, Yingzhuo; Zhang, Jingxiang; Wei, Jumeng; Huang, Peng; Zhang, Xin; Feng, Boxue

2015-07-01

Carbon quantum dots/CuAlO2 films were prepared by a simple route through which CuAlO2 films prepared by sol-gel on crystal quartz substrates were composited with carbon quantum dots on their surface. The characterization results indicated that CuAlO2 films were well combined with carbon quantum dots. The photoconductivity of carbon quantum dots/CuAlO2 films was investigated under illumination and darkness switching, and was demonstrated to be significantly enhanced compared with CuAlO2 films. Through analysis, this enhancement of photoconductivity was attributed to the carbon quantum dots with unique up-converted photoluminescence behavior.

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.

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.

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

Some properties of correlations of quantum lattice systems in thermal equilibrium

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fröhlich, Jürg, E-mail: juerg@phys.ethz.ch; Ueltschi, Daniel, E-mail: daniel@ueltschi.org

Simple proofs of uniqueness of the thermodynamic limit of KMS states and of the decay of equilibrium correlations are presented for a large class of quantum lattice systems at high temperatures. New quantum correlation inequalities for general Heisenberg models are described. Finally, a simplified derivation of a general result on power-law decay of correlations in 2D quantum lattice systems with continuous symmetries is given, extending results of McBryan and Spencer for the 2D classical XY model.

Spin fine structure of optically excited quantum dot molecules

NASA Astrophysics Data System (ADS)

Scheibner, M.; Doty, M. F.; Ponomarev, I. V.; Bracker, A. S.; Stinaff, E. A.; Korenev, V. L.; Reinecke, T. L.; Gammon, D.

2007-06-01

The interaction between spins in coupled quantum dots is revealed in distinct fine structure patterns in the measured optical spectra of InAs/GaAs double quantum dot molecules containing zero, one, or two excess holes. The fine structure is explained well in terms of a uniquely molecular interplay of spin-exchange interactions, Pauli exclusion, and orbital tunneling. This knowledge is critical for converting quantum dot molecule tunneling into a means of optically coupling not just orbitals but also spins.

The Interplay of Quantum Confinement and Hydrogenation in Amorphous Silicon Quantum Dots.

PubMed

Askari, Sadegh; Svrcek, Vladmir; Maguire, Paul; Mariotti, Davide

2015-12-22

Hydrogenation in amorphous silicon quantum dots (QDs) has a dramatic impact on the corresponding optical properties and band energy structure, leading to a quantum-confined composite material with unique characteristics. The synthesis of a-Si:H QDs is demonstrated with an atmospheric-pressure plasma process, which allows for accurate control of a highly chemically reactive non-equilibrium environment with temperatures well below the crystallization temperature of Si QDs. © 2015 The Authors. Published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Significance of a Recurring Function in Energy Transfer

NASA Astrophysics Data System (ADS)

Mishra, Subodha

2017-05-01

The appearance of a unique function in the energy transfer from one system to the other in different physical situations such as electrical, mechanical, optical, and quantum mechanical processes is established in this work. Though the laws governing the energy transformation and its transfer from system to system are well known, here we notice a unity in diversity; a unique function appears in various cases of energy transfer whether it is a classical or a quantum mechanical process. We consider four examples, well known in elementary physics, from the fields of electricity, mechanics, optics, and quantum mechanics. We find that this unique function is in fact the transfer function corresponding to all these physical situations, and the interesting and intriguing finding is that the inverse Laplace transform of this transfer function, which is the impulse-response function of the systems when multiplied by a factor of -½, is the solution of a linear differential equation for an "instantly forced critically damped harmonic oscillator." It is important to note that though the physical phenomena considered are quite distinct, the underlying process in the language of impulse-response of the system in the time domain is a unique one. To the best of our knowledge we have not seen anywhere the above analysis of determining the unique function or its description as a transfer function in literature.

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.

The application of microwave photonic detection in quantum communication

NASA Astrophysics Data System (ADS)

Diao, Wenting; Zhuang, Yongyong; Song, Xuerui; Wang, Liujun; Duan, Chongdi

2018-03-01

Quantum communication has attracted much attention in recent years, provides an ultimate level of security, and uniquely it is one of the most likely practical quantum technologies at present. In order to realize global coverage of quantum communication networks, not only need the help of satellite to realize wide area quantum communication, need implementation of optical fiber system to realize city to city quantum communication, but also, it is necessary to implement end-to-end quantum communications intercity and wireless quantum communications that can be received by handheld devices. Because of the limitation of application of light in buildings, it needs quantum communication with microwave band to achieve quantum reception of wireless handheld devices. The single microwave photon energy is very low, it is difficult to directly detect, which become a difficulty in microwave quantum detection. This paper summarizes the mode of single microwave photon detection methods and the possibility of application in microwave quantum communication, and promotes the development of quantum communication in microwave band and quantum radar.

Novel multistep BRET-FRET energy transfer using nanoconjugates of firefly proteins, quantum dots, and red fluorescent proteins

NASA Astrophysics Data System (ADS)

Alam, Rabeka; Zylstra, Joshua; Fontaine, Danielle M.; Branchini, Bruce R.; Maye, Mathew M.

2013-05-01

Sequential bioluminescence resonance energy transfer (BRET) and fluorescence resonance energy transfer (FRET) from firefly luciferase to red fluorescent proteins using quantum dot or rod acceptor/donor linkers is described. The effect of morphology and tuned optical properties on the efficiency of this unique BRET-FRET system was evaluated.Sequential bioluminescence resonance energy transfer (BRET) and fluorescence resonance energy transfer (FRET) from firefly luciferase to red fluorescent proteins using quantum dot or rod acceptor/donor linkers is described. The effect of morphology and tuned optical properties on the efficiency of this unique BRET-FRET system was evaluated. Electronic supplementary information (ESI) available: Experimental details, Fig. S1 and Table S1-S4. See DOI: 10.1039/c3nr01842c

Quantum key distribution with an entangled light emitting diode

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dzurnak, B.; Stevenson, R. M.; Nilsson, J.

Measurements performed on entangled photon pairs shared between two parties can allow unique quantum cryptographic keys to be formed, creating secure links between users. An advantage of using such entangled photon links is that they can be adapted to propagate entanglement to end users of quantum networks with only untrusted nodes. However, demonstrations of quantum key distribution with entangled photons have so far relied on sources optically excited with lasers. Here, we realize a quantum cryptography system based on an electrically driven entangled-light-emitting diode. Measurement bases are passively chosen and we show formation of an error-free quantum key. Our measurementsmore » also simultaneously reveal Bell's parameter for the detected light, which exceeds the threshold for quantum entanglement.« less

Quantum key distribution with an entangled light emitting diode

NASA Astrophysics Data System (ADS)

Dzurnak, B.; Stevenson, R. M.; Nilsson, J.; Dynes, J. F.; Yuan, Z. L.; Skiba-Szymanska, J.; Farrer, I.; Ritchie, D. A.; Shields, A. J.

2015-12-01

Measurements performed on entangled photon pairs shared between two parties can allow unique quantum cryptographic keys to be formed, creating secure links between users. An advantage of using such entangled photon links is that they can be adapted to propagate entanglement to end users of quantum networks with only untrusted nodes. However, demonstrations of quantum key distribution with entangled photons have so far relied on sources optically excited with lasers. Here, we realize a quantum cryptography system based on an electrically driven entangled-light-emitting diode. Measurement bases are passively chosen and we show formation of an error-free quantum key. Our measurements also simultaneously reveal Bell's parameter for the detected light, which exceeds the threshold for quantum entanglement.

Edge mixing dynamics in graphene p–n junctions in the quantum Hall regime

PubMed Central

Matsuo, Sadashige; Takeshita, Shunpei; Tanaka, Takahiro; Nakaharai, Shu; Tsukagoshi, Kazuhito; Moriyama, Takahiro; Ono, Teruo; Kobayashi, Kensuke

2015-01-01

Massless Dirac electron systems such as graphene exhibit a distinct half-integer quantum Hall effect, and in the bipolar transport regime co-propagating edge states along the p–n junction are realized. Additionally, these edge states are uniformly mixed at the junction, which makes it a unique structure to partition electrons in these edge states. Although many experimental works have addressed this issue, the microscopic dynamics of electron partition in this peculiar structure remains unclear. Here we performed shot-noise measurements on the junction in the quantum Hall regime as well as at zero magnetic field. We found that, in sharp contrast with the zero-field case, the shot noise in the quantum Hall regime is finite in the bipolar regime, but is strongly suppressed in the unipolar regime. Our observation is consistent with the theoretical prediction and gives microscopic evidence that the edge states are uniquely mixed along the p–n junction. PMID:26337445

Quantum dot behavior in transition metal dichalcogenides nanostructures

NASA Astrophysics Data System (ADS)

Luo, Gang; Zhang, Zhuo-Zhi; Li, Hai-Ou; Song, Xiang-Xiang; Deng, Guang-Wei; Cao, Gang; Xiao, Ming; Guo, Guo-Ping

2017-08-01

Recently, transition metal dichalcogenides (TMDCs) semiconductors have been utilized for investigating quantum phenomena because of their unique band structures and novel electronic properties. In a quantum dot (QD), electrons are confined in all lateral dimensions, offering the possibility for detailed investigation and controlled manipulation of individual quantum systems. Beyond the definition of graphene QDs by opening an energy gap in nanoconstrictions, with the presence of a bandgap, gate-defined QDs can be achieved on TMDCs semiconductors. In this paper, we review the confinement and transport of QDs in TMDCs nanostructures. The fabrication techniques for demonstrating two-dimensional (2D) materials nanostructures such as field-effect transistors and QDs, mainly based on e-beam lithography and transfer assembly techniques are discussed. Subsequently, we focus on electron transport through TMDCs nanostructures and QDs. With steady improvement in nanoscale materials characterization and using graphene as a springboard, 2D materials offer a platform that allows creation of heterostructure QDs integrated with a variety of crystals, each of which has entirely unique physical properties.

Bi-Exact Groups, Strongly Ergodic Actions and Group Measure Space Type III Factors with No Central Sequence

NASA Astrophysics Data System (ADS)

Houdayer, Cyril; Isono, Yusuke

2016-12-01

We investigate the asymptotic structure of (possibly type III) crossed product von Neumann algebras {M = B rtimes Γ} arising from arbitrary actions {Γ \\curvearrowright B} of bi-exact discrete groups (e.g. free groups) on amenable von Neumann algebras. We prove a spectral gap rigidity result for the central sequence algebra {N' \\cap M^ω} of any nonamenable von Neumann subalgebra with normal expectation {N subset M}. We use this result to show that for any strongly ergodic essentially free nonsingular action {Γ \\curvearrowright (X, μ)} of any bi-exact countable discrete group on a standard probability space, the corresponding group measure space factor {L^∞(X) rtimes Γ} has no nontrivial central sequence. Using recent results of Boutonnet et al. (Local spectral gap in simple Lie groups and applications, 2015), we construct, for every {0 < λ ≤ 1}, a type {III_λ} strongly ergodic essentially free nonsingular action {F_∞ \\curvearrowright (X_λ, μ_λ)} of the free group {{F}_∞} on a standard probability space so that the corresponding group measure space type {III_λ} factor {L^∞(X_λ, μ_λ) rtimes F_∞} has no nontrivial central sequence by our main result. In particular, we obtain the first examples of group measure space type {III} factors with no nontrivial central sequence.

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.

Perspective: The future of quantum dot photonic integrated circuits

NASA Astrophysics Data System (ADS)

Norman, Justin C.; Jung, Daehwan; Wan, Yating; Bowers, John E.

2018-03-01

Direct epitaxial integration of III-V materials on Si offers substantial manufacturing cost and scalability advantages over heterogeneous integration. The challenge is that epitaxial growth introduces high densities of crystalline defects that limit device performance and lifetime. Quantum dot lasers, amplifiers, modulators, and photodetectors epitaxially grown on Si are showing promise for achieving low-cost, scalable integration with silicon photonics. The unique electrical confinement properties of quantum dots provide reduced sensitivity to the crystalline defects that result from III-V/Si growth, while their unique gain dynamics show promise for improved performance and new functionalities relative to their quantum well counterparts in many devices. Clear advantages for using quantum dot active layers for lasers and amplifiers on and off Si have already been demonstrated, and results for quantum dot based photodetectors and modulators look promising. Laser performance on Si is improving rapidly with continuous-wave threshold currents below 1 mA, injection efficiencies of 87%, and output powers of 175 mW at 20 °C. 1500-h reliability tests at 35 °C showed an extrapolated mean-time-to-failure of more than ten million hours. This represents a significant stride toward efficient, scalable, and reliable III-V lasers on on-axis Si substrates for photonic integrate circuits that are fully compatible with complementary metal-oxide-semiconductor (CMOS) foundries.

Quantum entropy and uncertainty for two-mode squeezed, coherent and intelligent spin states

NASA Technical Reports Server (NTRS)

Aragone, C.; Mundarain, D.

1993-01-01

We compute the quantum entropy for monomode and two-mode systems set in squeezed states. Thereafter, the quantum entropy is also calculated for angular momentum algebra when the system is either in a coherent or in an intelligent spin state. These values are compared with the corresponding values of the respective uncertainties. In general, quantum entropies and uncertainties have the same minimum and maximum points. However, for coherent and intelligent spin states, it is found that some minima for the quantum entropy turn out to be uncertainty maxima. We feel that the quantum entropy we use provides the right answer, since it is given in an essentially unique way.

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.

Structure of chaotic magnetic field lines in IR-T1 tokamak due to ergodic magnetic limiter

NASA Astrophysics Data System (ADS)

Ahmadi, S.; Salar Elahi, A.; Ghorannevis, M.

2018-03-01

In this paper we have studied an Ergodic Magnetic Limiter (EML) based chaotic magnetic field for transport control in the edge plasma of IR-T1 tokamak. The resonance created by the EML causes perturbation of the equilibrium field line in tokamak and as a result, the field lines are chaotic in the vicinity of the dimerized island chains. Transport barriers are formed in the chaotic field line and actually observe in tokamak with reverse magnetic shear. We used area-preserving non-twist (and twist) Poincaré maps to describe the formation of transport barriers, which are actually features of Hamiltonian systems. This transport barrier is useful in reducing radial diffusion of the field line and thus improving the plasma confinement.

Kinetic control of the coverage of oil droplets by DNA-functionalized colloids

PubMed Central

Joshi, Darshana; Bargteil, Dylan; Caciagli, Alessio; Burelbach, Jerome; Xing, Zhongyang; Nunes, André S.; Pinto, Diogo E. P.; Araújo, Nuno A. M.; Brujic, Jasna; Eiser, Erika

2016-01-01

We report a study of reversible adsorption of DNA-coated colloids on complementary functionalized oil droplets. We show that it is possible to control the surface coverage of oil droplets using colloidal particles by exploiting the fact that, during slow adsorption, compositional arrest takes place well before structural arrest occurs. As a consequence, we can prepare colloid-coated oil droplets with a “frozen” degree of loading but with fully ergodic colloidal dynamics on the droplets. We illustrate the equilibrium nature of the adsorbed colloidal phase by exploring the quasi–two-dimensional phase behavior of the adsorbed colloids under the influence of depletion interactions and present simulations of a simple model that illustrates the nature of the compositional arrest and the structural ergodicity. PMID:27532053

Many-body delocalization with random vector potentials

NASA Astrophysics Data System (ADS)

Cheng, Chen; Mondaini, Rubem

2016-11-01

We study the ergodic properties of excited states in a model of interacting fermions in quasi-one-dimensional chains subjected to a random vector potential. In the noninteracting limit, we show that arbitrarily small values of this complex off-diagonal disorder trigger localization for the whole spectrum; the divergence of the localization length in the single-particle basis is characterized by a critical exponent ν which depends on the energy density being investigated. When short-range interactions are included, the localization is lost, and the system is ergodic regardless of the magnitude of disorder in finite chains. Our numerical results suggest a delocalization scheme for arbitrary small values of interactions. This finding indicates that the standard scenario of the many-body localization cannot be obtained in a model with random gauge fields.

Statistical Mechanics of Turbulent Dynamos

NASA Technical Reports Server (NTRS)

Shebalin, John V.

2014-01-01

Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much investigation, by greatly extending the statistical theory of ideal MHD turbulence. The mathematical details of broken ergodicity, in fact, give a quantitative explanation of how coherent structure, dynamic alignment and force-free states appear in turbulent magnetofluids. The relevance of these ideal results to real MHD turbulence occurs because broken ergodicity is most manifest in the ideal case at the largest length scales and it is in these largest scales that a real magnetofluid has the least dissipation, i.e., most closely approaches the behavior of an ideal magnetofluid. Furthermore, the effects grow stronger when cross and magnetic helicities grow large with respect to energy, and this is exactly what occurs with time in a real magnetofluid, where it is called selective decay. The relevance of these results found in ideal MHD turbulence theory to the real world is that they provide at least a qualitative explanation of why confined turbulent magnetofluids, such as the liquid iron that fills the Earth's outer core, produce stationary, large-scale magnetic fields, i.e., the geomagnetic field. These results should also apply to other planets as well as to plasma confinement devices on Earth and in space, and the effects should be manifest if Reynolds numbers are high enough and there is enough time for stationarity to occur, at least approximately. In the presentation, details will be given for both theoretical and numerical results, and references will be provided.

MHD Turbulence and Magnetic Dynamos

NASA Technical Reports Server (NTRS)

Shebalin, John V

2014-01-01

Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much investigation, by greatly extending the statistical theory of ideal MHD turbulence. The mathematical details of broken ergodicity, in fact, give a quantitative explanation of how coherent structure, dynamic alignment and force-free states appear in turbulent magnetofluids. The relevance of these ideal results to real MHD turbulence occurs because broken ergodicity is most manifest in the ideal case at the largest length scales and it is in these largest scales that a real magnetofluid has the least dissipation, i.e., most closely approaches the behavior of an ideal magnetofluid. Furthermore, the effects grow stronger when cross and magnetic helicities grow large with respect to energy, and this is exactly what occurs with time in a real magnetofluid, where it is called selective decay. The relevance of these results found in ideal MHD turbulence theory to the real world is that they provide at least a qualitative explanation of why confined turbulent magnetofluids, such as the liquid iron that fills the Earth's outer core, produce stationary, large-scale magnetic fields, i.e., the geomagnetic field. These results should also apply to other planets as well as to plasma confinement devices on Earth and in space, and the effects should be manifest if Reynolds numbers are high enough and there is enough time for stationarity to occur, at least approximately. In the presentation, details will be given for both theoretical and numerical results, and references will be provided.

Exploring quantum thermodynamics in continuous measurement of superconducting qubits

NASA Astrophysics Data System (ADS)

Murch, Kater

The extension of thermodynamics into the realm of quantum mechanics, where quantum fluctuations dominate and systems need not occupy definite states, poses unique challenges. Superconducting quantum circuits offer exquisite control over the environment of simple quantum systems allowing the exploration of thermodynamics at the quantum level through measurement and feedback control. We use a superconducting transmon qubit that is resonantly coupled to a waveguide cavity as an effectively one-dimensional quantum emitter. By driving the emitter and detecting the fluorescence with a near-quantum-limited Josephson parametric amplifier, we track the evolution of the quantum state and characterize the work and heat along single quantum trajectories. By using quantum feedback control to compensate for heat exchanged with the emitter's environment we are able to extract the work statistics associated with the quantum evolution and examine fundamental fluctuation theorems in non-equilibrium thermodynamics. This work was supported by the Alfred P. Sloan Foundation, the National Science Foundation, and the Office of Naval Research.

Noncommutative spherically symmetric spacetimes at semiclassical order

NASA Astrophysics Data System (ADS)

Fritz, Christopher; Majid, Shahn

2017-07-01

Working within the recent formalism of Poisson-Riemannian geometry, we completely solve the case of generic spherically symmetric metric and spherically symmetric Poisson-bracket to find a unique answer for the quantum differential calculus, quantum metric and quantum Levi-Civita connection at semiclassical order O(λ) . Here λ is the deformation parameter, plausibly the Planck scale. We find that r, t, d r, d t are all forced to be central, i.e. undeformed at order λ, while for each value of r, t we are forced to have a fuzzy sphere of radius r with a unique differential calculus which is necessarily nonassociative at order λ2 . We give the spherically symmetric quantisation of the FLRW cosmology in detail and also recover a previous analysis for the Schwarzschild black hole, now showing that the quantum Ricci tensor for the latter vanishes at order λ. The quantum Laplace-Beltrami operator for spherically symmetric models turns out to be undeformed at order λ while more generally in Poisson-Riemannian geometry we show that it deforms to □f+λ2ωαβ(Ricγα-Sγα)(∇^βdf)γ+O(λ2) in terms of the classical Levi-Civita connection \\widehat\

Synthetic Developments of Nontoxic Quantum Dots.

PubMed

Das, Adita; Snee, Preston T

2016-03-03

Semiconductor nanocrystals, or quantum dots (QDs), are candidates for biological sensing, photovoltaics, and catalysis due to their unique photophysical properties. The most studied QDs are composed of heavy metals like cadmium and lead. However, this engenders concerns over heavy metal toxicity. To address this issue, numerous studies have explored the development of nontoxic (or more accurately less toxic) quantum dots. In this Review, we select three major classes of nontoxic quantum dots composed of carbon, silicon and Group I-III-VI elements and discuss the myriad of synthetic strategies and surface modification methods to synthesize quantum dots composed of these material systems. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Current Application of Quantum Dots (QD) in Cancer Therapy: A Review.

PubMed

Babu, Lavanya Thilak; Paira, Priyankar

2017-01-01

Semiconductor quantum dots proved themselves as efficient fluorescent probes in cancer detection and treatment. Their size, high stability, non-photobleaching and water solubility made them a unique fluorophore in place of conventional organic dyes. Newly emerged theranostic drug delivery system using quantum dots helped us in better understanding of the drug delivery mechanism inside the cells. Surface modified Quantum dots and their applications became wide in bioimaging, immunohistochemistry, tracking intracellular drug and intracellular molecules target. We have highlighted various applications of quantum dots in cancer treatment, drug delivery, flow cytometry, and theranostics. Copyright© Bentham Science Publishers; For any queries, please email at epub@benthamscience.org.

The BIG Bell Test: quantum physics experiments with direct public participation

NASA Astrophysics Data System (ADS)

Mitchell, Morgan; Abellan, Carlos; Tura, Jordi; Garcia Matos, Marta; Hirschmann, Alina; Beduini, Federica; Pruneri, Valerio; Acin, Antonio; Marti, Maria; BIG Bell Test Collaboration

The BIG Bell Test is a suite of physics experiments - tests of quantum nonlocality, quantum communications, and related experiments - that use crowd-sourced human randomness as an experimental resource. By connecting participants - anyone with an internet connection - to state-of-the-art experiments on five continents, the project aims at two complementary goals: 1) to provide bits generated directly from human choices, a unique information resource, to physics experiments, and 2) to give the world public the opportunity to contribute in a meaningful way to quantum physics research. We also describe related outreach and educational efforts to spread awareness of quantum physics and its applications.

Obtaining highly excited eigenstates of the localized XX chain via DMRG-X.

PubMed

Devakul, Trithep; Khemani, Vedika; Pollmann, Frank; Huse, David A; Sondhi, S L

2017-12-13

We benchmark a variant of the recently introduced density matrix renormalization group (DMRG)-X algorithm against exact results for the localized random field XX chain. We find that the eigenstates obtained via DMRG-X exhibit a highly accurate l-bit description for system sizes much bigger than the direct, many-body, exact diagonalization in the spin variables is able to access. We take advantage of the underlying free fermion description of the XX model to accurately test the strengths and limitations of this algorithm for large system sizes. We discuss the theoretical constraints on the performance of the algorithm from the entanglement properties of the eigenstates, and its actual performance at different values of disorder. A small but significant improvement to the algorithm is also presented, which helps significantly with convergence. We find that, at high entanglement, DMRG-X shows a bias towards eigenstates with low entanglement, but can be improved with increased bond dimension. This result suggests that one must be careful when applying the algorithm for interacting many-body localized spin models near a transition.This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'. © 2017 The Author(s).

Obtaining highly excited eigenstates of the localized XX chain via DMRG-X

NASA Astrophysics Data System (ADS)

Devakul, Trithep; Khemani, Vedika; Pollmann, Frank; Huse, David A.; Sondhi, S. L.

2017-10-01

We benchmark a variant of the recently introduced density matrix renormalization group (DMRG)-X algorithm against exact results for the localized random field XX chain. We find that the eigenstates obtained via DMRG-X exhibit a highly accurate l-bit description for system sizes much bigger than the direct, many-body, exact diagonalization in the spin variables is able to access. We take advantage of the underlying free fermion description of the XX model to accurately test the strengths and limitations of this algorithm for large system sizes. We discuss the theoretical constraints on the performance of the algorithm from the entanglement properties of the eigenstates, and its actual performance at different values of disorder. A small but significant improvement to the algorithm is also presented, which helps significantly with convergence. We find that, at high entanglement, DMRG-X shows a bias towards eigenstates with low entanglement, but can be improved with increased bond dimension. This result suggests that one must be careful when applying the algorithm for interacting many-body localized spin models near a transition. This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.

Charge transfer reactions between gas-phase hydrated electrons, molecular oxygen and carbon dioxide at temperatures of 80-300 K.

PubMed

Akhgarnusch, Amou; Tang, Wai Kit; Zhang, Han; Siu, Chi-Kit; Beyer, Martin K

2016-09-14

The recombination reactions of gas-phase hydrated electrons (H2O)n˙(-) with CO2 and O2, as well as the charge exchange reaction of CO2˙(-)(H2O)n with O2, were studied by Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry in the temperature range T = 80-300 K. Comparison of the rate constants with collision models shows that CO2 reacts with 50% collision efficiency, while O2 reacts considerably slower. Nanocalorimetry yields internally consistent results for the three reactions. Converted to room temperature condensed phase, this yields hydration enthalpies of CO2˙(-) and O2˙(-), ΔHhyd(CO2˙(-)) = -334 ± 44 kJ mol(-1) and ΔHhyd(O2˙(-)) = -404 ± 28 kJ mol(-1). Quantum chemical calculations show that the charge exchange reaction proceeds via a CO4˙(-) intermediate, which is consistent with a fully ergodic reaction and also with the small efficiency. Ab initio molecular dynamics simulations corroborate this picture and indicate that the CO4˙(-) intermediate has a lifetime significantly above the ps regime.

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.

Pure Gaussian state generation via dissipation: a quantum stochastic differential equation approach.

PubMed

Yamamoto, Naoki

2012-11-28

Recently, the complete characterization of a general Gaussian dissipative system having a unique pure steady state was obtained. This result provides a clear guideline for engineering an environment such that the dissipative system has a desired pure steady state such as a cluster state. In this paper, we describe the system in terms of a quantum stochastic differential equation (QSDE) so that the environment channels can be explicitly dealt with. Then, a physical meaning of that characterization, which cannot be seen without the QSDE representation, is clarified; more specifically, the nullifier dynamics of any Gaussian system generating a unique pure steady state is passive. In addition, again based on the QSDE framework, we provide a general and practical method to implement a desired dissipative Gaussian system, which has a structure of quantum state transfer.

Ground State Structure of a Coupled 2-Fermion System in Supersymmetric Quantum Mechanics

NASA Astrophysics Data System (ADS)

Finster, Felix

1997-05-01

We prove the uniqueness of the ground state for a supersymmetric quantum mechanical system of two fermions and two bosons, which is closely related to theN=1 WZ-model. The proof is constructive and gives detailed information on what the ground state looks like

Nilpotent representations of classical quantum groups at roots of unity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Abe, Yuuki; Nakashima, Toshiki

2005-11-01

Properly specializing the parameters in 'Schnizer modules', for types A,B,C, and D, we get its unique primitive vector. Then we show that the module generated by the primitive vector is an irreducible highest weight module of finite dimensional classical quantum groups at roots of unity.

Anti-Noise Bidirectional Quantum Steganography Protocol with Large Payload

NASA Astrophysics Data System (ADS)

Qu, Zhiguo; Chen, Siyi; Ji, Sai; Ma, Songya; Wang, Xiaojun

2018-06-01

An anti-noise bidirectional quantum steganography protocol with large payload protocol is proposed in this paper. In the new protocol, Alice and Bob enable to transmit classical information bits to each other while teleporting secret quantum states covertly. The new protocol introduces the bidirectional quantum remote state preparation into the bidirectional quantum secure communication, not only to expand secret information from classical bits to quantum state, but also extract the phase and amplitude values of secret quantum state for greatly enlarging the capacity of secret information. The new protocol can also achieve better imperceptibility, since the eavesdropper can hardly detect the hidden channel or even obtain effective secret quantum states. Comparing with the previous quantum steganography achievements, due to its unique bidirectional quantum steganography, the new protocol can obtain higher transmission efficiency and better availability. Furthermore, the new algorithm can effectively resist quantum noises through theoretical analysis. Finally, the performance analysis proves the conclusion that the new protocol not only has good imperceptibility, high security, but also large payload.

Anti-Noise Bidirectional Quantum Steganography Protocol with Large Payload

NASA Astrophysics Data System (ADS)

Qu, Zhiguo; Chen, Siyi; Ji, Sai; Ma, Songya; Wang, Xiaojun

2018-03-01

An anti-noise bidirectional quantum steganography protocol with large payload protocol is proposed in this paper. In the new protocol, Alice and Bob enable to transmit classical information bits to each other while teleporting secret quantum states covertly. The new protocol introduces the bidirectional quantum remote state preparation into the bidirectional quantum secure communication, not only to expand secret information from classical bits to quantum state, but also extract the phase and amplitude values of secret quantum state for greatly enlarging the capacity of secret information. The new protocol can also achieve better imperceptibility, since the eavesdropper can hardly detect the hidden channel or even obtain effective secret quantum states. Comparing with the previous quantum steganography achievements, due to its unique bidirectional quantum steganography, the new protocol can obtain higher transmission efficiency and better availability. Furthermore, the new algorithm can effectively resist quantum noises through theoretical analysis. Finally, the performance analysis proves the conclusion that the new protocol not only has good imperceptibility, high security, but also large payload.

