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Sample records for linear polaron hamiltonian

  1. Problems of linear electron (polaron) transport theory in semiconductors

    CERN Document Server

    Klinger, M I

    1979-01-01

    Problems of Linear Electron (Polaron) Transport Theory in Semiconductors summarizes and discusses the development of areas in electron transport theory in semiconductors, with emphasis on the fundamental aspects of the theory and the essential physical nature of the transport processes. The book is organized into three parts. Part I focuses on some general topics in the theory of transport phenomena: the general dynamical theory of linear transport in dissipative systems (Kubo formulae) and the phenomenological theory. Part II deals with the theory of polaron transport in a crystalline semicon

  2. Hamiltonian structure of linearly extended Virasoro algebra

    International Nuclear Information System (INIS)

    Arakelyan, T.A.; Savvidi, G.K.

    1991-01-01

    The Hamiltonian structure of linearly extended Virasoro algebra which admits free bosonic field representation is described. An example of a non-trivial extension is found. The hierarchy of integrable non-linear equations corresponding to this Hamiltonian structure is constructed. This hierarchy admits the Lax representation by matrix Lax operator of second order

  3. Linear and non-linear infrared response of one-dimensional vibrational Holstein polarons in the anti-adiabatic limit: Optical and acoustical phonon models

    Science.gov (United States)

    Falvo, Cyril

    2018-02-01

    The theory of linear and non-linear infrared response of vibrational Holstein polarons in one-dimensional lattices is presented in order to identify the spectral signatures of self-trapping phenomena. Using a canonical transformation, the optical response is computed from the small polaron point of view which is valid in the anti-adiabatic limit. Two types of phonon baths are considered: optical phonons and acoustical phonons, and simple expressions are derived for the infrared response. It is shown that for the case of optical phonons, the linear response can directly probe the polaron density of states. The model is used to interpret the experimental spectrum of crystalline acetanilide in the C=O range. For the case of acoustical phonons, it is shown that two bound states can be observed in the two-dimensional infrared spectrum at low temperature. At high temperature, analysis of the time-dependence of the two-dimensional infrared spectrum indicates that bath mediated correlations slow down spectral diffusion. The model is used to interpret the experimental linear-spectroscopy of model α-helix and β-sheet polypeptides. This work shows that the Davydov Hamiltonian cannot explain the observations in the NH stretching range.

  4. Hamiltonian structures of some non-linear evolution equations

    International Nuclear Information System (INIS)

    Tu, G.Z.

    1983-06-01

    The Hamiltonian structure of the O(2,1) non-linear sigma model, generalized AKNS equations, are discussed. By reducing the O(2,1) non-linear sigma model to its Hamiltonian form some new conservation laws are derived. A new hierarchy of non-linear evolution equations is proposed and shown to be generalized Hamiltonian equations with an infinite number of conservation laws. (author)

  5. A Hamiltonian functional for the linearized Einstein vacuum field equations

    International Nuclear Information System (INIS)

    Rosas-RodrIguez, R

    2005-01-01

    By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a conserved functional as Hamiltonian; this Hamiltonian is not the analog of the energy of the field. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained. The generator of spatial translations associated with such bracket is also obtained

  6. Periodic solutions of asymptotically linear Hamiltonian systems without twist conditions

    Energy Technology Data Exchange (ETDEWEB)

    Cheng Rong [Coll. of Mathematics and Physics, Nanjing Univ. of Information Science and Tech., Nanjing (China); Dept. of Mathematics, Southeast Univ., Nanjing (China); Zhang Dongfeng [Dept. of Mathematics, Southeast Univ., Nanjing (China)

    2010-05-15

    In dynamical system theory, especially in many fields of applications from mechanics, Hamiltonian systems play an important role, since many related equations in mechanics can be written in an Hamiltonian form. In this paper, we study the existence of periodic solutions for a class of Hamiltonian systems. By applying the Galerkin approximation method together with a result of critical point theory, we establish the existence of periodic solutions of asymptotically linear Hamiltonian systems without twist conditions. Twist conditions play crucial roles in the study of periodic solutions for asymptotically linear Hamiltonian systems. The lack of twist conditions brings some difficulty to the study. To the authors' knowledge, very little is known about the case, where twist conditions do not hold. (orig.)

  7. A Hamiltonian structure for the linearized Einstein vacuum field equations

    International Nuclear Information System (INIS)

    Torres del Castillo, G.F.

    1991-01-01

    By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained (Author)

  8. Focal points and principal solutions of linear Hamiltonian systems revisited

    Science.gov (United States)

    Šepitka, Peter; Šimon Hilscher, Roman

    2018-05-01

    In this paper we present a novel view on the principal (and antiprincipal) solutions of linear Hamiltonian systems, as well as on the focal points of their conjoined bases. We present a new and unified theory of principal (and antiprincipal) solutions at a finite point and at infinity, and apply it to obtain new representation of the multiplicities of right and left proper focal points of conjoined bases. We show that these multiplicities can be characterized by the abnormality of the system in a neighborhood of the given point and by the rank of the associated T-matrix from the theory of principal (and antiprincipal) solutions. We also derive some additional important results concerning the representation of T-matrices and associated normalized conjoined bases. The results in this paper are new even for completely controllable linear Hamiltonian systems. We also discuss other potential applications of our main results, in particular in the singular Sturmian theory.

  9. Nonautonomous linear Hamiltonian systems oscillation, spectral theory and control

    CERN Document Server

    Johnson, Russell; Novo, Sylvia; Núñez, Carmen; Fabbri, Roberta

    2016-01-01

    This monograph contains an in-depth analysis of the dynamics given by a linear Hamiltonian system of general dimension with nonautonomous bounded and uniformly continuous coefficients, without other initial assumptions on time-recurrence. Particular attention is given to the oscillation properties of the solutions as well as to a spectral theory appropriate for such systems. The book contains extensions of results which are well known when the coefficients are autonomous or periodic, as well as in the nonautonomous two-dimensional case. However, a substantial part of the theory presented here is new even in those much simpler situations. The authors make systematic use of basic facts concerning Lagrange planes and symplectic matrices, and apply some fundamental methods of topological dynamics and ergodic theory. Among the tools used in the analysis, which include Lyapunov exponents, Weyl matrices, exponential dichotomy, and weak disconjugacy, a fundamental role is played by the rotation number for linear Hami...

  10. On the existence of star products on quotient spaces of linear Hamiltonian torus actions

    DEFF Research Database (Denmark)

    Herbig, Hans-Christian; Iyengar, Srikanth B.; Pflaum, Markus J.

    2009-01-01

    that the Koszul complex on the moment map of an effective linear Hamiltonian torus action is acyclic. We rephrase the nonpositivity condition of Arms and Gotay (Adv Math 79(1):43–103, 1990) for linear Hamiltonian torus actions. It follows that reduced spaces of such actions admit continuous star products....

  11. Hamiltonian analysis for linearly acceleration-dependent Lagrangians

    Energy Technology Data Exchange (ETDEWEB)

    Cruz, Miguel, E-mail: miguelcruz02@uv.mx, E-mail: roussjgc@gmail.com, E-mail: molgado@fc.uaslp.mx, E-mail: efrojas@uv.mx; Gómez-Cortés, Rosario, E-mail: miguelcruz02@uv.mx, E-mail: roussjgc@gmail.com, E-mail: molgado@fc.uaslp.mx, E-mail: efrojas@uv.mx; Rojas, Efraín, E-mail: miguelcruz02@uv.mx, E-mail: roussjgc@gmail.com, E-mail: molgado@fc.uaslp.mx, E-mail: efrojas@uv.mx [Facultad de Física, Universidad Veracruzana, 91000 Xalapa, Veracruz, México (Mexico); Molgado, Alberto, E-mail: miguelcruz02@uv.mx, E-mail: roussjgc@gmail.com, E-mail: molgado@fc.uaslp.mx, E-mail: efrojas@uv.mx [Facultad de Ciencias, Universidad Autónoma de San Luis Potosí, Avenida Salvador Nava S/N Zona Universitaria, CP 78290 San Luis Potosí, SLP, México (Mexico)

    2016-06-15

    We study the constrained Ostrogradski-Hamilton framework for the equations of motion provided by mechanical systems described by second-order derivative actions with a linear dependence in the accelerations. We stress out the peculiar features provided by the surface terms arising for this type of theories and we discuss some important properties for this kind of actions in order to pave the way for the construction of a well defined quantum counterpart by means of canonical methods. In particular, we analyse in detail the constraint structure for these theories and its relation to the inherent conserved quantities where the associated energies together with a Noether charge may be identified. The constraint structure is fully analyzed without the introduction of auxiliary variables, as proposed in recent works involving higher order Lagrangians. Finally, we also provide some examples where our approach is explicitly applied and emphasize the way in which our original arrangement results in propitious for the Hamiltonian formulation of covariant field theories.

  12. Linear Port-Hamiltonian Systems on Infinite-dimensional Spaces

    CERN Document Server

    Jacob, Birgit

    2012-01-01

    This book provides a self-contained introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems. The textbook starts with elementary known results, then progresses smoothly to advanced topics in current research. Many physical systems can be formulated using a Hamiltonian framework, leading to models described by ordinary or partial differential equations. For the purpose of control and for the interconnection of two or more Hamiltonian systems it is essential to take into account this interaction with the environment. This book is the fir

  13. Quantum vibrational polarons: Crystalline acetanilide revisited

    Science.gov (United States)

    Hamm, Peter; Edler, Julian

    2006-03-01

    We discuss a refined theoretical description of the peculiar spectroscopy of crystalline acetanilide (ACN). Acetanilide is a molecular crystal with quasi-one-dimensional chains of hydrogen-bonded units, which is often regarded as a model system for the vibrational spectroscopy of proteins. In linear spectroscopy, the CO stretching (amide I) band of ACN features a double-peak structure, the lower of which shows a pronounced temperature dependence which has been discussed in the context of polaron theory. In nonlinear spectroscopy, both of these peaks respond distinctly differently. The lower-frequency band exhibits the anharmonicity expected from polaron theory, while the higher-frequency band responds as if it were quasiharmonic. We have recently related the response of the higher-frequency band to that of a free exciton [J. Edler and P. Hamm, J. Chem. Phys. 117, 2415 (2002)]. However, as discussed in the present paper, the free exciton is not an eigenstate of the full quantum version of the Holstein polaron Hamiltonian, which is commonly used to describe these phenomena. In order to resolve this issue, we present a numerically exact solution of the Holstein polaron Hamiltonian in one dimension (1D) and 3D. In 1D, we find that the commonly used displaced oscillator picture remains qualitatively correct, even for relatively large exciton coupling. However, the result is not in agreement with the experiment, as it fails to explain the free-exciton band. In contrast, when taking into account the 3D nature of crystalline acetanilide, certain parameter regimes exist where the displaced oscillator picture breaks down and states appear in the spectrum that indeed exhibit the characteristics of a free exciton. The appearance of these states is a speciality of vibrational polarons, whose source of exciton coupling is transition dipole coupling which is expected to have opposite signs of interchain and intrachain coupling.

  14. A study of the linear free energy model for DNA structures using the generalized Hamiltonian formalism

    Energy Technology Data Exchange (ETDEWEB)

    Yavari, M., E-mail: yavari@iaukashan.ac.ir [Islamic Azad University, Kashan Branch (Iran, Islamic Republic of)

    2016-06-15

    We generalize the results of Nesterenko [13, 14] and Gogilidze and Surovtsev [15] for DNA structures. Using the generalized Hamiltonian formalism, we investigate solutions of the equilibrium shape equations for the linear free energy model.

  15. Adiabatic Hamiltonian deformation, linear response theory, and nonequilibrium molecular dynamics

    International Nuclear Information System (INIS)

    Hoover, W.G.

    1980-01-01

    Although Hamiltonians of various kinds have previously been used to derive Green-Kubo relations for the transport coefficients, the particular choice described is uniquely related to thermodynamics. This nonequilibrium Hamiltonian formulation of fluid flow provides pedagogically simple routes to nonequilibrium fluxes and distribution functions, to theoretical understanding of long-time effects, and to new numerical methods for simulating systems far from equilibrium. The same methods are now being applied to solid-phase problems. At the relatively high frequencies used in the viscous fluid calculations described, solids typically behave elastically. Lower frequencies lead to the formation of dislocations and other defects, making it possible to study plastic flow. A property of the nonequilibrium equations of motion which might be profitably explored is their effective irreversibility. Because only a few particles are necessary to generate irreversible behavior, simulations using adiabatic deformations of the kind described here could perhaps elucidate the instability in the equations of motion responsible for irreversibility

  16. The Bogolubov Representation of the Polaron Model and Its Completely Integrable RPA-Approximation

    International Nuclear Information System (INIS)

    Bogolubov, Nikolai N. Jr.; Prykarpatsky, Yarema A.; Ghazaryan, Anna A.

