Quantum systems that follow classical dynamics
Manfredi, G; Feix, M R
1993-01-01
For a special class of potentials, the dynamical evolution of any quantum wavepacket is entirely determined by the laws of classical mechanics. Here, the properties of this class are investigated both from the viewpoint of the Ehrenfest theorem (which provides the evolution of the average position and momentum), and the Wigner representation (which expresses quantum mechanics in a phase space formalism). Finally, these results are extended to the case of a charged particle in a uniform magnetic field. (author)
Planar dynamical systems selected classical problems
Liu, Yirong; Huang, Wentao
2014-01-01
This book presents in an elementary way the recent significant developments in the qualitative theory of planar dynamical systems. The subjects are covered as follows: the studies of center and isochronous center problems, multiple Hopf bifurcations and local and global bifurcations of the equivariant planar vector fields which concern with Hilbert's 16th problem. This book is intended for graduate students, post-doctors and researchers in the area of theories and applications of dynamical systems. For all engineers who are interested the theory of dynamical systems, it is also a reasona
Energy conservation in molecular dynamics simulations of classical systems
DEFF Research Database (Denmark)
Toxværd, Søren; Heilmann, Ole; Dyre, J. C.
2012-01-01
Classical Newtonian dynamics is analytic and the energy of an isolated system is conserved. The energy of such a system, obtained by the discrete “Verlet” algorithm commonly used in molecular dynamics simulations, fluctuates but is conserved in the mean. This is explained by the existence...
Information dynamics and open systems classical and quantum approach
Ingarden, R S; Ohya, M
1997-01-01
This book aims to present an information-theoretical approach to thermodynamics and its generalisations On the one hand, it generalises the concept of `information thermodynamics' to that of `information dynamics' in order to stress applications outside thermal phenomena On the other hand, it is a synthesis of the dynamics of state change and the theory of complexity, which provide a common framework to treat both physical and nonphysical systems together Both classical and quantum systems are discussed, and two appendices are included to explain principal definitions and some important aspects of the theory of Hilbert spaces and operator algebras The concept of higher-order temperatures is explained and applied to biological and linguistic systems The theory of open systems is presented in a new, much more general form Audience This volume is intended mainly for theoretical and mathematical physicists, but also for mathematicians, experimental physicists, physical chemists, theoretical biologists, communicat...
Greenwood, Donald T
1997-01-01
Graduate-level text for science and technology students provides strong background in the more abstract and intellectually satisfying areas of dynamical theory. Topics include d'Alembert's principle and the idea of virtual work, Hamilton's equations, Hamilton-Jacobi theory, canonical transformations, more. Problems and references at chapter ends.
Gaussian Dynamics is Classical Dynamics
Habib, Salman
2004-01-01
A direct comparison of quantum and classical dynamical systems can be accomplished through the use of distribution functions. This is useful for both fundamental investigations such as the nature of the quantum-classical transition as well as for applications such as quantum feedback control. By affording a clear separation between kinematical and dynamical quantum effects, the Wigner distribution is particularly valuable in this regard. Here we discuss some consequences of the fact that when...
Classical dynamics of triatomic system: energized harmonic molecules
International Nuclear Information System (INIS)
The dynamical assumptions underlying the Slater and RRK classical-mechanical theories of unimolecular reaction rates are investigated. The predictions of these theories for several nonlinear, triatomic, harmonically-bonded molecular models are compared with the results obtained from the integration of the classical equations of motion. The accuracy of the small-vibration and weak-coupling assumptions are found to break down at energies above about one quarter of a bond dissociation energy. Nonetheless, the small-vibration approximation predicts reaction frequencies in good agreement with the exact results for the models. The effects of rotation on intramolecular energy exchange are examined and found to be significant
Stability of molecular dynamics simulations of classical systems
DEFF Research Database (Denmark)
Toxværd, Søren
2012-01-01
The existence of a shadow Hamiltonian for discrete classical dynamics, obtained by an asymptotic expansion for a discrete symplectic algorithm, is employed to determine the limit of stability for molecular dynamics (MD) simulations with respect to the time-increment h of the discrete dynamics....... The method is also used to investigate higher-order central difference algorithms, which are symplectic and also have shadow Hamiltonians, and for which one can also determine the exact criteria for the limit of stability of a single harmonic mode. A fourth-order central difference algorithm gives...
Dynamics of mixed classical-quantum systems, geometric quantization and coherent states
Jauslin, H R
2011-01-01
We describe quantum and classical Hamiltonian dynamics in a common Hilbert space framework, that allows the treatment of mixed quantum-classical systems. The analysis of some examples illustrates the possibility of entanglement between classical and quantum systems. We give a summary of the main tools of Berezin-Toeplitz and geometric quantization, that provide a relation between the classical and the quantum models, based essentially on the selection of a subspace of the classical Hilbert space. Coherent states provide a systematic tool for the inverse process, called dequantization, that associates a classical Hamiltonian system to a given quantum dynamics through the choice of a complete set of coherent states.
Statistical and dynamical remastering of classic exoplanet systems
Nelson, Benjamin Earl
The most powerful constraints on planet formation will come from characterizing the dynamical state of complex multi-planet systems. Unfortunately, with that complexity comes a number of factors that make analyzing these systems a computationally challenging endeavor: the sheer number of model parameters, a wonky shaped posterior distribution, and hundreds to thousands of time series measurements. In this dissertation, I will review our efforts to improve the statistical analyses of radial velocity (RV) data and their applications to some renown, dynamically complex exoplanet system. In the first project (Chapters 2 and 4), we develop a differential evolution Markov chain Monte Carlo (RUN DMC) algorithm to tackle the aforementioned difficult aspects of data analysis. We test the robustness of the algorithm in regards to the number of modeled planets (model dimensionality) and increasing dynamical strength. We apply RUN DMC to a couple classic multi-planet systems and one highly debated system from radial velocity surveys. In the second project (Chapter 5), we analyze RV data of 55 Cancri, a wide binary system known to harbor five planetary orbiting the primary. We find the inner-most planet "e" must be coplanar to within 40 degrees of the outer planets, otherwise Kozai-like perturbations will cause the planet to enter the stellar photosphere through its periastron passage. We find the orbits of planets "b" and "c" are apsidally aligned and librating with low to median amplitude (50+/-6 10 degrees), but they are not orbiting in a mean-motion resonance. In the third project (Chapters 3, 4, 6), we analyze RV data of Gliese 876, a four planet system with three participating in a multi-body resonance, i.e. a Laplace resonance. From a combined observational and statistical analysis computing Bayes factors, we find a four-planet model is favored over one with three-planets. Conditioned on this preferred model, we meaningfully constrain the three-dimensional orbital
Dynamical Symmetries in Classical Mechanics
Boozer, A. D.
2012-01-01
We show how symmetries of a classical dynamical system can be described in terms of operators that act on the state space for the system. We illustrate our results by considering a number of possible symmetries that a classical dynamical system might have, and for each symmetry we give examples of dynamical systems that do and do not possess that…
A course in mathematical physics 1 and 2 classical dynamical systems and classical field theory
Thirring, Walter
1992-01-01
The last decade has seen a considerable renaissance in the realm of classical dynamical systems, and many things that may have appeared mathematically overly sophisticated at the time of the first appearance of this textbook have since become the everyday tools of working physicists. This new edition is intended to take this development into account. I have also tried to make the book more readable and to eradicate errors. Since the first edition already contained plenty of material for a one semester course, new material was added only when some of the original could be dropped or simplified. Even so, it was necessary to expand the chap ter with the proof of the K-A-M Theorem to make allowances for the cur rent trend in physics. This involved not only the use of more refined mathe matical tools, but also a reevaluation of the word "fundamental. " What was earlier dismissed as a grubby calculation is now seen as the consequence of a deep principle. Even Kepler's laws, which determine the radii of the ...
Construction of exact complex dynamical invariant of a two-dimensional classical system
Indian Academy of Sciences (India)
Fakir Chand; S C Mishra
2006-12-01
We present the construction of exact complex dynamical invariant of a two-dimensional classical dynamical system on an extended complex space utilizing Lie algebraic approach. These invariants are expected to play a vital role in understanding the complex trajectories of both classical and quantum systems.
Chaotic Dynamics and Transport in Classical and Quantum Systems
Energy Technology Data Exchange (ETDEWEB)
NONE
2003-07-01
The aim of this summer school is to provide a set of extended and pedagogical lectures, on the major present-day topics in dynamical systems and statistical mechanics including applications. Some articles are dedicated to chaotic transport in plasma turbulence and to quantum chaos. This document gathers the summaries of some presentations.
Chaotic Dynamics and Transport in Classical and Quantum Systems
International Nuclear Information System (INIS)
The aim of this summer school is to provide a set of extended and pedagogical lectures, on the major present-day topics in dynamical systems and statistical mechanics including applications. Some articles are dedicated to chaotic transport in plasma turbulence and to quantum chaos. This document gathers the summaries of some presentations
Classical dynamics a modern perspective
Sudarshan, Ennackal Chandy George
2016-01-01
Classical dynamics is traditionally treated as an early stage in the development of physics, a stage that has long been superseded by more ambitious theories. Here, in this book, classical dynamics is treated as a subject on its own as well as a research frontier. Incorporating insights gained over the past several decades, the essential principles of classical dynamics are presented, while demonstrating that a number of key results originally considered only in the context of quantum theory and particle physics, have their foundations in classical dynamics.Graduate students in physics and practicing physicists will welcome the present approach to classical dynamics that encompasses systems of particles, free and interacting fields, and coupled systems. Lie groups and Lie algebras are incorporated at a basic level and are used in describing space-time symmetry groups. There is an extensive discussion on constrained systems, Dirac brackets and their geometrical interpretation. The Lie-algebraic description of ...
Quantum dynamics for classical systems with applications of the number operator
Bagarello, Fabio
2013-01-01
Mathematics is increasingly applied to classical problems in finance, biology, economics, and elsewhere. Quantum Dynamics for Classical Systems describes how quantum tools—the number operator in particular—can be used to create dynamical systems in which the variables are operator-valued functions and whose results explain the presented model. The book presents mathematical results and their applications to concrete systems and discusses the methods used, results obtained, and techniques developed for the proofs of the results. The central ideas of number operators are illuminated while avoiding excessive technicalities that are unnecessary for understanding and learning the various mathematical applications. The presented dynamical systems address a variety of contexts and offer clear analyses and explanations of concluded results. Additional features in Quantum Dynamics for Classical Systems include: Applications across diverse fields including stock markets and population migration as well as a uniqu...
Indian Academy of Sciences (India)
Aparna Saha; Bidhan Chandra Bag; Pranab Sarkar
2007-03-01
We present a numerical investigation of the tunneling dynamics of a particle moving in a bistable potential with fluctuating barrier which is coupled to a non-integrable classical system and study the interplay between classical chaos and barrier fluctuation in the tunneling dynamics. We found that the coupling of the quantum system with the classical subsystem decreases the tunneling rate irrespective of whether the classical subsystem is regular or chaotic and also irrespective of the fact that whether the barrier fluctuates or not. Presence of classical chaos always enhances the tunneling rate constant. The effect of barrier fluctuation on the tunneling rate in a mixed quantum-classical system is to suppress the tunneling rate. In contrast to the case of regular subsystem, the suppression arising due to barrier fluctuation is more visible when the subsystem is chaotic.
Hamiltonian Structure of the Schrödinger Classical Dynamical System
Tessarotto, Massimo; Mond, Michael; Batic, Davide
2016-05-01
The connection between quantum mechanics and classical statistical mechanics has motivated in the past the representation of the Schrödinger quantum-wave equation in terms of "projections" onto the quantum configuration space of suitable phase-space asymptotic kinetic models. This feature has suggested the search of a possible exact super-dimensional classical dynamical system (CDS), denoted as Schrödinger CDS, which uniquely determines the time-evolution of the underlying quantum state describing a set of N like and mutually interacting quantum particles. In this paper the realization of the same CDS in terms of a coupled set of Hamiltonian systems is established. These are respectively associated with a quantum-hydrodynamic CDS advancing in time the quantum fluid velocity and a further one the RD-CDS, describing the relative dynamics with respect to the quantum fluid.
Quantum emulation of classical dynamics
Margolus, Norman
2011-01-01
In statistical mechanics, it is well known that finite-state classical lattice models can be recast as quantum models, with distinct classical configurations identified with orthogonal basis states. This mapping makes classical statistical mechanics on a lattice a special case of quantum statistical mechanics, and classical combinatorial entropy a special case of quantum entropy. In a similar manner, finite-state classical dynamics can be recast as finite-energy quantum dynamics. This mapping...
Nuclear alignment: classical dynamic model for 238U- 238U system
International Nuclear Information System (INIS)
Dynamical properties of 238U- 238U system at the classical turning point, specifically the distance of closest approach, the relative orientations of the nuclei and deformations have been studied at sub-coulomb energy of Elab = 6.07 MeV/nucleon using a classical dynamical model with a variable moment of inertia. Probability of favorable alignment for anomalous positron-electron pair emission through vacuum decay is calculated. The calculated small favorable alignment probability value of 0.116 is found to be enhanced by about 16% in comparison with the results of a similar study using a fixed moment of inertia as well as the results from a semiquantal calculation reported earlier. (author)
De Martino, S; Illuminati, F; Martino, Salvatore De; Siena, Silvio De; Illuminati, Fabrizio
1999-01-01
The possibility is discussed of inferring or simulating some aspects of quantum dynamics by adding classical statistical fluctuations to classical mechanics. We introduce a general principle of mechanical stability and derive a necessary condition for classical chaotic fluctuations to affect confined dynamical systems, on any scale, ranging from microscopic to macroscopic domains. As a consequence we obtain, both for microscopic and macroscopic aggregates, dimensional relations defining the minimum unit of action of individual constituents, yielding in all cases Planck action constant.
De Martino, Salvatore; De Siena, Silvio; Illuminati, Fabrizio
1999-01-01
The possibility is discussed of inferring or simulating some aspects of quantum dynamics by adding classical statistical fluctuations to classical mechanics. We introduce a general principle of mechanical stability and derive a necessary condition for classical chaotic fluctuations to affect confined dynamical systems, on any scale, ranging from microscopic to macroscopic domains. As a consequence we obtain, both for microscopic and macroscopic aggregates, dimensional relations defining the m...
Exceptional points in quantum and classical dynamics
Smilga, A V
2008-01-01
We notice that, when a quantum system involves exceptional points, i.e. the special values of parameters where the Hamiltonian loses its self-adjointness and acquires the Jordan block structure, the corresponding classical system also exhibits a singular behaviour associated with restructuring of classical trajectories. The system with the crypto-Hermitian Hamiltonian H = (p^2+z^2)/2 -igz^5 and hyper-ellictic classical dynamics is studied in details. Analogies with supersymmetric Yang-Mills dynamics are elucidated.
Exceptional points in quantum and classical dynamics
Smilga, A. V.
2009-03-01
We note that when a quantum system involves exceptional points, i.e. the special values of parameters where the Hamiltonian loses its self-adjointness and acquires the Jordan block structure, the corresponding classical system also exhibits singular behaviour associated with the restructuring of classical trajectories. A system with the crypto-Hermitian Hamiltonian H = (p2 + z2)/2 - igz5 and hyper-elliptic classical dynamics is studied in detail. Analogies with supersymmetric Yang-Mills dynamics are elucidated.
Guillemin, Ernst A
2013-01-01
An eminent electrical engineer and authority on linear system theory presents this advanced treatise, which approaches the subject from the viewpoint of classical dynamics and covers Fourier methods. This volume will assist upper-level undergraduates and graduate students in moving from introductory courses toward an understanding of advanced network synthesis. 1963 edition.
Mechanical Systems, Classical Models
Teodorescu, Petre P
2009-01-01
This third volume completes the Work Mechanical Systems, Classical Models. The first two volumes dealt with particle dynamics and with discrete and continuous mechanical systems. The present volume studies analytical mechanics. Topics like Lagrangian and Hamiltonian mechanics, the Hamilton-Jacobi method, and a study of systems with separate variables are thoroughly discussed. Also included are variational principles and canonical transformations, integral invariants and exterior differential calculus, and particular attention is given to non-holonomic mechanical systems. The author explains in detail all important aspects of the science of mechanics, regarded as a natural science, and shows how they are useful in understanding important natural phenomena and solving problems of interest in applied and engineering sciences. Professor Teodorescu has spent more than fifty years as a Professor of Mechanics at the University of Bucharest and this book relies on the extensive literature on the subject as well as th...
International Nuclear Information System (INIS)
We consider symmetry properties of differential equations in non-relativistic quantum mechanics and classical mechanics. Special emphasis is given to periodically driven systems. For a model system connections between symmetries of corresponding classical and quantal systems are established. The fundamental difference between variational symmetries and symmetries of the Euler-Lagrange-equations is discussed for the special case of classical mechanics. For nonintegrable systems with quasiregular regions in phase space we introduce the notion of approximate symmetry. As an example, we demonstrate the accuracy of such symmetry properties in certain domains of phase space for a periodically driven anharmonic oscillator. (orig.)
Dynamics of cascade three-level system interacting with the classical and quantized ﬁeld
Indian Academy of Sciences (India)
Mihir Ranjan Nath; Surajit Sen; Gautam Gangopadhyay
2003-12-01
We study the exact solutions of the cascade three-level atom interacting with a single mode classical and quantized ﬁeld with different initial conditions ofthe atom. For the semiclassical model, it is found that if the atom is initially in the middle level, the time-dependent populations of the upper and lower levels are always equal. This dynamical symmetry exhibited by the classical ﬁeld is spoiled on quantization of the ﬁeld mode. To reveal this non-classical effect, a Euler matrix formalism is developed to solve the dressed states of the cascade Jaynes–Cummings model (JCM). Possible modiﬁcation of such an effect on the collapse and revival phenomenon is also discussed by taking the quantized ﬁeld in a coherent state.
Classical Dynamics as Constrained Quantum Dynamics
Bartlett, Stephen D.; Rowe, David J.
2002-01-01
We show that the classical mechanics of an algebraic model are implied by its quantizations. An algebraic model is defined, and the corresponding classical and quantum realizations are given in terms of a spectrum generating algebra. Classical equations of motion are then obtained by constraining the quantal dynamics of an algebraic model to an appropriate coherent state manifold. For the cases where the coherent state manifold is not symplectic, it is shown that there exist natural projectio...
Collet, P; Métens, S; Neishtadt, A; Zaslavsky, G; Chaotic Dynamics and Transport in Classical and Quantum Systems
2005-01-01
This book offers a modern updated review on the most important activities in today dynamical systems and statistical mechanics by some of the best experts in the domain. It gives a contemporary and pedagogical view on theories of classical and quantum chaos and complexity in hamiltonian and ergodic systems and their applications to anomalous transport in fluids, plasmas, oceans and atom-optic devices and to control of chaotic transport. The book is issued from lecture notes of the International Summer School on "Chaotic Dynamics and Transport in Classical and Quantum Systems" held in Cargèse (Corsica) 18th to the 30th August 2003. It reflects the spirit of the School to provide lectures at the post-doctoral level on basic concepts and tools. The first part concerns ergodicity and mixing, complexity and entropy functions, SRB measures, fractal dimensions and bifurcations in hamiltonian systems. Then, models of dynamical evolutions of transport processes in classical and quantum systems have been largely expla...
Dynamics of Non-Classical Interval Exchanges
Gadre, Vaibhav S
2009-01-01
Train tracks with a single vertex are a generalization of interval exchange maps. Here, we consider non-classical interval exchanges: complete train tracks with a single vertex. These can be studied as a dynamical system by considering Rauzy induction in this context. This gives a refinement process on the parameter space similar to Kerckhoff's simplicial systems. We show that the refinement process gives an expansion that has a key dynamical property called uniform distortion. We use uniform distortion to prove normality of the expansion. Consequently we prove an analog of Keane's conjecture: almost every non-classical interval exchange is uniquely ergodic.
International Nuclear Information System (INIS)
We derive the fundamental equations of an optimal control theory for systems containing both quantum electrons and classical ions. The system is modeled with Ehrenfest dynamics, a non-adiabatic variant of molecular dynamics. The general formulation, that needs the fully correlated many-electron wavefunction, can be simplified by making use of time-dependent density-functional theory. In this case, the optimal control equations require some modifications that we will provide. The abstract general formulation is complemented with the simple example of the H2+ molecule in the presence of a laser field. (paper)
Geometry from dynamics, classical and quantum
Cariñena, José F; Marmo, Giuseppe; Morandi, Giuseppe
2015-01-01
This book describes, by using elementary techniques, how some geometrical structures widely used today in many areas of physics, like symplectic, Poisson, Lagrangian, Hermitian, etc., emerge from dynamics. It is assumed that what can be accessed in actual experiences when studying a given system is just its dynamical behavior that is described by using a family of variables ("observables" of the system). The book departs from the principle that ''dynamics is first'', and then tries to answer in what sense the sole dynamics determines the geometrical structures that have proved so useful to describe the dynamics in so many important instances. In this vein it is shown that most of the geometrical structures that are used in the standard presentations of classical dynamics (Jacobi, Poisson, symplectic, Hamiltonian, Lagrangian) are determined, though in general not uniquely, by the dynamics alone. The same program is accomplished for the geometrical structures relevant to describe quantum dynamics. Finall...
International Nuclear Information System (INIS)
We have analyzed the double-lined eclipsing binary system OGLE-LMC-CEP-1812 in the LMC and demonstrate that it contains a classical fundamental mode Cepheid pulsating with a period of 1.31 days. The secondary star is a stable giant. We derive the dynamical masses for both stars with an accuracy of 1.5%, making the Cepheid in this system the second classical Cepheid with a very accurate dynamical mass determination, following the OGLE-LMC-CEP-0227 system studied by Pietrzyński et al. The measured dynamical mass agrees very well with that predicted by pulsation models. We also derive the radii of both components and accurate orbital parameters for the binary system. This new, very accurate dynamical mass for a classical Cepheid will greatly contribute to the solution of the Cepheid mass discrepancy problem, and to our understanding of the structure and evolution of classical Cepheids.
Konopelchenko, B G
2012-01-01
Quasiclassical approximation in the intrinsic description of the vortex filament dynamics is discussed. Within this approximation the governing equations are given by elliptic system of quasi-linear PDEs of the first order. Dispersionless Da Rios system and dispersionless Hirota equation are among them. They describe motion of vortex filament with slow varying curvature and torsion without or with axial flow. Gradient catastrophe for governing equations is studied. It is shown that geometrically this catastrophe manifests as a fast oscillation of a filament curve around the rectifying plane which resembles the flutter of airfoils. Analytically it is the elliptic umbilic singularity in the terminology of the catastrophe theory. It is demonstrated that its double scaling regularization is governed by the Painleve' I equation.
Dynamical systems with classical spin in the Einstein-Maxwell-Cartan theory
International Nuclear Information System (INIS)
By using variational precedures, spinning charged particles and fluids, with magnetic dipole moment, are analysed. Electromagnetic and gravitational interactions are also dynamically considered. A relativistic formalism which describes the space-time as a Riemann-Cartan manifold caraccterized by curvature and torsion tensors was adopted. The specific features of the Einstein-Maxell-Cartan theory have been analised in detail for the considered models. Also the holonomy of the local Lorentz Frames and constraints has been studied, and as a consequence it has been possible to generate new equations of motion for particles with spin. It has also been possible to derive the complete differential system which includes the fluid, the electromagnetic, the curvature and the torsion fields. (author)
International Nuclear Information System (INIS)
This thesis develops a new model, and related numerical methods, to describe classical time-dependent many-body systems interacting through central forces, spin-orbit forces and spin-spin forces. The model is based on two-particle interactions. The two-body forces consist of attractive and repulsive parts. In this model the investigated multi-particle systems are self-bound. Also the total potential of the whole ensemble is derived from the two-particle potential and is not imposed 'from outside'. Each particle has the three degrees of freedom of its centre-of-mass motion and the spin degree of freedom. The model allows for the particles to be either charged or uncharged. Furthermore, each particle has an angular momentum, an intrinsic spin, and a magnetic dipole moment. Through the electromagnetic forces between these charges and moments there arise dynamical couplings between them. The internal interactions between the charges and moments are well described by electromagnetic coupling mechanisms. In fact, compared to conventional classical molecular dynamics calculations in van der Waals clusters, which have no spin degrees of freedom, or for Heisenberg spin Systems, which have no orbital degrees of freedom, the model presented here contains both types of degrees of freedom with a highly non-trivial coupling. The model allows to study the fundamental effects resulting from the dynamical coupling of the spin and the orbital-motion sub-systems. In particular, the dynamics of the particle mass points show a behaviour basically different from the one of particles in a potential with only central forces. Furthermore, a special type of quenching procedure was invented, which tends to drive the multi-particle Systems into states with highly periodic, non-ergodic behaviour. Application of the model to cluster simulations has provided evidence that the model can also be used to investigate items like solid-to-liquid phase transitions (melting), isomerism and specific heat
Quantum systems as classical systems
Cassa, A
2001-01-01
A characteristical property of a classical physical theory is that the observables are real functions taking an exact outcome on every (pure) state; in a quantum theory, at the contrary, a given observable on a given state can take several values with only a predictable probability. However, even in the classical case, when an observer is intrinsically unable to distinguish between some distinct states he can convince himself that the measure of its ''observables'' can have several values in a random way with a statistical character. What kind of statistical theory is obtainable in this way? It is possible, for example, to obtain exactly the statistical previsions of quantum mechanics? Or, in other words, can a physical system showing a classical behaviour appear to be a quantum system to a confusing observer? We show that from a mathematical viewpoint it is not difficult to produce a theory with hidden variables having this property. We don't even try to justify in physical terms the artificial construction ...
International Nuclear Information System (INIS)
We investigate a two-level atom interacting with a quantized cavity field and a classical driving field in the presence of phase decoherence and find that a stationary quantum discord can arise in the interaction of the atom and cavity field as the time turns to infinity. We also find that the stationary quantum discord can be increased by applying a classical driving field. Furthermore, we explore the quantum discord dynamics of two identical non-interacting two-level atoms independently interacting with a quantized cavity field and a classical driving field in the presence of phase decoherence. Results show that the quantum discord between two atoms is more robust than entanglement under phase decoherence and the classical driving field can help to improve the amount of quantum discord of the two atoms. (general)
Dispersions in Semi-Classical Dynamics
International Nuclear Information System (INIS)
Dispersions around mean values of one-body observables are obtained by restoring classical many-body correlations in Vlasov and Landau-Vlasov dynamics. The method is applied to the calculation of fluctuations in mass, charge and linear momentum in heavy-ion collisions. Results are compared to those obtained by the Balian-Veneroni variational principle in semi-classical approximation
Construction of exact dynamical invariants of two-dimensional classical system
Indian Academy of Sciences (India)
S C Mishra; Fakir Chand
2006-03-01
A general method is used for the construction of second constant of motion of fourth order in momenta using the complex coordinates $(z, \\bar{z})$. A fourth-order potential equation is obtained whose solutions directly provide a large class of integrable systems. The potential equation is tested with an interesting example which admits second constants of motion.
A True Equation to Couple Classical and Quantum Dynamics
Diosi, Lajos
1995-01-01
Starting from the Schr\\"odinger-equation of a composite system, we derive unified dynamics of a classical harmonic system coupled to an arbitrary quantized system. The classical subsystem is described by random phase-space coordinates entangled with the quantized variables of the complementary subsystem. Our semiclassical equation is {\\it true} in a sense that its predictions are identical to those of the fully quantized composite dynamics. This exact method applies to a broad class of theori...
Non-MarkovianDynamics of Quantum and Classical Correlations in the Presence of System-Bath Coherence
Institute of Scientific and Technical Information of China (English)
李传锋; 汪浩田; 袁弘渊; 葛荣春; 郭光灿
2011-01-01
We present a detailed study on the dynamics of two-qubit correlations in non-Markovian environments, applying the hierarchy equations approach. This treatment is free from the limitation of perturbative, Markovian or rotating wave approximations. It is shown that crossovers and sudden changes in the classical and quantum correlations can appear when the strength of the interaction between qubits is gradually reduced. For some special initial states, there are even sudden transitions between the classical and quantum correlations.%We present a detailed study on the dynamics of two-qubit correlations in non-Markovian environments,applying the hierarchy equations approach.This treatment is free from the limitation of perturbative,Markovian or rotating wave approximations.It is shown that crossovers and sudden changes in the classical and quantum correlations can appear when the strength of the interaction between qubits is gradually reduced.For some special initial states,there are even sudden transitions between the classical and quantum correlations.
Quantum systems as classical systems
Cassa, Antonio
2001-01-01
A characteristical property of a classical physical theory is that the observables are real functions taking an exact outcome on every (pure) state; in a quantum theory, at the contrary, a given observable on a given state can take several values with only a predictable probability. However, even in the classical case, when an observer is intrinsically unable to distinguish between some distinct states he can convince himself that the measure of its ''observables'' can have several values in ...
Classical diffusive dynamics for the quasiperiodic kicked rotor
Lemarié, Gabriel; Delande, Dominique; Garreau, Jean Claude; Szriftgiser, Pascal
2010-01-01
We study the classical dynamics of a quasiperiodic kicked rotor, whose quantum counterpart is known to be an equivalent of the 3D Anderson model. Using this correspondence allowed for a recent experimental observation of the Anderson transition with atomic matter waves. In such a context, it is particularly important to assert the chaotic character of the classical dynamics of this system. We show here that it is a 3D anisotropic diffusion. Our simple analytical predictions for the associated...
Classical Hamiltonian Dynamics and Lie Group Algebras
Aycock, B; Silverberg, J L; Widom, A
2008-01-01
The classical Hamilton equations of motion yield a structure sufficiently general to handle an almost arbitrary set of ordinary differential equations. Employing elementary algebraic methods, it is possible within the Hamiltonian structure to describe many physical systems exhibiting Lie group symmetries. Elementary examples include magnetic moment precession and the mechanical orbits of color charged particles in classical non-abelian chromodynamics.
International Nuclear Information System (INIS)
We look at the high-lying eigenstates (from the 10001 to the 13000) in the Robnik billiard (defined as a quadratic conformal map of the unit disk) with the shape parameter λ=0.15. All the 3000 eigenstates have been numerically calculated and examined in the configuration space and in the phase space which-in comparison with the classical phase space-enabled a clear cut classification of energy levels into regular and irregular. This is the first successful separation of energy levels based on purely dynamical rather than special geometrical symmetry properties. We calculate the fractional measure of regular levels as ρ1=0.365±0.01, which is in remarkable agreement with the classical estimate ρ1=0.360±0.001. This finding confirms the Percival's (1973) classification scheme, the assumption in Berry-Robnik (1984) theory and the rigorous result by Lazutkin (1981, 1991). The regular levels obey the Poissonian statistics quite well, whereas the irregular sequence exhibits the fractional power-law level repulsion and globally Brody-like statistics with β=0.286±0.001. This is due to the strong localization of irregular eigenstates in the classically chaotic regions. Therefore, in the entire spectrum we see that the Berry-Robnik regime is not yet fully established so that the level spacing distribution is correctly captured by the Berry-Robnik-Brody distribution. (author)
International Nuclear Information System (INIS)
We study coherent superpositions of clockwise and anticlockwise rotating intermediate complexes with overlapping resonances formed in bimolecular chemical reactions. Disintegration of such complexes represents an analog of a famous double-slit experiment. The time for disappearance of the interference fringes is estimated from heuristic arguments related to fingerprints of chaotic dynamics of a classical counterpart of the coherently rotating complex. Validity of this estimate is confirmed numerically for the H+D2 chemical reaction. Thus we demonstrate the quantum-classical transition in temporal behavior of highly excited quantum many-body systems in the absence of external noise and coupling to an environment
Sternberg, Shlomo
2010-01-01
Celebrated mathematician Shlomo Sternberg, a pioneer in the field of dynamical systems, created this modern one-semester introduction to the subject for his classes at Harvard University. Its wide-ranging treatment covers one-dimensional dynamics, differential equations, random walks, iterated function systems, symbolic dynamics, and Markov chains. Supplementary materials offer a variety of online components, including PowerPoint lecture slides for professors and MATLAB exercises.""Even though there are many dynamical systems books on the market, this book is bound to become a classic. The the
International Nuclear Information System (INIS)
The advent of free electron lasers and high harmonic sources enables the investigation of electronic and nuclear dynamics of molecules and solids with atomic spatial resolution and femtosecond/attosecond time resolution, using bright and ultrashort laser pulses of frequency from terahertz to hard x-ray range. With the help of ultrashort laser pulses, the nuclear and electronic dynamics can be initiated, monitored and actively controlled at the typical time scale in the femtosecond to attosecond realm. Meanwhile, theoretical tools are required to describe the underlying mechanism. This doctoral thesis focuses on the development of theoretical tools based on full quantum mechanical multiconfiguration time-dependent Hartree (MCTDH) and mixed quantum classical approaches, which can be applied to describe the dynamical behavior of gas phase molecules and strongly correlated solids in the presence of ultrashort laser pulses. In the first part of this thesis, the focus is on the motion of electron holes in gas phase molecular ions created by extreme ultraviolet (XUV) photoionization and watched by spectroscopic approaches. The XUV photons create electron-hole in the valence orbitals of molecules by photoionization, the electron hole, as a positively charged quasi-particle, can then interact with the nuclei and the rest of electrons, leading to coupled non-Born-Oppenheimer dynamics. I present our study on electron-hole relaxation dynamics in valence ionized molecular ions of moderate size, using quantum wave packet and mixed quantum-classical approaches, using photoionized [H+(H2O)n]+ molecular ion as example. We have shown that the coupled motion of the electron-hole and the nuclei can be mapped out with femtosecond resolution by core-level x-ray transient absorption spectroscopy. Furthermore, in specific cases, the XUV photon can create a coherent electron hole, that can maintain its coherence to time scales of ∝ 1 picosecond. Employing XUV pump - IR probe spectroscopy
Quantization of soluble classical constrained systems
Energy Technology Data Exchange (ETDEWEB)
Belhadi, Z. [Laboratoire de physique et chimie quantique, Faculté des sciences, Université Mouloud Mammeri, BP 17, 15000 Tizi Ouzou (Algeria); Laboratoire de physique théorique, Faculté des sciences exactes, Université de Bejaia, 06000 Bejaia (Algeria); Menas, F. [Laboratoire de physique et chimie quantique, Faculté des sciences, Université Mouloud Mammeri, BP 17, 15000 Tizi Ouzou (Algeria); Ecole Nationale Préparatoire aux Etudes d’ingéniorat, Laboratoire de physique, RN 5 Rouiba, Alger (Algeria); Bérard, A. [Equipe BioPhysStat, Laboratoire LCP-A2MC, ICPMB, IF CNRS No 2843, Université de Lorraine, 1 Bd Arago, 57078 Metz Cedex (France); Mohrbach, H., E-mail: herve.mohrbach@univ-lorraine.fr [Equipe BioPhysStat, Laboratoire LCP-A2MC, ICPMB, IF CNRS No 2843, Université de Lorraine, 1 Bd Arago, 57078 Metz Cedex (France)
2014-12-15
The derivation of the brackets among coordinates and momenta for classical constrained systems is a necessary step toward their quantization. Here we present a new approach for the determination of the classical brackets which does neither require Dirac’s formalism nor the symplectic method of Faddeev and Jackiw. This approach is based on the computation of the brackets between the constants of integration of the exact solutions of the equations of motion. From them all brackets of the dynamical variables of the system can be deduced in a straightforward way.
Effective dynamics of a classical point charges
Polonyi, Janos
2013-01-01
The effective Lagrangian of a point charge is derived by eliminating the electromagnetic field within the framework of the classical closed time path formalism. The short distance singularity of the electromagnetic field is regulated by an UV cutoff. The Abraham-Lorentz force is recovered and its similarity to anomalies is underlined. The full cutoff-dependent linearized equation of motion is obtained, no runaway trajectories are found but the effective dynamics shows acausality if the cutoff is beyond the classical charge radius. The strength of the radiation reaction force displays a pole in its cutoff-dependence in a manner reminiscent of the Landau-pole of perturbative QED. Similarity between the dynamical breakdown of the time reversal invariance and dynamical symmetry breaking is pointed out.
Indeterminism in Classical Dynamics of Particle Motion
Eyink, Gregory; Vishniac, Ethan; Lalescu, Cristian; Aluie, Hussein; Kanov, Kalin; Burns, Randal; Meneveau, Charles; Szalay, Alex
2013-03-01
We show that ``God plays dice'' not only in quantum mechanics but also in the classical dynamics of particles advected by turbulent fluids. With a fixed deterministic flow velocity and an exactly known initial position, the particle motion is nevertheless completely unpredictable! In analogy with spontaneous magnetization in ferromagnets which persists as external field is taken to zero, the particle trajectories in turbulent flow remain random as external noise vanishes. The necessary ingredient is a rough advecting field with a power-law energy spectrum extending to smaller scales as noise is taken to zero. The physical mechanism of ``spontaneous stochasticity'' is the explosive dispersion of particle pairs proposed by L. F. Richardson in 1926, so the phenomenon should be observable in laboratory and natural turbulent flows. We present here the first empirical corroboration of these effects in high Reynolds-number numerical simulations of hydrodynamic and magnetohydrodynamic fluid turbulence. Since power-law spectra are seen in many other systems in condensed matter, geophysics and astrophysics, the phenomenon should occur rather widely. Fast reconnection in solar flares and other astrophysical systems can be explained by spontaneous stochasticity of magnetic field-line motion
Classical models of the spin 1/2 system
Salazar-Lazaro, Carlos H.
We proposed a Quaternionic mechanical system motivated by the Foucault pendulum as a classical model for the dynamics of the spin ½ system. We showed that this mechanical system contains the dynamics of the spin state of the electron under a uniform magnetic field as it is given by the Schrodinger-Pauli-Equation (SPE). We closed with a characterization of the dynamics of this generalized classical system by showing that it is equivalent with the dynamics of the Schrodinger Pauli Equation as long as the solutions to the generalized classical system are roots of the Lagrangian, that is the condition L = 0 holds.
Classical transport in disordered systems
Papaioannou, Antonios
This thesis reports on the manifestation of structural disorder on molecular transport and it consists of two parts. Part I discusses the relations between classical transport and the underlying structural complexity of the system. Both types of molecular diffusion, namely Gaussian and non- Gaussian are presented and the relevant time regimes are discussed. In addition the concept of structural universality is introduced and connected with the diffusion metrics. One of the most robust techniques for measuring molecular mean square displacements is magnetic resonance. This method requires encoding and subsequently reading out after an experimentally controlled time, a phase φ to the spins using magnetic field gradients. The main limitation for probing short diffusion lengths L(t) ˜ 1micro m with magnetic resonance is the requirement to encode and decode the phase φ in very short time intervals. Therefore, to probe such displacements a special probe was developed equipped with a gradient coil capable of delivering magnetic field gradients of approximately 90 G/cmA . The design of the probe is reported. Part I also includes a discussion of experiments of transport in two qualitatively different disordered phantoms and reports on a direct observation of universality in one-dimension. The results reveal the universal power law scaling of the diffusion coefficient at the long-time regime and illustrate the essence of structural universality by experimentally determining the structure correlation function of the phantoms. In addition, the scaling of the diffusive permeability of the phantoms with respect to the pore size is investigated. Additional work presented includes a detailed study of adsorption of methane gas in Vycor disordered glass. The techniques described in Part I of this thesis are widely used for measuring structural parameters of porous media, such as the surface-to-volume ratio or diffusive permeability. Part II of this thesis discusses the
Papastavridis, John G
1999-01-01
Tensor Calculus and Analytical Dynamics provides a concise, comprehensive, and readable introduction to classical tensor calculus - in both holonomic and nonholonomic coordinates - as well as to its principal applications to the Lagrangean dynamics of discrete systems under positional or velocity constraints. The thrust of the book focuses on formal structure and basic geometrical/physical ideas underlying most general equations of motion of mechanical systems under linear velocity constraints.
The transition to chaos conservative classical systems and quantum manifestations
Reichl, Linda E
2004-01-01
This book provides a thorough and comprehensive discussion of classical and quantum chaos theory for bounded systems and for scattering processes Specific discussions include • Noether’s theorem, integrability, KAM theory, and a definition of chaotic behavior • Area-preserving maps, quantum billiards, semiclassical quantization, chaotic scattering, scaling in classical and quantum dynamics, dynamic localization, dynamic tunneling, effects of chaos in periodically driven systems and stochastic systems • Random matrix theory and supersymmetry The book is divided into several parts Chapters 2 through 4 deal with the dynamics of nonlinear conservative classical systems Chapter 5 and several appendices give a thorough grounding in random matrix theory and supersymmetry techniques Chapters 6 and 7 discuss the manifestations of chaos in bounded quantum systems and open quantum systems respectively Chapter 8 focuses on the semiclassical description of quantum systems with underlying classical chaos, and Chapt...
Emergence of cooperative dynamics in fully packed classical dimers
Oakes, Tom; Garrahan, Juan P.; Powell, Stephen
2016-03-01
The classical dimer model on the square lattice is a paradigmatic example of a system subject to strong local constraints. We study its behavior under local stochastic dynamics, by means of Monte Carlo simulations and theoretical arguments. We observe clear signatures of correlated dynamics in both global and local observables and over a broad range of time scales, indicating a breakdown of the simple continuum description that approximates well the statics. We show that this collective dynamics can be understood in terms of one-dimensional "strings" of high mobility, which govern both local and long-wavelength dynamical properties. We introduce a coarse-grained description of the strings, based on the Edwards-Wilkinson model, which leads to exact results in the limit of low string density and provides a detailed qualitative understanding of the dynamics in all flux sectors. We discuss the implications of our results for the dynamics of constrained systems more generally.
Quantum Gibbs distribution from dynamical thermalization in classical nonlinear lattices
International Nuclear Information System (INIS)
We study numerically time evolution in classical lattices with weak or moderate nonlinearity which leads to interactions between linear modes. Our results show that in a certain strength range a moderate nonlinearity generates a dynamical thermalization process which drives the system to the quantum Gibbs distribution of probabilities, or average oscillation amplitudes. The effective dynamical temperature of the lattice varies from large positive to large negative values depending on the energy of the initially excited modes. This quantum Gibbs distribution is drastically different from the usually expected energy equipartition over linear modes corresponding to a regime of classical thermalization. Possible experimental observations of this dynamical thermalization are discussed for cold atoms in optical lattices, nonlinear photonic lattices and optical fiber arrays. (paper)
Hidden Symmetries of Dynamics in Classical and Quantum Physics
Cariglia, Marco
2014-01-01
This article reviews the role of hidden symmetries of dynamics in the study of physical systems, from the basic concepts of symmetries in phase space to the forefront of current research. Such symmetries emerge naturally in the description of physical systems as varied as non-relativistic, relativistic, with or without gravity, classical or quantum, and are related to the existence of conserved quantities of the dynamics and integrability. In recent years their study has grown intensively, due to the discovery of non-trivial examples that apply to different types of theories and different numbers of dimensions. Applications encompass the study of integrable systems such as spinning tops, the Calogero model, systems described by the Lax equation, the physics of higher dimensional black holes, the Dirac equation, supergravity with and without fluxes, providing a tool to probe the dynamics of non-linear systems.
Decoherence and quantum-classical master equation dynamics
Grunwald, Robbie; Kapral, Raymond
2007-03-01
The conditions under which quantum-classical Liouville dynamics may be reduced to a master equation are investigated. Systems that can be partitioned into a quantum-classical subsystem interacting with a classical bath are considered. Starting with an exact non-Markovian equation for the diagonal elements of the density matrix, an evolution equation for the subsystem density matrix is derived. One contribution to this equation contains the bath average of a memory kernel that accounts for all coherences in the system. It is shown to be a rapidly decaying function, motivating a Markovian approximation on this term in the evolution equation. The resulting subsystem density matrix equation is still non-Markovian due to the fact that bath degrees of freedom have been projected out of the dynamics. Provided the computation of nonequilibrium average values or correlation functions is considered, the non-Markovian character of this equation can be removed by lifting the equation into the full phase space of the system. This leads to a trajectory description of the dynamics where each fictitious trajectory accounts for decoherence due to the bath degrees of freedom. The results are illustrated by computations of the rate constant of a model nonadiabatic chemical reaction.
Point vortex dynamics: A classical mathematics playground
DEFF Research Database (Denmark)
Aref, Hassan
2007-01-01
integrability of the three-vortex problem, the interplay of relative equilibria of identical vortices and the roots of certain polynomials, addition formulas for the cotangent and the Weierstrass zeta function, projective geometry, and other topics. The hope and intent of the article is to garner further...... participation in the exploration of this intriguing dynamical system from the mathematical physics community....
Classical and semiclassical aspects of chemical dynamics
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Tunneling in the unimolecular reactions H2C2 → HC2H, HNC → HCN, and H2CO → H2 + CO is studied with a classical Hamiltonian that allows the reaction coordinate and transverse vibrational modes to be considered directly. A combination of classical perturbation theory and the semiclassical WKB method allows tunneling probabilities to be obtained, and a statistical theory (RRKM) is used to construct rate constants for these reactions in the tunneling regime. In this fashion, it is found that tunneling may be important, particularly for low excitation energies. Nonadiabatic charge transfer in the reaction Na + I → Na + + I- is treated with classical trajectories based on a classical Hamiltonian that is the analogue of a quantum matrix representation. The charge transfer cross section obtained is found to agree reasonably well with the exact quantum results. An approximate semiclassical formula, valid at high energies, is also obtained. The interaction of radiation and matter is treated from a classical viewpoint. The excitation of an HF molecule in a strong laser is described with classical trajectories. Quantum mechanical results are also obtained and compared to the classical results. Although the detailed structure of the pulse time averaged energy absorption cannot be reproduced classically, classical mechanics does predict the correct magnitude of energy absorption, as well as certain other qualitative features. The classical behavior of a nonrotating diatomic molecule in a strong laser field is considered further, by generating a period advance map that allows the solution over many periods of oscillation of the laser to be obtained with relative ease. Classical states are found to form beautiful spirals in phase space as time progresses. A simple pendulum model is found to describe the major qualitative features
Relativistic and separable classical hamiltonian particle dynamics
International Nuclear Information System (INIS)
We show within the Hamiltonian formalism the existence of classical relativistic mechanics of N scalar particles interacting at a distance which satisfies the requirements of Poincare invariance, separability, world-line invariance and Einstein causality. The line of approach which is adopted here uses the methods of the theory of systems with constraints applied to manifestly covariant systems of particles. The study is limited to the case of scalar interactions remaining weak in the whole phase space and vanishing at large space-like separation distances of the particles. Poincare invariance requires the inclusion of many-body, up to N-body, potentials. Separability requires the use of individual or two-body variables and the construction of the total interaction from basic two-body interactions. Position variables of the particles are constructed in terms of the canonical variables of the theory according to the world-line invariance condition and the subsidiary conditions of the non-relativistic limit and separability. Positivity constraints on the interaction masses squared of the particles ensure that the velocities of the latter remain always smaller than the velocity of light
Interaction between classical and quantum systems
International Nuclear Information System (INIS)
An unconventional approach to the measurement problem in quantum mechanics is considered--the apparatus is treated as a classical system, belonging to the macro-world. In order to have a measurement the apparatus must interact with the quantum system. As a first step, the classical apparatus is embedded into a large quantum mechanical structure, making use of a superselection principle. The apparatus and system are coupled such that the apparatus remains classical (principle of integrity), and unambiguous information of the values of a quantum observable are transferred to the variables of the apparatus. Further measurement of the classical apparatus can be done, causing no problems of principle. Thus interactions causing pointers to move (which are not treated) can be added. The restrictions placed by the principle of integrity on the form of the interaction between classical and quantum systems are examined and illustration is given by means of a simple example in which one sees the principle of integrity at work
Comparisons of classical and quantum dynamics for initially localized states
International Nuclear Information System (INIS)
We compare the dynamics of quantum wave packets with the dynamics of classical trajectory ensembles. The wave packets are Gaussian with expectation values of position and momenta which centers them in phase space. The classical trajectory ensembles are generated directly from the quantum wave packets via the Wigner transform. Quantum and classical dynamics are then compared using several quantum measures and the analogous classical ones derived from the Wigner equivalent formalism. Comparisons are made for several model potentials and it is found that there is generally excellent classical--quantum correspondence except for certain specific cases of tunneling and interference. In general, this correspondence is also very good in regions of phase space where there is classical chaos
Classical and quantum stability of higher-derivative dynamics
Energy Technology Data Exchange (ETDEWEB)
Kaparulin, D.S.; Lyakhovich, S.L.; Sharapov, A.A. [Tomsk State University, Physics Faculty, Tomsk (Russian Federation)
2014-10-15
We observe that a wide class of higher-derivative systems admits a bounded integral of motion that ensures the classical stability of dynamics, while the canonical energy is unbounded. We use the concept of a Lagrange anchor to demonstrate that the bounded integral of motion is connected with the time-translation invariance. A procedure is suggested for switching on interactions in free higher-derivative systems without breaking their stability. We also demonstrate the quantization technique that keeps the higher-derivative dynamics stable at quantum level. The general construction is illustrated by the examples of the Pais-Uhlenbeck oscillator, higher-derivative scalar field model, and the Podolsky electrodynamics. For all these models, the positive integrals of motion are explicitly constructed and the interactions are included such that they keep the system stable. (orig.)