Interferometric Quantum-Nondemolition Single-Photon Detectors

NASA Technical Reports Server (NTRS)

Kok, Peter; Lee, Hwang; Dowling, Jonathan

2007-01-01

Two interferometric quantum-nondemolition (QND) devices have been proposed: (1) a polarization-independent device and (2) a polarization-preserving device. The prolarization-independent device works on an input state of up to two photons, whereas the polarization-preserving device works on a superposition of vacuum and single- photon states. The overall function of the device would be to probabilistically generate a unique detector output only when its input electromagnetic mode was populated by a single photon, in which case its output mode would also be populated by a single photon. Like other QND devices, the proposed devices are potentially useful for a variety of applications, including such areas of NASA interest as quantum computing, quantum communication, detection of gravity waves, as well as pedagogical demonstrations of the quantum nature of light. Many protocols in quantum computation and quantum communication require the possibility of detecting a photon without destroying it. The only prior single- photon-detecting QND device is based on quantum electrodynamics in a resonant cavity and, as such, it depends on the photon frequency. Moreover, the prior device can distinguish only between one photon and no photon. The proposed interferometric QND devices would not depend on frequency and could distinguish between (a) one photon and (b) zero or two photons. The first proposed device is depicted schematically in Figure 1. The input electromagnetic mode would be a superposition of a zero-, a one-, and a two-photon quantum state. The overall function of the device would be to probabilistically generate a unique detector output only when its input electromagnetic mode was populated by a single photon, in which case its output mode also would be populated by a single photon.

Observation of the Zero Hall Plateau in a Quantum Anomalous Hall Insulator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Feng, Yang; Feng, Xiao; Ou, Yunbo

We report experimental investigations on the quantum phase transition between the two opposite Hall plateaus of a quantum anomalous Hall insulator. We observe a well-defined plateau with zero Hall conductivity over a range of magnetic field around coercivity when the magnetization reverses. The features of the zero Hall plateau are shown to be closely related to that of the quantum anomalous Hall effect, but its temperature evolution exhibits a significant difference from the network model for a conventional quantum Hall plateau transition. We propose that the chiral edge states residing at the magnetic domain boundaries, which are unique to amore » quantum anomalous Hall insulator, are responsible for the novel features of the zero Hall plateau.« less

The thermoelectric efficiency of quantum dots in indium arsenide/indium phosphide nanowires

NASA Astrophysics Data System (ADS)

Hoffmann, Eric A.

State of the art semiconductor materials engineering provides the possibility to fabricate devices on the lower end of the mesoscopic scale and confine only a handful of electrons to a region of space. When the thermal energy is reduced below the energetic quantum level spacing, the confined electrons assume energy levels akin to the core-shell structure of natural atoms. Such "artificial atoms", also known as quantum dots, can be loaded with electrons, one-by-one, and subsequently unloaded using source and drain electrical contacts. As such, quantum dots are uniquely tunable platforms for performing quantum transport and quantum control experiments. Voltage-biased electron transport through quantum dots has been studied extensively. Far less attention has been given to thermoelectric effects in quantum dots, that is, electron transport induced by a temperature gradient. This dissertation focuses on the efficiency of direct thermal-to-electric energy conversion in InAs/InP quantum dots embedded in nanowires. The efficiency of thermoelectric heat engines is bounded by the same maximum efficiency as cyclic heat engines; namely, by Carnot efficiency. The efficiency of bulk thermoelectric materials suffers from their inability to transport charge carriers selectively based on energy. Owing to their three-dimensional momentum quantization, quantum dots operate as electron energy filters---a property which can be harnessed to minimize entropy production and therefore maximize efficiency. This research was motivated by the possibility to realize experimentally a thermodynamic heat engine operating with near-Carnot efficiency using the unique behavior of quantum dots. To this end, a microscopic heating scheme for the application of a temperature difference across a quantum dot was developed in conjunction with a novel quantum-dot thermometry technique used for quantifying the magnitude of the applied temperature difference. While pursuing high-efficiency thermoelectric performance, many mesoscopic thermoelectric effects were observed and studied, including Coulomb-blockade thermovoltage oscillations, thermoelectric power generation, and strong nonlinear behavior. In the end, a quantum-dot-based thermoelectric heat engine was achieved and demonstrated an electronic efficiency of up to 95% Carnot efficiency.

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.

Minimum-error quantum distinguishability bounds from matrix monotone functions: A comment on 'Two-sided estimates of minimum-error distinguishability of mixed quantum states via generalized Holevo-Curlander bounds' [J. Math. Phys. 50, 032106 (2009)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tyson, Jon

2009-06-15

Matrix monotonicity is used to obtain upper bounds on minimum-error distinguishability of arbitrary ensembles of mixed quantum states. This generalizes one direction of a two-sided bound recently obtained by the author [J. Tyson, J. Math. Phys. 50, 032106 (2009)]. It is shown that the previously obtained special case has unique properties.

Optimal state points of the subadditive ergodic theorem

NASA Astrophysics Data System (ADS)

Dai, Xiongping

2011-05-01

Let T\\colon (X,\\mathscr{B},\\mu)\\rightarrow(X,\\mathscr{B},\\mu) be an ergodic measure-preserving Borel measurable transformation of a separable metric space X that is not necessarily compact, and suppose that \\{\\varphi_n\\}_{n\\ge1}\\colon X\\rightarrow{R}\\cup\\{-\\infty\\} is a T-subadditive sequence of \\mathscr{B} -measurable upper-bounded functions. In this paper, we prove that, if the sets D_{\\varphi_n} of phivn-discontinuities are of μ-measure 0 for all n >= 1 and if the growth rates \\[ \\begin{equation*} {\\bvarphi}^*(x):=\\limsup_{n\\to+\\infty}\\frac{1}{n}\\varphi_n(x)<0\\tqs for \\mu-a.e. x\\in X, \\end{equation*} \\] then bold varphi*(x) < 0 for all points x in the basin BT(μ) of (T, μ). We apply this to considering the Oseledets regular points.

Supervised self-organization of homogeneous swarms using ergodic projections of Markov chains.

PubMed

Chattopadhyay, Ishanu; Ray, Asok

2009-12-01

This paper formulates a self-organization algorithm to address the problem of global behavior supervision in engineered swarms of arbitrarily large population sizes. The swarms considered in this paper are assumed to be homogeneous collections of independent identical finite-state agents, each of which is modeled by an irreducible finite Markov chain. The proposed algorithm computes the necessary perturbations in the local agents' behavior, which guarantees convergence to the desired observed state of the swarm. The ergodicity property of the swarm, which is induced as a result of the irreducibility of the agent models, implies that while the local behavior of the agents converges to the desired behavior only in the time average, the overall swarm behavior converges to the specification and stays there at all times. A simulation example illustrates the underlying concept.

A method for determining the weak statistical stationarity of a random process

NASA Technical Reports Server (NTRS)

Sadeh, W. Z.; Koper, C. A., Jr.

1978-01-01

A method for determining the weak statistical stationarity of a random process is presented. The core of this testing procedure consists of generating an equivalent ensemble which approximates a true ensemble. Formation of an equivalent ensemble is accomplished through segmenting a sufficiently long time history of a random process into equal, finite, and statistically independent sample records. The weak statistical stationarity is ascertained based on the time invariance of the equivalent-ensemble averages. Comparison of these averages with their corresponding time averages over a single sample record leads to a heuristic estimate of the ergodicity of a random process. Specific variance tests are introduced for evaluating the statistical independence of the sample records, the time invariance of the equivalent-ensemble autocorrelations, and the ergodicity. Examination and substantiation of these procedures were conducted utilizing turbulent velocity signals.

A symmetric version of the generalized alternating direction method of multipliers for two-block separable convex programming.

PubMed

Liu, Jing; Duan, Yongrui; Sun, Min

2017-01-01

This paper introduces a symmetric version of the generalized alternating direction method of multipliers for two-block separable convex programming with linear equality constraints, which inherits the superiorities of the classical alternating direction method of multipliers (ADMM), and which extends the feasible set of the relaxation factor α of the generalized ADMM to the infinite interval [Formula: see text]. Under the conditions that the objective function is convex and the solution set is nonempty, we establish the convergence results of the proposed method, including the global convergence, the worst-case [Formula: see text] convergence rate in both the ergodic and the non-ergodic senses, where k denotes the iteration counter. Numerical experiments to decode a sparse signal arising in compressed sensing are included to illustrate the efficiency of the new method.

Revisitation of the dipole tracer test for heterogeneous porous formations

NASA Astrophysics Data System (ADS)

Zech, Alraune; D'Angelo, Claudia; Attinger, Sabine; Fiori, Aldo

2018-05-01

In this paper, a new analytical solution for interpreting dipole tests in heterogeneous media is derived by associating the shape of the tracer breakthrough curve with the log-conductivity variance. It is presented how the solution can be used for interpretation of dipole field test in view of geostatistical aquifer characterization on three illustrative examples. The analytical solution for the tracer breakthrough curve at the pumping well in a dipole tracer test is developed by considering a perfectly stratified formation. The analysis is carried out making use of the travel time of a generic solute particle, from the injection to the pumping well. Injection conditions are adapted to different possible field setting. Solutions are presented for resident and flux proportional injection mode as well as for an instantaneous pulse of solute and continuous solute injections. The analytical form of the solution allows a detailed investigation on the impact of heterogeneity, the tracer input conditions and ergodicity conditions at the well. The impact of heterogeneity manifests in a significant spreading of solute particles that increases the natural tendency to spreading induced by the dipole setup. Furthermore, with increasing heterogeneity the number of layers needed to reach ergodic conditions become larger. Thus, dipole test in highly heterogeneous aquifers might take place under non-ergodic conditions giving that the log-conductivity variance is underestimated. The method is a promising geostatistical analyzing tool being the first analytical solution for dipole tracer test analysis taking heterogeneity of hydraulic conductivity into account.

Quantum criticality in the spin-1/2 Heisenberg chain system copper pyrazine dinitrate

PubMed Central

Breunig, Oliver; Garst, Markus; Klümper, Andreas; Rohrkamp, Jens; Turnbull, Mark M.; Lorenz, Thomas

2017-01-01

Low-dimensional quantum magnets promote strong correlations between magnetic moments that lead to fascinating quantum phenomena. A particularly interesting system is the antiferromagnetic spin-1/2 Heisenberg chain because it is exactly solvable by the Bethe-Ansatz method. It is approximately realized in the magnetic insulator copper pyrazine dinitrate, providing a unique opportunity for a quantitative comparison between theory and experiment. We investigate its thermodynamic properties with a particular focus on the field-induced quantum phase transition. Thermal expansion, magnetostriction, specific heat, magnetization, and magnetocaloric measurements are found to be in excellent agreement with exact Bethe-Ansatz predictions. Close to the critical field, thermodynamics obeys the expected quantum critical scaling behavior, and in particular, the magnetocaloric effect and the Grüneisen parameters diverge in a characteristic manner. Beyond its importance for quantum magnetism, our study establishes a paradigm of a quantum phase transition, which illustrates fundamental principles of quantum critical thermodynamics. PMID:29282449

Time-dependent wave packet simulations of transport through Aharanov-Bohm rings with an embedded quantum dot.

PubMed

Kreisbeck, C; Kramer, T; Molina, R A

2017-04-20

We have performed time-dependent wave packet simulations of realistic Aharonov-Bohm (AB) devices with a quantum dot embedded in one of the arms of the interferometer. The AB ring can function as a measurement device for the intrinsic transmission phase through the quantum dot, however, care has to be taken in analyzing the influence of scattering processes in the junctions of the interferometer arms. We consider a harmonic quantum dot and show how the Darwin-Fock spectrum emerges as a unique pattern in the interference fringes of the AB oscillations.

Electrical and mechanical tuning of a silicon vacancy defect in SiC for quantum information technology

NASA Astrophysics Data System (ADS)

Soykal, Oney O.; Reinecke, Thomas L.

We develop coherent control via Stark effect over the optical transition energies of silicon monovacancy deep center in hexagonal silicon carbide. We show that this defect's unique asymmetry properties of its piezoelectric tensor and Kramer's degenerate high-spin ground/excited state configurations can be used to create new possibilities in quantum information technology ranging from photonic networks to quantum key distribution. We also give examples of its qubit implementations via precise electric field control. This work was supported in part by ONR and by the Office of Secretary of Defense, Quantum Science and Engineering Program.

Quantum Approach to Cournot-type Competition

NASA Astrophysics Data System (ADS)

Frąckiewicz, Piotr

2018-02-01

The aim of this paper is to investigate Cournot-type competition in the quantum domain with the use of the Li-Du-Massar scheme for continuous-variable quantum games. We derive a formula which, in a simple way, determines a unique Nash equilibrium. The result concerns a large class of Cournot duopoly problems including the competition, where the demand and cost functions are not necessary linear. Further, we show that the Nash equilibrium converges to a Pareto-optimal strategy profile as the quantum correlation increases. In addition to illustrating how the formula works, we provide the readers with two examples.

Response to ``Comment on `Bohmian mechanics with complex action: A new trajectory-based formulation of quantum mechanics' '' [J. Chem. Phys. 127, 197101 (2007)

NASA Astrophysics Data System (ADS)

Goldfarb, Yair; Degani, Ilan; Tannor, David J.

2007-11-01

In their comment, Sanz and Miret-Artés (SMA) describe previous trajectory-based formalisms based on the quantum Hamilton-Jacobi (QHJ) formalism. In this reply, we highlight our unique contributions: the identification of the smallness of the quantum force in the complex QHJ and its solution using complex trajectories. SMA also raise the question of how the term locality should be used in quantum mechanics. We suggest that at least certain aspects of nonlocality can depend on the method used to solve the problem.

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.

1−1=Counterfactual: on the potency and significance of quantum non-events

PubMed Central

Cohen, E.

2016-01-01

We study the unique role played in quantum mechanics by non-events or ‘counterfactuals’. Our earlier analysis of ‘quantum oblivion’ has revealed some subtle stages in the measurement process, which may end up in self-cancellation. To these findings, we now add two insights derived by two time-symmetric interpretations of quantum mechanics. (i) Like all quantum interactions, the non-event is formed by the conjunction of forward-plus-backward-evolving wave functions. (ii) Then, it is another feature of such dual evolutions, namely the involvement of negative masses and energies, that enables Nature to make some events ‘unhappen’ while leaving causal traces. PMID:27091159

1-1=Counterfactual: on the potency and significance of quantum non-events.

PubMed

Elitzur, A C; Cohen, E

2016-05-28

We study the unique role played in quantum mechanics by non-events or 'counterfactuals'. Our earlier analysis of 'quantum oblivion' has revealed some subtle stages in the measurement process, which may end up in self-cancellation. To these findings, we now add two insights derived by two time-symmetric interpretations of quantum mechanics. (i) Like all quantum interactions, the non-event is formed by the conjunction of forward-plus-backward-evolving wave functions. (ii) Then, it is another feature of such dual evolutions, namely the involvement of negative masses and energies, that enables Nature to make some events 'unhappen' while leaving causal traces. © 2016 The Author(s).

Strategies in a symmetric quantum Kolkata restaurant problem

NASA Astrophysics Data System (ADS)

Sharif, Puya; Heydari, Hoshang

2012-12-01

The Quantum Kolkata restaurant problem is a multiple-choice version of the quantum minority game, where a set of n non-communicating players have to chose between one of m choices. A payoff is granted to the players that make a unique choice. It has previously been shown that shared entanglement and quantum operations can aid the players to coordinate their actions and acquire higher payoffs than is possible with classical randomization. In this paper the initial quantum state is expanded to a family of GHZ-type states and strategies are discussed in terms of possible final outcomes. It is shown that the players individually seek outcomes that maximize the collective good.

Communication theory of quantum systems. Ph.D. Thesis, 1970

NASA Technical Reports Server (NTRS)

Yuen, H. P. H.

1971-01-01

Communication theory problems incorporating quantum effects for optical-frequency applications are discussed. Under suitable conditions, a unique quantum channel model corresponding to a given classical space-time varying linear random channel is established. A procedure is described by which a proper density-operator representation applicable to any receiver configuration can be constructed directly from the channel output field. Some examples illustrating the application of our methods to the development of optical quantum channel representations are given. Optimizations of communication system performance under different criteria are considered. In particular, certain necessary and sufficient conditions on the optimal detector in M-ary quantum signal detection are derived. Some examples are presented. Parameter estimation and channel capacity are discussed briefly.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bishnoi, Dimple

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 bandmore » setup. PbSe (lead selenide) is commonly used in quantum dot solar cells.« less

Non-Hermitian photonics based on parity-time symmetry

NASA Astrophysics Data System (ADS)

Feng, Liang; El-Ganainy, Ramy; Ge, Li

2017-12-01

Nearly one century after the birth of quantum mechanics, parity-time symmetry is revolutionizing and extending quantum theories to include a unique family of non-Hermitian Hamiltonians. While conceptually striking, experimental demonstration of parity-time symmetry remains unexplored in quantum electronic systems. The flexibility of photonics allows for creating and superposing non-Hermitian eigenstates with ease using optical gain and loss, which makes it an ideal platform to explore various non-Hermitian quantum symmetry paradigms for novel device functionalities. Such explorations that employ classical photonic platforms not only deepen our understanding of fundamental quantum physics but also facilitate technological breakthroughs for photonic applications. Research into non-Hermitian photonics therefore advances and benefits both fields simultaneously.

Using of Quantum Dots in Biology and Medicine.

PubMed

Pleskova, Svetlana; Mikheeva, Elza; Gornostaeva, Ekaterina

2018-01-01

Quantum dots are nanoparticles, which due to their unique physical and chemical (first of all optical) properties, are promising in biology and medicine. There are many ways for quantum dots synthesis, both in the form of nanoislands self-forming on the surfaces, which can be used as single-photon emitters in electronics for storing information, and in the form of colloidal quantum dots for diagnostic and therapeutic purposes in living systems. The paper describes the main methods of quantum dots synthesis and summarizes medical and biological ways of their use. The main emphasis is laid on the ways of quantum dots surface modification. Influence of the size and form of nanoparticles, charge on the surfaces of quantum dots, and cover type on the efficiency of internalization by cells and cell compartments is shown. The main mechanisms of penetration are considered.

Quantum State Tomography via Reduced Density Matrices.

PubMed

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

2017-01-13

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.

Growth and quantum transport properties of vertical Bi2Se3 nanoplate films on Si substrates.

PubMed

Li, Mingze; Wang, Zhenhua; Yang, Liang; Pan, Desheng; Li, Da; Gao, Xuan P A; Zhang, Zhidong

2018-08-03

Controlling the growth direction (planar versus vertical) and surface-to-bulk ratio can lead to lots of unique properties for two-dimensional layered materials. We report a simple method to fabricate continuous films of vertical Bi 2 Se 3 nanoplates on Si substrate and investigate the quantum transport properties of such films. In contrast to (001) oriented planar Bi 2 Se 3 nanoplate film, vertical Bi 2 Se 3 nanoplate films are enclosed by (015) facets, which possess high surface-to-bulk ratio that can enhance the quantum transport property of topological surface states. And by controlling the compactness of vertical Bi 2 Se 3 nanoplates, we realized an effective tuning of the weak antilocalization effect from topological surface states in Bi 2 Se 3 films. Our work paves a way for exploring the unique transport properties of this unconventional structure topological insulator film.

Onsets of hierarchy truncation and self–consistent Born approximation with quantum mechanics prescriptions invariance

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Hou-Dao; Yan, YiJing, E-mail: yyan@ust.hk; iChEM and Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026

2015-12-07

The issue of efficient hierarchy truncation is related to many approximate theories. In this paper, we revisit this issue from both the numerical efficiency and quantum mechanics prescription invariance aspects. The latter requires that the truncation approximation made in Schrödinger picture, such as the quantum master equations and their self–consistent–Born–approximation improvements, should be transferable to their Heisenberg–picture correspondences, without further approximations. We address this issue with the dissipaton equation of motion (DEOM), which is a unique theory for the dynamics of not only reduced systems but also hybrid bath environments. We also highlight the DEOM theory is not only aboutmore » how its dynamical variables evolve in time, but also the underlying dissipaton algebra. We demonstrate this unique feature of DEOM with model systems and report some intriguing nonlinear Fano interferences characteristics that are experimentally measurable.« less

Divergence-free approach for obtaining decompositions of quantum-optical processes

NASA Astrophysics Data System (ADS)

Sabapathy, K. K.; Ivan, J. S.; García-Patrón, R.; Simon, R.

2018-02-01

Operator-sum representations of quantum channels can be obtained by applying the channel to one subsystem of a maximally entangled state and deploying the channel-state isomorphism. However, for continuous-variable systems, such schemes contain natural divergences since the maximally entangled state is ill defined. We introduce a method that avoids such divergences by utilizing finitely entangled (squeezed) states and then taking the limit of arbitrary large squeezing. Using this method, we derive an operator-sum representation for all single-mode bosonic Gaussian channels where a unique feature is that both quantum-limited and noisy channels are treated on an equal footing. This technique facilitates a proof that the rank-1 Kraus decomposition for Gaussian channels at its respective entanglement-breaking thresholds, obtained in the overcomplete coherent-state basis, is unique. The methods could have applications to simulation of continuous-variable channels.

Effects of increasing number of rings on the ion sensing ability of CdSe quantum dots: a theoretical study

NASA Astrophysics Data System (ADS)

Malik, Pragati; Kakkar, Rita

2018-04-01

A computational study on the structural and electronic properties of a special class of artificial atoms, known as quantum dots, has been carried out. These are semiconductors with unique optical and electronic properties and have been widely used in various applications, such as bio-sensing, bio-imaging, and so on. We have considered quantum dots belonging to II-VI types of semiconductors, due to their wide band gap, possession of large exciton binding energies and unique optical and electronic properties. We have studied their applications as chemical ion sensors by beginning with the study of the ion sensing ability of (CdSe) n ( n = 3, 6, 9 which are in the size range of 0.24, 0.49, 0.74 nm, respectively) quantum dots for cations of the zinc triad, namely Zn2+, Cd2+, Hg2+, and various anions of biological and environmental importance, and studied the effect of increasing number of rings on their ion sensing ability. The various structural, electronic, and optical properties, their interaction energies, and charge transfer on interaction with metal ions and anions have been calculated and reported. Our studies indicate that the CdSe quantum dots can be employed as sensors for both divalent cations and anions, but they can sense cations better than anions.

Resource Letter SPE-1: Single-Photon Experiments in the Undergraduate Laboratory

NASA Astrophysics Data System (ADS)

Galvez, Enrique J.

2014-11-01

This Resource Letter lists undergraduate-laboratory adaptations of landmark optical experiments on the fundamentals of quantum physics. Journal articles and websites give technical details of the adaptations, which offer students unique hands-on access to testing fundamental concepts and predictions of quantum mechanics. A selection of the original research articles that led to the implementations is included. These developments have motivated a rethinking of the way quantum mechanics is taught, so this Resource Letter also lists textbooks that provide these new approaches.

Lifetimes of the Vibrational States of DNA Molecules in Functionalized Complexes of Semiconductor Quantum Dots

NASA Astrophysics Data System (ADS)

Bayramov, F. B.; Poloskin, E. D.; Chernev, A. L.; Toporov, V. V.; Dubina, M. V.; Sprung, C.; Lipsanen, H. K.; Bairamov, B. Kh.

2018-01-01

Results of studying nanocrystalline nc-Si/SiO2 quantum dots (QDs) functionalized by short oligonucleotides show that complexes of isolated crystalline semiconductor QDs are unique objects for detecting the manifestation of new quantum confinement phenomena. It is established that narrow lines observed in high-resolution spectra of inelastic light scattering can be used for determining the characteristic time scale of vibrational excitations of separate nucleotide molecules and for studying structural-dynamic properties of fast oscillatory processes in biomacromolecules.

Quantum Dot Platform for Single-Cell Molecular Profiling

NASA Astrophysics Data System (ADS)

Zrazhevskiy, Pavel S.

In-depth understanding of the nature of cell physiology and ability to diagnose and control the progression of pathological processes heavily rely on untangling the complexity of intracellular molecular mechanisms and pathways. Therefore, comprehensive molecular profiling of individual cells within the context of their natural tissue or cell culture microenvironment is essential. In principle, this goal can be achieved by tagging each molecular target with a unique reporter probe and detecting its localization with high sensitivity at sub-cellular resolution, primarily via microscopy-based imaging. Yet, neither widely used conventional methods nor more advanced nanoparticle-based techniques have been able to address this task up to date. High multiplexing potential of fluorescent probes is heavily restrained by the inability to uniquely match probes with corresponding molecular targets. This issue is especially relevant for quantum dot probes---while simultaneous spectral imaging of up to 10 different probes is possible, only few can be used concurrently for staining with existing methods. To fully utilize multiplexing potential of quantum dots, it is necessary to design a new staining platform featuring unique assignment of each target to a corresponding quantum dot probe. This dissertation presents two complementary versatile approaches towards achieving comprehensive single-cell molecular profiling and describes engineering of quantum dot probes specifically tailored for each staining method. Analysis of expanded molecular profiles is achieved through augmenting parallel multiplexing capacity with performing several staining cycles on the same specimen in sequential manner. In contrast to other methods utilizing quantum dots or other nanoparticles, which often involve sophisticated probe synthesis, the platform technology presented here takes advantage of simple covalent bioconjugation and non-covalent self-assembly mechanisms for straightforward probe preparation and specimen labeling, requiring no advanced technical skills and being directly applicable for a wide range of molecular profiling studies. Utilization of quantum dot platform for single-cell molecular profiling promises to greatly benefit both biomedical research and clinical diagnostics by providing a tool for addressing phenotypic heterogeneity within large cell populations, opening access to studying low-abundance events often masked or completely erased by batch processing, and elucidating biomarker signatures of diseases critical for accurate diagnostics and targeted therapy.

Analysis of quantum information processors using quantum metrology

NASA Astrophysics Data System (ADS)

Kandula, Mark J.; Kok, Pieter

2018-06-01

Physical implementations of quantum information processing devices are generally not unique, and we are faced with the problem of choosing the best implementation. Here, we consider the sensitivity of quantum devices to variations in their different components. To measure this, we adopt a quantum metrological approach and find that the sensitivity of a device to variations in a component has a particularly simple general form. We use the concept of cost functions to establish a general practical criterion to decide between two different physical implementations of the same quantum device consisting of a variety of components. We give two practical examples of sensitivities of quantum devices to variations in beam splitter transmittivities: the Knill-Laflamme-Milburn (KLM) and reverse nonlinear sign gates for linear optical quantum computing with photonic qubits, and the enhanced optical Bell detectors by Grice and Ewert and van Loock. We briefly compare the sensitivity to the diamond distance and find that the latter is less suited for studying the behavior of components embedded within the larger quantum device.

Modification of quantum dots with nucleic acids

NASA Astrophysics Data System (ADS)

Kocherginskaya, P. B.; Romanova, A. V.; Prokhorenko, I. A.; Itkis, Daniil M.; Korshun, V. A.; Goodilin, Eugene A.; Tretyakov, Yuri D.

2011-12-01

The key principles and modern approaches to targeted modification of semiconductor colloidal nanoparticles, quantum dots, which exhibit unique photophysical properties and are a promising class of luminescent markers, are discussed. Attention is given to the preparation of their bioconjugates with nucleic acids, promising tools for biological microchips and resonance energy transfer sensors. The bibliography includes 80 references.

Entanglement classes of symmetric Werner states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lyons, David W.; Walck, Scott N.

2011-10-15

The symmetric Werner states for n qubits, important in the study of quantum nonlocality and useful for applications in quantum information, have a surprisingly simple and elegant structure in terms of tensor products of Pauli matrices. Further, each of these states forms a unique local unitary equivalence class, that is, no two of these states are interconvertible by local unitary operations.

The entropic cost of quantum generalized measurements

NASA Astrophysics Data System (ADS)

Mancino, Luca; Sbroscia, Marco; Roccia, Emanuele; Gianani, Ilaria; Somma, Fabrizia; Mataloni, Paolo; Paternostro, Mauro; Barbieri, Marco

2018-03-01

Landauer's principle introduces a symmetry between computational and physical processes: erasure of information, a logically irreversible operation, must be underlain by an irreversible transformation dissipating energy. Monitoring micro- and nano-systems needs to enter into the energetic balance of their control; hence, finding the ultimate limits is instrumental to the development of future thermal machines operating at the quantum level. We report on the experimental investigation of a lower bound to the irreversible entropy associated to generalized quantum measurements on a quantum bit. We adopted a quantum photonics gate to implement a device interpolating from the weakly disturbing to the fully invasive and maximally informative regime. Our experiment prompted us to introduce a bound taking into account both the classical result of the measurement and the outcoming quantum state; unlike previous investigation, our entropic bound is based uniquely on measurable quantities. Our results highlight what insights the information-theoretic approach provides on building blocks of quantum information processors.

Realization of Quantum Maxwell’s Demon with Solid-State Spins*

NASA Astrophysics Data System (ADS)

Wang, W.-B.; Chang, X.-Y.; Wang, F.; Hou, P.-Y.; Huang, Y.-Y.; Zhang, W.-G.; Ouyang, X.-L.; Huang, X.-Z.; Zhang, Z.-Y.; Wang, H.-Y.; He, L.; Duan, L.-M.

2018-04-01

Resolution of the century-long paradox on Maxwell's demon reveals a deep connection between information theory and thermodynamics. Although initially introduced as a thought experiment, Maxwell's demon can now be implemented in several physical systems, leading to intriguing test of information-thermodynamic relations. Here, we report experimental realization of a quantum version of Maxwell's demon using solid state spins where the information acquiring and feedback operations by the demon are achieved through conditional quantum gates. A unique feature of this implementation is that the demon can start in a quantum superposition state or in an entangled state with an ancilla observer. Through quantum state tomography, we measure the entropy in the system, demon, and the ancilla, showing the influence of coherence and entanglement on the result. A quantum implementation of Maxwell's demon adds more controllability to this paradoxical thermal machine and may find applications in quantum thermodynamics involving microscopic systems.

Feynman’s clock, a new variational principle, and parallel-in-time quantum dynamics

PubMed Central

McClean, Jarrod R.; Parkhill, John A.; Aspuru-Guzik, Alán

2013-01-01

We introduce a discrete-time variational principle inspired by the quantum clock originally proposed by Feynman and use it to write down quantum evolution as a ground-state eigenvalue problem. The construction allows one to apply ground-state quantum many-body theory to quantum dynamics, extending the reach of many highly developed tools from this fertile research area. Moreover, this formalism naturally leads to an algorithm to parallelize quantum simulation over time. We draw an explicit connection between previously known time-dependent variational principles and the time-embedded variational principle presented. Sample calculations are presented, applying the idea to a hydrogen molecule and the spin degrees of freedom of a model inorganic compound, demonstrating the parallel speedup of our method as well as its flexibility in applying ground-state methodologies. Finally, we take advantage of the unique perspective of this variational principle to examine the error of basis approximations in quantum dynamics. PMID:24062428

Melting of Boltzmann particles in different 2D trapping potential

NASA Astrophysics Data System (ADS)

Bhattacharya, Dyuti; Filinov, Alexei; Ghosal, Amit; Bonitz, Michael

2015-03-01

We analyze the quantum melting of two dimensional Wigner solid in several confined geometries and compare them with corresponding thermal melting in a purely classical system. Our results show that the geometry play little role in deciding the crossover quantum parameter nX, as the effects from boundary is well screened by the quantum zero point motion. The unique phase diagram in the plane of thermal and quantum fluctuations determined from independent melting criteria separates out the Wigner molecule ``phase'' from the classical and quantum ``liquids''. An intriguing signature of weakening liquidity with increasing temperature T have been found in the extreme quantum regime (n). This crossover is associated with production of defects, just like in case of thermal melting, though the role of them in determining the mechanism of the crossover appears different. Our study will help comprehending melting in a variety of experimental realization of confined system - from quantum dots to complex plasma.