    2009-12-01

    The polaron model in ionic crystal is studied in the N. Bogolubov representation using a special RPA-approximation. A new exactly solvable approximated polaron model is derived and described in detail. Its free energy at finite temperature is calculated analytically. The polaron free energy in the constant magnetic field at finite temperature is also discussed. Based on the structure of the N. Bogolubov unitary transformed polaron Hamiltonian a very important new result is stated: the full polaron model is exactly solvable. (author)

  17. Vibronic effects and destruction of exciton coherence in optical spectra of J-aggregates: A variational polaron transformation approach

    Energy Technology Data Exchange (ETDEWEB)

    Bloemsma, E.A.; Silvis, M.H.; Stradomska, A.; Knoester, J., E-mail: j.knoester@rug.nl

    2016-12-20

    Using a symmetry adapted polaron transformation of the Holstein Hamiltonian, we study the interplay of electronic excitation-vibration couplings, resonance excitation transfer interactions, and temperature in the linear absorption spectra of molecular J-aggregates. Semi-analytical expressions for the spectra are derived and compared with results obtained from direct numerical diagonalization of the Hamiltonian in the two-particle basis set representation. At zero temperature, we show that our polaron transformation reproduces both the collective (exciton) and single-molecule (vibrational) optical response associated with the appropriate standard perturbation limits. Specifically, for the molecular dimer excellent agreement with the spectra from the two-particle approach for the entire range of model parameters is obtained. This is in marked contrast to commonly used polaron transformations. Upon increasing the temperature, the spectra show a transition from the collective to the individual molecular features, which results from the thermal destruction of the exciton coherence.

  18. Riccati inequality, disconjugacy, and reciprocity principle for linear Hamiltonian dynamic systems

    Czech Academy of Sciences Publication Activity Database

    Hilscher, R.; Řehák, Pavel

    2003-01-01

    Roč. 12, č. 1 (2003), s. 171-189 ISSN 1056-2176 R&D Projects: GA ČR GA201/01/0079; GA ČR GP201/01/P041 Institutional research plan: CEZ:AV0Z1019905; CEZ:AV0Z1019905 Keywords : linear Hamiltonian dynamic systems * disconjugacy * Riccati inequality Subject RIV: BA - General Mathematics Impact factor: 0.256, year: 2002

  19. Linearly scaling and almost Hamiltonian dielectric continuum molecular dynamics simulations through fast multipole expansions

    Energy Technology Data Exchange (ETDEWEB)

    Lorenzen, Konstantin; Mathias, Gerald; Tavan, Paul, E-mail: tavan@physik.uni-muenchen.de [Lehrstuhl für BioMolekulare Optik, Ludig–Maximilians Universität München, Oettingenstr. 67, 80538 München (Germany)

    2015-11-14

    Hamiltonian Dielectric Solvent (HADES) is a recent method [S. Bauer et al., J. Chem. Phys. 140, 104103 (2014)] which enables atomistic Hamiltonian molecular dynamics (MD) simulations of peptides and proteins in dielectric solvent continua. Such simulations become rapidly impractical for large proteins, because the computational effort of HADES scales quadratically with the number N of atoms. If one tries to achieve linear scaling by applying a fast multipole method (FMM) to the computation of the HADES electrostatics, the Hamiltonian character (conservation of total energy, linear, and angular momenta) may get lost. Here, we show that the Hamiltonian character of HADES can be almost completely preserved, if the structure-adapted fast multipole method (SAMM) as recently redesigned by Lorenzen et al. [J. Chem. Theory Comput. 10, 3244-3259 (2014)] is suitably extended and is chosen as the FMM module. By this extension, the HADES/SAMM forces become exact gradients of the HADES/SAMM energy. Their translational and rotational invariance then guarantees (within the limits of numerical accuracy) the exact conservation of the linear and angular momenta. Also, the total energy is essentially conserved—up to residual algorithmic noise, which is caused by the periodically repeated SAMM interaction list updates. These updates entail very small temporal discontinuities of the force description, because the employed SAMM approximations represent deliberately balanced compromises between accuracy and efficiency. The energy-gradient corrected version of SAMM can also be applied, of course, to MD simulations of all-atom solvent-solute systems enclosed by periodic boundary conditions. However, as we demonstrate in passing, this choice does not offer any serious advantages.

  20. Quantum dynamics of a vibronically coupled linear chain using a surrogate Hamiltonian approach

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Myeong H., E-mail: myeong.lee@warwick.ac.uk; Troisi, Alessandro [Department of Chemistry and Centre for Scientific Computing, University of Warwick, Coventry CV4 7AL (United Kingdom)

    2016-06-07

    Vibronic coupling between the electronic and vibrational degrees of freedom has been reported to play an important role in charge and exciton transport in organic photovoltaic materials, molecular aggregates, and light-harvesting complexes. Explicitly accounting for effective vibrational modes rather than treating them as a thermal environment has been shown to be crucial to describe the effect of vibronic coupling. We present a methodology to study dissipative quantum dynamics of vibronically coupled systems based on a surrogate Hamiltonian approach, which is in principle not limited by Markov approximation or weak system-bath interaction, using a vibronic basis. We apply vibronic surrogate Hamiltonian method to a linear chain system and discuss how different types of relaxation process, intramolecular vibrational relaxation and intermolecular vibronic relaxation, influence population dynamics of dissipative vibronic systems.

  1. Second order approximation for optical polaron in the strong coupling case

    International Nuclear Information System (INIS)

    Bogolubov, N.N. Jr.

    1993-11-01

    Here we propose a method of construction second order approximation for ground state energy for class of model Hamiltonian with linear type interaction on Bose operators in strong coupling case. For the application of the above method we have considered polaron model and propose construction set of nonlinear differential equations for definition ground state energy in strong coupling case. We have considered also radial symmetry case. (author). 10 refs

  2. Polaron effects on the linear and the nonlinear optical absorption coefficients and refractive index changes in cylindrical quantum dots with applied magnetic field

    International Nuclear Information System (INIS)

    Wu Qingjie; Guo Kangxian; Liu Guanghui; Wu Jinghe

    2013-01-01

    Polaron effects on the linear and the nonlinear optical absorption coefficients and refractive index changes in cylindrical quantum dots with the radial parabolic potential and the z-direction linear potential with applied magnetic field are theoretically investigated. The optical absorption coefficients and refractive index changes are presented by using the compact-density-matrix approach and iterative method. Numerical calculations are presented for GaAs/AlGaAs. It is found that taking into account the electron-LO-phonon interaction, not only are the linear, the nonlinear and the total optical absorption coefficients and refractive index changes enhanced, but also the total optical absorption coefficients are more sensitive to the incident optical intensity. It is also found that no matter whether the electron-LO-phonon interaction is considered or not, the absorption coefficients and refractive index changes above are strongly dependent on the radial frequency, the magnetic field and the linear potential coefficient.

  3. Polaron crossover in molecular solids

    International Nuclear Information System (INIS)

    Zoli, Marco; Das, A N

    2004-01-01

    An analytical variational method is applied to the molecular Holstein Hamiltonian in which the dispersive features of the dimension dependent phonon spectrum are taken into account by a force constant approach. The crossover between a large and a small size polaron is monitored, in one, two and three dimensions and for different values of the adiabatic parameter, through the behaviour of the effective mass as a function of the electron-phonon coupling. By increasing the strength of the intermolecular forces the crossover becomes smoother and occurs at higher e-ph couplings. These effects are more evident in three dimensions. We show that our modified Lang-Firsov method starts to capture the occurrence of a polaron self-trapping transition when the electron energies become of order of the phonon energies. The self-trapping event persists in the fully adiabatic regime. At the crossover we estimate polaron effective masses of order ∼ 5-40 times the bare band mass according to the dimensionality and the value of the adiabatic parameter. Modified Lang-Firsov polaron masses are substantially reduced in two and three dimensions. There is no self-trapping in the antiadiabatic regime

  4. The linearity of quantum mechanics from the perspective of Hamiltonian cellular automata

    International Nuclear Information System (INIS)

    Enrico Fermi, Università di Pisa, Largo Pontecorvo 3, I-56127 Pisa (Italy))" data-affiliation=" (Dipartimento di Fisica Enrico Fermi, Università di Pisa, Largo Pontecorvo 3, I-56127 Pisa (Italy))" >Elze, Hans-Thomas

    2014-01-01

    We discuss the action principle and resulting Hamiltonian equations of motion for a class of integer-valued cellular automata introduced recently [1]. Employing sampling theory, these deterministic finite-difference equations are mapped reversibly on continuum equations describing a set of bandwidth limited harmonic oscillators. They represent the Schrödinger equation. However, modifications reflecting the bandwidth limit are incorporated, i.e., the presence of a time (or length) scale. When this discreteness scale is taken to zero, the usual results are obtained. Thus, the linearity of quantum mechanics can be traced to the postulated action principle of such cellular automata and its conservation laws to discrete ones. The cellular automaton conservation laws are in one-to-one correspondence with those of the related quantum mechanical model, while admissible symmetries are not.

  5. Polarons in advanced materials

    CERN Document Server

    Alexandrov, Alexandre Sergeevich

    2008-01-01

    Polarons in Advanced Materials will lead the reader from single-polaron problems to multi-polaron systems and finally to a description of many interesting phenomena in high-temperature superconductors, ferromagnetic oxides, conducting polymers and molecular nanowires. The book divides naturally into four parts. Part I introduces a single polaron and describes recent achievements in analytical and numerical studies of polaron properties in different electron-phonon models. Part II and Part III describe multi-polaron physics, and Part IV describes many key physical properties of high-temperature superconductors, colossal magnetoresistance oxides, conducting polymers and molecular nanowires, which were understood with polarons and bipolarons. The book is written in the form of self-consistent reviews authored by well-established researchers actively working in the field and will benefit scientists and postgraduate students with a background in condensed matter physics and materials sciences.

  6. Polarons in acetanilide

    Science.gov (United States)

    Scott, Alwyn C.; Bigio, Irving J.; Johnston, Clifford T.

    1989-06-01

    The best available data are presented of the integrated intensity of the 1650-cm-1 band in crystalline acetanilide as a function of temperature. A concise theory of polaron states is presented and used to interpret the data.

  7. Big magnetoresistance: magnetic polarons

    International Nuclear Information System (INIS)

    Teresa, J.M. de; Ibarra, M.R.

    1997-01-01

    By using several macro and microscopic experimental techniques we have given evidence for magnetoresistance in manganese oxides caused by the effect of the magnetic field on the magnetic polarons. (Author) 3 refs

  8. The polaron problem and the Boltzmann equation

    International Nuclear Information System (INIS)

    Devreese, J.

    1979-01-01

    A mobility theory for the Feynman polaron is developed. It is shown that the Boltzmann equation for polarons is valid for weak coupling and not too high electric fields. The analytical results indicate that for E → 0 the relaxation time approximation is valid. A comparison is made of three methods to calculate the mobility in a linear electron transport theory. An approximation to the Kubo formula, a mobility calculation using path integrals by Feynman and a calculation based on the displaced Maxwell distribution function are considered. The three methods lead to equivalent results in the weak scattering and small electric field limit

  9. Comparative analysis of magnetic resonance in the polaron pair recombination and the triplet exciton-polaron quenching models

    Science.gov (United States)

    Mkhitaryan, V. V.; Danilović, D.; Hippola, C.; Raikh, M. E.; Shinar, J.

    2018-01-01

    We present a comparative theoretical study of magnetic resonance within the polaron pair recombination (PPR) and the triplet exciton-polaron quenching (TPQ) models. Both models have been invoked to interpret the photoluminescence detected magnetic resonance (PLDMR) results in π -conjugated materials and devices. We show that resonance line shapes calculated within the two models differ dramatically in several regards. First, in the PPR model, the line shape exhibits unusual behavior upon increasing the microwave power: it evolves from fully positive at weak power to fully negative at strong power. In contrast, in the TPQ model, the PLDMR is completely positive, showing a monotonic saturation. Second, the two models predict different dependencies of the resonance signal on the photoexcitation power, PL. At low PL, the resonance amplitude Δ I /I is ∝PL within the PPR model, while it is ∝PL2 crossing over to PL3 within the TPQ model. On the physical level, the differences stem from different underlying spin dynamics. Most prominently, a negative resonance within the PPR model has its origin in the microwave-induced spin-Dicke effect, leading to the resonant quenching of photoluminescence. The spin-Dicke effect results from the spin-selective recombination, leading to a highly correlated precession of the on-resonance pair partners under the strong microwave power. This effect is not relevant for TPQ mechanism, where the strong zero-field splitting renders the majority of triplets off resonance. On the technical level, the analytical evaluation of the line shapes for the two models is enabled by the fact that these shapes can be expressed via the eigenvalues of a complex Hamiltonian. This bypasses the necessity of solving the much larger complex linear system of the stochastic Liouville equations. Our findings pave the way towards a reliable discrimination between the two mechanisms via cw PLDMR.

  10. Chiral plaquette polaron theory of cuprate superconductivity

    Science.gov (United States)

    Tahir-Kheli, Jamil; Goddard, William A., III

    2007-07-01

    separation distance from (π/a,π/a) given by δQ≈(2π/a)x , where x is the doping. When the perturbed x2-y2 band energy in mean field is included, incommensurability along the Cu-O bond direction is favored. A resistivity ˜Tμ+1 arises when the polaron energy separation density is of the form ˜Δμ due to Coulomb scattering of the x2-y2 band with polarons. A uniform density leads to linear resistivity. The coupling of the x2-y2 band to the undoped Cud9 spins leads to the angle-resolved photoemission pseudogap and its qualitative doping and temperature dependence. The chiral plaquette polaron leads to an explanation of the evolution of the bilayer splitting in Bi-2212.

  11. Polaronic transport in polysilanes

    Czech Academy of Sciences Publication Activity Database

    Nešpůrek, Stanislav; Nožár, Juraj; Kadashchuk, A.; Fishchuk, I. I.