The classical and quantum dynamics of molecular spins on graphene.
Cervetti, Christian; Rettori, Angelo; Pini, Maria Gloria; Cornia, Andrea; Repollés, Ana; Luis, Fernando; Dressel, Martin; Rauschenbach, Stephan; Kern, Klaus; Burghard, Marko; Bogani, Lapo
2016-02-01
Controlling the dynamics of spins on surfaces is pivotal to the design of spintronic and quantum computing devices. Proposed schemes involve the interaction of spins with graphene to enable surface-state spintronics and electrical spin manipulation. However, the influence of the graphene environment on the spin systems has yet to be unravelled. Here we explore the spin-graphene interaction by studying the classical and quantum dynamics of molecular magnets on graphene. Whereas the static spin response remains unaltered, the quantum spin dynamics and associated selection rules are profoundly modulated. The couplings to graphene phonons, to other spins, and to Dirac fermions are quantified using a newly developed model. Coupling to Dirac electrons introduces a dominant quantum relaxation channel that, by driving the spins over Villain's threshold, gives rise to fully coherent, resonant spin tunnelling. Our findings provide fundamental insight into the interaction between spins and graphene, establishing the basis for electrical spin manipulation in graphene nanodevices. PMID:26641019
The classical and quantum dynamics of molecular spins on graphene
Cervetti, Christian; Rettori, Angelo; Pini, Maria Gloria; Cornia, Andrea; Repollés, Ana; Luis, Fernando; Dressel, Martin; Rauschenbach, Stephan; Kern, Klaus; Burghard, Marko; Bogani, Lapo
2016-02-01
Controlling the dynamics of spins on surfaces is pivotal to the design of spintronic and quantum computing devices. Proposed schemes involve the interaction of spins with graphene to enable surface-state spintronics and electrical spin manipulation. However, the influence of the graphene environment on the spin systems has yet to be unravelled. Here we explore the spin-graphene interaction by studying the classical and quantum dynamics of molecular magnets on graphene. Whereas the static spin response remains unaltered, the quantum spin dynamics and associated selection rules are profoundly modulated. The couplings to graphene phonons, to other spins, and to Dirac fermions are quantified using a newly developed model. Coupling to Dirac electrons introduces a dominant quantum relaxation channel that, by driving the spins over Villain’s threshold, gives rise to fully coherent, resonant spin tunnelling. Our findings provide fundamental insight into the interaction between spins and graphene, establishing the basis for electrical spin manipulation in graphene nanodevices.
A Survey on the Classical Limit of Quantum Dynamical Entropies
Cappellini, Valerio
2007-01-01
We analyze the behavior of quantum dynamical entropies production from sequences of quantum approximants approaching their (chaotic) classical limit. The model of the quantized hyperbolic automorphisms of the 2-torus is examined in detail and a semi-classical analysis is performed on it using coherent states, fulfilling an appropriate dynamical localization property. Correspondence between quantum dynamical entropies and the Kolmogorov-Sinai invariant is found only over time scales that are logarithmic in the quantization parameter.
Isomorph invariance of the structure and dynamics of classical crystals
DEFF Research Database (Denmark)
Albrechtsen, Dan; Olsen, Andreas Elmerdahl; Pedersen, Ulf Rørbæk; Schrøder, Thomas; Dyre, J. C.
2014-01-01
, which is generally a good description except significantly below melting. The existence of isomorphs for crystals is validated by simulations of particles interacting via the Lennard-Jones pair potential arranged into a face-centered cubic (fcc) crystalline structure; the slow vacancy-jump dynamics of a......This paper shows by computer simulations that some crystalline systems have curves in their thermodynamic phase diagrams, so-called isomorphs, along which structure and dynamics in reduced units are invariant to a good approximation. The crystals are studied in a classical-mechanical framework...... defective fcc crystal is also shown to be isomorph invariant. In contrast, a NaCl crystal model does not exhibit isomorph invariances. Other systems simulated, though in less detail, are the Wahnström binary Lennard-Jones crystal with the MgZn2 Laves crystal structure, monatomic fcc crystals of particles...
Phase Space Cell in Nonextensive Classical Systems
Piero Quarati; Francesco Quarati
2003-01-01
We calculate the phase space volume $\\Omega$ occupied by a nonextensive system of $N$ classical particles described by an equilibrium (or steady-state, or long-term stationary state of a nonequilibrium system) distribution function, which slightly deviates from Maxwell-Boltzmann (MB) distribution in the high energy tail. We explicitly require that the number of accessible microstates does not change respect to the extensive MB case. We also derive, within a classical scheme, an analytical exp...
Directory of Open Access Journals (Sweden)
Wassim M. Haddad
2001-01-01
Full Text Available In this paper we develop a unified dynamical systems framework for a general class of systems possessing left-continuous flows; that is, left-continuous dynamical systems. These systems are shown to generalize virtually all existing notions of dynamical systems and include hybrid, impulsive, and switching dynamical systems as special cases. Furthermore, we generalize dissipativity, passivity, and nonexpansivity theory to left-continuous dynamical systems. Specifically, the classical concepts of system storage functions and supply rates are extended to left-continuous dynamical systems providing a generalized hybrid system energy interpretation in terms of stored energy, dissipated energy over the continuous-time dynamics, and dissipated energy over the resetting events. Finally, the generalized dissipativity notions are used to develop general stability criteria for feedback interconnections of left-continuous dynamical systems. These results generalize the positivity and small gain theorems to the case of left-continuous, hybrid, and impulsive dynamical systems.
Classical Dynamics of Free Electromagnetic Laser Pulses
Goto, S; Tucker, R. W.; Walton, T. J.
2015-01-01
We discuss a class of exact finite energy solutions to the vacuum source-free Maxwell field equations as models for multi- and single cycle laser pulses in classical interaction with relativistic charged test particles. These solutions are classified in terms of their chiral content based on their influence on particular charge configurations in space. Such solutions offer a computationally efficient parameterization of compact laser pulses used in laser-matter simulations and provide a poten...
Benet, L.; Chadderton, L. T.; Kun, S. Yu.; Qi, Wang
2006-01-01
We study coherent superpositions of clockwise and anti-clockwise rotating intermediate complexes with overlapping resonances formed in bimolecular chemical reactions. Disintegration of such complexes represents an analog of famous double-slit experiment. The time for disappearance of the interference fringes is estimated from heuristic arguments related to fingerprints of chaotic dynamics of a classical counterpart of the coherently rotating complex. Validity of this estimate is confirmed num...
Metamaterials: supra-classical dynamic homogenization
Caleap, Mihai; Drinkwater, Bruce W.
2015-12-01
Metamaterials are artificial composite structures designed for controlling waves or fields, and exhibit interaction phenomena that are unexpected on the basis of their chemical constituents. These phenomena are encoded in effective material parameters that can be electronic, magnetic, acoustic, or elastic, and must adequately represent the wave interaction behavior in the composite within desired frequency ranges. In some cases—for example, the low frequency regime—there exist various efficient ways by which effective material parameters for wave propagation in metamaterials may be found. However, the general problem of predicting frequency-dependent dynamic effective constants has remained unsolved. Here, we obtain novel mathematical expressions for the effective parameters of two-dimensional metamaterial systems valid at higher frequencies and wavelengths than previously possible. By way of an example, random configurations of cylindrical scatterers are considered, in various physical contexts: sound waves in a compressible fluid, anti-plane elastic waves, and electromagnetic waves. Our results point towards a paradigm shift in our understanding of these effective properties, and metamaterial designs with functionalities beyond the low-frequency regime are now open for innovation. Dedicated with gratitude to the memory of Prof Yves C Angel.
Classical and quantum dynamics of driven elliptical billiards
Energy Technology Data Exchange (ETDEWEB)
Lenz, Florian
2009-12-09
Subject of this thesis is the investigation of the classical dynamics of the driven elliptical billiard and the development of a numerical method allowing the propagation of arbitrary initial states in the quantum version of the system. In the classical case, we demonstrate that there is Fermi acceleration in the driven billiard. The corresponding transport process in momentum space shows a surprising crossover from sub- to normal diffusion. This crossover is not parameter induced, but rather occurs dynamically in the evolution of the ensemble. The four-dimensional phase space is analyzed in depth, especially how its composition changes in different velocity regimes. We show that the stickiness properties, which eventually determine the diffusion, are intimately connected with this change of the composition of the phase space with respect to velocity. In the course of the evolution, the accelerating ensemble thus explores regions of varying stickiness, leading to the mentioned crossover in the diffusion. In the quantum case, a series of transformations tailored to the elliptical billiard is applied to circumvent the time-dependent Dirichlet boundary conditions. By means of an expansion ansatz, this eventually yields a large system of coupled ordinary differential equations, which can be solved by standard techniques. (orig.)
Classical and quantum dynamics of driven elliptical billiards
International Nuclear Information System (INIS)
Subject of this thesis is the investigation of the classical dynamics of the driven elliptical billiard and the development of a numerical method allowing the propagation of arbitrary initial states in the quantum version of the system. In the classical case, we demonstrate that there is Fermi acceleration in the driven billiard. The corresponding transport process in momentum space shows a surprising crossover from sub- to normal diffusion. This crossover is not parameter induced, but rather occurs dynamically in the evolution of the ensemble. The four-dimensional phase space is analyzed in depth, especially how its composition changes in different velocity regimes. We show that the stickiness properties, which eventually determine the diffusion, are intimately connected with this change of the composition of the phase space with respect to velocity. In the course of the evolution, the accelerating ensemble thus explores regions of varying stickiness, leading to the mentioned crossover in the diffusion. In the quantum case, a series of transformations tailored to the elliptical billiard is applied to circumvent the time-dependent Dirichlet boundary conditions. By means of an expansion ansatz, this eventually yields a large system of coupled ordinary differential equations, which can be solved by standard techniques. (orig.)
Classical Dynamics of Free Electromagnetic Laser Pulses
Goto, S; Walton, T J
2015-01-01
We discuss a class of exact finite energy solutions to the vacuum source-free Maxwell field equations as models for multi- and single cycle laser pulses in classical interaction with relativistic charged test particles. These solutions are classified in terms of their chiral content based on their influence on particular charge configurations in space. Such solutions offer a computationally efficient parameterization of compact laser pulses used in laser-matter simulations and provide a potential means for experimentally bounding the fundamental length scale in the generalized electrodynamics of Bopp, Lande and Podolsky.
Fundamental laws of relativistic classical dynamics revisited
International Nuclear Information System (INIS)
By stating that a linear differential form, whose coefficients are the components of the momentum and the energy of a particle, has an antiderivative, the basic equations of the dynamics of points are obtained, in the relativistic case. From the point of view of optimization theory, a connection between our condition and the Bellman-Isaacs equation of dynamic programming is discussed, with a view to extending the theory to relativistic wave mechanics
International Nuclear Information System (INIS)
This book introduces systems thinking and conceptual tool and modeling tool of dynamics system such as tragedy of single thinking, accessible way of system dynamics, feedback structure and causal loop diagram analysis, basic of system dynamics modeling, causal loop diagram and system dynamics modeling, information delay modeling, discovery and application for policy, modeling of crisis of agricultural and stock breeding products, dynamic model and lesson in ecosystem, development and decadence of cites and innovation of education forward system thinking.
Identifying the Stern-Gerlach force of classical electron dynamics.
Wen, Meng; Bauke, Heiko; Keitel, Christoph H
2016-01-01
Different classical theories are commonly applied in various branches of physics to describe the relativistic dynamics of electrons by coupled equations for the orbital motion and spin precession. Exemplarily, we benchmark the Frenkel model and the classical Foldy-Wouthuysen model with spin-dependent forces (Stern-Gerlach forces) to the quantum dynamics as predicted by the Dirac equation. Both classical theories can lead to different or even contradicting predictions how the Stern-Gerlach forces modify the electron's orbital motion, when the electron moves in strong electromagnetic field configurations of emerging high-intensity laser facilities. In this way, one may evaluate the validity and identify the limits of these classical theories via a comparison with possible experiments to provide a proper description of spin-induced dynamics. Our results indicate that the Foldy-Wouthuysen model is qualitatively in better agreement with the Dirac theory than the widely used Frenkel model. PMID:27546820
On the classical dynamics of billiards on the sphere
Spina, M E
1999-01-01
We study the classical motion in bidimensional polygonal billiards on the sphere. In particular we investigate the dynamics in tiling and generic rational and irrational equilateral triangles. Unlike the plane or the negative curvature cases we obtain a complex but regular dynamics.
Opinion particles: Classical physics and opinion dynamics
International Nuclear Information System (INIS)
A model for Opinion Particles, based on Bayesian-inspired models of Opinion Dynamics such as the CODA model, is presented. By extending the discrete time characteristic of those models to continuous time, a theory for the movement of opinion particles is obtained, based only on inference ideas. This will allow inertia to be obtained as a consequence of an extended CODA model. For the general case, we will see that the likelihoods are associated with variables such as velocity and acceleration of the particles. Newtonian forces are easily defined and the relationship between a force and the equivalent likelihood provided. The case of the harmonic oscillator is solved as an example, to illustrate clearly the relationship between Opinion Particles and Mechanics. Finally, possible paths to apply these results to General Relativity are debated. - Highlights: • CODA model of Opinion Dynamics is extended to continuous time • The concept of Opinion Particles is introduced and inertia is obtained. • The relationship between opinion particle models and basic Physics is discussed. • Harmonic oscillator dynamics is obtained for opinion particles. • Possible equivalences to General Relativity are briefly discussed
Phase Space Cell in Nonextensive Classical Systems
Quarati, F
2003-01-01
We calculate the phase space volume $Omega$ occupied by a nonextensive system of $N$ classical particles described by an equilibrium (or steady-state, or long-term stationary state of a nonequilibrium system) distribution function, which slightly deviates from Maxwell-Boltzmann (MB) distribution in the high energy tail. We explicitly require that the number of accessible microstates does not change respect to the extensive MB case. We also derive, within a classical scheme, an analytical expression of the elementary cell that can be seen as a macrocell, different from the third power of Planck constant. Thermodynamic quantities like entropy, chemical potential and free energy of a classical ideal gas, depending on elementary cell, are evaluated. Considering the fractional deviation from MB distribution we can deduce a physical meaning of the nonextensive parameter $q$ of the Tsallis nonextensive thermostatistics in terms of particle correlation functions (valid at least in the case, discussed in this work, of...
Quantum and Classical Behavior in Interacting Bosonic Systems
Hertzberg, Mark P
2016-01-01
It is understood that in free bosonic theories, the classical field theory accurately describes the full quantum theory when the occupancy numbers of systems are very large. However, the situation is less understood in interacting theories, especially on time scales longer than the dynamical relaxation time. Recently there have been claims that the quantum theory deviates spectacularly from the classical theory on this time scale, even if the occupancy numbers are extremely large. Furthermore, it is claimed that the quantum theory quickly thermalizes while the classical theory does not. The evidence for these claims comes from noticing a spectacular difference in the time evolution of expectation values of quantum operators compared to the classical micro-state evolution. If true, this would have dramatic consequences for many important phenomena, including laboratory studies of interacting BECs, dark matter axions, preheating after inflation, etc. In this work we critically examine these claims. We show that...
Quantum-classical correspondence in steady states of nonadiabatic systems
International Nuclear Information System (INIS)
We first present nonadiabatic path integral which is exact formulation of quantum dynamics in nonadiabatic systems. Then, by applying the stationary phase approximations to the nonadiabatic path integral, a semiclassical quantization condition, i.e., quantum-classical correspondence, for steady states of nonadiabatic systems is presented as a nonadiabatic trace formula. The present quantum-classical correspondence indicates that a set of primitive hopping periodic orbits, which are invariant under time evolution in the phase space of the slow degree of freedom, should be quantized. The semiclassical quantization is then applied to a simple nonadiabatic model and accurately reproduces exact quantum energy levels
Classical and quantum particle dynamics in univariate background fields
Heinzl, Thomas; King, Ben
2016-01-01
We investigate deviations from the plane wave model in the interaction of charged particles with strong electromagnetic fields. A general result is that integrability of the dynamics is lost when going from lightlike to timelike or spacelike field dependence. For a special scenario in the classical regime we show how the radiation spectrum in the spacelike (undulator) case becomes well-approximated by the plane wave model in the high energy limit, despite the two systems being Lorentz inequivalent. In the quantum problem, there is no analogue of the WKB-exact Volkov solution. Nevertheless, WKB and uniform-WKB approaches give good approximations in all cases considered. Other approaches that reduce the underlying differential equations from second to first order are found to miss the correct physics for situations corresponding to barrier transmission and wide-angle scattering.
Classical molecular dynamics investigations of biphenyl-based carbon nanomembranes
Directory of Open Access Journals (Sweden)
Andreas Mrugalla
2014-06-01
Full Text Available Background: Free-standing carbon nanomembranes (CNM with molecular thickness and macroscopic size are fascinating objects both for fundamental reasons and for applications in nanotechnology. Although being made from simple and identical precursors their internal structure is not fully known and hard to simulate due to the large system size that is necessary to draw definite conclusions.Results: We performed large-scale classical molecular dynamics investigations of biphenyl-based carbon nanomembranes. We show that one-dimensional graphene-like stripes constitute a highly symmetric quasi one-dimensional energetically favorable ground state. This state does not cross-link. Instead cross-linked structures are formed from highly excited precursors with a sufficient amount of broken phenyls.Conclusion: The internal structure of the CNM is very likely described by a disordered metastable state which is formed in the energetic initial process of electron irradiation and depends on the process of relaxation into the sheet phase.
Dynamics of classical and quantum fields an introduction
Setlur, Girish S
2014-01-01
Dynamics of Classical and Quantum Fields: An Introduction focuses on dynamical fields in non-relativistic physics. Written by a physicist for physicists, the book is designed to help readers develop analytical skills related to classical and quantum fields at the non-relativistic level, and think about the concepts and theory through numerous problems. In-depth yet accessible, the book presents new and conventional topics in a self-contained manner that beginners would find useful. A partial list of topics covered includes: Geometrical meaning of Legendre transformation in classical mechanics Dynamical symmetries in the context of Noether's theorem The derivation of the stress energy tensor of the electromagnetic field, the expression for strain energy in elastic bodies, and the Navier Stokes equation Concepts of right and left movers in case of a Fermi gas explained Functional integration is interpreted as a limit of a sequence of ordinary integrations Path integrals for one and two quantum particles and for...
DYNAMIC AND CLASSICAL PRA: A BWR SBO CASE COMPARISON
Energy Technology Data Exchange (ETDEWEB)
Mandelli, Diego; Smith, Curtis L; Ma, Zhegang
2011-07-01
As part of the Light-Water Sustainability Program (LWRS), the purpose of the Risk Informed Safety Margin Characterization (RISMC) Pathway research and development is to support plant decisions for risk-informed margin management with the aim to improve economics, reliability, and sustain the safety of current NPPs. In this paper, we describe the RISMC analysis process illustrating how mechanistic (i.e., dynamic system simulators) and probabilistic (stochastic sampling strategies) approaches are combined in a dynamic PRA fashion in order to estimate safety margins. We use the scenario of a “station blackout” (SBO) wherein offsite power and onsite power are lost, thereby causing a challenge to plant safety systems. We describe the RISMC approach, illustrate the station blackout modeling, and compare this with traditional risk analysis modeling for this type of accident scenario. In the RISMC approach the dataset obtained consists of set of simulation runs (performed by using codes such as RELAP5/3D) where timing and ordering of events is changed accordingly to the stochastic sampling strategy adopted. On the other side, classical PRA methods, which are based on event-tree (FT) and fault-tree (FT) structures, generate minimal cut sets and probability values associated to each ET branch. The comparison of the classical and RISMC approaches is performed not only in terms of overall core damage probability but also considering statistical differences in the actual sequence of events. The outcome of this comparison analysis shows similarities and dissimilarities between the approaches but also highlights the greater amount of information that can be generated by using the RISMC approach.
Classical mechanical systems based on Poisson symmetry
Zakrzewski, S.
1996-01-01
The existence of the theory of `twisted cotangent bundles' (symplectic groupoids) allows to study classical mechanical systems which are generalized in the sense that their configurations form a Poisson manifold. It is natural to study from this point of view first such systems which arise in the context of some basic physical symmetry (space-time, rotations, etc.). We review results obtained so far in this direction.
Classical mechanical systems based on Poisson symmetry
Energy Technology Data Exchange (ETDEWEB)
Zakrzewski, S. [Department of Mathematical Methods in Physics, University of Warsaw, Warsaw (Poland)
1996-10-01
The existence of the theory of ``twisted cotangent bundles`` (symplectic groupoids) allows to study classical mechanical systems which are generalized in the sense that their configurations form a Poisson manifold. It is natural to study from this point of view first such systems which arise in the context of some basic physical symmetry (space-time, rotations, etc.). We review results obtained so far in this direction. (author)
Quantum and classical dynamics in adiabatic computation
Crowley, P. J. D.; Duric, T.; Vinci, W.; Warburton, P. A.; Green, A. G.
2014-01-01
Adiabatic transport provides a powerful way to manipulate quantum states. By preparing a system in a readily initialized state and then slowly changing its Hamiltonian, one may achieve quantum states that would otherwise be inaccessible. Moreover, a judicious choice of final Hamiltonian whose ground state encodes the solution to a problem allows adiabatic transport to be used for universal quantum computation. However, the dephasing effects of the environment limit the quantum correlations th...
International Nuclear Information System (INIS)
We study the dynamics of classical particles interacting with attractive Gaussian potentials. This system is thermodynamically not stable and exhibits negative specific heat. The results of the computer simulation of the dynamics are discussed in comparison with various theories. In particular, we find that the condensed phase is a stationary solution of the Vlasov equation, but the Vlasov dynamics cannot describe the collapse. 14 refs., 1 tab., 11 figs. (Authors)
Low temperature spin wave dynamics in classical Heisenberg chains
Energy Technology Data Exchange (ETDEWEB)
Heller, P.; Blume, M.
1977-11-01
A detailed and quantitative study of the low-temperature spin-wave dynamics was made for the classical Heisenberg-coupled chain using computer simulation. Results for the spin-wave damping rates and the renormalization of the spin-wave frequencies are presented and compared with existing predictions.
Clifford algebras and the classical dynamical Yang-Baxter equation
Alekseev, Anton; Meinrenken, E.
2003-01-01
We describe a relationship of the classical dynamical Yang-Baxter equation with the following elementary problem for Clifford algebras: Given a vector space $V$ with quadratic form $Q_V$, how is the exponential of an element in $\\wedge^2(V)$ under exterior algebra multiplication related to its exponential under Clifford multiplication?
Phonon dynamics in a compressible classical Heisenberg chain
Fivez, Jan; Raedt, Hans De; Raedt, Bart De
1980-01-01
The dynamic properties of the compressible classical Heisenberg chain with bilinear coupling are investigated. The sound velocity is calculated exactly. The Fourier-transformed displacement-displacement correlation function is studied as a function of temperature, wave vector, and the model paramete
Dynamics of Information Systems
Hirsch, Michael J; Murphey, Robert
2010-01-01
Our understanding of information and information dynamics has outgrown classical information theory. This book presents the research explaining the importance of information in the evolution of a distributed or networked system. It presents techniques for measuring the value or significance of information within the context of a system
Scattering theory for the quantum envelope of a classical system
International Nuclear Information System (INIS)
Classical dynamics, reformulated in terms of its quantum envelope is studied for the stationary states of the interacting system. The dynamical variable of ''elapsed time'' plays a crucial role in this study. It is shown that the perturbation series for the elapsed time can be summed in various simple cases even when standard perturbation series diverge. For the special class of systems where the interactions fall off sufficiently fast at infinity one could define ''in'' and ''out'' states; and consequently the wave matrices and scattering matrices. The scattering phase shifts bear a simple relation to the time delay in scattering
Phase Space Cell in Nonextensive Classical Systems
Directory of Open Access Journals (Sweden)
Piero Quarati
2003-06-01
Full Text Available Abstract: We calculate the phase space volume ÃŽÂ© occupied by a nonextensive system of N classical particles described by an equilibrium (or steady-state, or long-term stationary state of a nonequilibrium system distribution function, which slightly deviates from Maxwell-Boltzmann (MB distribution in the high energy tail. We explicitly require that the number of accessible microstates does not change respect to the extensive MB case. We also derive, within a classical scheme, an analytical expression of the elementary cell that can be seen as a macrocell, different from the third power of Planck constant. Thermodynamic quantities like entropy, chemical potential and free energy of a classical ideal gas, depending on elementary cell, are evaluated. Considering the fractional deviation from MB distribution we can deduce a physical meaning of the nonextensive parameter q of the Tsallis nonextensive thermostatistics in terms of particle correlation functions (valid at least in the case, discussed in this work, of small deviations from MB standard case.
Global aspects of classical integrable systems
Cushman, Richard H
2015-01-01
This book gives a uniquely complete description of the geometry of the energy momentum mapping of five classical integrable systems: the 2-dimensional harmonic oscillator, the geodesic flow on the 3-sphere, the Euler top, the spherical pendulum and the Lagrange top. It presents for the first time in book form a general theory of symmetry reduction which allows one to reduce the symmetries in the spherical pendulum and the Lagrange top. Also the monodromy obstruction to the existence of global action angle coordinates is calculated for the spherical pendulum and the Lagrange top. The book addresses professional mathematicians and graduate students and can be used as a textbook on advanced classical mechanics or global analysis.
Families of classical subgroup separable superintegrable systems
International Nuclear Information System (INIS)
We describe a method for determining a complete set of integrals for a classical Hamiltonian that separates in orthogonal subgroup coordinates. As examples, we use it to determine complete sets of integrals, polynomial in the momenta, for some families of generalized oscillator and Kepler-Coulomb systems, hence demonstrating their superintegrability. The latter generalizes recent results of Verrier and Evans, and RodrIguez, Tempesta and Winternitz. Another example is given of a superintegrable system on a non-conformally flat space. (fast track communication)
Correlation Functions in Open Quantum-Classical Systems
Directory of Open Access Journals (Sweden)
Chang-Yu Hsieh
2013-12-01
Full Text Available Quantum time correlation functions are often the principal objects of interest in experimental investigations of the dynamics of quantum systems. For instance, transport properties, such as diffusion and reaction rate coefficients, can be obtained by integrating these functions. The evaluation of such correlation functions entails sampling from quantum equilibrium density operators and quantum time evolution of operators. For condensed phase and complex systems, where quantum dynamics is difficult to carry out, approximations must often be made to compute these functions. We present a general scheme for the computation of correlation functions, which preserves the full quantum equilibrium structure of the system and approximates the time evolution with quantum-classical Liouville dynamics. Several aspects of the scheme are discussed, including a practical and general approach to sample the quantum equilibrium density, the properties of the quantum-classical Liouville equation in the context of correlation function computations, simulation schemes for the approximate dynamics and their interpretation and connections to other approximate quantum dynamical methods.
Dynamical entropy for infinite quantum systems
International Nuclear Information System (INIS)
We review the recent physical application of the so-called Connes-Narnhofer-Thirring entropy, which is the successful quantum mechanical generalization of the classical Kolmogorov-Sinai entropy and, by its very conception, is a dynamical entropy for infinite quantum systems. We thus comparingly review also the physical applications of the classical dynamical entropy for infinite classical systems. 41 refs. (Author)
Classical limit for semirelativistic Hartree systems
Aki, Gonca L.
2008-01-01
We consider the three-dimensional semirelativistic Hartree model for fast quantum mechanical particles moving in a self-consistent field. Under appropriate assumptions on the initial density matrix as a (fully) mixed quantum state we prove by using Wigner transformation techniques that its classical limit yields the well known relativistic Vlasov-Poisson system. The result holds for the case of attractive and repulsive mean-field interactions, with an additional size constraint in the attractive case. © 2008 American Institute of Physics.
Quasi-classical description of molecular dynamics based on Egorov's theorem
International Nuclear Information System (INIS)
Egorov's theorem on the classical propagation of quantum observables is related to prominent quasi-classical descriptions of quantum molecular dynamics as the linearized semiclassical initial value representation, the Wigner phase space method, or the statistical quasiclassical method. The error estimates show that different accuracies are achievable for the computation of expectation values and position densities. Numerical experiments for a Morse model of diatomic iodine and confined Henon–Heiles systems in various dimensions illustrate the theoretical results
Mathematica for Theoretical Physics Classical Mechanics and Nonlinear Dynamics
Baumann, Gerd
2005-01-01
Mathematica for Theoretical Physics: Classical Mechanics and Nonlinear Dynamics This second edition of Baumann's Mathematica® in Theoretical Physics shows readers how to solve physical problems and deal with their underlying theoretical concepts while using Mathematica® to derive numeric and symbolic solutions. Each example and calculation can be evaluated by the reader, and the reader can change the example calculations and adopt the given code to related or similar problems. The second edition has been completely revised and expanded into two volumes: The first volume covers classical mechanics and nonlinear dynamics. Both topics are the basis of a regular mechanics course. The second volume covers electrodynamics, quantum mechanics, relativity, and fractals and fractional calculus. New examples have been added and the representation has been reworked to provide a more interactive problem-solving presentation. This book can be used as a textbook or as a reference work, by students and researchers alike. A...
Electron-phonon interaction within classical molecular dynamics
Tamm, A.; Samolyuk, G.; Correa, A. A.; Klintenberg, M.; Aabloo, A.; Caro, A.
2016-07-01
We present a model for nonadiabatic classical molecular dynamics simulations that captures with high accuracy the wave-vector q dependence of the phonon lifetimes, in agreement with quantum mechanics calculations. It is based on a local view of the e -ph interaction where individual atom dynamics couples to electrons via a damping term that is obtained as the low-velocity limit of the stopping power of a moving ion in a host. The model is parameter free, as its components are derived from ab initio-type calculations, is readily extended to the case of alloys, and is adequate for large-scale molecular dynamics computer simulations. We also show how this model removes some oversimplifications of the traditional ionic damped dynamics commonly used to describe situations beyond the Born-Oppenheimer approximation.
Dynamics in the quantum/classical limit based on selective use of the quantum potential
International Nuclear Information System (INIS)
A classical limit of quantum dynamics can be defined by compensation of the quantum potential in the time-dependent Schrödinger equation. The quantum potential is a non-local quantity, defined in the trajectory-based form of the Schrödinger equation, due to Madelung, de Broglie, and Bohm, which formally generates the quantum-mechanical features in dynamics. Selective inclusion of the quantum potential for the degrees of freedom deemed “quantum,” defines a hybrid quantum/classical dynamics, appropriate for molecular systems comprised of light and heavy nuclei. The wavefunction is associated with all of the nuclei, and the Ehrenfest, or mean-field, averaging of the force acting on the classical degrees of freedom, typical of the mixed quantum/classical methods, is avoided. The hybrid approach is used to examine evolution of light/heavy systems in the harmonic and double-well potentials, using conventional grid-based and approximate quantum-trajectory time propagation. The approximate quantum force is defined on spatial domains, which removes unphysical coupling of the wavefunction fragments corresponding to distinct classical channels or configurations. The quantum potential, associated with the quantum particle, generates forces acting on both quantum and classical particles to describe the backreaction
Wigner function statistics in classically chaotic systems
Horvat, M; Horvat, Martin; Prosen, Tomaz
2003-01-01
We have studied statistical properties of the values of the Wigner function W(x) of 1D quantum maps on compact 2D phase space of finite area V. For this purpose we have defined a Wigner function probability distribution P(w) = (1/V) int delta(w-W(x)) dx, which has, by definition, fixed first and second moment. In particular, we concentrate on relaxation of time evolving quantum state in terms of W(x), starting from a coherent state. We have shown that for a classically chaotic quantum counterpart the distribution P(w) in the semi-classical limit becomes a Gaussian distribution that is fully determined by the first two moments. Numerical simulations have been performed for the quantum sawtooth map and the quantized kicked top. In a quantum system with Hilbert space dimension N (similar 1/hbar) the transition of P(w) to a Gaussian distribution was observed at times t proportional to log N. In addition, it has been shown that the statistics of Wigner functions of propagator eigenstates is Gaussian as well in the...
Wigner function statistics in classically chaotic systems
International Nuclear Information System (INIS)
We have studied statistical properties of the values of the Wigner function W(x) of 1D quantum maps on compact 2D phase space of finite area V. For this purpose we have defined a Wigner function probability distribution P(w) = (1/V) ∫ δ(w - W(x))dx, which has, by definition, fixed first and second moments. In particular, we concentrate on relaxation of time-evolving quantum states in terms of W(x), starting from a coherent state. We have shown that for a classically chaotic quantum counterpart the distribution P(w) in the semiclassical limit becomes a Gaussian distribution that is fully determined by the first two moments. Numerical simulations have been performed for the quantum sawtooth map and the quantized kicked top. In a quantum system with Hilbert space dimension N(∼1/h-bar ) the transition of P(w) to a Gaussian distribution was observed at times t ∝ log N. In addition, it has been shown that the statistics of Wigner functions of propagator eigenstates is Gaussian as well in the classically fully chaotic regime. We have also studied the structure of the nodal cells of the Wigner function, in particular the distribution of intersection points between the zero manifold and arbitrary straight lines
Classical and quantum dynamics in an inverse square potential
Energy Technology Data Exchange (ETDEWEB)
Guillaumín-España, Elisa, E-mail: ege@correo.azc.uam.mx [Laboratorio de Sistemas Dinámicos, Departamento de Ciencias Básicas, Universidad Autónoma Metropolitana, Unidad Azcapotzalco, Azcapotzalco CP 02200 D. F. (Mexico); Núñez-Yépez, H. N., E-mail: nyhn@xanum.uam.mx [Departamento de Física, Universidad Autónoma Metropolitana, Unidad Iztapalapa, Apartado Postal 55-534, Iztapalapa CP 09340 D. F. (Mexico); Salas-Brito, A. L., E-mail: asb@correo.azc.uam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México (ICN-UNAM), Apartado Postal 70-543, 04510 México D F (Mexico)
2014-10-15
The classical motion of a particle in a 3D inverse square potential with negative energy, E, is shown to be geodesic, i.e., equivalent to the particle's free motion on a non-compact phase space manifold irrespective of the sign of the coupling constant. We thus establish that all its classical orbits with E < 0 are unbounded. To analyse the corresponding quantum problem, the Schrödinger equation is solved in momentum space. No discrete energy levels exist in the unrenormalized case and the system shows a complete “fall-to-the-center” with an energy spectrum unbounded by below. Such behavior corresponds to the non-existence of bound classical orbits. The symmetry of the problem is SO(3) × SO(2, 1) corroborating previously obtained results.
Surface hopping from the perspective of quantum-classical Liouville dynamics
Kapral, Raymond
2016-01-01
Fewest-switches surface hopping is studied in the context of quantum-classical Liouville dynamics. Both approaches are mixed quantum-classical theories that provide a way to describe and simulate the nonadiabatic quantum dynamics of many-body systems. Starting from a surface-hopping solution of the quantum-classical Liouville equation, it is shown how fewest-switches dynamics can be obtained by dropping terms that are responsible for decoherence and restricting the nuclear momentum changes that accompany electronic transitions to those events that occur between population states. The analysis provides information on some of the elements that are essential for the construction of accurate and computationally tractable algorithms for nonadiabatic processes.
Common Axioms for Inferring Classical Ensemble Dynamics and Quantum Theory
Parwani, R R
2005-01-01
Within a hamiltonian framework, the same set of physically motivated axioms is used to construct both the classical ensemble Hamilton-Jacobi equation and Schrodingers equation. Crucial roles are played by the assumptions of universality and simplicity (Occam's Razor) which restrict the number and type of of arbitrary constants that appear in the hamiltonian. In this approach, non-relativistic quantum theory is seen as the unique single parameter extension of the classical ensemble dynamics. The method is contrasted with other related constructions in the literature. Possible generalisation to the relativistic case, and some consequences of relaxing the axioms, are also discussed: for example, simple extensions of the linear Schrodinger equation lead to higher-derivative nonlinear corrections that are possibly related to gravity.
Classical and quantum pumping in closed systems
Cohen, Doron
2002-01-01
Pumping of charge (Q) in a closed ring geometry is not quantized even in the strict adiabatic limit. The deviation form exact quantization can be related to the Thouless conductance. We use Kubo formalism as a starting point for the calculation of both the dissipative and the adiabatic contributions to Q. As an application we bring examples for classical dissipative pumping, classical adiabatic pumping, and in particular we make an explicit calculation for quantum pumping in case of the simpl...
Quantum field theory of classically unstable Hamiltonian dynamics
International Nuclear Information System (INIS)
We study a class of dynamical systems for which the motions can be described in terms of geodesics on a manifold (ordinary potential models can be cast into this form by means of a conformal map). It is rigorously proven that the geodesic deviation equation of Jacobi, constructed with a second covariant derivative, is unitarily equivalent to that of a parametric harmonic oscillator, and we study the second quantization of this oscillator. The excitations of the Fock space modes correspond to the emission and absorption of quanta into the dynamical medium, thus associating unstable behavior of the dynamical system with calculable fluctuations in an ensemble with possible thermodynamic consequences
Rapid learning dynamics in individual honeybees during classical conditioning
Directory of Open Access Journals (Sweden)
Evren Pamir
2014-09-01
Full Text Available Associative learning in insects has been studied extensively by a multitude of classical conditioning protocols. However, so far little emphasis has been put on the dynamics of learning in individuals. The honeybee is a well-established animal model for learning and memory. We here studied associative learning as expressed in individual behavior based on a large collection of data on olfactory classical conditioning (25 datasets, 3,298 animals. We show that the group-averaged learning curve and memory retention score confound three attributes of individual learning: the ability or inability to learn a given task, the generally fast acquisition of a conditioned response in learners, and the high stability of the conditioned response during consecutive training and memory retention trials. We reassessed the prevailing view that more training results in better memory performance and found that 24h memory retention can be indistinguishable after single-trial and multiple-trial conditioning in individuals. We explain how inter-individual differences in learning can be accommodated within the Rescorla-Wagner theory of associative learning. In both data-analysis and modeling we demonstrate how the conflict between population-level and single-animal perspectives on learning and memory can be disentangled.
Classical dynamics and stability of collapsing thick shells of matter
International Nuclear Information System (INIS)
We study the collapse towards the gravitational radius of a macroscopic spherical thick shell surrounding an inner massive core. This overall electrically neutral macroshell is composed of many nested δ-like massive microshells which can bear non-zero electric charge, and a possibly non-zero cosmological constant is also included. The dynamics of the shells is described by means of Israel's (Lanczos) junction conditions for singular hypersurfaces and, adopting a Hartree (mean-field) approach, an effective Hamiltonian for the motion of each microshell is derived which allows us to check the stability of the matter composing the macroshell. We end by briefly commenting on the quantum effects which may arise from the extension of our classical treatment to the semiclassical level
Particle physics and dark energy. Beyond classical dynamics
Energy Technology Data Exchange (ETDEWEB)
Garny, Mathias
2008-10-24
In this work, quantum corrections to classical equations of motion are investigated for dynamical models of dark energy featuring a time-evolving quintessence scalar field. Employing effective quantum field theory, the robustness of tracker quintessence potentials against quantum corrections as well as their impact on cosmological observables are discussed. Furthermore, it is demonstrated that a rolling quintessence field can also play an important role for baryogenesis in the early universe. The macroscopic time-evolution of scalar quantum fields can be described from first principles within nonequilibrium quantum field theory based on Kadanoff-Baym equations derived from the 2PI effective action. A framework for the nonperturbative renormalization of Kadanoff-Baym equations is provided. Renormalized Kadanoff-Baym equations are proposed and their finiteness is shown for a special case. (orig.)
Particle physics and dark energy. Beyond classical dynamics
International Nuclear Information System (INIS)
In this work, quantum corrections to classical equations of motion are investigated for dynamical models of dark energy featuring a time-evolving quintessence scalar field. Employing effective quantum field theory, the robustness of tracker quintessence potentials against quantum corrections as well as their impact on cosmological observables are discussed. Furthermore, it is demonstrated that a rolling quintessence field can also play an important role for baryogenesis in the early universe. The macroscopic time-evolution of scalar quantum fields can be described from first principles within nonequilibrium quantum field theory based on Kadanoff-Baym equations derived from the 2PI effective action. A framework for the nonperturbative renormalization of Kadanoff-Baym equations is provided. Renormalized Kadanoff-Baym equations are proposed and their finiteness is shown for a special case. (orig.)
Dynamic Logics of Dynamical Systems
Platzer, André
2012-01-01
We survey dynamic logics for specifying and verifying properties of dynamical systems, including hybrid systems, distributed hybrid systems, and stochastic hybrid systems. A dynamic logic is a first-order modal logic with a pair of parametrized modal operators for each dynamical system to express necessary or possible properties of their transition behavior. Due to their full basis of first-order modal logic operators, dynamic logics can express a rich variety of system properties, including safety, controllability, reactivity, liveness, and quantified parametrized properties, even about relations between multiple dynamical systems. In this survey, we focus on some of the representatives of the family of differential dynamic logics, which share the ability to express properties of dynamical systems having continuous dynamics described by various forms of differential equations. We explain the dynamical system models, dynamic logics of dynamical systems, their semantics, their axiomatizations, and proof calcul...
Classically induced suppression of energy growth in a chaotic quantum system
Indian Academy of Sciences (India)
Harinder Pal; M S Santhanam
2011-11-01
Recent experiments with Bose–Einstein condensates (BEC) in traps and speckle potentials have explored the dynamical regime in which the evolving BEC clouds localize due to the inﬂuence of classical dynamics. The growth of their mean energy is effectively arrested. This is in contrast with the well-known localization phenomena that originate due to quantum interferences. We show that classically induced localization can also be obtained in a classically chaotic, non-interacting system. In this work, we study the classical and quantum dynamics of non-interacting particles in a double-barrier structure. This is essentially a non-KAM system and, depending on the parameters, can display chaotic dynamics inside the ﬁnite well between the barriers. However, for the same set of parameters, it can display nearly regular dynamics above the barriers. We exploit this combination of two qualitatively different classical dynamical features to obtain saturation of energy growth. In the semiclassical regime, this classical mechanism strongly inﬂuences the quantum behaviour of the system.
Quantum Correlations Reduce Classical Correlations with Ancillary Systems
Institute of Scientific and Technical Information of China (English)
LUO Shun-Long; LI Nan
2010-01-01
@@ We illustrate the dichotomy of classical/quantum correlations by virtue of monogamy.More precisely,we show that correlations in a bipartite state are classical if and only if each party of the state can be perfectly correlated with other ancillary systems.In particular,this means that if there are quantum correlations between two parties,then the classical(as well as quantum)correlating capabilities of the two parties with other systems have to be strictly reduced.
Akimov, Alexey V
2016-06-30
The "methodology discovery" library for quantum and classical dynamics simulations is presented. One of the major foci of the code is on nonadiabatic molecular dynamics simulations with model and atomistic Hamiltonians treated on the same footing. The essential aspects of the methodology, design philosophy, and implementation are discussed. The code capabilities are demonstrated on a number of model and atomistic test cases. It is demonstrated how the library can be used to study methodologies for quantum and classical dynamics, as well as a tool for performing detailed atomistic studies of nonadiabatic processes in molecular systems. The source code and additional information are available on the Web at http://www.acsu.buffalo.edu/~alexeyak/libra/index.html. © 2016 Wiley Periodicals, Inc. PMID:27016373
Suzuki, Yasumitsu; Watanabe, Kazuyuki; Abedi, Ali; Agostini, Federica; Min, Seung Kyu; Maitra, Neepa; Gross, E. K. U.
The exact factorization of the electron-nuclear wave function allows to define the time-dependent potential energy surfaces (TDPESs) responsible for the nuclear dynamics and electron dynamics. Recently a novel coupled-trajectory mixed quantum-classical (CT-MQC) approach based on this TDPES has been developed, which accurately reproduces both nuclear and electron dynamics. Here we study the TDPES for laser-induced electron localization with a view to developing a MQC method for strong-field processes. We show our recent progress in applying the CT-MQC approach to the systems with many degrees of freedom.
International Nuclear Information System (INIS)
These lecture notes can be read in two ways. The first two Sections contain a review of the phenomenology of several physical systems with slow nonequilibrium dynamics. In the Conclusions we summarize the scenario for this temporal evolution derived from the solution to some solvable models (p spin and the like) that are intimately connected to the mode coupling approach (and similar ones) to super-cooled liquids. At the end we list a number of open problems of great relevance in this context. These Sections can be read independently of the body of the paper where we present some of the basic analytic techniques used to study the out of equilibrium dynamics of classical and quantum models with and without disorder. We start the technical part by briefly discussing the role played by the environment and by introducing and comparing its representation in the equilibrium and dynamic treatment of classical and quantum systems. We next explain the role played by explicit quenched disorder in both approaches. Later on we focus on analytical techniques; we expand on the dynamic functional methods, and the diagrammatic expansions and resummations used to derive macroscopic equations from the microscopic dynamics. We show why the macroscopic dynamic equations for disordered models and those resulting from self-consistent approximations to non-disordered ones coincide. We review some generic properties of dynamic systems evolving out of equilibrium like the modifications of the fluctuation-dissipation theorem, generic scaling forms of the correlation functions, etc. Finally we solve a family of mean-field models. The connection between the dynamic treatment and the analysis of the free-energy landscape of these models is also presented. We use pedagogical examples all along these lectures to illustrate the properties and results. (author)
Generalized microcanonical and Gibbs ensembles in classical and quantum integrable dynamics
Yuzbashyan, Emil A.
2016-04-01
We prove two statements about the long time dynamics of integrable Hamiltonian systems. In classical mechanics, we prove the microcanonical version of the Generalized Gibbs Ensemble (GGE) by mapping it to a known theorem and then extend it to the limit of infinite number of degrees of freedom. In quantum mechanics, we prove GGE for maximal Hamiltonians-a class of models stemming from a rigorous notion of quantum integrability understood as the existence of conserved charges with prescribed dependence on a system parameter, e.g. Hubbard U, anisotropy in the XXZ model etc. In analogy with classical integrability, the defining property of these models is that they have the maximum number of independent integrals. We contrast their dynamics induced by quenching the parameter to that of random matrix Hamiltonians.
Spin dynamics of quantum and classical Heisenberg dimers
Mentrup, D.; Schnack, J.; Luban, Marshall
1999-01-01
Analytical solutions for the time-dependent autocorrelation function of the classical and quantum mechanical spin dimer with arbitrary spin are presented and compared. For large spin quantum numbers or high temperature the classical and the quantum dimer become more and more similar, yet with the major difference that the quantum autocorrelation function is periodic in time whereas the classical is not.
Dynamical fluctuations in classical adiabatic processes: General description and their implications
Zhang, Qi; Gong, Jiangbin; Oh, C. H.
2010-01-01
Dynamical fluctuations in classical adiabatic processes are not considered by the conventional classical adiabatic theorem. In this work a general result is derived to describe the intrinsic dynamical fluctuations in classical adiabatic processes. Interesting implications of our general result are discussed via two subtopics, namely, an intriguing adiabatic geometric phase in a dynamical model with an adiabatically moving fixed-point solution, and the possible "pollution" to Hannay's angle or...
Soliton splitting in quenched classical integrable systems
Gamayun, O.; Semenyakin, M.
2016-08-01
We take a soliton solution of a classical non-linear integrable equation and quench (suddenly change) its non-linearity parameter. For that we multiply the amplitude or the width of a soliton by a numerical factor η and take the obtained profile as a new initial condition. We find the values of η for which the post-quench solution consists of only a finite number of solitons. The parameters of these solitons are found explicitly. Our approach is based on solving the direct scattering problem analytically. We demonstrate how it works for Korteweg–de Vries, sine-Gordon and non-linear Schrödinger integrable equations.
Inverse variational problem and ambiguity of classical system quantization
International Nuclear Information System (INIS)
It is shown that the problem of ambiguity of classical systems quantization is not limited by substitution of classical values for operators and by ordering of noncommutating operators. It is demonstrated that one and the same classical system can be described. Using an infinite number of various (differing more than for a total derivative) Lagrangians or Hamiltonians. The Feynman quantization is used by means of trajectory integrals. The problem of quantization of the classical system of equations of motion turns to be closely related to the inverse variational calculation problem. The inverse variational problem consists in finding a functional proceeding, from given equations, the extremals of which coincide with the solutions of the given equations. It is shown by concrete examples that with different Lagrangians though leading to identical classic equations of motion various quantum systems are obtained
Eburilitu; Alatancang
2010-03-01
The eigenfunction system of infinite-dimensional Hamiltonian operators appearing in the bending problem of rectangular plate with two opposites simply supported is studied. At first, the completeness of the extended eigenfunction system in the sense of Cauchy's principal value is proved. Then the incompleteness of the extended eigenfunction system in general sense is proved. So the completeness of the symplectic orthogonal system of the infinite-dimensional Hamiltonian operator of this kind of plate bending equation is proved. At last the general solution of the infinite dimensional Hamiltonian system is equivalent to the solution function system series expansion, so it gives to theoretical basis of the methods of separation of variables based on Hamiltonian system for this kind of equations.