Quantum criticality at the superconductor-insulator transition revealed by specific heat measurements

PubMed Central

Poran, S.; Nguyen-Duc, T.; Auerbach, A.; Dupuis, N.; Frydman, A.; Bourgeois, Olivier

2017-01-01

The superconductor–insulator transition (SIT) is considered an excellent example of a quantum phase transition that is driven by quantum fluctuations at zero temperature. The quantum critical point is characterized by a diverging correlation length and a vanishing energy scale. Low-energy fluctuations near quantum criticality may be experimentally detected by specific heat, cp, measurements. Here we use a unique highly sensitive experiment to measure cp of two-dimensional granular Pb films through the SIT. The specific heat shows the usual jump at the mean field superconducting transition temperature marking the onset of Cooper pairs formation. As the film thickness is tuned towards the SIT, is relatively unchanged, while the magnitude of the jump and low-temperature specific heat increase significantly. This behaviour is taken as the thermodynamic fingerprint of quantum criticality in the vicinity of a quantum phase transition. PMID:28224994

Quantum criticality at the superconductor-insulator transition revealed by specific heat measurements.

PubMed

Poran, S; Nguyen-Duc, T; Auerbach, A; Dupuis, N; Frydman, A; Bourgeois, Olivier

2017-02-22

The superconductor-insulator transition (SIT) is considered an excellent example of a quantum phase transition that is driven by quantum fluctuations at zero temperature. The quantum critical point is characterized by a diverging correlation length and a vanishing energy scale. Low-energy fluctuations near quantum criticality may be experimentally detected by specific heat, c p , measurements. Here we use a unique highly sensitive experiment to measure c p of two-dimensional granular Pb films through the SIT. The specific heat shows the usual jump at the mean field superconducting transition temperature marking the onset of Cooper pairs formation. As the film thickness is tuned towards the SIT, is relatively unchanged, while the magnitude of the jump and low-temperature specific heat increase significantly. This behaviour is taken as the thermodynamic fingerprint of quantum criticality in the vicinity of a quantum phase transition.

Persistence and ergodicity of a stochastic single species model with Allee effect under regime switching

NASA Astrophysics Data System (ADS)

Yu, Xingwang; Yuan, Sanling; Zhang, Tonghua

2018-06-01

Allee effect can interact with environment stochasticity and is active when population numbers are small. Our goal of this paper is to investigate such effect on population dynamics. More precisely, we develop and investigate a stochastic single species model with Allee effect under regime switching. We first prove the existence of global positive solution of the model. Then, we perform the survival analysis to seek sufficient conditions for the extinction, non-persistence in mean, persistence in mean and stochastic permanence. By constructing a suitable Lyapunov function, we show that the model is positive recurrent and ergodic. Our results indicate that the regime switching can suppress the extinction of the species. Finally, numerical simulations are carried out to illustrate the obtained theoretical results, where a real-life example is also discussed showing the inclusion of Allee effect in the model provides a better match to the data.

Understanding the impact of Light cone effect on the EoR/CD 21-cm power spectrum

NASA Astrophysics Data System (ADS)

Datta, Kanan K.; Mondal, Rajesh; Ghara, Raghunath; Bharadwaj, Somnath; Choudhury, T. Roy

2018-05-01

Redshifted HI 21-cm signal from the cosmic dawn and epoch of reionization evolve considerably along the LoS. We study the impact of this evolution (so called the light cone effect) on the HI 21-cm power spectrum. It is found that the LC effect has a significant impact on the 3D power spectrum and the change could be up to a factor of few. The LC effect is particularly strong during the cosmic dawn near the `peaks' and `dips' in the power spectrum when plotted with redshift. We also show that the 3D power spectrum, which could fully describe ergodic and periodic signal, losses out some information regarding the second order statistics of the signal as the EoR/CD 21-cm signal is non-ergodic and non-periodic along the line of sight. We show that the multi-frequency angular power spectrum (MAPS) \\ell (\

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Levnajić, Zoran; Department of Mechanical Engineering, University of California Santa Barbara, Santa Barbara, California 93106; Mezić, Igor

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,more » 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.« less

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.

Temporal correlation functions of concentration fluctuations: an anomalous case.

PubMed

Lubelski, Ariel; Klafter, Joseph

2008-10-09

We calculate, within the framework of the continuous time random walk (CTRW) model, multiparticle temporal correlation functions of concentration fluctuations (CCF) in systems that display anomalous subdiffusion. The subdiffusion stems from the nonstationary nature of the CTRW waiting times, which also lead to aging and ergodicity breaking. Due to aging, a system of diffusing particles tends to slow down as time progresses, and therefore, the temporal correlation functions strongly depend on the initial time of measurement. As a consequence, time averages of the CCF differ from ensemble averages, displaying therefore ergodicity breaking. We provide a simple example that demonstrates the difference between these two averages, a difference that might be amenable to experimental tests. We focus on the case of ensemble averaging and assume that the preparation time of the system coincides with the starting time of the measurement. Our analytical calculations are supported by computer simulations based on the CTRW model.

Performance analysis of OOK-based FSO systems in Gamma-Gamma turbulence with imprecise channel models

NASA Astrophysics Data System (ADS)

Feng, Jianfeng; Zhao, Xiaohui

2017-11-01

For an FSO communication system with imprecise channel model, we investigate its system performance based on outage probability, average BEP and ergodic capacity. The exact FSO links are modeled as Gamma-Gamma fading channel in consideration of both atmospheric turbulence and pointing errors, and the imprecise channel model is treated as the superposition of exact channel gain and a Gaussian random variable. After we derive the PDF, CDF and nth moment of the imprecise channel gain, and based on these statistics the expressions for the outage probability, the average BEP and the ergodic capacity in terms of the Meijer's G functions are obtained. Both numerical and analytical results are presented. The simulation results show that the communication performance deteriorates in the imprecise channel model, and approaches to the exact performance curves as the channel model becomes accurate.

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

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

DOE PAGES

Shukla, Anil K.

2017-09-01

Here, dissociation of methanol molecular cations, CH 3OH +, to CH 2OH + 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 angularmore » range close to the 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

Reformulation of time-convolutionless mode-coupling theory near the glass transition

NASA Astrophysics Data System (ADS)

Tokuyama, Michio

2017-10-01

The time-convolutionless mode-coupling theory (TMCT) recently proposed is reformulated under the condition that one of two approximations, which have been used to formulate the original TMCT in addition to the MCT approximations done on a derivation of nonlinear memory function in terms of the intermediate-scattering function, is not employed because it causes unphysical results for intermediate times. The improved TMCT equation is then derived consistently under another approximation. It is first checked that the ergodic to non-ergodic transition obtained by a new equation is exactly the same as that obtained by an old one because the long-time dynamics of both equations coincides with each other. However, it is emphasized that a difference between them appears in the intermediate-time dynamics of physical quantities. Such a difference is explored numerically in the dynamics of a non-Gaussian parameter by employing the Percus-Yevick static structure factor to calculate the nonlinear memory function.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shukla, Anil K.

Here, dissociation of methanol molecular cations, CH 3OH +, to CH 2OH + 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 angularmore » range close to the 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

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.

Quantum computer games: Schrödinger cat and hounds

NASA Astrophysics Data System (ADS)

Gordon, Michal; Gordon, Goren

2012-05-01

The quantum computer game 'Schrödinger 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. 'Schrödinger cat and hounds' demonstrates the effects of superposition, destructive and constructive interference, measurements and entanglement. More advanced concepts, like particle-wave duality and decoherence, can also be taught using the game as a model. The game that has an optimal solution in the classical version, can have many different solutions and a new balance of powers in the quantum world. Game-aided lectures were given to high-school students which showed that it is a valid and entertaining teaching platform.

Generalized Reduction Formula for Discrete Wigner Functions of Multiqubit Systems

NASA Astrophysics Data System (ADS)

Srinivasan, K.; Raghavan, G.

2018-03-01

Density matrices and Discrete Wigner Functions are equally valid representations of multiqubit quantum states. For density matrices, the partial trace operation is used to obtain the quantum state of subsystems, but an analogous prescription is not available for discrete Wigner Functions. Further, the discrete Wigner function corresponding to a density matrix is not unique but depends on the choice of the quantum net used for its reconstruction. In the present work, we derive a reduction formula for discrete Wigner functions of a general multiqubit state which works for arbitrary quantum nets. These results would be useful for the analysis and classification of entangled states and the study of decoherence purely in a discrete phase space setting and also in applications to quantum computing.

Practical Quantum Private Database Queries Based on Passive Round-Robin Differential Phase-shift Quantum Key Distribution.

PubMed

Li, Jian; Yang, Yu-Guang; Chen, Xiu-Bo; Zhou, Yi-Hua; Shi, Wei-Min

2016-08-19

A novel quantum private database query protocol is proposed, based on passive round-robin differential phase-shift quantum key distribution. Compared with previous quantum private database query protocols, the present protocol has the following unique merits: (i) the user Alice can obtain one and only one key bit so that both the efficiency and security of the present protocol can be ensured, and (ii) it does not require to change the length difference of the two arms in a Mach-Zehnder interferometer and just chooses two pulses passively to interfere with so that it is much simpler and more practical. The present protocol is also proved to be secure in terms of the user security and database security.

Dynamics of plasmonic field polarization induced by quantum coherence in quantum dot-metallic nanoshell structures.

PubMed

Sadeghi, S M

2014-09-01

When a hybrid system consisting of a semiconductor quantum dot and a metallic nanoparticle interacts with a laser field, the plasmonic field of the metallic nanoparticle can be normalized by the quantum coherence generated in the quantum dot. In this Letter, we study the states of polarization of such a coherent-plasmonic field and demonstrate how these states can reveal unique aspects of the collective molecular properties of the hybrid system formed via coherent exciton-plasmon coupling. We show that transition between the molecular states of this system can lead to ultrafast polarization dynamics, including sudden reversal of the sense of variations of the plasmonic field and formation of circular and elliptical polarization.

Implementation of a quantum controlled-SWAP gate with photonic circuits

NASA Astrophysics Data System (ADS)

Ono, Takafumi; Okamoto, Ryo; Tanida, Masato; Hofmann, Holger F.; Takeuchi, Shigeki

2017-03-01

Quantum information science addresses how the processing and transmission of information are affected by uniquely quantum mechanical phenomena. Combination of two-qubit gates has been used to realize quantum circuits, however, scalability is becoming a critical problem. The use of three-qubit gates may simplify the structure of quantum circuits dramatically. Among them, the controlled-SWAP (Fredkin) gates are essential since they can be directly applied to important protocols, e.g., error correction, fingerprinting, and optimal cloning. Here we report a realization of the Fredkin gate for photonic qubits. We achieve a fidelity of 0.85 in the computational basis and an output state fidelity of 0.81 for a 3-photon Greenberger-Horne-Zeilinger state. The estimated process fidelity of 0.77 indicates that our Fredkin gate can be applied to various quantum tasks.

Clinical Potential of Quantum Dots

PubMed Central

Iga, Arthur M.; Robertson, John H. P.; Winslet, Marc C.; Seifalian, Alexander M.

2007-01-01

Advances in nanotechnology have led to the development of novel fluorescent probes called quantum dots. Quantum dots have revolutionalized the processes of tagging molecules within research settings and are improving sentinel lymph node mapping and identification in vivo studies. As the unique physical and chemical properties of these fluorescent probes are being unraveled, new potential methods of early cancer detection, rapid spread and therapeutic management, that is, photodynamic therapy are being explored. Encouraging results of optical and real time identification of sentinel lymph nodes and lymph flow using quantum dots in vivo models are emerging. Quantum dots have also superseded many of the limitations of organic fluorophores and are a promising alternative as a research tool. In this review, we examine the promising clinical potential of quantum dots, their hindrances for clinical use and the current progress in abrogating their inherent toxicity. PMID:18317518

Edge physics of the quantum spin Hall insulator from a quantum dot excited by optical absorption.

PubMed

Vasseur, Romain; Moore, Joel E

2014-04-11

The gapless edge modes of the quantum spin Hall insulator form a helical liquid in which the direction of motion along the edge is determined by the spin orientation of the electrons. In order to probe the Luttinger liquid physics of these edge states and their interaction with a magnetic (Kondo) impurity, we consider a setup where the helical liquid is tunnel coupled to a semiconductor quantum dot that is excited by optical absorption, thereby inducing an effective quantum quench of the tunneling. At low energy, the absorption spectrum is dominated by a power-law singularity. The corresponding exponent is directly related to the interaction strength (Luttinger parameter) and can be computed exactly using boundary conformal field theory thanks to the unique nature of the quantum spin Hall edge.

Deutsch, Toffoli, and cnot Gates via Rydberg Blockade of Neutral Atoms

NASA Astrophysics Data System (ADS)

Shi, Xiao-Feng

2018-05-01

Universal quantum gates and quantum error correction (QEC) lie at the heart of quantum-information science. Large-scale quantum computing depends on a universal set of quantum gates, in which some gates may be easily carried out, while others are restricted to certain physical systems. There is a unique three-qubit quantum gate called the Deutsch gate [D (θ )], from which a circuit can be constructed so that any feasible quantum computing is attainable. We design an easily realizable D (θ ) by using the Rydberg blockade of neutral atoms, where θ can be tuned to any value in [0 ,π ] by adjusting the strengths of external control fields. Using similar protocols, we further show that both the Toffoli and controlled-not gates can be achieved with only three laser pulses. The Toffoli gate, being universal for classical reversible computing, is also useful for QEC, which plays an important role in quantum communication and fault-tolerant quantum computation. The possibility and speed of realizing these gates shed light on the study of quantum information with neutral atoms.

OpenFlow arbitrated programmable network channels for managing quantum metadata

DOE PAGES

Dasari, Venkat R.; Humble, Travis S.

2016-10-10

Quantum networks must classically exchange complex metadata between devices in order to carry out information for protocols such as teleportation, super-dense coding, and quantum key distribution. Demonstrating the integration of these new communication methods with existing network protocols, channels, and data forwarding mechanisms remains an open challenge. Software-defined networking (SDN) offers robust and flexible strategies for managing diverse network devices and uses. We adapt the principles of SDN to the deployment of quantum networks, which are composed from unique devices that operate according to the laws of quantum mechanics. We show how quantum metadata can be managed within a software-definedmore » network using the OpenFlow protocol, and we describe how OpenFlow management of classical optical channels is compatible with emerging quantum communication protocols. We next give an example specification of the metadata needed to manage and control quantum physical layer (QPHY) behavior and we extend the OpenFlow interface to accommodate this quantum metadata. Here, we conclude by discussing near-term experimental efforts that can realize SDN’s principles for quantum communication.« less

OpenFlow arbitrated programmable network channels for managing quantum metadata

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dasari, Venkat R.; Humble, Travis S.

Quantum networks must classically exchange complex metadata between devices in order to carry out information for protocols such as teleportation, super-dense coding, and quantum key distribution. Demonstrating the integration of these new communication methods with existing network protocols, channels, and data forwarding mechanisms remains an open challenge. Software-defined networking (SDN) offers robust and flexible strategies for managing diverse network devices and uses. We adapt the principles of SDN to the deployment of quantum networks, which are composed from unique devices that operate according to the laws of quantum mechanics. We show how quantum metadata can be managed within a software-definedmore » network using the OpenFlow protocol, and we describe how OpenFlow management of classical optical channels is compatible with emerging quantum communication protocols. We next give an example specification of the metadata needed to manage and control quantum physical layer (QPHY) behavior and we extend the OpenFlow interface to accommodate this quantum metadata. Here, we conclude by discussing near-term experimental efforts that can realize SDN’s principles for quantum communication.« less

Black hole based quantum computing in labs and in the sky

NASA Astrophysics Data System (ADS)

Dvali, Gia; Panchenko, Mischa

2016-08-01

Analyzing some well established facts, we give a model-independent parameterization of black hole quantum computing in terms of a set of macro and micro quantities and their relations. These include the relations between the extraordinarily-small energy gap of black hole qubits and important time-scales of information-processing, such as, scrambling time and Page's time. We then show, confirming and extending previous results, that other systems of nature with identical quantum informatics features are attractive Bose-Einstein systems at the critical point of quantum phase transition. Here we establish a complete isomorphy between the quantum computational properties of these two systems. In particular, we show that the quantum hair of a critical condensate is strikingly similar to the quantum hair of a black hole. Irrespectively whether one takes the similarity between the two systems as a remarkable coincidence or as a sign of a deeper underlying connection, the following is evident. Black holes are not unique in their way of quantum information processing and we can manufacture black hole based quantum computers in labs by taking advantage of quantum criticality.

Flow and transport in digitized images of Berea sandstone: ergodicity, stationarity and upscaling

NASA Astrophysics Data System (ADS)

Puyguiraud, A.; Dentz, M.; Gouze, P.

2017-12-01

We perform Stokes flow simulations on digitized images of a Berea sandstone sample obtained through micro-tomography imaging and segmentation processes. We obtain accurate information on the transport using a streamline reconstruction algorithm which uses the velocity field obtained from the flow simulation as input data. This technique is based on the method proposed by Pollock (Groundwater, 1988) but employs a quadratic interpolation near the rock mesh cells of the domain similarly to Mostaghimi et al. (SPE, 2012). This allows an accurate resolution of the velocity field near the solid interface which plays an important role on the transport characteristics, such as the probability density of first arrival times and the growth of the mean squared displacement, among others, which exhibit non-Fickian behavior. We analyze Lagrangian and Eulerian velocity statistics and their relation, and then focus on the ergodicity and the stationarity properties of the transport.We analyze the temporal evolution of Lagrangian velocity statistics for different injection conditions, and findd quick convergence to a limiting velocity distribution, indicating the transport to be near-stationary. The equivalence between velocity samplings within and across streamlines, as well as the independency of the statistics on the number of sampled streamlines, lead as to conclude that the transport may be modeled as ergodic.These characteristics then allow us to upscale the 3-dimensional simulations using a 1-dimensional Continuous Time Random Walk model. This model, parametrized by the velocity results and the characteristic correlation length obtained from the above mentioned simulations, is able to efficiently reproduce the results and to predict larger scale behaviors.

Symmetry, Statistics and Structure in MHD Turbulence

NASA Technical Reports Server (NTRS)

Shebalin, John V.

2007-01-01

Here, we examine homogeneous MHD turbulence in terms of truncated Fourier series. The ideal MHD equations and the associated statistical theory of absolute equilibrium ensembles are symmetric under P, C and T. However, the presence of invariant helicities, which are pseudoscalars under P and C, dynamically breaks this symmetry. This occurs because the surface of constant energy in phase space has disjoint parts, called components: while ensemble averages are taken over all components, a dynamical phase trajectory is confined to only one component. As the Birkhoff-Khinchin theorem tells us, ideal MHD turbulence is thus non-ergodic. This non-ergodicity manifests itself in low-wave number Fourier modes that have large mean values (while absolute ensemble theory predicts mean values of zero). Therefore, we have coherent structure in ideal MHD turbulence. The level of non-ergodicity and amount of energy contained in the associated coherent structure depends on the values of the helicities, as well as on the presence, or not, of a mean magnetic field and/or overall rotation. In addition to the well known cross and magnetic helicities, we also present a new invariant, which we call the parallel helicity, since it occurs when mean field and rotation axis are aligned. The question of applicability of these results to real (i.e., dissipative) MHD turbulence is also examined. Several long-time numerical simulations on a 64(exp 3) grid are given as examples. It is seen that coherent structure begins to form before decay dominates over nonlinearity. The connection of these results with inverse spectral cascades, selective decay, and magnetic dynamos is also discussed.

Probing the structural dependency of photoinduced properties of colloidal quantum dots using metal-oxide photo-active substrates.

PubMed

Patty, Kira; Sadeghi, Seyed M; Campbell, Quinn; Hamilton, Nathan; West, Robert G; Mao, Chuanbin

2014-09-21

We used photoactive substrates consisting of about 1 nm coating of a metal oxide on glass substrates to investigate the impact of the structures of colloidal quantum dots on their photophysical and photochemical properties. We showed during irradiation these substrates can interact uniquely with such quantum dots, inducing distinct forms of photo-induced processes when they have different cores, shells, or ligands. In particular, our results showed that for certain types of core-shell quantum dot structures an ultrathin layer of a metal oxide can reduce suppression of quantum efficiency of the quantum dots happening when they undergo extensive photo-oxidation. This suggests the possibility of shrinking the sizes of quantum dots without significant enhancement of their non-radiative decay rates. We show that such quantum dots are not influenced significantly by Coulomb blockade or photoionization, while those without a shell can undergo a large amount of photo-induced fluorescence enhancement via such blockade when they are in touch with the metal oxide.

Probing the structural dependency of photoinduced properties of colloidal quantum dots using metal-oxide photo-active substrates

PubMed Central

Patty, Kira; Sadeghi, Seyed M.; Campbell, Quinn; Hamilton, Nathan; West, Robert G.; Mao, Chuanbin

2014-01-01

We used photoactive substrates consisting of about 1 nm coating of a metal oxide on glass substrates to investigate the impact of the structures of colloidal quantum dots on their photophysical and photochemical properties. We showed during irradiation these substrates can interact uniquely with such quantum dots, inducing distinct forms of photo-induced processes when they have different cores, shells, or ligands. In particular, our results showed that for certain types of core-shell quantum dot structures an ultrathin layer of a metal oxide can reduce suppression of quantum efficiency of the quantum dots happening when they undergo extensive photo-oxidation. This suggests the possibility of shrinking the sizes of quantum dots without significant enhancement of their non-radiative decay rates. We show that such quantum dots are not influenced significantly by Coulomb blockade or photoionization, while those without a shell can undergo a large amount of photo-induced fluorescence enhancement via such blockade when they are in touch with the metal oxide. PMID:25316953

Quantum spin liquids: a review.

PubMed

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.

Quantum Entanglement and the Topological Order of Fractional Hall States

NASA Astrophysics Data System (ADS)

Rezayi, Edward

2015-03-01

Fractional quantum Hall states or, more generally, topological phases of matter defy Landau classification based on order parameter and broken symmetry. Instead they have been characterized by their topological order. Quantum information concepts, such as quantum entanglement, appear to provide the most efficient method of detecting topological order solely from the knowledge of the ground state wave function. This talk will focus on real-space bi-partitioning of quantum Hall states and will present both exact diagonalization and quantum Monte Carlo studies of topological entanglement entropy in various geometries. Results on the torus for non-contractible cuts are quite rich and, through the use of minimum entropy states, yield the modular S-matrix and hence uniquely determine the topological order, as shown in recent literature. Concrete examples of minimum entropy states from known quantum Hall wave functions and their corresponding quantum numbers, used in exact diagonalizations, will be given. In collaboration with Clare Abreu and Raul Herrera. Supported by DOE Grant DE-SC0002140.

On Schrödinger's bridge problem

NASA Astrophysics Data System (ADS)

Friedland, S.

2017-11-01

In the first part of this paper we generalize Georgiou-Pavon's result that a positive square matrix can be scaled uniquely to a column stochastic matrix which maps a given positive probability vector to another given positive probability vector. In the second part we prove that a positive quantum channel can be scaled to another positive quantum channel which maps a given positive definite density matrix to another given positive definite density matrix using Brouwer's fixed point theorem. This result proves the Georgiou-Pavon conjecture for two positive definite density matrices, made in their recent paper. We show that the fixed points are unique for certain pairs of positive definite density matrices. Bibliography: 15 titles.

Quantum-gravity predictions for the fine-structure constant

NASA Astrophysics Data System (ADS)

Eichhorn, Astrid; Held, Aaron; Wetterich, Christof

2018-07-01

Asymptotically safe quantum fluctuations of gravity can uniquely determine the value of the gauge coupling for a large class of grand unified models. In turn, this makes the electromagnetic fine-structure constant calculable. The balance of gravity and matter fluctuations results in a fixed point for the running of the gauge coupling. It is approached as the momentum scale is lowered in the transplanckian regime, leading to a uniquely predicted value of the gauge coupling at the Planck scale. The precise value of the predicted fine-structure constant depends on the matter content of the grand unified model. It is proportional to the gravitational fluctuation effects for which computational uncertainties remain to be settled.

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.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cheng, Liwen, E-mail: lwcheng@yzu.edu.cn; 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 droopmore » 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.« less

Structure of the thermodynamic arrow of time in classical and quantum theories

NASA Astrophysics Data System (ADS)

Korzekwa, Kamil

2017-05-01

In this work we analyze the structure of the thermodynamic arrow of time, defined by transformations that leave the thermal equilibrium state unchanged, in classical (incoherent) and quantum (coherent) regimes. We note that in the infinite-temperature limit, the thermodynamic ordering of states in both regimes exhibits a lattice structure. This means that when energy does not matter and the only thermodynamic resource is given by information, the thermodynamic arrow of time has a very specific structure. Namely, for any two states at present there exists a unique state in the past consistent with them and with all possible joint pasts. Similarly, there also exists a unique state in the future consistent with those states and with all possible joint futures. We also show that the lattice structure in the classical regime is broken at finite temperatures, i.e., when energy is a relevant thermodynamic resource. Surprisingly, however, we prove that in the simplest quantum scenario of a two-dimensional system, this structure is preserved at finite temperatures. We provide the physical interpretation of these results by introducing and analyzing the history erasure process, and point out that quantum coherence may be a necessary resource for the existence of an optimal erasure process.

TiO2 quantum dots embedded in bamboo-like porous carbon nanotubes as ultra high power and long life anodes for lithium ion batteries

NASA Astrophysics Data System (ADS)

Tang, Yakun; Liu, Lang; Wang, Xingchao; Jia, Dianzeng; Xia, Wei; Zhao, Zongbin; Qiu, Jieshan

2016-07-01

TiO2 quantum dots embedded in bamboo-like porous carbon nanotubes have been constructed through the pyrolysis of sulfonated polymer nanotubes and TiO2 hybrids. The TiO2 quantum dots are formed during the pyrolysis, due to the space confinement within the highly cross-linked copolymer networks. The sulfonation degree of the polymer nanotubes is a critical factor to ensure the formation of the unique interpenetrating structure. The nanocomposites exhibit high reversible capacity of 523 mAh g-1 at 100 mA g-1 after 200 cycles, excellent rate capability and superior long-term cycling stability at high current density, which could attain a high discharge capacity of 189 mAh g-1 at 2000 mA g-1 for up to 2000 cycles. The enhanced electrochemical performance of the nanocomposites benefit from the uniform distribution of TiO2 quantum dots, high electronic conductivity of porous carbons and unique interpenetrating structure, which simultaneously solved the major problems of TiO2 anode facing the pulverization, loss of electrical contact and particle aggregation.

Quantum Tunneling of Water in Beryl. A New State of the Water Molecule

DOE PAGES

Kolesnikov, Alexander I.; Reiter, George F.; Choudhury, Narayani; ...

2016-04-22

When using neutron scattering and ab initio simulations, we document the discovery of a new “quantum tunneling state” of the water molecule confined in 5 Å channels in the mineral beryl, characterized by extended proton and electron delocalization. We observed a number of peaks in the inelastic neutron scattering spectra that were uniquely assigned to water quantum tunneling. Additionally, the water proton momentum distribution was measured with deep inelastic neutron scattering, which directly revealed coherent delocalization of the protons in the ground state.

Quantum Tunneling of Water in Beryl. A New State of the Water Molecule

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kolesnikov, Alexander I.; Reiter, George F.; Choudhury, Narayani

When using neutron scattering and ab initio simulations, we document the discovery of a new “quantum tunneling state” of the water molecule confined in 5 Å channels in the mineral beryl, characterized by extended proton and electron delocalization. We observed a number of peaks in the inelastic neutron scattering spectra that were uniquely assigned to water quantum tunneling. Additionally, the water proton momentum distribution was measured with deep inelastic neutron scattering, which directly revealed coherent delocalization of the protons in the ground state.

High resolution study of magnetic ordering at absolute zero.

PubMed

Lee, M; Husmann, A; Rosenbaum, T F; Aeppli, G

2004-05-07

High resolution pressure measurements in the zero-temperature limit provide a unique opportunity to study the behavior of strongly interacting, itinerant electrons with coupled spin and charge degrees of freedom. Approaching the precision that has become the hallmark of experiments on classical critical phenomena, we characterize the quantum critical behavior of the model, elemental antiferromagnet chromium, lightly doped with vanadium. We resolve the sharp doubling of the Hall coefficient at the quantum critical point and trace the dominating effects of quantum fluctuations up to surprisingly high temperatures.

Berry phase jumps and giant nonreciprocity in Dirac quantum dots

NASA Astrophysics Data System (ADS)

Rodriguez-Nieva, Joaquin F.; Levitov, Leonid S.

2016-12-01

We predict that a strong nonreciprocity in the resonance spectra of Dirac quantum dots can be induced by the Berry phase. The nonreciprocity arises in relatively weak magnetic fields and is manifest in anomalously large field-induced splittings of quantum dot resonances which are degenerate at B =0 due to time-reversal symmetry. This exotic behavior, which is governed by field-induced jumps in the Berry phase of confined electronic states, is unique to quantum dots in Dirac materials and is absent in conventional quantum dots. The effect is strong for gapless Dirac particles and can overwhelm the B -induced orbital and Zeeman splittings. A finite Dirac mass suppresses the effect. The nonreciprocity, predicted for generic two-dimensional Dirac materials, is accessible through Faraday and Kerr optical rotation measurements and scanning tunneling spectroscopy.