    2009-01-01

    Roč. 193, č. 1 (2009), s. 1-4 ISSN 1742-6588. [International Conference on Electron Dynamics in Semiconductors, Optoelectronics and Nanostructures /16./. Montpellier, 24.08.2009-28.08.2009] R&D Projects: GA AV ČR IAA100100622; GA AV ČR KAN400720701 Institutional research plan: CEZ:AV0Z40500505 Keywords : polaronic transport * polysilanes * charge carrier mobility Subject RIV: CD - Macromolecular Chemistry

  12. Diagrams in the polaron model

    International Nuclear Information System (INIS)

    Smondyrev, M.A.

    1985-01-01

    The perturbation theory for the polaron energy is systematically treated on the diagrammatic basis. Feynman diagrams being constructed allow to calculate the polaron energy up to the third order in powers of the coupling constant. Similar calculations are performed for the average number of virtual phonons

  13. New proposal for non-linear ghost-free massive F(R) gravity: Cosmic acceleration and Hamiltonian analysis

    International Nuclear Information System (INIS)

    Klusoň, Josef; Nojiri, Shin'ichi; Odintsov, Sergei D.

    2013-01-01

    We propose new version of massive F(R) gravity which is natural generalization of convenient massive ghost-free gravity. Its Hamiltonian formulation in scalar-tensor frame is developed. We show that such F(R) theory is ghost-free. The cosmological evolution of such theory is investigated. Despite the strong Bianchi identity constraint the possibility of cosmic acceleration (especially, in the presence of cold dark matter) is established. Ghost-free massive F(R,T) gravity is also proposed

  14. Continual integration method in the polaron model

    International Nuclear Information System (INIS)

    Kochetov, E.A.; Kuleshov, S.P.; Smondyrev, M.A.

    1981-01-01

    The article is devoted to the investigation of a polaron system on the base of a variational approach formulated on the language of continuum integration. The variational method generalizing the Feynman one for the case of the system pulse different from zero has been formulated. The polaron state has been investigated at zero temperature. A problem of the bound state of two polarons exchanging quanta of a scalar field as well as a problem of polaron scattering with an external field in the Born approximation have been considered. Thermodynamics of the polaron system has been investigated, namely, high-temperature expansions for mean energy and effective polaron mass have been studied [ru

  15. Strong-coupling Bose polarons out of equilibrium: Dynamical renormalization-group approach

    Science.gov (United States)

    Grusdt, Fabian; Seetharam, Kushal; Shchadilova, Yulia; Demler, Eugene

    2018-03-01

    When a mobile impurity interacts with a surrounding bath of bosons, it forms a polaron. Numerous methods have been developed to calculate how the energy and the effective mass of the polaron are renormalized by the medium for equilibrium situations. Here, we address the much less studied nonequilibrium regime and investigate how polarons form dynamically in time. To this end, we develop a time-dependent renormalization-group approach which allows calculations of all dynamical properties of the system and takes into account the effects of quantum fluctuations in the polaron cloud. We apply this method to calculate trajectories of polarons following a sudden quench of the impurity-boson interaction strength, revealing how the polaronic cloud around the impurity forms in time. Such trajectories provide additional information about the polaron's properties which are challenging to extract directly from the spectral function measured experimentally using ultracold atoms. At strong couplings, our calculations predict the appearance of trajectories where the impurity wavers back at intermediate times as a result of quantum fluctuations. Our method is applicable to a broader class of nonequilibrium problems. As a check, we also apply it to calculate the spectral function and find good agreement with experimental results. At very strong couplings, we predict that quantum fluctuations lead to the appearance of a dark continuum with strongly suppressed spectral weight at low energies. While our calculations start from an effective Fröhlich Hamiltonian describing impurities in a three-dimensional Bose-Einstein condensate, we also calculate the effects of additional terms in the Hamiltonian beyond the Fröhlich paradigm. We demonstrate that the main effect of these additional terms on the attractive side of a Feshbach resonance is to renormalize the coupling strength of the effective Fröhlich model.

  16. O{sup -} bound small polarons in oxide materials

    Energy Technology Data Exchange (ETDEWEB)

    Schirmer, O F [Department of Physics, University of Osnabrueck, D-49076 Osnabrueck (Germany)

    2006-11-01

    can be used to explain radiation and light induced absorption especially in laser and non-linear oxide materials, the role of some defects in photorefractive compounds, the coloration of various gemstones, the structure of certain catalytic surface centres, etc. The relation to further phenomena is discussed: free small polarons, similar distorted centres in the sulfides and selenides, acceptor defects trapping two holes. (topical review)

  17. Hamiltonian ABC

    NARCIS (Netherlands)

    Meeds, E.; Leenders, R.; Welling, M.; Meila, M.; Heskes, T.

    2015-01-01

    Approximate Bayesian computation (ABC) is a powerful and elegant framework for performing inference in simulation-based models. However, due to the difficulty in scaling likelihood estimates, ABC remains useful for relatively lowdimensional problems. We introduce Hamiltonian ABC (HABC), a set of

  18. Possibility of observation of polaron normal modes at the far-infrared spectrum of acetanilide and related organics

    Science.gov (United States)

    Kalosakas, G.; Aubry, S.; Tsironis, G. P.

    1998-10-01

    We use a stationary and normal mode analysis of the semiclassical Holstein model in order to connect the low-frequency linear polaron modes to low-lying far-infrared lines of the acetanilide spectrum and through parameter fitting we comment on the validity of the polaron results in this system.

  19. Gross–Tulub polaron functional in the region of intermediate and strong coupling

    Directory of Open Access Journals (Sweden)

    N.I. Kashirina

    2017-10-01

    Full Text Available Properties of the polaron functional obtained as a result of averaging the Fröhlich Hamiltonian on the translation-invariant function have been investigated. The polaron functional can be represented in two different forms. It has been shown that the functional of translationally invariant Gross–Tulub polaron cannot be applied in the strong coupling region, where the real part of the complex quantity takes negative values. The function coincides in its structure with the dynamic susceptibility of degenerate electron gas. The necessary condition for obtaining correct results is investigation of the region of admissible values of the Gross–Tulub functional depending on properties of the function , variational parameters, and the electron-phonon interaction parameter α (Fröhlich coupling constant. A simple and exact formula for the recoil energy of the translationally invariant polaron has been derived, which makes it possible to extend the range of admissible values of the parameters of the electron-phonon interaction to the region of extremely strong coupling (α > 10, where . Numerical investigation of different forms of polaron functionals obtained using the field theory methods has been carried out.

  20. Hamiltonian dynamics

    CERN Document Server

    Vilasi, Gaetano

    2001-01-01

    This is both a textbook and a monograph. It is partially based on a two-semester course, held by the author for third-year students in physics and mathematics at the University of Salerno, on analytical mechanics, differential geometry, symplectic manifolds and integrable systems. As a textbook, it provides a systematic and self-consistent formulation of Hamiltonian dynamics both in a rigorous coordinate language and in the modern language of differential geometry. It also presents powerful mathematical methods of theoretical physics, especially in gauge theories and general relativity. As a m

  1. Empirical Hamiltonians

    International Nuclear Information System (INIS)

    Peggs, S.; Talman, R.

    1987-01-01

    As proton accelerators get larger, and include more magnets, the conventional tracking programs which simulate them run slower. The purpose of this paper is to describe a method, still under development, in which element-by-element tracking around one turn is replaced by a single man, which can be processed far faster. It is assumed for this method that a conventional program exists which can perform faithful tracking in the lattice under study for some hundreds of turns, with all lattice parameters held constant. An empirical map is then generated by comparison with the tracking program. A procedure has been outlined for determining an empirical Hamiltonian, which can represent motion through many nonlinear kicks, by taking data from a conventional tracking program. Though derived by an approximate method this Hamiltonian is analytic in form and can be subjected to further analysis of varying degrees of mathematical rigor. Even though the empirical procedure has only been described in one transverse dimension, there is good reason to hope that it can be extended to include two transverse dimensions, so that it can become a more practical tool in realistic cases

  2. Dynamics of a charged particle in a linearly polarized traveling wave. Hamiltonian approach to laser-matter interaction at very high intensities

    International Nuclear Information System (INIS)

    Bourdier, A.; Patin, D.

    2005-01-01

    The basic physical processes in laser-matter interaction, up to 10 17 W/cm 2 (for a neodymium laser) are now well understood, on the other hand, new phenomena evidenced in particle-in-cell code simulations have to be investigated above 10 18 W/cm 2 . Thus, the relativistic motion of a charged particle in a linearly polarized homogeneous electromagnetic wave is studied, here, using the Hamiltonian formalism. First, the motion of a single particle in a linearly polarized traveling wave propagating in a non-magnetized space is explored. The problem is shown to be integrable. The results obtained are compared to those derived considering a cold electron plasma model. When the phase velocity is close to c, it is shown that the two approaches are in good agreement during a finite time. After this short time, when the plasma response is taken into account no chaos take place at least when considering low densities and/or high wave intensities. The case of a charged particle in a traveling wave propagating along a constant homogeneous magnetic field is then considered. The problem is shown to be integrable when the wave propagates in vacuum. The existence of a synchronous solution is shown very simply. In the case when the wave propagates in a low density plasma, using a simplifying Lorentz transformation, it is shown that the system can be reduced to a time-dependent system with two degrees of freedom. The system is shown to be non-integrable, chaos appears when a secondary resonance and a primary resonance overlap. Finally, stochastic instabilities are studied by considering the motion of one particle in a very high intensity wave perturbed by one or two low intensity traveling waves. Resonances are identified and conditions for resonance overlap are studied. (authors)

  3. Polarons and Mobile Impurities Near a Quantum Phase Transition

    Science.gov (United States)

    Shadkhoo, Shahriar

    This dissertation aims at improving the current understanding of the physics of mobile impurities in highly correlated liquid-like phases of matter. Impurity problems pose challenging and intricate questions in different realms of many-body physics. For instance, the problem of ''solvation'' of charged solutes in polar solvents, has been the subject of longstanding debates among chemical physicists. The significant role of quantum fluctuations of the solvent, as well as the break down of linear response theory, render the ordinary treatments intractable. Inspired by this complicated problem, we first attempt to understand the role of non-specific quantum fluctuations in the solvation process. To this end, we calculate the dynamic structure factor of a model polar liquid, using the classical Molecular Dynamics (MD) simulations. We verify the failure of linear response approximation in the vicinity of a hydrated electron, by comparing the outcomes of MD simulations with the predictions of linear response theory. This nonlinear behavior is associated with the pronounced peaks of the structure factor, which reflect the strong fluctuations of the local modes. A cavity picture is constructed based on heuristic arguments, which suggests that the electron, along with the surrounding polarization cloud, behave like a frozen sphere, for which the linear response theory is broken inside and valid outside. The inverse radius of the spherical region serves as a UV momentum cutoff for the linear response approximation to be applicable. The problem of mobile impurities in polar liquids can be also addressed in the framework of the ''polaron'' problem. Polaron is a quasiparticle that typically acquires an extended state at weak couplings, and crossovers to a self-trapped state at strong couplings. Using the analytical fits to the numerically obtained charge-charge structure factor, a phenomenological approach is proposed within the Leggett's influence functional formalism, which

  4. Noncanonical Hamiltonian methods in plasma dynamics

    International Nuclear Information System (INIS)

    Kaufman, A.N.

    1981-11-01

    A Hamiltonian approach to plasma dynamics has numerous advantages over equivalent formulations which ignore the underlying Hamiltonian structure. In addition to achieving a deeper understanding of processes, Hamiltonian methods yield concise expressions (such as the Kubo form for linear susceptibility), greatly shorten the length of calculations, expose relationships (such as between the ponderomotive Hamiltonian and the linear susceptibility), determine invariants in terms of symmetry operations, and cover situations of great generality. In addition, they yield the Poincare invariants, in particular Liouville volume and adiabatic actions

  5. Polaron interaction energies in reduced tungsten trioxide

    International Nuclear Information System (INIS)

    Iguchi, E.; Salje, E.; Tilley, R.J.D.

    1981-01-01

    Consideration of the properties of reduced tungsten trioxide suggest that the mobile charge carriers are polarons. As it is uncertain how the presence of polarons will influence the microstructures of the crystallographic shear (CS) planes present in reduced tungsten trioxide we have calculated both the polaron-CS plane and polaron-polaron interaction energy for a variety of circumstances. Three CS plane geometries were considered, (102), (103), and (001) CS plane arrays, and the nominal compositions of the crystals ranged from WO 2 70 to WO 3 0 . The polarons were assumed to have radii from 0.6 to 1.0 nm and the polaron-CS plane electrostatic interaction was assumed to be screened. The results suggest that for the most part the total interaction energy is small and is unlikely to be of major importance in controlling the microstructures found in CS planes. However, at very high polaron densities the interaction energy could be appreciable and may have some influence on the existence range of CS phases

  6. Diagrammatic Monte Carlo study of Fröhlich polaron dispersion in two and three dimensions

    Science.gov (United States)

    Hahn, Thomas; Klimin, Sergei; Tempere, Jacques; Devreese, Jozef T.; Franchini, Cesare

    2018-04-01

    We present results for the solution of the large polaron Fröhlich Hamiltonian in 3 dimensions (3D) and 2 dimensions (2D) obtained via the diagrammatic Monte Carlo (DMC) method. Our implementation is based on the approach by Mishchenko [A. S. Mishchenko et al., Phys. Rev. B 62, 6317 (2000), 10.1103/PhysRevB.62.6317]. Polaron ground state energies and effective polaron masses are successfully benchmarked with data obtained using Feynman's path integral formalism. By comparing 3D and 2D data, we verify the analytically exact scaling relations for energies and effective masses from 3 D →2 D , which provides a stringent test for the quality of DMC predictions. The accuracy of our results is further proven by providing values for the exactly known coefficients in weak- and strong-coupling expansions. Moreover, we compute polaron dispersion curves which are validated with analytically known lower and upper limits in the small-coupling regime and verify the first-order expansion results for larger couplings, thus disproving previous critiques on the apparent incompatibility of DMC with analytical results and furnishing useful reference for a wide range of coupling strengths.