McMillan, Ryan J; Grüning, Myrta
2016-01-01
We introduce a hybrid method for dielectric-metal composites that describes the dynamics of the metallic system classically whilst retaining a quantum description of the dielectric. The time-dependent dipole moment of the classical system is mimicked by the introduction of projected equations of motion (PEOM) and the coupling between the two systems is achieved through an effective dipole-dipole interaction. To benchmark this method, we model a test system (semiconducting quantum dot-metal nanoparticle hybrid). We begin by examining the energy absorption rate, showing agreement between the PEOM method and the analytical rotating wave approximation (RWA) solution. We then investigate population inversion and show that the PEOM method provides an accurate model for the interaction under ultrashort pulse excitation where the traditional RWA breaks down.
Classical and thermodynamic limits for generalised quantum spin systems
Duffield, N. G.
1990-01-01
We prove that the rescaled upper and lower symbols for arbitrary generalised quantum spin systems converge in the classical limit. For a large class of models this enables us to derive the asyptotics of quantum free energies in the classical and in the thermodynamic limit.
Intrinsic Chaoticity in Stable Classical Systems and Quantum Fluctuations
De Martino, S; Illuminati, F
1997-01-01
We postulate the existence of a universal Keplerian tremor for any stable classical complex system on every scale. Deriving the characteristic unit of action $\\alpha$ for each classical interaction, we obtain in all cases $\\alpha connected to an intrinsic chaoticity needed to assure stability of matter. Introducing temperature, we provide further consistency checks corroborating our hypothesis.
Cleaning graphene: A first quantum/classical molecular dynamics approach
Delfour, L.; Davydova, A.; Despiau-Pujo, E.; Cunge, G.; Graves, D. B.; Magaud, L.
2016-03-01
Graphene outstanding properties created a huge interest in the condensed matter community and unprecedented fundings at the international scale in the hope of application developments. Recently, there have been several reports of incomplete removal of the polymer resists used to transfer as-grown graphene from one substrate to another, resulting in altered graphene transport properties. Finding a large-scale solution to clean graphene from adsorbed residues is highly desirable and one promising possibility would be to use hydrogen plasmas. In this spirit, we couple here quantum and classical molecular dynamics simulations to explore the kinetic energy ranges required by atomic hydrogen to selectively etch a simple residue—a CH3 group—without irreversibly damaging the graphene. For incident energies in the 2-15 eV range, the CH3 radical can be etched by forming a volatile CH4 compound which leaves the surface, either in the CH4 form or breaking into CH3 + H fragments, without further defect formation. At this energy, adsorption of H atoms on graphene is possible and further annealing will be required to recover pristine graphene.
Directory of Open Access Journals (Sweden)
Wayne Cheng-Wei Huang
2013-01-01
Full Text Available Stochastic electrodynamics (SED predicts a Gaussian probability distribution for a classical harmonic oscillator in the vacuum field. This probability distribution is identical to that of the ground state quantum harmonic oscillator. Thus, the Heisenberg minimum uncertainty relation is recovered in SED. To understand the dynamics that give rise to the uncertainty relation and the Gaussian probability distribution, we perform a numerical simulation and follow the motion of the oscillator. The dynamical information obtained through the simulation provides insight to the connection between the classic double-peak probability distribution and the Gaussian probability distribution. A main objective for SED research is to establish to what extent the results of quantum mechanics can be obtained. The present simulation method can be applied to other physical systems, and it may assist in evaluating the validity range of SED.
Classicism and Romanticism : Dynamics of Jane Austen's Novels
Yamaneki, Kanako
1996-01-01
This dissertation explores Jane Austen's six completed novels, Northanger Abb~9y (1818), Sense and Sensibility(1811), Pride and Prejudice (1813), Mansfield Park (1814), Emma (1815), and Persuasion (1818), from the perspectives of classicism and romanticism. It is imperative to investigate her works from these perspectives because she historically belongs to the time of transition from the classical period to the romantic. Although many critics tend to see mainly the notable aspects of classic...
Power dissipation in nanoscale conductors: classical, semi-classical and quantum dynamics
International Nuclear Information System (INIS)
Modelling Joule heating is a difficult problem because of the need to introduce correct correlations between the motions of the ions and the electrons. In this paper we analyse three different models of current induced heating (a purely classical model, a fully quantum model and a hybrid model in which the electrons are treated quantum mechanically and the atoms are treated classically). We find that all three models allow for both heating and cooling processes in the presence of a current, and furthermore the purely classical and purely quantum models show remarkable agreement in the limit of high biases. However, the hybrid model in the Ehrenfest approximation tends to suppress heating. Analysis of the equations of motion reveals that this is a consequence of two things: the electrons are being treated as a continuous fluid and the atoms cannot undergo quantum fluctuations. A means for correcting this is suggested
Fate of classical solitons in one-dimensional quantum systems.
Energy Technology Data Exchange (ETDEWEB)
Pustilnik, M.; Matveev, K. A.
2015-11-23
We study one-dimensional quantum systems near the classical limit described by the Korteweg-de Vries (KdV) equation. The excitations near this limit are the well-known solitons and phonons. The classical description breaks down at long wavelengths, where quantum effects become dominant. Focusing on the spectra of the elementary excitations, we describe analytically the entire classical-to-quantum crossover. We show that the ultimate quantum fate of the classical KdV excitations is to become fermionic quasiparticles and quasiholes. We discuss in detail two exactly solvable models exhibiting such crossover, the Lieb-Liniger model of bosons with weak contact repulsion and the quantum Toda model, and argue that the results obtained for these models are universally applicable to all quantum one-dimensional systems with a well-defined classical limit described by the KdV equation.
Zeng, Qi-Jun; Cheng, Ze
2010-06-01
In a Kerr nonlinear blackbody, bare photons with opposite wave vectors and helicities are bound into pairs and unpaired photons are transformed into a different kind of quasiparticle, the nonpolariton. The present paper investigates the influence of a single frequency electromagnetic wave on the energy spectrum of the nonpolariton system. We find that the wave can lead to an energy shift of nonpolaritons. Moreover, we calculate the first-order energy shift on certain conditions.
Passage from quantum to classical molecular dynamics in the presence of Coulomb interactions
Ambrosio, Luigi; Friesecke, Gero; Giannoulis, Jannis
2009-01-01
We present a rigorous derivation of classical molecular dynamics (MD) from quantum molecular dynamics (QMD) that applies to the standard Hamiltonians of molecular physics with Coulomb interactions. The derivation is valid away from possible electronic eigenvalue crossings.
Numerical approaches to complex quantum, semiclassical and classical systems
International Nuclear Information System (INIS)
anharmonicity. To this end we consider the linearised semiclassical propagator method, the Wigner-Moyal approach and the recently proposed quantum tomography. Finally, in chapter 4 we calculate the dynamics of a classical many-particle system under the influence of external fields. Considering a low-temperature rf-plasma, we investigate the interplay of the plasma dynamics and the motion of dust particles, immersed into the plasma for diagnostic reasons. (orig.)
Numerical approaches to complex quantum, semiclassical and classical systems
Energy Technology Data Exchange (ETDEWEB)
Schubert, Gerald
2008-11-03
anharmonicity. To this end we consider the linearised semiclassical propagator method, the Wigner-Moyal approach and the recently proposed quantum tomography. Finally, in chapter 4 we calculate the dynamics of a classical many-particle system under the influence of external fields. Considering a low-temperature rf-plasma, we investigate the interplay of the plasma dynamics and the motion of dust particles, immersed into the plasma for diagnostic reasons. (orig.)
Violation of classical physics by a mesoscopic system
Hu, Jiazhong; Chen, Wenlan; Zhang, Hao; McConnell, Robert; Sørensen, Anders S; Vuletić, Vladan
2016-01-01
We experimentally demonstrate the violation of classical physics in a many-atom system using a recently derived criterion [E. Kot et al., Phys. Rev. Lett. 108, 233601 (2013)] that explicitly does not make use of quantum mechanics. We thereby show that the magnetic moment distribution measured by McConnell et al. [R. McConnell et al., Nature 519, 439 (2015)] in a system with a total mass of $2.6\\times 10^5$ atomic mass units is inconsistent with classical physics. Notably, the violation of classical physics affects an area in phase space $10^3$ times larger than the Planck quantum $\\hbar$.
Second invariant for two-dimensional classical super systems
Indian Academy of Sciences (India)
S C Mishra; Roshan Lal; Veena Mishra
2003-10-01
Construction of superpotentials for two-dimensional classical super systems (for ≥ 2) is carried out. Some interesting potentials have been studied in their super form and also their integrability.
Alekseev, K N; Perina, J; Alekseev, Kirill N.; Alekseeva, Natasha V.; Perina, Jan
1999-01-01
We develop a semiclassical method for the determination of the nonlinear dynamics of dissipative quantum optical systems in the limit of large number of photons N, based on the 1/N-expansion and the quantum-classical correspondence. The method has been used to tackle two problems: to study the dynamics of nonclassical state generation in higher-order anharmonic dissipative oscillators and to establish the difference between the quantum and classical dynamics of the second-harmonic generation in a self-pulsing regime. In addressing the first problem, we have obtained an explicit time dependence of the squeezing and the Fano factor for an arbitrary degree of anharmonism in the short-time approximation. For the second problem, we have established analytically a characteristic time scale when the quantum dynamics differs insignificantly from the classical one.
QUANTUM AND CLASSICAL CORRELATIONS IN GAUSSIAN OPEN QUANTUM SYSTEMS
Directory of Open Access Journals (Sweden)
Aurelian ISAR
2015-01-01
Full Text Available In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuous-variable quantum correlations (quantum entanglement and quantum discord for a system consisting of two noninteracting bosonic modes embedded in a thermal environment. We solve the Kossakowski-Lindblad master equation for the time evolution of the considered system and describe the entanglement and discord in terms of the covariance matrix for Gaussian input states. For all values of the temperature of the thermal reservoir, an initial separable Gaussian state remains separable for all times. We study the time evolution of logarithmic negativity, which characterizes the degree of entanglement, and show that in the case of an entangled initial squeezed thermal state, entanglement suppression takes place for all temperatures of the environment, including zero temperature. We analyze the time evolution of the Gaussian quantum discord, which is a measure of all quantum correlations in the bipartite state, including entanglement, and show that it decays asymptotically in time under the effect of the thermal bath. This is in contrast with the sudden death of entanglement. Before the suppression of the entanglement, the qualitative evolution of quantum discord is very similar to that of the entanglement. We describe also the time evolution of the degree of classical correlations and of quantum mutual information, which measures the total correlations of the quantum system.
Catalyst dynamics: consequences for classical kinetic descriptions of reactors
DEFF Research Database (Denmark)
Johannessen, Tue; Larsen, Jane Hvolbæk; Chorkendorff, Ib; Livbjerg, Hans; Topsøe, Henrik
The modelling of catalytic reactions/reactors has undergone great improvements since the introduction of empirical power-law kinetics in chemical reaction engineering and micro-kinetic models based on insight into the nature of elementary steps have appeared for many reactions. However, recent in...... situ studies and surface science investigations has brought added attention to the fact that catalysts may behave in a dynamic manner and reconstruct depending on the reaction conditions. This feature severely limits traditional kinetic descriptions. In the present paper, we present examples of the...... dynamical behaviour of some catalytic systems and discuss the corresponding Limitations in existing models for catalytic reactions and reactors. Catalytic reactors operated in non-steady-state are becoming more frequent in industry. The additional efforts needed to accurately simulate these types of...
Wigner's dynamical transition state theory in phase space: classical and quantum
International Nuclear Information System (INIS)
We develop Wigner's approach to a dynamical transition state theory in phase space in both the classical and quantum mechanical settings. The key to our development is the construction of a normal form for describing the dynamics in the neighbourhood of a specific type of saddle point that governs the evolution from reactants to products in high dimensional systems. In the classical case this is the standard Poincaré–Birkhoff normal form. In the quantum case we develop a normal form based on the Weyl calculus and an explicit algorithm for computing this quantum normal form. The classical normal form allows us to discover and compute the phase space structures that govern classical reaction dynamics. From this knowledge we are able to provide a direct construction of an energy dependent dividing surface in phase space having the properties that trajectories do not locally 're-cross' the surface and the directional flux across the surface is minimal. Using this, we are able to give a formula for the directional flux through the dividing surface that goes beyond the harmonic approximation. We relate this construction to the flux–flux autocorrelation function which is a standard ingredient in the expression for the reaction rate in the chemistry community. We also give a classical mechanical interpretation of the activated complex as a normally hyperbolic invariant manifold (NHIM), and further describe the structure of the NHIM. The quantum normal form provides us with an efficient algorithm to compute quantum reaction rates and we relate this algorithm to the quantum version of the flux–flux autocorrelation function formalism. The significance of the classical phase space structures for the quantum mechanics of reactions is elucidated by studying the phase space distribution of scattering states. The quantum normal form also provides an efficient way of computing Gamov–Siegert resonances. We relate these resonances to the lifetimes of the quantum activated
Directory of Open Access Journals (Sweden)
Orlando – Regalón Anias
2012-11-01
Full Text Available Existen múltiples sistemas dinámicos cuyos modelos matemáticos se caracterizan por ser de primer orden yparámetros variables con el tiempo. En estos casos las herramientas clásicas no siempre logran un sistema decontrol que sea estable, posea un buen desempeño dinámico y rechace adecuadamente las perturbaciones, cuandoel modelo de la planta se desvía del nominal, para el cual se realizó el diseño.En este trabajo se evalúa elcomportamiento de tres estrategias de control en presencia de variación de parámetros. Estas son: control clásico,control adaptable y control robusto. Se realiza un estudio comparativo de las mismas en cuanto a complejidad deldiseño, costo computacional de la implementación y sensibilidad ante variaciones en los parámetros y/o presencia dedisturbios. Se llega a conclusiones que permiten disponer de criterios para la elección más adecuada, endependencia de los requerimientos dinámicos que la aplicación demande, así como de los medios técnicos de que sedisponga.Many dynamic systems have first order mathematic models, with time variable parameters. In these cases, theclassical tools do not satisfy at all control system stability, good performance and perturbation rejection, when theplant model differs from the nominal one, for which the controller was designed.In this article, three control strategiesare evaluated in parameter variations and disturbance presence. The strategies are the followings: classical control,adaptive control and robust control. A comparative study is carried out, taking into account the design complexity, thecomputational cost and the sensitivity. The obtained conclusions helps to provide the criterion to choose the mostadequate control strategy, according to the necessary dynamic, as well as the available technical means.
Classical molecular dynamics simulation on the dynamical properties of H2 on silicene layer
Casuyac Miqueas; Bantaculo Rolando
2016-01-01
This study investigates the diffusion of hydrogen molecule physisorbed on the surface of silicene nanoribbon (SiNR)using the classical molecular dynamic (MD) simulation in LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). The interactions between silicon atoms are modeled using the modified Tersoff potential, the Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential for hydrogen – hydrogen interaction and the Lennard – Jones potential for the physisorbed H...
Classical dynamical description of heavy ion sequential fission
International Nuclear Information System (INIS)
Sequential fission processes are investigated in a classical fragmentation model. Dissipative forces are included. In the fissioning process the recoupling of excitational degrees of freedom to kinetic degrees of freedom is found important. 6 figures
The classical limit of non-integrable quantum systems
Castagnino, M; Castagnino, Mario; Lombardi, Olimpia
2005-01-01
The classical limit of non-integrable quantum systems is studied. We define non-integrable quantum systems as those which have, as their classical limit, a non-integrable classical system. In order to obtain this limit, the self-induced decoherence approach and the corresponding classical limit are generalized from integrable to non-integrable systems. In this approach, the lost of information, usually conceived as the result of a coarse-graining or the trace of an environment, is produced by a particular choice of the algebra of observables and the systematic use of mean values, that project the unitary evolution onto an effective non-unitary one. The decoherence times computed with this approach coincide with those of the literature. By means of our method, we can obtain the classical limit of the quantum state of a non-integrable system, which turns out to be a set of unstable, potentially chaotic classical trajectories contained in the Wigner transformation of the quantum state.
Quantum Dynamics in Classical Time Evolution of Correlation Functions
Wetterich, C
1997-01-01
The time-dependence of correlation functions under the influence of cla= ssical equations of motion is described by an exact evolution equation. For conservative systems thermodynamic equilibrium is a fixed point of these equations. We show that this fixed point is not universally stable, since infinitely many conserved correlation functions obstruct the approach to equilibrium. Equilibrium can therefore be reached at most for suitably av= eraged quantities or for subsystems, similar to quantum statistics. The classica= l time evolution of correlation functions shows many dynamical features of quant= um mechanics.
AMMARI, Zied; Falconi, Marco
2014-01-01
We consider the classical limit of the Nelson model, a system of stable nucleons interacting with a meson field. We prove convergence of the quantum dynamics towards the evolution of the coupled Klein-Gordon-Schr\\"odinger equation. Also, we show that the ground state energy level of $N$ nucleons, when $N$ is large and the meson field approaches its classical value, is given by the infimum of the classical energy functional at a fixed density of particles. Our study relies on a recently elabor...
The uncertainty principle enables non-classical dynamics in an interferometer
Dahlsten, Oscar C. O.; Garner, Andrew J. P.; Vedral, Vlatko
2014-08-01
The quantum uncertainty principle stipulates that when one observable is predictable there must be some other observables that are unpredictable. The principle is viewed as holding the key to many quantum phenomena and understanding it deeper is of great interest in the study of the foundations of quantum theory. Here we show that apart from being restrictive, the principle also plays a positive role as the enabler of non-classical dynamics in an interferometer. First we note that instantaneous action at a distance should not be possible. We show that for general probabilistic theories this heavily curtails the non-classical dynamics. We prove that there is a trade-off with the uncertainty principle that allows theories to evade this restriction. On one extreme, non-classical theories with maximal certainty have their non-classical dynamics absolutely restricted to only the identity operation. On the other extreme, quantum theory minimizes certainty in return for maximal non-classical dynamics.
Generalization of the classical trigonometric system of functions
International Nuclear Information System (INIS)
A generalization of the trigonometric system of functions has been proposed for the mathematical modeling of physical processes. A method for finding the coefficients of the expansion of functions in series in systems of special functions that are generalizations of the classical trigonometric system has been demonstrated
Boltzmann-conserving classical dynamics in quantum time-correlation functions: Matsubara dynamics
Hele, Timothy J H; Muolo, Andrea; Althorpe, Stuart C
2015-01-01
We show that a single change in the derivation of the linearized semiclassical-initial value representation (LSC-IVR or classical Wigner approximation) results in a classical dynamics which conserves the quantum Boltzmann distribution. We rederive the (standard) LSC-IVR approach by writing the (exact) quantum time-correlation function in terms of the normal modes of a free ring-polymer (i.e. a discrete imaginary-time Feynman path), taking the limit that the number of polymer beads $N \\to \\infty$, such that the lowest normal-mode frequencies take their Matsubara values. The change we propose is to truncate the quantum Liouvillian, not explicitly in powers of $\\hbar^2$ at $\\hbar^0$ (which gives back the standard LSC-IVR approximation), but in the normal-mode derivatives corresponding to the lowest Matsubara frequencies. The resulting Matsubara dynamics is inherently classical (since all terms $\\mathcal{O}\\left(\\hbar^{2}\\right)$ disappear from the Matsubara Liouvillian in the limit $N \\to \\infty$), and conserves...
Trigonometric version of quantum-classical duality in integrable systems
Beketov, M.; Liashyk, A.; Zabrodin, A.; Zotov, A.
2016-02-01
We extend the quantum-classical duality to the trigonometric (hyperbolic) case. The duality establishes an explicit relationship between the classical N-body trigonometric Ruijsenaars-Schneider model and the inhomogeneous twisted XXZ spin chain on N sites. Similarly to the rational version, the spin chain data fixes a certain Lagrangian submanifold in the phase space of the classical integrable system. The inhomogeneity parameters are equal to the coordinates of particles while the velocities of classical particles are proportional to the eigenvalues of the spin chain Hamiltonians (residues of the properly normalized transfer matrix). In the rational version of the duality, the action variables of the Ruijsenaars-Schneider model are equal to the twist parameters with some multiplicities defined by quantum (occupation) numbers. In contrast to the rational version, in the trigonometric case there is a splitting of the spectrum of action variables (eigenvalues of the classical Lax matrix). The limit corresponding to the classical Calogero-Sutherland system and quantum trigonometric Gaudin model is also described as well as the XX limit to free fermions.
Transport properties of room temperature ionic liquids from classical molecular dynamics
Andreussi, Oliviero
2012-01-01
Room Temperature Ionic Liquids (RTILs) have attracted much of the attention of the scientific community in the past decade due the their novel and highly customizable properties. Nonetheless their high viscosities pose serious limitations to the use of RTILs in practical applications. To elucidate some of the physical aspects behind transport properties of RTILs, extensive classical molecular dynamics (MD) calculations are reported. Bulk viscosities and ionic conductivities of butyl-methyl-imidazole based RTILs are presented over a wide range of temperatures. The dependence of the properties of the liquids on simulation parameters, e.g. system size effects and choice of the interaction potential, is analyzed.
Classical and quantum simulations of many-body systems
International Nuclear Information System (INIS)
This thesis is devoted to recent developments in the fields of classical and quantum simulations of many-body systems. We describe new classical algorithms that overcome problems apparent in conventional renormalization group and Monte Carlo methods. These algorithms make possible the detailed study of finite temperature properties of 2-D classical and 1-D quantum systems, the investigation of ground states of 2-D frustrated or fermionic systems and the analysis of time evolutions of 2-D quantum systems. Furthermore, we propose new ''analog'' quantum simulators that are able to realize interesting models such as a Tonks-Girardeau gas or a frustrated spin-1/2 XY model on a trigonal lattice. These quantum simulators make use of optical lattices and trapped ions and are technically feasible. In fact, the Tonks-Girardeau gas has been realized experimentally and we provide a detailed comparison between the experimental data and the theoretical predictions. (orig.)
International Nuclear Information System (INIS)
Quasiclassical trajectory calculations are compared, with classical and Wigner sampling of transition state (TS) energy levels, for C2H5F≠→HF+C2H4 product energy partitioning and [Cl···CH3···Cl]- central barrier dynamics. The calculations with Wigner sampling are reported here for comparison with the previously reported calculations with classical sampling [Y. J. Cho et al., J. Chem. Phys. 96, 8275 (1992); L. Sun and W. L. Hase, J. Chem. Phys. 121, 8831 (2004)]. The C2H5F≠ calculations were performed with direct dynamics at the MP2/6-31G* level of theory. Classical and Wigner sampling give post-transition state dynamics, for these two chemical systems, which are the same within statistical uncertainties. This is a result of important equivalences in these two sampling methods for selecting initial conditions at a TS. In contrast, classical and Wigner sampling often give different photodissociation dynamics [R. Schinke, J. Phys. Chem. 92, 3195 (1988)]. Here the sampling is performed for a vibrational state of the ground electronic state potential energy surface (PES), which is then projected onto the excited electronic state's PES. Differences between the ground and the excited PESs may give rise to substantially different excitations of the vibrational and dissociative coordinates on the excited state PES by classical and Wigner sampling, resulting in different photodissociation dynamics.
The Dynamic Ebbinghaus: motion dynamics greatly enhance the classic contextual size illusion
Directory of Open Access Journals (Sweden)
Ryan E.B. Mruczek
2015-02-01
Full Text Available The Ebbinghaus illusion is a classic example of the influence of a contextual surround on the perceived size of an object. Here, we introduce a novel variant of this illusion called the Dynamic Ebbinghaus illusion in which the size and eccentricity of the surrounding inducers modulates dynamically over time. Under these conditions, the size of the central circle is perceived to change in opposition with the size of the inducers. Interestingly, this illusory effect is relatively weak when participants are fixating a stationary central target, less than half the magnitude of the classic static illusion. However, when the entire stimulus translates in space requiring a smooth pursuit eye movement to track the target, the illusory effect is greatly enhanced, almost twice the magnitude of the classic static illusion. A variety of manipulations including target motion, peripheral viewing, and smooth pursuit eye movements all lead to dramatic illusory effects, with the largest effect nearly four times the strength of the classic static illusion. We interpret these results in light of the fact that motion-related manipulations lead to uncertainty in the image size representation of the target, specifically due to added noise at the level of the retinal input. We propose that the neural circuits integrating visual cues for size perception, such as retinal image size, perceived distance, and various contextual factors, weight each cue according to the level of noise or uncertainty in their neural representation. Thus, more weight is given to the influence of contextual information in deriving perceived size in the presence of stimulus and eye motion. Biologically plausible models of size perception should be able to account for the reweighting of different visual cues under varying levels of certainty.
Vol, E. D.
2011-01-01
We propose the consistent statistical approach to consider a wide class of classical open systems whose states are specified by a set of positive integers(occupation numbers).Such systems are often encountered in physics, chemistry, ecology, economics and other sciences.Our statistical method based on ideas of quantum theory of open systems takes into account both discreteness of the system variables and their time fluctuations - two effects which are ignored in usual mean field dynamical app...
GRAVITATIONAL WAVES AND EMERGENCE PARAMETER OF CLASSICAL AND QUANTUM SYSTEMS
Directory of Open Access Journals (Sweden)
Trunev A. P.
2014-03-01
Full Text Available It was established that the Fermi-Dirac statistics, Bose-Einstein and Maxwell-Boltzmann distribution can be described by a single equation, which follows from Einstein's equations for systems with central symmetry. Emergence parameter of classical and quantum systems composed by the rays of gravitational waves interacting with gravitational field of the universe has been computed
Breakdown of the classical description of a local system
DEFF Research Database (Denmark)
Eran, Kot; Grønbech-Jensen, Niels; Nielsen, Bo Melholt; Neergaard-Nielsen, Jonas Schou; Polzik, Eugene Simon; Sørensen, Anders Søndberg
2012-01-01
We provide a straightforward demonstration of a fundamental difference between classical and quantum mechanics for a single local system: namely, the absence of a joint probability distribution of the position x and momentum p. Elaborating on a recently reported criterion by Bednorz and Belzig...... breakdown of a classical description of the underlying state. Most importantly, the criterion used does not rely on quantum mechanics and can thus be used to demonstrate nonclassicality of systems not immediately apparent to exhibit quantum behavior. The criterion is directly applicable to any system...... [ Phys. Rev. A 83 052113 (2011)] we derive a simple criterion that must be fulfilled for any joint probability distribution in classical physics. We demonstrate the violation of this criterion using the homodyne measurement of a single photon state, thus proving a straightforward signature of the...
Effects of complex parameters on classical trajectories of Hamiltonian systems
Indian Academy of Sciences (India)
Asiri Nanayakkara; Thilagarajah Mathanaranjan
2014-06-01
Anderson et al have shown that for complex energies, the classical trajectories of real quartic potentials are closed and periodic only on a discrete set of eigencurves. Moreover, recently it was revealed that when time is complex $t(t = t_r e^{i_})$, certain real Hermitian systems possess close periodic trajectories only for a discrete set of values of . On the other hand, it is generally true that even for real energies, classical trajectories of non-PT symmetric Hamiltonians with complex parameters are mostly non-periodic and open. In this paper, we show that for given real energy, the classical trajectories of complex quartic Hamiltonians $H = p^2 + ax^4 + bx^k$ (where is real, is complex and = 1 or 2) are closed and periodic only for a discrete set of parameter curves in the complex -plane. It was further found that given complex parameter , the classical trajectories are periodic for a discrete set of real energies (i.e., classical energy gets discretized or quantized by imposing the condition that trajectories are periodic and closed). Moreover, we show that for real and positive energies (continuous), the classical trajectories of complex Hamiltonian $H = p^2 + x^4$, ($= _r$ e$^{i}$) are periodic when $ = 4 \\tan^{−1}$[($n/(2m + n)$)] for $\\forall n$ and $m \\mathbb{Z}$.
Dynamical structure factor and collective modes in classical one-component plasmas
International Nuclear Information System (INIS)
The dynamical structure factor and collective modes in classical one-component plasmas are studied by employing the memory-function formalism. A response function for density fluctuations of ions in the system is treated in a self-consistent manner to express it in terms of that of a free ion system and an effective potential. An exact formal expression for the effective potential is composed of two parts, static and dynamic, the latter originating from an interaction-part of a second order memory function (ISMF). By studying the properties of the effective potential and of dampings of collective modes, the latter of which are separated into Landau damping and collisional damping, a criterion for the appearance of collective modes in intermediate wave number and frequency domains is obtained as a simple inequality. The dynamical structure factor is calculated by evaluating characteristic frequencies associated with several elementary factors of dynamics of ions in the system and by taking the ISMF to be Gaussian. The result so obtained is compared with the computer-experimental data of Hansen et al. Fairly good agreement with the experimental data is obtained for the plasma parameters 0.993 <= GAMMA <= 152.4. (author)
Simulating quantum systems on classical computers with matrix product states
International Nuclear Information System (INIS)
In this thesis, the numerical simulation of strongly-interacting many-body quantum-mechanical systems using matrix product states (MPS) is considered. Matrix-Product-States are a novel representation of arbitrary quantum many-body states. Using quantum information theory, it is possible to show that Matrix-Product-States provide a polynomial-sized representation of one-dimensional quantum systems, thus allowing an efficient simulation of one-dimensional quantum system on classical computers. Matrix-Product-States form the conceptual framework of the density-matrix renormalization group (DMRG). After a general introduction in the first chapter of this thesis, the second chapter deals with Matrix-Product-States, focusing on the development of fast and stable algorithms. To obtain algorithms to efficiently calculate ground states, the density-matrix renormalization group is reformulated using the Matrix-Product-States framework. Further, time-dependent problems are considered. Two different algorithms are presented, one based on a Trotter decomposition of the time-evolution operator, the other one on Krylov subspaces. Finally, the evaluation of dynamical spectral functions is discussed, and a correction vector-based method is presented. In the following chapters, the methods presented in the second chapter, are applied to a number of different physical problems. The third chapter deals with the existence of chiral phases in isotropic one-dimensional quantum spin systems. A preceding analytical study based on a mean-field approach indicated the possible existence of those phases in an isotropic Heisenberg model with a frustrating zig-zag interaction and a magnetic field. In this thesis, the existence of the chiral phases is shown numerically by using Matrix-Product-States-based algorithms. In the fourth chapter, we propose an experiment using ultracold atomic gases in optical lattices, which allows a well controlled observation of the spin-charge separation (of
Simulating quantum systems on classical computers with matrix product states
Energy Technology Data Exchange (ETDEWEB)
Kleine, Adrian
2010-11-08
In this thesis, the numerical simulation of strongly-interacting many-body quantum-mechanical systems using matrix product states (MPS) is considered. Matrix-Product-States are a novel representation of arbitrary quantum many-body states. Using quantum information theory, it is possible to show that Matrix-Product-States provide a polynomial-sized representation of one-dimensional quantum systems, thus allowing an efficient simulation of one-dimensional quantum system on classical computers. Matrix-Product-States form the conceptual framework of the density-matrix renormalization group (DMRG). After a general introduction in the first chapter of this thesis, the second chapter deals with Matrix-Product-States, focusing on the development of fast and stable algorithms. To obtain algorithms to efficiently calculate ground states, the density-matrix renormalization group is reformulated using the Matrix-Product-States framework. Further, time-dependent problems are considered. Two different algorithms are presented, one based on a Trotter decomposition of the time-evolution operator, the other one on Krylov subspaces. Finally, the evaluation of dynamical spectral functions is discussed, and a correction vector-based method is presented. In the following chapters, the methods presented in the second chapter, are applied to a number of different physical problems. The third chapter deals with the existence of chiral phases in isotropic one-dimensional quantum spin systems. A preceding analytical study based on a mean-field approach indicated the possible existence of those phases in an isotropic Heisenberg model with a frustrating zig-zag interaction and a magnetic field. In this thesis, the existence of the chiral phases is shown numerically by using Matrix-Product-States-based algorithms. In the fourth chapter, we propose an experiment using ultracold atomic gases in optical lattices, which allows a well controlled observation of the spin-charge separation (of
Effect of Markov and Non-Markov Classical Noise on Entanglement Dynamics
Bordone, Paolo; Benedetti, Claudia
2012-01-01
We analyze the effect of a classical noise into the entanglement dynamics between two particles, initially entangled, subject to continuous time quantum walks in a one-dimensional lattice. The noise is modeled by randomizing the transition amplitudes from one site to another. Both Markovian and non-Markovian environments are considered. For the Markov regime an exponential decay of the initial quantum correlation is found, while the loss of coherence of the quantum state increases monotonically with time up to a saturation value depending upon the degrees of freedom of the system. For the non-Markov regime the presence or absence of entanglement revival and entanglement sudden death phenomena is found or deduced depending on the peculiar characteristics of the noise. Our results indicate that the entanglement dynamics in the non-Markovian regime is affected by the persistence of the memory effects of the environment and by its intrinsic features.
Classical and quantum dynamics of a perfect fluid scalar-energy dependent metric cosmology
Khodadi, M.; Nozari, K.; Vakili, B.
2016-05-01
Inspired from the idea of minimally coupling of a real scalar field to geometry, we investigate the classical and quantum models of a flat energy-dependent FRW cosmology coupled to a perfect fluid in the framework of the scalar-rainbow metric gravity. We use the standard Schutz' representation for the perfect fluid and show that under a particular energy-dependent gauge fixing, it may lead to the identification of a time parameter for the corresponding dynamical system. It is shown that, under some circumstances on the minisuperspace prob energy, the classical evolution of the of the universe represents a late time expansion coming from a bounce instead of the big-bang singularity. Then we go forward by showing that this formalism gives rise to a Schrödinger-Wheeler-DeWitt equation for the quantum-mechanical description of the model under consideration, the eigenfunctions of which can be used to construct the wave function of the universe. We use the resulting wave function in order to investigate the possibility of the avoidance of classical singularities due to quantum effects by means of the many-worlds and Bohmian interpretation of quantum cosmology.
CSADP, a classical control system analysis and design package
Couture, Scott A.
1985-01-01
The Control System Analysis and Design Package (CSADP) is a computer-aided design package for applying classical control system analysis and design tools to experimental frequency response measurements. CSADP allows the user to analyze and manipulate measured frequency response data, design control systems using these measurements, and determine the operational amplifier hardware required to implement the design. To perform these tasks, CSADP provides tools that allow the us...
Structure and Spectrum of Binary Classic Systems Confined in a Parabolic Trap
Institute of Scientific and Technical Information of China (English)
YANG Wen; ZENG Zhi
2009-01-01
@@ The static and dynamic properties of the two-dimensional classic system of two-species interacting charged par-ticles in a parabolic trap are studied. The ground state energy and configuration for different kinds of binary systems are obtained by Monte Carlo simulation and Newton optimization. The spectrum and normal modes vectors can be gained by diagonalizing the dynamical matrix of the system. It is found that the total particle number, particle number and mass-to-charge ratio of each species are decisive factors for the system structure and spectrum. The three intrinsic normal modes of single species Coulomb clusters are inherent, concluded from our numerical simulations and analytical results.
Dynamics of classical particles in oval or elliptic billiards with a dispersing mechanism
Energy Technology Data Exchange (ETDEWEB)
Costa, Diogo Ricardo da [Instituto de Física da USP, Rua do Matão, Travessa R, 187, Cidade Universitária, CEP 05314-970 São Paulo, SP (Brazil); School of Mathematics, University of Bristol, Bristol (United Kingdom); Departamento de Física, UNESP-Univ Estadual Paulista, Av. 24A, 1515, 13506-900 Rio Claro, SP (Brazil); Dettmann, Carl P. [School of Mathematics, University of Bristol, Bristol (United Kingdom); Oliveira, Juliano A. de [UNESP-Univ Estadual Paulista, Câmpus de São João da Boa Vista, São João da Boa Vista, SP (Brazil); Leonel, Edson D. [Departamento de Física, UNESP-Univ Estadual Paulista, Av. 24A, 1515, 13506-900 Rio Claro, SP (Brazil)
2015-03-15
Some dynamical properties for an oval billiard with a scatterer in its interior are studied. The dynamics consists of a classical particle colliding between an inner circle and an external boundary given by an oval, elliptical, or circle shapes, exploring for the first time some natural generalizations. The billiard is indeed a generalization of the annular billiard, which is of strong interest for understanding marginally unstable periodic orbits and their role in the boundary between regular and chaotic regions in both classical and quantum (including experimental) systems. For the oval billiard, which has a mixed phase space, the presence of an obstacle is an interesting addition. We demonstrate, with details, how to obtain the equations of the mapping, and the changes in the phase space are discussed. We study the linear stability of some fixed points and show both analytically and numerically the occurrence of direct and inverse parabolic bifurcations. Lyapunov exponents and generalized bifurcation diagrams are obtained. Moreover, histograms of the number of successive iterations for orbits that stay in a cusp are studied. These histograms are shown to be scaling invariant when changing the radius of the scatterer, and they have a power law slope around −3. The results here can be generalized to other kinds of external boundaries.
An Approach to Some Non-Classical Eigenvalue Problems of Structural Dynamics
Directory of Open Access Journals (Sweden)
Sandi Horea
2015-12-01
Full Text Available Two main shortcomings of common formulations, encountered in the literature concerning the linear problems of structural dynamics are revealed: the implicit, not discussed, postulation, of the use of Kelvin – Voigt constitutive laws (which is often infirmed by experience and the calculation difficulties involved by the attempts to use other constitutive laws. In order to overcome these two categories of shortcomings, the use of the bilateral Laplace – Carson transformation is adopted. Instead of the dependence on time, t, of a certain function f (t, the dependence of its image f# (p on the complex parameter p = χ + iω (ω: circular frequency will occur. This leads to the formulation of associated non-classical eigenvalue problems. The basic relations satisfied by the eigenvalues λr#(p and the eigenvectors vr#(p of dynamic systems are examined (among other, the property of orthogonality of eigenvectors is replaced by the property of pseudo-orthogonality. The case of points p = p’, where multiple eigenvalues occur and where, as a rule, chains of principal vectors are to be considered, is discussed. An illustrative case, concerning a non-classical eigenvalue problem, is presented. Plots of variation along the ω axis, for the real and imaginary components of eigenvalues and eigenvectors, are presented. A brief final discussion closes the paper.
Plimak, L. I.; Ivanov, Misha; Aiello, A.; Stenholm, S.
2015-08-01
Quantum electrodynamics under conditions of distinguishability of interacting matter entities, and of controlled actions and back-actions between them, is considered. Such "mesoscopic quantum electrodynamics" is shown to share its dynamical structure with the classical stochastic electrodynamics. In formal terms, we demonstrate that all general relations of the mesoscopic quantum electrodynamics may be recast in a form lacking Planck's constant. Mesoscopic quantum electrodynamics is therefore subject to "doing quantum electrodynamics while thinking classically," allowing one to substitute essentially classical considerations for quantum ones without any loss in generality. Implications of these results for the quantum measurement theory are discussed.
Fluctuation and Dissipation in Classical Many-Particle Systems
Csernai, L. P.; Jeon, S.; Kapusta, J. I.
1997-01-01
Coarse-grained Langevin-type effective field equations are derived for classical systems of particles. These equations include the effects of thermal fluctuation and dissipation which may arise from coupling to an external bath, as in the Brownian motion of a single particle, or which may arise from statistical fluctuations in small parts of an isolated many-particle system, as in sound waves. These equations may provide some guidance for the analysis of mesoscopic or microscopic molecular sy...
Noether-Lie Symmetry of Generalized Classical Mechanical Systems
Institute of Scientific and Technical Information of China (English)
JIA Wen-Zhi; ZHANG Xiao-Ni; WANG Shun-Jin; FANG Jian-Hui; WANG Peng; DING Ning
2008-01-01
In this paper, the Noether-Lie symmetry and conserved quantities of generalized classical mechanical system are studied. The definition and the criterion of the Noether Lie symmetry for the system under the general infinitesimal transformations of groups are given. The Noether conserved quantity and the Hojman conserved quantity deduced from the Noether-Lie symmetry are obtained. An example is given to illustrate the application of the results.
Symmetries and casimir of an extended classical long wave system
Indian Academy of Sciences (India)
K M Tamizhmani; R Ilangovane; B Dubrovin
2013-04-01
In this paper, we derive Lie point, generalized, master and time-dependent symmetries of a dispersionless equation, which is an extension of a classical long wave system. This equation also admits an infinite-dimensional Lie algebraic structure of Virasoro-type, as in the dispersive integrable systems. We discuss the construction of a sequence of negative ranking symmetries through the property of uniformity in rank. More interestingly, we obtain the conserved quantities directly from the casimir of Poisson pencil.
Classical black holes: the nonlinear dynamics of curved spacetime.
Thorne, Kip S
2012-08-01
Numerical simulations have revealed two types of physical structures, made from curved spacetime, that are attached to black holes: tendexes, which stretch or squeeze anything they encounter, and vortexes, which twist adjacent inertial frames relative to each other. When black holes collide, their tendexes and vortexes interact and oscillate (a form of nonlinear dynamics of curved spacetime). These oscillations generate gravitational waves, which can give kicks up to 4000 kilometers per second to the merged black hole. The gravitational waves encode details of the spacetime dynamics and will soon be observed and studied by the Laser Interferometer Gravitational Wave Observatory and its international partners. PMID:22859479
Classical Information Storage in an n-Level Quantum System
Frenkel, Péter E.; Weiner, Mihály
2015-12-01
A game is played by a team of two—say Alice and Bob—in which the value of a random variable x is revealed to Alice only, who cannot freely communicate with Bob. Instead, she is given a quantum n-level system, respectively a classical n-state system, which she can put in possession of Bob in any state she wishes. We evaluate how successfully they managed to store and recover the value of x by requiring Bob to specify a value z and giving a reward of value f ( x, z) to the team. We show that whatever the probability distribution of x and the reward function f are, when using a quantum n-level system, the maximum expected reward obtainable with the best possible team strategy is equal to that obtainable with the use of a classical n-state system. The proof relies on mixed discriminants of positive matrices and—perhaps surprisingly—an application of the Supply-Demand Theorem for bipartite graphs. As a corollary, we get an infinite set of new, dimension dependent inequalities regarding positive operator valued measures and density operators on complex n-space. As a further corollary, we see that the greatest value, with respect to a given distribution of x, of the mutual information I ( x; z) that is obtainable using an n-level quantum system equals the analogous maximum for a classical n-state system.
International Nuclear Information System (INIS)
We study the properties of the classical electromagnetic radiation produced by two physically different yet closely related systems, which may be regarded as classical analogues of the dynamical Casimir effect. They correspond to two flat, infinite, parallel planes, one of them static and imposing perfect-conductor boundary conditions, while the other performs a rigid oscillatory motion. The systems differ just in the electrical properties of the oscillating plane: one of them is just a planar dipole layer (representing, for instance, a small-width electret). The other, instead, has a dipole layer on the side which faces the static plane, but behaves as a conductor on the other side: this can be used as a representation of a conductor endowed with patch potentials (on the side which faces the conducting plane). We evaluate, in both cases, the dissipative flux of energy between the system and its environment, showing that, at least for small mechanical oscillation amplitudes, it can be written in terms of the dipole layer autocorrelation function. We show that there are resonances as a function of the frequency of the mechanical oscillation
Energy Technology Data Exchange (ETDEWEB)
Fosco, Cesar D. [Comision Nacional de Energia Atomica, Centro Atomico Bariloche, Instituto Balseiro, Bariloche (Argentina); Lombardo, Fernando C. [Ciudad Universitaria, Departamento de Fisica Juan Jose Giambiagi, FCEyN UBA y IFIBA CONICET-UBA, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina)
2015-12-15
We study the properties of the classical electromagnetic radiation produced by two physically different yet closely related systems, which may be regarded as classical analogues of the dynamical Casimir effect. They correspond to two flat, infinite, parallel planes, one of them static and imposing perfect-conductor boundary conditions, while the other performs a rigid oscillatory motion. The systems differ just in the electrical properties of the oscillating plane: one of them is just a planar dipole layer (representing, for instance, a small-width electret). The other, instead, has a dipole layer on the side which faces the static plane, but behaves as a conductor on the other side: this can be used as a representation of a conductor endowed with patch potentials (on the side which faces the conducting plane). We evaluate, in both cases, the dissipative flux of energy between the system and its environment, showing that, at least for small mechanical oscillation amplitudes, it can be written in terms of the dipole layer autocorrelation function. We show that there are resonances as a function of the frequency of the mechanical oscillation. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Fosco, César D. [Centro Atómico Bariloche, Instituto Balseiro, Comisión Nacional de Energía Atómica, R8402AGP, Bariloche (Argentina); Lombardo, Fernando C., E-mail: lombardo@df.uba.ar [Departamento de Física Juan José Giambiagi, FCEyN UBA and IFIBA CONICET-UBA, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Pabellón I, 1428, Buenos Aires (Argentina)
2015-12-17
We study the properties of the classical electromagnetic radiation produced by two physically different yet closely related systems, which may be regarded as classical analogues of the dynamical Casimir effect. They correspond to two flat, infinite, parallel planes, one of them static and imposing perfect-conductor boundary conditions, while the other performs a rigid oscillatory motion. The systems differ just in the electrical properties of the oscillating plane: one of them is just a planar dipole layer (representing, for instance, a small-width electret). The other, instead, has a dipole layer on the side which faces the static plane, but behaves as a conductor on the other side: this can be used as a representation of a conductor endowed with patch potentials (on the side which faces the conducting plane). We evaluate, in both cases, the dissipative flux of energy between the system and its environment, showing that, at least for small mechanical oscillation amplitudes, it can be written in terms of the dipole layer autocorrelation function. We show that there are resonances as a function of the frequency of the mechanical oscillation.
Orbits of hybrid systems as qualitative indicators of quantum dynamics
Energy Technology Data Exchange (ETDEWEB)
Burić, N., E-mail: buric@ipb.ac.rs; Popović, D.B.; Radonjić, M.; Prvanović, S.
2014-03-01
Hamiltonian theory of hybrid quantum–classical systems is used to study dynamics of the classical subsystem coupled to different types of quantum systems. It is shown that the qualitative properties of orbits of the classical subsystem clearly indicate if the quantum subsystem does or does not have additional conserved observables.
Three-stage classical molecular dynamics model for simulation of heavy-ion fusion
Directory of Open Access Journals (Sweden)
Godre Subodh S.
2015-01-01
Full Text Available A three-stage Classical Molecular Dynamics (3S-CMD approach for heavy-ion fusion is developed. In this approach the Classical Rigid-Body Dynamics simulation for heavy-ion collision involving light deformed nucleus is initiated on their Rutherford trajectories at very large initial separation. Collision simulation is then followed by relaxation of the rigid-body constrains for one or both the colliding nuclei at distances close to the barrier when the trajectories of all the nucleons are obtained in a Classical Molecular Dynamics approach. This 3S-CMD approach explicitly takes into account not only the long range Coulomb reorientation of the deformed collision partner but also the internal vibrational excitations of one or both the nuclei at distances close to the barrier. The results of the dynamical simulation for 24Mg+208Pb collision show significant modification of the fusion barrier and calculated fusion cross sections due to internal excitations.
Quantum-Classical Nonadiabatic Dynamics: Coupled- vs Independent-Trajectory Methods.
Agostini, Federica; Min, Seung Kyu; Abedi, Ali; Gross, E K U
2016-05-10
Trajectory-based mixed quantum-classical approaches to coupled electron-nuclear dynamics suffer from well-studied problems such as the lack of (or incorrect account for) decoherence in the trajectory surface hopping method and the inability of reproducing the spatial splitting of a nuclear wave packet in Ehrenfest-like dynamics. In the context of electronic nonadiabatic processes, these problems can result in wrong predictions for quantum populations and in unphysical outcomes for the nuclear dynamics. In this paper, we propose a solution to these issues by approximating the coupled electronic and nuclear equations within the framework of the exact factorization of the electron-nuclear wave function. We present a simple quantum-classical scheme based on coupled classical trajectories and test it against the full quantum mechanical solution from wave packet dynamics for some model situations which represent particularly challenging problems for the above-mentioned traditional methods. PMID:27030209
Classical molecular dynamics simulation on the dynamical properties of H2 on silicene layer
Directory of Open Access Journals (Sweden)
Casuyac Miqueas
2016-01-01
Full Text Available This study investigates the diffusion of hydrogen molecule physisorbed on the surface of silicene nanoribbon (SiNRusing the classical molecular dynamic (MD simulation in LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator. The interactions between silicon atoms are modeled using the modified Tersoff potential, the Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO potential for hydrogen – hydrogen interaction and the Lennard – Jones potential for the physisorbed H2 on SiNR. By varying the temperatures (60 K Δ 130 K, we observed that the Δxdisplacement of H2 on the surface SiNR shows a Brownian motion on a Lennard-Jones potential and a Gaussian probability distribution can be plotted describing the diffusion of H2. The calculated mean square displacement (MSD was approximately increasing in time and the activation energy barrier for diffusion has been found to be 43.23meV.
Establishments Dynamics and Matching Frictions in Classical Competitive Equilibrium
Veracierto, Marcelo
2008-01-01
This paper develops a Walrasian equilibrium theory of establishment level dynamics and matching frictions and uses it to evaluate the effects of congestion externalities in the matching process and determine the government interventions that are needed to implement a Pareto optimal allocation. The optimal policy, which involves a tax on the creation of help-wanted ads and an unemployment subsidy, is highly contractionary. However, it leads to large welfare gains. The policy also plays an impo...