Practical Quantum Private Database Queries Based on Passive Round-Robin Differential Phase-shift Quantum Key Distribution

PubMed Central

Li, Jian; Yang, Yu-Guang; Chen, Xiu-Bo; Zhou, Yi-Hua; Shi, Wei-Min

2016-01-01

A novel quantum private database query protocol is proposed, based on passive round-robin differential phase-shift quantum key distribution. Compared with previous quantum private database query protocols, the present protocol has the following unique merits: (i) the user Alice can obtain one and only one key bit so that both the efficiency and security of the present protocol can be ensured, and (ii) it does not require to change the length difference of the two arms in a Mach-Zehnder interferometer and just chooses two pulses passively to interfere with so that it is much simpler and more practical. The present protocol is also proved to be secure in terms of the user security and database security. PMID:27539654

Phase transition with trivial quantum criticality in an anisotropic Weyl semimetal

NASA Astrophysics Data System (ADS)

Li, Xin; Wang, Jing-Rong; Liu, Guo-Zhu

2018-05-01

When a metal undergoes continuous quantum phase transition, the correlation length diverges at the critical point and the quantum fluctuation of order parameter behaves as a gapless bosonic mode. Generically, the coupling of this boson to fermions induces a variety of unusual quantum critical phenomena, such as non-Fermi liquid behavior and various emergent symmetries. Here, we perform a renormalization group analysis of the semimetal-superconductor quantum criticality in a three-dimensional anisotropic Weyl semimetal. Surprisingly, distinct from previously studied quantum critical systems, the anomalous dimension of anisotropic Weyl fermions flows to zero very quickly with decreasing energy, and the quasiparticle residue takes a nonzero value. These results indicate that the quantum fluctuation of superconducting order parameter is irrelevant at low energies, and a simple mean-field calculation suffices to capture the essential physics of the superconducting transition. We thus obtain a phase transition that exhibits trivial quantum criticality, which is unique comparing to other invariably nontrivial quantum critical systems. Our theoretical prediction can be experimentally verified by measuring the fermion spectral function and specific heat.

Electrical control of single hole spins in nanowire quantum dots.

PubMed

Pribiag, V S; Nadj-Perge, S; Frolov, S M; van den Berg, J W G; van Weperen, I; Plissard, S R; Bakkers, E P A M; Kouwenhoven, L P

2013-03-01

The development of viable quantum computation devices will require the ability to preserve the coherence of quantum bits (qubits). Single electron spins in semiconductor quantum dots are a versatile platform for quantum information processing, but controlling decoherence remains a considerable challenge. Hole spins in III-V semiconductors have unique properties, such as a strong spin-orbit interaction and weak coupling to nuclear spins, and therefore, have the potential for enhanced spin control and longer coherence times. A weaker hyperfine interaction has previously been reported in self-assembled quantum dots using quantum optics techniques, but the development of hole-spin-based electronic devices in conventional III-V heterostructures has been limited by fabrication challenges. Here, we show that gate-tunable hole quantum dots can be formed in InSb nanowires and used to demonstrate Pauli spin blockade and electrical control of single hole spins. The devices are fully tunable between hole and electron quantum dots, which allows the hyperfine interaction strengths, g-factors and spin blockade anisotropies to be compared directly in the two regimes.

Quantum measurement-induced antiferromagnetic order and density modulations in ultracold Fermi gases in optical lattices

NASA Astrophysics Data System (ADS)

Mazzucchi, Gabriel; Caballero-Benitez, Santiago F.; Mekhov, Igor B.

2016-08-01

Ultracold atomic systems offer a unique tool for understanding behavior of matter in the quantum degenerate regime, promising studies of a vast range of phenomena covering many disciplines from condensed matter to quantum information and particle physics. Coupling these systems to quantized light fields opens further possibilities of observing delicate effects typical of quantum optics in the context of strongly correlated systems. Measurement backaction is one of the most funda- mental manifestations of quantum mechanics and it is at the core of many famous quantum optics experiments. Here we show that quantum backaction of weak measurement can be used for tailoring long-range correlations of ultracold fermions, realizing quantum states with spatial modulations of the density and magnetization, thus overcoming usual requirement for a strong interatomic interactions. We propose detection schemes for implementing antiferromagnetic states and density waves. We demonstrate that such long-range correlations cannot be realized with local addressing, and they are a consequence of the competition between global but spatially structured backaction of weak quantum measurement and unitary dynamics of fermions.

Protecting Information

NASA Astrophysics Data System (ADS)

Loepp, Susan; Wootters, William K.

2006-09-01

For many everyday transmissions, it is essential to protect digital information from noise or eavesdropping. This undergraduate introduction to error correction and cryptography is unique in devoting several chapters to quantum cryptography and quantum computing, thus providing a context in which ideas from mathematics and physics meet. By covering such topics as Shor's quantum factoring algorithm, this text informs the reader about current thinking in quantum information theory and encourages an appreciation of the connections between mathematics and science.Of particular interest are the potential impacts of quantum physics:(i) a quantum computer, if built, could crack our currently used public-key cryptosystems; and (ii) quantum cryptography promises to provide an alternative to these cryptosystems, basing its security on the laws of nature rather than on computational complexity. No prior knowledge of quantum mechanics is assumed, but students should have a basic knowledge of complex numbers, vectors, and matrices. Accessible to readers familiar with matrix algebra, vector spaces and complex numbers First undergraduate text to cover cryptography, error-correction, and quantum computation together Features exercises designed to enhance understanding, including a number of computational problems, available from www.cambridge.org/9780521534765

Spatially selective assembly of quantum dot light emitters in an LED using engineered peptides.

PubMed

Demir, Hilmi Volkan; Seker, Urartu Ozgur Safak; Zengin, Gulis; Mutlugun, Evren; Sari, Emre; Tamerler, Candan; Sarikaya, Mehmet

2011-04-26

Semiconductor nanocrystal quantum dots are utilized in numerous applications in nano- and biotechnology. In device applications, where several different material components are involved, quantum dots typically need to be assembled at explicit locations for enhanced functionality. Conventional approaches cannot meet these requirements where assembly of nanocrystals is usually material-nonspecific, thereby limiting the control of their spatial distribution. Here we demonstrate directed self-assembly of quantum dot emitters at material-specific locations in a color-conversion LED containing several material components including a metal, a dielectric, and a semiconductor. We achieve a spatially selective immobilization of quantum dot emitters by using the unique material selectivity characteristics provided by the engineered solid-binding peptides as smart linkers. Peptide-decorated quantum dots exhibited several orders of magnitude higher photoluminescence compared to the control groups, thus, potentially opening up novel ways to advance these photonic platforms in applications ranging from chemical to biodetection.

Time-resolved energy transduction in a quantum capacitor

PubMed Central

Jung, Woojin; Cho, Doohee; Kim, Min-Kook; Choi, Hyoung Joon; Lyo, In-Whan

2011-01-01

The capability to deposit charge and energy quantum-by-quantum into a specific atomic site could lead to many previously unidentified applications. Here we report on the quantum capacitor formed by a strongly localized field possessing such capability. We investigated the charging dynamics of such a capacitor by using the unique scanning tunneling microscopy that combines nanosecond temporal and subangstrom spatial resolutions, and by using Si(001) as the electrode as well as the detector for excitations produced by the charging transitions. We show that sudden switching of a localized field induces a transiently empty quantum dot at the surface and that the dot acts as a tunable excitation source with subangstrom site selectivity. The timescale in the deexcitation of the dot suggests the formation of long-lived, excited states. Our study illustrates that a quantum capacitor has serious implications not only for the bottom-up nanotechnology but also for future switching devices. PMID:21817067

Gate-controlled electromechanical backaction induced by a quantum dot

NASA Astrophysics Data System (ADS)

Okazaki, Yuma; Mahboob, Imran; Onomitsu, Koji; Sasaki, Satoshi; Yamaguchi, Hiroshi

2016-04-01

Semiconductor-based quantum structures integrated into mechanical resonators have emerged as a unique platform for generating entanglement between macroscopic phononic and mesocopic electronic degrees of freedom. A key challenge to realizing this is the ability to create and control the coupling between two vastly dissimilar systems. Here, such coupling is demonstrated in a hybrid device composed of a gate-defined quantum dot integrated into a piezoelectricity-based mechanical resonator enabling milli-Kelvin phonon states to be detected via charge fluctuations in the quantum dot. Conversely, the single electron transport in the quantum dot can induce a backaction onto the mechanics where appropriate bias of the quantum dot can enable damping and even current-driven amplification of the mechanical motion. Such electron transport induced control of the mechanical resonator dynamics paves the way towards a new class of hybrid semiconductor devices including a current injected phonon laser and an on-demand single phonon emitter.

CGS-MSFSS Project report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Harvey-Collard, Patrick

2015-10-27

From January 2015 to July 2015, I was doing research at Sandia National Laboratories in Albuquerque, United States. My work there consisted of performing experimental measurements using Sandia’s unique silicon quantum computing platform. The project is about coupling donor spin quantum bits, or qubits, to quantum dots in a silicon nanostructure based on conventional microchip technology. During the project, I devised a new quantum state readout mechanism that allow better, longer lived measurement signals. The measurement (or readout) mechanism is key to any qubit architecture. Next, I was able to demonstrate a quantum manipulation of the two-electron spin states ofmore » the coupled donor and quantum dot system. This constitutes a breakthrough for donor spin qubits in silicon because it could enable larger systems consisting of many qubits. This project will lead to publications in scientific journals, presentations in international conferences, and generates exciting new opportunities for manipulating nature at the nanoscale.« less

Quantum solitonic wave-packet of a meso-scopic system in singularity free gravity

NASA Astrophysics Data System (ADS)

Buoninfante, Luca; Lambiase, Gaetano; Mazumdar, Anupam

2018-06-01

In this paper we will discuss how to localise a quantum wave-packet due to self-gravitating meso-scopic object by taking into account gravitational self-interaction in the Schrödinger equation beyond General Relativity. In particular, we will study soliton-like solutions in infinite derivative ghost free theories of gravity, which resolves the gravitational 1 / r singularity in the potential. We will show a unique feature that the quantum spread of such a gravitational system is larger than that of the Newtonian gravity, therefore enabling us a window of opportunity to test classical and quantum properties of such theories of gravity in the near future at a table-top experiment.

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.

Identifying a correlated spin fluctuation in an entangled spin chain subject to a quantum phase transition.

PubMed

Shimizu, Kaoru; Tokura, Yasuhiro

2015-12-01

This paper presents a theoretical framework for analyzing the quantum fluctuation properties of a quantum spin chain subject to a quantum phase transition. We can quantify the fluctuation properties by examining the correlation between the fluctuations of two neighboring spins subject to the quantum uncertainty. To do this, we first compute the reduced density matrix ρ of the spin pair from the ground state |Ψ⟩ of a spin chain, and then identify the quantum correlation part ρ(q) embedded in ρ. If the spin chain is translationally symmetric and characterized by a nearest-neighbor two-body spin interaction, we can determine uniquely the form of ρ(q) as W|Φ〉〈Φ| with the weight W ≤1, and quantify the fluctuation properties using the two-spin entangled state |Φ〉. We demonstrate the framework for a transverse-field quantum Ising spin chain and indicate its validity for more general spin chain models.

On homogeneous second order linear general quantum difference equations.

PubMed

Faried, Nashat; Shehata, Enas M; El Zafarani, Rasha M

2017-01-01

In this paper, we prove the existence and uniqueness of solutions of the β -Cauchy problem of second order β -difference equations [Formula: see text] [Formula: see text], in a neighborhood of the unique fixed point [Formula: see text] of the strictly increasing continuous function β , defined on an interval [Formula: see text]. These equations are based on the general quantum difference operator [Formula: see text], which is defined by [Formula: see text], [Formula: see text]. We also construct a fundamental set of solutions for the second order linear homogeneous β -difference equations when the coefficients are constants and study the different cases of the roots of their characteristic equations. Finally, we drive the Euler-Cauchy β -difference equation.

Temporal behavior of the effective diffusion coefficients for transport in heterogeneous saturated aquifers

NASA Astrophysics Data System (ADS)

Suciu, N.; Vamos, C.; Vereecken, H.; Vanderborght, J.; Hardelauf, H.

2003-04-01

When the small scale transport is modeled by a Wiener process and the large scale heterogeneity by a random velocity field, the effective coefficients, Deff, can be decomposed as sums between the local coefficient, D, a contribution of the random advection, Dadv, and a contribution of the randomness of the trajectory of plume center of mass, Dcm: Deff=D+Dadv-Dcm. The coefficient Dadv is similar to that introduced by Taylor in 1921, and more recent works associate it with the thermodynamic equilibrium. The ``ergodic hypothesis'' says that over large time intervals Dcm vanishes and the effect of the heterogeneity is described by Dadv=Deff-D. In this work we investigate numerically the long time behavior of the effective coefficients as well as the validity of the ergodic hypothesis. The transport in every realization of the velocity field is modeled with the Global Random Walk Algorithm, which is able to track as many particles as necessary to achieve a statistically reliable simulation of the process. Averages over realizations are further used to estimate mean coefficients and standard deviations. In order to remain in the frame of most of the theoretical approaches, the velocity field was generated in a linear approximation and the logarithm of the hydraulic conductivity was taken to be exponential decaying correlated with variance equal to 0.1. Our results show that even in these idealized conditions, the effective coefficients tend to asymptotic constant values only when the plume travels thousands of correlations lengths (while the first order theories usually predict Fickian behavior after tens of correlations lengths) and that the ergodicity conditions are still far from being met.

Single-Station Sigma for the Iranian Strong Motion Stations

NASA Astrophysics Data System (ADS)

Zafarani, H.; Soghrat, M. R.

2017-11-01

In development of ground motion prediction equations (GMPEs), the residuals are assumed to have a log-normal distribution with a zero mean and a standard deviation, designated as sigma. Sigma has significant effect on evaluation of seismic hazard for designing important infrastructures such as nuclear power plants and dams. Both aleatory and epistemic uncertainties are involved in the sigma parameter. However, ground-motion observations over long time periods are not available at specific sites and the GMPEs have been derived using observed data from multiple sites for a small number of well-recorded earthquakes. Therefore, sigma is dominantly related to the statistics of the spatial variability of ground motion instead of temporal variability at a single point (ergodic assumption). The main purpose of this study is to reduce the variability of the residuals so as to handle it as epistemic uncertainty. In this regard, it is tried to partially apply the non-ergodic assumption by removing repeatable site effects from total variability of six GMPEs driven from the local, Europe-Middle East and worldwide data. For this purpose, we used 1837 acceleration time histories from 374 shallow earthquakes with moment magnitudes ranging from M w 4.0 to 7.3 recorded at 370 stations with at least two recordings per station. According to estimated single-station sigma for the Iranian strong motion stations, the ratio of event-corrected single-station standard deviation ( Φ ss) to within-event standard deviation ( Φ) is about 0.75. In other words, removing the ergodic assumption on site response resulted in 25% reduction of the within-event standard deviation that reduced the total standard deviation by about 15%.

Ground Motion Uncertainty and Variability (single-station sigma): Insights from Euroseistest, Greece

NASA Astrophysics Data System (ADS)

Ktenidou, O. J.; Roumelioti, Z.; Abrahamson, N. A.; Cotton, F.; Pitilakis, K.

2014-12-01

Despite recent improvements in networks and data, the global aleatory uncertainty (sigma) in GMPEs is still large. One reason is the ergodic approach, where we combine data in space to make up for lack of data in time. By estimating the systematic site response, we can make site-specific GMPEs and use a lower, site-specific uncertainty: single-station sigma. In this study we use the EUROSEISTEST database (http://euroseisdb.civil.auth.gr), which has two distinct advantages: good existing knowledge of site conditions at all stations, and careful relocation of the recorded events. Constraining the site and source parameters as best we can, we minimise the within- and between-events components of the global, ergodic sigma. Following that, knowledge of the site response from empirical and theoretical approaches permits us to move on to single-station sigma. The variability per site is not clearly correlated to the site class. We show that in some cases knowledge of Vs30 is not sufficient, and that site-specific data are needed to capture the response, possibly due to 2D/3D effects from complex geometry. Our values of single-station sigma are low compared to the literature. This may be due to the good ray coverage we have in all directions for small, nearby records. Indeed, our single-station sigma values are similar to published single-path values, which means that they may correspond to a fully -rather than partially- non-ergodic approach. We find larger ground motion variability for short distances and small magnitudes. This may be related to the uncertainty in the depth affecting nearby records more, or to stress drop and causing trade-offs between the source and site terms for small magnitudes.

Nonequilibrium viscosity of glass

NASA Astrophysics Data System (ADS)

Mauro, John C.; Allan, Douglas C.; Potuzak, Marcel

2009-09-01

Since glass is a nonequilibrium material, its properties depend on both composition and thermal history. While most prior studies have focused on equilibrium liquid viscosity, an accurate description of nonequilibrium viscosity is essential for understanding the low temperature dynamics of glass. Departure from equilibrium occurs as a glass-forming system is cooled through the glass transition range. The glass transition involves a continuous breakdown of ergodicity as the system gradually becomes trapped in a subset of the available configurational phase space. At very low temperatures a glass is perfectly nonergodic (or “isostructural”), and the viscosity is described well by an Arrhenius form. However, the behavior of viscosity during the glass transition range itself is not yet understood. In this paper, we address the problem of glass viscosity using the enthalpy landscape model of Mauro and Loucks [Phys. Rev. B 76, 174202 (2007)] for selenium, an elemental glass former. To study a wide range of thermal histories, we compute nonequilibrium viscosity with cooling rates from 10-12 to 1012K/s . Based on these detailed landscape calculations, we propose a simplified phenomenological model capturing the essential physics of glass viscosity. The phenomenological model incorporates an ergodicity parameter that accounts for the continuous breakdown of ergodicity at the glass transition. We show a direct relationship between the nonequilibrium viscosity parameters and the fragility of the supercooled liquid. The nonequilibrium viscosity model is validated against experimental measurements of Corning EAGLE XG™ glass. The measurements are performed using a specially designed beam-bending apparatus capable of accurate nonequilibrium viscosity measurements up to 1016Pas . Using a common set of parameters, the phenomenological model provides an accurate description of EAGLE XG™ viscosity over the full range of measured temperatures and fictive temperatures.

Simulation of a broadband nano-biosensor based on an onion-like quantum dot-quantum well structure

DOE Office of Scientific and Technical Information (OSTI.GOV)

Absalan, H; SalmanOgli, A; Rostami, R

The fluorescence resonance energy transfer is studied between modified quantum-dots and quantum-wells used as a donor and an acceptor. Because of the unique properties of quantum dots, including diverse surface modification flexibility, bio-compatibility, high quantum yields and wide absorption, their use as nano-biosensors and bio-markers used in diagnosis of cancer is suggested. The fluorescence resonance energy transfer is simulated in a quantum dot-quantum well system, where the energy can flow from donor to acceptor. If the energy transfer can be either turned on or off by a specific interaction, such as interaction with any dyes, a molecular binding event ormore » a cleavage reaction, a sensor can be designed (under assumption that the healthy cells have a known effect or unyielding effect on output parameters while cancerous cells, due to their pandemic optical properties, can impact the fluorescence resonance energy transfer parameters). The developed nano-biosensor can operate in a wide range of wavelengths (310 - 760 nm). (laser applications in biology and medicine)« less

Probing the structural dependency of photoinduced properties of colloidal quantum dots using metal-oxide photo-active substrates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Patty, Kira; Campbell, Quinn; Hamilton, Nathan

We used photoactive substrates consisting of about 1 nm coating of a metal oxide on glass substrates to investigate the impact of the structures of colloidal quantum dots on their photophysical and photochemical properties. We showed during irradiation these substrates can interact uniquely with such quantum dots, inducing distinct forms of photo-induced processes when they have different cores, shells, or ligands. In particular, our results showed that for certain types of core-shell quantum dot structures an ultrathin layer of a metal oxide can reduce suppression of quantum efficiency of the quantum dots happening when they undergo extensive photo-oxidation. This suggestsmore » the possibility of shrinking the sizes of quantum dots without significant enhancement of their non-radiative decay rates. We show that such quantum dots are not influenced significantly by Coulomb blockade or photoionization, while those without a shell can undergo a large amount of photo-induced fluorescence enhancement via such blockade when they are in touch with the metal oxide.« less

InGaAs/InP quantum wires grown on silicon with adjustable emission wavelength at telecom bands

NASA Astrophysics Data System (ADS)

Han, Yu; Li, Qiang; Ng, Kar Wei; Zhu, Si; Lau, Kei May

2018-06-01

We report the growth of vertically stacked InGaAs/InP quantum wires on (001) Si substrates with adjustable room-temperature emission at telecom bands. Based on a self-limiting growth mode in selective area metal–organic chemical vapor deposition, crescent-shaped InGaAs quantum wires with variable dimensions are embedded within InP nano-ridges. With extensive transmission electron microscopy studies, the growth transition and morphology change from quantum wires to ridge quantum wells (QWs) have been revealed. As a result, we are able to decouple the quantum wires from ridge QWs and manipulate their dimensions by scaling the growth time. With minimized lateral dimension and their unique positioning, the InGaAs/InP quantum wires are more immune to dislocations and more efficient in radiative processes, as evidenced by their excellent optical quality at telecom-bands. These promising results thus highlight the potential of combining low-dimensional quantum wire structures with the aspect ratio trapping process for integrating III–V nano-light emitters on mainstream (001) Si substrates.

InGaAs/InP quantum wires grown on silicon with adjustable emission wavelength at telecom bands.

PubMed

Han, Yu; Li, Qiang; Ng, Kar Wei; Zhu, Si; Lau, Kei May

2018-06-01

We report the growth of vertically stacked InGaAs/InP quantum wires on (001) Si substrates with adjustable room-temperature emission at telecom bands. Based on a self-limiting growth mode in selective area metal-organic chemical vapor deposition, crescent-shaped InGaAs quantum wires with variable dimensions are embedded within InP nano-ridges. With extensive transmission electron microscopy studies, the growth transition and morphology change from quantum wires to ridge quantum wells (QWs) have been revealed. As a result, we are able to decouple the quantum wires from ridge QWs and manipulate their dimensions by scaling the growth time. With minimized lateral dimension and their unique positioning, the InGaAs/InP quantum wires are more immune to dislocations and more efficient in radiative processes, as evidenced by their excellent optical quality at telecom-bands. These promising results thus highlight the potential of combining low-dimensional quantum wire structures with the aspect ratio trapping process for integrating III-V nano-light emitters on mainstream (001) Si substrates.

Deep-UV emission at 219 nm from ultrathin MBE GaN/AlN quantum heterostructures

NASA Astrophysics Data System (ADS)

Islam, S. M.; Protasenko, Vladimir; Lee, Kevin; Rouvimov, Sergei; Verma, Jai; Xing, Huili Grace; Jena, Debdeep

2017-08-01

Deep ultraviolet (UV) optical emission below 250 nm (˜5 eV) in semiconductors is traditionally obtained from high aluminum containing AlGaN alloy quantum wells. It is shown here that high-quality epitaxial ultrathin binary GaN quantum disks embedded in an AlN matrix can produce efficient optical emission in the 219-235 nm (˜5.7-5.3 eV) spectral range, far above the bulk bandgap (3.4 eV) of GaN. The quantum confinement energy in these heterostructures is larger than the bandgaps of traditional semiconductors, made possible by the large band offsets. These molecular beam epitaxy-grown extreme quantum-confinement GaN/AlN heterostructures exhibit an internal quantum efficiency of 40% at wavelengths as short as 219 nm. These observations together with the ability to engineer the interband optical matrix elements to control the direction of photon emission in such binary quantum disk active regions offer unique advantages over alloy AlGaN quantum well counterparts for the realization of deep-UV light-emitting diodes and lasers.

Self-assembling complexes of quantum dots and scFv antibodies for cancer cell targeting and imaging.

PubMed

Zdobnova, Tatiana A; Stremovskiy, Oleg A; Lebedenko, Ekaterina N; Deyev, Sergey M

2012-01-01

Semiconductor quantum dots represent a novel class of fluorophores with unique physical and chemical properties which could enable a remarkable broadening of the current applications of fluorescent imaging and optical diagnostics. Complexes of quantum dots and antibodies are promising visualising agents for fluorescent detection of selective biomarkers overexpressed in tumor tissues. Here we describe the construction of self-assembling fluorescent complexes of quantum dots and anti-HER1 or anti-HER2/neu scFv antibodies and their interactions with cultured tumor cells. A binding strategy based on a very specific non-covalent interaction between two proteins, barnase and barstar, was used to connect quantum dots and the targeting antibodies. Such a strategy allows combining the targeting and visualization functions simply by varying the corresponding modules of the fluorescent complex.

Self-Assembling Complexes of Quantum Dots and scFv Antibodies for Cancer Cell Targeting and Imaging

PubMed Central

Zdobnova, Tatiana A.; Stremovskiy, Oleg A.; Lebedenko, Ekaterina N.; Deyev, Sergey M.

2012-01-01

Semiconductor quantum dots represent a novel class of fluorophores with unique physical and chemical properties which could enable a remarkable broadening of the current applications of fluorescent imaging and optical diagnostics. Complexes of quantum dots and antibodies are promising visualising agents for fluorescent detection of selective biomarkers overexpressed in tumor tissues. Here we describe the construction of self-assembling fluorescent complexes of quantum dots and anti-HER1 or anti-HER2/neu scFv antibodies and their interactions with cultured tumor cells. A binding strategy based on a very specific non-covalent interaction between two proteins, barnase and barstar, was used to connect quantum dots and the targeting antibodies. Such a strategy allows combining the targeting and visualization functions simply by varying the corresponding modules of the fluorescent complex. PMID:23133578

Observing the operational significance of discord consumption

NASA Astrophysics Data System (ADS)

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

2012-09-01

Coherent interactions that generate negligible entanglement can still exhibit unique quantum behaviour. This observation has motivated a search beyond entanglement for a complete description of all quantum correlations. Quantum discord is a promising candidate. Here, we 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'. We experimentally encode information within the discordant correlations of two separable Gaussian states. The amount of extra information recovered by coherent interaction is quantified and directly linked with the discord consumed during encoding. No entanglement exists at any point of this experiment. Thus we introduce and demonstrate an operational method to use discord as a physical resource.

Faster quantum walk search on a weighted graph

NASA Astrophysics Data System (ADS)

Wong, Thomas G.

2015-09-01

A randomly walking quantum particle evolving by Schrödinger's equation searches for a unique marked vertex on the "simplex of complete graphs" in time Θ (N3 /4) . We give a weighted version of this graph that preserves vertex transitivity, and we show that the time to search on it can be reduced to nearly Θ (√{N }) . To prove this, we introduce two extensions to degenerate perturbation theory: an adjustment that distinguishes the weights of the edges and a method to determine how precisely the jumping rate of the quantum walk must be chosen.

What Exactly is the Information Paradox?

NASA Astrophysics Data System (ADS)

Mathur, S. D.

The black hole information paradox tells us something important about the way quantum mechanics and gravity fit together. In these lectures I try to give a pedagogical review of the essential physics leading to the paradox, using mostly pictures. Hawking's argument is recast as a "theorem": if quantum gravity effects are confined to within a given length scale and the vacuum is assumed to be unique, then there will be information loss. We conclude with a brief summary of how quantum effects in string theory violate the first condition and make the interior of the hole a "fuzzball".

Visualizing Pure Quantum Turbulence in Superfluid 3He: Andreev Reflection and its Spectral Properties.

PubMed

Baggaley, A W; Tsepelin, V; Barenghi, C F; Fisher, S N; Pickett, G R; Sergeev, Y A; Suramlishvili, N

2015-07-03

Superfluid 3He-B in the zero-temperature limit offers a unique means of studying quantum turbulence by the Andreev reflection of quasiparticle excitations by the vortex flow fields. We validate the experimental visualization of turbulence in 3He-B by showing the relation between the vortex-line density and the Andreev reflectance of the vortex tangle in the first simulations of the Andreev reflectance by a realistic 3D vortex tangle, and comparing the results with the first experimental measurements able to probe quantum turbulence on length scales smaller than the intervortex separation.

Quantum-state reconstruction by maximizing likelihood and entropy.

PubMed

Teo, Yong Siah; Zhu, Huangjun; Englert, Berthold-Georg; Řeháček, Jaroslav; Hradil, Zdeněk

2011-07-08

Quantum-state reconstruction on a finite number of copies of a quantum system with informationally incomplete measurements, as a rule, does not yield a unique result. We derive a reconstruction scheme where both the likelihood and the von Neumann entropy functionals are maximized in order to systematically select the most-likely estimator with the largest entropy, that is, the least-bias estimator, consistent with a given set of measurement data. This is equivalent to the joint consideration of our partial knowledge and ignorance about the ensemble to reconstruct its identity. An interesting structure of such estimators will also be explored.

New Directions in Phthalocyanine Pigments

NASA Technical Reports Server (NTRS)

Vandemark, Michael R.

1992-01-01

The objectives were the following: (1) investigation of the synthesis of new phthalocyanines; (2) characterization of the new phthalocyanines synthesized; (3) investigate the properties of the newly synthesized phthalocyanines with emphasis on UV protection of plastics and coatings; and (4) utilize quantum mechanics to evaluate the structural relationships with possible properties and synthetic approaches. The proposed research targeted the synthesis of phthalocyanines containing an aromatic bridge between two phthalocyanine rings. The goal was to synthesize pigments which would protect plastics when exposed to the photodegradation effects of the sun in space. The stability and extended conjugation of the phthalocyanines offer a unique opportunity for energy absorption and numerous radiative and non-radiative energy loss mechanisms. Although the original targeted phthalocyanines were changed early in the project, several new and unique phthalocyanine compounds were prepared. The basic goals of this work were met and some unique and unexpected outcomes of the work were the result of the integral use of quantum mechanics and molecular modeling with the synthetic effort.

Improved Scheduling Mechanisms for Synchronous Information and Energy Transmission.

PubMed

Qin, Danyang; Yang, Songxiang; Zhang, Yan; Ma, Jingya; Ding, Qun

2017-06-09

Wireless energy collecting technology can effectively reduce the network time overhead and prolong the wireless sensor network (WSN) lifetime. However, the traditional energy collecting technology cannot achieve the balance between ergodic channel capacity and average collected energy. In order to solve the problem of the network transmission efficiency and the limited energy of wireless devices, three improved scheduling mechanisms are proposed: improved signal noise ratio (SNR) scheduling mechanism (IS2M), improved N-SNR scheduling mechanism (INS2M) and an improved Equal Throughput scheduling mechanism (IETSM) for different channel conditions to improve the whole network performance. Meanwhile, the average collected energy of single users and the ergodic channel capacity of three scheduling mechanisms can be obtained through the order statistical theory in Rayleig, Ricean, Nakagami- m and Weibull fading channels. It is concluded that the proposed scheduling mechanisms can achieve better balance between energy collection and data transmission, so as to provide a new solution to realize synchronous information and energy transmission for WSNs.