  7. Large polarons in lead halide perovskites

    OpenAIRE

    Miyata, Kiyoshi; Meggiolaro, Daniele; Trinh, M. Tuan; Joshi, Prakriti P.; Mosconi, Edoardo; Jones, Skyler C.; De Angelis, Filippo; Zhu, X.-Y.

    2017-01-01

    Lead halide perovskites show marked defect tolerance responsible for their excellent optoelectronic properties. These properties might be explained by the formation of large polarons, but how they are formed and whether organic cations are essential remain open questions. We provide a direct time domain view of large polaron formation in single-crystal lead bromide perovskites CH3NH3PbBr3 and CsPbBr3. We found that large polaron forms predominantly from the deformation of the PbBr3 ? framewor...

  8. Polaron-Driven Surface Reconstructions

    Directory of Open Access Journals (Sweden)

    Michele Reticcioli

    2017-09-01

    Full Text Available Geometric and electronic surface reconstructions determine the physical and chemical properties of surfaces and, consequently, their functionality in applications. The reconstruction of a surface minimizes its surface free energy in otherwise thermodynamically unstable situations, typically caused by dangling bonds, lattice stress, or a divergent surface potential, and it is achieved by a cooperative modification of the atomic and electronic structure. Here, we combined first-principles calculations and surface techniques (scanning tunneling microscopy, non-contact atomic force microscopy, scanning tunneling spectroscopy to report that the repulsion between negatively charged polaronic quasiparticles, formed by the interaction between excess electrons and the lattice phonon field, plays a key role in surface reconstructions. As a paradigmatic example, we explain the (1×1 to (1×2 transition in rutile TiO_{2}(110.

  9. Hamiltonian cycles in polyhedral maps

    Indian Academy of Sciences (India)

    We present a necessary and sufficient condition for existence of a contractible, non-separating and non-contractible separating Hamiltonian cycle in the edge graph of polyhedral maps on surfaces.We also present algorithms to construct such cycles whenever it exists where one of them is linear time and another is ...

  10. Maslov index for Hamiltonian systems

    Directory of Open Access Journals (Sweden)

    Alessandro Portaluri

    2008-01-01

    Full Text Available The aim of this article is to give an explicit formula for computing the Maslov index of the fundamental solutions of linear autonomous Hamiltonian systems in terms of the Conley-Zehnder index and the map time one flow.

  11. Effect of thermodynamic fluctuations of magnetization on the bound magnetic polaron state in ferromagnetic semiconductors

    International Nuclear Information System (INIS)

    Bednarski, Henryk; Spałek, Józef

    2014-01-01

    We extend the theory of the bound magnetic polaron (BMP) in diluted paramagnetic semiconductors to the situation with a ferromagnetic phase transition. This is achieved by including the classical Gaussian fluctuations of magnetization from the quartic (non-Gaussian) term in the effective Ginzburg–Landau Hamiltonian for the spins. Within this approach, we find a ferromagnetically ordered state within the BMP in the temperature range well above the Curie temperature for the host magnetic semiconductor. Numerical results are compared directly with the recently available experimental data for the ferromagnetic semiconductor GdN. The agreement is excellent, given the simplicity of our model, and is because the polaron size (≃1.4 nm) encompasses a relatively large but finite number (N≈400) of quasiclassical spins S=7/2 coming from Gd 3+ ions. The presence of BMP invalidates the notion of critical temperature and thus makes the incorporation of classical Gaussian fluctuations sufficient to realistically describe the situation. (paper)

  12. Small polaron hopping in magnetic semiconductors

    International Nuclear Information System (INIS)

    Emin, D.; Liu, N.L.H.

    1978-01-01

    In a number of magnetic insulators it has been hypothesized that the charge carriers form small polarons. The transfer of an electron between magnetic sites and how the magnetic nature of the material affects the rate which characterizes small-polaron hops between magnetic sites were studied. The basic transfer processes are addressed from a many-electron point in which the itinerant electron is treated as indistinguishable from those which contribute unpaired spins at the magnetic sites

  13. Stability and amplitude ranges of two dimensional non-linear oscillations with periodical Hamiltonian applied to betatron oscillations in circular particle accelerators: Part 1 and Part 2

    Energy Technology Data Exchange (ETDEWEB)

    Hagedorn, R

    1957-03-07

    A mechanical system of two degrees of freedom is considered which can be described by a system of canonical differential equations. The Hamiltonian is assumed to be explicitly time-dependent with period 2. The aim is to bring this system by a sequence of canonical and periodical transformations into a form where the new Hamiltonian is constant and as simple as possible. The general theory is then brought to a stage where it becomes immediately applicable to given particular cases, particularly to circular particle accelerators. More general results are given on exciting strengths of different subresonance lines of equal order, on symmetry relations and on the one-dimensional case. An example is also given where the theory is overstressed and its predictions become wrong.

  14. Non-relativistic Limit of a Dirac Polaron in Relativistic Quantum Electrodynamics

    CERN Document Server

    Arai, A

    2006-01-01

    A quantum system of a Dirac particle interacting with the quantum radiation field is considered in the case where no external potentials exist. Then the total momentum of the system is conserved and the total Hamiltonian is unitarily equivalent to the direct integral $\\int_{{\\bf R}^3}^\\oplus\\overline{H({\\bf p})}d{\\bf p}$ of a family of self-adjoint operators $\\overline{H({\\bf p})}$ acting in the Hilbert space $\\oplus^4{\\cal F}_{\\rm rad}$, where ${\\cal F}_{\\rm rad}$ is the Hilbert space of the quantum radiation field. The fibre operator $\\overline{H({\\bf p})}$ is called the Hamiltonian of the Dirac polaron with total momentum ${\\bf p} \\in {\\bf R}^3$. The main result of this paper is concerned with the non-relativistic (scaling) limit of $\\overline{H({\\bf p})}$. It is proven that the non-relativistic limit of $\\overline{H({\\bf p})}$ yields a self-adjoint extension of a Hamiltonian of a polaron with spin $1/2$ in non-relativistic quantum electrodynamics.

  15. Dynamics of photogenerated polarons and polaron pairs in P3HT thin films

    Czech Academy of Sciences Publication Activity Database

    Menšík, Miroslav; Pfleger, Jiří; Toman, Petr

    2017-01-01

    Roč. 677, 1 June (2017), s. 87-91 ISSN 0009-2614 R&D Projects: GA MŠk(CZ) LO1507 Institutional support: RVO:61389013 Keywords : poly(3-hexyl thiophene) * transient absorption spectroscopy * polaron and polaron pairs Subject RIV: CD - Macromolecular Chemistry OBOR OECD: Polymer science Impact factor: 1.815, year: 2016

  16. Empirical Hamiltonians

    International Nuclear Information System (INIS)

    Peggs, S.; Talman, R.

    1986-08-01

    As proton accelerators get larger, and include more magnets, the conventional tracking programs which simulate them run slower. At the same time, in order to more carefully optimize the higher cost of the accelerators, they must return more accurate results, even in the presence of a longer list of realistic effects, such as magnet errors and misalignments. For these reasons conventional tracking programs continue to be computationally bound, despite the continually increasing computing power available. This limitation is especially severe for a class of problems in which some lattice parameter is slowly varying, when a faithful description is only obtained by tracking for an exceedingly large number of turns. Examples are synchrotron oscillations in which the energy varies slowly with a period of, say, hundreds of turns, or magnet ripple or noise on a comparably slow time scale. In these cases one may with to track for hundreds of periods of the slowly varying parameter. The purpose of this paper is to describe a method, still under development, in which element-by-element tracking around one turn is replaced by a single map, which can be processed far faster. Similar programs have already been written in which successive elements are ''concatenated'' with truncation to linear, sextupole, or octupole order, et cetera, using Lie algebraic techniques to preserve symplecticity. The method described here is rather more empirical than this but, in principle, contains information to all orders and is able to handle resonances in a more straightforward fashion

  17. Hamiltonian analysis of transverse dynamics in axisymmetric rf photoinjectors

    International Nuclear Information System (INIS)

    Wang, C.-x.

    2006-01-01

    A general Hamiltonian that governs the beam dynamics in an rf photoinjector is derived from first principles. With proper choice of coordinates, the resulting Hamiltonian has a simple and familiar form, while taking into account the rapid acceleration, rf focusing, magnetic focusing, and space-charge forces. From the linear Hamiltonian, beam-envelope evolution is readily obtained, which better illuminates the theory of emittance compensation. Preliminary results on the third-order nonlinear Hamiltonian will be given as well.

  18. Hamiltonian Algorithm Sound Synthesis

    OpenAIRE

    大矢, 健一

    2013-01-01

    Hamiltonian Algorithm (HA) is an algorithm for searching solutions is optimization problems. This paper introduces a sound synthesis technique using Hamiltonian Algorithm and shows a simple example. "Hamiltonian Algorithm Sound Synthesis" uses phase transition effect in HA. Because of this transition effect, totally new waveforms are produced.

  19. Contact Hamiltonian mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Bravetti, Alessandro, E-mail: alessandro.bravetti@iimas.unam.mx [Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, A. P. 70543, México, DF 04510 (Mexico); Cruz, Hans, E-mail: hans@ciencias.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A. P. 70543, México, DF 04510 (Mexico); Tapias, Diego, E-mail: diego.tapias@nucleares.unam.mx [Facultad de Ciencias, Universidad Nacional Autónoma de México, A.P. 70543, México, DF 04510 (Mexico)

    2017-01-15

    In this work we introduce contact Hamiltonian mechanics, an extension of symplectic Hamiltonian mechanics, and show that it is a natural candidate for a geometric description of non-dissipative and dissipative systems. For this purpose we review in detail the major features of standard symplectic Hamiltonian dynamics and show that all of them can be generalized to the contact case.

  20. Large polarons in lead halide perovskites

    Science.gov (United States)

    Miyata, Kiyoshi; Meggiolaro, Daniele; Trinh, M. Tuan; Joshi, Prakriti P.; Mosconi, Edoardo; Jones, Skyler C.; De Angelis, Filippo; Zhu, X.-Y.

    2017-01-01

    Lead halide perovskites show marked defect tolerance responsible for their excellent optoelectronic properties. These properties might be explained by the formation of large polarons, but how they are formed and whether organic cations are essential remain open questions. We provide a direct time domain view of large polaron formation in single-crystal lead bromide perovskites CH3NH3PbBr3 and CsPbBr3. We found that large polaron forms predominantly from the deformation of the PbBr3− frameworks, irrespective of the cation type. The difference lies in the polaron formation time, which, in CH3NH3PbBr3 (0.3 ps), is less than half of that in CsPbBr3 (0.7 ps). First-principles calculations confirm large polaron formation, identify the Pb-Br-Pb deformation modes as responsible, and explain quantitatively the rate difference between CH3NH3PbBr3 and CsPbBr3. The findings reveal the general advantage of the soft [PbX3]− sublattice in charge carrier protection and suggest that there is likely no mechanistic limitations in using all-inorganic or mixed-cation lead halide perovskites to overcome instability problems and to tune the balance between charge carrier protection and mobility. PMID:28819647

  1. Importance of polaron effects for charge carrier mobility above and ...

    Indian Academy of Sciences (India)

    Orifjon Ganiev

    2017-05-30

    May 30, 2017 ... sizes and effective masses are large polarons. According ... nating metallic and insulating domains with mobile ... The mobile polaronic carriers are con- ..... [51] T Kondo, Y Hamaya, A D Palczewski, T Takeuchi, J S Wen,.

  2. Polaron as the extended particle model

    International Nuclear Information System (INIS)

    Kochetov, E.A.; Kuleshov, S.P.; Smondyrev, M.A.

    1977-01-01

    The polaron (a moving electron with concomitant lattice distortion) mass and energy are calculated. The problem of finding the Green function in the polaron model is solved. A number of the simplest approximations corresponding to the approximation in the picture of straight-line paths is considered. The case of strong coupling requires more detailed study of the particle motion in the effective field, caused by the significant polarization of vacuum near the particle. As a consequence, a more complex approximation of functional integrals is required. A variation method is used in this case. The bound state of a polaron interacting not only with photons, but also with some external classical field is investigated as well. A classical potential is considered as an example

  3. Importance of polaron effects for charge carrier mobility above and ...

    Indian Academy of Sciences (India)

    It is shown that the scattering of polaronic charge carriers and bosonic Cooper pairs at acoustic and optical phonons are responsible for the charge carrier mobility above and below the PG temperature. We show that the energy scales of the binding energies of large polarons and polaronic Cooper pairs can be identified by ...