Kinetic Theory of Dynamical Systems
1999-01-01
It is generally believed that the dynamics of simple fluids can be considered to be chaotic, at least to the extent that they can be modeled as classical systems of particles interacting with short range, repulsive forces. Here we give a brief introduction to those parts of chaos theory that are relevant for understanding some features of non-equilibrium processes in fluids. We introduce the notions of Lyapunov exponents, Kolmogorov-Sinai entropy and related quantities using some simple low-d...
Real-time quantum trajectories for classically allowed dynamics in strong laser fields
Plimak, L I
2015-01-01
Both the physical picture of the dynamics of atoms and molecules in intense infrared fields and its theoretical description use the concept of electron trajectories. Here we address a key question which arises in this context: Are distinctly quantum features of these trajectories, such as the complex-valued coordinates, physically relevant in the classically allowed region of phase space, and what is their origin? First, we argue that solutions of classical equations of motion can account for quantum effects. To this end, we construct an exact solution to the classical Hamilton-Jacobi equation which accounts for dynamics of the wave packet, and show that this solution is physically correct in the limit $\\hbar \\to 0$. Second, we show that imaginary components of classical trajectories are directly linked to the finite size of the initial wavepacket in momentum space. This way, if the electronic wavepacket produced by optical tunneling in strong infrared fiels is localised both in coordinate and momentum, its m...
Mixed quantum-classical dynamics from the exact decomposition of electron-nuclear motion
Abedi, Ali; Gross, E K U
2014-01-01
We present a novel mixed quantum-classical approach to the coupled electron-nuclear dynamics based on the exact factorization of the electron-nuclear wave function, recently proposed in [A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010)]. In this framework, classical nuclear dynamics is derived as the lowest order approximation of the time dependent Schr\\"odinger equation that describes the evolution of the nuclei. The effect of the time dependent scalar and vector potentials, representing the exact electronic back-reaction on the nuclear subsystem, is consistently derived within the classical approximation. We examine with an example the performance of the proposed mixed quantum-classical scheme in comparison with exact calculations.
Using Neural Networks to improve classical Operating System Fingerprinting techniques
Sarraute, Carlos; Burroni, Javier
2010-01-01
We present remote Operating System detection as an inference problem: given a set of observations (the target host responses to a set of tests), we want to infer the OS type which most probably generated these observations. Classical techniques used to perform this analysis present several limitations. To improve the analysis, we have developed tools using neural networks and Statistics tools. We present two working modules: one which uses DCE-RPC endpoints to distinguish Windows versions, an...
GRAVITATIONAL WAVES AND STATIONARY STATES OF QUANTUM AND CLASSICAL SYSTEMS
Directory of Open Access Journals (Sweden)
Trunev A. P.
2014-03-01
Full Text Available In this paper, we consider gravitation theory in multidimensional space. The model of the metric satisfying the basic requirements of quantum theory is proposed. It is shown that gravitational waves are described by the Liouville equation and the Schrodinger equation as well. The solutions of the Einstein equations describing the stationary states of arbitrary quantum and classical systems with central symmetry have been obtained. Thus, it is proved that atoms and atomic nuclei can be represented as standing gravitational waves
Wayne Cheng-Wei Huang; Herman Batelaan
2013-01-01
In the past decades, Random Electrodynamics (also called Stochastic Electrodynamics) has been used to study the classical harmonic oscillator immersed in the classical electromagnetic zero-point radiation. Random Electrodynamics (RED) predicts an identical probability distribution for the harmonic oscillator compared to the quantum mechanical prediction for the ground state. Moreover, the Heisenberg minimum uncertainty relation is also recovered with RED. To understand the dynamics that gives...
Classical dynamics of a charged particle in a laser field beyond the dipole approximation
Jameson, Paul
2008-01-01
The classical dynamics of a charged particle traveling in a laser field modeled by an elliptically polarized monochromatic electromagnetic plane wave is discussed within the time reparametrization invariant form of the non-relativistic Hamilton-Jacobi theory. The exact parametric representation for a particle's orbit in an arbitrary plane wave background beyond the dipole approximation and including effect of the magnetic field is derived. For an elliptically polarized monochromatic plane wave the particle's trajectory, as an explicit function of the laboratory frame's time, is given in terms of the Jacobian elliptic functions, whose modulus is proportional to the laser's intensity and depends on the polarization of radiation. It is shown that the system exposes the ``intensity duality'', correspondence between the motion in the backgrounds with various intensities. In virtue of the modular properties of the Jacobian functions, by starting with the representative ``fundamental solution'' and applying a certai...
Computational physics simulation of classical and quantum systems
Scherer, Philipp O J
2013-01-01
This textbook presents basic and advanced computational physics in a very didactic style. It contains very-well-presented and simple mathematical descriptions of many of the most important algorithms used in computational physics. Many clear mathematical descriptions of important techniques in computational physics are given. The first part of the book discusses the basic numerical methods. A large number of exercises and computer experiments allows to study the properties of these methods. The second part concentrates on simulation of classical and quantum systems. It uses a rather general concept for the equation of motion which can be applied to ordinary and partial differential equations. Several classes of integration methods are discussed including not only the standard Euler and Runge Kutta method but also multistep methods and the class of Verlet methods which is introduced by studying the motion in Liouville space. Besides the classical methods, inverse interpolation is discussed, together with the p...
Iterative quantum-classical path integral with dynamically consistent state hopping.
Walters, Peter L; Makri, Nancy
2016-01-28
We investigate the convergence of iterative quantum-classical path integral calculations in sluggish environments strongly coupled to a quantum system. The number of classical trajectories, thus the computational cost, grows rapidly (exponentially, unless filtering techniques are employed) with the memory length included in the calculation. We argue that the choice of the (single) trajectory branch during the time preceding the memory interval can significantly affect the memory length required for convergence. At short times, the trajectory branch associated with the reactant state improves convergence by eliminating spurious memory. We also introduce an instantaneous population-based probabilistic scheme which introduces state-to-state hops in the retained pre-memory trajectory branch, and which is designed to choose primarily the trajectory branch associated with the reactant at early times, but to favor the product state more as the reaction progresses to completion. Test calculations show that the dynamically consistent state hopping scheme leads to accelerated convergence and a dramatic reduction of computational effort. PMID:26827203
Iterative quantum-classical path integral with dynamically consistent state hopping
Walters, Peter L.; Makri, Nancy
2016-01-01
We investigate the convergence of iterative quantum-classical path integral calculations in sluggish environments strongly coupled to a quantum system. The number of classical trajectories, thus the computational cost, grows rapidly (exponentially, unless filtering techniques are employed) with the memory length included in the calculation. We argue that the choice of the (single) trajectory branch during the time preceding the memory interval can significantly affect the memory length required for convergence. At short times, the trajectory branch associated with the reactant state improves convergence by eliminating spurious memory. We also introduce an instantaneous population-based probabilistic scheme which introduces state-to-state hops in the retained pre-memory trajectory branch, and which is designed to choose primarily the trajectory branch associated with the reactant at early times, but to favor the product state more as the reaction progresses to completion. Test calculations show that the dynamically consistent state hopping scheme leads to accelerated convergence and a dramatic reduction of computational effort.
Iterative quantum-classical path integral with dynamically consistent state hopping
Energy Technology Data Exchange (ETDEWEB)
Walters, Peter L.; Makri, Nancy [Department of Chemistry, University of Illinois, Urbana, Illinois 61801 (United States)
2016-01-28
We investigate the convergence of iterative quantum-classical path integral calculations in sluggish environments strongly coupled to a quantum system. The number of classical trajectories, thus the computational cost, grows rapidly (exponentially, unless filtering techniques are employed) with the memory length included in the calculation. We argue that the choice of the (single) trajectory branch during the time preceding the memory interval can significantly affect the memory length required for convergence. At short times, the trajectory branch associated with the reactant state improves convergence by eliminating spurious memory. We also introduce an instantaneous population-based probabilistic scheme which introduces state-to-state hops in the retained pre-memory trajectory branch, and which is designed to choose primarily the trajectory branch associated with the reactant at early times, but to favor the product state more as the reaction progresses to completion. Test calculations show that the dynamically consistent state hopping scheme leads to accelerated convergence and a dramatic reduction of computational effort.
Classical and quantum dynamics of a perfect fluid scalar-energy dependent metric cosmology
Khodadi, M; Vakili, B
2016-01-01
Inspired from the idea of minimally coupling of a real scalar field to geometry, we investigate the classical and quantum models of a flat energy-dependent FRW cosmology coupled to a perfect fluid in the framework of the scalar-rainbow metric gravity. We use the standard Schutz' representation for the perfect fluid and show that under a particular energy-dependent gauge fixing, it may lead to the identification of a time parameter for the corresponding dynamical system. It is shown that, under some circumstances on the minisuperspace prob energy, the classical evolution of the of the universe represents a late time expansion coming from a bounce instead of the big-bang singularity. Then we go forward by showing that this formalism gives rise to a Schr\\"{o}dinger-Wheeler-DeWitt (SWD) equation for the quantum-mechanical description of the model under consideration, the eigenfunctions of which can be used to construct the wave function of the universe. We use the resulting wave function in order to investigate t...
Iterative quantum-classical path integral with dynamically consistent state hopping
International Nuclear Information System (INIS)
We investigate the convergence of iterative quantum-classical path integral calculations in sluggish environments strongly coupled to a quantum system. The number of classical trajectories, thus the computational cost, grows rapidly (exponentially, unless filtering techniques are employed) with the memory length included in the calculation. We argue that the choice of the (single) trajectory branch during the time preceding the memory interval can significantly affect the memory length required for convergence. At short times, the trajectory branch associated with the reactant state improves convergence by eliminating spurious memory. We also introduce an instantaneous population-based probabilistic scheme which introduces state-to-state hops in the retained pre-memory trajectory branch, and which is designed to choose primarily the trajectory branch associated with the reactant at early times, but to favor the product state more as the reaction progresses to completion. Test calculations show that the dynamically consistent state hopping scheme leads to accelerated convergence and a dramatic reduction of computational effort
Interplay of classical and quantum dynamics in a thermal ensemble of atoms
Warsi Laskar, Arif; Singh, Niharika; Mukherjee, Arunabh; Ghosh, Saikat
2016-05-01
In a thermal ensemble of atoms driven by coherent fields, how does evolution of quantum superposition compete with classical dynamics of optical pumping and atomic diffusion? Is it optical pumping that first prepares a thermal ensemble, with coherent superposition developing subsequently or is it the other way round: coherently superposed atoms driven to steady state via optical pumping? Using a stroboscopic probing technique, here we experimentally explore these questions. A 100 ns pulse is used to probe an experimentally simulated, closed three-level, Λ-like configuration in rubidium atoms, driven by strong coherent (control) and incoherent fields. Temporal evolution of probe transmission shows an initial overshoot with turn-on of control, resulting in a scenario akin to lasing without inversion. The corresponding rise time is dictated by coherent dynamics, with a distinct experimental signature of half-cycle Rabi flop in a thermal ensemble of atoms. Our results indicate that, in fact, optical pumping drives the atoms to a steady state in a significantly longer time-scale that sustains superposed dark states. Eventual control turn-off leads to a sudden fall in transmission with an ubiquitous signature for identifying closed and open systems. Numerical simulations and toy-model predictions confirm our claims. These studies reveal new insights into a rich and complex dynamics associated with atoms in thermal ensemble, which are otherwise absent in state-prepared, cold atomic ensembles.
DNA as a Model for Probing Polymer Entanglements: Circular Polymers and Non-Classical Dynamics
Directory of Open Access Journals (Sweden)
Kathryn Regan
2016-09-01
Full Text Available Double-stranded DNA offers a robust platform for investigating fundamental questions regarding the dynamics of entangled polymer solutions. The exceptional monodispersity and multiple naturally occurring topologies of DNA, as well as a wide range of tunable lengths and concentrations that encompass the entanglement regime, enable direct testing of molecular-level entanglement theories and corresponding scaling laws. DNA is also amenable to a wide range of techniques from passive to nonlinear measurements and from single-molecule to bulk macroscopic experiments. Over the past two decades, researchers have developed methods to directly visualize and manipulate single entangled DNA molecules in steady-state and stressed conditions using fluorescence microscopy, particle tracking and optical tweezers. Developments in microfluidics, microrheology and bulk rheology have also enabled characterization of the viscoelastic response of entangled DNA from molecular levels to macroscopic scales and over timescales that span from linear to nonlinear regimes. Experiments using DNA have uniquely elucidated the debated entanglement properties of circular polymers and blends of linear and circular polymers. Experiments have also revealed important lengthscale and timescale dependent entanglement dynamics not predicted by classical tube models, both validating and refuting new proposed extensions and alternatives to tube theory and motivating further theoretical work to describe the rich dynamics exhibited in entangled polymer systems.
Kuwahara, Y; Nakamura, Y; Yamanaka, Y
2013-01-01
The $2 \\times 2$-matrix structure of Green's functions is a common feature for the real-time formalisms of quantum field theory under thermal situations, such as the closed time path formalism and Thermo Field Dynamics (TFD). It has been believed to originate from quantum nature. Recently, Galley has proposed the Hamilton's principle with initial data for nonconservative classical systems, doubling each degree of freedom [Phys. Rev. Lett. 110, 174301 (2013)]. We show that the Galley's Hamilto...
Classical Conditioning with Pulsed Integrated Neural Networks: Circuits and System
DEFF Research Database (Denmark)
Lehmann, Torsten
1998-01-01
In this paper we investigate on-chip learning for pulsed, integrated neural networks. We discuss the implementational problems the technology imposes on learning systems and we find that abiologically inspired approach using simple circuit structures is most likely to bring success. We develop a...... suitable learning algorithm -- a continuous-time version of a temporal differential Hebbian learning algorithm for pulsed neural systems with non-linear synapses -- as well as circuits for the electronic implementation. Measurements from an experimental CMOS chip are presented. Finally, we use our test...... chip to solve simple classical conditioning tasks, thus verifying the design methodologies put forward in the paper....
Quantum versus classical hyperfine-induced dynamics in a quantum dota)
Coish, W. A.; Loss, Daniel; Yuzbashyan, E. A.; Altshuler, B. L.
2007-04-01
In this article we analyze spin dynamics for electrons confined to semiconductor quantum dots due to the contact hyperfine interaction. We compare mean-field (classical) evolution of an electron spin in the presence of a nuclear field with the exact quantum evolution for the special case of uniform hyperfine coupling constants. We find that (in this special case) the zero-magnetic-field dynamics due to the mean-field approximation and quantum evolution are similar. However, in a finite magnetic field, the quantum and classical solutions agree only up to a certain time scale t <τc, after which they differ markedly.
Quantum and classical dynamics of reactive scattering of H2 from metal surfaces.
Kroes, Geert-Jan; Díaz, Cristina
2016-06-27
We review the state-of-the art in dynamics calculations on the reactive scattering of H2 from metal surfaces, which is an important model system of an elementary reaction that is relevant to heterogeneous catalysis. In many applications, quantum dynamics and classical trajectory calculations are performed within the Born-Oppenheimer static surface model. However, ab initio molecular dynamics (AIMD) is finding increased use in applications aimed at modeling the effect of surface phonons on the dynamics. Molecular dynamics with electronic friction has been used to model the effect of electron-hole pair excitation. Most applications are still based on potential energy surfaces (PESs) or forces computed with density functional theory (DFT), using a density functional within the generalized gradient approximation to the exchange-correlation energy. A new development is the use of a semi-empirical version of DFT (the specific reaction parameter (SRP) approach to DFT). We also discuss the accurate methods that have become available to represent electronic structure data for the molecule-surface interaction in global PESs. It has now become possible to describe highly activated H2 + metal surface reactions with chemical accuracy using the SRP-DFT approach, as has been shown for H2 + Cu(111) and Cu(100). However, chemical accuracy with SRP-DFT has yet to be demonstrated for weakly activated systems like H2 + Ru(0001) and non-activated systems like H2 + Pd(111), for which SRP DFs are not yet available. There is now considerable evidence that electron-hole pair (ehp) excitation does not need to be modeled to achieve the (chemically) accurate calculation of dissociative chemisorption and scattering probabilities. Dynamics calculations show that phonons can be safely neglected in the chemically accurate calculation of sticking probabilities on cold metal surfaces for activated systems, and in the calculation of a number of other observables. However, there is now sufficient
Asano, Masanari; Khrennikov, Andrei; Ohya, Masanori; Yamato, Ichiro
2011-01-01
There exist several phenomena (systems) breaking the classical probability laws. Such systems are contextual dependent adaptive systems. In this paper, we present a new mathematical formula to compute the probability in those systems by using the concepts of the adaptive dynamics and quantum information theory -- quantum channels and the lifting. The basic examples of the contextual dependent phenomena can be found in quantum physics. And recently similar examples were found in biological and psychological sciences. Our novel approach is motivated by traditional quantum probability, but it is general enough to describe aforementioned phenomena outside of quantum physics.
Energy Technology Data Exchange (ETDEWEB)
Hu, Zixuan; Ratner, Mark A.; Seideman, Tamar, E-mail: t-seideman@northwestern.edu [Department of Chemistry, Northwestern University, Evanston, Illinois 60208-3113 (United States)
2014-12-14
We develop a numerical approach for simulating light-induced charge transport dynamics across a metal-molecule-metal conductance junction. The finite-difference time-domain method is used to simulate the plasmonic response of the metal structures. The Huygens subgridding technique, as adapted to Lorentz media, is used to bridge the vastly disparate length scales of the plasmonic metal electrodes and the molecular system, maintaining accuracy. The charge and current densities calculated with classical electrodynamics are transformed to an electronic wavefunction, which is then propagated through the molecular linker via the Heisenberg equations of motion. We focus mainly on development of the theory and exemplify our approach by a numerical illustration of a simple system consisting of two silver cylinders bridged by a three-site molecular linker. The electronic subsystem exhibits fascinating light driven dynamics, wherein the charge density oscillates at the driving optical frequency, exhibiting also the natural system timescales, and a resonance phenomenon leads to strong conductance enhancement.
Hu, Zixuan; Ratner, Mark A.; Seideman, Tamar
2014-12-01
We develop a numerical approach for simulating light-induced charge transport dynamics across a metal-molecule-metal conductance junction. The finite-difference time-domain method is used to simulate the plasmonic response of the metal structures. The Huygens subgridding technique, as adapted to Lorentz media, is used to bridge the vastly disparate length scales of the plasmonic metal electrodes and the molecular system, maintaining accuracy. The charge and current densities calculated with classical electrodynamics are transformed to an electronic wavefunction, which is then propagated through the molecular linker via the Heisenberg equations of motion. We focus mainly on development of the theory and exemplify our approach by a numerical illustration of a simple system consisting of two silver cylinders bridged by a three-site molecular linker. The electronic subsystem exhibits fascinating light driven dynamics, wherein the charge density oscillates at the driving optical frequency, exhibiting also the natural system timescales, and a resonance phenomenon leads to strong conductance enhancement.
International Nuclear Information System (INIS)
We develop a numerical approach for simulating light-induced charge transport dynamics across a metal-molecule-metal conductance junction. The finite-difference time-domain method is used to simulate the plasmonic response of the metal structures. The Huygens subgridding technique, as adapted to Lorentz media, is used to bridge the vastly disparate length scales of the plasmonic metal electrodes and the molecular system, maintaining accuracy. The charge and current densities calculated with classical electrodynamics are transformed to an electronic wavefunction, which is then propagated through the molecular linker via the Heisenberg equations of motion. We focus mainly on development of the theory and exemplify our approach by a numerical illustration of a simple system consisting of two silver cylinders bridged by a three-site molecular linker. The electronic subsystem exhibits fascinating light driven dynamics, wherein the charge density oscillates at the driving optical frequency, exhibiting also the natural system timescales, and a resonance phenomenon leads to strong conductance enhancement
Self-consistent nonperturbative theory for classical systems.
Mederos, L; Navascués, G; Velasco, E
2002-01-01
We construct a self-consistent nonperturbative theory for the structure and thermodynamics of a classical system of particles that goes beyond the usual approaches based on perturbation theory. Our theory, which gives accurate predictions for the phase diagram, is based on two ingredients: first, use is made of an exact expression for the free energy of a many-body system in terms of a reference system and a coupling integral connecting the latter to the final system; second, correlation functions may be very accurately approximated using a number of sum rules relating the radial distribution function with thermodynamic quantities. Consistency between the coupling integral expression and the sum rules may be achieved by means of a self-consistent process. PMID:11800760
International Nuclear Information System (INIS)
We present the first molecular dynamics simulation of the vacuum deposition of amorphous selenium films. We compare the classical, tight-binding and Hubbard-term corrected tight-binding molecular dynamics simulation methods. Densities, coordination defects, radial distribution functions, bond angles, dihedral angles, intrachain and interchain atomic correlations were investigated in the obtained amorphous films. Local atomic arrangements were compared to results of diffraction measurements
Quantum mechanics classical results, modern systems, and visualized examples
Robinett, Richard W
2006-01-01
`Quantum Mechanics'' is a comprehensive introduction to quantum mechanics for advanced undergraduate students in physics. It provides the reader with a strong conceptual background in the subject, extensive experience with the necessary mathematical background, as well as numerous visualizations of quantum concepts and phenomena. - ;Quantum Mechanics: Classical Results, Modern Systems, and Visualized Examples is a comprehensive introduction to non-relativistic quantum mechanics for advanced undergraduate students in physics and related fields. It provides students with a strong conceptual background in the most important theoretical aspects of quantum mechanics, extensive experience with the mathematical tools required to solve problems, the opportunity to use quantum ideas to confront modern experimental. realizations of quantum systems, and numerous visualizations of quantum concepts and phenomena. Changes from the First Edition include many new discussions of modern quantum systems (such as Bose-Einstein c...
Real-time quantum trajectories for classically allowed dynamics in strong laser fields
Plimak, L. I.; Ivanov, Misha Yu.
2015-10-01
Both the physical picture of the dynamics of atoms and molecules in intense infrared fields and its theoretical description use the concept of electron trajectories. Here, we address a key question which arises in this context: Are distinctly quantum features of these trajectories, such as the complex-valued coordinates, physically relevant in the classically allowed region of phase space, and what is their origin? First, we argue that solutions of classical equations of motion can account for quantum effects. To this end, we construct an exact solution to the classical Hamilton-Jacobi equation which accounts for dynamics of the wave packet, and show that this solution is physically correct in the limit ?. Second, we show that imaginary components of classical trajectories are directly linked to the finite size of the initial wave packet in momentum space. This way, if the electronic wave packet produced by optical tunnelling in strong infrared fields is localised both in coordinate and momentum, its motion after tunnelling ipso facto cannot be described with purely classical trajectories - in contrast to popular models in the literature.
Semiclassical approach to mesoscopic systems. Classical trajectory correlations and wave interface
Energy Technology Data Exchange (ETDEWEB)
Waltner, Daniel [Regensburg Univ. (Germany). Institut fuer Theoretische Physik
2012-07-01
This volume describes mesoscopic systems with classically chaotic dynamics using semiclassical methods which combine elements of classical dynamics and quantum interference effects. Experiments and numerical studies show that Random Matrix Theory (RMT) explains physical properties of these systems well. This was conjectured more than 25 years ago by Bohigas, Giannoni and Schmit for the spectral properties. Since then, it has been a challenge to understand this connection analytically. The author offers his readers a clearly-written and up-to-date treatment of the topics covered. He extends previous semiclassical approaches that treated spectral and conductance properties. He shows that RMT results can in general only be obtained semiclassically when taking into account classical configurations not considered previously, for example those containing multiply traversed periodic orbits. Furthermore, semiclassics is capable of describing effects beyond RMT. In this context he studies the effect of a non-zero Ehrenfest time, which is the minimal time needed for an initially spatially localized wave packet to show interference. He derives its signature on several quantities characterizing mesoscopic systems, e. g. dc and ac conductance, dc conductance variance, n-pair correlation functions of scattering matrices and the gap in the density of states of Andreev billiards. (orig.)
Using Neural Networks to improve classical Operating System Fingerprinting techniques
Sarraute, Carlos
2010-01-01
We present remote Operating System detection as an inference problem: given a set of observations (the target host responses to a set of tests), we want to infer the OS type which most probably generated these observations. Classical techniques used to perform this analysis present several limitations. To improve the analysis, we have developed tools using neural networks and Statistics tools. We present two working modules: one which uses DCE-RPC endpoints to distinguish Windows versions, and another which uses Nmap signatures to distinguish different version of Windows, Linux, Solaris, OpenBSD, FreeBSD and NetBSD systems. We explain the details of the topology and inner workings of the neural networks used, and the fine tuning of their parameters. Finally we show positive experimental results.
Plimak, L. I.; Ivanov, Misha; Aiello, A.; Stenholm, S.
2015-01-01
Quantum electrodynamics under conditions of distinguishability of interacting matter entities, and of controlled actions and back-actions between them, is considered. Such "mesoscopic quantum electrodynamics" is shown to share its dynamical structure with the classical stochastic electrodynamics. In formal terms, we demonstrate that all general relations of the mesoscopic quantum electrodynamics may be recast in a form lacking Planck's constant. Mesoscopic quantum electrodynamics is therefore...
Dynamical systems of algebraic origin
Schmidt, Klaus
1995-01-01
Although much of classical ergodic theory is concerned with single transformations and one-parameter flows, the subject inherits from statistical mechanics not only its name, but also an obligation to analyze spatially extended systems with multidimensional symmetry groups. However, the wealth of concrete and natural examples which has contributed so much to the appeal and development of classical dynamics, is noticeably absent in this more general theory. The purpose of this book is to help remedy this scarcity of explicit examples by introducing a class of continuous Zd-actions diverse enough to exhibit many of the new phenomena encountered in the transition from Z to Zd, but which nevertheless lends itself to systematic study: the Zd-actions by automorphisms of compact, abelian groups. One aspect of these actions, not surprising in itself but quite striking in its extent and depth nonetheless, is the connection with commutative algebra and arithmetical algebraic geometry. The algebraic framework resulting...
Multibody system dynamics, robotics and control
Gerstmayr, Johannes
2013-01-01
The volume contains 19 contributions by international experts in the field of multibody system dynamics, robotics and control. The book aims to bridge the gap between the modeling of mechanical systems by means of multibody dynamics formulations and robotics. In the classical approach, a multibody dynamics model contains a very high level of detail, however, the application of such models to robotics or control is usually limited. The papers aim to connect the different scientific communities in multibody dynamics, robotics and control. Main topics are flexible multibody systems, humanoid robots, elastic robots, nonlinear control, optimal path planning, and identification.
Compressive and classical hyperspectral systems: a fundamental comparison
Shay, Adi; August, Isaac Y.; Stern, Adrian
2015-05-01
Hyperspectral imagery involves capturing and processing a tremendous amount of data, which sets severe system resource requirements. This has motivated the application of compressive sensing for different spectroscopic and spectroscopic imager systems. Several new compressive hyperspectral architectures have been designed to stretch the common limitations of classical systems. However, the application of the compressive sensing framework involves design of system architectures that differ significantly from the conventional ones. Since compressive sensing differs essentially from conventional sensing, it cannot be implemented for hyperspectral imaging by simply modifying one of the components of a conventional hyperspectral system, rather it requires a complete new design. In this work we present a comparison between four compressive hyperspectral architectures to conventional architectures. The compressive hyperspectral sensing compared are: Coded Aperture Snapshot Spectral Imaging (CASSI), Compressive HS Imaging by Separable Spatial And Spectral Operators (CHISSS), (Liquid-crystal Compressive spectral Imager) LiCSI and (Spectral Single-Pixel) SSP systems. Those methods are compared to conventional spatial/spectral scanning hyperspectral such as pushbroom, whiskbroom and color filter techniques. A fundamental comparison between these architectures is presented in terms of optical system volume and radiometric efficiency.
Nonautonomous dynamical systems in the life sciences
Pötzsche, Christian
2013-01-01
Nonautonomous dynamics describes the qualitative behavior of evolutionary differential and difference equations, whose right-hand side is explicitly time dependent. Over recent years, the theory of such systems has developed into a highly active field related to, yet recognizably distinct from that of classical autonomous dynamical systems. This development was motivated by problems of applied mathematics, in particular in the life sciences where genuinely nonautonomous systems abound. The purpose of this monograph is to indicate through selected, representative examples how often nonautonomous systems occur in the life sciences and to outline the new concepts and tools from the theory of nonautonomous dynamical systems that are now available for their investigation.
Accretion dynamics in the classical T Tauri star V2129 Oph
Alencar, S H P; Walter, F M; Dougados, C; Donati, J -F; Kurosawa, R; Romanova, M; Bonfils, X; Lima, G H R A; Massaro, S; Ibrahimov, M; Poretti, E
2012-01-01
We analyze the photometric and spectroscopic variability of the classical T Tauri star V2129 Oph over several rotational cycles to test the dynamical predictions of magnetospheric accretion models. The photometric variability and the radial velocity variations in the photospheric lines can be explained by rotational modulation due to cold spots, while the radial velocity variations of the He I (5876 \\AA) line and the veiling variability are due to hot spot rotational modulation. The hot and cold spots are located at high latitudes and about the same phase, but the hot spot is expected to sit at the chromospheric level, while the cold spot is at the photospheric level. Using the dipole+octupole magnetic-field configuration previously proposed in the literature for the system, we compute 3D MHD magnetospheric simulations of the star-disk system. We use the simulation's density, velocity and scaled temperature structures as input to a radiative transfer code, from which we calculate theoretical line profiles at ...
Marsalek, Ondrej; Markland, Thomas E.
2016-02-01
Path integral molecular dynamics simulations, combined with an ab initio evaluation of interactions using electronic structure theory, incorporate the quantum mechanical nature of both the electrons and nuclei, which are essential to accurately describe systems containing light nuclei. However, path integral simulations have traditionally required a computational cost around two orders of magnitude greater than treating the nuclei classically, making them prohibitively costly for most applications. Here we show that the cost of path integral simulations can be dramatically reduced by extending our ring polymer contraction approach to ab initio molecular dynamics simulations. By using density functional tight binding as a reference system, we show that our ring polymer contraction scheme gives rapid and systematic convergence to the full path integral density functional theory result. We demonstrate the efficiency of this approach in ab initio simulations of liquid water and the reactive protonated and deprotonated water dimer systems. We find that the vast majority of the nuclear quantum effects are accurately captured using contraction to just the ring polymer centroid, which requires the same number of density functional theory calculations as a classical simulation. Combined with a multiple time step scheme using the same reference system, which allows the time step to be increased, this approach is as fast as a typical classical ab initio molecular dynamics simulation and 35× faster than a full path integral calculation, while still exactly including the quantum sampling of nuclei. This development thus offers a route to routinely include nuclear quantum effects in ab initio molecular dynamics simulations at negligible computational cost.
Marsalek, Ondrej; Markland, Thomas E
2016-02-01
Path integral molecular dynamics simulations, combined with an ab initio evaluation of interactions using electronic structure theory, incorporate the quantum mechanical nature of both the electrons and nuclei, which are essential to accurately describe systems containing light nuclei. However, path integral simulations have traditionally required a computational cost around two orders of magnitude greater than treating the nuclei classically, making them prohibitively costly for most applications. Here we show that the cost of path integral simulations can be dramatically reduced by extending our ring polymer contraction approach to ab initio molecular dynamics simulations. By using density functional tight binding as a reference system, we show that our ring polymer contraction scheme gives rapid and systematic convergence to the full path integral density functional theory result. We demonstrate the efficiency of this approach in ab initio simulations of liquid water and the reactive protonated and deprotonated water dimer systems. We find that the vast majority of the nuclear quantum effects are accurately captured using contraction to just the ring polymer centroid, which requires the same number of density functional theory calculations as a classical simulation. Combined with a multiple time step scheme using the same reference system, which allows the time step to be increased, this approach is as fast as a typical classical ab initio molecular dynamics simulation and 35× faster than a full path integral calculation, while still exactly including the quantum sampling of nuclei. This development thus offers a route to routinely include nuclear quantum effects in ab initio molecular dynamics simulations at negligible computational cost. PMID:26851913
International Nuclear Information System (INIS)
Path integral molecular dynamics simulations, combined with an ab initio evaluation of interactions using electronic structure theory, incorporate the quantum mechanical nature of both the electrons and nuclei, which are essential to accurately describe systems containing light nuclei. However, path integral simulations have traditionally required a computational cost around two orders of magnitude greater than treating the nuclei classically, making them prohibitively costly for most applications. Here we show that the cost of path integral simulations can be dramatically reduced by extending our ring polymer contraction approach to ab initio molecular dynamics simulations. By using density functional tight binding as a reference system, we show that our ring polymer contraction scheme gives rapid and systematic convergence to the full path integral density functional theory result. We demonstrate the efficiency of this approach in ab initio simulations of liquid water and the reactive protonated and deprotonated water dimer systems. We find that the vast majority of the nuclear quantum effects are accurately captured using contraction to just the ring polymer centroid, which requires the same number of density functional theory calculations as a classical simulation. Combined with a multiple time step scheme using the same reference system, which allows the time step to be increased, this approach is as fast as a typical classical ab initio molecular dynamics simulation and 35× faster than a full path integral calculation, while still exactly including the quantum sampling of nuclei. This development thus offers a route to routinely include nuclear quantum effects in ab initio molecular dynamics simulations at negligible computational cost
Energy Technology Data Exchange (ETDEWEB)
Marsalek, Ondrej; Markland, Thomas E., E-mail: tmarkland@stanford.edu [Department of Chemistry, Stanford University, Stanford, California 94305 (United States)
2016-02-07
Path integral molecular dynamics simulations, combined with an ab initio evaluation of interactions using electronic structure theory, incorporate the quantum mechanical nature of both the electrons and nuclei, which are essential to accurately describe systems containing light nuclei. However, path integral simulations have traditionally required a computational cost around two orders of magnitude greater than treating the nuclei classically, making them prohibitively costly for most applications. Here we show that the cost of path integral simulations can be dramatically reduced by extending our ring polymer contraction approach to ab initio molecular dynamics simulations. By using density functional tight binding as a reference system, we show that our ring polymer contraction scheme gives rapid and systematic convergence to the full path integral density functional theory result. We demonstrate the efficiency of this approach in ab initio simulations of liquid water and the reactive protonated and deprotonated water dimer systems. We find that the vast majority of the nuclear quantum effects are accurately captured using contraction to just the ring polymer centroid, which requires the same number of density functional theory calculations as a classical simulation. Combined with a multiple time step scheme using the same reference system, which allows the time step to be increased, this approach is as fast as a typical classical ab initio molecular dynamics simulation and 35× faster than a full path integral calculation, while still exactly including the quantum sampling of nuclei. This development thus offers a route to routinely include nuclear quantum effects in ab initio molecular dynamics simulations at negligible computational cost.
Gils, S; Hoveijn, I; Takens, F; Nonlinear Dynamical Systems and Chaos
1996-01-01
Symmetries in dynamical systems, "KAM theory and other perturbation theories", "Infinite dimensional systems", "Time series analysis" and "Numerical continuation and bifurcation analysis" were the main topics of the December 1995 Dynamical Systems Conference held in Groningen in honour of Johann Bernoulli. They now form the core of this work which seeks to present the state of the art in various branches of the theory of dynamical systems. A number of articles have a survey character whereas others deal with recent results in current research. It contains interesting material for all members of the dynamical systems community, ranging from geometric and analytic aspects from a mathematical point of view to applications in various sciences.
Classical interventions in quantum systems; 1, The measuring process
Peres, A
2000-01-01
The measuring process is an external intervention in the dynamics of a quantum system. It involves a unitary interaction of that system with a measuring apparatus, a further interaction of both with an unknown environment causing decoherence, and then the deletion of a subsystem. No ancilla is needed. The final result is represented by a completely positive map of the quantum state $\\rho$ (possibly with a change of the dimensions of $\\rho$). A continuous limit of this process leads to the Lindblad equation.
Gauge fixing and classical dynamical r-matrices in (2+1)-gravity
Energy Technology Data Exchange (ETDEWEB)
Schoenfeld, Torsten
2012-11-20
We apply the Dirac gauge fixing procedure to the combinatorial description of the moduli space of flat ISO(2,1)-connections. This is motivated by two goals: one originates from physics while the other is of a mathematical nature. The first goal is to investigate the application of gauge fixing in Lorentzian (2+1)-gravity with vanishing cosmological constant, whose phase space is closely related to the moduli space of flat ISO(2,1)-connections. To this end, we first show that specifying gauge fixing conditions amounts to introducing an observer into the theory. Then we determine explicit expressions for the Dirac brackets of specific sets of gauge fixing conditions and give a physical interpretation of the results in terms of the geometry of spacetimes and their effective symmetries. To investigate the mathematical structures underlying the Dirac gauge fixing procedure we then consider general gauge fixing conditions. We first show that the resulting Dirac brackets are in one-to-one correspondence with solutions of the classical dynamical Yang-Baxter equation. We then analyze the relation between the Dirac brackets associated with two different sets of gauge fixing conditions. We find that this relation is given by the action of certain dynamical Poincare transformations which generalize the gauge transformations of classical dynamical r-matrices. Using these transformations, we give a classification of all resulting Dirac brackets and the associated solutions of the classical dynamical Yang-Baxter equation.
Gauge fixing and classical dynamical r-matrices in (2+1)-gravity
International Nuclear Information System (INIS)
We apply the Dirac gauge fixing procedure to the combinatorial description of the moduli space of flat ISO(2,1)-connections. This is motivated by two goals: one originates from physics while the other is of a mathematical nature. The first goal is to investigate the application of gauge fixing in Lorentzian (2+1)-gravity with vanishing cosmological constant, whose phase space is closely related to the moduli space of flat ISO(2,1)-connections. To this end, we first show that specifying gauge fixing conditions amounts to introducing an observer into the theory. Then we determine explicit expressions for the Dirac brackets of specific sets of gauge fixing conditions and give a physical interpretation of the results in terms of the geometry of spacetimes and their effective symmetries. To investigate the mathematical structures underlying the Dirac gauge fixing procedure we then consider general gauge fixing conditions. We first show that the resulting Dirac brackets are in one-to-one correspondence with solutions of the classical dynamical Yang-Baxter equation. We then analyze the relation between the Dirac brackets associated with two different sets of gauge fixing conditions. We find that this relation is given by the action of certain dynamical Poincare transformations which generalize the gauge transformations of classical dynamical r-matrices. Using these transformations, we give a classification of all resulting Dirac brackets and the associated solutions of the classical dynamical Yang-Baxter equation.
Comparative study of classic friction among different archwire ligation systems
Directory of Open Access Journals (Sweden)
Gilberto Vilanova Queiroz
2012-06-01
Full Text Available OBJECTIVE: To describe and compare three alternative methods for controlling classical friction: Self-ligating brackets (SLB, special brackets (SB and special elastomeric ligatures (SEB. METHODS: The study compared Damon MX, Smart Clip, In-Ovation and Easy Clip self-ligating bracket systems, the special Synergy brackets and Morelli's twin bracket with special 8-shaped elastomeric ligatures. New and used Morelli brackets with new and used elastomeric ligatures were used as control. All brackets had 0.022 x 0.028-in slots. 0.014-in nickel-titanium and stainless steel 0.019 x 0.025-in wires were tied to first premolar steel brackets using each archwire ligation method and pulled by an Instron machine at a speed of 0.5 mm/minute. Prior to the mechanical tests the absence of binding in the device was ruled out. Statistical analysis consisted of the Kruskal-Wallis test and multiple non-parametric analyses at a 1% significance level. RESULTS: When a 0.014-in archwire was employed, all ligation methods exhibited classical friction forces close to zero, except Morelli brackets with new and old elastomeric ligatures, which displayed 64 and 44 centiNewtons, respectively. When a 0.019 x 0.025-in archwire was employed, all ligation methods exhibited values close to zero, except the In-Ovation brackets, which yielded 45 cN, and the Morelli brackets with new and old elastomeric ligatures, which displayed 82 and 49 centiNewtons, respectively. CONCLUSIONS: Damon MX, Easy Clip, Smart Clip, Synergy bracket systems and 8-shaped ligatures proved to be equally effective alternatives for controlling classical friction using 0.014-in nickel-titanium archwires and 0.019 x 0.025-in steel archwires, while the In-Ovation was efficient with 0.014-in archwires but with 0.019 x 0.025-in archwires it exhibited friction that was similar to conventional brackets with used elastomeric ligatures.
Lagrangian theoretical framework of dynamics of nonholonomic systems
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
@@ By the generalized variational principle of two kinds of variables in general mechanics, it was demonstrated that two Lagrangian classical relationships can be applied to both holonomic systems and nonholonomic systems. And the restriction that two Lagrangian classical relationships cannot be applied to nonholonomic systems for a long time was overcome. Then, one important formula of similar Lagrangian classical relationship called the popularized Lagrangian classical relationship was derived. From Vakonomic model, by two Lagrangian classical relationships and the popularized Lagrangian classical relationship, the result is the same with Chetaev's model, and thus Chetaev's model and Vakonomic model were unified. Simultaneously, the Lagrangian theoretical framework of dynamics of nonholonomic system was established. By some representative examples, it was validated that the Lagrangian theoretical framework of dynamics of nonholonomic systems is right.
Lagrangian theoretical framework of dynamics of nonholonomic systems
Institute of Scientific and Technical Information of China (English)
LIANG; LiFu
2007-01-01
By the generalized variational principle of two kinds of variables in general mechanics, it was demonstrated that two Lagrangian classical relationships can be applied to both holonomic systems and nonholonomic systems. And the restriction that two Lagrangian classical relationships cannot be applied to nonholonomic systems for a long time was overcome. Then, one important formula of similar Lagrangian classical relationship called the popularized Lagrangian classical relationship was derived. From Vakonomic model, by two Lagrangian classical relationships and the popularized Lagrangian classical relationship, the result is the same with Chetaev's model, and thus Chetaev's model and Vakonomic model were unified. Simultaneously, the Lagrangian theoretical framework of dynamics of nonholonomic system was established. By some representative examples, it was validated that the Lagrangian theoretical framework of dynamics of nonholonomic systems is right. ……
ON THE UNIQUENESS THEOREMS FOR THE UNBOUNDED CLASSICAL SOLUTION OF THE MAGNETIC B NARD SYSTEM
Institute of Scientific and Technical Information of China (English)
MIAO Changxing
2000-01-01
In this note we prove two theorems on the uniqueness of unbounded classical solutions of the magnetic Bénard system which includes the classical Navier-Stokes equation, the Boussinesq equation and the magnetohydrodynamic equation as special cases.
Protocol for classical molecular dynamics simulations of nano-junctions in solution
Gkionis, Konstantinos
2012-10-19
Modeling of nanoscale electronic devices in water requires the evaluation of the transport properties averaged over the possible configurations of the solvent. They can be obtained from classical molecular dynamics for water confined in the device. A series of classical molecular dynamics simulations is performed to establish a methodology for estimating the average number of water molecules N confined between two static and semi-infinite goldelectrodes. Variations in key parameters of the simulations, as well as simulations with non-static infinite goldsurfaces of constant area and with anisotropically fluctuating cell dimensions lead to less than 1% discrepancies in the calculated N. Our approach is then applied to a carbon nanotube placed between the goldelectrodes. The atomic density profile along the axis separating the slabs shows the typical pattern of confined liquids, irrespective of the presence of the nanotube, while parallel to the slabs the nanotube perturbs the obtained profile.
Long-Term Dynamics and the Orbital Inclinations of the Classical Kuiper Belt Objects
Kuchner, M J; Holman, M; Kuchner, Marc J.; Brown, Michael E.; Holman, Matthew
2002-01-01
We numerically integrated the orbits of 1458 particles in the region of the classical Kuiper Belt (41 AU < a < 47 AU) to explore the role of dynamical instabilities in sculpting the inclination distribution of the classical Kuiper Belt Objects (KBOs). We find that the selective removal of low-inclination objects by overlapping secular resonances (nu_17 and nu_18) acts to raise the mean inclination of the surviving population of particles over 4 billion years of interactions with Jupiter, Saturn, Uranus and Neptune, though these long-term dynamical effects do not themselves appear to explain the discovery of KBOs with inclinations near 30 degrees. Our integrations also imply that after 3 billion years of interaction with the massive planets, high inclination KBOs more efficiently supply Neptune-encountering objects, the likely progenitors of short-period comets, Centaurs, and scattered KBOs. The secular resonances at low inclinations may indirectly cause this effect by weeding out objects unprotected by ...
Socio-Cultural Dynamics of Education in the Context of the Post-Non-Classical Science
Directory of Open Access Journals (Sweden)
V. A. Ignatova
2015-02-01
Full Text Available The paper deals with the interrelations between society, education and culture. Using the comparative analysis of classical approaches to defining the above spheres, the author comes to conclusion that the nature of socio-cultural processes can be explored and described most consistently by applying comprehensive models of the post-non-classical science and considering civilization, education and culture in the context of the unified dynamic flow of socio-cultural genesis. The research investigates the dialectics of socio-cultural processes in the light of systematic synergetic approach, the advancing role of education in socio-cultural dynamics being revealed and substantiated. The author emphasizes its inevitably rising priority due to sustained development of civilization bringing about the new environmentally-oriented meta-culture.The obtained results can be used in pedagogic research methodology, designing and modeling the educational process, its content, technology and organization.
A general solution for classical sequential growth dynamics of Causal Sets
Varadarajan, Madhavan; Rideout, David
2005-01-01
A classical precursor to a full quantum dynamics for causal sets has been forumlated in terms of a stochastic sequential growth process in which the elements of the causal set arise in a sort of accretion process. The transition probabilities of the Markov growth process satisfy certain physical requirements of causality and general covariance, and the generic solution with all transition probabilities non-zero has been found. Here we remove the assumption of non-zero probabilities, define a ...
Classical dynamics of a charged particle in a laser field beyond the dipole approximation
Jameson, Paul; Khvedelidze, Arsen
2008-01-01
The classical dynamics of a charged particle traveling in a laser field modeled by an elliptically polarized monochromatic electromagnetic plane wave is discussed within the time reparametrization invariant form of the non-relativistic Hamilton-Jacobi theory. The exact parametric representation for a particle's orbit in an arbitrary plane wave background beyond the dipole approximation and including effect of the magnetic field is derived. For an elliptically polarized monochromatic plane wav...
Floating-point performance of ARM cores and their efficiency in classical molecular dynamics
Nikolskiy, V.; Stegailov, V.
2016-02-01
Supercomputing of the exascale era is going to be inevitably limited by power efficiency. Nowadays different possible variants of CPU architectures are considered. Recently the development of ARM processors has come to the point when their floating point performance can be seriously considered for a range of scientific applications. In this work we present the analysis of the floating point performance of the latest ARM cores and their efficiency for the algorithms of classical molecular dynamics.
Ovaskainen, Otso; Hanski, Ilkka
2004-01-01
Spatially structured populations in patchy habitats show much variation in migration rate, from patchy populations in which individuals move repeatedly among habitat patches to classic metapopulations with infrequent migration among discrete populations. To establish a common framework for population dynamics in patchy habitats, we describe an individual-based model (IBM) involving a diffusion approximation of correlated random walk of individual movements. As an example, we apply the model t...
Quantum-classical transition in the electron dynamics of thin metal films
Jasiak, Rafal; Manfredi, Giovanni; Hervieux, Paul-Antoine; Haefele, Matthieu
2009-01-01
International audience The quantum electrons dynamics in a thin metal film is studied numerically using the self-consistent Wigner-Poisson equations. The initial equilibrium is computed from the Kohn-Sham equations at finite temperature, and then mapped into the phase-space Wigner function. The time-dependent results are compared systematically with those obtained previously with a classical approach (Vlasov-Poisson equations). It is found that, for large excitations, the quantum and class...
Classical dynamics of a charged particle in a laser field beyond the dipole approximation
Jameson, Paul; Khvedelidze, Arsen
2008-05-01
The classical dynamics of a charged particle traveling in a laser field modeled by an elliptically polarized monochromatic electromagnetic plane wave is discussed within the time reparametrization invariant form of the nonrelativistic Hamilton-Jacobi theory. The exact parametric representation for a particle’s orbit in an arbitrary plane wave background beyond the dipole approximation and including effect of the magnetic field is derived. For an elliptically polarized monochromatic plane wave the particle’s trajectory, as an explicit function of the laboratory frame’s time, is given in terms of the Jacobian elliptic functions, whose modulus is proportional to the laser’s intensity and depends on the polarization of radiation. It is shown that the system exposes the intensity duality, correspondence between the motion in the backgrounds with various intensities. In virtue of the modular properties of the Jacobian functions, by starting with the representative “fundamental solution” and applying a certain modular transformation one can obtain the particle’s orbit in the monochromatic plane wave background with arbitrarily prescribed characteristics.
International Nuclear Information System (INIS)
Nonstationary heat conduction in a single-walled carbon nanotube was investigated by applying a local heat pulse with duration of subpicoseconds. The investigation was based on classical molecular dynamics simulations, where the heat pulse was generated as coherent fluctuations by connecting a thermostat to the local cell for a short duration. The heat conduction through the nanotube was observed in terms of spatiotemporal temperature profiles. Results of the simulations exhibit non-Fourier heat conduction where a distinct amount of heat is transported in a wavelike form. The geometry of carbon nanotubes allows us to observe such a phenomenon in the actual scale of the material. The resulting spatiotemporal profile was compared with the available macroscopic equations, the so-called non-Fourier heat conduction equations, in order to investigate the applicability of the phenomenological models to a quasi-one-dimensional system. The conventional hyperbolic diffusion equation fails to predict the heat conduction due to the lack of local diffusion. It is shown that this can be remedied by adopting a model with dual relaxation time. Further modal analyses using wavelet transformations reveal a significant contribution of the optical phonon modes to the observed wavelike heat conduction. The result suggests that, in carbon nanotubes with finite length where the long-wavelength acoustic phonons behave ballistically, even optical phonons can play a major role in the non-Fourier heat conduction
Agostini, Federica; Abedi, Ali; Suzuki, Yasumitsu; Min, Seung Kyu; Maitra, Neepa T.; Gross, E. K. U.