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

Nanoprobe diffusion in entangled polymer solutions: Linear vs. unconcatenated ring chains

NASA Astrophysics Data System (ADS)

Nahali, Negar; Rosa, Angelo

2018-05-01

We employ large-scale molecular dynamics computer simulations to study the problem of nanoprobe diffusion in entangled solutions of linear polymers and unknotted and unconcatenated circular (ring) polymers. By tuning both the diameter of the nanoprobe and the density of the solution, we show that nanoprobes of diameter smaller than the entanglement distance (tube diameter) of the solution display the same (Rouse-like) behavior in solutions of both polymer architectures. Instead, nanoprobes with larger diameters appear to diffuse markedly faster in solutions of rings than in solutions of linear chains. Finally, by analysing the distribution functions of spatial displacements, we find that nanoprobe motion in rings' solutions shows both Gaussian and ergodic behaviors, in all regimes considered, while, in solutions of linear chains, nanoprobes exceeding the size of the tube diameter show a transition to non-Gaussian and non-ergodic motion. Our results emphasize the role of chain architecture in the motion of nanoprobes dispersed in polymer solutions.

Fractional Stochastic Differential Equations Satisfying Fluctuation-Dissipation Theorem

NASA Astrophysics Data System (ADS)

Li, Lei; Liu, Jian-Guo; Lu, Jianfeng

2017-10-01

We propose in this work a fractional stochastic differential equation (FSDE) model consistent with the over-damped limit of the generalized Langevin equation model. As a result of the `fluctuation-dissipation theorem', the differential equations driven by fractional Brownian noise to model memory effects should be paired with Caputo derivatives, and this FSDE model should be understood in an integral form. We establish the existence of strong solutions for such equations and discuss the ergodicity and convergence to Gibbs measure. In the linear forcing regime, we show rigorously the algebraic convergence to Gibbs measure when the `fluctuation-dissipation theorem' is satisfied, and this verifies that satisfying `fluctuation-dissipation theorem' indeed leads to the correct physical behavior. We further discuss possible approaches to analyze the ergodicity and convergence to Gibbs measure in the nonlinear forcing regime, while leave the rigorous analysis for future works. The FSDE model proposed is suitable for systems in contact with heat bath with power-law kernel and subdiffusion behaviors.

Improved Scheduling Mechanisms for Synchronous Information and Energy Transmission

PubMed Central

Qin, Danyang; Yang, Songxiang; Zhang, Yan; Ma, Jingya; Ding, Qun

2017-01-01

Wireless energy collecting technology can effectively reduce the network time overhead and prolong the wireless sensor network (WSN) lifetime. However, the traditional energy collecting technology cannot achieve the balance between ergodic channel capacity and average collected energy. In order to solve the problem of the network transmission efficiency and the limited energy of wireless devices, three improved scheduling mechanisms are proposed: improved signal noise ratio (SNR) scheduling mechanism (IS2M), improved N-SNR scheduling mechanism (INS2M) and an improved Equal Throughput scheduling mechanism (IETSM) for different channel conditions to improve the whole network performance. Meanwhile, the average collected energy of single users and the ergodic channel capacity of three scheduling mechanisms can be obtained through the order statistical theory in Rayleig, Ricean, Nakagami-m and Weibull fading channels. It is concluded that the proposed scheduling mechanisms can achieve better balance between energy collection and data transmission, so as to provide a new solution to realize synchronous information and energy transmission for WSNs. PMID:28598395

Stability and instability towards delocalization in many-body localization systems

NASA Astrophysics Data System (ADS)

De Roeck, Wojciech; Huveneers, François

2017-04-01

We propose a theory that describes quantitatively the (in)stability of fully many-body localization (MBL) systems due to ergodic, i.e., delocalized, grains, that can be, for example, due to disorder fluctuations. The theory is based on the ETH hypothesis and elementary notions of perturbation theory. The main idea is that we assume as much chaoticity as is consistent with conservation laws. The theory describes correctly—even without relying on the theory of local integrals of motion (LIOM)—the MBL phase in one dimension at strong disorder. It yields an explicit and quantitative picture of the spatial boundary between localized and ergodic systems. We provide numerical evidence for this picture. When the theory is taken to its extreme logical consequences, it predicts that the MBL phase is destabilised in the long time limit whenever (1) interactions decay slower than exponentially in d =1 and (2) always in d >1 . Finer numerics is required to assess these predictions.

A model relating radiated power and impurity concentrations during Ne, N and Ar injection in Tore Supra

NASA Astrophysics Data System (ADS)

Hogan, J.; Demichelis, C.; Monier-Garbet, P.; Guirlet, R.; Hess, W.; Schunke, B.

2000-10-01

A model combining the MIST (core symmetric) and BBQ (SOL asymmetric) codes is used to study the relation between impurity density and radiated power for representative cases from Tore Supra experiments on strong radiation regimes using the ergodic divertor. Transport predictions of external radiation are compared with observation to estimate the absolute impurity density. BBQ provides the incoming distribution of recycling impurity charge states for the radial transport calculation. The shots studied use the ergodic divertor and high ICRH power. Power is first applied and then the extrinsic impurity (Ne, N or Ar) is injected. Separate time dependent intrinsic (C and O) impurity transport calculations match radiation levels before and during the high power and impurity injection phases. Empirical diffusivities are sought to reproduce the UV (CV R, I lines), CVI Lya, OVIII Lya, Zeff, and horizontal bolometer data. The model has been used to calculate the relative radiative efficiency (radiated power / extrinsically contributed electron) for the sample database.

Fractional Brownian motion and motion governed by the fractional Langevin equation in confined geometries.

PubMed

Jeon, Jae-Hyung; Metzler, Ralf

2010-02-01

Motivated by subdiffusive motion of biomolecules observed in living cells, we study the stochastic properties of a non-Brownian particle whose motion is governed by either fractional Brownian motion or the fractional Langevin equation and restricted to a finite domain. We investigate by analytic calculations and simulations how time-averaged observables (e.g., the time-averaged mean-squared displacement and displacement correlation) are affected by spatial confinement and dimensionality. In particular, we study the degree of weak ergodicity breaking and scatter between different single trajectories for this confined motion in the subdiffusive domain. The general trend is that deviations from ergodicity are decreased with decreasing size of the movement volume and with increasing dimensionality. We define the displacement correlation function and find that this quantity shows distinct features for fractional Brownian motion, fractional Langevin equation, and continuous time subdiffusion, such that it appears an efficient measure to distinguish these different processes based on single-particle trajectory data.

On the continuing relevance of Mandelbrot's non-ergodic fractional renewal models of 1963 to 1967

NASA Astrophysics Data System (ADS)

Watkins, Nicholas W.

2017-12-01

The problem of "1/f" noise has been with us for about a century. Because it is so often framed in Fourier spectral language, the most famous solutions have tended to be the stationary long range dependent (LRD) models such as Mandelbrot's fractional Gaussian noise. In view of the increasing importance to physics of non-ergodic fractional renewal models, and their links to the CTRW, I present preliminary results of my research into the history of Mandelbrot's very little known work in that area from 1963 to 1967. I speculate about how the lack of awareness of this work in the physics and statistics communities may have affected the development of complexity science, and I discuss the differences between the Hurst effect, "1/f" noise and LRD, concepts which are often treated as equivalent. Contribution to the "Topical Issue: Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.

Random walk to a nonergodic equilibrium concept

NASA Astrophysics Data System (ADS)

Bel, G.; Barkai, E.

2006-01-01

Random walk models, such as the trap model, continuous time random walks, and comb models, exhibit weak ergodicity breaking, when the average waiting time is infinite. The open question is, what statistical mechanical theory replaces the canonical Boltzmann-Gibbs theory for such systems? In this paper a nonergodic equilibrium concept is investigated, for a continuous time random walk model in a potential field. In particular we show that in the nonergodic phase the distribution of the occupation time of the particle in a finite region of space approaches U- or W-shaped distributions related to the arcsine law. We show that when conditions of detailed balance are applied, these distributions depend on the partition function of the problem, thus establishing a relation between the nonergodic dynamics and canonical statistical mechanics. In the ergodic phase the distribution function of the occupation times approaches a δ function centered on the value predicted based on standard Boltzmann-Gibbs statistics. The relation of our work to single-molecule experiments is briefly discussed.

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).

Many-body delocalization with random vector potentials

NASA Astrophysics Data System (ADS)

Cheng, Chen; Mondaini, Rubem

In this talk we present the ergodic properties of excited states in a model of interacting fermions in quasi-one dimensional chains subjected to a random vector potential. In the non-interacting limit, we show that arbitrarily small values of this complex off-diagonal disorder triggers localization for the whole spectrum; the divergence of the localization length in the single particle basis is characterized by a critical exponent ν which depends on the energy density being investigated. However, when short-ranged interactions are included, the localization is lost and the system is ergodic regardless of the magnitude of disorder in finite chains. Our numerical results suggest a delocalization scheme for arbitrary small values of interactions. This finding indicates that the standard scenario of the many-body localization cannot be obtained in a model with random gauge fields. This research is financially supported by the National Natural Science Foundation of China (NSFC) (Grant Nos. U1530401 and 11674021). RM also acknowledges support from NSFC (Grant No. 11650110441).

Fabrication of green dye-sensitized solar cell based on ZnO nanoparticles as a photoanode and graphene quantum dots as a photo-sensitizer.

PubMed

Zamiri, Golnoush; Bagheri, Samira

2018-02-01

Zero-dimensional graphene quantum dots (GQDs) consist of single- or few-layer graphene with a size less than 20 nm and stand for a new type of QDs with unique properties combining the graphene nature and size-resulted quantum effects. GQDs possess unique optical and electronic properties, and in particular possess a band-gap less than 2.0 eV because of quantum confinement and edge effects. In this study, we investigated the performance of DSSCs using different thicknesses of ZnO nanoparticles as a photo-anode and GQDs as a green photosensitizer. The current voltage (I-V) test results indicate that the performance of DSSCs is improved by increasing the thickness of the photo-anode and the thickness of 40 μm shows the highest efficiency for DSSC device based on ZnO nanoparticles photo-anodes. The DSSC using ZnO nanoparticles as a photo-anode with thickness of 40 μm shows almost same efficiency when we replaced N-719 with GQDs which is confirmed that using GQDs as an alternative to ruthenium based dyes is a new approach for DSSCs. Copyright © 2017 Elsevier Inc. All rights reserved.

Experimental two-dimensional quantum walk on a photonic chip

PubMed Central

Lin, Xiao-Feng; Feng, Zhen; Chen, Jing-Yuan; Gao, Jun; Sun, Ke; Wang, Chao-Yue; Lai, Peng-Cheng; Xu, Xiao-Yun; Wang, Yao; Qiao, Lu-Feng; Yang, Ai-Lin

2018-01-01

Quantum walks, in virtue of the coherent superposition and quantum interference, have exponential superiority over their classical counterpart in applications of quantum searching and quantum simulation. The quantum-enhanced power is highly related to the state space of quantum walks, which can be expanded by enlarging the photon number and/or the dimensions of the evolution network, but the former is considerably challenging due to probabilistic generation of single photons and multiplicative loss. We demonstrate a two-dimensional continuous-time quantum walk by using the external geometry of photonic waveguide arrays, rather than the inner degree of freedoms of photons. Using femtosecond laser direct writing, we construct a large-scale three-dimensional structure that forms a two-dimensional lattice with up to 49 × 49 nodes on a photonic chip. We demonstrate spatial two-dimensional quantum walks using heralded single photons and single photon–level imaging. We analyze the quantum transport properties via observing the ballistic evolution pattern and the variance profile, which agree well with simulation results. We further reveal the transient nature that is the unique feature for quantum walks of beyond one dimension. An architecture that allows a quantum walk to freely evolve in all directions and at a large scale, combining with defect and disorder control, may bring up powerful and versatile quantum walk machines for classically intractable problems. PMID:29756040

Experimental two-dimensional quantum walk on a photonic chip.

PubMed

Tang, Hao; Lin, Xiao-Feng; Feng, Zhen; Chen, Jing-Yuan; Gao, Jun; Sun, Ke; Wang, Chao-Yue; Lai, Peng-Cheng; Xu, Xiao-Yun; Wang, Yao; Qiao, Lu-Feng; Yang, Ai-Lin; Jin, Xian-Min

2018-05-01

Quantum walks, in virtue of the coherent superposition and quantum interference, have exponential superiority over their classical counterpart in applications of quantum searching and quantum simulation. The quantum-enhanced power is highly related to the state space of quantum walks, which can be expanded by enlarging the photon number and/or the dimensions of the evolution network, but the former is considerably challenging due to probabilistic generation of single photons and multiplicative loss. We demonstrate a two-dimensional continuous-time quantum walk by using the external geometry of photonic waveguide arrays, rather than the inner degree of freedoms of photons. Using femtosecond laser direct writing, we construct a large-scale three-dimensional structure that forms a two-dimensional lattice with up to 49 × 49 nodes on a photonic chip. We demonstrate spatial two-dimensional quantum walks using heralded single photons and single photon-level imaging. We analyze the quantum transport properties via observing the ballistic evolution pattern and the variance profile, which agree well with simulation results. We further reveal the transient nature that is the unique feature for quantum walks of beyond one dimension. An architecture that allows a quantum walk to freely evolve in all directions and at a large scale, combining with defect and disorder control, may bring up powerful and versatile quantum walk machines for classically intractable problems.

Quantumness and the role of locality on quantum correlations

NASA Astrophysics Data System (ADS)

Bellomo, G.; Plastino, A.; Plastino, A. R.

2016-06-01

Quantum correlations in a physical system are usually studied with respect to a unique and fixed decomposition of the system into subsystems, without fully exploiting the rich structure of the state space. Here, we show several examples in which the consideration of different ways to decompose a physical system enhances the quantum resources and accounts for a more flexible definition of quantumness measures. Furthermore, we give a different perspective regarding how to reassess the fact that local operations play a key role in general quantumness measures that go beyond entanglement—as discordlike ones. We propose a family of measures to quantify the maximum quantumness of a given state. For the discord-based case, we present some analytical results for 2 ×d -dimensional states. Applying our definition to low-dimensional bipartite states, we show that different behaviors can be reported for separable and entangled states vis-à-vis those corresponding to the usual measures of quantum correlations. We show that there is a close link between our proposal and the criterion to witness quantum correlations based on the rank of the correlation matrix, proposed by Dakić, Vedral, and Brukner [Phys. Rev. Lett. 105, 190502 (2010), 10.1103/PhysRevLett.105.190502].

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hsiang, J.-T., E-mail: cosmology@gmail.com; Department of Physics, National Dong Hwa University, Hualien 97401, Taiwan; Hu, B.L.

2015-11-15

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

Inkjet printed fluorescent nanorod layers exhibit superior optical performance over quantum dots

NASA Astrophysics Data System (ADS)

Halivni, Shira; Shemesh, Shay; Waiskopf, Nir; Vinetsky, Yelena; Magdassi, Shlomo; Banin, Uri

2015-11-01

Semiconductor nanocrystals exhibit unique fluorescence properties which are tunable in size, shape and composition. The high quantum yield and enhanced stability have led to their use in biomedical imaging and flat panel displays. Here, semiconductor nanorod based inkjet inks are presented, overcoming limitations of the commonly reported quantum dots in printing applications. Fluorescent seeded nanorods were found to be outstanding candidates for fluorescent inks, due to their low particle-particle interactions and negligible self-absorption. This is manifested by insignificant emission shifts upon printing, even in highly concentrated printed layers and by maintenance of a high fluorescence quantum yield, unlike quantum dots which exhibit fluorescence wavelength shifts and quenching effects. This behavior results from the reduced absorption/emission overlap, accompanied by low energy transfer efficiencies between the nanorods as supported by steady state and time resolved fluorescence measurements. The new seeded nanorod inks enable patterning of thin fluorescent layers, for demanding light emission applications such as signage and displays.Semiconductor nanocrystals exhibit unique fluorescence properties which are tunable in size, shape and composition. The high quantum yield and enhanced stability have led to their use in biomedical imaging and flat panel displays. Here, semiconductor nanorod based inkjet inks are presented, overcoming limitations of the commonly reported quantum dots in printing applications. Fluorescent seeded nanorods were found to be outstanding candidates for fluorescent inks, due to their low particle-particle interactions and negligible self-absorption. This is manifested by insignificant emission shifts upon printing, even in highly concentrated printed layers and by maintenance of a high fluorescence quantum yield, unlike quantum dots which exhibit fluorescence wavelength shifts and quenching effects. This behavior results from the reduced absorption/emission overlap, accompanied by low energy transfer efficiencies between the nanorods as supported by steady state and time resolved fluorescence measurements. The new seeded nanorod inks enable patterning of thin fluorescent layers, for demanding light emission applications such as signage and displays. Electronic supplementary information (ESI) available. See DOI: 10.1039/c5nr06248a

Role of magnetic and diamagnetic interactions in molecular optics and scattering

NASA Astrophysics Data System (ADS)

Forbes, Kayn A.

2018-05-01

This paper aims to explicitly clarify the role and interpretation of diamagnetic interactions between molecules and light in quantum electrodynamics. In contrast to their electric and magnetic counterparts, the diamagnetic couplings between light and matter have received relatively little interest in the field of molecular optics. This intriguing disregard of an interaction term is puzzling. The diamagnetic couplings possess unique physical properties that warrant their inclusion in any multiphoton process, and the lack of gauge invariance for paramagnetic and diamagnetic susceptibilities necessitates their inclusion. Their role and importance within nonrelativistic molecular quantum electrodynamics in the Coulomb gauge is illuminated, and it is highlighted how for any multiphoton process their inclusion should be implicit. As an indicative example of the theory presented, the diamagnetic contributions to both forward and nonforward Rayleigh scattering are derived and put into context alongside the electric and magnetic molecular responses. The work represents clarification of diamagnetic couplings in molecular quantum electrodynamics, which subsequently should proffer the study of diamagnetic interactions in molecular optics due to their unique physical attributes and necessary inclusion in multiphoton processes.

Thermal Decoherence of a Nonequilibrium Polariton Fluid

NASA Astrophysics Data System (ADS)

Klembt, Sebastian; Stepanov, Petr; Klein, Thorsten; Minguzzi, Anna; Richard, Maxime

2018-01-01

Exciton polaritons constitute a unique realization of a quantum fluid interacting with its environment. Using selenide-based microcavities, we exploit this feature to warm up a polariton condensate in a controlled way and monitor its spatial coherence. We determine directly the amount of heat picked up by the condensate by measuring the phonon-polariton scattering rate and comparing it with the loss rate. We find that, upon increasing the heating rate, the spatial coherence length decreases markedly, while localized phase structures vanish, in good agreement with a stochastic mean-field theory. From the thermodynamical point of view, this regime is unique, as it involves a nonequilibrium quantum fluid with no well-defined temperature but which is nevertheless able to pick up heat with dramatic effects on the order parameter.

All-optical control and super-resolution imaging of quantum emitters in layered materials.

PubMed

Kianinia, Mehran; Bradac, Carlo; Sontheimer, Bernd; Wang, Fan; Tran, Toan Trong; Nguyen, Minh; Kim, Sejeong; Xu, Zai-Quan; Jin, Dayong; Schell, Andreas W; Lobo, Charlene J; Aharonovich, Igor; Toth, Milos

2018-02-28

Layered van der Waals materials are emerging as compelling two-dimensional platforms for nanophotonics, polaritonics, valleytronics and spintronics, and have the potential to transform applications in sensing, imaging and quantum information processing. Among these, hexagonal boron nitride (hBN) is known to host ultra-bright, room-temperature quantum emitters, whose nature is yet to be fully understood. Here we present a set of measurements that give unique insight into the photophysical properties and level structure of hBN quantum emitters. Specifically, we report the existence of a class of hBN quantum emitters with a fast-decaying intermediate and a long-lived metastable state accessible from the first excited electronic state. Furthermore, by means of a two-laser repumping scheme, we show an enhanced photoluminescence and emission intensity, which can be utilized to realize a new modality of far-field super-resolution imaging. Our findings expand current understanding of quantum emitters in hBN and show new potential ways of harnessing their nonlinear optical properties in sub-diffraction nanoscopy.

Quantum Dot-Based Luminescent Oxygen Channeling Assay for Potential Application in Homogeneous Bioassays.

PubMed

Zhuang, Si-Hui; Guo, Xin-Xin; Wu, Ying-Song; Chen, Zhen-Hua; Chen, Yao; Ren, Zhi-Qi; Liu, Tian-Cai

2016-01-01

The unique photoproperties of quantum dots are promising for potential application in bioassays. In the present study, quantum dots were applied to a luminescent oxygen channeling assay. The reaction system developed in this study was based on interaction of biotin with streptavidin. Carboxyl-modified polystyrene microspheres doped with quantum dots were biotinylated and used as acceptors. Photosensitizer-doped carboxyl-modified polystyrene microspheres were conjugated with streptavidin and used as donors. The results indicated that the singlet oxygen that was released from the donor beads diffused into the acceptor beads. The acceptor beads were then exited via thioxene, and were subsequently fluoresced. To avoid generating false positives, a high concentration (0.01 mg/mL) of quantum dots is required for application in homogeneous immunoassays. Compared to a conventional luminescent oxygen channeling assay, this quantum dots-based technique requires less time, and would be easier to automate and miniaturize because it requires no washing to remove excess labels.

Modulated phases of graphene quantum Hall polariton fluids

PubMed Central

Pellegrino, Francesco M. D.; Giovannetti, Vittorio; MacDonald, Allan H.; Polini, Marco

2016-01-01

There is a growing experimental interest in coupling cavity photons to the cyclotron resonance excitations of electron liquids in high-mobility semiconductor quantum wells or graphene sheets. These media offer unique platforms to carry out fundamental studies of exciton-polariton condensation and cavity quantum electrodynamics in a regime, in which electron–electron interactions are expected to play a pivotal role. Here, focusing on graphene, we present a theoretical study of the impact of electron–electron interactions on a quantum Hall polariton fluid, that is a fluid of magneto-excitons resonantly coupled to cavity photons. We show that electron–electron interactions are responsible for an instability of graphene integer quantum Hall polariton fluids towards a modulated phase. We demonstrate that this phase can be detected by measuring the collective excitation spectra, which is often at a characteristic wave vector of the order of the inverse magnetic length. PMID:27841346

Efficient and Stable CsPb(Br/I)3@Anthracene Composites for White Light-Emitting Devices.

PubMed

Shen, Xinyu; Sun, Chun; Bai, Xue; Zhang, Xiaoyu; Wang, Yu; Wang, Yiding; Song, Hongwei; Yu, William W

2018-05-16

Inorganic perovskite quantum dots bear many unique properties that make them potential candidates for optoelectronic applications, including color display and lighting. However, the white emission with inorganic perovskite quantum dots has rarely been realized due to the anion-exchange reaction. Here, we proposed a one-pot preparation to fabricate inorganic perovskite quantum dot-based white light-emitting composites by introducing anthracene as a blue emission component. The as-prepared white light-emitting composite exhibited a photoluminescence quantum yield of 41.9%. By combining CsPb(Br/I) 3 @anthracene composites with UV light-emitting device (LED) chips, white light-emitting devices with a color rendering index of 90 were realized with tunable color temperature from warm white to cool white. These results can promote the application of inorganic perovskite quantum dots in the field of white LEDs.

Dopant atoms as quantum components in silicon nanoscale devices

NASA Astrophysics Data System (ADS)

Zhao, Xiaosong; Han, Weihua; Wang, Hao; Ma, Liuhong; Li, Xiaoming; Zhang, Wang; Yan, Wei; Yang, Fuhua

2018-06-01

Recent progress in nanoscale fabrication allows many fundamental studies of the few dopant atoms in various semiconductor nanostructures. Since the size of nanoscale devices has touched the limit of the nature, a single dopant atom may dominate the performance of the device. Besides, the quantum computing considered as a future choice beyond Moore's law also utilizes dopant atoms as functional units. Therefore, the dopant atoms will play a significant role in the future novel nanoscale devices. This review focuses on the study of few dopant atoms as quantum components in silicon nanoscale device. The control of the number of dopant atoms and unique quantum transport characteristics induced by dopant atoms are presented. It can be predicted that the development of nanoelectronics based on dopant atoms will pave the way for new possibilities in quantum electronics. Project supported by National Key R&D Program of China (No. 2016YFA0200503).

Observation of topologically protected bound states in photonic quantum walks.

PubMed

Kitagawa, Takuya; Broome, Matthew A; Fedrizzi, Alessandro; Rudner, Mark S; Berg, Erez; Kassal, Ivan; Aspuru-Guzik, Alán; Demler, Eugene; White, Andrew G

2012-06-06

Topological phases exhibit some of the most striking phenomena in modern physics. Much of the rich behaviour of quantum Hall systems, topological insulators, and topological superconductors can be traced to the existence of robust bound states at interfaces between different topological phases. This robustness has applications in metrology and holds promise for future uses in quantum computing. Engineered quantum systems--notably in photonics, where wavefunctions can be observed directly--provide versatile platforms for creating and probing a variety of topological phases. Here we use photonic quantum walks to observe bound states between systems with different bulk topological properties and demonstrate their robustness to perturbations--a signature of topological protection. Although such bound states are usually discussed for static (time-independent) systems, here we demonstrate their existence in an explicitly time-dependent situation. Moreover, we discover a new phenomenon: a topologically protected pair of bound states unique to periodically driven systems.

Excluding joint probabilities from quantum theory

NASA Astrophysics Data System (ADS)

Allahverdyan, Armen E.; Danageozian, Arshag

2018-03-01

Quantum theory does not provide a unique definition for the joint probability of two noncommuting observables, which is the next important question after the Born's probability for a single observable. Instead, various definitions were suggested, e.g., via quasiprobabilities or via hidden-variable theories. After reviewing open issues of the joint probability, we relate it to quantum imprecise probabilities, which are noncontextual and are consistent with all constraints expected from a quantum probability. We study two noncommuting observables in a two-dimensional Hilbert space and show that there is no precise joint probability that applies for any quantum state and is consistent with imprecise probabilities. This contrasts with theorems by Bell and Kochen-Specker that exclude joint probabilities for more than two noncommuting observables, in Hilbert space with dimension larger than two. If measurement contexts are included into the definition, joint probabilities are not excluded anymore, but they are still constrained by imprecise probabilities.

Coal as an abundant source of graphene quantum dots

NASA Astrophysics Data System (ADS)

Ye, Ruquan; Xiang, Changsheng; Lin, Jian; Peng, Zhiwei; Huang, Kewei; Yan, Zheng; Cook, Nathan P.; Samuel, Errol L. G.; Hwang, Chih-Chau; Ruan, Gedeng; Ceriotti, Gabriel; Raji, Abdul-Rahman O.; Martí, Angel A.; Tour, James M.

2013-12-01

Coal is the most abundant and readily combustible energy resource being used worldwide. However, its structural characteristic creates a perception that coal is only useful for producing energy via burning. Here we report a facile approach to synthesize tunable graphene quantum dots from various types of coal, and establish that the unique coal structure has an advantage over pure sp2-carbon allotropes for producing quantum dots. The crystalline carbon within the coal structure is easier to oxidatively displace than when pure sp2-carbon structures are used, resulting in nanometre-sized graphene quantum dots with amorphous carbon addends on the edges. The synthesized graphene quantum dots, produced in up to 20% isolated yield from coal, are soluble and fluorescent in aqueous solution, providing promise for applications in areas such as bioimaging, biomedicine, photovoltaics and optoelectronics, in addition to being inexpensive additives for structural composites.

Coal as an abundant source of graphene quantum dots.

PubMed

Ye, Ruquan; Xiang, Changsheng; Lin, Jian; Peng, Zhiwei; Huang, Kewei; Yan, Zheng; Cook, Nathan P; Samuel, Errol L G; Hwang, Chih-Chau; Ruan, Gedeng; Ceriotti, Gabriel; Raji, Abdul-Rahman O; Martí, Angel A; Tour, James M

2013-01-01

Coal is the most abundant and readily combustible energy resource being used worldwide. However, its structural characteristic creates a perception that coal is only useful for producing energy via burning. Here we report a facile approach to synthesize tunable graphene quantum dots from various types of coal, and establish that the unique coal structure has an advantage over pure sp2-carbon allotropes for producing quantum dots. The crystalline carbon within the coal structure is easier to oxidatively displace than when pure sp2-carbon structures are used, resulting in nanometre-sized graphene quantum dots with amorphous carbon addends on the edges. The synthesized graphene quantum dots, produced in up to 20% isolated yield from coal, are soluble and fluorescent in aqueous solution, providing promise for applications in areas such as bioimaging, biomedicine, photovoltaics and optoelectronics, in addition to being inexpensive additives for structural composites.

Quantum Accelerators for High-performance Computing Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Humble, Travis S.; Britt, Keith A.; Mohiyaddin, Fahd A.

We define some of the programming and system-level challenges facing the application of quantum processing to high-performance computing. Alongside barriers to physical integration, prominent differences in the execution of quantum and conventional programs challenges the intersection of these computational models. Following a brief overview of the state of the art, we discuss recent advances in programming and execution models for hybrid quantum-classical computing. We discuss a novel quantum-accelerator framework that uses specialized kernels to offload select workloads while integrating with existing computing infrastructure. We elaborate on the role of the host operating system to manage these unique accelerator resources, themore » prospects for deploying quantum modules, and the requirements placed on the language hierarchy connecting these different system components. We draw on recent advances in the modeling and simulation of quantum computing systems with the development of architectures for hybrid high-performance computing systems and the realization of software stacks for controlling quantum devices. Finally, we present simulation results that describe the expected system-level behavior of high-performance computing systems composed from compute nodes with quantum processing units. We describe performance for these hybrid systems in terms of time-to-solution, accuracy, and energy consumption, and we use simple application examples to estimate the performance advantage of quantum acceleration.« less

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.

Measurement-based quantum computation on two-body interacting qubits with adiabatic evolution.

PubMed

Kyaw, Thi Ha; Li, Ying; Kwek, Leong-Chuan

2014-10-31

A cluster state cannot be a unique ground state of a two-body interacting Hamiltonian. Here, we propose the creation of a cluster state of logical qubits encoded in spin-1/2 particles by adiabatically weakening two-body interactions. The proposal is valid for any spatial dimensional cluster states. Errors induced by thermal fluctuations and adiabatic evolution within finite time can be eliminated ensuring fault-tolerant quantum computing schemes.

Cavity cooling of an optically levitated submicron particle

PubMed Central

Kiesel, Nikolai; Blaser, Florian; Delić, Uroš; Grass, David; Kaltenbaek, Rainer; Aspelmeyer, Markus

2013-01-01

The coupling of a levitated submicron particle and an optical cavity field promises access to a unique parameter regime both for macroscopic quantum experiments and for high-precision force sensing. We report a demonstration of such controlled interactions by cavity cooling the center-of-mass motion of an optically trapped submicron particle. This paves the way for a light–matter interface that can enable room-temperature quantum experiments with mesoscopic mechanical systems. PMID:23940352

Groenewold-Moyal product, α*-cohomology, and classification of translation-invariant non-commutative structures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Varshovi, Amir Abbass

2013-07-15

The theory of α*-cohomology is studied thoroughly and it is shown that in each cohomology class there exists a unique 2-cocycle, the harmonic form, which generates a particular Groenewold-Moyal star product. This leads to an algebraic classification of translation-invariant non-commutative structures and shows that any general translation-invariant non-commutative quantum field theory is physically equivalent to a Groenewold-Moyal non-commutative quantum field theory.