  4. Polaron in the dilute critical Bose condensate

    Science.gov (United States)

    Pastukhov, Volodymyr

    2018-05-01

    The properties of an impurity immersed in a dilute D-dimensional Bose gas at temperatures close to its second-order phase transition point are considered. Particularly by means of the 1/N-expansion, we calculate the leading-order polaron energy and the damping rate in the limit of vanishing boson–boson interaction. It is shown that the perturbative effective mass and the quasiparticle residue diverge logarithmically in the long-length limit, signalling the non-analytic behavior of the impurity spectrum and pole-free structure of the polaron Green’s function in the infrared region, respectively.

  5. Explanation for the temperature dependence of plasma frequencies in SrTiO3 using mixed-polaron theory

    International Nuclear Information System (INIS)

    Eagles, D.M.; Georgiev, M.; Petrova, P.C.

    1996-01-01

    A theory of mixed polarons is used to interpret the published experimental results of Gervais et al. on temperature-dependent plasma frequencies in Nb-doped SrTiO 3 . For given polaron masses before mixing, the appropriate average mixed-polaron mass at any temperature T depends on two quantities, δ and b, which are measures of the separation between the bottoms of large and nearly small polaron bands before mixing and of a mixing matrix element; δ and b are assumed to have arbitrary linear dependences on T, probably related to a T dependence of the bare mass, and a term quadratic in T is included in δ, determined from the T dependence of large-polaron binding energies. Including a constraint on the ratio δ/|b| at low T from known masses from specific-heat data, satisfactory agreement is obtained with masses determined from plasma frequencies. This gives further support for the theory of mixed polarons in SrTiO 3 in addition to that already published. copyright 1996 The American Physical Society

  6. Derivation of Hamiltonians for accelerators

    Energy Technology Data Exchange (ETDEWEB)

    Symon, K.R.

    1997-09-12

    In this report various forms of the Hamiltonian for particle motion in an accelerator will be derived. Except where noted, the treatment will apply generally to linear and circular accelerators, storage rings, and beamlines. The generic term accelerator will be used to refer to any of these devices. The author will use the usual accelerator coordinate system, which will be introduced first, along with a list of handy formulas. He then starts from the general Hamiltonian for a particle in an electromagnetic field, using the accelerator coordinate system, with time t as independent variable. He switches to a form more convenient for most purposes using the distance s along the reference orbit as independent variable. In section 2, formulas will be derived for the vector potentials that describe the various lattice components. In sections 3, 4, and 5, special forms of the Hamiltonian will be derived for transverse horizontal and vertical motion, for longitudinal motion, and for synchrobetatron coupling of horizontal and longitudinal motions. Hamiltonians will be expanded to fourth order in the variables.

  7. Single-particle dynamics - Hamiltonian formulation

    International Nuclear Information System (INIS)

    Montague, B.W.

    1977-01-01

    In this paper the Hamiltonian formalism is applied to the linear theory of accelerator dynamics. The reasons for the introduction of this method rather than the more straightforward use of second order differential equations of motion are briefly discussed. An outline of Lagrangian and Hamiltonian formalism is given, some properties of the Hamiltonian are discussed and canonical transformations are illustrated. The methods are demonstrated using elementary examples such as the simple pendulum and the procedures adopted to handle specific problems in accelerator theory are indicated. (B.D.)

  8. Small polarons in 2D perovskites

    KAUST Repository

    Cortecchia, Daniele

    2017-11-02

    We demonstrate that white light luminescence in two-dimensional (2D) perovskites stems from photoinduced formation of small polarons confined at specific sites of the inorganic framework in the form of self-trapped electrons and holes. We discuss their application in white light emitting devices and X-ray scintillators.

  9. Polaron scattering by an external field

    International Nuclear Information System (INIS)

    Kochetov, E.A.

    1980-01-01

    The problem of polaron scattering by an external field is studied. The problem is solved using the stationary scattering theory formalism based on two operators: the G Green function operator and the T scattering operator. The dependence of the scattering amplitude on the quasi particle structure is studied. The variation approach is used for estimation of the ground energy level

  10. Small polarons in 2D perovskites

    KAUST Repository

    Cortecchia, Daniele; Yin, Jun; Birowosuto, Muhammad D.; Lo, Shu-Zee A.; Gurzadyan, Gagik G.; Bruno, Annalisa; Bredas, Jean-Luc; Soci, Cesare

    2017-01-01

    We demonstrate that white light luminescence in two-dimensional (2D) perovskites stems from photoinduced formation of small polarons confined at specific sites of the inorganic framework in the form of self-trapped electrons and holes. We discuss their application in white light emitting devices and X-ray scintillators.

  11. Spin-polaron theory of high-Tc superconductivity: I, spin polarons and high-Tc pairing

    International Nuclear Information System (INIS)

    Wood, R.F.

    1993-06-01

    The concept of a spin polaron is introduced and contrasted with the more familiar ionic polaron picture. A brief review of aspects of ionic bipolaronic superconductivity is given with particular emphasis on the real-space pairing and true Bose condensation characteristics. The formation energy of spin polarons is then calculated in analogy with ionic polarons. The spin-flip energy of a Cu spin in an antiferromagnetically aligned CuO 2 plane is discussed. It is shown that the introduction of holes into the CuO 2 planes will always lead to the destruction of long-range AF ordering due to the formation of spin polarons. The pairing of two spin polarons can be expected because of the reestablishment of local (short-range) AF ordering; the magnitude of the pairing energy is estimated using a simplified model. The paper closes with a brief discussion of the formal theory of spin polarons

  12. Hamiltonian PDEs and Frobenius manifolds

    International Nuclear Information System (INIS)

    Dubrovin, Boris A

    2008-01-01

    In the first part of this paper the theory of Frobenius manifolds is applied to the problem of classification of Hamiltonian systems of partial differential equations depending on a small parameter. Also developed is a deformation theory of integrable hierarchies including the subclass of integrable hierarchies of topological type. Many well-known examples of integrable hierarchies, such as the Korteweg-de Vries, non-linear Schroedinger, Toda, Boussinesq equations, and so on, belong to this subclass that also contains new integrable hierarchies. Some of these new integrable hierarchies may be important for applications. Properties of the solutions to these equations are studied in the second part. Consideration is given to the comparative study of the local properties of perturbed and unperturbed solutions near a point of gradient catastrophe. A Universality Conjecture is formulated describing the various types of critical behaviour of solutions to perturbed Hamiltonian systems near the point of gradient catastrophe of the unperturbed solution.

  13. Hamiltonian PDEs and Frobenius manifolds

    Energy Technology Data Exchange (ETDEWEB)

    Dubrovin, Boris A [Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)

    2008-12-31

    In the first part of this paper the theory of Frobenius manifolds is applied to the problem of classification of Hamiltonian systems of partial differential equations depending on a small parameter. Also developed is a deformation theory of integrable hierarchies including the subclass of integrable hierarchies of topological type. Many well-known examples of integrable hierarchies, such as the Korteweg-de Vries, non-linear Schroedinger, Toda, Boussinesq equations, and so on, belong to this subclass that also contains new integrable hierarchies. Some of these new integrable hierarchies may be important for applications. Properties of the solutions to these equations are studied in the second part. Consideration is given to the comparative study of the local properties of perturbed and unperturbed solutions near a point of gradient catastrophe. A Universality Conjecture is formulated describing the various types of critical behaviour of solutions to perturbed Hamiltonian systems near the point of gradient catastrophe of the unperturbed solution.

  14. Renormalization of Hamiltonian QCD

    International Nuclear Information System (INIS)

    Andrasi, A.; Taylor, John C.

    2009-01-01

    We study to one-loop order the renormalization of QCD in the Coulomb gauge using the Hamiltonian formalism. Divergences occur which might require counter-terms outside the Hamiltonian formalism, but they can be cancelled by a redefinition of the Yang-Mills electric field.

  15. Magnetic field line Hamiltonian

    International Nuclear Information System (INIS)

    Boozer, A.H.

    1984-03-01

    The magnetic field line Hamiltonian and the associated canonical form for the magnetic field are important concepts both for understanding toroidal plasma physics and for practical calculations. A number of important properties of the canonical or Hamiltonian representation are derived and their importance is explained

  16. Geometry of Hamiltonian chaos

    DEFF Research Database (Denmark)

    Horwitz, Lawrence; Zion, Yossi Ben; Lewkowicz, Meir

    2007-01-01

    The characterization of chaotic Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor in the structure of the Hamiltonian is extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce ...

  17. Magnetic field line Hamiltonian

    International Nuclear Information System (INIS)

    Boozer, A.H.

    1985-02-01

    The basic properties of the Hamiltonian representation of magnetic fields in canonical form are reviewed. The theory of canonical magnetic perturbation theory is then developed and applied to the time evolution of a magnetic field embedded in a toroidal plasma. Finally, the extension of the energy principle to tearing modes, utilizing the magnetic field line Hamiltonian, is outlined

  18. Diagonalization of Hamiltonian; Diagonalization of Hamiltonian

    Energy Technology Data Exchange (ETDEWEB)

    Garrido, L M; Pascual, P

    1960-07-01

    We present a general method to diagonalized the Hamiltonian of particles of arbitrary spin. In particular we study the cases of spin 0,1/2, 1 and see that for spin 1/2 our transformation agrees with Foldy's and obtain the expression for different observables for particles of spin C and 1 in the new representation. (Author) 7 refs.

  19. Magnetic polarons in a nonequilibrium polariton condensate

    Science.gov (United States)

    Mietki, Paweł; Matuszewski, Michał

    2017-09-01

    We consider a condensate of exciton polaritons in a diluted magnetic semiconductor microcavity. Such a system may exhibit magnetic self-trapping in the case of sufficiently strong coupling between polaritons and magnetic ions embedded in the semiconductor. We investigate the effect of the nonequilibrium nature of exciton polaritons on the physics of the resulting self-trapped magnetic polarons. We find that multiple polarons can exist at the same time, and we derive a critical condition for self-trapping that is different from the one predicted previously in the equilibrium case. Using the Bogoliubov-de Gennes approximation, we calculate the excitation spectrum and provide a physical explanation in terms of the effective magnetic attraction between polaritons, mediated by the ion subsystem.

  20. Transport through a vibrating quantum dot: Polaronic effects

    International Nuclear Information System (INIS)

    Koch, T; Alvermann, A; Fehske, H; Loos, J; Bishop, A R

    2010-01-01

    We present a Green's function based treatment of the effects of electron-phonon coupling on transport through a molecular quantum dot in the quantum limit. Thereby we combine an incomplete variational Lang-Firsov approach with a perturbative calculation of the electron-phonon self energy in the framework of generalised Matsubara Green functions and a Landauer-type transport description. Calculating the ground-state energy, the dot single-particle spectral function and the linear conductance at finite carrier density, we study the low-temperature transport properties of the vibrating quantum dot sandwiched between metallic leads in the whole electron-phonon coupling strength regime. We discuss corrections to the concept of an anti-adiabatic dot polaron and show how a deformable quantum dot can act as a molecular switch.

  1. Magnon Polarons in the Spin Seebeck Effect.

    Science.gov (United States)

    Kikkawa, Takashi; Shen, Ka; Flebus, Benedetta; Duine, Rembert A; Uchida, Ken-Ichi; Qiu, Zhiyong; Bauer, Gerrit E W; Saitoh, Eiji

    2016-11-11

    Sharp structures in the magnetic field-dependent spin Seebeck effect (SSE) voltages of Pt/Y_{3}Fe_{5}O_{12} at low temperatures are attributed to the magnon-phonon interaction. Experimental results are well reproduced by a Boltzmann theory that includes magnetoelastic coupling. The SSE anomalies coincide with magnetic fields tuned to the threshold of magnon-polaron formation. The effect gives insight into the relative quality of the lattice and magnetization dynamics.

  2. Strong-coupling polaron effect in quantum dots

    International Nuclear Information System (INIS)

    Zhu Kadi; Gu Shiwei

    1993-11-01

    Strong-coupling polaron in a parabolic quantum dot is investigated by the Landau-Pekar variational treatment. The polaron binding energy and the average number of virtual phonons around the electron as a function of the effective confinement length of the quantum dot are obtained in Gaussian function approximation. It is shown that both the polaron binding energy and the average number of virtual phonons around the electron decrease by increasing the effective confinement length. The results indicate that the polaronic effects are more pronounced in quantum dots than those in two-dimensional and three-dimensional cases. (author). 15 refs, 4 figs

  3. Homoclinic Orbits for a Class of Nonperiodic Hamiltonian Systems with Some Twisted Conditions

    Directory of Open Access Journals (Sweden)

    Qi Wang

    2013-01-01

    Full Text Available By the Maslov index theory, we will study the existence and multiplicity of homoclinic orbits for a class of asymptotically linear nonperiodic Hamiltonian systems with some twisted conditions on the Hamiltonian functions.

  4. Integrable and nonintegrable Hamiltonian systems

    International Nuclear Information System (INIS)

    Percival, I.