2015-03-01
The Born-Oppenheimer (BO) approximation allows to visualize the coupled electron-nuclear dynamics in molecular systems as a set of nuclei moving on a single potential energy surface representing the effect of the electrons in a given eigenstate. Many interesting phenomena, however, such as vision or charge separation in organic photovoltaic materials, take place in conditions beyond its range of validity. Nevertheless, the basic construct of the adiabatic treatment, the BO potential energy surfaces, is employed to describe non-adiabatic processes and the full problem is represented in terms of adiabatic states and transitions among them in regions of strong non-adiabatic coupling. But the concept of single potential energy is lost. The alternative point of view arising in the framework of the exact factorization of the electron-nuclear wave function will be presented. A single, time-dependent, potential energy provides the force driving the nuclear motion and is adopted as starting point for the development of quantum-classical approximations to the full quantum mechanical problem.
Dynamics of an electron spin in strong classical and quantized electromagnetic fields
Energy Technology Data Exchange (ETDEWEB)
Skoromnik, Oleg
2014-07-09
The electron motion in the presence of a strong classical and quantized pulse of an electromagnetic field is studied with a special emphasis on the spin degree of freedom. It is shown that the Hamiltonian of this system can be separated into two parts with the help of canonical transformations of the field variables, namely the interaction between an electron and a single collective mode of the field and fluctuations relatively to this collective mode. The application of perturbation theory to the fluctuations allows the conditions of applicability of the single-mode approximation for the quantized external field to be formulated. Furthermore, within this approximation the electron spin evolution is investigated. In addition to fast spin oscillations at the laser frequency, a second time scale is identified due to the intensity-dependent emissions and absorptions of field quanta, that is collapse and revival dynamics. The effect is observable at the experimentally feasible intensity of 10{sup 18} Wcm{sup 2}. After this, we switch to the regime of higher intensities, when the fluctuations of the external field can be neglected. We investigate the asymmetries in the electron scattering arising due to the electron polarization and pulse duration, and constrain the optimal conditions for the asymmetry observation.
Analog computation with dynamical systems
Siegelmann, Hava T.; Fishman, Shmuel
1998-09-01
Physical systems exhibit various levels of complexity: their long term dynamics may converge to fixed points or exhibit complex chaotic behavior. This paper presents a theory that enables to interpret natural processes as special purpose analog computers. Since physical systems are naturally described in continuous time, a definition of computational complexity for continuous time systems is required. In analogy with the classical discrete theory we develop fundamentals of computational complexity for dynamical systems, discrete or continuous in time, on the basis of an intrinsic time scale of the system. Dissipative dynamical systems are classified into the computational complexity classes P d, Co-RP d, NP d and EXP d, corresponding to their standard counterparts, according to the complexity of their long term behavior. The complexity of chaotic attractors relative to regular ones leads to the conjecture P d ≠ NP d. Continuous time flows have been proven useful in solving various practical problems. Our theory provides the tools for an algorithmic analysis of such flows. As an example we analyze the continuous Hopfield network.
On the classical r-matrix structure of the rational BCn Ruijsenaars-Schneider-van Diejen system
Pusztai, B. G.
2015-11-01
In this paper, we construct a quadratic r-matrix structure for the classical rational BCn Ruijsenaars-Schneider-van Diejen system with the maximal number of three independent coupling parameters. As a byproduct, we provide a Lax representation of the dynamics as well.
Kuwahara, Y.; Nakamura, Y.; Yamanaka, Y.
2013-12-01
The 2×2-matrix structure of Green's functions is a common feature for the real-time formalisms of quantum field theory under thermal situations, such as the closed time path formalism and Thermo Field Dynamics (TFD). It has been believed to originate from quantum nature. Recently, Galley has proposed the Hamilton's principle with initial data for nonconservative classical systems, doubling each degree of freedom [1]. We show that the Galley's Hamilton formalism can be extended to quantum field and that the resulting theory is naturally identical with nonequilibrium TFD.
Energy Technology Data Exchange (ETDEWEB)
Kuwahara, Y., E-mail: a.kuwahara1224@asagi.waseda.jp; Nakamura, Y., E-mail: nakamura@aoni.waseda.jp; Yamanaka, Y., E-mail: yamanaka@waseda.jp
2013-12-09
The 2×2-matrix structure of Green's functions is a common feature for the real-time formalisms of quantum field theory under thermal situations, such as the closed time path formalism and Thermo Field Dynamics (TFD). It has been believed to originate from quantum nature. Recently, Galley has proposed the Hamilton's principle with initial data for nonconservative classical systems, doubling each degree of freedom. We show that the Galley's Hamilton formalism can be extended to quantum field and that the resulting theory is naturally identical with nonequilibrium TFD.
Bisimulation of dynamical systems
Schaft, van der Arjan; Alur, Rajeev; Pappas, George J.
2004-01-01
A general notion of bisimulation is studied for dynamical systems. An algebraic characterization of bisimulation together, with an algorithm for computing the maximal bisimulation relation is derived using geometric control theory. Bisimulation of dynamical systems is shown to be a concept which uni
Bisimulation of Dynamical Systems
Schaft, Arjan van der
2004-01-01
A general notion of bisimulation is studied for dynamical systems. An algebraic characterization of bisimulation together with an algorithm for computing the maximal bisimulation relation is derived using geometric control theory. Bisimulation of dynamical systems is shown to be a concept which unif
Batygin, Konstantin; Fraser, Wesley C
2011-01-01
The cold classical population of the Kuiper belt exhibits a wide variety of unique physical characteristics, which collectively suggest that its dynamical coherence has been maintained through out the solar system's lifetime. Simultaneously, the retention of the cold population's relatively unexcited orbital state has remained a mystery, especially in the context of a solar system formation model, that is driven by a transient period of instability, where Neptune is temporarily eccentric. Here, we show that the cold belt can survive the instability, and its dynamical structure can be reproduced. We develop a simple analytical model for secular excitation of cold KBOs and show that comparatively fast apsidal precession and nodal recession of Neptune, during the eccentric phase, are essential for preservation of an unexcited state in the cold classical region. Subsequently, we confirm our results with self-consistent N-body simulations. We further show that contamination of the hot classical and scattered popul...
SIAM conference on applications of dynamical systems
Energy Technology Data Exchange (ETDEWEB)
1992-01-01
A conference (Oct.15--19, 1992, Snowbird, Utah; sponsored by SIAM (Society for Industrial and Applied Mathematics) Activity Group on Dynamical Systems) was held that highlighted recent developments in applied dynamical systems. The main lectures and minisymposia covered theory about chaotic motion, applications in high energy physics and heart fibrillations, turbulent motion, Henon map and attractor, integrable problems in classical physics, pattern formation in chemical reactions, etc. The conference fostered an exchange between mathematicians working on theoretical issues of modern dynamical systems and applied scientists. This two-part document contains abstracts, conference program, and an author index.
Graefe, Eva-Maria; Korsch, Hans Jürgen; Rush, Alexander
2016-04-01
Bosonic quantum conversion systems can be modeled by many-particle single-mode Hamiltonians describing a conversion of m molecules of type A into n molecules of type B and vice versa. These Hamiltonians are analyzed in terms of generators of a polynomially deformed su(2) algebra. In the mean-field limit of large particle numbers, these systems become classical and their Hamiltonian dynamics can again be described by polynomial deformations of a Lie algebra, where quantum commutators are replaced by Poisson brackets. The Casimir operator restricts the motion to Kummer shapes, deformed Bloch spheres with cusp singularities depending on m and n . It is demonstrated that the many-particle eigenvalues can be recovered from the mean-field dynamics using a WKB-type quantization condition. The many-particle state densities can be semiclassically approximated by the time periods of periodic orbits, which show characteristic steps and singularities related to the fixed points, whose bifurcation properties are analyzed.
The convergence problem for dissipative autonomous systems classical methods and recent advances
Haraux, Alain
2015-01-01
The book investigates classical and more recent methods of study for the asymptotic behavior of dissipative continuous dynamical systems with applications to ordinary and partial differential equations, the main question being convergence (or not) of the solutions to an equilibrium. After reviewing the basic concepts of topological dynamics and the definition of gradient-like systems on a metric space, the authors present a comprehensive exposition of stability theory relying on the so-called linearization method. For the convergence problem itself, when the set of equilibria is infinite, the only general results that do not require very special features of the non-linearities are presently consequences of a gradient inequality discovered by S. Lojasiewicz. The application of this inequality jointly with the so-called Liapunov-Schmidt reduction requires a rigorous exposition of Semi-Fredholm operator theory and the theory of real analytic maps on infinite dimensional Banach spaces, which cannot be found anywh...
Horzela, Andrzej; Kapuscik, Edward
1993-01-01
An alternative picture of classical many body mechanics is proposed. In this picture particles possess individual kinematics but are deprived from individual dynamics. Dynamics exists only for the many particle system as a whole. The theory is complete and allows to determine the trajectories of each particle. It is proposed to use our picture as a classical prototype for a realistic theory of confined particles.
Minoshima, Yusuke; Seki, Yusuke; Takayanagi, Toshiyuki; Shiga, Motoyuki
2016-06-01
The dynamical process of electron attachment to a guanine-cytosine pair in the normal (h-GC) and deuterated (d-GC) forms has been studied theoretically by semiclassical ring-polymer molecular dynamics (RPMD) simulations using the empirical valence bond model. The initially formed dipole-bound anion is converted rapidly to the valence-bound anion within about 0.1 ps in both h-GC and d-GC. However, the subsequent proton transfer in h-GC occurs with a rate five times greater than the deuteron transfer in d-GC. The change of rates with isotopic substitution and temperature variation in the RPMD simulations are quantitatively and qualitatively different from those in the classical molecular dynamics (MD) simulations, demonstrating the importance of nuclear quantum effects on the dynamics of this system.
Budini, Adrian A
2010-01-01
In this paper, we develop a quantum-jump approach for describing the photon-emission process of single fluorophore systems coupled to complex classically fluctuating reservoirs. The formalism relies on an open quantum system approach where the dynamic of the system and the reservoir fluctuations are described through a density matrix whose evolution is defined by a Lindblad rate equation. For each realization of the photon measurement processes it is possible to define a conditional system state (stochastic density matrix) whose evolution depends on both the photon detection events and the fluctuations between the configurational states of the reservoir. In contrast to standard fluorescent systems the photon-to-photon emission process is not a renewal one, being defined by a (stochastic) waiting time distribution that in each recording event parametrically depends on the conditional state. The formalism allows calculating experimental observables such as the full hierarchy of joint probabilities associated to...
Stability of dynamical systems
Liao, Xiaoxin; Yu, P 0
2007-01-01
The main purpose of developing stability theory is to examine dynamic responses of a system to disturbances as the time approaches infinity. It has been and still is the object of intense investigations due to its intrinsic interest and its relevance to all practical systems in engineering, finance, natural science and social science. This monograph provides some state-of-the-art expositions of major advances in fundamental stability theories and methods for dynamic systems of ODE and DDE types and in limit cycle, normal form and Hopf bifurcation control of nonlinear dynamic systems.ʺ Presents
Guo, Rui; Tian, Bo; Lü, Xing; Zhang, Hai-Qiang; Xu, Tao
2010-09-01
For the propagation of the ultrashort pulses in an inhomogeneous multi-component nonlinear medium, a system of coupled equations is analytically studied in this paper. Painlevé analysis shows that this system admits the Painlevé property under some constraints. By means of the Ablowitz-Kaup-Newell-Segur procedure, the Lax pair of this system is derived, and the Darboux transformation (DT) is constructed with the help of the obtained Lax pair. With symbolic computation, the soliton solutions are obtained by virtue of the DT algorithm. Figures are plotted to illustrate the dynamical features of the soliton solutions. Characteristics of the solitons propagating in an inhomogeneous multi-component nonlinear medium are discussed: (i) Propagation of one soliton and two-peak soliton; (ii) Elastic interactions of the parabolic two solitons; (iii) Overlap phenomenon between two solitons; (iv) Collision of two head-on solitons and two head-on two-peak solitons; (v) Two different types of interactions of the three solitons; (vi) Decomposition phenomenon of one soliton into two solitons. The results might be useful in the study on the ultrashort-pulse propagation in the inhomogeneous multi-component nonlinear media.
Marsalek, Ondrej
2015-01-01
Path integral molecular dynamics simulations, combined with an ab initio evaluation of interactions using electronic structure theory, incorporate the quantum mechanical nature of both the electrons and nuclei, which are essential to accurately describe systems containing light nuclei. However, path integral simulations have traditionally required a computational cost around two orders of magnitude greater than treating the nuclei classically, making them prohibitively costly for most applications. Here we show that the cost of path integral simulations can be dramatically reduced by extending our ring polymer contraction approach to ab initio molecular dynamics simulations. By using density functional tight binding as a reference system, we show that our ab initio ring polymer contraction (AI-RPC) scheme gives rapid and systematic convergence to the full path integral density functional theory result. We demonstrate the efficiency of this approach in ab initio simulations of liquid water and the reactive pro...
A census of the expected properties of classical Milky Way dwarfs in Milgromian dynamics
Lüghausen, Fabian; Kroupa, Pavel
2014-01-01
Prompted by the recent successful predictions of the internal dynamics of Andromeda's satellite galaxies (McGaugh & Milgrom 2013a,b), we revisit the classical Milky Way dwarf spheroidal satellites Draco, Sculptor, Sextans, Carina, and Fornax in the framework of Milgromian dynamics (MOND). We use for the first time a Poisson solver with adaptive mesh refinement in order to account simultaneously for the gravitational influence of the Milky Way and its satellites. This allows to rigorously model the important external field effect (EFE) of Milgromian dynamics, which can reduce the effective acceleration significantly. We make predictions on the dynamical mass-to-light ratio (Mdyn/L) expected to be measured by an observer who assumes Newtonian dynamics to be valid. We show that Milgromian dynamics predicts typical Mdyn/L ~ 10...50 Msun/Lsun. The results for the most luminous ones, Fornax and Sculptor, agree well with available velocity dispersion data. Moreover, the central power law slopes of the dynamical ...
Edelman, Mark
2014-01-01
In this paper the author presents the results of the preliminary investigation of fractional dynamical systems based on the results of numerical simulations of fractional maps. Fractional maps are equivalent to fractional differential equations describing systems experiencing periodic kicks. Their properties depend on the value of two parameters: the non-linearity parameter, which arises from the corresponding regular dynamical systems; and the memory parameter which is the order of the fractional derivative in the corresponding non-linear fractional differential equations. The examples of the fractional Standard and Logistic maps demonstrate that phase space of non-linear fractional dynamical systems may contain periodic sinks, attracting slow diverging trajectories, attracting accelerator mode trajectories, chaotic attractors, and cascade of bifurcations type trajectories whose properties are different from properties of attractors in regular dynamical systems. The author argues that discovered properties s...
International Nuclear Information System (INIS)
The presence of plasmonic material influences the optical properties of nearby molecules in untrivial ways due to the dynamical plasmon-molecule coupling. We combine quantum and classical calculation schemes to study this phenomenon in a hybrid system that consists of a Na2 molecule located in the gap between two Au/Ag nanoparticles. The molecule is treated quantum-mechanically with time-dependent density-functional theory, and the nanoparticles with quasistatic classical electrodynamics. The nanoparticle dimer has a plasmon resonance in the visible part of the electromagnetic spectrum, and the Na2 molecule has an electron-hole excitation in the same energy range. Due to the dynamical interaction of the two subsystems the plasmon and the molecular excitations couple, creating a hybridized molecular-plasmon excited state. This state has unique properties that yield e.g. enhanced photoabsorption compared to the freestanding Na2 molecule. The computational approach used enables decoupling of the mutual plasmon-molecule interaction, and our analysis verifies that it is not legitimate to neglect the backcoupling effect when describing the dynamical interaction between plasmonic material and nearby molecules. Time-resolved analysis shows nearly instantaneous formation of the coupled state, and provides an intuitive picture of the underlying physics. (paper)
Sakko, Arto; Rossi, Tuomas P.; Nieminen, Risto M.
2014-08-01
The presence of plasmonic material influences the optical properties of nearby molecules in untrivial ways due to the dynamical plasmon-molecule coupling. We combine quantum and classical calculation schemes to study this phenomenon in a hybrid system that consists of a Na2 molecule located in the gap between two Au/Ag nanoparticles. The molecule is treated quantum-mechanically with time-dependent density-functional theory, and the nanoparticles with quasistatic classical electrodynamics. The nanoparticle dimer has a plasmon resonance in the visible part of the electromagnetic spectrum, and the Na2 molecule has an electron-hole excitation in the same energy range. Due to the dynamical interaction of the two subsystems the plasmon and the molecular excitations couple, creating a hybridized molecular-plasmon excited state. This state has unique properties that yield e.g. enhanced photoabsorption compared to the freestanding Na2 molecule. The computational approach used enables decoupling of the mutual plasmon-molecule interaction, and our analysis verifies that it is not legitimate to neglect the backcoupling effect when describing the dynamical interaction between plasmonic material and nearby molecules. Time-resolved analysis shows nearly instantaneous formation of the coupled state, and provides an intuitive picture of the underlying physics.
Šimović, Vladimir
2001-01-01
The objective of this study is to present research on classical and intelligent information system solutions used in criminal intelligence analysis in Croatian security system theory. The study analyses objective and classical methods of information science, including artificial intelligence and other scientific methods. The intelligence and classical software solutions researched, proposed, and presented in this study were used in developing the integrated information system for the Croatian...
Yoo, Jejoong; Wilson, James; Aksimentiev, Aleksei
2016-10-01
Calcium ions (Ca(2+) ) play key roles in various fundamental biological processes such as cell signaling and brain function. Molecular dynamics (MD) simulations have been used to study such interactions, however, the accuracy of the Ca(2+) models provided by the standard MD force fields has not been rigorously tested. Here, we assess the performance of the Ca(2+) models from the most popular classical force fields AMBER and CHARMM by computing the osmotic pressure of model compounds and the free energy of DNA-DNA interactions. In the simulations performed using the two standard models, Ca(2+) ions are seen to form artificial clusters with chloride, acetate, and phosphate species; the osmotic pressure of CaAc2 and CaCl2 solutions is a small fraction of the experimental values for both force fields. Using the standard parameterization of Ca(2+) ions in the simulations of Ca(2+) -mediated DNA-DNA interactions leads to qualitatively wrong outcomes: both AMBER and CHARMM simulations suggest strong inter-DNA attraction whereas, in experiment, DNA molecules repel one another. The artificial attraction of Ca(2+) to DNA phosphate is strong enough to affect the direction of the electric field-driven translocation of DNA through a solid-state nanopore. To address these shortcomings of the standard Ca(2+) model, we introduce a custom model of a hydrated Ca(2+) ion and show that using our model brings the results of the above MD simulations in quantitative agreement with experiment. Our improved model of Ca(2+) can be readily applied to MD simulations of various biomolecular systems, including nucleic acids, proteins and lipid bilayer membranes. © 2016 Wiley Periodicals, Inc. Biopolymers 105: 752-763, 2016. PMID:27144470
Roy, S.
2015-06-27
Classically or alternatively activated macrophages (M1 and M2, respectively) play distinct and important roles for microbiocidal activity, regulation of inflammation and tissue homeostasis. Despite this, their transcriptional regulatory dynamics are poorly understood. Using promoter-level expression profiling by non-biased deepCAGE we have studied the transcriptional dynamics of classically and alternatively activated macrophages. Transcription factor (TF) binding motif activity analysis revealed four motifs, NFKB1_REL_RELA, IRF1,2, IRF7 and TBP that are commonly activated but have distinct activity dynamics in M1 and M2 activation. We observe matching changes in the expression profiles of the corresponding TFs and show that only a restricted set of TFs change expression. There is an overall drastic and transient up-regulation in M1 and a weaker and more sustainable up-regulation in M2. Novel TFs, such as Thap6, Maff, (M1) and Hivep1, Nfil3, Prdm1, (M2) among others, were suggested to be involved in the activation processes. Additionally, 52 (M1) and 67 (M2) novel differentially expressed genes and, for the first time, several differentially expressed long non-coding RNA (lncRNA) transcriptome markers were identified. In conclusion, the finding of novel motifs, TFs and protein-coding and lncRNA genes is an important step forward to fully understand the transcriptional machinery of macrophage activation.
Dynamic information theory and information description of dynamic systems
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper, we develop dynamic statistical information theory established by the author. Starting from the ideas that the state variable evolution equations of stochastic dynamic systems, classical and quantum nonequilibrium statistical physical systems and special electromagnetic field systems can be regarded as their information symbol evolution equations and the definitions of dynamic information and dynamic entropy, we derive the evolution equations of dynamic information and dynamic entropy that describe the evolution laws of dynamic information. These four kinds of evolution equations are of the same mathematical type. They show in unison when information transmits in coordinate space outside the systems that the time rate of change of dynamic information densities originates from their drift, diffusion and dissipation in state variable space inside the systems and coordinate space in the transmission processes, and that the time rate of change of dynamic entropy densities is caused by their drift, diffusion and production in state variable space inside the systems and coordinate space in the transmission processes. When space noise can be neglected, an information wave will appear. If we only consider the information change inside the systems, dynamic information evolution equations reduce to information equations corresponding to the dynamic equations which describe evolution laws of the above dynamic systems. This reveals that the evolution laws of respective dynamic systems can be described by information equations in a unified fashion. Hence, the evolution processes of these dynamic systems can be abstracted as the evolution processes of information. Furthermore, we present the formulas for information flow, information dissipation rate, and entropy production rate. We prove that the information production probably emerges in a dynamic system with internal attractive interaction between the elements, and derive a formula for this information
Energy Technology Data Exchange (ETDEWEB)
Draeger, E W; Bennion, B; Gygi, F; Lightstone, F
2006-02-10
The reaction mechanism of the human P450 CYP1A2 enzyme plays a fundamental role in understanding the effects of environmental carcinogens and mutagens on humans. Despite extensive experimental research on this enzyme system, key questions regarding its catalytic cycle and oxygen activation mechanism remain unanswered. In order to elucidate the reaction mechanism in human P450, new computational methods are needed to accurately represent this system. To enable us to perform computational simulations of unprecedented accuracy on these systems, we developed a dynamic quantum-classical (QM/MM) hybrid method, in which ab initio molecular dynamics are coupled with classical molecular mechanics. This will provide the accuracy needed to address such a complex, large biological system in a fully dynamic environment. We also present detailed calculations of the P450 active site, including the relative charge transfer between iron porphine and tetraphenyl porphyrin.
Genetic Sequential Dynamical Systems
Avino-Diaz, Maria A.; Ortiz, Humberto; Moreno, Oscar
2006-01-01
The whole complex process to obtain a protein encoded by a gene is difficult to include in a mathematical model. There are many models for describing different aspects of a genetic network. Finding a better model is one of the most important and interesting questions in computational biology. Sequential dynamical systems have been developed for a theory of computer simulation, and in this paper, a genetic sequential dynamical system is introduced. A gene is considered to be a function which c...
Dynamic performance management system
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
An integrated, efficient and effective performance management system, "dynamic performance management system", is presented, which covers the entire performance management process including measures design, analysis, and dynamic update. The analysis of performance measures using causal loop diagrams, qualitative inference and analytic network process is mainly discussed. A real world case study is carried out throughout the paper to explain how the framework works. A software tool for DPMS, Performance Analyzer, is also introduced.
Takatsuka, Kazuo; Matsumoto, Kentaro
2016-01-21
We present a basic theory to study real-time dynamics embedded in a large environment that is treated using a statistical method. In light of great progress in the molecular-level studies on time-resolved spectroscopies, chemical reaction dynamics, and so on, not only in the gas phase but also in condensed phases like liquid solvents and even in crowded environments in living cells, we need to bridge over a gap between statistical mechanics and microscopic real-time dynamics. For instance, an analogy to gas-phase dynamics in which molecules are driven by the gradient of the potential energy hyper-surfaces (PESs) suggests that particles in condensed phases should run on the free energy surface instead. The question is whether this anticipation is correct. To answer it, we here propose a mixed dynamics and statistical representation to treat chemical dynamics embedded in a statistical ensemble. We first define the entropy functional, which is a function of the phase-space position of the dynamical subsystem, being dressed with statistical weights from the statistical counterpart. We then consider the functionals of temperature, free energy, and chemical potential as their extensions in statistical mechanics, through which one can clarify the relationship between real-time microscopic dynamics and statistical quantities. As an illustrative example we show that molecules in the dynamical subsystem should run on the free-energy functional surface, if and only if the spatial gradients of the temperature functional are all zero. Otherwise, additional forces emerge from the gradient of the temperature functional. Numerical demonstrations are presented at the very basic level of this theory of molecular dissociation in atomic cluster solvents. PMID:26674298
Non-Kolmogorovian Approach to the Context-Dependent Systems Breaking the Classical Probability Law
Asano, Masanari; Basieva, Irina; Khrennikov, Andrei; Ohya, Masanori; Yamato, Ichiro
2013-07-01
There exist several phenomena breaking the classical probability laws. The systems related to such phenomena are context-dependent, so that they are adaptive to other systems. In this paper, we present a new mathematical formalism to compute the joint probability distribution for two event-systems by using concepts of the adaptive dynamics and quantum information theory, e.g., quantum channels and liftings. In physics the basic example of the context-dependent phenomena is the famous double-slit experiment. Recently similar examples have been found in biological and psychological sciences. Our approach is an extension of traditional quantum probability theory, and it is general enough to describe aforementioned contextual phenomena outside of quantum physics.
Semi-Classical Quantization of the Many-Anyon System
Illuminati, Fabrizio
1992-01-01
We discuss the problem of N anyons in harmonic well, and derive the semi-classical spectrum as an exactly solvable limit of the many-anyon Hamiltonian. The relevance of our result to the solution of the anyon-gas model is discussed.
Semi-Classical Quantization of the Many-Anyon System
Illuminati, F
1993-01-01
We discuss the problem of N anyons in harmonic well, and derive the semi-classical spectrum as an exactly solvable limit of the many-anyon Hamiltonian. The relevance of our result to the solution of the anyon-gas model is discussed.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Based on the cascade two-photon laser dynamic equation derived with the technique of quantum Langevin operators with the considerations of coherently prepared three-level atoms and the classical field injected into the cavity, we numerically study the effects of atomic coherence and classical field on the chaotic dynamics of a two-photon laser. Lyapunov exponent and bifurcation diagram calculations show that the Lorenz chaos and hyperchaos can be induced or inhibited by the atomic coherence and the classical field via crisis or Hopf bifurcations.
Coherence and chaos in extended dynamical systems
International Nuclear Information System (INIS)
Coherence, chaos, and pattern formation are characteristic elements of the nonequilibrium statistical mechanics controlling mesoscopic order and disorder in many-degree-of-freedom nonlinear dynamical systems. Competing length scales and/or time scales are the underlying microscopic driving forces for many of these aspects of ''complexity.'' We illustrate the basic concepts with some model examples of classical and quantum, ordered and disordered, nonlinear systems
Computational quantum-classical boundary of complex and noisy quantum systems
Fujii, Keisuke; Tamate, Shuhei
2014-01-01
It is often said that the transition from quantum to classical worlds is caused by decoherence originated from an interaction between a system of interest and its surrounding environment. Here we establish a computational quantum-classical boundary from the viewpoint of classical simulatability of a quantum system under decoherence. Specifically, we consider commuting quantum circuits being subject to decoherence. Or equivalently, we can regard them as measurement-based quantum computation on...
Srivastava, Deepak; Saini, Subhash (Technical Monitor)
1998-01-01
The tubular forms of fullerenes popularly known as carbon nanotubes are experimentally produced as single-, multiwall, and rope configurations. The nanotubes and nanoropes have shown to exhibit unusual mechanical and electronic properties. The single wall nanotubes exhibit both semiconducting and metallic behavior. In short undefected lengths they are the known strongest fibers which are unbreakable even when bent in half. Grown in ropes their tensile strength is approximately 100 times greater than steel at only one sixth the weight. Employing large scale classical and quantum molecular dynamics simulations we will explore the use of carbon nanotubes and carbon nanotube junctions in 2-, 3-, and 4-point molecular electronic device components, dynamic strength characterization for compressive, bending and torsional strains, and chemical functionalization for possible use in a nanoscale molecular motor. The above is an unclassified material produced for non-competitive basic research in the nanotechnology area.
Communication: Adiabatic and non-adiabatic electron-nuclear motion: Quantum and classical dynamics
Albert, Julian; Kaiser, Dustin; Engel, Volker
2016-05-01
Using a model for coupled electronic-nuclear motion we investigate the range from negligible to strong non-adiabatic coupling. In the adiabatic case, the quantum dynamics proceeds in a single electronic state, whereas for strong coupling a complete transition between two adiabatic electronic states takes place. It is shown that in all coupling regimes the short-time wave-packet dynamics can be described using ensembles of classical trajectories in the phase space spanned by electronic and nuclear degrees of freedom. We thus provide an example which documents that the quantum concept of non-adiabatic transitions is not necessarily needed if electronic and nuclear motion is treated on the same footing.
Interplay of classical and quantum dynamics in a thermal ensemble of atoms
Laskar, Arif Warsi; Mukherjee, Arunabh; Ghosh, Saikat
2016-01-01
In a thermal ensemble of atoms driven by coherent fields, how does evolution of quantum superposition compete with classical dynamics of optical pumping and atomic diffusion? Is it optical pumping that first prepares a thermal ensemble, with coherent superposition developing subsequently or is it the other way round: coherently superposed atoms driven to steady state via optical pumping? Using a stroboscopic probing technique, here we experimentally explore these questions. A 100 ns pulse is used to probe an experimentally simulated, closed three-level, lambda-like configuration in rubidium atoms, driven by strong coherent control and incoherent fields. Temporal evolution of probe transmission shows an initial overshoot with turn-on of control, resulting in a scenario akin to lasing without inversion (LWI). The corresponding rise time is dictated by coherent dynamics, with a distinct experimental signature of half-cycle Rabi flop in a thermal ensemble of atoms. Our results indicate that, in fact, optical pump...
Lattice thermal conductivity of UO2 using ab-initio and classical molecular dynamics
International Nuclear Information System (INIS)
We applied the non-equilibrium ab-initio molecular dynamics and predict the lattice thermal conductivity of the pristine uranium dioxide for up to 2000 K. We also use the equilibrium classical molecular dynamics and heat-current autocorrelation decay theory to decompose the lattice thermal conductivity into acoustic and optical components. The predicted optical phonon transport is temperature independent and small, while the acoustic component follows the Slack relation and is in good agreement with the limited single-crystal experimental results. Considering the phonon grain-boundary and pore scatterings, the effective lattice thermal conductivity is reduced, and we show it is in general agreement with the sintered-powder experimental results. The charge and photon thermal conductivities are also addressed, and we find small roles for electron, surface polaron, and photon in the defect-free structures and for temperatures below 1500 K
Pillet, Claude-Alain
2006-01-01
This notes are an expanded version of the lectures given by the author at the Grenoble "Open Quantum Systems" summer school in 2003. They provide a short introduction to quantum dynamical systems and their ergodic properties with particular emphasis on the quantum Koopman–von Neumann spectral theory.
Sidles, John A; Jacky, Jonathan P; Picone, Rico A R; Harsila, Scott A
2010-01-01
The practical focus of this work is the dynamical simulation of polarization transport processes in quantum spin microscopy and spectroscopy. The simulation framework is built-up progressively, beginning with state-spaces (configuration manifolds) that are geometrically natural, introducing coordinates that are algebraically natural; and finally specifying dynamical potentials that are physically natural; in each respect explicit criteria are given for "naturality." The resulting framework encompasses Hamiltonian flow (both classical and quantum), quantum Lindbladian processes, and classical thermostatic processes. Constructive validation and verification criteria are given for metric and symplectic flows on classical, quantum, and hybrid state-spaces, with particular emphasis to tensor network state-spaces. Both classical and quantum examples are presented, including dynamic nuclear polarization (DNP). A broad span of applications and challenges is discussed, ranging from the design and simulation of quantum...
Computability and dynamical systems
Buescu, Jorge; Graça, Daniel; Zhong, Ning
2011-01-01
In this paper we explore results that establish a link between dynamical systems and computability theory (not numerical analysis). In the last few decades, computers have increasingly been used as simulation tools for gaining insight into dynamical behavior. However, due to the presence of errors inherent in such numerical simulations, with few exceptions, computers have not been used for the nobler task of proving mathematical results. Nevertheless, there have been some recen...
Mithen, James P.; Daligault, Jérôme; Gregori, G.
2011-01-01
The complementarity of the liquid and plasma descriptions of the classical one-component plasma (OCP) is explored by studying wavevector and frequency dependent dynamical quantities: the dynamical structure factor (DSF), and the dynamic local field correction (LFC). Accurate Molecular Dynamics (MD) simulations are used to validate/test models of the DSF and LFC. Our simulations, which span the entire fluid regime ($\\Gamma = 0.1 - 175$), show that the DSF is very well represented by a simple a...
Pumpe, Daniel; Müller, Ewald; Enßlin, Torsten A
2016-01-01
Stochastic differential equations describe well many physical, biological and sociological systems, despite the simplification often made in their derivation. Here the usage of simple stochastic differential equations to characterize and classify complex dynamical systems is proposed within a Bayesian framework. To this end, we develop a dynamic system classifier (DSC). The DSC first abstracts training data of a system in terms of time dependent coefficients of the descriptive stochastic differential equation. Thereby the DSC identifies unique correlation structures within the training data. For definiteness we restrict the presentation of DSC to oscillation processes with a time dependent frequency {\\omega}(t) and damping factor {\\gamma}(t). Although real systems might be more complex, this simple oscillator captures many characteristic features. The {\\omega} and {\\gamma} timelines represent the abstract system characterization and permit the construction of efficient signal classifiers. Numerical experiment...
Energy Technology Data Exchange (ETDEWEB)
Belyaev, Andrey K., E-mail: belyaev@herzen.spb.ru [Department of Theoretical Physics, Herzen University, St. Petersburg 191186 (Russian Federation); Domcke, Wolfgang, E-mail: wolfgang.domcke@ch.tum.de [Department Chemie, Technische Universität München, D-85747 Garching (Germany); Lasser, Caroline, E-mail: classer@ma.tum.de; Trigila, Giulio, E-mail: trigila@ma.tum.de [Zentrum Mathematik, Technische Universität München, D-85747 Garching (Germany)
2015-03-14
The Landau–Zener (LZ) type classical-trajectory surface-hopping algorithm is applied to the nonadiabatic nuclear dynamics of the ammonia cation after photoionization of the ground-state neutral molecule to the excited states of the cation. The algorithm employs a recently proposed formula for nonadiabatic LZ transition probabilities derived from the adiabatic potential energy surfaces. The evolution of the populations of the ground state and the two lowest excited adiabatic states is calculated up to 200 fs. The results agree well with quantum simulations available for the first 100 fs based on the same potential energy surfaces. Three different time scales are detected for the nuclear dynamics: Ultrafast Jahn–Teller dynamics between the excited states on a 5 fs time scale; fast transitions between the excited state and the ground state within a time scale of 20 fs; and relatively slow partial conversion of a first-excited-state population to the ground state within a time scale of 100 fs. Beyond 100 fs, the adiabatic electronic populations are nearly constant due to a dynamic equilibrium between the three states. The ultrafast nonradiative decay of the excited-state populations provides a qualitative explanation of the experimental evidence that the ammonia cation is nonfluorescent.
Vol, E D
2011-01-01
We propose the consistent statistical approach to consider a wide class of classical open systems whose states are specified by a set of positive integers(occupation numbers).Such systems are often encountered in physics, chemistry, ecology, economics and other sciences.Our statistical method based on ideas of quantum theory of open systems takes into account both discreteness of the system variables and their time fluctuations - two effects which are ignored in usual mean field dynamical approach.The method let one to calculate the distribution function and (or)all moments of the system of interest at any instant.As descriptive examples illustrating the effectiveness of the method we consider some simple models:one relating to nonlinear mechanics,and others taken from population biology .In all this examples the results obtained by the method for large occupation numbers coincide with results of purely dynamical approach but for small numbers interesting differences and new effects arise.The possible observa...
Complexified dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Bender, Carl M [Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Holm, Darryl D [Department of Mathematics, Imperial College, London SW7 2AZ (United Kingdom); Hook, Daniel W [Blackest Laboratory, Imperial College, London SW7 2BZ (United Kingdom)
2007-08-10
Many dynamical systems, such as the Lotka-Volterra predator-prey model and the Euler equations for the free rotation of a rigid body, are PT symmetric. The standard and well-known real solutions to such dynamical systems constitute an infinitessimal subclass of the full set of complex solutions. This paper examines a subset of the complex solutions that contains the real solutions, namely those having PT symmetry. The condition of PT symmetry selects out complex solutions that are periodic. (fast track communication)
Labarca, Rafael; Palis, Jacob
1988-01-01
This volume contains original research papers on topics central to Dynamical Systems, such as fractional dimensions (Hausdorff dimension, limity capacity) and limit cycles of polynomial vector fields concerning the well-known Dulac and Hilbert's 16th problems. Stability and bifurcations, intermittency, normal forms, Anosov flows and foliations are also themes treated in the papers. Many of the authors are renowned for their important contributions to the field. This volume should be of much interest to people working in dynamical systems, including, physicists, biologists and engineers.
Dynamical Vertex Approximation for Nanoscopic Systems
International Nuclear Information System (INIS)
Full text: We present model calculations for nanoscopic systems including Hubbard-like Coulomb repulsion and double exchange interactions with localized, classical spins. We compare the results of the recently introduced nanoscopic version of the dynamical vertex approximation at dynamical mean field level against exact diagonalization for a Benzene-like ring, where the latter is doable. This comparison allows us to investigate the reliability of the approximation. It shows that, already at the simplest approximation level (i.e. including only local correlations) the results are very accurate in a rather wide range of parameters. Since the computational effort is highly reduced, it is suitable for studying more complex systems. (author)
International Nuclear Information System (INIS)
We recall results concerning one-dimensional classical and quantum systems with ladder operators. We obtain the most general one-dimensional classical systems, respectively, with a third and a fourth-order ladder operators satisfying polynomial Heisenberg algebras. These systems are written in terms of the solutions of quartic and quintic equations. They are the classical equivalent of quantum systems involving the fourth and fifth Painleve transcendents. We use these results to present two new families of superintegrable systems and examples of trajectories that are deformation of Lissajous's figures.
System dynamics with interaction discontinuity
Luo, Albert C J
2015-01-01
This book describes system dynamics with discontinuity caused by system interactions and presents the theory of flow singularity and switchability at the boundary in discontinuous dynamical systems. Based on such a theory, the authors address dynamics and motion mechanism of engineering discontinuous systems due to interaction. Stability and bifurcations of fixed points in nonlinear discrete dynamical systems are presented, and mapping dynamics are developed for analytical predictions of periodic motions in engineering discontinuous dynamical systems. Ultimately, the book provides an alternative way to discuss the periodic and chaotic behaviors in discontinuous dynamical systems.
Quantum and quasi-classical collisional dynamics of O2-Ar at high temperatures
Ulusoy, Inga S.; Andrienko, Daniil A.; Boyd, Iain D.; Hernandez, Rigoberto
2016-06-01
A hypersonic vehicle traveling at a high speed disrupts the distribution of internal states in the ambient flow and introduces a nonequilibrium distribution in the post-shock conditions. We investigate the vibrational relaxation in diatom-atom collisions in the range of temperatures between 1000 and 10 000 K by comparing results of extensive fully quantum-mechanical and quasi-classical simulations with available experimental data. The present paper simulates the interaction of molecular oxygen with argon as the first step in developing the aerothermodynamics models based on first principles. We devise a routine to standardize such calculations also for other scattering systems. Our results demonstrate very good agreement of vibrational relaxation time, derived from quantum-mechanical calculations with the experimental measurements conducted in shock tube facilities. At the same time, the quasi-classical simulations fail to accurately predict rates of vibrationally inelastic transitions at temperatures lower than 3000 K. This observation and the computational cost of adopted methods suggest that the next generation of high fidelity thermochemical models should be a combination of quantum and quasi-classical approaches.
Decoherence as irreversible dynamical process in open quantum systems
International Nuclear Information System (INIS)
Full text: A framework for a general discussion in Heisenberg's representation of environmentally induced decoherence will be proposed. Example showing that classical properties do not have to be postulated as an independent ingredient will be given. It will be also shown that infinite open quantum systems in some case after decoherence behave like - simple classical dynamical systems; simples quantum mechanical systems representing one particle. (author)
Getting excited: Challenges in quantum-classical studies of excitons in polymeric systems
Bagheri, Behnaz; Karttunen, Mikko
2016-01-01
A combination of classical molecular dynamics (MM/MD) and quantum chemical calculations based on the density functional theory (DFT) was performed to describe conformational properties of diphenylethyne (DPE), methylated-DPE and poly para phenylene ethynylene (PPE). DFT calculations were employed to improve and develop force field parameters for MM/MD simulations. Many-body Green's functions theory within the GW approximation and the Bethe-Salpeter equation were utilized to describe excited states of the systems. Reliability of the excitation energies based on the MM/MD conformations was examined and compared to the excitation energies from DFT conformations. The results show an overall agreement between the optical excitations based on MM/MD conformations and DFT conformations. This allows for calculation of excitation energies based on MM/MD conformations.
Belyaev, Andrey K; Lasser, Caroline; Trigila, Giulio
2014-01-01
The Landau--Zener (LZ) type classical-trajectory surface-hopping algorithm is applied to the nonadiabatic nuclear dynamics of the ammonia cation after photoionization of the ground-state neutral molecule to the excited states of the cation. The algorithm employs the recently proposed formula for nonadiabatic LZ transition probabilities derived from the adiabatic potential energy surfaces. The evolution of the populations of the ground state and the two lowest excited adiabatic states is calculated up to 200 fs. The results agree well with quantum simulations available for the first 100 fs based on the same potential energy surfaces. Four different time scales are detected for the nuclear dynamics: Ultrafast Jahn--Teller dynamics between the excited states on a 5 fs time scale; fast transitions between the excited state and the ground state within a time scale of 20 fs; relatively slow partial conversion of a first-excited-state population to the ground state within a time scale of 100 fs; and nearly constant ...
A general solution for classical sequential growth dynamics of Causal Sets
Varadarajan, M; Rideout, David; Varadarajan, Madhavan
2006-01-01
A classical precursor to a full quantum dynamics for causal sets has been forumlated in terms of a stochastic sequential growth process in which the elements of the causal set arise in a sort of accretion process. The transition probabilities of the Markov growth process satisfy certain physical requirements of causality and general covariance, and the generic solution with all transition probabilities non-zero has been found. Here we remove the assumption of non-zero probabilities, define a reasonable extension of the physical requirements to cover the case of vanishing probabilities, and find the completely general solution to these physical conditions. The resulting family of growth processes has an interesting structure reminiscent of an ``infinite tower of turtles'' cosmology.
International Nuclear Information System (INIS)
Molecular dynamics simulations using a combined quantum/classical force field have been carried out to investigate the properties of hydrogen peroxide in aqueous solution. Radial distribution functions exhibit close similarities with those obtained for the OH radical. They show that H2O2 is a better proton donor than H2O but a weaker proton acceptor. Solvent effects modify the O-H bonds, which are weakened and elongated by 0.02 A. The HOOH dihedral angle decreases by 11 deg. and the dipole moment increases by 0.8 D. The O-O bond length and bond order do not change much. Fluctuations of the frontier orbital energies are analyzed in detail as a function of both, the HOOH geometry and the solvent configuration. Hydrogen-bonds with solvent molecules appear to have an opposite influence depending on their donor/acceptor character. Interconversion between energy minima always proceeds through a transoid transition state
Kirilyuk, A P
2002-01-01
Any real interaction process produces many incompatible system versions, or realisations, giving rise to the omnipresent dynamic randomness and universally defined complexity (physics/9806002). Since quantum behaviour dynamically emerges as the lowest complexity level (quant-ph/9902016), quantum interaction randomness can only be relatively strong, which reveals the causal origin of quantum indeterminacy (quant-ph/9511037) and true quantum chaos (quant-ph/9511035), but rigorously excludes a possibility of unitary quantum computation, even in the 'ideal', noiseless system. Any real computation is an internally chaotic (multivalued) process of system complexity development realised in different regimes. The unitary quantum machines, including their postulated 'magic', cannot be realised as such because their dynamically single-valued scheme is incompatible with the irreducibly high dynamic randomness at quantum complexity levels and should be replaced by the explicitly chaotic, intrinsically creative machines a...
Stochastic theory for classical and quantum mechanical systems
International Nuclear Information System (INIS)
From first principles a theory of stochastic processes in configuration space is formulated. The fundamental equations of the theory are an equation of motion which generalizes Newton's second law and an equation which expresses the condition of conservation of matter. Two types of stochastic motion are possible, both described by the same general equations, but leading in one case to classical Brownian motion behavior and in the other to quantum mechanical behavior. The Schroedinger equation, which is derived with no further assumption, is thus shown to describe a specific stochastic process. It is explicitly shown that only in the quantum mechanical process does the superposition of probability amplitudes give rise to interference phenomena; moreover, the presence of dissipative forces in the Brownian motion equations invalidates the superposition principle. At no point are any special assumptions made concerning the physical nature of the underlying stochastic medium, although some suggestions are discussed in the last section
International Nuclear Information System (INIS)
In this paper, we investigate the effects of a classical gravitational field on the dynamical behaviour of the nonlinear atom-field interaction within the framework of the f-deformed Jaynes-Cummings model. For this purpose, we first introduce a set of new atomic operators obeying an f-deformed su(2) algebraic structure to derive an effective Hamiltonian for the system under consideration. Then by solving the Schroedinger equation in the interaction picture and considering certain initial quantum states for the atomic and radiation subsystems, we analyse the influence of gravity on the temporal evolution of the atomic population inversion, atomic dipole squeezing, atomic momentum diffusion, photon counting statistics and deformed quadrature squeezing of the radiation field.
Energy Technology Data Exchange (ETDEWEB)
Miller, William H., E-mail: millerwh@berkeley.edu; Cotton, Stephen J., E-mail: StephenJCotton47@gmail.com [Department of Chemistry and Kenneth S. Pitzer Center for Theoretical Chemistry, University of California and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States)
2015-04-07
It is noted that the recently developed symmetrical quasi-classical (SQC) treatment of the Meyer-Miller (MM) model for the simulation of electronically non-adiabatic dynamics provides a good description of detailed balance, even though the dynamics which results from the classical MM Hamiltonian is “Ehrenfest dynamics” (i.e., the force on the nuclei is an instantaneous coherent average over all electronic states). This is seen to be a consequence of the SQC windowing methodology for “processing” the results of the trajectory calculation. For a particularly simple model discussed here, this is shown to be true regardless of the choice of windowing function employed in the SQC model, and for a more realistic full classical molecular dynamics simulation, it is seen to be maintained correctly for very long time.
International Nuclear Information System (INIS)
It is noted that the recently developed symmetrical quasi-classical (SQC) treatment of the Meyer-Miller (MM) model for the simulation of electronically non-adiabatic dynamics provides a good description of detailed balance, even though the dynamics which results from the classical MM Hamiltonian is “Ehrenfest dynamics” (i.e., the force on the nuclei is an instantaneous coherent average over all electronic states). This is seen to be a consequence of the SQC windowing methodology for “processing” the results of the trajectory calculation. For a particularly simple model discussed here, this is shown to be true regardless of the choice of windowing function employed in the SQC model, and for a more realistic full classical molecular dynamics simulation, it is seen to be maintained correctly for very long time
Kauffmann, Steven Kenneth
2010-01-01
The time-dependent Schroedinger equation with time-independent Hamiltonian matrix is a homogeneous linear oscillatory system in canonical form. We investigate whether any classical system that itself is linear, homogeneous, oscillatory and conservative is guaranteed to linearly map into a Schroedinger equation. Such oscillatory classical systems can be analyzed into their normal modes, which are mutually independent, uncoupled simple harmonic oscillators, and the equation of motion of such a ...