DNA nanosensor based on biocompatible graphene quantum dots and carbon nanotubes.

PubMed

Qian, Zhao Sheng; Shan, Xiao Yue; Chai, Lu Jing; Ma, Juan Juan; Chen, Jian Rong; Feng, Hui

2014-10-15

An ultrasensitive nanosensor based on fluorescence resonance energy transfer (FRET) between biocompatible graphene quantum dots and carbon nanotubes for DNA detection was reported. We take advantage of good biocompatibility and strong fluorescence of graphene quantum dots, base pairing specificity of DNA and unique fluorescence resonance energy transfer between graphene quantum dots and carbon nanotubes to achieve the analysis of low concentrations of DNA. Graphene quantum dots with high quantum yield up to 0.20 were prepared and served as the fluorophore of DNA probe. FRET process between graphene quantum dots-labeled probe and oxidized carbon nanotubes is easily achieved due to their efficient self-assembly through specific π-π interaction. This nanosensor can distinguish complementary and mismatched nucleic acid sequences with high sensitivity and good reproducibility. The detection method based on this nanosensor possesses a broad linear span of up to 133.0 nM and ultralow detection limit of 0.4 nM. The constructed nanosensor is expected to be highly biocompatible because of all its components with excellent biocompatibility. Copyright © 2014 Elsevier B.V. All rights reserved.

A Transfer Hamiltonian Model for Devices Based on Quantum Dot Arrays

PubMed Central

Illera, S.; Prades, J. D.; Cirera, A.; Cornet, A.

2015-01-01

We present a model of electron transport through a random distribution of interacting quantum dots embedded in a dielectric matrix to simulate realistic devices. The method underlying the model depends only on fundamental parameters of the system and it is based on the Transfer Hamiltonian approach. A set of noncoherent rate equations can be written and the interaction between the quantum dots and between the quantum dots and the electrodes is introduced by transition rates and capacitive couplings. A realistic modelization of the capacitive couplings, the transmission coefficients, the electron/hole tunneling currents, and the density of states of each quantum dot have been taken into account. The effects of the local potential are computed within the self-consistent field regime. While the description of the theoretical framework is kept as general as possible, two specific prototypical devices, an arbitrary array of quantum dots embedded in a matrix insulator and a transistor device based on quantum dots, are used to illustrate the kind of unique insight that numerical simulations based on the theory are able to provide. PMID:25879055

A transfer hamiltonian model for devices based on quantum dot arrays.

PubMed

Illera, S; Prades, J D; Cirera, A; Cornet, A

2015-01-01

We present a model of electron transport through a random distribution of interacting quantum dots embedded in a dielectric matrix to simulate realistic devices. The method underlying the model depends only on fundamental parameters of the system and it is based on the Transfer Hamiltonian approach. A set of noncoherent rate equations can be written and the interaction between the quantum dots and between the quantum dots and the electrodes is introduced by transition rates and capacitive couplings. A realistic modelization of the capacitive couplings, the transmission coefficients, the electron/hole tunneling currents, and the density of states of each quantum dot have been taken into account. The effects of the local potential are computed within the self-consistent field regime. While the description of the theoretical framework is kept as general as possible, two specific prototypical devices, an arbitrary array of quantum dots embedded in a matrix insulator and a transistor device based on quantum dots, are used to illustrate the kind of unique insight that numerical simulations based on the theory are able to provide.

What is dynamics in quantum gravity?

NASA Astrophysics Data System (ADS)

Małkiewicz, Przemysław

2017-10-01

The appearance of the Hamiltonian constraint in the canonical formalism for general relativity reflects the lack of a fixed external time. The dynamics of general relativistic systems can be expressed with respect to an arbitrarily chosen internal degree of freedom, the so-called internal clock. We investigate the way in which the choice of internal clock determines the quantum dynamics and how much different quantum dynamics induced by different clocks are. We develop our method of comparison by extending the Hamilton-Jacobi theory of contact transformations to include a new type of transformation which transforms both the canonical variables and the internal clock. We employ our method to study the quantum dynamics of the Friedmann-Lemaitre model and obtain semiclassical corrections to the classical dynamics, which depend on the choice of internal clock. For a unique quantisation map we find the abundance of inequivalent semiclassical corrections induced by quantum dynamics taking place in different internal clocks. It follows that the concepts like minimal volume, maximal curvature and the number of quantum bounces, often used to describe quantum effects in cosmological models, depend on the choice of internal clock.

Characterizing and engineering tunable spin functionality inside indium arsenide/gallium arsenide quantum dot molecules

NASA Astrophysics Data System (ADS)

Liu, Weiwen

The continual downsizing of the basic functional units used in the electronics industry has motivated the study of the quantum computation and related topics. To overcome the limitations of classical physics and engineering, some unique quantum mechanical features, especially entanglement and superpositions have begun to be considered as important properties for future bits. Including these quantum mechanical features is attractive because the ability to utilize quantum mechanics can dramatically enhance computational power. Among the various ways of constructing the basic building blocks for quantum computation, we are particularly interested in using spins inside epitaxially grown InAs/GaAs quantum dot molecules as quantum bits (qubits). The ability to design and engineer nanostructures with tailored quantum properties is critical to engineering quantum computers and other novel electro-optical devices and is one of the key challenges for scaling up new ideas for device application. In this thesis, we will focus on how the structure and composition of quantum dot molecules can be used to control spin properties and charge interactions. Tunable spin and charge properties can enable new, more scalable, methods of initializing and manipulating quantum information. In this thesis, we demonstrate one method to enable electric-field tunability of Zeeman splitting for a single electron spin inside a quantum dot molecules by using heterostructure engineering techniques to modify the barrier that separates quantum dots. We describe how these structural changes to the quantum dot molecules also change charge interactions and propose ways to use this effect to enable accurate measurement of coulomb interactions and possibly charge occupancy inside these complicated quantum dot molecules.

Phase-space foundations of electron holography

NASA Astrophysics Data System (ADS)

Lubk, A.; Röder, F.

2015-09-01

We present a unified formalism for describing various forms of electron holography in quantum mechanical phase space including their extensions to quantum-state reconstructions. The phase-space perspective allows for taking into account partial coherence as well as the quantum mechanical detection process typically hampering the unique reconstruction of a wave function. We elaborate on the limitations imposed by the electron optical elements of the transmission electron microscope as well as the scattering at the target. The results provide the basis for vastly extending the scope of electron holographic techniques towards analyzing partially coherent signals such as inelastically scattered electrons or electron pulses used in ultrafast transmission electron microscopy.

BFV-BRST analysis of the classical and quantum q-deformations of the sl(2) algebra

NASA Astrophysics Data System (ADS)

Dayi, O. F.

1994-01-01

BFV--BRST charge for q-deformed algebras is not unique. Different constructions of it in the classical as well as in the quantum phase space for the $q$-deformed algebra sl_q(2) are discussed. Moreover, deformation of the phase space without deforming the generators of sl(2) is considered. $\\hbar$-q-deformation of the phase space is shown to yield the Witten's second deformation. To study the BFV--BRST cohomology problem when both the quantum phase space and the group are deformed, a two parameter deformation of sl(2) is proposed, and its BFV-BRST charge is given.

Thermodynamic output of single-atom quantum optical amplifiers and their phase-space fingerprint

NASA Astrophysics Data System (ADS)

Perl, Y.; Band, Y. B.; Boukobza, E.

2017-05-01

We analyze a resonant single-atom two-photon quantum optical amplifier both dynamically and thermodynamically. A detailed thermodynamic analysis shows that the nonlinear amplifier is thermodynamically equivalent to the linear amplifier. However, by calculating the Wigner quasiprobability distribution for various initial field states, we show that unique quantum features in optical phase space, absent in the linear amplifier, are retained for extended times, despite the fact that dissipation tends to wash out dynamical features observed at early evolution times. These features are related to the discrete nature of the two-photon matter-field interaction and fingerprint the initial field state at thermodynamic times.

When Time Makes a Difference: Addressing Ergodicity and Complexity in Education

ERIC Educational Resources Information Center

Koopmans, Matthijs

2015-01-01

The detection of complexity in behavioral outcomes often requires an estimation of their variability over a prolonged time spectrum to assess processes of stability and transformation. Conventional scholarship typically relies on time-independent measures, "snapshots", to analyze those outcomes, assuming that group means and their…

Coherence Properties of Strongly Interacting Atomic Vapors in Waveguides

DTIC Science & Technology

2011-12-31

lattice in the mean-field regime [22]. There the goal was to repeat, for our system, the Chirikiov-lzrailev program for Fermi- Pasta -Ulam chain and...define a typical deviation from ergodicity), we introduce a geometric structure— based on the Frobenius or Hilbert-Schmidt inner product—to the space of

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.

Optical Radiation from Integer Quantum Hall States in Dirac Materials

NASA Astrophysics Data System (ADS)

Gullans, Michael; Taylor, Jacob; Ghaemi, Pouyan; Hafezi, Mohammad

Quantum Hall systems exhibit topologically protected edge states, which can have a macroscopic spatial extent. Such edge states provide a unique opportunity to study a quantum emitter whose size far exceeds the wavelength of emitted light. To better understand this limit, we theoretically characterize the optical radiation from integer quantum Hall states in two-dimensional Dirac materials. We show that the scattered light from the bulk reflects the spatial profile of the wavefunctions, enabling spatial imaging of the disorder landscape. We find that the radiation from the edge states are characterized by the presence of large multipole moments in the far-field. This multipole radiation arises from the transfer of angular momentum from the electrons into the scattered light, enabling the generation of coherent light with high orbital angular momentum.

Book Review: John von Neumann and the foundations of quantum physics. (Vienna Circle Institute yearbook (2000), 8) Miklos Redei and Michael Stoltzner (Eds.); Kluwer Academic Publishers, Dordrecht, 2001, pp., US 125, ISBN 0792368126

NASA Astrophysics Data System (ADS)

Lupher, Tracy

2003-12-01

Some people may be surprised to learn that John von Neumann's work on the foundations of quantum physics went far beyond what is contained within the pages of his Mathematical Foundations of Quantum Mechanics (MFQM) (von Neumann, 1955). However, this narrow focus often ignores von Neumann's later work on quantum logic and what are now called in his honor, von Neumann algebras. This volume honoring von Neumann's contributions to physics is unique in that, while it contains 12 papers that examine various aspects of von Neumann's work, it also contains two of his previously unpublished papers and some of his previously unpublished correspondence.

Emerging Connections: Quantum & Classical Optics Incubator Program Book

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lesky, Marcia

The Emerging Connections: Quantum & Classical Optics Incubator was a scientific meeting held in Washington, DC on 6-8 November 2016. This Incubator provided unique and focused experiences and valuable opportunities to discuss advances, challenges and opportunities regarding this important area of research. Quantum optics and classical optics have coexisted for nearly a century as two distinct, but consistent descriptions of light in their respective domains. Recently, a number of detailed examinations of the structure of classical light beams have revealed that effects widely thought to be solely quantum in origin also have a place in classical optics. These new quantum-classicalmore » connections are informing classical optics in meaningful ways specifically by expanding understanding of optical coherence. Simultaneously, relationships discovered with classical light beams now also serve as a vehicle to illuminate concepts that no longer solely belong to the quantum realm. Interference, polarization, coherence, complementarity and entanglement are a partial list of elementary notions that now appear to belong to both quantum and classical optics. The goal of this meeting was to bring emerging quantum-classical links into wider view and to indicate directions in which forthcoming and future work would promote discussion and lead to a more unified understanding of optics.« less

Nonlinear Dynamics, Chaotic and Complex Systems

NASA Astrophysics Data System (ADS)

Infeld, E.; Zelazny, R.; Galkowski, A.

2011-04-01

Part I. Dynamic Systems Bifurcation Theory and Chaos: 1. Chaos in random dynamical systems V. M. Gunldach; 2. Controlling chaos using embedded unstable periodic orbits: the problem of optimal periodic orbits B. R. Hunt and E. Ott; 3. Chaotic tracer dynamics in open hydrodynamical flows G. Karolyi, A. Pentek, T. Tel and Z. Toroczkai; 4. Homoclinic chaos L. P. Shilnikov; Part II. Spatially Extended Systems: 5. Hydrodynamics of relativistic probability flows I. Bialynicki-Birula; 6. Waves in ionic reaction-diffusion-migration systems P. Hasal, V. Nevoral, I. Schreiber, H. Sevcikova, D. Snita, and M. Marek; 7. Anomalous scaling in turbulence: a field theoretical approach V. Lvov and I. Procaccia; 8. Abelian sandpile cellular automata M. Markosova; 9. Transport in an incompletely chaotic magnetic field F. Spineanu; Part III. Dynamical Chaos Quantum Physics and Foundations Of Statistical Mechanics: 10. Non-equilibrium statistical mechanics and ergodic theory L. A. Bunimovich; 11. Pseudochaos in statistical physics B. Chirikov; 12. Foundations of non-equilibrium statistical mechanics J. P. Dougherty; 13. Thermomechanical particle simulations W. G. Hoover, H. A. Posch, C. H. Dellago, O. Kum, C. G. Hoover, A. J. De Groot and B. L. Holian; 14. Quantum dynamics on a Markov background and irreversibility B. Pavlov; 15. Time chaos and the laws of nature I. Prigogine and D. J. Driebe; 16. Evolutionary Q and cognitive systems: dynamic entropies and predictability of evolutionary processes W. Ebeling; 17. Spatiotemporal chaos information processing in neural networks H. Szu; 18. Phase transitions and learning in neural networks C. Van den Broeck; 19. Synthesis of chaos A. Vanecek and S. Celikovsky; 20. Computational complexity of continuous problems H. Wozniakowski; Part IV. Complex Systems As An Interface Between Natural Sciences and Environmental Social and Economic Sciences: 21. Stochastic differential geometry in finance studies V. G. Makhankov; Part V. Conference Banquet Speech: Where will the future go? M. J. Feigenbaum.

Initial condition of stochastic self-assembly

NASA Astrophysics Data System (ADS)

Davis, Jason K.; Sindi, Suzanne S.

2016-02-01

The formation of a stable protein aggregate is regarded as the rate limiting step in the establishment of prion diseases. In these systems, once aggregates reach a critical size the growth process accelerates and thus the waiting time until the appearance of the first critically sized aggregate is a key determinant of disease onset. In addition to prion diseases, aggregation and nucleation is a central step of many physical, chemical, and biological process. Previous studies have examined the first-arrival time at a critical nucleus size during homogeneous self-assembly under the assumption that at time t =0 the system was in the all-monomer state. However, in order to compare to in vivo biological experiments where protein constituents inherited by a newly born cell likely contain intermediate aggregates, other possibilities must be considered. We consider one such possibility by conditioning the unique ergodic size distribution on subcritical aggregate sizes; this least-informed distribution is then used as an initial condition. We make the claim that this initial condition carries fewer assumptions than an all-monomer one and verify that it can yield significantly different averaged waiting times relative to the all-monomer condition under various models of assembly.

Gate-defined Quantum Confinement in Suspended Bilayer Graphene

NASA Astrophysics Data System (ADS)

Allen, Monica

2013-03-01

Quantum confined devices in carbon-based materials offer unique possibilities for applications ranging from quantum computation to sensing. In particular, nanostructured carbon is a promising candidate for spin-based quantum computation due to the ability to suppress hyperfine coupling to nuclear spins, a dominant source of spin decoherence. Yet graphene lacks an intrinsic bandgap, which poses a serious challenge for the creation of such devices. We present a novel approach to quantum confinement utilizing tunnel barriers defined by local electric fields that break sublattice symmetry in suspended bilayer graphene. This technique electrostatically confines charges via band structure control, thereby eliminating the edge and substrate disorder that hinders on-chip etched nanostructures to date. We report clean single electron tunneling through gate-defined quantum dots in two regimes: at zero magnetic field using the energy gap induced by a perpendicular electric field and at finite magnetic fields using Landau level confinement. The observed Coulomb blockade periodicity agrees with electrostatic simulations based on local top-gate geometry, a direct demonstration of local control over the band structure of graphene. This technology integrates quantum confinement with pristine device quality and access to vibrational modes, enabling wide applications from electromechanical sensors to quantum bits. More broadly, the ability to externally tailor the graphene bandgap over nanometer scales opens a new unexplored avenue for creating quantum devices.

Heralded entanglement between solid-state qubits separated by three metres.

PubMed

Bernien, H; Hensen, B; Pfaff, W; Koolstra, G; Blok, M S; Robledo, L; Taminiau, T H; Markham, M; Twitchen, D J; Childress, L; Hanson, R

2013-05-02

Quantum entanglement between spatially separated objects is one of the most intriguing phenomena in physics. The outcomes of independent measurements on entangled objects show correlations that cannot be explained by classical physics. As well as being of fundamental interest, entanglement is a unique resource for quantum information processing and communication. Entangled quantum bits (qubits) can be used to share private information or implement quantum logical gates. Such capabilities are particularly useful when the entangled qubits are spatially separated, providing the opportunity to create highly connected quantum networks or extend quantum cryptography to long distances. Here we report entanglement of two electron spin qubits in diamond with a spatial separation of three metres. We establish this entanglement using a robust protocol based on creation of spin-photon entanglement at each location and a subsequent joint measurement of the photons. Detection of the photons heralds the projection of the spin qubits onto an entangled state. We verify the resulting non-local quantum correlations by performing single-shot readout on the qubits in different bases. The long-distance entanglement reported here can be combined with recently achieved initialization, readout and entanglement operations on local long-lived nuclear spin registers, paving the way for deterministic long-distance teleportation, quantum repeaters and extended quantum networks.

On-chip single photon filtering and multiplexing in hybrid quantum photonic circuits.

PubMed

Elshaari, Ali W; Zadeh, Iman Esmaeil; Fognini, Andreas; Reimer, Michael E; Dalacu, Dan; Poole, Philip J; Zwiller, Val; Jöns, Klaus D

2017-08-30

Quantum light plays a pivotal role in modern science and future photonic applications. Since the advent of integrated quantum nanophotonics different material platforms based on III-V nanostructures-, colour centers-, and nonlinear waveguides as on-chip light sources have been investigated. Each platform has unique advantages and limitations; however, all implementations face major challenges with filtering of individual quantum states, scalable integration, deterministic multiplexing of selected quantum emitters, and on-chip excitation suppression. Here we overcome all of these challenges with a hybrid and scalable approach, where single III-V quantum emitters are positioned and deterministically integrated in a complementary metal-oxide-semiconductor-compatible photonic circuit. We demonstrate reconfigurable on-chip single-photon filtering and wavelength division multiplexing with a foot print one million times smaller than similar table-top approaches, while offering excitation suppression of more than 95 dB and efficient routing of single photons over a bandwidth of 40 nm. Our work marks an important step to harvest quantum optical technologies' full potential.Combining different integration platforms on the same chip is currently one of the main challenges for quantum technologies. Here, Elshaari et al. show III-V Quantum Dots embedded in nanowires operating in a CMOS compatible circuit, with controlled on-chip filtering and tunable routing.

Experimental quantum simulations of many-body physics with trapped ions.

PubMed

Schneider, Ch; Porras, Diego; Schaetz, Tobias

2012-02-01

Direct experimental access to some of the most intriguing quantum phenomena is not granted due to the lack of precise control of the relevant parameters in their naturally intricate environment. Their simulation on conventional computers is impossible, since quantum behaviour arising with superposition states or entanglement is not efficiently translatable into the classical language. However, one could gain deeper insight into complex quantum dynamics by experimentally simulating the quantum behaviour of interest in another quantum system, where the relevant parameters and interactions can be controlled and robust effects detected sufficiently well. Systems of trapped ions provide unique control of both the internal (electronic) and external (motional) degrees of freedom. The mutual Coulomb interaction between the ions allows for large interaction strengths at comparatively large mutual ion distances enabling individual control and readout. Systems of trapped ions therefore exhibit a prominent system in several physical disciplines, for example, quantum information processing or metrology. Here, we will give an overview of different trapping techniques of ions as well as implementations for coherent manipulation of their quantum states and discuss the related theoretical basics. We then report on the experimental and theoretical progress in simulating quantum many-body physics with trapped ions and present current approaches for scaling up to more ions and more-dimensional systems.

Design of Quantum Algorithms Using Physics Tools

DTIC Science & Technology

2014-06-02

invariant spin-1 chain that has a unique highly entangled ground state and exhibits some signatures of critical behavior. The entanglement entropy of one... entangled and found them hard to approximate using the MPS method. In follow on work Shor along with Sergey Bravyi, Libor Caha, Movassagh and Nagaj...They asked how entangled the ground state of a FF quantum spin-s chain with nearest-neighbor interactions can be for small values of s. While FF spin-1

Quantum gravity boundary terms from the spectral action of noncommutative space.

PubMed

Chamseddine, Ali H; Connes, Alain

2007-08-17

We study the boundary terms of the spectral action of the noncommutative space, defined by the spectral triple dictated by the physical spectrum of the standard model, unifying gravity with all other fundamental interactions. We prove that the spectral action predicts uniquely the gravitational boundary term required for consistency of quantum gravity with the correct sign and coefficient. This is a remarkable result given the lack of freedom in the spectral action to tune this term.

Uniqueness of the joint measurement and the structure of the set of compatible quantum measurements

NASA Astrophysics Data System (ADS)

Guerini, Leonardo; Terra Cunha, Marcelo

2018-04-01

We address the problem of characterising the compatible tuples of measurements that admit a unique joint measurement. We derive a uniqueness criterion based on the method of perturbations and apply it to show that extremal points of the set of compatible tuples admit a unique joint measurement, while all tuples that admit a unique joint measurement lie in the boundary of such a set. We also provide counter-examples showing that none of these properties are both necessary and sufficient, thus completely describing the relation between the joint measurement uniqueness and the structure of the compatible set. As a by-product of our investigations, we completely characterise the extremal and boundary points of the set of general tuples of measurements and of the subset of compatible tuples.

Quantum-Sequencing: Fast electronic single DNA molecule sequencing

NASA Astrophysics Data System (ADS)

Casamada Ribot, Josep; Chatterjee, Anushree; Nagpal, Prashant

2014-03-01

A major goal of third-generation sequencing technologies is to develop a fast, reliable, enzyme-free, high-throughput and cost-effective, single-molecule sequencing method. Here, we present the first demonstration of unique ``electronic fingerprint'' of all nucleotides (A, G, T, C), with single-molecule DNA sequencing, using Quantum-tunneling Sequencing (Q-Seq) at room temperature. We show that the electronic state of the nucleobases shift depending on the pH, with most distinct states identified at acidic pH. We also demonstrate identification of single nucleotide modifications (methylation here). Using these unique electronic fingerprints (or tunneling data), we report a partial sequence of beta lactamase (bla) gene, which encodes resistance to beta-lactam antibiotics, with over 95% success rate. These results highlight the potential of Q-Seq as a robust technique for next-generation sequencing.

Visualizing the BEC-BCS crossover in a two-dimensional Fermi gas: Pairing gaps and dynamical response functions from ab initio computations

NASA Astrophysics Data System (ADS)

Vitali, Ettore; Shi, Hao; Qin, Mingpu; Zhang, Shiwei

2017-12-01

Experiments with ultracold atoms provide a highly controllable laboratory setting with many unique opportunities for precision exploration of quantum many-body phenomena. The nature of such systems, with strong interaction and quantum entanglement, makes reliable theoretical calculations challenging. Especially difficult are excitation and dynamical properties, which are often the most directly relevant to experiment. We carry out exact numerical calculations, by Monte Carlo sampling of imaginary-time propagation of Slater determinants, to compute the pairing gap in the two-dimensional Fermi gas from first principles. Applying state-of-the-art analytic continuation techniques, we obtain the spectral function and the density and spin structure factors providing unique tools to visualize the BEC-BCS crossover. These quantities will allow for a direct comparison with experiments.

Plasticity and Kinky Chemistry of Carbon Nanotubes

NASA Technical Reports Server (NTRS)

Srivastava, Deepak; Dzegilenko, Fedor

2000-01-01

Since their discovery in 1991, carbon nanotubes have been the subject of intense research interest based on early predictions of their unique mechanical, electronic, and chemical properties. Materials with the predicted unique properties of carbon nanotubes are of great interest for use in future generations of aerospace vehicles. For their structural properties, carbon nanotubes could be used as reinforcing fibers in ultralight multifunctional composites. For their electronic properties, carbon nanotubes offer the potential of very high-speed, low-power computing elements, high-density data storage, and unique sensors. In a continuing effort to model and predict the properties of carbon nanotubes, Ames accomplished three significant results during FY99. First, accurate values of the nanomechanics and plasticity of carbon nanotubes based on quantum molecular dynamics simulations were computed. Second, the concept of mechanical deformation catalyzed-kinky-chemistry as a means to control local chemistry of nanotubes was discovered. Third, the ease of nano-indentation of silicon surfaces with carbon nanotubes was established. The elastic response and plastic failure mechanisms of single-wall nanotubes were investigated by means of quantum molecular dynamics simulations.

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.

Role of confinements on the melting of Wigner molecules in quantum dots

NASA Astrophysics Data System (ADS)

Bhattacharya, Dyuti; Filinov, Alexei V.; Ghosal, Amit; Bonitz, Michael

2016-03-01

We explore the stability of a Wigner molecule (WM) formed in confinements with different geometries emulating the role of disorder and analyze the melting (or crossover) of such a system. Building on a recent calculation [D. Bhattacharya, A. Ghosal, Eur. Phys. J. B 86, 499 (2013)] that discussed the effects of irregularities on the thermal crossover in classical systems, we expand our studies in the untested territory by including both the effects of quantum fluctuations and of disorder. Our results, using classical and quantum (path integral) Monte Carlo techniques, unfold complementary mechanisms that drive the quantum and thermal crossovers in a WM and show that the symmetry of the confinement plays no significant role in determining the quantum crossover scale n X . This is because the zero-point motion screens the boundary effects within short distances. The phase diagram as a function of thermal and quantum fluctuations determined from independent criteria is unique, and shows "melting" from the WM to both the classical and quantum "liquids". An intriguing signature of weakening liquidity with increasing temperature, T, is found in the extreme quantum regime. The crossover is associated with production of defects. However, these defects appear to play distinct roles in driving the quantum and thermal "melting". Our analyses carry serious implications for a variety of experiments on many-particle systems - semiconductor heterostructure quantum dots, trapped ions, nanoclusters, colloids and complex plasma.

Universal adiabatic quantum computation via the space-time circuit-to-Hamiltonian construction.

PubMed

Gosset, David; Terhal, Barbara M; Vershynina, Anna

2015-04-10

We show how to perform universal adiabatic quantum computation using a Hamiltonian which describes a set of particles with local interactions on a two-dimensional grid. A single parameter in the Hamiltonian is adiabatically changed as a function of time to simulate the quantum circuit. We bound the eigenvalue gap above the unique ground state by mapping our model onto the ferromagnetic XXZ chain with kink boundary conditions; the gap of this spin chain was computed exactly by Koma and Nachtergaele using its q-deformed version of SU(2) symmetry. We also discuss a related time-independent Hamiltonian which was shown by Janzing to be capable of universal computation. We observe that in the limit of large system size, the time evolution is equivalent to the exactly solvable quantum walk on Young's lattice.

Quantum hacking of two-way continuous-variable quantum key distribution using Trojan-horse attack

NASA Astrophysics Data System (ADS)

Ma, Hong-Xin; Bao, Wan-Su; Li, Hong-Wei; Chou, Chun

2016-08-01

We present a Trojan-horse attack on the practical two-way continuous-variable quantum key distribution system. Our attack mainly focuses on the imperfection of the practical system that the modulator has a redundancy of modulation pulse-width, which leaves a loophole for the eavesdropper inserting a Trojan-horse pulse. Utilizing the unique characteristics of two-way continuous-variable quantum key distribution that Alice only takes modulation operation on the received mode without any measurement, this attack allows the eavesdropper to render all of the final keys shared between the legitimate parties insecure without being detected. After analyzing the feasibility of the attack, the corresponding countermeasures are put forward. Project supported by the National Basic Research Program of China (Grant No. 2013CB338002) and the National Natural Science Foundation of China (Grant Nos. 11304397 and 61505261).

Topics in black holes and quantum cosmology

NASA Astrophysics Data System (ADS)

Campiglia, Miguel

2012-06-01

Black holes and the big bang beginning of the universe are among the most spectacular predictions of general relativity, having a broad impact that ranges from observational astronomy to quantum gravity. In this thesis we will focus on classical and quantum aspects of these subjects: In the first part we present a coordinate-free way of describing the approach to equilibrium of black holes within the framework of dynamical and isolated horizons. In the second part we focus on loop quantum cosmology. We present a uniqueness theorem of its kinematics, and explore the possible ways to implement its dynamics via path integrals.¹ ¹The topics presented here form part of the research done during my PhD studies. See the Vita at the end of the Thesis for a complete list of my work during this period.

Universal Adiabatic Quantum Computation via the Space-Time Circuit-to-Hamiltonian Construction

NASA Astrophysics Data System (ADS)

Gosset, David; Terhal, Barbara M.; Vershynina, Anna

2015-04-01

We show how to perform universal adiabatic quantum computation using a Hamiltonian which describes a set of particles with local interactions on a two-dimensional grid. A single parameter in the Hamiltonian is adiabatically changed as a function of time to simulate the quantum circuit. We bound the eigenvalue gap above the unique ground state by mapping our model onto the ferromagnetic X X Z chain with kink boundary conditions; the gap of this spin chain was computed exactly by Koma and Nachtergaele using its q -deformed version of SU(2) symmetry. We also discuss a related time-independent Hamiltonian which was shown by Janzing to be capable of universal computation. We observe that in the limit of large system size, the time evolution is equivalent to the exactly solvable quantum walk on Young's lattice.

A Manifesto on Psychology as Idiographic Science: Bringing the Person Back into Scientific Psychology, This Time Forever

ERIC Educational Resources Information Center

Molenaar, Peter C. M.