    1986-01-01

    Traditionally Hamiltonian systems with a finite number of degrees of freedom have been divided into those with few degrees of freedom which were supposed to exhibit some kind of regular ordered motions and those with large numbers of degrees of freedom for which the methods of statistical mechanics should be used. The last few decades have seen a complete change of view. The change of view affects almost all the practical applications, particularly in mathematical physics, which has been dominated for many decades by linear mathematics, coming from quantum theory. The authors consider how this change of view affects some specific applications of dynamics and also the relation between dynamical theory and applications

  5. Dynamical invariants for variable quadratic Hamiltonians

    International Nuclear Information System (INIS)

    Suslov, Sergei K

    2010-01-01

    We consider linear and quadratic integrals of motion for general variable quadratic Hamiltonians. Fundamental relations between the eigenvalue problem for linear dynamical invariants and solutions of the corresponding Cauchy initial value problem for the time-dependent Schroedinger equation are emphasized. An eigenfunction expansion of the solution of the initial value problem is also found. A nonlinear superposition principle for generalized Ermakov systems is established as a result of decomposition of the general quadratic invariant in terms of the linear ones.

  6. Modelling chaotic Hamiltonian systems as a Markov Chain ...

    African Journals Online (AJOL)

    The behaviour of chaotic Hamiltonian system has been characterised qualitatively in recent times by its appearance on the Poincaré section and quantitatively by the Lyapunov exponent. Studying the dynamics of the two chaotic Hamiltonian systems: the Henon-Heiles system and non-linearly coupled oscillators as their ...

  7. Renormalization of Hamiltonians

    International Nuclear Information System (INIS)

    Glazek, S.D.; Wilson, K.G.

    1993-01-01

    This paper presents a new renormalization procedure for Hamiltonians such as those of light-front field theory. The bare Hamiltonian with an arbitrarily large, but finite cutoff, is transformed by a specially chosen similarity transformation. The similarity transformation has two desirable features. First, the transformed Hamiltonian is band diagonal: in particular, all matrix elements vanish which would otherwise have caused transitions with big energy jumps, such as from a state of bounded energy to a state with an energy of the order of the cutoff. At the same time, neither the similarity transformation nor the transformed Hamiltonian, computed in perturbation theory, contain vanishing or near-vanishing energy denominators. Instead, energy differences in denominators can be replaced by energy sums for purposes of order of magnitude estimates needed to determine cutoff dependences. These two properties make it possible to determine relatively easily the list of counterterms needed to obtain finite low energy results (such as for eigenvalues). A simple model Hamiltonian is discussed to illustrate the method

  8. Theory of collective Hamiltonian

    Energy Technology Data Exchange (ETDEWEB)

    Zhang Qingying

    1982-02-01

    Starting from the cranking model, we derive the nuclear collective Hamiltonian. We expand the total energy of the collective motion of the ground state of even--even nuclei in powers of the deformation parameter ..beta... In the first approximation, we only take the lowest-order non-vanished terms in the expansion. The collective Hamiltonian thus obtained rather differs from the A. Bohr's Hamiltonian obtained by the irrotational incompressible liquid drop model. If we neglect the coupling term between ..beta..-and ..gamma..-vibration, our Hamiltonian then has the same form as that of A. Bohr. But there is a difference between these collective parameters. Our collective parameters are determined by the state of motion of the nucleous in the nuclei. They are the microscopic expressions. On the contrary, A. Bohr's collective parameters are only the simple functions of the microscopic physical quantities (such as nuclear radius and surface tension, etc.), and independent of the state of motion of the nucleons in the nuclei. Furthermore, there exist the coupling term between ..beta..-and ..gamma..-vibration and the higher-order terms in our expansion. They can be treated as the perturbations. There are no such terms in A. Bohr's Hamiltonian. These perturbation terms will influence the rotational, vibrational spectra and the ..gamma..-transition process, etc.

  9. Neutron diffuse scattering in magnetite due to molecular polarons

    International Nuclear Information System (INIS)

    Yamada, Y.; Wakabayashi, N.; Nicklow, R.M.

    1980-01-01

    A detailed neutron diffuse scattering study has been carried out in order to verify a model which describes the property of valence fluctuations in magnetite above T/sub V/. This model assumes the existence of a complex which is composed of two excess electrons and a local displacement mode of oxygens within the fcc primitive cell. The complex is called a molecular polaron. It is assumed that at sufficiently high temperatures there is a random distribution of molecular polarons, which are fluctuating independently by making hopping motions through the crystal or by dissociating into smaller polarons. The lifetime of each molecular polaron is assumed to be long enough to induce an instantaneous strain field around it. Based on this model, the neutron diffuse scattering cross section due to randomly distributed dressed molecular polarons has been calculated. A precise measurement of the quasielastic scattering of neutrons has been carried out at 150 K. The observed results definitely show the characteristics which are predicted by the model calculation and, thus, give evidence for the existence of the proposed molecular polarons. From this standpoint, the Verwey transition of magnetite may be viewed as the cooperative ordering process of dressed molecular polarons. Possible extensions of the model to describe the ordering and the dynamical behavior of the molecular polarons are discussed

  10. Small-polaron formation and motion in magnetic semiconductors

    International Nuclear Information System (INIS)

    Emin, D.

    1979-01-01

    The fundamental physical processes associated with small-polaron formation are described with various magnetic semi-conductors being cited as examples. Attention is then directed toward the mechanisms of charge transfer and small-polaron hopping motion in magnetic semiconductors

  11. Polaron binding energy in polymers: poly[methyl(phenyl)silylene

    Czech Academy of Sciences Publication Activity Database

    Nožár, Juraj; Nešpůrek, Stanislav; Šebera, Jakub

    2012-01-01

    Roč. 18, č. 2 (2012), s. 623-629 ISSN 1610-2940 R&D Projects: GA AV ČR KAN400720701 Institutional research plan: CEZ:AV0Z40500505 Keywords : polaron * polaron binding energy * polysilane Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.984, year: 2012

  12. Soliton and polaron generation in polyacetylene

    International Nuclear Information System (INIS)

    Su, Zhao-bin; Yu, Lu.

    1984-07-01

    The nonradiative decay of an e-h pair into soliton pair and that of an electron (hole) into polaron as well as the photoproduction of soliton pairs are considered using the lattice relaxation theory of multiphonon processes generalized to include the self-consistency of the multi-electron states with the lattice symmetry breaking. The selection rule which forbids the direct process of photogeneration for neutral pair is derived from the symmetry arguments. The branching ratio of the photogenerated neutral to charged soliton pairs is estimated. The recent related experiments are discussed. (author)

  13. Properties of a Bound Polaron under a Perpendicular Magnetic Field

    International Nuclear Information System (INIS)

    Liu Jia; Chen Ziyu; Xiao Jinglin; Huo Shufen

    2007-01-01

    We investigate the influence of a perpendicular magnetic field on a bound polaron near the interface of a polar-polar semiconductor with Rashba effect. The external magnetic field strongly changes the ground state binding energy of the polaron and the Rashba spin-orbit (SO) interaction originating from the inversion asymmetry in the heterostructure splits the ground state binding energy of the bound polaron. In this paper, we have shown how the ground state binding energy will be with the change of the external magnetic field, the location of a single impurity, the wave vector of the electron and the electron areal density, taking into account the SO coupling. Due to the presence of the phonons, whose energy gives negative contribution to the polaron's, the spin-splitting states of the bound polaron are more stable, and we find that in the condition of week magnetic field, the Zeeaman effect can be neglected.

  14. Weak coupling polaron and Landau-Zener scenario: Qubits modeling

    Science.gov (United States)

    Jipdi, M. N.; Tchoffo, M.; Fokou, I. F.; Fai, L. C.; Ateuafack, M. E.

    2017-06-01

    The paper presents a weak coupling polaron in a spherical dot with magnetic impurities and investigates conditions for which the system mimics a qubit. Particularly, the work focuses on the Landau-Zener (LZ) scenario undergone by the polaron and derives transition coefficients (transition probabilities) as well as selection rules for polaron's transitions. It is proven that, the magnetic impurities drive the polaron to a two-state superposition leading to a qubit structure. We also showed that the symmetry deficiency induced by the magnetic impurities (strong magnetic field) yields to the banishment of transition coefficients with non-stacking states. However, the transition coefficients revived for large confinement frequency (or weak magnetic field) with the orbital quantum numbers escorting transitions. The polaron is then shown to map a qubit independently of the number of relevant states with the transition coefficients lifted as LZ probabilities and given as a function of the electron-phonon coupling constant (Fröhlich constant).

  15. Time dependent drift Hamiltonian

    International Nuclear Information System (INIS)

    Boozer, A.H.

    1982-04-01

    The motion of individual charged particles in a given magnetic and an electric fields is discussed. An idea of a guiding center distribution function f is introduced. The guiding center distribution function is connected to the asymptotic Hamiltonian through the drift kinetic equation. The general non-stochastic magnetic field can be written in a contravariant and a covariant forms. The drift Hamiltonian is proposed, and the canonical gyroradius is presented. The proposed drift Hamiltonian agrees with Alfven's drift velocity to lowest non-vanishing order in the gyroradius. The relation between the exact, time dependent equations of motion and the guiding center equation is clarified by a Lagrangian analysis. The deduced Lagrangian represents the drift motion. (Kato, T.)

  16. Lagrangian and Hamiltonian dynamics

    CERN Document Server

    Mann, Peter

    2018-01-01

    An introductory textbook exploring the subject of Lagrangian and Hamiltonian dynamics, with a relaxed and self-contained setting. Lagrangian and Hamiltonian dynamics is the continuation of Newton's classical physics into new formalisms, each highlighting novel aspects of mechanics that gradually build in complexity to form the basis for almost all of theoretical physics. Lagrangian and Hamiltonian dynamics also acts as a gateway to more abstract concepts routed in differential geometry and field theories and can be used to introduce these subject areas to newcomers. Journeying in a self-contained manner from the very basics, through the fundamentals and onwards to the cutting edge of the subject, along the way the reader is supported by all the necessary background mathematics, fully worked examples, thoughtful and vibrant illustrations as well as an informal narrative and numerous fresh, modern and inter-disciplinary applications. The book contains some unusual topics for a classical mechanics textbook. Mo...

  17. Bäcklund transformations and Hamiltonian flows

    International Nuclear Information System (INIS)

    Zullo, Federico

    2013-01-01

    In this work we show that, under certain conditions, parametric Bäcklund transformations for a finite dimensional integrable system can be interpreted as solutions to the equations of motion defined by an associated non-autonomous Hamiltonian. The two systems share the same constants of motion. This observation leads to the identification of the Hamiltonian interpolating the iteration of the discrete map defined by the transformations, which indeed in numerical applications can be considered a linear combination of the integrals appearing in the spectral curve of the Lax matrix. An example with the periodic Toda lattice is given. (paper)

  18. Magnetic Polarons in Anisotropic Quantum Dots

    Science.gov (United States)

    Oszwaldowski, Rafal; Petukhov, Andre; Zutic, Igor

    2010-03-01

    Tunability of confinement in magnetically-doped quantum dots (QDs) allows to tailor magnetism to an extent not available in bulk semiconductors. Versatile control of magnetic ordering, along with piezomagnetism, has been predicted even at a fixed number of carriers [1]. Recent experiments on colloidal QDs revealed strongly bound magnetic polarons (MPs) [2]. Previous studies of MPs in bulk semiconductors showed that the mean-field theory predicts a spurious magnetic phase transition, which is removed by taking into account spin fluctuations [3]. Here we present our theoretical results for MPs forming in QDs with pronounced magnetic anisotropy, which influences the spin fluctuations. We apply our findings to explain some peculiarities of the magnetic behavior of type-II ZnSe/(Zn,Mn)Te QDs, where magnetic polarons are found to persist to at least 200K [4]. Supported by ONR, AFOSR, and NSF-ECCS CAREER. [4pt] [1] R. M. Abolfath, A. G. Petukhov, and I. Zutic, Phys. Rev. Lett. 101, 207202 (2008); I. Zutic and A. G. Petukhov, Nature Mater.4, 623 (2009). [0pt] [2] R. Beaulac et al., Science 325, 973 (2009). [0pt] [3] T. Dietl and J. Spalek, Phys. Rev. Lett. 48, 355 (1982). [0pt] [4] I. R. Sellers, R. Oszwaldowski, et al., preprint; I. R. Sellers et al., Phys. Rev. Lett. 100, 136405 (2008).

  19. Size dependent polaronic conduction in hematite

    Energy Technology Data Exchange (ETDEWEB)

    Sharma, Monika; Banday, Azeem; Murugavel, Sevi [Department of Physics and Astrophysics, University of Delhi, Delhi – 110 007 (India)

    2016-05-23

    Lithium Ion Batteries have been attracted as the major renewable energy source for all portable electronic devices because of its advantages like superior energy density, high theoretical capacity, high specific energy, stable cycling and less memory effects. Recently, α-Fe{sub 2}O{sub 3} has been considered as a potential anode material due to high specific capacity, low cost, high abundance and environmental benignity. We have synthesized α-Fe{sub 2}O{sub 3} with various sizes by using the ball milling and sol-gel procedure. Here, we report the dc conductivity measurement for the crystallite size ranging from 15 nm to 50 nm. It has been observed that the enhancement in the polaronic conductivity nearly two orders in magnitude while reducing the crystallite size from bulk into nano scale level. The enhancement in the conductivity is due to the augmented to compressive strain developed in the material which leads to pronounced decrease in the hopping length of polarons. Thus, nanocrystaline α-Fe{sub 2}O{sub 3} may be a better alternative anode material for lithium ion batteries than earlier reported systems.