Interactive Dynamic-System Simulation
Korn, Granino A
2010-01-01
Showing you how to use personal computers for modeling and simulation, Interactive Dynamic-System Simulation, Second Edition provides a practical tutorial on interactive dynamic-system modeling and simulation. It discusses how to effectively simulate dynamical systems, such as aerospace vehicles, power plants, chemical processes, control systems, and physiological systems. Written by a pioneer in simulation, the book introduces dynamic-system models and explains how software for solving differential equations works. After demonstrating real simulation programs with simple examples, the author
Brambila, Danilo
2012-05-01
Quantum chaos has emerged in the half of the last century with the notorious problem of scattering of heavy nuclei. Since then, theoreticians have developed powerful techniques to approach disordered quantum systems. In the late 70\\'s, Casati and Chirikov initiated a new field of research by studying the quantum counterpart of classical problems that are known to exhibit chaos. Among the several quantum-classical chaotic systems studied, the kicked rotor stimulated a lot of enthusiasm in the scientific community due to its equivalence to the Anderson tight binding model. This equivalence allows one to map the random Anderson model into a set of fully deterministic equations, making the theoretical analysis of Anderson localization considerably simpler. In the one-dimensional linear regime, it is known that Anderson localization always prevents the diffusion of the momentum. On the other hand, for higher dimensions it was demonstrated that for certain conditions of the disorder parameter, Anderson localized modes can be inhibited, allowing then a phase transition from localized (insulating) to delocalized (metallic) states. In this thesis we will numerically and theoretically investigate the properties of a multidimensional quantum kicked rotor in a nonlinear medium. The presence of nonlinearity is particularly interesting as it raises the possibility of having soliton waves as eigenfunctions of the systems. We keep the generality of our approach by using an adjustable diffusive nonlinearity, which can describe several physical phenomena. By means of Variational Calculus we develop a chaotic map which fully describes the soliton dynamics. The analysis of such a map shows a rich physical scenario that evidences the wave-particle behavior of a soliton. Through the nonlinearity, we trace a correspondence between quantum and classical mechanics, which has no equivalent in linearized systems. Matter waves experiments provide an ideal environment for studying Anderson
Energy Technology Data Exchange (ETDEWEB)
Sewell, T. D. (Thomas D.); Gan, C. K. (Chee Kwan); Jaramillo, E. (Eugenio); Strachan, A. H. (Alejandro H.)
2004-01-01
We are using classical molecular dynamics and condensed phase electronic-structure methods to predict some of the thermophysical and mechanical properties that are needed as input to realistic mesoscale models for plastic-bonded explosives. The main materials studied to date are HMX, PETN, Estane copolymer, and bi(2,2-dinitropropyl) formal/acetal (BDNPF/A). Emphasis is placed on non-reactive properties and thermodynamic states relevant to cookoff and shock initiation phenomena. Both crystal and liquid-state properties are of interest. Typical simulation sizes and times are {approx}10{sup 2} molecules and 2-10 ns, respectively. The overarching goal is to develop internally consistent model thermodynamic and elastic mechanical descriptions for the materials. Prioritization among the set of properties amenable to atomistic simulation is made based on ongoing interactions with mesoscale modelers at Los Alamos and elsewhere. Recent work will be summarized and our view of profitable directions for future research will be discussed, including preliminary results for large-scale molecular dynamics simulations of shock response of crystalline HMX.
Costandy, Joseph; Michalis, Vasileios K; Tsimpanogiannis, Ioannis N; Stubos, Athanassios K; Economou, Ioannis G
2016-03-28
We introduce a simple correction to the calculation of the lattice constants of fully occupied structure sI methane or carbon dioxide pure hydrates that are obtained from classical molecular dynamics simulations using the TIP4PQ/2005 water force field. The obtained corrected lattice constants are subsequently used in order to obtain isobaric thermal expansion coefficients of the pure gas hydrates that exhibit a trend that is significantly closer to the experimental behavior than previously reported classical molecular dynamics studies. PMID:27036466
Dou, Wenjie; Subotnik, Joseph E
2016-01-14
A broadened classical master equation (BCME) is proposed for modeling nonadiabatic dynamics for molecules near metal surfaces over a wide range of parameter values and with arbitrary initial conditions. Compared with a standard classical master equation-which is valid in the limit of weak molecule-metal couplings-this BCME should be valid for both weak and strong molecule-metal couplings. (The BCME can be mapped to a Fokker-Planck equation that captures level broadening correctly.) Finally, our BCME can be solved with a simple surface hopping algorithm; numerical tests of equilibrium and dynamical observables look very promising. PMID:26772563
Wisdom, Jack
2002-01-01
In these 18 years, the research has touched every major dynamical problem in the solar system, including: the effect of chaotic zones on the distribution of asteroids, the delivery of meteorites along chaotic pathways, the chaotic motion of Pluto, the chaotic motion of the outer planets and that of the whole solar system, the delivery of short period comets from the Kuiper belt, the tidal evolution of the Uranian arid Galilean satellites, the chaotic tumbling of Hyperion and other irregular satellites, the large chaotic variations of the obliquity of Mars, the evolution of the Earth-Moon system, and the resonant core- mantle dynamics of Earth and Venus. It has introduced new analytical and numerical tools that are in widespread use. Today, nearly every long-term integration of our solar system, its subsystems, and other solar systems uses algorithms that was invented. This research has all been primarily Supported by this sequence of PGG NASA grants. During this period published major investigations of tidal evolution of the Earth-Moon system and of the passage of the Earth and Venus through non-linear core-mantle resonances were completed. It has published a major innovation in symplectic algorithms: the symplectic corrector. A paper was completed on non-perturbative hydrostatic equilibrium.
International Nuclear Information System (INIS)
In order to investigate proton transfer reaction in solution, mixed quantum-classical molecular dynamics calculations have been carried out based on our previously proposed quantum equation of motion for the reacting system [A. Yamada and S. Okazaki, J. Chem. Phys. 128, 044507 (2008)]. Surface hopping method was applied to describe forces acting on the solvent classical degrees of freedom. In a series of our studies, quantum and solvent effects on the reaction dynamics in solutions have been analysed in detail. Here, we report our mixed quantum-classical molecular dynamics calculations for intramolecular proton transfer of malonaldehyde in water. Thermally activated proton transfer process, i.e., vibrational excitation in the reactant state followed by transition to the product state and vibrational relaxation in the product state, as well as tunneling reaction can be described by solving the equation of motion. Zero point energy is, of course, included, too. The quantum simulation in water has been compared with the fully classical one and the wave packet calculation in vacuum. The calculated quantum reaction rate in water was 0.70 ps−1, which is about 2.5 times faster than that in vacuum, 0.27 ps−1. This indicates that the solvent water accelerates the reaction. Further, the quantum calculation resulted in the reaction rate about 2 times faster than the fully classical calculation, which indicates that quantum effect enhances the reaction rate, too. Contribution from three reaction mechanisms, i.e., tunneling, thermal activation, and barrier vanishing reactions, is 33:46:21 in the mixed quantum-classical calculations. This clearly shows that the tunneling effect is important in the reaction
Galapon, E A
2001-01-01
We raise the problem of constructing quantum observables that have classical counterparts without quantization. Specifically we seek to define and motivate a solution to the quantum-classical correspondence problem independent from quantization and discuss the general insufficiency of prescriptive quantization, particularly the Weyl quantization. We demonstrate our points by constructing time of arrival operators without quantization and from these recover their classical counterparts.
Dynamical systems theory for music dynamics
Boon, J P
1994-01-01
Abstract:We show that, when music pieces are cast in the form of time series of pitch variations, the concepts and tools of dynamical systems theory can be applied to the analysis of {\\it temporal dynamics} in music. (i) Phase space portraits are constructed from the time series wherefrom the dimensionality is evaluated as a measure of the {\\pit global} dynamics of each piece. (ii) Spectral analysis of the time series yields power spectra (\\sim f^{-\
Directory of Open Access Journals (Sweden)
Tang Bo
2011-05-01
Full Text Available Abstract Background Classical swine fever (CSF, caused by the Classical swine fever virus (CSFV, is an Office International des Epizooties (OIE notifiable disease. However, we are far from fully understand the distribution, tissue tropism, pathogenesis, replication and excretion of CSFV in pigs. In this report, we investigated the dynamic distribution and tissue tropism of the virus in internal organs of the experimentally infected pigs using real-time RT-PCR and immunohistochemistry (IHC. Results A relative quantification real-time PCR was established and used to detect the virus load in internal organs of the experimentally infected pigs. The study revealed that the virus was detected in all 21 of the internal organs and blood collected from pigs at day 1 to day 8 post infections, and had an increasing virus load from day 1 to day 8 post infections. However, there was irregular distribution virus load in most internal organs over the first 2 days post infection. Blood, lymphoid tissue, pancreas and ileum usually contain the highest viral loads, while heart, duodenum and brain show relatively low viral loads. Conclusions All the data suggest that CSFV had an increasing virus load from day 1 to day 8 post infections in experimentally infected pigs detected by real-time RT-PCR, which was in consistent with the result of the IHC staining. The data also show that CSFV was likely to reproduce in blood, lymphoid tissue, pancreas and the ileum, while unlikely to replicate in the heart, duodenum and brain. The results provide a foundation for further clarification of the pathogenic mechanism of CSFV in internal organs, and indicate that blood, lymphoid tissue, pancreas and ileum may be preferred sites of acute infection.
Quantum-mechanical aspects of classically chaotic driven systems
International Nuclear Information System (INIS)
This paper treats atoms and molecules in laser fields as periodically driven quantum systems. The paper concludes by determining that stochastic excitation is possible in quantum systems with quasiperiodic driving. 17 refs
From classical to quantum theory of open systems
International Nuclear Information System (INIS)
The paper presents a short survey of some results concerning the physical interpretation of the basic equations for quantum open systems. The concept of continuous medium for quantum systems is introduced. From this point of view, the question of completeness of a description and hidden parameters (scale) for quantum open systems are considered. The Heisenberg uncertainty principle in the physics of open quantum systems is represented
A New Approach to the Classical and Quantum Dynamics of Branes
Pavšič, Matej
2016-01-01
It is shown that the Dirac-nambu-Goto brane can be described as a point particle in an infinite dimensional brane space with a particular metric. This suggests a generalization to brane spaces with arbitrary metric, including the "flat" metric. Then quantization of such a system is straightforward: it is just like quantization of a bunch of non interacting particles. This leads us to a system of a continuous set of scalar fields. For a particular choice of the metric in the space of fields we find that the classical Dirac-Nambu-Goto brane theory arises as an effective theory of such an underlying quantum field theory. Quantization of branes is important for the brane world scenarios, and thus for "quantum gravity".
A new approach to the classical and quantum dynamics of branes
Pavšič, Matej
2016-07-01
It is shown that the Dirac-Nambu-Goto brane can be described as a point particle in an infinite-dimensional brane space with a particular metric. This suggests a generalization to brane spaces with arbitrary metric, including the “flat” metric. Then quantization of such a system is straightforward: it is just like quantization of a bunch of noninteracting particles. This leads us to a system of a continuous set of scalar fields. For a particular choice of the metric in the space of fields we find that the classical Dirac-Nambu-Goto brane theory arises as an effective theory of such an underlying quantum field theory. Quantization of branes is important for the brane world scenarios, and thus for “quantum gravity.”
Mithen, James P; Gregori, G
2011-01-01
The complementarity of the liquid and plasma descriptions of the classical one-component plasma (OCP) is explored by studying wavevector and frequency dependent dynamical quantities: the dynamical structure factor (DSF), and the dynamic local field correction (LFC). Accurate Molecular Dynamics (MD) simulations are used to validate/test models of the DSF and LFC. Our simulations, which span the entire fluid regime ($\\Gamma = 0.1 - 175$), show that the DSF is very well represented by a simple and well known memory function model of generalized hydrodynamics. On the other hand, the LFC, which we have computed using MD for the first time, is not well described by existing models.
Rodríguez-Lara, B M
2012-01-01
The stability analysis of a generalized Dicke model, in the semi-classical limit, describing the interaction of a two-species Bose-Einstein condensate driven by a quantized field in the presence of Kerr and spontaneous parametric processes is presented. The transitions from Rabi to Josephson dynamics are identified depending on the relative value of the involved parameters. Symmetry-breaking dynamics are shown for both types of coherent oscillations due to the quantized field and nonlinear optical processes.
Modeling temporal morphological systems via lattice dynamical systems
Barrera, Junior; Dougherty, Edward R.; Gubitoso, Marco D.; Hirata, Nina S. T.
2001-05-01
This paper introduces the family of Finite Lattice Dynamical Systems (FLDS), that includes, for example, the family of finite chain dynamical systems. It also gives a constructive algebraic representation for these systems, based on classical lattice operator morphological representations, and formalizes the problem of FLDS identification from stochastic initial condition, input and ideal output. Under acceptable practical conditions, the identification problem reduces to a set of problems of lattice operator design from observed input-output data, that has been extensively studied in the context of designing morphological image operators. Finally, an application of this technique for the identification of Boolean Networks (i.e., Boolean lattice dynamical systems) from simulated data is presented and analyzed.
A Classically Intuitive Discussion of Quantum Spin-1/2 Systems
Durfee, Dallin S
2012-01-01
We arrive at expressions for the x and y basis states for a spin-1/2 system. But rather than deriving them, we come to them using semi-classical arguments about what properties these basis states should have. This approach yields the well known results, but in a way which increases the pedagogical value of the exercise by highlighting the correspondence of the properties of these states with classical notions of orthogonality. We use semi-classical arguments to show that these states must have a certain form but involve several arbitrary parameters. Aside from a global phase factor for each basis state, we show that the arbitrary parameters have a one-to-one correspondence with classical parameters used when defining a three-dimensional Cartesian coordinate system.
Quantum-Classical Connection for Hydrogen Atom-Like Systems
Syam, Debapriyo; Roy, Arup
2011-01-01
The Bohr-Sommerfeld quantum theory specifies the rules of quantization for circular and elliptical orbits for a one-electron hydrogen atom-like system. This article illustrates how a formula connecting the principal quantum number "n" and the length of the major axis of an elliptical orbit may be arrived at starting from the quantum…
Nonadiabatic nuclear dynamics of atomic collisions based on branching classical trajectories
International Nuclear Information System (INIS)
The branching classical trajectory method for inelastic atomic collision processes is proposed. The approach is based on two features: (i) branching of a classical trajectory in a nonadiabatic region and (ii) the nonadiabatic transition probability formulas particularly adapted for a classical trajectory treatment. In addition to transition probabilities and inelastic cross sections, the proposed approach allows one to calculate incoming and outgoing currents. The method is applied to inelastic Na + H collisions providing the results in reasonable agreement with full quantum calculations.
Quantum to Classical Transition in a System of Two Coupled Kicked Rotors
Institute of Scientific and Technical Information of China (English)
ZHAO Wen-Lei; JIE Quan-Lin
2009-01-01
We investigate the quantum-classical transition in a system of two coupled kicked rotors. We find that when the mass of one kicked rotor is much smaller than the other's, the influence of the light kicked rotor is still able to make decoherence of the heavy one. This leads to the quantum-classical transition of the heavy kicked rotor. We demonstrate this by two different coupling potentials.
Unified analysis of terminal-time control in classical and quantum systems
Pechen, Alexander; Rabitz, Herschel
2010-01-01
Many phenomena in physics, chemistry, and biology involve seeking an optimal control to maximize an objective for a classical or quantum system which is open and interacting with its environment. The complexity of finding an optimal control for maximizing an objective is strongly affected by the possible existence of sub-optimal maxima. Within a unified framework under specified conditions, control objectives for maximizing at a terminal time physical observables of open classical and quantum...
Dynamics of stochastic systems
Klyatskin, Valery I
2005-01-01
Fluctuating parameters appear in a variety of physical systems and phenomena. They typically come either as random forces/sources, or advecting velocities, or media (material) parameters, like refraction index, conductivity, diffusivity, etc. The well known example of Brownian particle suspended in fluid and subjected to random molecular bombardment laid the foundation for modern stochastic calculus and statistical physics. Other important examples include turbulent transport and diffusion of particle-tracers (pollutants), or continuous densities (''''oil slicks''''), wave propagation and scattering in randomly inhomogeneous media, for instance light or sound propagating in the turbulent atmosphere.Such models naturally render to statistical description, where the input parameters and solutions are expressed by random processes and fields.The fundamental problem of stochastic dynamics is to identify the essential characteristics of system (its state and evolution), and relate those to the input parameters of ...
Cosmological dynamical systems
Leon, Genly
2014-01-01
In this book are studied, from the perspective of the dynamical systems, several Universe models. In chapter 1 we give a bird's eye view on cosmology and cosmological problems. Chapter 2 is devoted to a brief review on some results and useful tools from the qualitative theory of dynamical systems. They provide the theoretical basis for the qualitative study of concrete cosmological models. Chapters 1 and 2 are a review of well-known results. Chapters 3, 4, 5 and 6 are devoted to our main results. In these chapters are extended and settled in a substantially different, more strict mathematical language, several results obtained by one of us in arXiv:0812.1013 [gr-qc]; arXiv:1009.0689 [gr-qc]; arXiv:0904.1577[gr-qc]; and arXiv:0909.3571 [hep-th]. In chapter 6, we provide a different approach to the subject discussed in astro-ph/0503478. Additionally, we perform a Poincar\\'e compactification process allowing to construct a global phase space containing all the cosmological information in both finite and infinite...
A Monitoring Approach for Dynamic Service-Oriented Architecture Systems
Dan, Yufang; Stouls, Nicolas; Frénot, Stéphane; Colombo, Christian
2012-01-01
International audience In the context of Dynamic Service-oriented Architecture(SOA), where services may dynamically appear or disappear transparently to the user, classical monitoring approaches which inject monitors into services cannot be used. We argue that, since SOA services are loosely coupled, monitors must also be loosely coupled. In this paper, we describe an ongoing work proposing a monitoring approach dedicated to dynamic SOA systems. We defined two key properties of loosely cou...
Field theory and weak Euler-Lagrange equation for classical particle-field systems
Qin, Hong; Davidson, Ronald C
2015-01-01
It is commonly believed as a fundamental principle that energy-momentum conservation of a physical system is the result of space-time symmetry. However, for classical particle-field systems, e.g., charged particles interacting through self-consistent electromagnetic or electrostatic fields, such a connection has only been cautiously suggested. It has not been formally established. The difficulty is due to the fact that the dynamics of particles and the electromagnetic fields reside on different manifolds. We show how to overcome this difficulty and establish the connection by generalizing the Euler-Lagrange equation, the central component of a field theory, to a so-called weak form. The weak Euler-Lagrange equation induces a new type of flux, called the weak Euler-Lagrange current, which enters conservation laws. Using field theory together with the weak Euler-Lagrange equation developed here, energy-momentum conservation laws that are difficult to find otherwise can be systematically derived from the underly...
Rydberg atoms in external fields as an example of open quantum systems with classical chaos
International Nuclear Information System (INIS)
We examine the quantum spectra of hydrogen atoms in external magnetic and electric fields above the ionization threshold with respect to signatures of classical chaos characteristics of open systems. The spectra are obtained by calculating wavefunctions and photionization cross sections in the continuum region with the aid of the complex-coordinate-rotation method. We find that the photoionization cross sections exhibit strong Ericson fluctuations, a quantum feature characteristic of classically chaotic scattering, in energy-field regions where classical trajectory calculations reveal a fractal dependence of the classical ionization time on the initial conditions. We also compare the nearest-neighbour-spacing distributions of complex resonance energies with predictions of random-matrix theories and find that our results are well reproduced by a Ginibre distribution. (author)
Durt, Thomas
2010-01-01
According to the so-called Quantum Darwinist approach, the emergence of "classical islands" from a quantum background is assumed to obey a (selection) principle of maximal information. We illustrate this idea by considering the coupling of two oscillators (modes). As our approach suggests that the classical limit could have emerged throughout a long and progressive Evolution mechanism, it is likely that primitive living organisms behave in a "more quantum", "less classical" way than more evolved ones. This brings us to seriously consider the possibility to measure departures from classicality exhibited by biological systems. We describe an experimental proposal the aimed at revealing the presence of entanglement in the biophotonic radiation emitted by biological sources.
Magnetism of classical and quantum systems of localized spins
International Nuclear Information System (INIS)
The static critical properties of localized are studied spin systems. Several models are discussed: (a) the anisotropic quantum Heisenberg ferromagnet on square lattice (with quenched bond-dilution and random anisotropy) and on simple cubic lattice; (b) the Z(4) ferromagnetic model on square lattice; (c) the Ising model on the Cayley tree, in the presence of competing interactions. The (a) and (b) problems are studied within a real-space Renormalisation Group (RG) approach. In both cases, methods to perform the relevant partial tracings, that are better than those available in the literature are developed. The critical frontiers obtained reproduce all known exact results, and they are high precision ones everywhere. Correlation lenght critical exponents (υ) and the crossover exponents (Φ) are also calculated. The values are, in degree of approximation, equal or superior to those obtained using the Migdal-Kadanoff RG. The (c) problem is investigated by constructing recursive relations (similar to RG); the resulting phase diagram (numerically exact) presents a set of modulated phases, besides the ferromagnetic, antiferromagnetic and paramagnetic ones. It is worth to stress the presence of metastability phenomena and the existence of the paramagnetic phase at arbitrary non-vanishing small temperatures. In addition to the previous works a study of the energy eigenvalues and the specific heat of a general anharmonic single quantum oscillator, by using the Turschner and WKB approximations was performed. Comparisons between them, exhibit the superiority of the Turschner approximation. (author)
Adapting classical Systems Engineering to Department of Energy (DOE) needs
Energy Technology Data Exchange (ETDEWEB)
NONE
1996-07-01
Rather than discuss Systems Engineering (SE) as applied by aerospace contractors to military programs, this document provides an adapted model well suited for use by DOE and represents 18 months of applying SE principles to the challenges faced by INEL. The real-life examples are drawn from INEL`s ongoing effort to integrate activities across the entire spectrum of within its Environmental Management program. Since the traditional SE process, with its initial focus on requirements identification and analysis, must be modified to provide tangible results in the short term, the adapted SE model starts with the external driver of ``reducing costs without increasing risks`` and performs an initial integration effort to identify high-potential, cost-saving opportunities. Elements from traditional alternatives development and analysis stages are used; then the adapted model cycles back to include more traditional requirements analysis activities. These cycles continue in an iterative manner, adding rigor and detail at each successive iteration, throughout the life-cycle of a program or project. Detailed lessons learned are included.
Solar system dynamics in general relativity
Battista, Emmanuele; Esposito, Giampiero; Di Fiore, Luciano; Simo, Jules; Grado, Aniello
2016-01-01
Recent work in the literature has advocated using the Earth-Moon-planetoid Lagrangian points as observables, in order to test general relativity and effective field theories of gravity in the solar system. However, since the three-body problem of classical celestial mechanics is just an approximation of a much more complicated setting, where all celestial bodies in the solar system are subject to their mutual gravitational interactions, while solar radiation pressure and other sources of nongravitational perturbations also affect the dynamics, it is conceptually desirable to improve the current understanding of solar system dynamics in general relativity, as a first step towards a more accurate theoretical study of orbital motion in the weak-gravity regime. For this purpose, starting from the Einstein equations in the de Donder-Lanczos gauge, this paper arrives first at the Levi-Civita Lagrangian for the geodesic motion of celestial bodies, showing in detail under which conditions the effects of internal stru...
Horwitz, L. P.; Land, Martin C.; Gill, Tepper; Lusanna, Luca; Salucci, Paolo
2013-04-01
Although the subject of relativistic dynamics has been explored, from both classical and quantum mechanical points of view, since the work of Einstein and Dirac, its most striking development has been in the framework of quantum field theory. The very accurate calculations of spectral and scattering properties, for example, of the anomalous magnetic moment of the electron and the Lamb shift in quantum electrodynamics, and many qualitative features of the strong and electroweak interactions, demonstrate the very great power of description achieved in this framework. Yet, many fundamental questions remain to be clarified, such as the structure of classical relativistic dynamical theories on the level of Hamilton and Lagrange in Minkowski space as well as on the curved manifolds of general relativity. There moreover remains the important question of the covariant classical description of systems at high energy for which particle production effects are not large, such as discussed in Synge's book, The Relativistic Gas, and in Balescu's book on relativistic statistical mechanics. In recent years, the study of high energy plasmas and heavy ion collisions has emphasized the importance of developing the techniques of relativistic mechanics. The results of Lindner et al [Physical Review Letters 95 0040401 (2005)] as well as the more recent proposal of Palacios et al [Phys. Rev. Lett. 103 253001 (2009)] and others, have shown that there must be a quantum theory with coherence in time. Such a theory, manifestly covariant under the transformations of special relativity with an invariant evolution parameter, such as that of Stueckelberg [Helv. Phys. Acta 14 322, 588 (1941); 15 23 (1942); see also R P Feynman Phys. Rev. 80 4401 and J S Schwinger Phys. Rev. 82 664 (1951)] could provide a suitable basis for the study of such questions, as well as many others for which the application of the standard methods of quantum field theory are difficult to manage, involving, in particular
Generation of a Tunable Environment for the Simulation of Excitonic Transport in Classical Systems
León-Montiel, R de J; Torres, Juan P
2014-01-01
The simulation and modeling of open systems has become an invaluable tool for understanding several processes that take place in physical, chemical and biological systems. An example of paramount importance is photosynthesis, a biological process that involves the transport of energy with a remarkable high efficiency to a reaction center. Recently, it has been shown that classical oscillator systems can be used to model the transport and coherence properties of molecular aggregates, in particular those of light-harvesting complexes. Even though the simulation of coherent evolution of classical oscillator systems can be easily implemented, the question on how to experimentally introduce and control dephasing effects due to a surrounding environment remains open. Here, we put forward a setup that provides an unique tool to generate a tunable environment for classical electrical oscillators. We illustrate the operation of the setup by considering the case of a damped random frequency harmonic oscillator. To demo...
Upper quantum Lyapunov Exponent and Anosov relations for quantum systems driven by a classical flow
Sapin, O; Weigert, S
2005-01-01
We generalize the definition of quantum Anosov properties and the related Lyapunov exponents to the case of quantum systems driven by a classical flow, i.e. skew-product systems. We show that the skew Anosov properties can be interpreted as regular Anosov properties in an enlarged Hilbert space, in the framework of a generalized Floquet theory. This extension allows us to describe the hyperbolicity properties of almost-periodic quantum parametric oscillators and we show that their upper Lyapunov exponents are positive and equal to the Lyapunov exponent of the corresponding classical parametric oscillators. As second example, we show that the configurational quantum cat system satisfies quantum Anosov properties.
Particle dynamics in nanopore systems
Krems, Matthew A.
2011-01-01
In this dissertation, I discuss various aspects of the dynamics of charged particles in nanopore systems. In recent years, there have been numerous studies of organic and inorganic nanopores. Nonetheless, there is still much to be understood about these systems. I begin by summarizing some of the important literature on nanopore systems as well as the dynamics of ions in aqueous solutions. An important tool for studying these systems at the nanoscopic level has been molecular dynamics. Some o...
Torrielli, Alessandro
2016-08-01
We review some essential aspects of classically integrable systems. The detailed outline of the sections consists of: 1. Introduction and motivation, with historical remarks; 2. Liouville theorem and action-angle variables, with examples (harmonic oscillator, Kepler problem); 3. Algebraic tools: Lax pairs, monodromy and transfer matrices, classical r-matrices and exchange relations, non-ultralocal Poisson brackets, with examples (non-linear Schrödinger model, principal chiral field); 4. Features of classical r-matrices: Belavin–Drinfeld theorems, analyticity properties, and lift of the classical structures to quantum groups; 5. Classical inverse scattering method to solve integrable differential equations: soliton solutions, spectral properties and the Gel’fand–Levitan–Marchenko equation, with examples (KdV equation, Sine-Gordon model). Prepared for the Durham Young Researchers Integrability School, organised by the GATIS network. This is part of a collection of lecture notes.
Mould, Richard A
2003-01-01
Preciously given rules allow conscious systems to be included in quantum mechanical systems. There rules are derived from the empirical experience of an observer who witnesses a quantum mechanical interaction leading to the capture of a single particle. In the present paper it is shown that purely classical changes experienced by an observer are consistent with these rules. Three different interactions are considered, two of which combine classical and quantum mechanical changes. The previous...
Dynamic Modeling of ALS Systems
Jones, Harry
2002-01-01
The purpose of dynamic modeling and simulation of Advanced Life Support (ALS) systems is to help design them. Static steady state systems analysis provides basic information and is necessary to guide dynamic modeling, but static analysis is not sufficient to design and compare systems. ALS systems must respond to external input variations and internal off-nominal behavior. Buffer sizing, resupply scheduling, failure response, and control system design are aspects of dynamic system design. We develop two dynamic mass flow models and use them in simulations to evaluate systems issues, optimize designs, and make system design trades. One model is of nitrogen leakage in the space station, the other is of a waste processor failure in a regenerative life support system. Most systems analyses are concerned with optimizing the cost/benefit of a system at its nominal steady-state operating point. ALS analysis must go beyond the static steady state to include dynamic system design. All life support systems exhibit behavior that varies over time. ALS systems must respond to equipment operating cycles, repair schedules, and occasional off-nominal behavior or malfunctions. Biological components, such as bioreactors, composters, and food plant growth chambers, usually have operating cycles or other complex time behavior. Buffer sizes, material stocks, and resupply rates determine dynamic system behavior and directly affect system mass and cost. Dynamic simulation is needed to avoid the extremes of costly over-design of buffers and material reserves or system failure due to insufficient buffers and lack of stored material.
Pilecki, B; Gieren, W; Pietrzyński, G; Thompson, I B; Smolec, R; Udalski, A; Soszyński, I; Konorski, P; Taormina, M; Gallenne, A; Minniti, D; Catelan, M
2015-01-01
We present here the first spectroscopic and photometric analysis of the double-lined eclipsing binary containing the classical, first-overtone Cepheid OGLE-LMC-CEP-2532 (MACHO 81.8997.87). The system has an orbital period of 800 days and the Cepheid is pulsating with a period of 2.035 days. Using spectroscopic data from three high-class telescopes and photometry from three surveys spanning 7500 days we are able to derive the dynamical masses for both stars with an accuracy better than 3%. This makes the Cepheid in this system one of a few classical Cepheids with an accurate dynamical mass determination (M_1=3.90 +/- 0.10 M_sun). The companion is probably slightly less massive (3.82 +/- 0.10 M_sun), but may have the same mass within errors (M_2/M_1= 0.981 +/- 0.015). The system has an age of about 185 million years and the Cepheid is in a more advanced evolutionary stage. For the first time precise parameters are derived for both stars in this system. Due to the lack of the secondary eclipse for many years not...
Directory of Open Access Journals (Sweden)
Stanislaw Sieniutycz
1998-06-01
Full Text Available We deal with applications of thermodynamics and availability theory to practical systems where a certain external control is possible in order to achieve improved performance. In particular, results of optimization of endoreversible processes which yield mechanical work are discussed. Equations of dynamics which follow from energy balance and transfer equations are difference constraints for optimizing work. Irreversibilities caused by the energy transport are essential. A model system is developed which incorporates finite heat resistances for an energy conversion process, and may be extended to take into account friction, heat leakage, mixing and other effects decreasing the thermodynamic efficiency. Deviation of efficiencies from their limiting Carnot values are analyzed in terms of the finite heat flux. The variational calculus and optimal control theories are shown to be the basic tools when formulating and solving problems with maximizing work. For a finite-time passage of a resource body between two given temperatures, optimality of an irreversible process manifests itself as a connection between the process duration and an optimal intensity. Extremal performance functions which describe extremal work are found in terms of final states and process duration measured in terms of the number of the heat transfer units. An extended exergy that has an irreversible component and simplifies to the classical thermal exergy in the limit of infinite duration is discussed. With this exergy performance criteria and bounds are defined for real processes occurring in a finite time. Enhanced bounds for the work released from an engine system or added to a heat-pump system are evaluated. A comparison between the optimization in thermodynamics (with exergy and in economics (with costs is made. Examples of exergy analysis to seek the best adjustable parameters of solar collectors, separation processes (distillation and a chemical process with catalyst
On the quantum dynamics of non-commutative systems
Bemfica, F. S.; Girotti, H. O.
2007-01-01
This is a review paper concerned with the global consistency of the quantum dynamics of non-commutative systems. Our point of departure is the theory of constrained systems, since it provides a unified description of the classical and quantum dynamics for the models under investigation. We then elaborate on recently reported results concerned with the sufficient conditions for the existence of the Born series and unitarity and turn, afterwards, into analyzing the functional quantization of no...
Energy Technology Data Exchange (ETDEWEB)
Ganster, P
2004-10-15
A calcium aluminosilicate glass of molar composition 67 % SiO{sub 2} - 12 % Al{sub 2}O{sub 3} - 21 % CaO was modelled by classical and ab initio molecular dynamics. The size effect study in classical MD shows that the systems of 100 atoms are more ordered than the larger ones. These effects are mainly due to the 3-body terms in the empirical potentials. Nevertheless, these effects are small and the structures generated are in agreement with experimental data. In such kind of glass, we denote an aluminium avoidance and an excess of non bridging oxygens which can be compensated by tri coordinated oxygens. When the dynamics of systems of 100 and 200 atoms is followed by ab initio MD, some local arrangements occurs (bond length, angular distributions). Thus, more realistic vibrational properties are obtained in ab initio MD. The modelling of thin films shows that aluminium atoms extend to the most external part of the surface and they are all tri-coordinated. Calcium atoms are set in the sub layer part of the surface and they produce a depolymerization of the network. In classical MD, tri-coordinated aluminium atoms produce an important electric field above the surface. With non bridging oxygens, they constitute attractive sites for single water molecules. (author)
Cotton, Stephen J; Miller, William H
2016-03-01
In a recent series of papers, it has been illustrated that a symmetrical quasi-classical (SQC) windowing model applied to the Meyer-Miller (MM) classical vibronic Hamiltonian provides an excellent description of a variety of electronically non-adiabatic benchmark model systems for which exact quantum results are available for comparison. In this paper, the SQC/MM approach is used to treat energy transfer dynamics in site-exciton models of light-harvesting complexes, and in particular, the well-known 7-state Fenna-Mathews-Olson (FMO) complex. Again, numerically "exact" results are available for comparison, here via the hierarchical equation of motion (HEOM) approach of Ishizaki and Fleming, and it is seen that the simple SQC/MM approach provides very reasonable agreement with the previous HEOM results. It is noted, however, that unlike most (if not all) simple approaches for treating these systems, because the SQC/MM approach presents a fully atomistic simulation based on classical trajectory simulation, it places no restrictions on the characteristics of the thermal baths coupled to each two-level site, e.g., bath spectral densities (SD) of any analytic functional form may be employed as well as discrete SD determined experimentally or from MD simulation (nor is there any restriction that the baths be harmonic), opening up the possibility of simulating more realistic variations on the basic site-exciton framework for describing the non-adiabatic dynamics of photosynthetic pigment complexes. PMID:26761191
Collective dynamics of multicellular systems
Indian Academy of Sciences (India)
R Maithreye; C Suguna; Somdatta Sinha
2011-11-01
We have studied the collective behaviour of a one-dimensional ring of cells for conditions when the individual uncoupled cells show stable, bistable and oscillatory dynamics. We show that the global dynamics of this model multicellular system depends on the system size, coupling strength and the intrinsic dynamics of the cells. The intrinsic variability in dynamics of the constituent cells are suppressed to stable dynamics, or modiﬁed to intermittency under different conditions. This simple model study reveals that cell–cell communication, system size and intrinsic cellular dynamics can lead to evolution of collective dynamics in structured multicellular biological systems that is signiﬁcantly different from its constituent single-cell behaviour.
Non-existence of Physical Classical Solutions to Euler's Equations of Rigid Body Dynamics
Wilkinson, Mark
2015-01-01
We prove that one cannot construct, for arbitrary initial data, global-in-time physical classical solutions to Euler's equations of continuum rigid body mechanics when the constituent rigid bodies are not perfect spheres. By 'physical' solutions, we mean those that conserve the total linear momentum, angular momentum and kinetic energy of any given initial datum. The reason for absence of classical solutions is due to the non-existence of velocity scattering maps which resolve a collision bet...
On precise time integration method for non-classically damped MDOF systems
Institute of Scientific and Technical Information of China (English)
Wang Mengfu; Zhou Xiyuan
2006-01-01
In the complex mode superposition method, the equations of motion for non-classically damped multipledegree-of-freedom (MDOF) discrete systems can be transferred into a combination of some generalized SDOF complex oscillators. Based on the state space theory, a precise recurrence relationship for these complex oscillators is set up; then a delicate general solution of non-classically damped MDOF systems, completely in real value form, is presented in this paper.In the proposed method, no calculation of the matrix exponential function is needed and the algorithm is unconditionally stable. A numerical example is given to demonstrate the validity and efficiency of the proposed method.
Popa, Alexandru
2013-01-01
Applications of Quantum and Classical Connections in Modeling Atomic, Molecular and Electrodynamical Systems is a reference on the new field of relativistic optics, examining topics related to relativistic interactions between very intense laser beams and particles. Based on 30 years of research, this unique book connects the properties of quantum equations to corresponding classical equations used to calculate the energetic values and the symmetry properties of atomic, molecular and electrodynamical systems. In addition, it examines applications for these methods, and for the calculation of
Milburn, T J; Vanner, M R
2016-01-01
Non-classical state generation is an important component throughout experimental quantum science for quantum information applications and probing the fundamentals of physics. Here, we investigate permutations of quantum measurements of discrete and continuous degrees-of-freedom to prepare quantum superposition states in bosonic systems. Our approach is ideally suited for implementation in light-matter systems such as quantum optomechanics and atomic spin ensembles, and offers considerable robustness to initial thermal occupation. The performance of each measurement permutation is quantified and compared using several different non-classicality criteria.
Carnevale, V.; Raugei, S.
2009-12-01
Lysine acetylation is a post-translational modification, which modulates the affinity of protein-protein and/or protein-DNA complexes. Its crucial role as a switch in signaling pathways highlights the relevance of charged chemical groups in determining the interactions between water and biomolecules. A great effort has been recently devoted to assess the reliability of classical molecular dynamics simulations in describing the solvation properties of charged moieties. In the spirit of these investigations, we performed classical and Car-Parrinello molecular dynamics simulations on lysine and acetylated-lysine in aqueous solution. A comparative analysis between the two computational schemes is presented with a focus on the first solvation shell of the charged groups. An accurate structural analysis unveils subtle, yet statistically significant, differences which are discussed in connection to the significant electronic density charge transfer occurring between the solute and the surrounding water molecules.
International Nuclear Information System (INIS)
Lysine acetylation is a post-translational modification, which modulates the affinity of protein-protein and/or protein-DNA complexes. Its crucial role as a switch in signaling pathways highlights the relevance of charged chemical groups in determining the interactions between water and biomolecules. A great effort has been recently devoted to assess the reliability of classical molecular dynamics simulations in describing the solvation properties of charged moieties. In the spirit of these investigations, we performed classical and Car-Parrinello molecular dynamics simulations on lysine and acetylated-lysine in aqueous solution. A comparative analysis between the two computational schemes is presented with a focus on the first solvation shell of the charged groups. An accurate structural analysis unveils subtle, yet statistically significant, differences which are discussed in connection to the significant electronic density charge transfer occurring between the solute and the surrounding water molecules.
Classical linear-control analysis applied to business-cycle dynamics and stability
Wingrove, R. C.
1983-01-01
Linear control analysis is applied as an aid in understanding the fluctuations of business cycles in the past, and to examine monetary policies that might improve stabilization. The analysis shows how different policies change the frequency and damping of the economic system dynamics, and how they modify the amplitude of the fluctuations that are caused by random disturbances. Examples are used to show how policy feedbacks and policy lags can be incorporated, and how different monetary strategies for stabilization can be analytically compared. Representative numerical results are used to illustrate the main points.
Landscape Construction in Dynamical Systems
Tang, Ying; Yuan, Ruoshi; Wang, Gaowei; Ao, Ping
The idea of landscape has been recently applied to study various of biological problems. We demonstrate that a dynamical structure built into nonlinear dynamical systems allows us to construct such a global optimization landscape, which serves as the Lyapunov function for the ordinary differential equation. We find exact constructions on the landscape for a class of dynamical systems, including a van der Pol type oscillator, competitive Lotka-Volterra systems, and a chaotic system. The landscape constructed provides a new angle for understanding and modelling biological network dynamics.
Solving dynamical inverse problems by means of Metabolic P systems.
Manca, V; Marchetti, L
2012-07-01
MP (Metabolic P) systems are a class of P systems introduced for modelling metabolic processes. We refer to the dynamical inverse problem as the problem of identifying (discrete) mathematical models exhibiting an observed dynamics. In this paper, we complete the definition of the algorithm LGSS (Log-gain Stoichiometric Stepwise regression) introduced in Manca and Marchetti (2011) for solving a general class of dynamical inverse problems. To this aim, we develop a reformulation of the classical stepwise regression in the context of MP systems. We conclude with a short review of two applications of LGSS for discovering the internal regulation logic of two phenomena relevant in systems biology. PMID:22261639
Modelling of Classical and Rotary Inverted Pendulum Systems - A Generalized Approach
Jadlovský, Slávka; Sarnovský, Ján
2013-01-01
The purpose of this paper is to present the design and program implementation of a general procedure which yields the mathematical model for a classical or rotary inverted pendulum system with an arbitrary number of pendulum links. Lagrange equations of the second kind with an integrated Rayleigh dissipation function are employed in model design, and the energetic balance relations, derived for the base and all pendulum links in a generalized (n-link) classical and rotary inverted pendulum system, are implemented in form of symbolic MATLAB functions and a MATLAB GUI application. The validity and accuracy of motion equations generated by the application are demonstrated by evaluating the open-loop responses of simulation models of classical double and rotary single inverted pendulum.
Spectrum of quantum transfer matrices via classical many-body systems
International Nuclear Information System (INIS)
In this paper we clarify the relationship between inhomogeneous quantum spin chains and classical integrable many-body systems. It provides an alternative (to the nested Bethe ansatz) method for computation of spectra of the spin chains. Namely, the spectrum of the quantum transfer matrix for the inhomogeneous gln-invariant XXX spin chain on N sites with twisted boundary conditions can be found in terms of velocities of particles in the rational N-body Ruijsenaars-Schneider model. The possible values of the velocities are to be found from intersection points of two Lagrangian submanifolds in the phase space of the classical model. One of them is the Lagrangian hyperplane corresponding to fixed coordinates of all N particles and the other one is an N-dimensional Lagrangian submanifold obtained by fixing levels of N classical Hamiltonians in involution. The latter are determined by eigenvalues of the twist matrix. To support this picture, we give a direct proof that the eigenvalues of the Lax matrix for the classical Ruijsenaars-Schneider model, where velocities of particles are substituted by eigenvalues of the spin chain Hamiltonians, calculated through the Bethe equations, coincide with eigenvalues of the twist matrix, with certain multiplicities. We also prove a similar statement for the gln Gaudin model with N marked points (on the quantum side) and the Calogero-Moser system with N particles (on the classical side). The realization of the results obtained in terms of branes and supersymmetric gauge theories is also discussed
International Nuclear Information System (INIS)
Dynamic equations in the theory of a relativistic string with point masses at the ends are formulated in terms of geometric invariants of the world trajectories of the massive ends of the string (curvature ki and torsion κi(τ), i=1,2 of the trajectories). With these characteristics we reproduce the string world surface up to its position in Minkowski space E21. The torsions κi(τ), i=1,2 obey a system of second order differential equations with delay arguments describing the retardation effects of the interaction of masses through the string, ki being constants. The constant torsions are investigated in detail. In this case the string world sheet is a helicoid in E21. A nonlinear relation (the Regge trajectory) between the angular momentum of the system, J and the mass squared, M2, is derived. For given meson masses (M) and spin (J), the masses of quarks are calculated. 14 refs., 1 fig., 1 tab
Propagation of General Wave Packets in Some Classical and Quantum Systems
Institute of Scientific and Technical Information of China (English)
LIN Qiong-Gui
2006-01-01
In quantum mechanics the center of a wave packet is precisely defined as the center of probability. The center-of-probability velocity describes the entire motion of the wave packet. In classical physics there is no precise counterpart to the center-of-probability velocity of quantum mechanics, in spite of the fact that there exist in the literature at least eight different velocities for the electromagnetic wave. We propose a center-of-energy velocity to describe the entire motion of general wave packets in classical physical systems. It is a measurable quantity, and is well defined for both continuous and discrete systems. For electromagnetic wave packets it is a generalization of the velocity of energy transport. General wave packets in several classical systems are studied and the center-of-energy velocity is calculated and expressed in terms of the dispersion relation and the Fourier coefficients. These systems include string subject to an external force, monatomic chain and diatomic chain in one dimension, and classical Heisenberg model in one dimension. In most cases the center-of-energy velocity reduces to the group velocity for quasi-monochromatic wave packets. Thus it also appears to be the generalization of the group velocity. Wave packets of the relativistic Dirac equation are discussed briefly.
Energy Technology Data Exchange (ETDEWEB)
Morisseau, Francois [Laboratoire de Physique Corpusculaire de CAEN, ENSICAEN, Universite de Caen Basse-Normandie, UFR des Sciences, 6 bd Marechal Juin, 14050 Caen Cedex (France)
2006-05-15
The Classical N-body Dynamics (CNBD) is dedicated to the simulation of collisions between classical systems. The 2-body interaction used here has the properties of the Van der Waals potential and depends on just a few parameters. This work has two main goals. First, some theoretical approaches assume that the dynamical stage of the collisions plays an important role. Moreover, colliding nuclei are supposed to present a 1. order liquid-gas phase transition. Several signals have been introduced to show this transition. We have searched for two of them: the bimodality of the mass asymmetry and negative heat capacity. We have found them and we give an explanation of their presence in our calculations. Second, we have improved the interaction by adding a Coulomb like potential and by taking into account the stronger proton-neutron interaction in nuclei. Then we have figured out the relations that exist between the parameters of the 2-body interaction and the properties of the systems. These studies allow us to fit the properties of the classical systems to those of the nuclei. In this manuscript the first results of this fit are shown. (author)
Quantum Dynamics on the Worldvolume from Classical su(n Cohomology
Directory of Open Access Journals (Sweden)
José M. Isidro
2008-04-01
Full Text Available A key symmetry of classical p-branes is invariance under worldvolume diffeomorphisms. Under the assumption that the worldvolume, at fixed values of the time, is a compact, quantisable Kähler manifold, we prove that the Lie algebra of volume-preserving diffeomorphisms of the worldvolume can be approximated by su(n, for n → ∞. We also prove, under the same assumptions regarding the worldvolume at fixed time, that classical Nambu brackets on the worldvolume are quantised by the multibrackets corresponding to cocycles in the cohomology of the Lie algebra su(n.
Semi-classical Dynamics of Superradiant Rayleigh Scattering in a Bose-Einstein Condensate
Müller, J H; Targat, R le; Arlt, J J; Polzik, E S; Hilliard, A J
2016-01-01
Due to its coherence properties and high optical depth, a Bose-Einstein condensate provides an ideal setting to investigate collective atom-light interactions. Superradiant light scattering in a Bose-Einstein condensate is a fascinating example of such an interaction. It is an analogous process to Dicke superradiance, in which an electronically inverted sample decays collectively, leading to the emission of one or more light pulses in a well-defined direction. Through time-resolved measurements of the superradiant light pulses emitted by an end-pumped BEC, we study the close connection of superradiant light scattering with Dicke superradiance. A 1D model of the system yields good agreement with the experimental data and shows that the dynamics results from the structures that build up in the light and matter-wave fields along the BEC. This paves the way for exploiting the atom-photon correlations generated by the superradiance.
New formulation of the classical dynamics of the relativistic string with massive ends
International Nuclear Information System (INIS)
Dynamic equations in the theory of a relativistic string with point masses at the ends are formulated only in terms of geometric invariants of the world trajectories of the massive ends of the string (curvature k1 and torsion k1 of the trajectories). These characteristics allow us to reproduce the string world surface up to shifts and rotations in the Minkowski space E21. The torsions k1(r) (1=1,2) obey a system of differential equations of the second order with shifted arguments describing the retardation effects of the interaction of masses through the string, k1 being constant. New particular solutions to these equations that correspond to periodic torsions will be discussed in the next paper. 12 refs
Pilecki, Bogumił; Graczyk, Dariusz; Gieren, Wolfgang; Pietrzyński, Grzegorz; Thompson, Ian B.; Smolec, Radosław; Udalski, Andrzej; Soszyński, Igor; Konorski, Piotr; Taormina, Mónica; Gallenne, Alexandre; Minniti, Dante; Catelan, Márcio
2015-06-01
We present here the first spectroscopic and photometric analysis of the double-lined eclipsing binary containing the classical, first-overtone (FO) Cepheid OGLE-LMC-CEP-2532 (MACHO 81.8997.87). The system has an orbital period of 800 days and the Cepheid is pulsating with a period of 2.035 days. Using spectroscopic data from three high-class telescopes and photometry from three surveys spanning 7500 days, we are able to derive the dynamical masses for both stars with an accuracy better than 3%. This makes the Cepheid in this system one of a few classical Cepheids with an accurate dynamical mass determination ({{M}1}=3.90+/- 0.10 {{M}⊙ }). The companion is probably slightly less massive (3.82+/- 0.10 {{M}⊙ }), but may have the same mass within errors ({{M}2}/{{M}1}=0.981+/- 0.015). The system has an age of about 185 million years and the Cepheid is in a more advanced evolutionary stage. For the first time precise parameters are derived for both stars in this system. Due to the lack of the secondary eclipse for many years, not much was known about the Cepheid’s companion. In our analysis, we used extra information from the pulsations and the orbital solution from the radial velocity curve. The best model predicts a grazing secondary eclipse shallower than 1 mmag, hence undetectable in the data, about 370 days after the primary eclipse. The dynamical mass obtained here is the most accurate known for a FO Cepheid and will contribute to the solution of the Cepheid mass discrepancy problem. The research is based on observations obtained with the ESO VLT and 3.6 m telescopes for Programmes 092.D-0295(A), 091.D-0393(A), 089.D-0330(A), 088.D-0447(A), 086.D-0103(A), and 085.D-0398(A), and with the Magellan Clay and Warsaw telescopes at Las Campanas Observatory.