2004-01-01

Psychology is focused on variation between cases (interindividual variation). Results thus obtained are considered to be generalizable to the understanding and explanation of variation within single cases (intraindividual variation). It is indicated, however, that the direct consequences of the classical ergodic theorems for psychology and…

A Proposal for Research on Complex Media, Imagining and Uncertainty Quantification

DTIC Science & Technology

2013-11-26

demonstration that the Green’s function for wave propagation in an ergodic cavity can be recovered exactly by cross correlation of signals at two points...the continuation of a project in which we have developed autofocus methods based on a phase space formulation ( Wigner transform) of the array data and

A fast ergodic algorithm for generating ensembles of equilateral random polygons

NASA Astrophysics Data System (ADS)

Varela, R.; Hinson, K.; Arsuaga, J.; Diao, Y.

2009-03-01

Knotted structures are commonly found in circular DNA and along the backbone of certain proteins. In order to properly estimate properties of these three-dimensional structures it is often necessary to generate large ensembles of simulated closed chains (i.e. polygons) of equal edge lengths (such polygons are called equilateral random polygons). However finding efficient algorithms that properly sample the space of equilateral random polygons is a difficult problem. Currently there are no proven algorithms that generate equilateral random polygons with its theoretical distribution. In this paper we propose a method that generates equilateral random polygons in a 'step-wise uniform' way. We prove that this method is ergodic in the sense that any given equilateral random polygon can be generated by this method and we show that the time needed to generate an equilateral random polygon of length n is linear in terms of n. These two properties make this algorithm a big improvement over the existing generating methods. Detailed numerical comparisons of our algorithm with other widely used algorithms are provided.

Revealing nonergodic dynamics in living cells from a single particle trajectory

NASA Astrophysics Data System (ADS)

Lanoiselée, Yann; Grebenkov, Denis S.

2016-05-01

We propose the improved ergodicity and mixing estimators to identify nonergodic dynamics from a single particle trajectory. The estimators are based on the time-averaged characteristic function of the increments and can thus capture additional information on the process as compared to the conventional time-averaged mean-square displacement. The estimators are first investigated and validated for several models of anomalous diffusion, such as ergodic fractional Brownian motion and diffusion on percolating clusters, and nonergodic continuous-time random walks and scaled Brownian motion. The estimators are then applied to two sets of earlier published trajectories of mRNA molecules inside live Escherichia coli cells and of Kv2.1 potassium channels in the plasma membrane. These statistical tests did not reveal nonergodic features in the former set, while some trajectories of the latter set could be classified as nonergodic. Time averages along such trajectories are thus not representative and may be strongly misleading. Since the estimators do not rely on ensemble averages, the nonergodic features can be revealed separately for each trajectory, providing a more flexible and reliable analysis of single-particle tracking experiments in microbiology.

Statistical Analysis of the First Passage Path Ensemble of Jump Processes

NASA Astrophysics Data System (ADS)

von Kleist, Max; Schütte, Christof; Zhang, Wei

2018-02-01

The transition mechanism of jump processes between two different subsets in state space reveals important dynamical information of the processes and therefore has attracted considerable attention in the past years. In this paper, we study the first passage path ensemble of both discrete-time and continuous-time jump processes on a finite state space. The main approach is to divide each first passage path into nonreactive and reactive segments and to study them separately. The analysis can be applied to jump processes which are non-ergodic, as well as continuous-time jump processes where the waiting time distributions are non-exponential. In the particular case that the jump processes are both Markovian and ergodic, our analysis elucidates the relations between the study of the first passage paths and the study of the transition paths in transition path theory. We provide algorithms to numerically compute statistics of the first passage path ensemble. The computational complexity of these algorithms scales with the complexity of solving a linear system, for which efficient methods are available. Several examples demonstrate the wide applicability of the derived results across research areas.

A Spectral Approach for Quenched Limit Theorems for Random Expanding Dynamical Systems

NASA Astrophysics Data System (ADS)

Dragičević, D.; Froyland, G.; González-Tokman, C.; Vaienti, S.

2018-06-01

We prove quenched versions of (i) a large deviations principle (LDP), (ii) a central limit theorem (CLT), and (iii) a local central limit theorem for non-autonomous dynamical systems. A key advance is the extension of the spectral method, commonly used in limit laws for deterministic maps, to the general random setting. We achieve this via multiplicative ergodic theory and the development of a general framework to control the regularity of Lyapunov exponents of twisted transfer operator cocycles with respect to a twist parameter. While some versions of the LDP and CLT have previously been proved with other techniques, the local central limit theorem is, to our knowledge, a completely new result, and one that demonstrates the strength of our method. Applications include non-autonomous (piecewise) expanding maps, defined by random compositions of the form {T_{σ^{n-1} ω} circ\\cdotscirc T_{σω}circ T_ω}. An important aspect of our results is that we only assume ergodicity and invertibility of the random driving {σ:Ω\\toΩ} ; in particular no expansivity or mixing properties are required.

Linking density functional and mode coupling models for supercooled liquids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Premkumar, Leishangthem; Bidhoodi, Neeta; Das, Shankar P.

2016-03-28

We compare predictions from two familiar models of the metastable supercooled liquid, respectively, constructed with thermodynamic and dynamic approaches. In the so called density functional theory the free energy F[ρ] of the liquid is a functional of the inhomogeneous density ρ(r). The metastable state is identified as a local minimum of F[ρ]. The sharp density profile characterizing ρ(r) is identified as a single particle oscillator, whose frequency is obtained from the parameters of the optimum density function. On the other hand, a dynamic approach to supercooled liquids is taken in the mode coupling theory (MCT) which predict a sharp ergodicity-non-ergodicitymore » transition at a critical density. The single particle dynamics in the non-ergodic state, treated approximately, represents a propagating mode whose characteristic frequency is computed from the corresponding memory function of the MCT. The mass localization parameters in the above two models (treated in their simplest forms) are obtained, respectively, in terms of the corresponding natural frequencies depicted and are shown to have comparable magnitudes.« less

A Spectral Approach for Quenched Limit Theorems for Random Expanding Dynamical Systems

NASA Astrophysics Data System (ADS)

Dragičević, D.; Froyland, G.; González-Tokman, C.; Vaienti, S.

2018-01-01

We prove quenched versions of (i) a large deviations principle (LDP), (ii) a central limit theorem (CLT), and (iii) a local central limit theorem for non-autonomous dynamical systems. A key advance is the extension of the spectral method, commonly used in limit laws for deterministic maps, to the general random setting. We achieve this via multiplicative ergodic theory and the development of a general framework to control the regularity of Lyapunov exponents of twisted transfer operator cocycles with respect to a twist parameter. While some versions of the LDP and CLT have previously been proved with other techniques, the local central limit theorem is, to our knowledge, a completely new result, and one that demonstrates the strength of our method. Applications include non-autonomous (piecewise) expanding maps, defined by random compositions of the form {T_{σ^{n-1} ω} circ\\cdotscirc T_{σω}circ T_ω} . An important aspect of our results is that we only assume ergodicity and invertibility of the random driving {σ:Ω\\toΩ} ; in particular no expansivity or mixing properties are required.

Collision-induced evaporation of water clusters and contribution of momentum transfer

NASA Astrophysics Data System (ADS)

Calvo, Florent; Berthias, Francis; Feketeová, Linda; Abdoul-Carime, Hassan; Farizon, Bernadette; Farizon, Michel

2017-05-01

The evaporation of water molecules from high-velocity argon atoms impinging on protonated water clusters has been computationally investigated using molecular dynamics simulations with the reactive OSS2 potential to model water clusters and the ZBL pair potential to represent their interaction with the projectile. Swarms of trajectories and an event-by-event analysis reveal the conditions under which a specific number of molecular evaporation events is found one nanosecond after impact, thereby excluding direct knockout events from the analysis. These simulations provide velocity distributions that exhibit two main features, with a major statistical component arising from a global redistribution of the collision energy into intermolecular degrees of freedom, and another minor but non-ergodic feature at high velocities. The latter feature is produced by direct impacts on the peripheral water molecules and reflects a more complete momentum transfer. These two components are consistent with recent experimental measurements and confirm that electronic processes are not explicitly needed to explain the observed non-ergodic behavior. Contribution to the Topical Issue "Dynamics of Systems at the Nanoscale", edited by Andrey Solov'yov and Andrei Korol.

Quantum oscillations in a biaxial pair density wave state.

PubMed

Norman, M R; Davis, J C Séamus

2018-05-22

There has been growing speculation that a pair density wave state is a key component of the phenomenology of the pseudogap phase in the cuprates. Recently, direct evidence for such a state has emerged from an analysis of scanning tunneling microscopy data in halos around the vortex cores. By extrapolation, these vortex halos would then overlap at a magnetic-field scale where quantum oscillations have been observed. Here, we show that a biaxial pair density wave state gives a unique description of the quantum oscillation data, bolstering the case that the pseudogap phase in the cuprates may be a pair density wave state. Copyright © 2018 the Author(s). Published by PNAS.

Quantum spreading of a self-gravitating wave-packet in singularity free gravity

NASA Astrophysics Data System (ADS)

Buoninfante, Luca; Lambiase, Gaetano; Mazumdar, Anupam

2018-01-01

In this paper we will study for the first time how the wave-packet of a self-gravitating meso-scopic system spreads in theories beyond Einstein's general relativity. In particular, we will consider a ghost-free infinite derivative gravity, which resolves the 1 / r singularity in the potential - such that the gradient of the potential vanishes within the scale of non-locality. We will show that a quantum wave-packet spreads faster for a ghost-free and singularity-free gravity as compared to the Newtonian case, therefore providing us a unique scenario for testing classical and quantum properties of short-distance gravity in a laboratory in the near future.

Effect of the depolarization field on coherent optical properties in semiconductor quantum dots

NASA Astrophysics Data System (ADS)

Mitsumori, Yasuyoshi; Watanabe, Shunta; Asakura, Kenta; Seki, Keisuke; Edamatsu, Keiichi; Akahane, Kouichi; Yamamoto, Naokatsu

2018-06-01

We study the photon echo spectrum of self-assembled semiconductor quantum dots using femtosecond light pulses. The spectrum shape changes from a single-peaked to a double-peaked structure as the time delay between the two excitation pulses is increased. The spectrum change is reproduced by numerical calculations, which include the depolarization field induced by the biexciton-exciton transition as well as the conventional local-field effect for the exciton-ground-state transition in a quantum dot. Our findings suggest that various optical transitions in tightly localized systems generate a depolarization field, which renormalizes the resonant frequency with a change in the polarization itself, leading to unique optical properties.

Multimode analysis of highly tunable, quantum cascade powered, circular graphene spaser

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jayasekara, Charith, E-mail: charith.jayasekara@monash.edu; Premaratne, Malin; Stockman, Mark I.

2015-11-07

We carried out a detailed analysis of a circular graphene spaser made of a circular graphene flake and a quantum cascade well structure. Owing to unique properties of graphene and quantum cascade well structure, the proposed design shows high mechanical and thermal stability and low optical losses. Additionally, operation characteristics of the model are analysed and tunability of the device is demonstrated. Some advantages of the proposed design include compact size, lower power operation, and the ability to set the operating wavelength over a wide range from Mid-IR to Near-IR. Thus, it can have wide spread applications including designing ofmore » ultracompact and ultrafast devices, nanoscopy and biomedical applications.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen Lin; Chen Yixin

We show that no universal quantum cloning machine exists that can broadcast an arbitrary mixed qubit with a constant fidelity. Based on this result, we investigate the dependent quantum cloner in the sense that some parameter of the input qubit {rho}{sub s}({theta},{omega},{lambda}) is regarded as constant in the fidelity. For the case of constant {omega}, we establish the 1{yields}2 optimal symmetric dependent cloner with a fidelity 1/2. It is also shown that the 1{yields}M optimal quantum cloning machine for pure qubits is also optimal for mixed qubits, when {lambda} is the unique parameter in the fidelity. For general N{yields}M broadcastingmore » of mixed qubits, the situation is very different.« less

Measuring entanglement entropy of a generic many-body system with a quantum switch.

PubMed

Abanin, Dmitry A; Demler, Eugene

2012-07-13

Entanglement entropy has become an important theoretical concept in condensed matter physics because it provides a unique tool for characterizing quantum mechanical many-body phases and new kinds of quantum order. However, the experimental measurement of entanglement entropy in a many-body system is widely believed to be unfeasible, owing to the nonlocal character of this quantity. Here, we propose a general method to measure the entanglement entropy. The method is based on a quantum switch (a two-level system) coupled to a composite system consisting of several copies of the original many-body system. The state of the switch controls how different parts of the composite system connect to each other. We show that, by studying the dynamics of the quantum switch only, the Rényi entanglement entropy of the many-body system can be extracted. We propose a possible design of the quantum switch, which can be realized in cold atomic systems. Our work provides a route towards testing the scaling of entanglement in critical systems as well as a method for a direct experimental detection of topological order.

Exchange interaction and the tunneling induced transparency in coupled quantum dots

NASA Astrophysics Data System (ADS)

Borges, Halyne; Alcalde, Augusto; Ulloa, Sergio

2014-03-01

Stacked semiconductor quantum dots coupled by tunneling are unique ``quantum molecule'' where it is possible to create a multilevel structure of excitonic states. This structure allows the investigation of quantum interference processes and their control via electric external fields. In this work, we investigate the optical response of a quantum molecule coherently driven by a polarized laser, considering the splitting in excitonic levels caused by isotropic and anisotropic exchange interactions. In our model we consider interdot transitions mediated by the the hole tunneling between states with the same total spin and, between bright and dark exciton states. Using realistic experimental parameters, we demonstrate that the excitonic states coupled by tunneling exhibit an enriched and controllable optical response. Our results show that through the appropriate control of the external electric field and light polarization, the tunneling coupling establishes an efficient destructive quantum interference path that creates a transparency window in the absorption spectra, whenever states of appropriate symmetry are mixed by the hole tunneling. We explore the relevant parameters space that would allows with the experiments. CAPES, INCT-IQ and MWN/CIAM-NSF.

Exploring the nonequilibrium dynamics of ultracold quantum gases by using numerical tools

NASA Astrophysics Data System (ADS)

Heidrich-Meisner, Fabian

Numerical tools such as exact diagonalization or the density matrix renormalization group method have been vital for the study of the nonequilibrium dynamics of strongly correlated many-body systems. Moreover, they provided unique insight for the interpretation of quantum gas experiments, whenever a direct comparison with theory is possible. By considering the example of the experiment by Ronzheimer et al., in which both an interaction quench and the release of bosons from a trap into an empty optical lattice (sudden expansion) was realized, I discuss several nonequilibrium effects of strongly interacting quantum gases. These include the thermalization of a closed quantum system and its connection to the eigenstate thermalization hypothesis, nonequilibrium mass transport, dynamical fermionization, and transient phenomena such as quantum distillation or dynamical quasicondensation. I highlight the role of integrability in giving rise to ballistic transport in strongly interacting 1D systems and in determining the asymptotic state after a quantum quench. The talk concludes with a perspective on open questions concerning 2D systems and the numerical simulation of their nonequilibrium dynamics. Supported by Deutsche Forschungsgemeinschaft (DFG) via FOR 801.

High-fidelity entanglement between a trapped ion and a telecom photon via quantum frequency conversion.

PubMed

Bock, Matthias; Eich, Pascal; Kucera, Stephan; Kreis, Matthias; Lenhard, Andreas; Becher, Christoph; Eschner, Jürgen

2018-05-21

Entanglement between a stationary quantum system and a flying qubit is an essential ingredient of a quantum-repeater network. It has been demonstrated for trapped ions, trapped atoms, color centers in diamond, or quantum dots. These systems have transition wavelengths in the blue, red or near-infrared spectral regions, whereas long-range fiber-communication requires wavelengths in the low-loss, low-dispersion telecom regime. A proven tool to interconnect flying qubits at visible/NIR wavelengths to the telecom bands is quantum frequency conversion. Here we use an efficient polarization-preserving frequency converter connecting 854 nm to the telecom O-band at 1310 nm to demonstrate entanglement between a trapped 40 Ca + ion and the polarization state of a telecom photon with a high fidelity of 98.2 ± 0.2%. The unique combination of 99.75 ± 0.18% process fidelity in the polarization-state conversion, 26.5% external frequency conversion efficiency and only 11.4 photons/s conversion-induced unconditional background makes the converter a powerful ion-telecom quantum interface.

Measurement and control of a Coulomb-blockaded parafermion box

NASA Astrophysics Data System (ADS)

Snizhko, Kyrylo; Egger, Reinhold; Gefen, Yuval

2018-02-01

Parafermionic zero modes are fractional topologically protected quasiparticles expected to arise in various platforms. We show that Coulomb charging effects define a parafermion box with unique access options via fractional edge states and/or quantum antidots. Basic protocols for the detection, manipulation, and control of parafermionic quantum states are formulated. With those tools, one may directly observe the dimension of the zero-mode Hilbert space, prove the degeneracy of this space, and perform on-demand digital operations satisfying a parafermionic algebra.

Importance of parametrizing constraints in quantum-mechanical variational calculations

NASA Technical Reports Server (NTRS)

Chung, Kwong T.; Bhatia, A. K.

1992-01-01

In variational calculations of quantum mechanics, constraints are sometimes imposed explicitly on the wave function. These constraints, which are deduced by physical arguments, are often not uniquely defined. In this work, the advantage of parametrizing constraints and letting the variational principle determine the best possible constraint for the problem is pointed out. Examples are carried out to show the surprising effectiveness of the variational method if constraints are parameterized. It is also shown that misleading results may be obtained if a constraint is not parameterized.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bianchi, Eugenio; Speziale, Simone; Dona, Pietro

Intertwiners are the building blocks of spin-network states. The space of intertwiners is the quantization of a classical symplectic manifold introduced by Kapovich and Millson. Here we show that a theorem by Minkowski allows us to interpret generic configurations in this space as bounded convex polyhedra in R{sup 3}: A polyhedron is uniquely described by the areas and normals to its faces. We provide a reconstruction of the geometry of the polyhedron: We give formulas for the edge lengths, the volume, and the adjacency of its faces. At the quantum level, this correspondence allows us to identify an intertwiner withmore » the state of a quantum polyhedron, thus generalizing the notion of the quantum tetrahedron familiar in the loop quantum gravity literature. Moreover, coherent intertwiners result to be peaked on the classical geometry of polyhedra. We discuss the relevance of this result for loop quantum gravity. In particular, coherent spin-network states with nodes of arbitrary valence represent a collection of semiclassical polyhedra. Furthermore, we introduce an operator that measures the volume of a quantum polyhedron and examine its relation with the standard volume operator of loop quantum gravity. We also comment on the semiclassical limit of spin foams with nonsimplicial graphs.« less

Control of spontaneous emission of quantum dots using correlated effects of metal oxides and dielectric materials

NASA Astrophysics Data System (ADS)

Sadeghi, S. M.; Wing, W. J.; Gutha, R. R.; Capps, L.

2017-03-01

We study the emission dynamics of semiconductor quantum dots in the presence of the correlated impact of metal oxides and dielectric materials. For this we used layered material structures consisting of a base substrate, a dielectric layer, and an ultrathin layer of a metal oxide. After depositing colloidal CdSe/ZnS quantum dots on the top of the metal oxide, we used spectral and time-resolved techniques to show that, depending on the type and thickness of the dielectric material, the metal oxide can characteristically change the interplay between intrinsic excitons, defect states, and the environment, offering new material properties. Our results show that aluminum oxide, in particular, can strongly change the impact of amorphous silicon on the emission dynamics of quantum dots by balancing the intrinsic near band emission and fast trapping of carriers. In such a system the silicon/aluminum oxide charge barrier can lead to large variation of the radiative lifetime of quantum dots and control of the photo-ejection rate of electrons in quantum dots. The results provide unique techniques to investigate and modify physical properties of dielectrics and manage optical and electrical properties of quantum dots.

Control of spontaneous emission of quantum dots using correlated effects of metal oxides and dielectric materials.

PubMed

Sadeghi, S M; Wing, W J; Gutha, R R; Capps, L

2017-03-03

We study the emission dynamics of semiconductor quantum dots in the presence of the correlated impact of metal oxides and dielectric materials. For this we used layered material structures consisting of a base substrate, a dielectric layer, and an ultrathin layer of a metal oxide. After depositing colloidal CdSe/ZnS quantum dots on the top of the metal oxide, we used spectral and time-resolved techniques to show that, depending on the type and thickness of the dielectric material, the metal oxide can characteristically change the interplay between intrinsic excitons, defect states, and the environment, offering new material properties. Our results show that aluminum oxide, in particular, can strongly change the impact of amorphous silicon on the emission dynamics of quantum dots by balancing the intrinsic near band emission and fast trapping of carriers. In such a system the silicon/aluminum oxide charge barrier can lead to large variation of the radiative lifetime of quantum dots and control of the photo-ejection rate of electrons in quantum dots. The results provide unique techniques to investigate and modify physical properties of dielectrics and manage optical and electrical properties of quantum dots.

Autonomous quantum to classical transitions and the generalized imaging theorem

NASA Astrophysics Data System (ADS)

Briggs, John S.; Feagin, James M.

2016-03-01

The mechanism of the transition of a dynamical system from quantum to classical mechanics is of continuing interest. Practically it is of importance for the interpretation of multi-particle coincidence measurements performed at macroscopic distances from a microscopic reaction zone. Here we prove the generalized imaging theorem which shows that the spatial wave function of any multi-particle quantum system, propagating over distances and times large on an atomic scale but still microscopic, and subject to deterministic external fields and particle interactions, becomes proportional to the initial momentum wave function where the position and momentum coordinates define a classical trajectory. Currently, the quantum to classical transition is considered to occur via decoherence caused by stochastic interaction with an environment. The imaging theorem arises from unitary Schrödinger propagation and so is valid without any environmental interaction. It implies that a simultaneous measurement of both position and momentum will define a unique classical trajectory, whereas a less complete measurement of say position alone can lead to quantum interference effects.

An integrated approach to realizing high-performance liquid-junction quantum dot sensitized solar cells

PubMed Central

McDaniel, Hunter; Fuke, Nobuhiro; Makarov, Nikolay S.; Pietryga, Jeffrey M.; Klimov, Victor I.

2013-01-01

Solution-processed semiconductor quantum dot solar cells offer a path towards both reduced fabrication cost and higher efficiency enabled by novel processes such as hot-electron extraction and carrier multiplication. Here we use a new class of low-cost, low-toxicity CuInSexS2−x quantum dots to demonstrate sensitized solar cells with certified efficiencies exceeding 5%. Among other material and device design improvements studied, use of a methanol-based polysulfide electrolyte results in a particularly dramatic enhancement in photocurrent and reduced series resistance. Despite the high vapour pressure of methanol, the solar cells are stable for months under ambient conditions, which is much longer than any previously reported quantum dot sensitized solar cell. This study demonstrates the large potential of CuInSexS2−x quantum dots as active materials for the realization of low-cost, robust and efficient photovoltaics as well as a platform for investigating various advanced concepts derived from the unique physics of the nanoscale size regime. PMID:24322379

Blue and green electroluminescence from CdSe nanocrystal quantum-dot-quantum-wells

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lu, Y. F.; Cao, X. A., E-mail: xacao@mail.wvu.edu

2014-11-17

CdS/CdSe/ZnS quantum dot quantum well (QDQW) nanocrystals were synthesized using the successive ion layer adsorption and reaction technique, and their optical properties were tuned by bandgap and strain engineering. 3-monolayer (ML) CdSe QWs emitted blue photoluminescence at 467 nm with a spectral full-width-at-half-maximum of ∼30 nm. With a 3 ML ZnS cladding layer, which also acts as a passivating and strain-compensating layer, the QDQWs acquired a ∼35% quantum yield of the QW emission. Blue and green electroluminescence (EL) was obtained from QDQW light-emitting devices with 3–4.5 ML CdSe QWs. It was found that as the peak blueshifted, the overall EL was increasinglymore » dominated by defect state emission due to poor hole injection into the QDQWs. The weak EL was also attributed to strong field-induced charge separation resulting from the unique QDQW geometry, weakening the oscillator strength of optical transitions.« less

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.

Utilizing a CdTe quantum dots-enzyme hybrid system for the determination of both phenolic compounds and hydrogen peroxide.

PubMed

Yuan, Jipei; Guo, Weiwei; Wang, Erkang

2008-02-15

In this paper, we attempt to construct a simple and sensitive detection method for both phenolic compounds and hydrogen peroxide, with the successful combination of the unique property of quantum dots and the specificity of enzymatic reactions. In the presence of H2O2 and horseradish peroxidase, phenolic compounds can quench quantum dots' photoluminescence efficiently, and the extent of quenching is severalfold to more than 100-fold increase. Quinone intermediates produced from the enzymatic catalyzed oxidation of phenolic compounds were believed to play the main role in the photoluminescence quenching. Using a quantum dots-enzyme system, the detection limits for phenolic compounds and hydrogen peroxide were detected to be approximately 10(-7) mol L(-1). The coupling of efficient quenching of quantum dot photoluminescence by quinone and the effective enzymatic reactions make this a simple and sensitive method for phenolic compound detection and great potential in the development of H2O2 biosensors for various analytes.

A Pumping Algorithm for Ergodic Stochastic Mean Payoff Games with Perfect Information

NASA Astrophysics Data System (ADS)

Boros, Endre; Elbassioni, Khaled; Gurvich, Vladimir; Makino, Kazuhisa

In this paper, we consider two-person zero-sum stochastic mean payoff games with perfect information, or BWR-games, given by a digraph G = (V = V B ∪ V W ∪ V R , E), with local rewards r: E to { R}, and three types of vertices: black V B , white V W , and random V R . The game is played by two players, White and Black: When the play is at a white (black) vertex v, White (Black) selects an outgoing arc (v,u). When the play is at a random vertex v, a vertex u is picked with the given probability p(v,u). In all cases, Black pays White the value r(v,u). The play continues forever, and White aims to maximize (Black aims to minimize) the limiting mean (that is, average) payoff. It was recently shown in [7] that BWR-games are polynomially equivalent with the classical Gillette games, which include many well-known subclasses, such as cyclic games, simple stochastic games (SSG's), stochastic parity games, and Markov decision processes. In this paper, we give a new algorithm for solving BWR-games in the ergodic case, that is when the optimal values do not depend on the initial position. Our algorithm solves a BWR-game by reducing it, using a potential transformation, to a canonical form in which the optimal strategies of both players and the value for every initial position are obvious, since a locally optimal move in it is optimal in the whole game. We show that this algorithm is pseudo-polynomial when the number of random nodes is constant. We also provide an almost matching lower bound on its running time, and show that this bound holds for a wider class of algorithms. Let us add that the general (non-ergodic) case is at least as hard as SSG's, for which no pseudo-polynomial algorithm is known.

Local and global approaches to the problem of Poincaré recurrences. Applications in nonlinear dynamics

NASA Astrophysics Data System (ADS)

Anishchenko, V. S.; Boev, Ya. I.; Semenova, N. I.; Strelkova, G. I.

2015-07-01

We review rigorous and numerical results on the statistics of Poincaré recurrences which are related to the modern development of the Poincaré recurrence problem. We analyze and describe the rigorous results which are achieved both in the classical (local) approach and in the recently developed global approach. These results are illustrated by numerical simulation data for simple chaotic and ergodic systems. It is shown that the basic theoretical laws can be applied to noisy systems if the probability measure is ergodic and stationary. Poincaré recurrences are studied numerically in nonautonomous systems. Statistical characteristics of recurrences are analyzed in the framework of the global approach for the cases of positive and zero topological entropy. We show that for the positive entropy, there is a relationship between the Afraimovich-Pesin dimension, Lyapunov exponents and the Kolmogorov-Sinai entropy either without and in the presence of external noise. The case of zero topological entropy is exemplified by numerical results for the Poincare recurrence statistics in the circle map. We show and prove that the dependence of minimal recurrence times on the return region size demonstrates universal properties for the golden and the silver ratio. The behavior of Poincaré recurrences is analyzed at the critical point of Feigenbaum attractor birth. We explore Poincaré recurrences for an ergodic set which is generated in the stroboscopic section of a nonautonomous oscillator and is similar to a circle shift. Based on the obtained results we show how the Poincaré recurrence statistics can be applied for solving a number of nonlinear dynamics issues. We propose and illustrate alternative methods for diagnosing effects of external and mutual synchronization of chaotic systems in the context of the local and global approaches. The properties of the recurrence time probability density can be used to detect the stochastic resonance phenomenon. We also discuss how the fractal dimension of chaotic attractors can be estimated using the Poincaré recurrence statistics.

Quantum supremacy in constant-time measurement-based computation: A unified architecture for sampling and verification

NASA Astrophysics Data System (ADS)

Miller, Jacob; Sanders, Stephen; Miyake, Akimasa

2017-12-01

While quantum speed-up in solving certain decision problems by a fault-tolerant universal quantum computer has been promised, a timely research interest includes how far one can reduce the resource requirement to demonstrate a provable advantage in quantum devices without demanding quantum error correction, which is crucial for prolonging the coherence time of qubits. We propose a model device made of locally interacting multiple qubits, designed such that simultaneous single-qubit measurements on it can output probability distributions whose average-case sampling is classically intractable, under similar assumptions as the sampling of noninteracting bosons and instantaneous quantum circuits. Notably, in contrast to these previous unitary-based realizations, our measurement-based implementation has two distinctive features. (i) Our implementation involves no adaptation of measurement bases, leading output probability distributions to be generated in constant time, independent of the system size. Thus, it could be implemented in principle without quantum error correction. (ii) Verifying the classical intractability of our sampling is done by changing the Pauli measurement bases only at certain output qubits. Our usage of random commuting quantum circuits in place of computationally universal circuits allows a unique unification of sampling and verification, so they require the same physical resource requirements in contrast to the more demanding verification protocols seen elsewhere in the literature.

Quantum realization of the nearest neighbor value interpolation method for INEQR

NASA Astrophysics Data System (ADS)

Zhou, RiGui; Hu, WenWen; Luo, GaoFeng; Liu, XingAo; Fan, Ping

2018-07-01

This paper presents the nearest neighbor value (NNV) interpolation algorithm for the improved novel enhanced quantum representation of digital images (INEQR). It is necessary to use interpolation in image scaling because there is an increase or a decrease in the number of pixels. The difference between the proposed scheme and nearest neighbor interpolation is that the concept applied, to estimate the missing pixel value, is guided by the nearest value rather than the distance. Firstly, a sequence of quantum operations is predefined, such as cyclic shift transformations and the basic arithmetic operations. Then, the feasibility of the nearest neighbor value interpolation method for quantum image of INEQR is proven using the previously designed quantum operations. Furthermore, quantum image scaling algorithm in the form of circuits of the NNV interpolation for INEQR is constructed for the first time. The merit of the proposed INEQR circuit lies in their low complexity, which is achieved by utilizing the unique properties of quantum superposition and entanglement. Finally, simulation-based experimental results involving different classical images and ratios (i.e., conventional or non-quantum) are simulated based on the classical computer's MATLAB 2014b software, which demonstrates that the proposed interpolation method has higher performances in terms of high resolution compared to the nearest neighbor and bilinear interpolation.