  20. Size dependent polaronic conduction in hematite

    International Nuclear Information System (INIS)

    Sharma, Monika; Banday, Azeem; Murugavel, Sevi

    2016-01-01

    Lithium Ion Batteries have been attracted as the major renewable energy source for all portable electronic devices because of its advantages like superior energy density, high theoretical capacity, high specific energy, stable cycling and less memory effects. Recently, α-Fe_2O_3 has been considered as a potential anode material due to high specific capacity, low cost, high abundance and environmental benignity. We have synthesized α-Fe_2O_3 with various sizes by using the ball milling and sol-gel procedure. Here, we report the dc conductivity measurement for the crystallite size ranging from 15 nm to 50 nm. It has been observed that the enhancement in the polaronic conductivity nearly two orders in magnitude while reducing the crystallite size from bulk into nano scale level. The enhancement in the conductivity is due to the augmented to compressive strain developed in the material which leads to pronounced decrease in the hopping length of polarons. Thus, nanocrystaline α-Fe_2O_3 may be a better alternative anode material for lithium ion batteries than earlier reported systems.

  1. g Algebra and two-dimensional quasiexactly solvable Hamiltonian ...

    Indian Academy of Sciences (India)

    Keywords. g2 algebra; quasiexactly solvable Hamiltonian; hidden algebra; Poschl–Teller potential. ... space of the polynomials, restricting to a linear transformation on this space, the associ- .... The operators L6 and L7 are the positive root.

  2. Effective magnetic Hamiltonians

    Czech Academy of Sciences Publication Activity Database

    Drchal, Václav; Kudrnovský, Josef; Turek, I.

    2013-01-01

    Roč. 26, č. 5 (2013), s. 1997-2000 ISSN 1557-1939 R&D Projects: GA ČR GA202/09/0775 Institutional support: RVO:68378271 Keywords : effective magnetic Hamiltonian * ab initio * magnetic structure Subject RIV: BE - Theoretical Physics Impact factor: 0.930, year: 2013

  3. Dissipative systems and Bateman's Hamiltonian

    International Nuclear Information System (INIS)

    Pedrosa, I.A.; Baseia, B.

    1983-01-01

    It is shown, by using canonical transformations, that one can construct Bateman's Hamiltonian from a Hamiltonian for a conservative system and obtain a clear physical interpretation which explains the ambiguities emerging from its application to describe dissipative systems. (Author) [pt

  4. The role of hydrostatic pressure and temperature on bound polaron in semiconductor quantum dot

    International Nuclear Information System (INIS)

    El Moussaouy, A.; Ouchani, N.

    2014-01-01

    We studied theoretically the effects of hydrostatic pressure and temperature on the binding energy of shallow hydrogenic impurity in a cylindrical quantum dot (QD) using a variational approach within the effective mass approximation. The hydrostatic stress was applied along the QD growth axis. The interactions between the charge carriers and confined longitudinal optical (LO) phonon modes are taken into account. The numerical computation for GaAs/Ga 1−x Al x As QD has shown that the binding energy with and without the polaronic correction depends on the location of the impurity and the pressure effect and it is more pronounced for impurities in the QD center. Both the binding energy and the polaronic contribution increase linearly with increasing stress. For each pressure value, these energies are also found to decrease as the temperature increases. The results obtained show that in experimental studies of optical and electronic properties of QDs, the effects of pressure, temperature and polaronic correction on donor impurity binding energy should be taken into consideration

  5. Screening effect on the polaron by surface plasmons

    Science.gov (United States)

    Xu, Xiaoying; Xu, Xiaoshan; Seal, Katyayani; Guo, Hangwen; Shen, Jian; Low Dimensional Materials Physics, Oak Ridge National Lab Team; University of Tennessee Team; Physics Department, Fudan University Team

    2011-03-01

    Surface plasmons occur when the conduction electrons at a metal/dielectric interface resonantly interact with external electromagnetic fields. While surface plasmons in vicinity of a polaron in the dielectric material, a strong screening effect on polaron characteristics is introduced. In this work, we observed the reduction of polarons in multiferroic LuFe2O4, which is mainly contributed by surface plasmons. Research sponsored by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the U. S. Department of Energy.

  6. Bi-Polaron Condensation in High Tc Superconductors

    International Nuclear Information System (INIS)

    Ranninger, J.

    1995-01-01

    On the basis of optical measurements-, photoemission-, EXAFS- and neutron scattering-experiments we conclude that itinerant valence electrons coexist with localized bi-polarons.Entering the metallic phase upon chemical doping, a charge transfer between the two electronic subsystems is triggered off. We show that as the temperature is lowered towards Tc this process leads to a delocalization of bi-polarons due to a precursor effect of superfluidity of those bi-polarons. Upon entering the superconducting phase, these bipolarons ultimately condense into a superfluid state which is expected to largely determine the superconducting properties of high Tc materials. (authors)

  7. Method of T-products in polaron theory

    International Nuclear Information System (INIS)

    Bogolubov, N.N. Jr.; Kurbatov, A.M.; Kireev, A.N.

    1985-11-01

    T-products method is used for the investigation of equilibrium thermodynamic properties of Frohlich's model in polaron theory. Polaron free energy at finite temperatures is calculated on the basis of Bogolubov's variational principle. A trial function is chosen in the most general form corresponding to arbitrary number of oscillators harmonically interacting with electron. The upper bound to the polaron ground state energy in limiting case of weak interaction and low temperatures is obtained and investigated in detail. It is shown that the result becomes more exact by increasing the number of oscillators. (author)

  8. Multiphonon generation during photodissociation of slow Landau-Pekar polarons

    International Nuclear Information System (INIS)

    Myasnikov, E. N.; Myasnikova, A. E.; Mastropas, Z. P.

    2006-01-01

    The spectra of the low-temperature photodissociation (photoionization) of Landau-Pekar polarons are calculated using the theory of quantum-coherent states and a new method of variation with respect to the parameters of phonon vacuum deformation. It is shown that the final polaron states upon photodissociation may have different numbers of phonons produced in a single dissociation event and different momenta of charge carriers. The spectrum of optical absorption related to the photodissociation of polarons exhibits a superposition of bands corresponding to various numbers of phonons formed as a result of dissociation of a single polaron. Due to a large width of the energy region corresponding to the final states of charge carriers, the halfwidth of each band is on the order of the energy of polaron coupling and is much greater than the phonon energy. For this reason, the individual phonon bands exhibit strong overlap. The very broad and, probably, structureless band formed as a result of the superposition of all these components begins at an energy equal to the sum of the polaron coupling energy (E p ) and the phonon energy. This band has a maximum at a frequency of about 5.6E p /ℎ and a halfwidth on the order of 5.6E p /ℎ at a unit effective mass (m* = m e ) of band electrons. For an effective charge carrier mass within m* = (1-3)m e , the energy of the polaron band maximum can be estimated as 5E p with an error of about 10%, and the halfwidth falls within 3.4E p 1/2 p . The multiphonon character of this band is related to a decay of the phonon condensate after the escape of charge carrier from a polaron. Such polarons are likely to be observed in the spectra of complex metal oxides, including high-temperature superconductors. Examples of such polaron bands in the reported absorption and photoconductivity spectra of nonstoichiometric cuprates, manganites, nickelates, and titanates are presented. A theory of the formation of Landau-Pekar polarons with the

  9. Semiclassical and quantum polarons in crystalline acetanilide

    Science.gov (United States)

    Hamm, P.; Tsironis, G. P.

    2007-08-01

    Crystalline acetanilide is a an organic solid with peptide bond structure similar to that of proteins. Two states appear in the amide I spectral region having drastically different properties: one is strongly temperature dependent and disappears at high temperatures while the other is stable at all temperatures. Experimental and theoretical work over the past twenty five years has assigned the former to a selftrapped state while the latter to an extended free exciton state. In this article we review the experimental and theoretical developments on acetanilide paying particular attention to issues that are still pending. Although the interpretation of the states is experimentally sound, we find that specific theoretical comprehension is still lacking. Among the issues that that appear not well understood is the effective dimensionality of the selftrapped polaron and free exciton states.

  10. Complex Hamiltonian Dynamics

    CERN Document Server

    Bountis, Tassos

    2012-01-01

    This book introduces and explores modern developments in the well established field of Hamiltonian dynamical systems. It focuses on high degree-of-freedom systems and the transitional regimes between regular and chaotic motion. The role of nonlinear normal modes is highlighted and the importance of low-dimensional tori in the resolution of the famous FPU paradox is emphasized. Novel powerful numerical methods are used to study localization phenomena and distinguish order from strongly and weakly chaotic regimes. The emerging hierarchy of complex structures in such regimes gives rise to particularly long-lived patterns and phenomena called quasi-stationary states, which are explored in particular in the concrete setting of one-dimensional Hamiltonian lattices and physical applications in condensed matter systems.  The self-contained and pedagogical approach is blended with a unique balance between mathematical rigor, physics insights and concrete applications. End of chapter exercises and (more demanding) res...

  11. Noncanonical Hamiltonian mechanics

    International Nuclear Information System (INIS)

    Litteljohn, R.G.

    1986-01-01

    Noncanonical variables in Hamiltonian mechanics were first used by Lagrange in 1808. In spite of this, most work in Hamiltonian mechanics has been carried out in canonical variables, up to this day. One reason for this is that noncanonical coordinates are seldom needed for mechanical problems based on Lagrangians of the form L = T - V, where T is the kinetic energy and V is the potential energy. Of course, such Lagrangians arise naturally in celestial mechanics, and as a result they form the paradigms of nineteenth-century mechanics and have become enshrined in all the mechanics textbooks. Certain features of modern problems, however, lead to the use of noncanonical coordinates. Among these are issues of gauge invariance and singular Lagrange a Poisson structures. In addition, certain problems, like the flow of magnetic-field lines in physical space, are naturally formulated in terms of noncanonical coordinates. None of these features is present in the nineteenth-century paradigms of mechanics, but they do arise in problems involving particle motion in the presence of magnetic fields. For example, the motion of a particle in an electromagnetic wave is an important one in plasma physics, but the usual Hamiltonian formulation is gauge dependent. For this problem, noncanonical approaches based on Lagrangians in phase space lead to powerful computational techniques which are gauge invariant. In the limit of strong magnetic fields, particle motion becomes 'guiding-center motion'. Guiding-center motion is also best understood in terms of noncanonical coordinates. Finally the flow of magnetic-field lines through physical space is a Hamiltonian system which is best understood with noncanonical coordinates. No doubt many more systems will arise in the future for which these noncanonical techniques can be applied. (author)

  12. Instability in Hamiltonian systems

    Directory of Open Access Journals (Sweden)

    A. Pumarino

    2005-11-01

    Besides proving the existence of Arnold diffusion for a new family of three degrees of freedom Hamiltonian systems, another goal of this book is not only to show how Arnold-like results can be extended to substantially larger sets of parameters, but also how to obtain effective estimates on the splitting of separatrices size when the frequency of the perturbation belongs to open real sets.

  13. Discrete variational Hamiltonian mechanics

    International Nuclear Information System (INIS)

    Lall, S; West, M

    2006-01-01

    The main contribution of this paper is to present a canonical choice of a Hamiltonian theory corresponding to the theory of discrete Lagrangian mechanics. We make use of Lagrange duality and follow a path parallel to that used for construction of the Pontryagin principle in optimal control theory. We use duality results regarding sensitivity and separability to show the relationship between generating functions and symplectic integrators. We also discuss connections to optimal control theory and numerical algorithms

  14. Approximate symmetries of Hamiltonians

    Science.gov (United States)

    Chubb, Christopher T.; Flammia, Steven T.

    2017-08-01

    We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest.

  15. Influence of impurities on the polaron effective mass

    International Nuclear Information System (INIS)

    Lima, R.A.T. de.

    1975-01-01

    Using the Green Function formalism, it is verified the Rodriguez's model for the effective mass of the polaron at finite temperature in the presence of 'traps'. Some aspects of this model were discussed. (M.W.O.) [pt

  16. A generalized AKNS hierarchy and its bi-Hamiltonian structures

    International Nuclear Information System (INIS)

    Xia Tiecheng; You Fucai; Chen Dengyuan

    2005-01-01

    First we construct a new isospectral problem with 8 potentials in the present paper. And then a new Lax pair is presented. By making use of Tu scheme, a class of new soliton hierarchy of equations is derived, which is integrable in the sense of Liouville and possesses bi-Hamiltonian structures. After making some reductions, the well-known AKNS hierarchy and other hierarchies of evolution equations are obtained. Finally, in order to illustrate that soliton hierarchy obtained in the paper possesses bi-Hamiltonian structures exactly, we prove that the linear combination of two-Hamiltonian operators admitted are also a Hamiltonian operator constantly. We point out that two Hamiltonian operators obtained of the system are directly derived from a recurrence relations, not from a recurrence operator

  17. Tracking polaron generation in electrochemically doped polyaniline thin films

    Science.gov (United States)

    Kalagi, S. S.; Patil, P. S.

    2018-04-01

    Electrochemically deposited polyaniline films on ITO substrates have been studied for their optical properties. π-π*transitions inducing the formation of polarons and bipolarons have been studied from the optical spectra. The generation of these quasiparticles and the corresponding quantum of energy stored has been analysed and calculated from the experimental data. The evolution of polaron with increased levels of protonation has been identified and the necessary energy required for the transitions have been explained with the help of band structure diagram.

  18. Spin-polarons and high-Tc superconductivity

    International Nuclear Information System (INIS)

    Wood, R.F.