Schwörer, Magnus; Lorenzen, Konstantin; Mathias, Gerald; Tavan, Paul
2015-03-14
Recently, a novel approach to hybrid quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) simulations has been suggested [Schwörer et al., J. Chem. Phys. 138, 244103 (2013)]. Here, the forces acting on the atoms are calculated by grid-based density functional theory (DFT) for a solute molecule and by a polarizable molecular mechanics (PMM) force field for a large solvent environment composed of several 10(3)-10(5) molecules as negative gradients of a DFT/PMM hybrid Hamiltonian. The electrostatic interactions are efficiently described by a hierarchical fast multipole method (FMM). Adopting recent progress of this FMM technique [Lorenzen et al., J. Chem. Theory Comput. 10, 3244 (2014)], which particularly entails a strictly linear scaling of the computational effort with the system size, and adapting this revised FMM approach to the computation of the interactions between the DFT and PMM fragments of a simulation system, here, we show how one can further enhance the efficiency and accuracy of such DFT/PMM-MD simulations. The resulting gain of total performance, as measured for alanine dipeptide (DFT) embedded in water (PMM) by the product of the gains in efficiency and accuracy, amounts to about one order of magnitude. We also demonstrate that the jointly parallelized implementation of the DFT and PMM-MD parts of the computation enables the efficient use of high-performance computing systems. The associated software is available online. PMID:25770527
Roy, H.; Chandraker, S.; Dutt, J. K.; Roy, T.
2016-05-01
Inherent material damping plays a very significant role on dynamic behaviour of rotors. The material damping in a spinning rotor produces a tangential force along the whirl direction and its magnitude being proportional to spin speed. After certain value of spin speed, decided by the characteristic of the system, the tangential force becomes strong enough to throw the rotor centre out of the whirl orbit by inflating it progressively. This leads to destabilization of the system and corresponding speed is known as stability limit of spin speed. Stability limit of spin speed for Jeffcott rotor, by using viscous form of material damping model is straight forward and has been reported by several researchers, however the same analysis for viscoelastic material characteristics is not reported much. This analysis is very relevant for industrial requirements to replace bulky and heavy metal rotor by light but strong rotors. This is achieved either by reinforcing fibre or multi layering arrangements. Both of which are represented by viscoelastic constitutive behaviour. This paper gives mathematical derivation of equations of motion for multi-disc, multi-layered rotor-shaft-system. Both lumped mass and discretized approach (finite element) are presented here mathematically and numerical simulation results are compared. The lumped mass approach gives a concise yet acceptable accuracy of the results.
Semiclassical Aspects of Quantum Mechanics by Classical Fluctuations
De Martino, S; Illuminati, F; Martino, Salvatore De; Siena, Silvio De
1998-01-01
Building on a model recently proposed by F. Calogero, we postulate the existence of a coherent, long--range universal tremor affecting any stable and confined classical dynamical system. Deriving the characteristic fluctuative unit of action for each classical interaction, we obtain in all cases its numerical coincidence with the Planck action constant. We therefore suggest that quantum corrections to classical dynamics can be simulated by suitable classical stochastic fluctuations.
On Causality in Dynamical Systems
Harnack, Daniel
2016-01-01
Identification of causal links is fundamental for the analysis of complex systems. In dynamical systems, however, nonlinear interactions may hamper separability of subsystems which poses a challenge for attempts to determine the directions and strengths of their mutual influences. We found that asymmetric causal influences between parts of a dynamical system lead to characteristic distortions in the mappings between the attractor manifolds reconstructed from respective local observables. These distortions can be measured in a model-free, data-driven manner. This approach extends basic intuitions about cause-effect relations to deterministic dynamical systems and suggests a mathematically well defined explanation of results obtained from previous methods based on state space reconstruction.
International Nuclear Information System (INIS)
Under the auspices of the U.S. Nuclear Regulatory Commission (NRC), Brookhaven National Laboratory (BNL) developed a comprehensive program to evaluate state-of-the-art methods and computer programs for seismic analysis of typical coupled nuclear power plant (NPP) systems with non-classical damping. In this program, four benchmark models of coupled building-piping/equipment systems with different damping characteristics were developed and analyzed by BNL for a suite of earthquakes. The BNL analysis was carried out by the Wilson-θ time domain integration method with the system-damping matrix computed using a synthesis formulation as presented in a companion paper [Nucl. Eng. Des. (2002)]. These benchmark problems were subsequently distributed to and analyzed by program participants applying their uniquely developed methods and computer programs. This paper is intended to offer a glimpse at the program, and provide a summary of major findings and principle conclusions with some representative results. The participant's analysis results established using complex modal time history methods showed good comparison with the BNL solutions, while the analyses produced with either complex-mode response spectrum methods or classical normal-mode response spectrum method, in general, produced more conservative results, when averaged over a suite of earthquakes. However, when coupling due to damping is significant, complex-mode response spectrum methods performed better than the classical normal-mode response spectrum method. Furthermore, as part of the program objectives, a parametric assessment is also presented in this paper, aimed at evaluation of the applicability of various analysis methods to problems with different dynamic characteristics unique to coupled NPP systems. It is believed that the findings and insights learned from this program will be useful in developing new acceptance criteria and providing guidance for future regulatory activities involving license
Danforth, Douglas G.
2001-01-01
Classical systems can be entangled. Entanglement is defined by coincidence correlations. Quantum entanglement experiments can be mimicked by a mechanical system with a single conserved variable and 77.8% conditional efficiency. Experiments are replicated for four particle entanglement swapping and GHZ entanglement.
Systems approaches to study root architecture dynamics
Directory of Open Access Journals (Sweden)
Candela eCuesta
2013-12-01
Full Text Available The plant root system is essential for providing anchorage to the soil, supplying minerals and water, and synthesizing metabolites. It is a dynamic organ modulated by external cues such as environmental signals, water and nutrients availability, salinity and others. Lateral roots are initiated from the primary root post-embryonically, after which they progress through discrete developmental stages which can be independently controlled, providing a high level of plasticity during root system formation.Within this review, main contributions are presented, from the classical forward genetic screens to the more recent high-throughput approaches, combined with computer model predictions, dissecting how lateral roots and thereby root system architecture is established and developed.
Stabilizability of oscillatory systems: a classical approach supported by symbolic computation
Directory of Open Access Journals (Sweden)
Andrea Bacciotti
1990-11-01
Full Text Available In this paper we study the stabilization of planar single-input non-linear systems, whose linearization at the origin has purely immaginary eigenvalues. A classical recursive procedure based on polar coordinates transformation is applied to obtain some sufficient conditions. Then we focus on bilinear systems; a complete solution of the problem is given in this case. Explicit statements of the conditions are possible thanks to the use of symbolic computation packages.
Upper quantum Lyapunov Exponent and Anosov relations for quantum systems driven by a classical flow
Sapin, O.; Jauslin, H. R.; Weigert, S.
2005-01-01
We generalize the definition of quantum Anosov properties and the related Lyapunov exponents to the case of quantum systems driven by a classical flow, i.e. skew-product systems. We show that the skew Anosov properties can be interpreted as regular Anosov properties in an enlarged Hilbert space, in the framework of a generalized Floquet theory. This extension allows us to describe the hyperbolicity properties of almost-periodic quantum parametric oscillators and we show that their upper Lyapu...
Psychoanalysis and dynamical systems theory: prediction and self similarity.
Galatzer-Levy, R M
1995-01-01
The theory of dynamical systems (sometimes called chaos theory) has emerged in the past two decades as a powerful tool for understanding the evolution of complex systems. Attempts to develop psychoanalysis along the lines of nineteenth century physical science have proven unsatisfactory. The theory of dynamical systems provides another route for development. It suggests that prediction should aim at describing the overall evolution of systems and that the possibilities for such evolution are broader than classical theory suggested. It also shows that complex systems often involve structures that repeat basic features on several different levels of observation. This suggests a method for systematically exploring the overly rich data of psychoanalysis. PMID:8926326
Bryan, W A; King, R B; Nemeth, G R A J; Greenwood, J B; Williams, I D; Newell, W R
2010-01-01
A quasi-classical model (QCM) of molecular dynamics in intense femtosecond laser fields has been developed, and applied to a study of the effect of an ultrashort `control' pulse on the vibrational motion of a deuterium molecular ion in its ground electronic state. A nonadiabatic treatment accounts for the initial ionization-induced vibrational population caused by an ultrashort `pump' pulse. In the QCM, the nuclei move classically on the molecular potential as it is distorted by the laser-induced Stark shift and transition dipole. The nuclei then adjust to the modified potential, non-destructively shifting the vibrational population and relative phase. This shift has been studied as a function of control pulse parameters. Excellent agreement is observed with predictions of time-dependent quantum simulations, lending confidence to the validity of the model and permitting new observations to be made. The applicability of the QCM to more complex multi-potential energy surface molecules (where a quantum treatment...
Ateto, M. S.
2015-08-01
Entanglement dynamics of two identical non-interacting atoms (qubits) coupled individually with simultaneous classical and quantum fields are studied. The cavity field is filled with a nonlinear Kerr medium and initially prepared in a coherent state. The atoms are initially set up as a Bell-like pure state (BS). We present an approach for diagonalization of time-dependent nonlinear Hamiltonian of the system exactly. Connection between the change in the degree of entanglement and tomography of field state in phase space are also illustrated and interpreted. We demonstrate the possibility of atom-atom (qubit-qubit) entanglement optimization by suitably choosing initial interaction settings. Overall, we show that both classical driving amplitude and detuning as well as Kerr media and initial atomic states acts as the control parameters for the qubit-qubit entanglement. By adjusting of these parameters, accurately, entanglement can be enhanced noticeably and high degree of steady periodical entanglement can be generated. Moreover, starting with initial atomic BSs in presence of classical driving suppresses coherences randomness and considerably accompanied with (for specific values of detuning) slight decrease in their amplitudes. Furthermore, the addition of cross Kerr term suppresses degree of entanglement noticeably, where entanglement creation and enhancement could just be possible if cross Kerr effect is moved out from interaction. Our present approach promises the great advantage of being suitable for large quantum systems of various kinds of nonlinearities.
A Comparison of Classical Force-Fields for Molecular Dynamics Simulations of Lubricants
Directory of Open Access Journals (Sweden)
James P. Ewen
2016-08-01
Full Text Available For the successful development and application of lubricants, a full understanding of their complex nanoscale behavior under a wide range of external conditions is required, but this is difficult to obtain experimentally. Nonequilibrium molecular dynamics (NEMD simulations can be used to yield unique insights into the atomic-scale structure and friction of lubricants and additives; however, the accuracy of the results depend on the chosen force-field. In this study, we demonstrate that the use of an accurate, all-atom force-field is critical in order to; (i accurately predict important properties of long-chain, linear molecules; and (ii reproduce experimental friction behavior of multi-component tribological systems. In particular, we focus on n-hexadecane, an important model lubricant with a wide range of industrial applications. Moreover, simulating conditions common in tribological systems, i.e., high temperatures and pressures (HTHP, allows the limits of the selected force-fields to be tested. In the first section, a large number of united-atom and all-atom force-fields are benchmarked in terms of their density and viscosity prediction accuracy of n-hexadecane using equilibrium molecular dynamics (EMD simulations at ambient and HTHP conditions. Whilst united-atom force-fields accurately reproduce experimental density, the viscosity is significantly under-predicted compared to all-atom force-fields and experiments. Moreover, some all-tom force-fields yield elevated melting points, leading to significant overestimation of both the density and viscosity. In the second section, the most accurate united-atom and all-atom force-field are compared in confined NEMD simulations which probe the structure and friction of stearic acid adsorbed on iron oxide and separated by a thin layer of n-hexadecane. The united-atom force-field provides an accurate representation of the structure of the confined stearic acid film; however, friction coefficients are
International Nuclear Information System (INIS)
Very recently (Cai et al 2010 Phys. Rev. E 82 021921), a simple mechanism was presented by which a molecule subjected to forced oscillations, out of thermal equilibrium, can maintain quantum entanglement between two of its quantum degrees of freedom. Crucially, entanglement can be maintained even in the presence of very intense noise, so intense that no entanglement is possible when the forced oscillations cease. This mechanism may allow for the presence of nontrivial quantum entanglement in biological systems. Here we significantly enlarge the study of this model. In particular, we show that the persistent generation of dynamic entanglement is not restricted to the bosonic heat bath model, but can also be observed in other decoherence models, e.g. the spin gas model, and in non-Markovian scenarios. We also show how conformational changes can be used by an elementary machine to generate entanglement even in unfavorable conditions. In biological systems, similar mechanisms could be exploited by more complex molecular machines or motors. (paper)
Diaz-Torres, Alexis
2011-04-01
A self-contained Fortran-90 program based on a three-dimensional classical dynamical reaction model with stochastic breakup is presented, which is a useful tool for quantifying complete and incomplete fusion, and breakup in reactions induced by weakly-bound two-body projectiles near the Coulomb barrier. The code calculates (i) integrated complete and incomplete fusion cross sections and their angular momentum distribution, (ii) the excitation energy distribution of the primary incomplete-fusion products, (iii) the asymptotic angular distribution of the incomplete-fusion products and the surviving breakup fragments, and (iv) breakup observables, such as angle, kinetic energy and relative energy distributions. Program summaryProgram title: PLATYPUS Catalogue identifier: AEIG_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIG_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 332 342 No. of bytes in distributed program, including test data, etc.: 344 124 Distribution format: tar.gz Programming language: Fortran-90 Computer: Any Unix/Linux workstation or PC with a Fortran-90 compiler Operating system: Linux or Unix RAM: 10 MB Classification: 16.9, 17.7, 17.8, 17.11 Nature of problem: The program calculates a wide range of observables in reactions induced by weakly-bound two-body nuclei near the Coulomb barrier. These include integrated complete and incomplete fusion cross sections and their spin distribution, as well as breakup observables (e.g. the angle, kinetic energy, and relative energy distributions of the fragments). Solution method: All the observables are calculated using a three-dimensional classical dynamical model combined with the Monte Carlo sampling of probability-density distributions. See Refs. [1,2] for further details. Restrictions: The
Dynamics of Coulombic and gravitational periodic systems
Kumar, Pankaj; Miller, Bruce N.
2016-04-01
We study the dynamics and the phase-space structures of Coulombic and self-gravitating versions of the classical one-dimensional three-body system with periodic boundary conditions. We demonstrate that such a three-body system may be reduced isomorphically to a spatially periodic system of a single particle experiencing a two-dimensional potential on a rhombic plane. For the case of both Coulombic and gravitational versions, exact expressions of the Hamiltonian have been derived in rhombic coordinates. We simulate the phase-space evolution through an event-driven algorithm that utilizes analytic solutions to the equations of motion. The simulation results show that the motion exhibits chaotic, quasiperiodic, and periodic behaviors in segmented regions of the phase space. While there is no evidence of global chaos in either the Coulombic or the gravitational system, the former exhibits a transition from a completely nonchaotic phase space at low energies to a mixed behavior. Gradual yet striking transitions from mild to intense chaos are indicated with changing energy, a behavior that differentiates the spatially periodic systems studied in this Rapid Communication from the well-understood free-boundary versions of the three-body problem. Our treatment of the three-body systems opens avenues for analysis of the dynamical properties exhibited by spatially periodic versions of various classes of systems studied in plasma and gravitational physics as well as in cosmology.
Mould, R A
2003-01-01
Preciously given rules allow conscious systems to be included in quantum mechanical systems. There rules are derived from the empirical experience of an observer who witnesses a quantum mechanical interaction leading to the capture of a single particle. In the present paper it is shown that purely classical changes experienced by an observer are consistent with these rules. Three different interactions are considered, two of which combine classical and quantum mechanical changes. The previously given rules support all of these cases. Key Words: brain states, conscious observer, detector, measurement, probability current, state reduction, von Neumann, wave collapse.
DEFF Research Database (Denmark)
Thomsen, Per Grove
1996-01-01
A one-dimensional model with axial discretization of engine components has been formulated using tha balance equations for mass energy and momentum and the ideal gas equation of state. ODE's that govern the dynamic behaviour of the regenerator matrix temperatures are included in the model. Known ...
DEFF Research Database (Denmark)
Thomsen, Per Grove
A one-dimensional model with axial discretization of engine components has been formulated using tha balance equations for mass energy and momentum and the ideal gas equation of state. ODE's that govern the dynamic behaviour of the regenerator matrix temperatures are included in the model. Known ...
Highly-efficient noise-assisted energy transport in classical oscillator systems
León-Montiel, R de J
2013-01-01
Photosynthesis is a biological process that involves the highly-efficient transport of energy captured from the sun to a reaction center, where conversion into useful biochemical energy takes place. Even though one can always use a quantum perspective to describe any physical process, since everything follows the laws of Quantum Mechanics, is the use of quantum theory imperative to explain this high efficiency? Several theoretical studies suggest that the high efficiency can only be understood as a result of the interplay between the quantum coherent evolution of the photosynthetic system, and noise introduced by its surrounding environment. Notwithstanding, we show here that noise-assisted highly-efficient energy transport can be found as well in purely classical systems; therefore, we might conclude that high efficiency energy transfer in photosynthetic systems could also be anticipated by classical models, without the need to resorting to quantum effects. Strikingly, the wider scope of applicability of the...
Permutation Complexity in Dynamical Systems
Amigo, Jose
2010-01-01
The study of permutation complexity can be envisioned as a new kind of symbolic dynamics whose basic blocks are ordinal patterns, that is, permutations defined by the order relations among points in the orbits of dynamical systems. Since its inception in 2002 the concept of permutation entropy has sparked a new branch of research in particular regarding the time series analysis of dynamical systems that capitalizes on the order structure of the state space. Indeed, on one hand ordinal patterns and periodic points are closely related, yet ordinal patterns are amenable to numerical methods, while periodicity is not. Another interesting feature is that since it can be shown that random (unconstrained) dynamics has no forbidden patterns with probability one, their existence can be used as a fingerprint to identify any deterministic origin of orbit generation. This book is primarily addressed to researchers working in the field of nonlinear dynamics and complex systems, yet will also be suitable for graduate stude...
Dynamical macroeconomic models from the Keynesian, Walrasian and Classical point of view
Czech Academy of Sciences Publication Activity Database
Kodera, Jan; Sladký, Karel; Vošvrda, Miloslav
Bratislava : University of Economics, 2004 - (Lukáčik, M.), s. 118-127 ISBN 80-8078-012-9. [Quantitative Methods in Economics. Multiple Criteria Decision Making /12./. Virt (SK), 02.06.2004-04.06.2004] R&D Projects: GA AV ČR IAA7075202; GA ČR GA402/02/1015 Institutional research plan: CEZ:AV0Z1075907 Keywords : macroeconomic models * Keynesian, Walrasian and Classical model * nonlinear differential equations Subject RIV: AH - Economics
Directory of Open Access Journals (Sweden)
Collings Matthew D
2002-11-01
Full Text Available Highly concentrated NaCl brines are important geothermal fluids; chloride complexation of metals in such brines increases the solubility of minerals and plays a fundamental role in the genesis of hydrothermal ore deposits. There is experimental evidence that the molecular nature of the NaCl–water system changes over the pressure–temperature range of the Earth's crust. A transition of concentrated NaCl–H2O brines to a "hydrous molten salt" at high P and T has been argued to stabilize an aqueous fluid phase in the deep crust. In this work, we have done molecular dynamic simulations using classical potentials to determine the nature of concentrated (0.5–16 m NaCl–water mixtures under ambient (25°C, 1 bar, hydrothermal (325°C, 1 kbar and deep crustal (625°C, 15 kbar conditions. We used the well-established SPCE model for water together with the Smith and Dang Lennard-Jones potentials for the ions (J. Chem. Phys., 1994, 100, 3757. With increasing temperature at 1 kbar, the dielectric constant of water decreases to give extensive ion-association and the formation of polyatomic (NanClmn-m clusters in addition to simple NaCl ion pairs. Large polyatomic (NanClmn-m clusters resemble what would be expected in a hydrous NaCl melt in which water and NaCl were completely miscible. Although ion association decreases with pressure, temperatures of 625°C are not enough to overcome pressures of 15 kbar; consequently, there is still enhanced Na–Cl association in brines under deep crustal conditions.
From Classical to Quantum: New Canonical Tools for the Dynamics of Gravity
Höhn, P.A.
2012-01-01
In a gravitational context, canonical methods offer an intuitive picture of the dynamics and simplify an identification of the degrees of freedom. Nevertheless, extracting dynamical information from background independent approaches to quantum gravity is a highly non-trivial challenge. In this thesis, the conundrum of (quantum) gravitational dynamics is approached from two different directions by means of new canonical tools. This thesis is accordingly divided into two parts: In the first par...
Isomorphic classical molecular dynamics model for an excess electron in a supercritical fluid
Miller III, Thomas F.
2009-01-01
Ring polymer molecular dynamics (RPMD) is used to directly simulate the dynamics of an excess electron in a supercritical fluid over a broad range of densities. The accuracy of the RPMD model is tested against numerically exact path integral statistics through the use of analytical continuation techniques. At low fluid densities, the RPMD model substantially underestimates the contribution of delocalized states to the dynamics of the excess electron. However, with increasing solvent density, ...
Classical, non-linear, internal dynamics of large, isolated, vibrationally excited molecules
Papoular, R J
2002-01-01
This work reports numerical experiments intended to clarify the internal equilibration process in large molecules, following vibrational excitation. A model of amorphous and oxygenated hydrocarbon macromolecule (about 500 atoms)--simulating interstellar dust-- is built up by means of a chemical simulation code. Its structure is optimized, and its normal modes determined. About 4.5 eV of potential energy is then deposited locally by perturbing one of the C-H peripheral bonds, thus simulating the capture of a free H atom by a dangling C bond. The ensuing relaxation of the system is followed for up to 300 ps, using a molecular mechanics code. When steady state is reached, spectra and time correlation functions of kinetic energy and bond length fluctuations indicate that most normal modes have been activated, but the motion remains quasi-periodic or regular. By contrast, when the molecule is violently excited or embedded in a thermal bath (modelled by Langevin dynamics), the same markers clearly depict chaotic mo...
On non-autonomous dynamical systems
International Nuclear Information System (INIS)
In usual realistic classical dynamical systems, the Hamiltonian depends explicitly on time. In this work, a class of classical systems with time dependent nonlinear Hamiltonians is analyzed. This type of problems allows to find invariants by a family of Veronese maps. The motivation to develop this method results from the observation that the Poisson-Lie algebra of monomials in the coordinates and momenta is clearly defined in terms of its brackets and leads naturally to an infinite linear set of differential equations, under certain circumstances. To perform explicit analytic and numerical calculations, two examples are presented to estimate the trajectories, the first given by a nonlinear problem and the second by a quadratic Hamiltonian with three time dependent parameters. In the nonlinear problem, the Veronese approach using jets is shown to be equivalent to a direct procedure using elliptic functions identities, and linear invariants are constructed. For the second example, linear and quadratic invariants as well as stability conditions are given. Explicit solutions are also obtained for stepwise constant forces. For the quadratic Hamiltonian, an appropriated set of coordinates relates the geometric setting to that of the three dimensional manifold of central conic sections. It is shown further that the quantum mechanical problem of scattering in a superlattice leads to mathematically equivalent equations for the wave function, if the classical time is replaced by the space coordinate along a superlattice. The mathematical method used to compute the trajectories for stepwise constant parameters can be applied to both problems. It is the standard method in quantum scattering calculations, as known for locally periodic systems including a space dependent effective mass
Theory of hybrid systems; 1, The operator formulation of classical mechanics and semiclassical limit
Prvanovic, S
2001-01-01
The algebra of polynomials in operators that represent generalized coordinate and momentum and depend on the Planck constant is defined. The Planck constant is treated as the parameter taking values between zero and some nonvanishing $h_0$. For the second of these two extreme values, introduced operatorial algebra becomes equivalent to the algebra of observables of quantum mechanical system defined in the standard manner by operators in the Hilbert space. For the vanishing Planck constant, the generalized algebra gives the operator formulation of classical mechanics since it is equivalent to the algebra of variables of classical mechanical system defined, as usually, by functions over the phase space. In this way, the semiclassical limit of kinematical part of quantum mechanics is established through the generalized operatorial framework.
Preliminary Concepts of Dynamical Systems
Directory of Open Access Journals (Sweden)
Nayana Mukherjee
2012-08-01
Full Text Available Dynamical system is a young and vigorously growing area of research which promises enormous potential and opportunities. This paper aims to introduce some of the preliminary concepts of dynamical systems. Many application sides of the subject are noted to encourage the reader for future developments. Resources are supplied in the references for further reading.
Dynamic changes in Prebiotic Systems
Riofrio, Walter
2006-01-01
This paper aims to contribute with the debate about the causes that produced the emergence of dynamic organization in living organisms. Understanding the origin of living systems is grasping the most basic capacities that are used in the construction of the organization of these systems. It is possible to think that in the prebiotic epoch the conditions should have existed that enabled the development of the rudiments of a dynamic organization containing the essentials for the subsequent emer...
From Classical to Quantum: New Canonical Tools for the Dynamics of Gravity
Höhn, P.A.
2012-01-01
In a gravitational context, canonical methods offer an intuitive picture of the dynamics and simplify an identification of the degrees of freedom. Nevertheless, extracting dynamical information from background independent approaches to quantum gravity is a highly non-trivial challenge. In this thesi
Classical and Quantum Chaos in Atom Optics
Saif, Farhan
2006-01-01
The interaction of an atom with an electromagnetic field is discussed in the presence of a time periodic external modulating force. It is explained that a control on atom by electromagnetic fields helps to design the quantum analog of classical optical systems. In these atom optical systems chaos may appear at the onset of external fields. The classical and quantum chaotic dynamics is discussed, in particular in an atom optics Fermi accelerator. It is found that the quantum dynamics exhibits ...
Corradini, Dario; Coudert, François-Xavier; Vuilleumier, Rodolphe
2016-03-01
We use molecular dynamics simulations to study the thermodynamics, structure, and dynamics of the Li2CO3-K2CO3 (62:38 mol. %) eutectic mixture. We present a new classical non-polarizable force field for this molten salt mixture, optimized using experimental and first principles molecular dynamics simulations data as reference. This simple force field allows efficient molecular simulations of phenomena at long time scales. We use this optimized force field to describe the behavior of the eutectic mixture in the 900-1100 K temperature range, at pressures between 0 and 5 GPa. After studying the equation of state in these thermodynamic conditions, we present molecular insight into the structure and dynamics of the melt. In particular, we present an analysis of the temperature and pressure dependence of the eutectic mixture's self-diffusion coefficients, viscosity, and ionic conductivity.
Juvenile onset classical pityriasis rubra pilaris: every patient may not require systemic therapy
International Nuclear Information System (INIS)
Juvenile onset classical Pityriasis Rubra Pilaris (PRP), although rare, is the most common presentation of PRP in children. It has good prognosis and resolution over a few months. Use of potentially hazardous systemic drugs in a disease, that is likely to resolve spontaneously, needs to be assessed carefully. We report a 09 years old boy suffering from this rare disorder, whose disease is well under control with emollients and a combination of diluted topical steroids and keratolytics, for over 06 months. (author)
Distributed correlations and information flows within a hybrid multipartite quantum-classical system
Leggio, B.; Lo Franco, R; Soares-Pinto, D. O.; Horodecki, P.; Compagno, G
2015-01-01
Understanding the non-Markovian mechanisms underlying the revivals of quantum entanglement in the presence of classical environments is central in the theory of quantum information. Tentative interpretations have been given by either the role of the environment as a control device or the concept of hidden entanglement. We address this issue from an information-theoretic point of view. To this aim, we consider a paradigmatic tripartite system, already realized in the laboratory, made of two in...
Substructure modal superposition method for non-classical analysis of soil-structure systems
International Nuclear Information System (INIS)
In this paper a method to obtain the step-by-step solution of coupled soil-structure systems is presented. The method requires two real eigenvalue problems and a complex one. The first two eigenproblems define an admissible coordinate transformation matrix and the third one is able to construct the unconditionally stable approximation operator to give the incremental solution of the non-classically damped reduced equations
Fellner, Klemens; Laamri, El-Haj
2015-01-01
We consider a system of reaction-diffusion equations describing the reversible reaction of two species $\\mathcal{U}, \\mathcal{V}$ forming a third species $\\mathcal{W}$ and vice versa according to mass action law kinetics with arbitrary stochiometric coefficients (equal or larger than one). Firstly, we prove existence of global classical solutions via improved duality estimates under the assumption that one of the diffusion coefficients of $\\mathcal{U}$ or $\\mathcal{V}$ is sufficiently close t...
EVOLUTION OF THE CLASSICAL CHARACTER SYSTEM IN THE ANTIUTOPIAN NOVEL "LIVING" BY A. STAROBINETS
Directory of Open Access Journals (Sweden)
Zhilinka V. V.
2015-10-01
Full Text Available The transformation of the model of the characters system organization in the anti-utopian novel by A. Starobinets "Living" has been analyzed in this article. The typical anti-utopia identifies three types of personages: a tyrant, a rebel and a victim. The evolution of this classical trinity in contemporary antiutopian literature has been investigated by the example of the analysis of the image of the main characters of the novel
LOCAL CLASSICAL SOLUTION OF FREE BOUNDARY PROBLEM FOR A COUPLED SYSTEM
Institute of Scientific and Technical Information of China (English)
Wang Xiaohua; Yi Fahuai; Yang Zhou
2005-01-01
This paper considers a two-phase free boundary problem for coupled system including one parabolic equation and two elliptic equations. The problem comes from the discussion of a growth model of self-maintaining protocell in multidimensional case. The local classical solution of the problem with free boundary Γ:y = g(x, t) between two domains is being seeked. The local existence and uniqueness of the problem will be proved in multidimensional case.
Taylor, Zachary
2014-01-01
A practical, step-by-step guide to designing world-class, high availability systems using both classical and DFSS reliability techniques Whether designing telecom, aerospace, automotive, medical, financial, or public safety systems, every engineer aims for the utmost reliability and availability in the systems he, or she, designs. But between the dream of world-class performance and reality falls the shadow of complexities that can bedevil even the most rigorous design process. While there are an array of robust predictive engineering tools, there has been no single-source guide to understan
Heat control in opto-mechanical system using quantum non-classicality
Sharma, Sushamana; Senwar, Subash
2016-05-01
Cooling of matter to the quantum ground state is a primary directive of quantum control. In other words, to extract entropy from a quantum system, efficient indirect quantum measurements may be implemented. The main objective is the cooling of the oscillator either to its motional ground state or to non-classical states, such as low-number Fock states, squeezed states or entangled states. It is shown that the use of quantum control procedure is better choice for even experimental realizations because it leads to a squeezed steady state with less than one phonon on average. The steady state of system corresponds to cooling of the system.
NATO Advanced Study Institute on Hamiltonian Dynamical Systems and Applications
2008-01-01
Physical laws are for the most part expressed in terms of differential equations, and natural classes of these are in the form of conservation laws or of problems of the calculus of variations for an action functional. These problems can generally be posed as Hamiltonian systems, whether dynamical systems on finite dimensional phase space as in classical mechanics, or partial differential equations (PDE) which are naturally of infinitely many degrees of freedom. This volume is the collected and extended notes from the lectures on Hamiltonian dynamical systems and their applications that were given at the NATO Advanced Study Institute in Montreal in 2007. Many aspects of the modern theory of the subject were covered at this event, including low dimensional problems as well as the theory of Hamiltonian systems in infinite dimensional phase space; these are described in depth in this volume. Applications are also presented to several important areas of research, including problems in classical mechanics, continu...
Indian Academy of Sciences (India)
Y Pathania; P K Ahluwalla
2005-09-01
We have carried out a molecular dynamics simulation of two- and three- dimensional double Yukawa fluids near the triple point. We have compared some of the static and dynamic correlation functions with those of Lennard{Jones, when parameters occurring in double Yukawa potential are chosen to fit Lennard-Jones potential. The results are in good agreement. However, when repulsive and attractive parameters occurring in double Yukawa potential are varied, we found distinct differences in static and dynamic correlation functions. We have also compared the two-dimensional correlation functions with those of three-dimensional to study the effect of dimensionality, near the triple point region.
Realization of dynamical electronic systems
Hammari, Elena; Catthoor, Francky; Iasemidis, Leonidas; Kjeldsberg, Per Gunnar; Huisken, Jos; Tsakalis, Konstantinos
2014-04-01
This article gives an overview of a methodology for building dynamical electronic systems. As an example a part of a system for epileptic seizure prediction is used, which monitors EEG signals and continuously calculates the largest short-term Lyapunov exponents. In dynamical electronic systems, the cost of exploitation, for instance energy consumption, may vary substantially with the values of input signals. In addition, the functions describing the variations are not known at the time the system is designed. As a result, the architecture of the system must accommodate for the worst case exploitation costs, which rapidly exceed the available resources (for instance battery life) when accumulated over time. The presented system scenario methodology solves these challenges by identifying at design time groups of possible exploitation costs, called system scenarios, and implementing a mechanism to detect system scenarios at run time and re-configure the system to cost-efficiently accommodate them. During reconfiguration, the optimized system architecture settings for the active system scenario are selected and the total exploitation cost is reduced. When the dynamic behavior is due to input data variables with a large number of possible values, current techniques for bottom-up scenario identification and detection becomes too complex. A new top-down technique, based on polygonal regions, is presented in this paper. The results for the example system indicate that with 10 system scenarios the average energy consumption of the system can be reduced by 28% and brought within 5% of the theoretically best solution.
Realization of dynamical electronic systems
Directory of Open Access Journals (Sweden)
Hammari Elena
2014-04-01
Full Text Available This article gives an overview of a methodology for building dynamical electronic systems. As an example a part of a system for epileptic seizure prediction is used, which monitors EEG signals and continuously calculates the largest short-term Lyapunov exponents. In dynamical electronic systems, the cost of exploitation, for instance energy consumption, may vary substantially with the values of input signals. In addition, the functions describing the variations are not known at the time the system is designed. As a result, the architecture of the system must accommodate for the worst case exploitation costs, which rapidly exceed the available resources (for instance battery life when accumulated over time. The presented system scenario methodology solves these challenges by identifying at design time groups of possible exploitation costs, called system scenarios, and implementing a mechanism to detect system scenarios at run time and re-configure the system to cost-efficiently accommodate them. During reconfiguration, the optimized system architecture settings for the active system scenario are selected and the total exploitation cost is reduced. When the dynamic behavior is due to input data variables with a large number of possible values, current techniques for bottom-up scenario identification and detection becomes too complex. A new top-down technique, based on polygonal regions, is presented in this paper. The results for the example system indicate that with 10 system scenarios the average energy consumption of the system can be reduced by 28% and brought within 5% of the theoretically best solution.
Classical dynamics of the Bianchi IX model: space-like and time-like singularity cases
Parnovsky, S L
2016-01-01
We present the comparison of the dynamics of the vacuum Bianchi IX model near the space-like and time-like singularities. In both cases there exist oscillatory type solutions with diverging asymptotically curvature invariants. The dynamics of the time-like singularity case includes additionally the singular solutions with diverging volume density, but vanishing curvature invariants. Our numerical results are consistent with qualitative analytical considerations underlying finding the generic singular solutions to general relativity.
Classical and quantum dynamics of a gravitational theory with absolute teleparallelism
International Nuclear Information System (INIS)
The dynamics of an alternative theory of gravitation with absolute teleparallelism is sustied. In the Cauchy problem of this theory four constraint relations are obtained, as in general relativity, because of the existence of the manifold mapping group. Propagation equations for the dynamical variables are also derived by applying Dirac's Hamiltonian methods. In addition, an algebra of generators related to the global Lorentz group and the correspondence principle leading to a quantum version of the theory are also discussed. (author)
Application of the GRC Stirling Convertor System Dynamic Model
Regan, Timothy F.; Lewandowski, Edward J.; Schreiber, Jeffrey G. (Technical Monitor)
2004-01-01
The GRC Stirling Convertor System Dynamic Model (SDM) has been developed to simulate dynamic performance of power systems incorporating free-piston Stirling convertors. This paper discusses its use in evaluating system dynamics and other systems concerns. Detailed examples are provided showing the use of the model in evaluation of off-nominal operating conditions. The many degrees of freedom in both the mechanical and electrical domains inherent in the Stirling convertor and the nonlinear dynamics make simulation an attractive analysis tool in conjunction with classical analysis. Application of SDM in studying the relationship of the size of the resonant circuit quality factor (commonly referred to as Q) in the various resonant mechanical and electrical sub-systems is discussed.
Coherent dynamics on hierarchical systems
Blumen, Alexander; Bierbaum, Veronika; Mülken, Oliver
2006-11-01
We study the coherent transport modeled by continuous-time quantum walks, focussing on hierarchical structures. For these we use Husimi cacti, lattices dual to the dendrimers. We find that the transport depends strongly on the initial site of the excitation. For systems of sizes N⩽21, we find that processes which start at central sites are nearly recurrent. Furthermore, we compare the classical limiting probability distribution to the long time average of the quantum mechanical transition probability which shows characteristic patterns. We succeed in finding a good lower bound for the (space) average of the quantum mechanical probability to be still or again at the initial site.
Classical behavior in quantum systems: the case of straight tracks in a cloud chamber
Teta, Alessandro
2009-01-01
The aim of this review is to discuss in a pedagogical way the problem of the emergence of a classical behavior in certain physical systems which, in principle, are correctly described by quantum mechanics. It is stressed that the limit $\\hbar \\to 0$ is not sufficient and the crucial role played by the environment must be taken into account. In particular it is recalled the old problem raised by Mott in 1929 (\\cite{m}) concerning the straight tracks observed in a cloud chamber, produced by an $\\alpha$-particle emitted by a source in the form of a spherical wave. The conceptual relevance of the problem for a clearer understanding of the classical limit is discussed in a historical perspective. Moreover a simple mathematical model is proposed, where the result of Mott is obtained in a rigorous mathematical way.
Multiparty Quantum Secret Sharing of Classical Message using Cavity Quantum Electrodynamic System
Institute of Scientific and Technical Information of China (English)
HAN Lian-Fang; LIU Yi-Min; ZHANG Zhan-Jun
2006-01-01
@@ An experimental feasible scheme of multiparty secret sharing of classical messages is proposed, based on a cavity quantum electrodynamic system. The secret messages are imposed on atomic Bell states initially in the sender's possession by local unitary operations. By swapping quantum entanglement of atomic Bell states, the secret messages are split into several parts and each part is distributed to a separate party. In this case, any subset of the entire party group can not read out the secret message but the entirety via mutual cooperations. In this scheme, to discriminate atomic Bell states, additional classical fields are employed besides the same highly-detuned single-mode cavities used to prepare atomic Bell states. This scheme is insensitive to the cavity decay and the thermal field, and usual joint Bell-state measurements are unnecessary.
VERIFICATION OF TORSIONAL OSCILLATING MECHANICAL SYSTEM DYNAMIC CALCULATION RESULTS
Directory of Open Access Journals (Sweden)
Peter KAŠŠAY
2014-09-01
Full Text Available On our department we deal with optimization and tuning of torsional oscillating mechanical systems. When solving these problems we often use results of dynamic calculation. The goal of this article is to compare values obtained by computation and experimentally. For this purpose, a mechanical system built in our laboratory was used. At first, classical HARDY type flexible coupling has been applied into the system, then we used a pneumatic flexible shaft coupling developed by us. The main difference of these couplings over conventional flexible couplings is that they can change their dynamic properties during operation, by changing the pressure of the gaseous medium in their flexible elements.
The dynamics of system effectiveness
International Nuclear Information System (INIS)
The modern control theory has been applied to study the dynamics of system effectiveness of a nuclear reactor power system. The various contributory functions towards system effectiveness are formulated in terms of state variables with weightage functions chosen to satisfy asymptotic stability criteria. The sensitivity of system effectiveness to the variations of weighting function is investigated. The transient response and root locus are also furnished. (M.G.B.)
Nonlinear dynamics in biological systems
Carballido-Landeira, Jorge
2016-01-01
This book presents recent research results relating to applications of nonlinear dynamics, focusing specifically on four topics of wide interest: heart dynamics, DNA/RNA, cell mobility, and proteins. The book derives from the First BCAM Workshop on Nonlinear Dynamics in Biological Systems, held in June 2014 at the Basque Center of Applied Mathematics (BCAM). At this international meeting, researchers from different but complementary backgrounds, including molecular dynamics, physical chemistry, bio-informatics and biophysics, presented their most recent results and discussed the future direction of their studies using theoretical, mathematical modeling and experimental approaches. Such was the level of interest stimulated that the decision was taken to produce this publication, with the organizers of the event acting as editors. All of the contributing authors are researchers working on diverse biological problems that can be approached using nonlinear dynamics. The book will appeal especially to applied math...
Zakharov, A Yu
2016-01-01
The exact closed equation of motion for microscopic distribution function of classical many-body system with account of interactions retardation between particles is derived. It is shown that interactions retardation leads to irreversible behaviour of many-body systems.
Dynamically reconfigurable photovoltaic system
Energy Technology Data Exchange (ETDEWEB)
Okandan, Murat; Nielson, Gregory N.
2016-05-31
A PV system composed of sub-arrays, each having a group of PV cells that are electrically connected to each other. A power management circuit for each sub-array has a communications interface and serves to connect or disconnect the sub-array to a programmable power grid. The power grid has bus rows and bus columns. A bus management circuit is positioned at a respective junction of a bus column and a bus row and is programmable through its communication interface to connect or disconnect a power path in the grid. As a result, selected sub-arrays are connected by selected power paths to be in parallel so as to produce a low system voltage, and, alternately in series so as to produce a high system voltage that is greater than the low voltage by at least a factor of ten.
Institute of Scientific and Technical Information of China (English)
LI Chao-Hong; DUAN Yi-Wu; Wing-Ki Liu; Jian-Min Yuan
2001-01-01
Within Born-Oppenheimer approximation, by using the classical trajectory theory, a description for the high order harmonic generation of the hydrogen molecular ion interacting with ultrashort laser pulses has been pre sented. The Coulomb singularities have been remedied by the regularization. The action-angle variables have been used to generate the initial inversion symmetry microcanonical distribution. Within a proper intensity range, a harmonic plateau with only odd harmonics appears. For a larger intensity, because of the existence of chaos, the harmonic spectra become noisier. For a large enough intensity, the ionization takes place and the harmonics disappear. So the chaos causes the noises, the ionization suppresses the harmonic generation, and the onset of the ionization follows the onset of chaos.
On the dynamics of a polaron in a classical chain with finite temperature
International Nuclear Information System (INIS)
In today’s literature, polaron states in classical molecular chains are mostly calculated at zero temperature. It is assumed that the properties of these states change little if the temperature is different from zero but is much less than the characteristic energy equal to the depth of the polaron level. By numerical experiments, we demonstrate that the temperature decay of a polaron depends on the chain length. The longer the chain, the lower the critical temperature above which the charge is in a delocalized state, and, conversely, the shorter the chain, the higher the decay temperature of a polaron. The results of numerical experiments lead to a conclusion that, in an indefinitely long chain, polaron states decay at temperatures differing arbitrarily little from zero
On the tomographic description of classical fields
International Nuclear Information System (INIS)
After a general description of the tomographic picture for classical systems, a tomographic description of free classical scalar fields is proposed both in a finite cavity and the continuum. The tomographic description is constructed in analogy with the classical tomographic picture of an ensemble of harmonic oscillators. The tomograms of a number of relevant states such as the canonical distribution, the classical counterpart of quantum coherent states and a new family of so-called Gauss–Laguerre states, are discussed. Finally the Liouville equation for field states is described in the tomographic picture offering an alternative description of the dynamics of the system that can be extended naturally to other fields.
On the tomographic description of classical fields
Energy Technology Data Exchange (ETDEWEB)
Ibort, A., E-mail: albertoi@math.uc3m.es [Departamento de Matemáticas, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganés, Madrid (Spain); López-Yela, A., E-mail: alyela@math.uc3m.es [Departamento de Matemáticas, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganés, Madrid (Spain); Man' ko, V.I., E-mail: manko@na.infn.it [P.N. Lebedev Physical Institute, Leninskii Prospect 53, Moscow 119991 (Russian Federation); Marmo, G., E-mail: marmo@na.infn.it [Dipartimento di Scienze Fisiche dell' Università “Federico II” e Sezione INFN di Napoli, Complesso Universitario di Monte S. Angelo, via Cintia, 80126 Naples (Italy); Simoni, A., E-mail: simoni@na.infn.it [Dipartimento di Scienze Fisiche dell' Università “Federico II” e Sezione INFN di Napoli, Complesso Universitario di Monte S. Angelo, via Cintia, 80126 Naples (Italy); Sudarshan, E.C.G., E-mail: bhamathig@gmail.com [Physics Department, Center for Particle Physics, University of Texas, Austin, TX 78712 (United States); Ventriglia, F., E-mail: ventriglia@na.infn.it [Dipartimento di Scienze Fisiche dell' Università “Federico II” e Sezione INFN di Napoli, Complesso Universitario di Monte S. Angelo, via Cintia, 80126 Naples (Italy)
2012-03-26
After a general description of the tomographic picture for classical systems, a tomographic description of free classical scalar fields is proposed both in a finite cavity and the continuum. The tomographic description is constructed in analogy with the classical tomographic picture of an ensemble of harmonic oscillators. The tomograms of a number of relevant states such as the canonical distribution, the classical counterpart of quantum coherent states and a new family of so-called Gauss–Laguerre states, are discussed. Finally the Liouville equation for field states is described in the tomographic picture offering an alternative description of the dynamics of the system that can be extended naturally to other fields.
On the tomographic description of classical fields
Ibort, A; Man'ko, V I; Marmo, G; Simoni, A; Sudarshan, E C G; Ventriglia, F
2012-01-01
After a general description of the tomographic picture for classical systems, a tomographic description of free classical scalar fields is proposed both in a finite cavity and the continuum. The tomographic description is constructed in analogy with the classical tomographic picture of an ensemble of harmonic oscillators. The tomograms of a number of relevant states such as the canonical distribution, the classical counterpart of quantum coherent states and a new family of so called Gauss--Laguerre states, are discussed. Finally the Liouville equation for field states is described in the tomographic picture offering an alternative description of the dynamics of the system that can be extended naturally to other fields.
Horwitz, Lawrence; Hu, Bei-Lok; Lee, Da-Shin; Gill, Tepper; Land, Martin
2011-12-01
Although the subject of relativistic dynamics has been explored from both classical and quantum mechanical points of view since the work of Einstein and Dirac, its most striking development has been in the framework of quantum field theory. The very accurate calculations of spectral and scattering properties, for example, of the anamolous magnetic moment of the electron and the Lamb shift in quantum electrodynamics, and many qualitative features of the strong and electroweak interactions, demonstrate the very great power of description achieved in this framework. Yet, many fundamental questions remain to be clarified, such as the structure of classical realtivistic dynamical theories on the level of Hamilton and Lagrange in Minkowski space as well as on the curved manifolds of general relativity. There moreover remains the important question of the covariant classical description of systems at high energy for which particle production effects are not large, such as discussed in Synge's book, The Relativistic Gas, and in Balescu's book on relativistic statistical mechanics. In recent years, the study of high energy plasmas and heavy ion collisions has emphasized the importance of developing the techniques of relativistic mechanics. The results of Linder et al (Phys. Rev. Lett. 95 0040401 (2005)) as well as the more recent work of Palacios et al (Phys. Rev. Lett. 103 253001 (2009)) and others, have shown that there must be a quantum theory with coherence in time. Such a theory, manifestly covariant under the transformations of special relativity with an invariant evolution parameter, such as that of Stueckelberg (Helv. Phys. Acta 14 322, 588 (1941); 15 23 (1942); see also R P Feynman Phys. Rev. 80 4401 and J S Schwinger Phys. Rev. 82 664 (1951)) could provide a suitable basis for the study of such questions, as well as many others for which the application of the standard methods of quantum field theory are difficult to manage, involving, in particular, local
Howard, Ronald A
2007-01-01
This book is an integrated work published in two volumes. The first volume treats the basic Markov process and its variants; the second, semi-Markov and decision processes. Its intent is to equip readers to formulate, analyze, and evaluate simple and advanced Markov models of systems, ranging from genetics and space engineering to marketing. More than a collection of techniques, it constitutes a guide to the consistent application of the fundamental principles of probability and linear system theory.Author Ronald A. Howard, Professor of Management Science and Engineering at Stanford University
Nonnegative and Compartmental Dynamical Systems
Haddad, Wassim M; Hui, Qing
2010-01-01
This comprehensive book provides the first unified framework for stability and dissipativity analysis and control design for nonnegative and compartmental dynamical systems, which play a key role in a wide range of fields, including engineering, thermal sciences, biology, ecology, economics, genetics, chemistry, medicine, and sociology. Using the highest standards of exposition and rigor, the authors explain these systems and advance the state of the art in their analysis and active control design. Nonnegative and Compartmental Dynamical Systems presents the most complete treatment available o
Field theory and weak Euler-Lagrange equation for classical particle-field systems
Energy Technology Data Exchange (ETDEWEB)
Qin, Hong [PPPL; Burby, Joshua W [PPPL; Davidson, Ronald C [PPPL
2014-10-01
It is commonly believed that energy-momentum conservation is the result of space-time symmetry. However, for classical particle-field systems, e.g., Klimontovich-Maxwell and Klimontovich- Poisson systems, such a connection hasn't been formally established. The difficulty is due to the fact that particles and the electromagnetic fields reside on different manifolds. To establish the connection, the standard Euler-Lagrange equation needs to be generalized to a weak form. Using this technique, energy-momentum conservation laws that are difficult to find otherwise can be systematically derived.