Realization of a Knill-Laflamme-Milburn controlled-NOT photonic quantum circuit combining effective optical nonlinearities

PubMed Central

Okamoto, Ryo; O’Brien, Jeremy L.; Hofmann, Holger F.; Takeuchi, Shigeki

2011-01-01

Quantum information science addresses how uniquely quantum mechanical phenomena such as superposition and entanglement can enhance communication, information processing, and precision measurement. Photons are appealing for their low-noise, light-speed transmission and ease of manipulation using conventional optical components. However, the lack of highly efficient optical Kerr nonlinearities at the single photon level was a major obstacle. In a breakthrough, Knill, Laflamme, and Milburn (KLM) showed that such an efficient nonlinearity can be achieved using only linear optical elements, auxiliary photons, and measurement [Knill E, Laflamme R, Milburn GJ (2001) Nature 409:46–52]. KLM proposed a heralded controlled-NOT (CNOT) gate for scalable quantum computation using a photonic quantum circuit to combine two such nonlinear elements. Here we experimentally demonstrate a KLM CNOT gate. We developed a stable architecture to realize the required four-photon network of nested multiple interferometers based on a displaced-Sagnac interferometer and several partially polarizing beamsplitters. This result confirms the first step in the original KLM “recipe” for all-optical quantum computation, and should be useful for on-demand entanglement generation and purification. Optical quantum circuits combining giant optical nonlinearities may find wide applications in quantum information processing, communication, and sensing. PMID:21646543

Quantum gravity in timeless configuration space

NASA Astrophysics Data System (ADS)

Gomes, Henrique

2017-12-01

On the path towards quantum gravity we find friction between temporal relations in quantum mechanics (QM) (where they are fixed and field-independent), and in general relativity (where they are field-dependent and dynamic). This paper aims to attenuate that friction, by encoding gravity in the timeless configuration space of spatial fields with dynamics given by a path integral. The framework demands that boundary conditions for this path integral be uniquely given, but unlike other approaches where they are prescribed—such as the no-boundary and the tunneling proposals—here I postulate basic principles to identify boundary conditions in a large class of theories. Uniqueness arises only if a reduced configuration space can be defined and if it has a profoundly asymmetric fundamental structure. These requirements place strong restrictions on the field and symmetry content of theories encompassed here; shape dynamics is one such theory. When these constraints are met, any emerging theory will have a Born rule given merely by a particular volume element built from the path integral in (reduced) configuration space. Also as in other boundary proposals, Time, including space-time, emerges as an effective concept; valid for certain curves in configuration space but not assumed from the start. When some such notion of time becomes available, conservation of (positive) probability currents ensues. I show that, in the appropriate limits, a Schrödinger equation dictates the evolution of weakly coupled source fields on a classical gravitational background. Due to the asymmetry of reduced configuration space, these probabilities and currents avoid a known difficulty of standard WKB approximations for Wheeler DeWitt in minisuperspace: the selection of a unique Hamilton–Jacobi solution to serve as background. I illustrate these constructions with a simple example of a full quantum gravitational theory (i.e. not in minisuperspace) for which the formalism is applicable, and give a formula for calculating gravitational semi-classical relative probabilities in it.

Existence of a coupled system of fractional differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ibrahim, Rabha W.; Siri, Zailan

2015-10-22

We manage the existence and uniqueness of a fractional coupled system containing Schrödinger equations. Such a system appears in quantum mechanics. We confirm that the fractional system under consideration admits a global solution in appropriate functional spaces. The solution is shown to be unique. The method is based on analytic technique of the fixed point theory. The fractional differential operator is considered from the virtue of the Riemann-Liouville differential operator.

He-Ion Microscopy as a High-Resolution Probe for Complex Quantum Heterostructures in Core-Shell Nanowires.

PubMed

Pöpsel, Christian; Becker, Jonathan; Jeon, Nari; Döblinger, Markus; Stettner, Thomas; Gottschalk, Yeanitza Trujillo; Loitsch, Bernhard; Matich, Sonja; Altzschner, Marcus; Holleitner, Alexander W; Finley, Jonathan J; Lauhon, Lincoln J; Koblmüller, Gregor

2018-06-13

Core-shell semiconductor nanowires (NW) with internal quantum heterostructures are amongst the most complex nanostructured materials to be explored for assessing the ultimate capabilities of diverse ultrahigh-resolution imaging techniques. To probe the structure and composition of these materials in their native environment with minimal damage and sample preparation calls for high-resolution electron or ion microscopy methods, which have not yet been tested on such classes of ultrasmall quantum nanostructures. Here, we demonstrate that scanning helium ion microscopy (SHeIM) provides a powerful and straightforward method to map quantum heterostructures embedded in complex III-V semiconductor NWs with unique material contrast at ∼1 nm resolution. By probing the cross sections of GaAs-Al(Ga)As core-shell NWs with coaxial GaAs quantum wells as well as short-period GaAs/AlAs superlattice (SL) structures in the shell, the Al-rich and Ga-rich layers are accurately discriminated by their image contrast in excellent agreement with correlated, yet destructive, scanning transmission electron microscopy and atom probe tomography analysis. Most interestingly, quantitative He-ion dose-dependent SHeIM analysis of the ternary AlGaAs shell layers and of compositionally nonuniform GaAs/AlAs SLs reveals distinct alloy composition fluctuations in the form of Al-rich clusters with size distributions between ∼1-10 nm. In the GaAs/AlAs SLs the alloy clustering vanishes with increasing SL-period (>5 nm-GaAs/4 nm-AlAs), providing insights into critical size dimensions for atomic intermixing effects in short-period SLs within a NW geometry. The straightforward SHeIM technique therefore provides unique benefits in imaging the tiniest nanoscale features in topography, structure and composition of a multitude of diverse complex semiconductor nanostructures.

Specific detection of the cleavage activity of mycobacterial enzymes using a quantum dot based DNA nanosensor

NASA Astrophysics Data System (ADS)

Jepsen, Morten Leth; Harmsen, Charlotte; Godbole, Adwait Anand; Nagaraja, Valakunja; Knudsen, Birgitta R.; Ho, Yi-Ping

2015-12-01

We present a quantum dot based DNA nanosensor specifically targeting the cleavage step in the reaction cycle of the essential DNA-modifying enzyme, mycobacterial topoisomerase I. The design takes advantages of the unique photophysical properties of quantum dots to generate visible fluorescence recovery upon specific cleavage by mycobacterial topoisomerase I. This report, for the first time, demonstrates the possibility to quantify the cleavage activity of the mycobacterial enzyme without the pre-processing sample purification or post-processing signal amplification. The cleavage induced signal response has also proven reliable in biological matrices, such as whole cell extracts prepared from Escherichia coli and human Caco-2 cells. It is expected that the assay may contribute to the clinical diagnostics of bacterial diseases, as well as the evaluation of treatment outcomes.We present a quantum dot based DNA nanosensor specifically targeting the cleavage step in the reaction cycle of the essential DNA-modifying enzyme, mycobacterial topoisomerase I. The design takes advantages of the unique photophysical properties of quantum dots to generate visible fluorescence recovery upon specific cleavage by mycobacterial topoisomerase I. This report, for the first time, demonstrates the possibility to quantify the cleavage activity of the mycobacterial enzyme without the pre-processing sample purification or post-processing signal amplification. The cleavage induced signal response has also proven reliable in biological matrices, such as whole cell extracts prepared from Escherichia coli and human Caco-2 cells. It is expected that the assay may contribute to the clinical diagnostics of bacterial diseases, as well as the evaluation of treatment outcomes. Electronic supplementary information (ESI) available: Characterization of the QD-based DNA Nanosensor. See DOI: 10.1039/c5nr06326d

Resource-aware system architecture model for implementation of quantum aided Byzantine agreement on quantum repeater networks

NASA Astrophysics Data System (ADS)

Taherkhani, Mohammand Amin; Navi, Keivan; Van Meter, Rodney

2018-01-01

Quantum aided Byzantine agreement is an important distributed quantum algorithm with unique features in comparison to classical deterministic and randomized algorithms, requiring only a constant expected number of rounds in addition to giving a higher level of security. In this paper, we analyze details of the high level multi-party algorithm, and propose elements of the design for the quantum architecture and circuits required at each node to run the algorithm on a quantum repeater network (QRN). Our optimization techniques have reduced the quantum circuit depth by 44% and the number of qubits in each node by 20% for a minimum five-node setup compared to the design based on the standard arithmetic circuits. These improvements lead to a quantum system architecture with 160 qubits per node, space-time product (an estimate of the required fidelity) {KQ}≈ 1.3× {10}5 per node and error threshold 1.1× {10}-6 for the total nodes in the network. The evaluation of the designed architecture shows that to execute the algorithm once on the minimum setup, we need to successfully distribute a total of 648 Bell pairs across the network, spread evenly between all pairs of nodes. This framework can be considered a starting point for establishing a road-map for light-weight demonstration of a distributed quantum application on QRNs.

Suppression of population transport and control of exciton distributions by entangled photons

PubMed Central

Schlawin, Frank; Dorfman, Konstantin E.; Fingerhut, Benjamin P.; Mukamel, Shaul

2013-01-01

Entangled photons provide an important tool for secure quantum communication, computing and lithography. Low intensity requirements for multi-photon processes make them idealy suited for minimizing damage in imaging applications. Here we show how their unique temporal and spectral features may be used in nonlinear spectroscopy to reveal properties of multiexcitons in chromophore aggregates. Simulations demostrate that they provide unique control tools for two-exciton states in the bacterial reaction centre of Blastochloris viridis. Population transport in the intermediate single-exciton manifold may be suppressed by the absorption of photon pairs with short entanglement time, thus allowing the manipulation of the distribution of two-exciton states. The quantum nature of the light is essential for achieving this degree of control, which cannot be reproduced by stochastic or chirped light. Classical light is fundamentally limited by the frequency-time uncertainty, whereas entangled photons have independent temporal and spectral characteristics not subjected to this uncertainty. PMID:23653194

Terahertz magneto-optical spectroscopy of a two-dimensional hole gas

DOE PAGES

Kamaraju, N.; Pan, W.; Ekenberg, U.; ...

2015-01-21

Two-dimensional hole gases (2DHGs) have attracted recent attention for their unique quantum physics and potential applications in areas including spintronics and quantum computing. However, their properties remain relatively unexplored, motivating the use of different techniques to study them. We used terahertz magneto-optical spectroscopy to investigate the cyclotron resonance frequency in a high mobility 2DHG, revealing a nonlinear dependence on the applied magnetic field. This is also shown to be due to the complex non-parabolic valence band structure of the 2DHG, as verified by multiband Landau level calculations. We also find that impurity scattering dominates cyclotron resonance decay in the 2DHG,more » in contrast with the dominance of superradiant damping in two-dimensional electron gases. Furthermore, these results shed light on the properties of 2DHGs, motivating further studies of these unique 2D nanosystems.« less

Large-area ordered Ge-Si compound quantum dot molecules on dot-patterned Si (001) substrates

NASA Astrophysics Data System (ADS)

Lei, Hui; Zhou, Tong; Wang, Shuguang; Fan, Yongliang; Zhong, Zhenyang

2014-08-01

We report on the formation of large-area ordered Ge-Si compound quantum dot molecules (CQDMs) in a combination of nanosphere lithography and self-assembly. Truncated-pyramid-like Si dots with {11n} facets are readily formed, which are spatially ordered in a large area with controlled period and size. Each Si dot induces four self-assembled Ge-rich dots at its base edges that can be fourfold symmetric along <110> directions. A model based on surface chemical potential accounts well for these phenomena. Our results disclose the critical effect of surface curvature on the diffusion and the aggregation of Ge adatoms and shed new light on the unique features and the inherent mechanism of self-assembled QDs on patterned substrates. Such a configuration of one Si QD surrounded by fourfold symmetric Ge-rich QDs can be seen as a CQDM with unique features, which will have potential applications in novel devices.

Terahertz magneto-optical spectroscopy of a two-dimensional hole gas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kamaraju, N., E-mail: nkamaraju@lanl.gov; Taylor, A. J.; Prasankumar, R. P., E-mail: rpprasan@lanl.gov

2015-01-19

Two-dimensional hole gases (2DHGs) have attracted recent attention for their unique quantum physics and potential applications in areas including spintronics and quantum computing. However, their properties remain relatively unexplored, motivating the use of different techniques to study them. We used terahertz magneto-optical spectroscopy to investigate the cyclotron resonance frequency in a high mobility 2DHG, revealing a nonlinear dependence on the applied magnetic field. This is shown to be due to the complex non-parabolic valence band structure of the 2DHG, as verified by multiband Landau level calculations. We also find that impurity scattering dominates cyclotron resonance decay in the 2DHG, inmore » contrast with the dominance of superradiant damping in two-dimensional electron gases. Our results shed light on the properties of 2DHGs, motivating further studies of these unique 2D nanosystems.« less

Synthesis and applications of crack-free SiO2 monolith containing CdSe/ZnS quantum dots as passive lighting sources.

PubMed

Yi, Dong Kee

2008-09-01

A reverse microemulsion technique has been used to synthesize quantum dot nanocomposites within a SiO2 surface coating. With this approach, the unique optical properties of the CdSe/ZnS quantum dots were preserved. CdSe/ZnS/SiO2 nanoparticles were homogeneously distributed in a tetramethyl orthosilicate ethanol solution and gelation process was initiated within a 10 min, and was left over night at room temperature and dried fully to achieve a solid SiO, monolith. The resulting monolith was transparent and fluorescent under ultraviolet (UV) lamp. Moreover the monolith produced was crack-free. Further studies on the photo stability of the monolith were performed using a high power UV LED device. Remarkably, quantum dots in the SiO, monolith showed better photo stability compared with those dispersed in a polymer matrix.

Evolution and Control of Electronic Structures near the Interface of Complex Oxide Heterostructure SmTiO3/SrTiO3

NASA Astrophysics Data System (ADS)

Mori, Ryo; Marshall, Patrick; Isaac, Brandon; Denlinger, Jonathan; Stemmer, Susanne; Lanzara, Alessandra

The confined electron system in the quantum well of the transition metal oxide, SrTiO3, embedded in the rare earth titanate, SmTiO3, shows unique properties, such as high carrier density, fermi liquid to non-fermi liquid transition, and pseudo-gap, which can be controlled by changing the shape of the quantum well. We will present a distinct difference in the electronic structures between the different quantum well structures obtained by angle-resolved photoemission spectroscopy (ARPES) measurements, suggesting the possibility to control the orbital character and the electron correlation near the interface as well as carrier density. The work was supported by the Quantum Materials Program at LBNL, funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract No. DE-AC02-05CH11231.

Full-Counting Many-Particle Dynamics: Nonlocal and Chiral Propagation of Correlations

NASA Astrophysics Data System (ADS)

Ashida, Yuto; Ueda, Masahito

2018-05-01

The ability to measure single quanta allows the complete characterization of small quantum systems known as full-counting statistics. Quantum gas microscopy enables one to observe many-body systems at the single-atom precision. We extend the idea of full-counting statistics to nonequilibrium open many-particle dynamics and apply it to discuss the quench dynamics. By way of illustration, we consider an exactly solvable model to demonstrate the emergence of unique phenomena such as nonlocal and chiral propagation of correlations, leading to a concomitant oscillatory entanglement growth. We find that correlations can propagate beyond the conventional maximal speed, known as the Lieb-Robinson bound, at the cost of probabilistic nature of quantum measurement. These features become most prominent at the real-to-complex spectrum transition point of an underlying parity-time-symmetric effective non-Hermitian Hamiltonian. A possible experimental situation with quantum gas microscopy is discussed.

Pulsar-black hole binaries as a window on quantum gravity

NASA Astrophysics Data System (ADS)

Estes, John; Kavic, Michael; Lippert, Matthew; Simonetti, John H.

Pulsars (PSRs) are some of the most accurate clocks found in nature, while black holes (BHs) offer a unique arena for the study of quantum gravity. As such, PSR-BH binaries provide ideal astrophysical systems for detecting effects of quantum gravity. With the success of aLIGO and the advent of instruments like the Square Kilometer Array (SKA) and Evolved Laser Interferometer Space Antenna (eLISA), the prospects for discovery of such PSR-BH binaries are very promising. We argue that PSR-BH binaries can serve as ready-made testing grounds for proposed resolutions to the BH information paradox. We propose using timing signals from a PSR beam passing through the region near a BH event horizon as a probe of quantum gravitational effects. In particular, we demonstrate that fluctuations of the geometry outside a BH lead to an increase in the measured root-mean-square deviation of arrival times of PSR pulsar traveling near the horizon.

Parametric excitation and squeezing in a many-body spinor condensate

PubMed Central

Hoang, T. M.; Anquez, M.; Robbins, B. A.; Yang, X. Y.; Land, B. J.; Hamley, C. D.; Chapman, M. S.

2016-01-01

Atomic spins are usually manipulated using radio frequency or microwave fields to excite Rabi oscillations between different spin states. These are single-particle quantum control techniques that perform ideally with individual particles or non-interacting ensembles. In many-body systems, inter-particle interactions are unavoidable; however, interactions can be used to realize new control schemes unique to interacting systems. Here we demonstrate a many-body control scheme to coherently excite and control the quantum spin states of an atomic Bose gas that realizes parametric excitation of many-body collective spin states by time varying the relative strength of the Zeeman and spin-dependent collisional interaction energies at multiples of the natural frequency of the system. Although parametric excitation of a classical system is ineffective from the ground state, we show that in our experiment, parametric excitation from the quantum ground state leads to the generation of quantum squeezed states. PMID:27044675

Selected Aspects of Markovian and Non-Markovian Quantum Master Equations

NASA Astrophysics Data System (ADS)

Lendi, K.

A few particular marked properties of quantum dynamical equations accounting for general relaxation and dissipation are selected and summarized in brief. Most results derive from the universal concept of complete positivity. The considerations mainly regard genuinely irreversible processes as characterized by a unique asymptotically stationary final state for arbitrary initial conditions. From ordinary Markovian master equations and associated quantum dynamical semigroup time-evolution, derivations of higher order Onsager coefficients and related entropy production are discussed. For general processes including non-faithful states a regularized version of quantum relative entropy is introduced. Further considerations extend to time-dependent infinitesimal generators of time-evolution and to a possible description of propagation of initial states entangled between open system and environment. In the coherence-vector representation of the full non-Markovian equations including entangled initial states, first results are outlined towards identifying mathematical properties of a restricted class of trial integral-kernel functions suited to phenomenological applications.

Shot noise generated by graphene p–n junctions in the quantum Hall effect regime

PubMed Central

Kumada, N.; Parmentier, F. D.; Hibino, H.; Glattli, D. C.; Roulleau, P.

2015-01-01

Graphene offers a unique system to investigate transport of Dirac Fermions at p–n junctions. In a magnetic field, combination of quantum Hall physics and the characteristic transport across p–n junctions leads to a fractionally quantized conductance associated with the mixing of electron-like and hole-like modes and their subsequent partitioning. The mixing and partitioning suggest that a p–n junction could be used as an electronic beam splitter. Here we report the shot noise study of the mode-mixing process and demonstrate the crucial role of the p–n junction length. For short p–n junctions, the amplitude of the noise is consistent with an electronic beam-splitter behaviour, whereas, for longer p–n junctions, it is reduced by the energy relaxation. Remarkably, the relaxation length is much larger than typical size of mesoscopic devices, encouraging using graphene for electron quantum optics and quantum information processing. PMID:26337067

What can we learn from noise? — Mesoscopic nonequilibrium statistical physics —

PubMed Central

KOBAYASHI, Kensuke

2016-01-01

Mesoscopic systems — small electric circuits working in quantum regime — offer us a unique experimental stage to explorer quantum transport in a tunable and precise way. The purpose of this Review is to show how they can contribute to statistical physics. We introduce the significance of fluctuation, or equivalently noise, as noise measurement enables us to address the fundamental aspects of a physical system. The significance of the fluctuation theorem (FT) in statistical physics is noted. We explain what information can be deduced from the current noise measurement in mesoscopic systems. As an important application of the noise measurement to statistical physics, we describe our experimental work on the current and current noise in an electron interferometer, which is the first experimental test of FT in quantum regime. Our attempt will shed new light in the research field of mesoscopic quantum statistical physics. PMID:27477456

All pure bipartite entangled states can be self-tested

PubMed Central

Coladangelo, Andrea; Goh, Koon Tong; Scarani, Valerio

2017-01-01

Quantum technologies promise advantages over their classical counterparts in the fields of computation, security and sensing. It is thus desirable that classical users are able to obtain guarantees on quantum devices, even without any knowledge of their inner workings. That such classical certification is possible at all is remarkable: it is a consequence of the violation of Bell inequalities by entangled quantum systems. Device-independent self-testing refers to the most complete such certification: it enables a classical user to uniquely identify the quantum state shared by uncharacterized devices by simply inspecting the correlations of measurement outcomes. Self-testing was first demonstrated for the singlet state and a few other examples of self-testable states were reported in recent years. Here, we address the long-standing open question of whether every pure bipartite entangled state is self-testable. We answer it affirmatively by providing explicit self-testing correlations for all such states. PMID:28548093

Biocompatible magnetofluorescent probes: luminescent silicon quantum dots coupled with superparamagnetic iron(III) oxide.

PubMed

Erogbogbo, Folarin; Yong, Ken-Tye; Hu, Rui; Law, Wing-Cheung; Ding, Hong; Chang, Ching-Wen; Prasad, Paras N; Swihart, Mark T

2010-09-28

Luminescent silicon quantum dots (SiQDs) are gaining momentum in bioimaging applications, based on their unique combination of optical properties and biocompatibility. Here, we report the development of a multimodal probe that combines the optical properties of silicon quantum dots with the superparamagnetic properties of iron oxide nanoparticles to create biocompatible magnetofluorescent nanoprobes. Multiple nanoparticles of each type are coencapsulated within the hydrophobic core of biocompatible phospholipid-polyethyleneglycol (DSPE-PEG) micelles. The size distribution and composition of the magnetofluorescent nanoprobes were characterized by transmission electron microscopy (TEM) and energy-dispersive X-ray spectroscopy (EDS). Enhanced cellular uptake of these probes in the presence of a magnetic field was demonstrated in vitro. Their luminescence stability in a prostate cancer tumor model microenvironment was demonstrated in vivo. This paves the way for multimodal silicon quantum-dot-based nanoplatforms for a variety of imaging and delivery applications.

All pure bipartite entangled states can be self-tested

NASA Astrophysics Data System (ADS)

Coladangelo, Andrea; Goh, Koon Tong; Scarani, Valerio

2017-05-01

Quantum technologies promise advantages over their classical counterparts in the fields of computation, security and sensing. It is thus desirable that classical users are able to obtain guarantees on quantum devices, even without any knowledge of their inner workings. That such classical certification is possible at all is remarkable: it is a consequence of the violation of Bell inequalities by entangled quantum systems. Device-independent self-testing refers to the most complete such certification: it enables a classical user to uniquely identify the quantum state shared by uncharacterized devices by simply inspecting the correlations of measurement outcomes. Self-testing was first demonstrated for the singlet state and a few other examples of self-testable states were reported in recent years. Here, we address the long-standing open question of whether every pure bipartite entangled state is self-testable. We answer it affirmatively by providing explicit self-testing correlations for all such states.

All pure bipartite entangled states can be self-tested.

PubMed

Coladangelo, Andrea; Goh, Koon Tong; Scarani, Valerio

2017-05-26

Quantum technologies promise advantages over their classical counterparts in the fields of computation, security and sensing. It is thus desirable that classical users are able to obtain guarantees on quantum devices, even without any knowledge of their inner workings. That such classical certification is possible at all is remarkable: it is a consequence of the violation of Bell inequalities by entangled quantum systems. Device-independent self-testing refers to the most complete such certification: it enables a classical user to uniquely identify the quantum state shared by uncharacterized devices by simply inspecting the correlations of measurement outcomes. Self-testing was first demonstrated for the singlet state and a few other examples of self-testable states were reported in recent years. Here, we address the long-standing open question of whether every pure bipartite entangled state is self-testable. We answer it affirmatively by providing explicit self-testing correlations for all such states.

Ensembles and Experiments in Classical and Quantum Physics

NASA Astrophysics Data System (ADS)

Neumaier, Arnold

A philosophically consistent axiomatic approach to classical and quantum mechanics is given. The approach realizes a strong formal implementation of Bohr's correspondence principle. In all instances, classical and quantum concepts are fully parallel: the same general theory has a classical realization and a quantum realization. Extending the ''probability via expectation'' approach of Whittle to noncommuting quantities, this paper defines quantities, ensembles, and experiments as mathematical concepts and shows how to model complementarity, uncertainty, probability, nonlocality and dynamics in these terms. The approach carries no connotation of unlimited repeatability; hence it can be applied to unique systems such as the universe. Consistent experiments provide an elegant solution to the reality problem, confirming the insistence of the orthodox Copenhagen interpretation on that there is nothing but ensembles, while avoiding its elusive reality picture. The weak law of large numbers explains the emergence of classical properties for macroscopic systems.

Quantum-Sequencing: Biophysics of quantum tunneling through nucleic acids

NASA Astrophysics Data System (ADS)

Casamada Ribot, Josep; Chatterjee, Anushree; Nagpal, Prashant

2014-03-01

Tunneling microscopy and spectroscopy has extensively been used in physical surface sciences to study quantum tunneling to measure electronic local density of states of nanomaterials and to characterize adsorbed species. Quantum-Sequencing (Q-Seq) is a new method based on tunneling microscopy for electronic sequencing of single molecule of nucleic acids. A major goal of third-generation sequencing technologies is to develop a fast, reliable, enzyme-free single-molecule sequencing method. Here, we present the unique ``electronic fingerprints'' for all nucleotides on DNA and RNA using Q-Seq along their intrinsic biophysical parameters. We have analyzed tunneling spectra for the nucleotides at different pH conditions and analyzed the HOMO, LUMO and energy gap for all of them. In addition we show a number of biophysical parameters to further characterize all nucleobases (electron and hole transition voltage and energy barriers). These results highlight the robustness of Q-Seq as a technique for next-generation sequencing.

Parametric excitation and squeezing in a many-body spinor condensate

NASA Astrophysics Data System (ADS)

Hoang, T. M.; Anquez, M.; Robbins, B. A.; Yang, X. Y.; Land, B. J.; Hamley, C. D.; Chapman, M. S.

2016-04-01

Atomic spins are usually manipulated using radio frequency or microwave fields to excite Rabi oscillations between different spin states. These are single-particle quantum control techniques that perform ideally with individual particles or non-interacting ensembles. In many-body systems, inter-particle interactions are unavoidable; however, interactions can be used to realize new control schemes unique to interacting systems. Here we demonstrate a many-body control scheme to coherently excite and control the quantum spin states of an atomic Bose gas that realizes parametric excitation of many-body collective spin states by time varying the relative strength of the Zeeman and spin-dependent collisional interaction energies at multiples of the natural frequency of the system. Although parametric excitation of a classical system is ineffective from the ground state, we show that in our experiment, parametric excitation from the quantum ground state leads to the generation of quantum squeezed states.

What can we learn from noise? - Mesoscopic nonequilibrium statistical physics.

PubMed

Kobayashi, Kensuke

2016-01-01

Mesoscopic systems - small electric circuits working in quantum regime - offer us a unique experimental stage to explorer quantum transport in a tunable and precise way. The purpose of this Review is to show how they can contribute to statistical physics. We introduce the significance of fluctuation, or equivalently noise, as noise measurement enables us to address the fundamental aspects of a physical system. The significance of the fluctuation theorem (FT) in statistical physics is noted. We explain what information can be deduced from the current noise measurement in mesoscopic systems. As an important application of the noise measurement to statistical physics, we describe our experimental work on the current and current noise in an electron interferometer, which is the first experimental test of FT in quantum regime. Our attempt will shed new light in the research field of mesoscopic quantum statistical physics.

Squeezed cooling of mechanical motion beyond the resolved-sideband limit

NASA Astrophysics Data System (ADS)

Yang, Cheng; Zhang, Lin; Zhang, Weiping

2018-04-01

Cavity optomechanics provides a unique platform for controlling micromechanical systems by means of optical fields that cross the classical-quantum boundary to achieve solid foundations for quantum technologies. Currently, optomechanical resonators have become promising candidates for the development of precisely controlled nano-motors, ultrasensitive sensors and robust quantum information processors. For all these applications, a crucial requirement is to cool the mechanical resonators down to their quantum ground states. In this paper, we present a novel cooling scheme to further cool a micromechanical resonator via the noise squeezing effect. One quadrature in such a resonator can be squeezed to induce enhanced fluctuations in the other, “heated” quadrature, which can then be used to cool the mechanical motion via conventional optomechanical coupling. Our theoretical analysis and numerical calculations demonstrate that this squeeze-and-cool mechanism offers a quick technique for deeply cooling a macroscopic mechanical resonator to an unprecedented temperature region below the zero-point fluctuations.

Sub-Shot-Noise Transmission Measurement Enabled by Active Feed-Forward of Heralded Single Photons

NASA Astrophysics Data System (ADS)

Sabines-Chesterking, J.; Whittaker, R.; Joshi, S. K.; Birchall, P. M.; Moreau, P. A.; McMillan, A.; Cable, H. V.; O'Brien, J. L.; Rarity, J. G.; Matthews, J. C. F.

2017-07-01

Harnessing the unique properties of quantum mechanics offers the possibility of delivering alternative technologies that can fundamentally outperform their classical counterparts. These technologies deliver advantages only when components operate with performance beyond specific thresholds. For optical quantum metrology, the biggest challenge that impacts on performance thresholds is optical loss. Here, we demonstrate how including an optical delay and an optical switch in a feed-forward configuration with a stable and efficient correlated photon-pair source reduces the detector efficiency required to enable quantum-enhanced sensing down to the detection level of single photons and without postselection. When the switch is active, we observe a factor of improvement in precision of 1.27 for transmission measurement on a per-input-photon basis compared to the performance of a laser emitting an ideal coherent state and measured with the same detection efficiency as our setup. When the switch is inoperative, we observe no quantum advantage.

Dynamics of a stochastic tuberculosis model with constant recruitment and varying total population size

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing; Shi, Ningzhong; Hayat, Tasawar; Alsaedi, Ahmed

2017-03-01

In this paper, we develop a mathematical model for a tuberculosis model with constant recruitment and varying total population size by incorporating stochastic perturbations. By constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of an ergodic stationary distribution as well as extinction of the disease to the stochastic system.