Parametric Resonance in Dynamical Systems
Nijmeijer, Henk
2012-01-01
Parametric Resonance in Dynamical Systems discusses the phenomenon of parametric resonance and its occurrence in mechanical systems,vehicles, motorcycles, aircraft and marine craft, and micro-electro-mechanical systems. The contributors provide an introduction to the root causes of this phenomenon and its mathematical equivalent, the Mathieu-Hill equation. Also included is a discussion of how parametric resonance occurs on ships and offshore systems and its frequency in mechanical and electrical systems. This book also: Presents the theory and principles behind parametric resonance Provides a unique collection of the different fields where parametric resonance appears including ships and offshore structures, automotive vehicles and mechanical systems Discusses ways to combat, cope with and prevent parametric resonance including passive design measures and active control methods Parametric Resonance in Dynamical Systems is ideal for researchers and mechanical engineers working in application fields such as MEM...
Managing Complex Dynamical Systems
Cox, John C.; Webster, Robert L.; Curry, Jeanie A.; Hammond, Kevin L.
2011-01-01
Management commonly engages in a variety of research designed to provide insight into the motivation and relationships of individuals, departments, organizations, etc. This paper demonstrates how the application of concepts associated with the analysis of complex systems applied to such data sets can yield enhanced insights for managerial action.
Butschli Dynamic Droplet System
DEFF Research Database (Denmark)
Armstrong, R.; Hanczyc, M.
2013-01-01
a technology with living properties. Otto Butschli first described the system in 1898, when he used alkaline water droplets in olive oil to initiate a saponification reaction. This simple recipe produced structures that moved and exhibited characteristics that resembled, at least superficially, the...
Spectrum analysis with quantum dynamical systems
Ng, Shilin; Ang, Shan Zheng; Wheatley, Trevor A.; Yonezawa, Hidehiro; Furusawa, Akira; Huntington, Elanor H.; Tsang, Mankei
2016-04-01
Measuring the power spectral density of a stochastic process, such as a stochastic force or magnetic field, is a fundamental task in many sensing applications. Quantum noise is becoming a major limiting factor to such a task in future technology, especially in optomechanics for temperature, stochastic gravitational wave, and decoherence measurements. Motivated by this concern, here we prove a measurement-independent quantum limit to the accuracy of estimating the spectrum parameters of a classical stochastic process coupled to a quantum dynamical system. We demonstrate our results by analyzing the data from a continuous-optical-phase-estimation experiment and showing that the experimental performance with homodyne detection is close to the quantum limit. We further propose a spectral photon-counting method that can attain quantum-optimal performance for weak modulation and a coherent-state input, with an error scaling superior to that of homodyne detection at low signal-to-noise ratios.
Hamiltonian Dynamics of Darwin Systems
A. V. Shapovalov; Evdokimov, E. V.
1997-01-01
We present a Hamiltonian approach for the wellknown Eigen model of the Darwin selection dynamics. Hamiltonization is carried out by means of the embedding of the population variable space, describing behavior of the system, into the space of doubled dimension by introducing additional dynamic variables. Besides the study of the formalism, we try to interpret its basic elements (phase space, Hamiltonian, geometry of solutions) in terms of the theoretical biology. A geometric treatment is given...
Brambila, Danilo
2012-01-01
We have theoretically studied Anderson localization in a 2D+1 nonlinear kicked rotor model. The system shows a very rich dynamical behavior, where the Anderson localization is suppressed and soliton wave-particles undergo a superdiffusive motion.
Chakraborty, Debdutta; Kar, Susmita; Chattaraj, Pratim Kumar
2015-12-21
The orbital free density functional theory and the single density equation approach are formally equivalent. An orbital free density based quantum dynamical strategy is used to study the quantum-classical correspondence in both weakly and strongly coupled van der Pol and Duffing oscillators in the presence of an external electric field in one dimension. The resulting quantum hydrodynamic equations of motion are solved through an implicit Euler type real space method involving a moving weighted least square technique. The Lagrangian framework used here allows the numerical grid points to follow the wave packet trajectory. The associated classical equations of motion are solved using a sixth order Runge-Kutta method and the Ehrenfest dynamics is followed through the solution of the time dependent Schrodinger equation using a time dependent Fourier Grid Hamiltonian technique. Various diagnostics reveal a close parallelism between classical regular as well as chaotic dynamics and that obtained from the Bohmian mechanics. PMID:26033095
Spectrum of Quantum Transfer Matrices via Classical Many-Body Systems
Gorsky, A; Zotov, A
2014-01-01
In this paper we clarify the relationship between inhomogeneous quantum spin chains and classical integrable many-body systems. It provides an alternative (to the nested Bethe ansatz) method for computation of spectra of the spin chains. Namely, the spectrum of the quantum transfer matrix for the inhomogeneous ${\\mathfrak g}{\\mathfrak l}_n$-invariant XXX spin chain on $N$ sites with twisted boundary conditions can be found in terms of velocities of particles in the rational $N$-body Ruijsenaars-Schneider model. The possible values of the velocities are to be found from intersection points of two Lagrangian submanifolds in the phase space of the classical model. One of them is the Lagrangian hyperplane corresponding to fixed coordinates of all $N$ particles and the other one is an $N$-dimensional Lagrangian submanifold obtained by fixing levels of $N$ classical Hamiltonians in involution. The latter are determined by eigenvalues of the twist matrix. To support this picture, we give a direct proof that the eige...
Deciphering mechanism of the 'myristoyl switch' with classical and accelerated molecular dynamics
Czech Academy of Sciences Publication Activity Database
Magarkar, Aniket; Kohagen, Miriam; Jungwirth, Pavel
2015-01-01
Roč. 44, Suppl 1 (2015), S169. ISSN 0175-7571. [EBSA European Biophysics Congress /10./. 18.07.2015-22.07.2015, Dresden] Institutional support: RVO:61388963 Keywords : molecular dynamics * myristoyl switch * calcium ion binding Subject RIV: CF - Physical ; Theoretical Chemistry
ON COMPLEX DYNAMIC CONTROL SYSTEMS
Institute of Scientific and Technical Information of China (English)
CHENG Daizhan
2003-01-01
This paper presents some recent works on the control of dynamic systems, which have certain complex properties caused by singularity of the nonlinear structures, structure-varyings, or evolution process etc. First, we consider the structure singularity of nonlinear control systems. It was revealed that the focus of researches on nonlinear control theory is shifting from regular systems to singular systems. The singularity of nonlinear systems causes certain complexity. Secondly, the switched systems are considered. For such systems the complexity is caused by the structure varying. We show that the switched systems have significant characteristics of complex systems. Finally, we investigate the evolution systems. The evolution structure makes complexity, and itself is a proper model for complex systems.
Dynamic design of piping systems
International Nuclear Information System (INIS)
A methodology for design of piping systems and their supports/restraints to satisfactorily perform under normal, expected, and postulated dynamic loads is presented. The methodology relies on a synthesis process utilizing preanalyzed equivalent piping elements such as straight spans, spans with concentrated weights, cantilever spans and elbow spans, and a set of procedural rules to construct the piping system. The application of the methodology is illustrated for the case of seismic excitations, so chosen because the present methodology can be directly compared with previously proposed and used simplified dynamic analyses methods. Comparison of this methodology with those methods indicates that it more closely predicts the dynamic behavior of piping systems as determined by detailed computer analyses. (orig.)
Semi-classical description of matter wave interferometers and hybrid quantum systems
Energy Technology Data Exchange (ETDEWEB)
Schneider, Mathias
2015-02-16
This work considers the semi-classical description of two applications involving cold atoms. This is, on one hand, the behavior of a BOSE-EINSTEIN condensate in hybrid systems, i.e. in contact with a microscopic object (carbon nanotubes, fullerenes, etc.). On the other, the evolution of phase space distributions in matter wave interferometers utilizing ray tracing methods was discussed. For describing condensates in hybrid systems, one can map the GROSS-PITAEVSKII equation, a differential equation in the complex-valued macroscopic wave function, onto a system of two differential equations in density and phase. Neglecting quantum dispersion, one obtains a semiclassical description which is easily modified to incorporate interactions between condensate and microscopical object. In our model, these interactions comprise attractive forces (CASIMIR-POLDER forces) and loss of condensed atoms due to inelastic collisions at the surface of the object. Our model exhibited the excitation of sound waves that are triggered by the object's rapid immersion, and spread across the condensate thereafter. Moreover, local particle loss leads to a shrinking of the bulk condensate. We showed that the total number of condensed particles is decreasing potentially in the beginning (large condensate, strong mean field interaction), while it decays exponentially in the long-time limit (small condensate, mean field inetraction negligible). For representing the physics of matter wave interferometers in phase space, we utilized the WIGNER function. In semi-classical approximation, which again consists in ignoring the quantum dispersion, this representation is subject to the same equation of motion as classical phase space distributions, i.e. the LIOUVILLE equation. This implies that time evolution of theWIGNER function follows a phase space flow that consists of classical trajectories (classical transport). This means, for calculating a time-evolved distribution, one has know the initial
Semi-classical description of matter wave interferometers and hybrid quantum systems
International Nuclear Information System (INIS)
This work considers the semi-classical description of two applications involving cold atoms. This is, on one hand, the behavior of a BOSE-EINSTEIN condensate in hybrid systems, i.e. in contact with a microscopic object (carbon nanotubes, fullerenes, etc.). On the other, the evolution of phase space distributions in matter wave interferometers utilizing ray tracing methods was discussed. For describing condensates in hybrid systems, one can map the GROSS-PITAEVSKII equation, a differential equation in the complex-valued macroscopic wave function, onto a system of two differential equations in density and phase. Neglecting quantum dispersion, one obtains a semiclassical description which is easily modified to incorporate interactions between condensate and microscopical object. In our model, these interactions comprise attractive forces (CASIMIR-POLDER forces) and loss of condensed atoms due to inelastic collisions at the surface of the object. Our model exhibited the excitation of sound waves that are triggered by the object's rapid immersion, and spread across the condensate thereafter. Moreover, local particle loss leads to a shrinking of the bulk condensate. We showed that the total number of condensed particles is decreasing potentially in the beginning (large condensate, strong mean field interaction), while it decays exponentially in the long-time limit (small condensate, mean field inetraction negligible). For representing the physics of matter wave interferometers in phase space, we utilized the WIGNER function. In semi-classical approximation, which again consists in ignoring the quantum dispersion, this representation is subject to the same equation of motion as classical phase space distributions, i.e. the LIOUVILLE equation. This implies that time evolution of theWIGNER function follows a phase space flow that consists of classical trajectories (classical transport). This means, for calculating a time-evolved distribution, one has know the initial
Classical non-linear wave dynamics and gluon spin operator in SU(2) QCD
Kim, Youngman; Tsukioka, Takuya; Zhang, P M
2016-01-01
We study various types of classical non-linear wave solutions with mass scale parameters in a pure SU(2) quantum chromodynamics. It has been shown that there are two gauge non-equivalent solutions for non-linear plane waves with a mass parameter. One of them corresponds to embedding \\lambda \\phi^4 theory into the SU(2) Yang-Mills theory, another represents essentially Yang-Mills type solution. We describe a wide class of stationary and non-stationary wave solutions among which kink like solitons and non-linear wave packet solutions have been found. A regular stationary monopole like solution with a finite energy density is proposed. The solution can be treated as a Wu-Yang monopole dressed in off-diagonal gluons. All non-linear wave solutions have common features: presence of a mass scale parameter, non-vanishing projection of the color magnetic field along the propagation direction and a total spin zero. Gauge invariant and Lorentz frame independent definitions of the gluon spin operator are considered.
Dynamical system approach to phyllotaxis
DEFF Research Database (Denmark)
D'ovidio, Francesco; Mosekilde, Erik
2000-01-01
and not a dynamical system, mainly because new active elements are added at each step, and thus the dimension of the "natural" phase space is not conserved. Here a construction is presented by which a well defined dynamical system can be obtained, and a bifurcation analysis can be carried out. Stable...... and unstable patterns are found by an analytical relation, in which the roles of different growth mechanisms determining the shape is clarified. Then bifurcations are studied, especially anomalous scenarios due to discontinuities embedded in the original model. Finally, an explicit formula for...
Energy Technology Data Exchange (ETDEWEB)
De Roeck, W., E-mail: wojciech.deroeck@fys.kuleuven.be, E-mail: christian.maes@fys.kuleuven.be, E-mail: netocny@fzu.cz, E-mail: marius.schutz@fys.kuleuven.be; Maes, C., E-mail: wojciech.deroeck@fys.kuleuven.be, E-mail: christian.maes@fys.kuleuven.be, E-mail: netocny@fzu.cz, E-mail: marius.schutz@fys.kuleuven.be; Schütz, M., E-mail: wojciech.deroeck@fys.kuleuven.be, E-mail: christian.maes@fys.kuleuven.be, E-mail: netocny@fzu.cz, E-mail: marius.schutz@fys.kuleuven.be [Instituut voor Theoretische Fysica, KU Leuven, Leuven (Belgium); Netočný, K., E-mail: wojciech.deroeck@fys.kuleuven.be, E-mail: christian.maes@fys.kuleuven.be, E-mail: netocny@fzu.cz, E-mail: marius.schutz@fys.kuleuven.be [Institute of Physics AS CR, Prague (Czech Republic)
2015-02-15
We study the projection on classical spins starting from quantum equilibria. We show Gibbsianness or quasi-locality of the resulting classical spin system for a class of gapped quantum systems at low temperatures including quantum ground states. A consequence of Gibbsianness is the validity of a large deviation principle in the quantum system which is known and here recovered in regimes of high temperature or for thermal states in one dimension. On the other hand, we give an example of a quantum ground state with strong nonlocality in the classical restriction, giving rise to what we call measurement induced entanglement and still satisfying a large deviation principle.
International Nuclear Information System (INIS)
We study the projection on classical spins starting from quantum equilibria. We show Gibbsianness or quasi-locality of the resulting classical spin system for a class of gapped quantum systems at low temperatures including quantum ground states. A consequence of Gibbsianness is the validity of a large deviation principle in the quantum system which is known and here recovered in regimes of high temperature or for thermal states in one dimension. On the other hand, we give an example of a quantum ground state with strong nonlocality in the classical restriction, giving rise to what we call measurement induced entanglement and still satisfying a large deviation principle
Czech Academy of Sciences Publication Activity Database
Brown, E. C.; Mucha, Martin; Jungwirth, Pavel; Tobias, D. J.
2005-01-01
Roč. 109, - (2005), s. 7934-7940. ISSN 1520-6106 R&D Projects: GA MŠk(CZ) ME 644; GA MŠk(CZ) LC512 Grant ostatní: NSF(US) CHE 0431512 Institutional research plan: CEZ:AV0Z40550506 Keywords : vibrational spectroscopy * salt water * molecular dynamics Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 4.033, year: 2005
Structure Theory for Extended Kepler-Coulomb 3D Classical Superintegrable Systems
Directory of Open Access Journals (Sweden)
Ernie G. Kalnins
2012-06-01
Full Text Available The classical Kepler-Coulomb system in 3 dimensions is well known to be 2nd order superintegrable, with a symmetry algebra that closes polynomially under Poisson brackets. This polynomial closure is typical for 2nd order superintegrable systems in 2D and for 2nd order systems in 3D with nondegenerate (4-parameter potentials. However the degenerate 3-parameter potential for the 3D extended Kepler-Coulomb system (also 2nd order superintegrable is an exception, as its quadratic symmetry algebra doesn't close polynomially. The 3D 4-parameter potential for the extended Kepler-Coulomb system is not even 2nd order superintegrable. However, Verrier and Evans (2008 showed it was 4th order superintegrable, and Tanoudis and Daskaloyannis (2011 showed that in the quantum case, if a second 4th order symmetry is added to the generators, the double commutators in the symmetry algebra close polynomially. Here, based on the Tremblay, Turbiner and Winternitz construction, we consider an infinite class of classical extended Kepler-Coulomb 3- and 4-parameter systems indexed by a pair of rational numbers (k_1,k_2 and reducing to the usual systems when k_1=k_2=1. We show these systems to be superintegrable of arbitrarily high order and work out explicitly the structure of the symmetry algebras determined by the 5 basis generators we have constructed. We demonstrate that the symmetry algebras close rationally; only for systems admitting extra discrete symmetries is polynomial closure achieved. Underlying the structure theory is the existence of raising and lowering constants of the motion, not themselves polynomials in the momenta, that can be employed to construct the polynomial symmetries and their structure relations.
Tethered satellite system dynamics and control
Musetti, B.; Cibrario, B.; Bussolino, L.; Bodley, C. S.; Flanders, H. A.; Mowery, D. K.; Tomlin, D. D.
1990-01-01
The first tethered satellite system, scheduled for launch in May 1991, is reviewed. The system dynamics, dynamics control, and dynamics simulations are discussed. Particular attention is given to in-plane and out-of-plane librations; tether oscillation modes; orbiter and sub-satellite dynamics; deployer control system; the sub-satellite attitude measurement and control system; the Aeritalia Dynamics Model; the Martin-Marietta and NASA-MSFC Dynamics Model; and simulation results.
Extension of Chronological Calculus for Dynamical Systems on Manifolds
Kipka, Robert J.; Ledyaev, Yuri S.
2014-01-01
We propose an extension of the Chronological Calculus, developed by Agrachev and Gamkrelidze for the case of $C^\\infty$-smooth dynamical systems on finite-dimensional $C^\\infty$-smooth manifolds, to the case of $C^m$-smooth dynamical systems and infinite-dimensional $C^m$-manifolds. Due to a relaxation in the underlying structure of the calculus, this extension provides a powerful computational tool without recourse to the theory of calculus in Fr\\'echet spaces required by the classical Chron...
Derrouazin, A.; Aillerie, M.; Mekkakia-Maaza, N.; Charles, J. P.
2016-07-01
Several researches for management of diverse hybrid energy systems and many techniques have been proposed for robustness, savings and environmental purpose. In this work we aim to make a comparative study between two supervision and control techniques: fuzzy and classic logics to manage the hybrid energy system applied for typical housing fed by solar and wind power, with rack of batteries for storage. The system is assisted by the electric grid during energy drop moments. A hydrogen production device is integrated into the system to retrieve surplus energy production from renewable sources for the household purposes, intending the maximum exploitation of these sources over years. The models have been achieved and generated signals for electronic switches command of proposed both techniques are presented and discussed in this paper.
A dynamical systems view of network centrality.
Grindrod, Peter; Higham, Desmond J
2014-05-01
To gain insights about dynamic networks, the dominant paradigm is to study discrete snapshots, or timeslices, as the interactions evolve. Here, we develop and test a new mathematical framework where network evolution is handled over continuous time, giving an elegant dynamical systems representation for the important concept of node centrality. The resulting system allows us to track the relative influence of each individual. This new setting is natural in many digital applications, offering both conceptual and computational advantages. The novel differential equations approach is convenient for modelling and analysis of network evolution and gives rise to an interesting application of the matrix logarithm function. From a computational perspective, it avoids the awkward up-front compromises between accuracy, efficiency and redundancy required in the prevalent discrete-time setting. Instead, we can rely on state-of-the-art ODE software, where discretization takes place adaptively in response to the prevailing system dynamics. The new centrality system generalizes the widely used Katz measure, and allows us to identify and track, at any resolution, the most influential nodes in terms of broadcasting and receiving information through time-dependent links. In addition to the classical static network notion of attenuation across edges, the new ODE also allows for attenuation over time, as information becomes stale. This allows 'running measures' to be computed, so that networks can be monitored in real time over arbitrarily long intervals. With regard to computational efficiency, we explain why it is cheaper to track good receivers of information than good broadcasters. An important consequence is that the overall broadcast activity in the network can also be monitored efficiently. We use two synthetic examples to validate the relevance of the new measures. We then illustrate the ideas on a large-scale voice call network, where key features are discovered that are not
Popa, Alexandru
2013-01-01
Quantum and Classical Connections in Modeling Atomic, Molecular and Electrodynamic Systems is intended for scientists and graduate students interested in the foundations of quantum mechanics and applied scientists interested in accurate atomic and molecular models. This is a reference to those working in the new field of relativistic optics, in topics related to relativistic interactions between very intense laser beams and particles, and is based on 30 years of research. The novelty of this work consists of accurate connections between the properties of quantum equations and correspon
Substructure modal superposition method for non-classical analysis of soil-structure systems
International Nuclear Information System (INIS)
By using a substructure solution technique, the time domain response of the coupled soil-structure systems is determined. The proposed technique can be represented by two different steps. In the first one, by means of a suitable transformation of coordinates, based on the component-mode synthesis, the nodal equations of motion are reduced to a set of equations having non-classical normal modes. In the second one, the reduced equations are solved by means of a step-by-step solution method particularly suited to this kind of equations. Some computational aspects are also evidenced to demonstrate the accuracy of the method. (orig./HP)
Load Frequency Control in Interconnected Power System by Using Classical Controller
Lusika Roy; Bikash Dey
2014-01-01
In modern powers systems change of dynamic load in interconnected power systems is a real life problem in recent era. So to have a constant frequency of operation irrespective of load change in the interconnected power systems, load frequency controllers are employed. To achieve load frequency control, controllers need to maintain a zero steady state errors in multi area interconnected power systems. In this paper we controlled power deviation and frequency deviation of two area interconnecte...
Hamiltonian Dynamics of Darwin Systems
Shapovalov, A V
1997-01-01
We present a Hamiltonian approach for the wellknown Eigen model of the Darwin selection dynamics. Hamiltonization is carried out by means of the embedding of the population variable space, describing behavior of the system, into the space of doubled dimension by introducing additional dynamic variables. Besides the study of the formalism, we try to interpret its basic elements (phase space, Hamiltonian, geometry of solutions) in terms of the theoretical biology. A geometric treatment is given for the considered system dynamics in terms of the geodesic flows in the Euclidean space where the population variables serve as curvilinear coordinates. The evolution of the distribution function is found for arbitrary distributed initial values of the population variables.
Disease processes as hybrid dynamical systems
Directory of Open Access Journals (Sweden)
Pietro Liò
2012-08-01
Full Text Available We investigate the use of hybrid techniques in complex processes of infectious diseases. Since predictive disease models in biomedicine require a multiscale approach for understanding the molecule-cell-tissue-organ-body interactions, heterogeneous methodologies are often employed for describing the different biological scales. Hybrid models provide effective means for complex disease modelling where the action and dosage of a drug or a therapy could be meaningfully investigated: the infection dynamics can be classically described in a continuous fashion, while the scheduling of multiple treatment discretely. We define an algebraic language for specifying general disease processes and multiple treatments, from which a semantics in terms of hybrid dynamical system can be derived. Then, the application of control-theoretic tools is proposed in order to compute the optimal scheduling of multiple therapies. The potentialities of our approach are shown in the case study of the SIR epidemic model and we discuss its applicability on osteomyelitis, a bacterial infection affecting the bone remodelling system in a specific and multiscale manner. We report that formal languages are helpful in giving a general homogeneous formulation for the different scales involved in a multiscale disease process; and that the combination of hybrid modelling and control theory provides solid grounds for computational medicine.
Dynamics of Variable Mass Systems
Eke, Fidelis O.
1998-01-01
This report presents the results of an investigation of the effects of mass loss on the attitude behavior of spinning bodies in flight. The principal goal is to determine whether there are circumstances under which the motion of variable mass systems can become unstable in the sense that their transverse angular velocities become unbounded. Obviously, results from a study of this kind would find immediate application in the aerospace field. The first part of this study features a complete and mathematically rigorous derivation of a set of equations that govern both the translational and rotational motions of general variable mass systems. The remainder of the study is then devoted to the application of the equations obtained to a systematic investigation of the effect of various mass loss scenarios on the dynamics of increasingly complex models of variable mass systems. It is found that mass loss can have a major impact on the dynamics of mechanical systems, including a possible change in the systems stability picture. Factors such as nozzle geometry, combustion chamber geometry, propellant's initial shape, size and relative mass, and propellant location can all have important influences on the system's dynamic behavior. The relative importance of these parameters on-system motion are quantified in a way that is useful for design purposes.
International Nuclear Information System (INIS)
Using the multi-body Classical Molecular Dynamics simulation of 6Li+209Bi reaction it is shown that: (i) the breakup of a projectile fragment near the barrier leads to substantial increase in the ICF probabilities; (ii) the expected increase in σCF on relaxation of the rigid-body (RB) constraint on the projectile is compensated by reduction in the flux leading to CF, due to ICF events; (iii) the breakup probability increases with ECM and, for given ECM it also increases as b increases and peaks around some b>0, while cross sections σCF and σTF were calculated for b=0 only Therefore, we present the results of σCF (Complete Fusion) and σTF (Total Fusion) calculations which are obtained at critical impact parameter, bcr, where many ICF channels open up and compare with the calculations performed at b=0 only, where only few ICF channels open up
Franco, Paula F; Silva, Naylene C S; Fazito do Vale, Vladimir; Abreu, Jéssica F; Santos, Vânia C; Gontijo, Nelder F; Valenzuela, Jesus G; Pereira, Marcos H; Sant'Anna, Mauricio R V; Gomes, Alessandra P S; Araujo, Ricardo N
2016-05-01
Inhibition of the complement system during and after haematophagy is of utmost importance for tick success in feeding and tick development. The role of such inhibition is to minimise damage to the intestinal epithelium as well as avoiding inflammation and opsonisation of salivary molecules at the bite site. Despite its importance, the salivary anti-complement activity has been characterised only in species belonging to the Ixodes ricinus complex which saliva is able to inhibit the alternative and lectin pathways. Little is known about this activity in other species of the Ixodidae family. Thus, the aim of this study was to describe the inhibition of the classical pathway of the complement system by the saliva of Amblyomma cajennense at different stages of the haematophagy. The A. cajennense saliva and salivary gland extract (SGE) were able to inhibit the complement classical pathway through haemolytic assays with higher activity observed when saliva was used. The anti-complement activity is present in the salivary glands of starving females and also in females throughout the whole feeding process, with significant higher activity soon after tick detachment. The SGE activity from both females fed on mice or horses had no significant correlation (p > 0.05) with tick body weight. The pH found in the intestinal lumen of A. cajennense was 8.04 ± 0.08 and haemolytic assays performed at pH 8.0 showed activation of the classical pathway similarly to what occurs at pH 7.4. Consequently, inhibition could be necessary to protect the tick enterocytes. Indeed, the inhibition observed by SGE was higher in pH 8.0 in comparison to pH 7.4 reinforcing the role of saliva in protecting the intestinal cells. Further studies should be carried out in order to identify the inhibitor molecule and characterise its inhibition mechanism. PMID:26948715
Mass properties measurement system dynamics
Doty, Keith L.
1993-01-01
The MPMS mechanism possess two revolute degrees-of-freedom and allows the user to measure the mass, center of gravity, and the inertia tensor of an unknown mass. The dynamics of the Mass Properties Measurement System (MPMS) from the Lagrangian approach to illustrate the dependency of the motion on the unknown parameters.
Dynamical stability of Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Dynamical stability has become the center of study on Hamiltonian system. In this article we intro-duce the recent development in some areas closely related to this topic, such as the KAM theory, Mather theory, Arnolddiffusion and non-singular collision of n-body problem.
Controlling dynamics in diatomic systems
Indian Academy of Sciences (India)
Praveen Kumar; Harjinder Singh
2007-09-01
Controlling molecular energetics using laser pulses is exemplified for nuclear motion in two different diatomic systems. The problem of finding the optimized field for maximizing a desired quantum dynamical target is formulated using an iterative method. The method is applied for two diatomic systems, HF and OH. The power spectra of the fields and evolution of populations of different vibrational states during transitions are obtained.
Advanced dynamics of mechanical systems
Cheli, Federico
2015-01-01
This book introduces a general approach for schematization of mechanical systems with rigid and deformable bodies. It proposes a systems approach to reproduce the interaction of the mechanical system with different force fields such as those due to the action of fluids or contact forces between bodies, i.e., with forces dependent on the system states, introducing the concepts of the stability of motion. In the first part of the text mechanical systems with one or more degrees of freedom with large motion and subsequently perturbed in the neighborhood of the steady state position are analyzed. Both discrete and continuous systems (modal approach, finite elements) are analyzed. The second part is devoted to the study of mechanical systems subject to force fields, the rotor dynamics, techniques of experimental identification of the parameters, and random excitations. The book will be especially valuable for students of engineering courses in Mechanical Systems, Aerospace, Automation, and Energy but will also b...
Adaptive, dynamic, and resilient systems
Suri, Niranjan
2015-01-01
As the complexity of today's networked computer systems grows, they become increasingly difficult to understand, predict, and control. Addressing these challenges requires new approaches to building these systems. Adaptive, Dynamic, and Resilient Systems supplies readers with various perspectives of the critical infrastructure that systems of networked computers rely on. It introduces the key issues, describes their interrelationships, and presents new research in support of these areas.The book presents the insights of a different group of international experts in each chapter. Reporting on r
Quantum simulation of open-system dynamical maps with trapped ions
Schindler, P.; Müller, M.; D. Nigg; Barreiro, J. T.; Martinez, E. A.; M Hennrich; Monz, T.; Diehl, S.; Zoller, P.; Blatt, R.
2012-01-01
Dynamical maps describe general transformations of the state of a physical system, and their iteration can be interpreted as generating a discrete time evolution. Prime examples include classical nonlinear systems undergoing transitions to chaos. Quantum mechanical counterparts show intriguing phenomena such as dynamical localization on the single particle level. Here we extend the concept of dynamical maps to an open-system, many-particle context: We experimentally explore the stroboscopic d...
BILL2D - A software package for classical two-dimensional Hamiltonian systems
Solanpää, J.; Luukko, P. J. J.; Räsänen, E.
2016-02-01
We present BILL2D, a modern and efficient C++ package for classical simulations of two-dimensional Hamiltonian systems. BILL2D can be used for various billiard and diffusion problems with one or more charged particles with interactions, different external potentials, an external magnetic field, periodic and open boundaries, etc. The software package can also calculate many key quantities in complex systems such as Poincaré sections, survival probabilities, and diffusion coefficients. While aiming at a large class of applicable systems, the code also strives for ease-of-use, efficiency, and modularity for the implementation of additional features. The package comes along with a user guide, a developer's manual, and a documentation of the application program interface (API).
Floquet topological system based on frequency-modulated classical coupled harmonic oscillators
Salerno, Grazia; Ozawa, Tomoki; Price, Hannah M.; Carusotto, Iacopo
2016-02-01
We theoretically propose how to observe topological effects in a generic classical system of coupled harmonic oscillators, such as classical pendula or lumped-element electric circuits, whose oscillation frequency is modulated fast in time. Making use of Floquet theory in the high-frequency limit, we identify a regime in which the system is accurately described by a Harper-Hofstadter model where the synthetic magnetic field can be externally tuned via the phase of the frequency modulation of the different oscillators. We illustrate how the topologically protected chiral edge states, as well as the Hofstadter butterfly of bulk bands, can be observed in the driven-dissipative steady state under a monochromatic drive. In analogy with the integer quantum Hall effect, we show how the topological Chern numbers of the bands can be extracted from the mean transverse shift of the steady-state oscillation amplitude distribution. Finally, we discuss the regime where the analogy with the Harper-Hofstadter model breaks down.
Classical integrable systems and soliton equations related to eleven-vertex R-matrix
Levin, A; Zotov, A
2014-01-01
In our recent paper we suggested a natural construction of the classical relativistic integrable tops in terms of the quantum $R$-matrices. Here we study the simplest case -- the 11-vertex $R$-matrix and related ${\\rm gl}_2$ rational models. The corresponding top is equivalent to the 2-body Ruijsenaars-Schneider (RS) or the 2-body Calogero-Moser (CM) model depending on its description. We give different descriptions of the integrable tops and use them as building blocks for construction of more complicated integrable systems such as Gaudin models and classical spin chains (periodic and with boundaries). The known relation between the top and CM (or RS) models allows to re-write the Gaudin models (or the spin chains) in the canonical variables. Then they assume the form of $n$-particle integrable systems with $2n$ constants. We also describe the generalization of the top to 1+1 field theories. It allows us to get the Landau-Lifshitz type equation. The latter can be treated as non-trivial deformation of the cla...
Energy Technology Data Exchange (ETDEWEB)
Gao Yi; Neuhauser, Daniel [Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095-1569 (United States)
2013-05-14
We show how to obtain the correct electronic response of a large system by embedding; a small region is propagated by TDDFT (time-dependent density functional theory) simultaneously with a classical electrodynamics evolution using the Near-Field method over a larger external region. The propagations are coupled through a combined time-dependent density yielding a common Coulomb potential. We show that the embedding correctly describes the plasmonic response of a Mg(0001) slab and its influence on the dynamical charge transfer between an adsorbed H{sub 2}O molecule and the substrate, giving the same spectral shape as full TDDFT (similar plasmon peak and molecular-dependent differential spectra) with much less computational effort. The results demonstrate that atomistic embedding electrodynamics is promising for nanoplasmonics and nanopolaritonics.
International Nuclear Information System (INIS)
We show how to obtain the correct electronic response of a large system by embedding; a small region is propagated by TDDFT (time-dependent density functional theory) simultaneously with a classical electrodynamics evolution using the Near-Field method over a larger external region. The propagations are coupled through a combined time-dependent density yielding a common Coulomb potential. We show that the embedding correctly describes the plasmonic response of a Mg(0001) slab and its influence on the dynamical charge transfer between an adsorbed H2O molecule and the substrate, giving the same spectral shape as full TDDFT (similar plasmon peak and molecular-dependent differential spectra) with much less computational effort. The results demonstrate that atomistic embedding electrodynamics is promising for nanoplasmonics and nanopolaritonics.
Gao, Yi; Neuhauser, Daniel
2013-05-14
We show how to obtain the correct electronic response of a large system by embedding; a small region is propagated by TDDFT (time-dependent density functional theory) simultaneously with a classical electrodynamics evolution using the Near-Field method over a larger external region. The propagations are coupled through a combined time-dependent density yielding a common Coulomb potential. We show that the embedding correctly describes the plasmonic response of a Mg(0001) slab and its influence on the dynamical charge transfer between an adsorbed H2O molecule and the substrate, giving the same spectral shape as full TDDFT (similar plasmon peak and molecular-dependent differential spectra) with much less computational effort. The results demonstrate that atomistic embedding electrodynamics is promising for nanoplasmonics and nanopolaritonics. PMID:23676021
Optimal estimation of dynamic systems
Crassidis, John L
2004-01-01
Most newcomers to the field of linear stochastic estimation go through a difficult process in understanding and applying the theory.This book minimizes the process while introducing the fundamentals of optimal estimation.Optimal Estimation of Dynamic Systems explores topics that are important in the field of control where the signals received are used to determine highly sensitive processes such as the flight path of a plane, the orbit of a space vehicle, or the control of a machine. The authors use dynamic models from mechanical and aerospace engineering to provide immediate results of estim
Dynamics of immune system vulnerabilities
Stromberg, Sean P.
The adaptive immune system can be viewed as a complex system, which adapts, over time, to reflect the history of infections experienced by the organism. Understanding its operation requires viewing it in terms of tradeoffs under constraints and evolutionary history. It typically displays "robust, yet fragile" behavior, meaning common tasks are robust to small changes but novel threats or changes in environment can have dire consequences. In this dissertation we use mechanistic models to study several biological processes: the immune response, the homeostasis of cells in the lymphatic system, and the process that normally prevents autoreactive cells from entering the lymphatic system. Using these models we then study the effects of these processes interacting. We show that the mechanisms that regulate the numbers of cells in the immune system, in conjunction with the immune response, can act to suppress autoreactive cells from proliferating, thus showing quantitatively how pathogenic infections can suppress autoimmune disease. We also show that over long periods of time this same effect can thin the repertoire of cells that defend against novel threats, leading to an age correlated vulnerability. This vulnerability is shown to be a consequence of system dynamics, not due to degradation of immune system components with age. Finally, modeling a specific tolerance mechanism that normally prevents autoimmune disease, in conjunction with models of the immune response and homeostasis we look at the consequences of the immune system mistakenly incorporating pathogenic molecules into its tolerizing mechanisms. The signature of this dynamic matches closely that of the dengue virus system.
Dynamical systems probabilistic risk assessment.
Energy Technology Data Exchange (ETDEWEB)
Denman, Matthew R.; Ames, Arlo Leroy
2014-03-01
Probabilistic Risk Assessment (PRA) is the primary tool used to risk-inform nuclear power regulatory and licensing activities. Risk-informed regulations are intended to reduce inherent conservatism in regulatory metrics (e.g., allowable operating conditions and technical specifications) which are built into the regulatory framework by quantifying both the total risk profile as well as the change in the risk profile caused by an event or action (e.g., in-service inspection procedures or power uprates). Dynamical Systems (DS) analysis has been used to understand unintended time-dependent feedbacks in both industrial and organizational settings. In dynamical systems analysis, feedback loops can be characterized and studied as a function of time to describe the changes to the reliability of plant Structures, Systems and Components (SSCs). While DS has been used in many subject areas, some even within the PRA community, it has not been applied toward creating long-time horizon, dynamic PRAs (with time scales ranging between days and decades depending upon the analysis). Understanding slowly developing dynamic effects, such as wear-out, on SSC reliabilities may be instrumental in ensuring a safely and reliably operating nuclear fleet. Improving the estimation of a plant's continuously changing risk profile will allow for more meaningful risk insights, greater stakeholder confidence in risk insights, and increased operational flexibility.
International Nuclear Information System (INIS)
We explore an instantaneous decoherence correction (IDC) approach for the decoherence and energy relaxation in the quantum-classical dynamics of charge transport in organic semiconducting crystals. These effects, originating from environmental fluctuations, are essential ingredients of the carrier dynamics. The IDC is carried out by measurement-like operations in the adiabatic representation. While decoherence is inherent in the IDC, energy relaxation is taken into account by considering the detailed balance through the introduction of energy-dependent reweighing factors, which could be either Boltzmann (IDC-BM) or Miller-Abrahams (IDC-MA) type. For a non-diagonal electron-phonon coupling model, it is shown that IDC tends to enhance diffusion while energy relaxation weakens this enhancement. As expected, both the IDC-BM and IDC-MA achieve a near-equilibrium distribution at finite temperatures in the diffusion process, while in the Ehrenfest dynamics the electronic system tends to infinite temperature limit. The resulting energy relaxation times with the two kinds of factors lie in different regimes and exhibit different dependences on temperature, decoherence time, and electron-phonon coupling strength, due to different dominant relaxation processes
International Nuclear Information System (INIS)
A self-consistent approximation scheme is formulated for the calculation of the dynamical linear polarizability of classical electron monolayers. The derivation is carried out in two stages. In the first stage, the authors formulate a simple response function relation linking linear and quadratic polarizabilities; the dynamical coupling function is expressed entirely in terms of the latter. The basic elements in the derivation are the first BBGKY kinetic equation (prepared in the velocity average approximation) and the non-linear fluctuation-dissipation theorem. The new response function relation is exact at zero frequency and exactly satisfies the third frequency moment sum rule. In the second stage, self-consistency is guaranteed by approximating the quadratic polarizability in terms of linear ones. The theory is examined in the weak coupling limit where it is found that a dominant γ-independent non-RPA contribution to the damping is missing. The structure of the missing term is identified at arbitrary coupling strengths. Work is in progress to see how it can be incorporated into the approximation scheme. (author)
International Nuclear Information System (INIS)
We present converged quantum dynamics for the H + D2 reaction at a total energy high enough to produce HD in the v' = 3, j' = 7 vibrational-rotational state and for total angular momenta J = 0, 1, and 2. We compare state-to-state partial cross sections for H + D2 (v = 0-2, j = 0, J = 0-2) → HD (v' = 0-2, j') + H and H + D2 (v = 1, j = 6, J = 0-2) → HD (v' = 0-2, j') + H as calculated from classical trajectory calculations with quantized initial conditions, i.e., a quasiclassical trajectory (QCT) simulation, to the results of converged quantum dynamics calculations involving up to 654 coupled channels. Final states in the QCT calculations are assigned by the quadratic smooth sampling (QSS) method. Since the quasiclassical and quantal calculations are carried out with the same potential energy surface, the comparison provides a direct test of the accuracy of the quasiclassical simulations as a function of the initial vibrational-rotational state and the final vibrational-rotational state
Hidden attractors in dynamical systems
Dudkowski, Dawid; Jafari, Sajad; Kapitaniak, Tomasz; Kuznetsov, Nikolay V.; Leonov, Gennady A.; Prasad, Awadhesh
2016-06-01
Complex dynamical systems, ranging from the climate, ecosystems to financial markets and engineering applications typically have many coexisting attractors. This property of the system is called multistability. The final state, i.e., the attractor on which the multistable system evolves strongly depends on the initial conditions. Additionally, such systems are very sensitive towards noise and system parameters so a sudden shift to a contrasting regime may occur. To understand the dynamics of these systems one has to identify all possible attractors and their basins of attraction. Recently, it has been shown that multistability is connected with the occurrence of unpredictable attractors which have been called hidden attractors. The basins of attraction of the hidden attractors do not touch unstable fixed points (if exists) and are located far away from such points. Numerical localization of the hidden attractors is not straightforward since there are no transient processes leading to them from the neighborhoods of unstable fixed points and one has to use the special analytical-numerical procedures. From the viewpoint of applications, the identification of hidden attractors is the major issue. The knowledge about the emergence and properties of hidden attractors can increase the likelihood that the system will remain on the most desirable attractor and reduce the risk of the sudden jump to undesired behavior. We review the most representative examples of hidden attractors, discuss their theoretical properties and experimental observations. We also describe numerical methods which allow identification of the hidden attractors.
Variational Gaussian Process Dynamical Systems
Damianou, Andreas C.; Titsias, Michalis K.; Lawrence, Neil D.
2011-01-01
High dimensional time series are endemic in applications of machine learning such as robotics (sensor data), computational biology (gene expression data), vision (video sequences) and graphics (motion capture data). Practical nonlinear probabilistic approaches to this data are required. In this paper we introduce the variational Gaussian process dynamical system. Our work builds on recent variational approximations for Gaussian process latent variable models to allow for nonlinear dimensional...
DYNAMICS OF FINANCIAL SYSTEM: A SYSTEM DYNAMICS APPROACH
Directory of Open Access Journals (Sweden)
Girish K Nair
2013-01-01
Full Text Available There are several ratios which define the financial health of an organization but the importance of Net cash flow, Gross income, Net income, Pending bills, Receivable bills, Debt, and Book value can never be undermined as they give the exact picture of the financial condition. While there are several approaches to study the dynamics of these variables, system dynamics based modelling and simulation is one of the modern techniques. The paper explores this method to simulate the before mentioned parameters during production capacity expansion in an electronic industry. Debt and Book value have shown a non-linear pattern of variation which is discussed. The model can be used by the financial experts as a decision support tool in arriving at conclusions in connection to the expansion plans of the organization.
On Rank Driven Dynamical Systems
Veerman, J. J. P.; Prieto, F. J.
2014-08-01
We investigate a class of models related to the Bak-Sneppen (BS) model, initially proposed to study evolution. The BS model is extremely simple and yet captures some forms of "complex behavior" such as self-organized criticality that is often observed in physical and biological systems. In this model, random fitnesses in are associated to agents located at the vertices of a graph . Their fitnesses are ranked from worst (0) to best (1). At every time-step the agent with the worst fitness and some others with a priori given rank probabilities are replaced by new agents with random fitnesses. We consider two cases: The exogenous case where the new fitnesses are taken from an a priori fixed distribution, and the endogenous case where the new fitnesses are taken from the current distribution as it evolves. We approximate the dynamics by making a simplifying independence assumption. We use Order Statistics and Dynamical Systems to define a rank-driven dynamical system that approximates the evolution of the distribution of the fitnesses in these rank-driven models, as well as in the BS model. For this simplified model we can find the limiting marginal distribution as a function of the initial conditions. Agreement with experimental results of the BS model is excellent.
Classification of Dynamic Vehicle Routing Systems
DEFF Research Database (Denmark)
Larsen, Allan; Madsen, Oli B.G.; Solomon, Marius M.
2007-01-01
classify dynamic vehicle routing systems. Methods for evaluation of the performance of algorithms that solve on-line routing problems are discussed and we list some of the most important issues to include in the system objective. Finally, we provide a three-echelon classification of dynamic vehicle routing...... systems based on their degree of dynamism and the system objective....
Numerical solution of ordinary differential equations. For classical, relativistic and nano systems
International Nuclear Information System (INIS)
An up-to-date survey on numerical solutions with theory, intuition and applications. Ordinary differential equations (ODE) play a significant role in mathematics, physics and engineering sciences, and thus are part of relevant college and university courses. Many problems, however, both traditional and modern, do not possess exact solutions, and must be treated numerically. Usually this is done with software packages, but for this to be efficient requires a sound understanding of the mathematics involved. This work meets the need for an affordable textbook that helps in understanding numerical solutions of ODE. Carefully structured by an experienced textbook author, it provides a survey of ODE for various applications, both classical and modern, including such special applications as relativistic and nano systems. The examples are carefully explained and compiled into an algorithm, each of which is presented generically, independent of a specific programming language, while each chapter is rounded off with exercises. The text meets the demands of MA200 courses and of the newly created Numerical Solution of Differential Equations courses, making it ideal for both students and lecturers in physics, mathematics, mechanical engineering, electrical engineering, as well as for physicists, mathematicians, engineers, and electrical engineers. From the Contents - Euler's Method - Runge-Kutta Methods - The Method of Taylor Expansions - Large Second Order Systems with Application to Nano Systems - Completely Conservative, Covariant Numerical Methodology - Instability - Numerical Solution of Tridiagonal Linear Algebraic Systems and Related Nonlinear Systems - Approximate Solution of Boundary Value Problems - Special Relativistic Motion - Special Topics - Appendix: Basic Matrix Operations - Bibliography. (orig.) (orig.)
Driving linear systems towards non-classical states with the help of noise
Genoni, Marco G; Serafini, Alessio
2012-01-01
We study the possibility of taking bosonic systems subject to quadratic Hamiltonians and a noisy thermal environment to non-classical stationary states by weak Gaussian measurements and conditioned linear driving. We derive general analytical upper bounds for the single mode squeezing and multimode entanglement at steady state, depending only on the Hamiltonian parameters and on the number of thermal excitations of the bath. Our findings show that, rather surprisingly, larger number of thermal excitations in the bath allow for larger steady-state squeezing and entanglement if the efficiency of the Gaussian measurements conditioning the feedback loop is high enough. Such efficiencies are included in our exact treatment, which allows us to determine efficiency thresholds for the noise-enhancement of quantum resources to take place.
On the Hamilton-Jacobi method in classical and quantum nonconservative systems
Dutra, A de Souza; Moraes, P H R S
2015-01-01
In this work we show how to complete some Hamilton-Jacobi solutions of linear, nonconservative classical oscillatory systems which appeared in the literature and we extend these complete solutions to the quantum mechanical case. In addition, we get the solution of the quantum Hamilton-Jacobi equation for an electric charge in an oscillating pulsing magnetic field. We also argue that for the case where a charged particle is under the action of an oscillating magnetic field, one can apply nuclear magnetic resonance techniques in order to find experimental results regarding this problem. We obtain all results analytically, showing that the quantum Hamilton-Jacobi formalism is a powerful tool to describe quantum mechanics.
Paradoxical probabilistic behavior for strongly correlated many-body classical systems
Jauregui, Max; Tsallis, Constantino
2015-09-01
Using a simple probabilistic model, we illustrate that a small part of a strongly correlated many-body classical system can show a paradoxical behavior, namely asymptotic stochastic independence. We consider a triangular array such that each row is a list of n strongly correlated random variables. The correlations are preserved even when n → ∞, since the standard central limit theorem does not hold for this array. We show that, if we choose a fixed number m < n of random variables of the nth row and trace over the other n - m variables, and then consider n → ∞, the m chosen ones can, paradoxically, turn out to be independent. However, the scenario can be different if m increases with n. Finally, we suggest a possible experimental verification of our results near criticality of a second-order phase transition.
Indian Academy of Sciences (India)
R S Kaushal
2009-08-01
Certain aspects of classical and quantum mechanics of complex Hamiltonian systems in one dimension investigated within the framework of an extended complex phase space approach, characterized by the transformation = 1 + 2, = 1 + 2, are revisited. It is argued that Carl Bender inducted $\\mathcal{PT}$ symmetry in the studies of complex power potentials as a particular case of the present general framework in which two additional degrees of freedom are produced by extending each coordinate and momentum into complex planes. With a view to account for the subjective component of physical reality inherent in the collected data, e.g., using a Chevreul (hand-held) pendulum, a generalization of the Hamilton’s principle of least action is suggested.