    1994-03-01

    The spin-polaron concept is introduced in analogy to ionic and electronic polarons and the assumptions underlying the author's approach to spin-polaron mediated high-T c superconductivity are discussed. Elementary considerations about the spin-polaron formation energy are reviewed and the possible origin of the pairing mechanism illustrated schematically. The electronic structure of the CuO 2 planes is treated from the standpoint of antiferromagnetic band calculations that lead directly to the picture of holes predominantly on the oxygen sublattice in a Mott-Hubbard/charge transfer insulator. Assuming the holes to be described in a Bloch representation but with the effective mass renormalized by spin-polaron formation, equations for the superconducting gap, Δ, and transition temperature, T c , are developed and the symmetry of Δ discussed. After further simplifications, T c is calculated as a function of the carrier concentration, x. It is shown that the calculated behavior of T c (x) follows the experimental results closely and leads to a natural explanation of the effects of under- and over-doping. The paper concludes with a few remarks about the evidence for the carriers being fermions (polarons) or bosons (bipolarons)

  19. Hamiltonian kinetic theory of plasma ponderomotive processes

    International Nuclear Information System (INIS)

    McDonald, S.W.; Kaufman, A.N.

    1982-01-01

    The nonlinear nonresonant interaction of plasma waves and particles is formulated in Hamiltonian kinetic theory which treats the wave-action and particle distributions on an equal footing, thereby displaying reciprocity relations. In the quasistatic limit, a nonlinear wave-kinetic equation is obtained. The generality of the formalism allows for applications to arbitrary geometry, with the nonlinear effects expressed in terms of the linear susceptibility

  20. Quantization of non-Hamiltonian physical systems

    International Nuclear Information System (INIS)

    Bolivar, A.O.

    1998-09-01

    We propose a general method of quantization of non-Hamiltonian physical systems. Applying it, for example, to a dissipative system coupled to a thermal reservoir described by the Fokker-Planck equation, we are able to obtain the Caldeira-Leggett master equation, the non-linear Schroedinger-Langevin equation and Caldirola-Kanai equation (with an additional term), as particular cases. (author)

  1. Hamiltonian kinetic theory of plasma ponderomotive processes

    International Nuclear Information System (INIS)

    McDonald, S.W.; Kaufman, A.N.

    1981-12-01

    The nonlinear nonresonant interaction of plasma waves and particles is formulated in a Hamiltonian kinetic theory which treats the wave-action and particle distributions on an equal footing, thereby displaying reciprocity relations. In the quasistatic limit, a nonlinear wave-kinetic equation is obtained. The generality of the formalism allows for applications to arbitrary geometry, with the nonlinear effects expressed in terms of the linear susceptibility

  2. Hole polaron-polaron interaction in transition metal oxides and its limit to p-type doping

    Science.gov (United States)

    Chen, Shiyou; Wang, Lin-Wang

    2014-03-01

    Traditionally the origin of the poor p-type conductivity in some transition metal oxides (TMOs) was attributed to the limited hole concentration: the charge-compensating donor defects, such as oxygen vacancies and cation interstitials, can form spontaneously as the Fermi energy shifts down to near the valence band maximum. Besides the thermodynamic limit to the hole concentration, the limit to the hole mobility can be another possible reason, e.g., the hole carrier can form self-trapped polarons with very low carrier mobility. Although isolated hole polarons had been found in some TMOs, the polaron-polaron interaction is not well-studied. Here we show that in TMOs such as TiO2 and V2O5, the hole polarons prefer to bind with each other to form bipolarons, which are more stable than free hole carriers or separated polarons. This pushes the hole states upward into the conduction band and traps the holes. The rise of the Fermi energy suppresses the spontaneous formation of the charge-compensating donor defects, so the conventional mechanism becomes ineffective. Since it can happen in the impurity-free TMO lattices, independent of any extrinsic dopant, it acts as an intrinsic and general limit to the p-type conductivity in these TMOs. This material is based upon work performed by the JCAP, a US DOE Energy Innovation Hub, the NSFC (No. 61106087 and 91233121) and special funds for major state basic research (No. 2012CB921401).

  3. Hamiltonian path integrals

    International Nuclear Information System (INIS)

    Prokhorov, L.V.

    1982-01-01

    Problems related to consideration of operator nonpermutability in Hamiltonian path integral (HPI) are considered in the review. Integrals are investigated using trajectories in configuration space (nonrelativistic quantum mechanics). Problems related to trajectory integrals in HPI phase space are discussed: the problem of operator nonpermutability consideration (extra terms problem) and corresponding equivalence rules; ambiguity of HPI usual recording; transition to curvilinear coordinates. Problem of quantization of dynamical systems with couplings has been studied. As in the case of canonical transformations, quantization of the systems with couplings of the first kind requires the consideration of extra terms

  4. The Hamiltonian structure of general relativistic perfect fluids

    International Nuclear Information System (INIS)

    Bao, D.; Houston Univ., TX; Marsden, J.; Walton, R.

    1985-01-01

    We show that the evolution equations for a perfect fluid coupled to general relativity in a general lapse and shift, are Hamiltonian relative to a certain Poisson structure. For the fluid variables, a Lie-Poisson structure associated to the dual of a semi-direct product Lie algebra is used, while the bracket for the gravitational variables has the usual canonical symplectic structure. The evolution is governed by a Hamiltonian which is equivalent to that obtained from a canonical analysis. The relationship of our Hamiltonian structure with other approaches in the literature, such as Clebsch potentials, Lagrangian to Eulerian transformations, and its use in clarifying linearization stability, are discussed. (orig.)

  5. Inelastic scattering in a local polaron model with quadratic coupling to bosons

    DEFF Research Database (Denmark)

    Olsen, Thomas

    2009-01-01

    We calculate the inelastic scattering probabilities in the wide band limit of a local polaron model with quadratic coupling to bosons. The central object is a two-particle Green's function which is calculated exactly using a purely algebraic approach. Compared with the usual linear interaction term...... a quadratic interaction term gives higher probabilities for inelastic scattering involving a large number of bosons. As an application we consider the problem hot-electron-mediated energy transfer at surfaces and use the delta self-consistent field extension of density-functional theory to calculate...

  6. Theory of super-para-electric large polaron for gigantic photo-enhancements of dielectric constant and electronic conductivity in SrTiO3

    International Nuclear Information System (INIS)

    Yu Qiu; Nasu, Keiichiro

    2005-01-01

    In connection with the recent experimental discoveries on gigantic photoenhancements of the electronic conductivity and the quasi-static dielectric susceptibility in SrTiO 3 , we theoretically study a photo-generation mechanism of a charged ferroelectric domain in this quantum dielectric. The photo-generated electron, being quite itinerant in the 3d band of Ti 4+ , is assumed to couple weakly but quadratically with soft-anharmonic T 1u phonons in this quantum dielectric. The photo-generated electron is also assumed to couple strongly but linearly with the breathing type high energy phonons. Using a tight binding model for electron, we will show that these two types of electron-phonon couplings result in two types of polarons, a 'super-para-electric (SPE) large polaron' with a quasi-global parity violation, and an 'off-centre type self-trapped polaron' with only a local parity violation. We will also show that this SPE large polaron is nothing else but a singly charged (e - ) and conductive ferroelectric (or SPE) domain with a quasi macroscopic size. This polaron or domain is also shown to have a high mobility and a large quasi-static dielectric susceptibility

  7. Robust online Hamiltonian learning

    International Nuclear Information System (INIS)

    Granade, Christopher E; Ferrie, Christopher; Wiebe, Nathan; Cory, D G

    2012-01-01

    In this work we combine two distinct machine learning methodologies, sequential Monte Carlo and Bayesian experimental design, and apply them to the problem of inferring the dynamical parameters of a quantum system. We design the algorithm with practicality in mind by including parameters that control trade-offs between the requirements on computational and experimental resources. The algorithm can be implemented online (during experimental data collection), avoiding the need for storage and post-processing. Most importantly, our algorithm is capable of learning Hamiltonian parameters even when the parameters change from experiment-to-experiment, and also when additional noise processes are present and unknown. The algorithm also numerically estimates the Cramer–Rao lower bound, certifying its own performance. (paper)

  8. Chromatic roots and hamiltonian paths

    DEFF Research Database (Denmark)

    Thomassen, Carsten

    2000-01-01

    We present a new connection between colorings and hamiltonian paths: If the chromatic polynomial of a graph has a noninteger root less than or equal to t(n) = 2/3 + 1/3 (3)root (26 + 6 root (33)) + 1/3 (3)root (26 - 6 root (33)) = 1.29559.... then the graph has no hamiltonian path. This result...

  9. Small-polaron model of light atom diffusion

    International Nuclear Information System (INIS)

    Emin, D.

    1977-01-01

    A number of researchers have treated the diffusion of light interstitials in metals in strict analogy with the theory for the hopping diffusion of electrons in low-mobility insulators. In other words, these authors view the diffusion of light atoms as simply being an example of small-polaron hopping motion. In this paper the motion of a small polaron is introduced, and the mechanism of its motion is described. The experimental results are then succinctly presented. Next the physical assumptions implicit in the theory are compared with the situation which is believed to characterize the existence and motion of light interstitial atoms in metals. Concomitantly, the modifications of the small-polaron theory required in applying it to light atom diffusion are ennumerated

  10. Model Hamiltonian Calculations of the Nonlinear Polarizabilities of Conjugated Molecules.

    Science.gov (United States)

    Risser, Steven Michael

    This dissertation advances the theoretical knowledge of the nonlinear polarizabilities of conjugated molecules. The unifying feature of these molecules is an extended delocalized pi electron structure. The pi electrons dominate the electronic properties of the molecules, allowing prediction of molecular properties based on the treatment of just the pi electrons. Two separate pi electron Hamiltonians are used in the research. The principal Hamiltonian used is the non-interacting single-particle Huckel Hamiltonian, which replaces the Coulomb interaction among the pi electrons with a mean field interaction. The simplification allows for exact solution of the Hamiltonian for large molecules. The second Hamiltonian used for this research is the interacting multi-particle Pariser-Parr-Pople (PPP) Hamiltonian, which retains explicit Coulomb interactions. This limits exact solutions to molecules containing at most eight electrons. The molecular properties being investigated are the linear polarizability, and the second and third order hyperpolarizabilities. The hyperpolarizabilities determine the nonlinear optical response of materials. These molecular parameters are determined by two independent approaches. The results from the Huckel Hamiltonian are obtained through first, second and third order perturbation theory. The results from the PPP Hamiltonian are obtained by including the applied field directly in the Hamiltonian and determining the ground state energy at a series of field strengths. By fitting the energy to a polynomial in field strength, the polarizability and hyperpolarizabilities are determined. The Huckel Hamiltonian is used to calculate the third order hyperpolarizability of polyenes. These calculations were the first to show the average hyperpolarizability of the polyenes to be positive, and also to show the saturation of the hyperpolarizability. Comparison of these Huckel results to those from the PPP Hamiltonian shows the lack of explicit Coulomb

  11. The bi-Hamiltonian structures of the Manin-Radul super KP hierarchy

    International Nuclear Information System (INIS)

    Panda, S.; Roy, S.

    1992-05-01

    We consider the ''even-time'' flow of the Manin-Radul supersymmetric KP hierarchy and show that it possesses bi-Hamiltonian structures by deriving two distinct Gelfand-Dikii brackets corresponding to two successive Hamiltonians of the system. A recursion relation involving them is also obtained. We observe that the first Hamiltonian structure defines a supersymmetric Lie algebra since it is a linear algebra among the super fields appearing in the Lax operator whereas the second Hamiltonian structure is a non-linear algebra and so it does not define a Lie algebra. (author). 25 refs

  12. Finite-dimensional Liouville integrable Hamiltonian systems generated from Lax pairs of a bi-Hamiltonian soliton hierarchy by symmetry constraints

    Science.gov (United States)

    Manukure, Solomon

    2018-04-01

    We construct finite-dimensional Hamiltonian systems by means of symmetry constraints from the Lax pairs and adjoint Lax pairs of a bi-Hamiltonian hierarchy of soliton equations associated with the 3-dimensional special linear Lie algebra, and discuss the Liouville integrability of these systems based on the existence of sufficiently many integrals of motion.

  13. Logarithmic corrections in a quantization rule. The polaron spectrum

    International Nuclear Information System (INIS)

    Karasev, M.V.; Pereskokov, A.V.

    1994-01-01

    A nonlinear integrodifferential equation that arises in polaron theory is considered. The integral nonlinearity is given by a convolution with the Coulomb potential. Radially symmetric solutions are sought. In the semiclassical limit, an equation for the self-consistent potential is found and studied. The potential has a logarithmic singularity at the origin, and also a turning point at 1. The phase shifts at these points are determined. The quantization rule that takes into account the logarithmic corrections gives a simple asymptotic formula for the polaron spectrum. Global semiclassical solutions of the original nonlinear equation are constructed. 18 refs., 1 tab

  14. Polaronic and dressed molecular states in orbital Feshbach resonances

    Science.gov (United States)

    Xu, Junjun; Qi, Ran

    2018-04-01

    We consider the impurity problem in an orbital Feshbach resonance (OFR), with a single excited clock state | e ↑⟩ atom immersed in a Fermi sea of electronic ground state | g ↓⟩. We calculate the polaron effective mass and quasi-particle residue, as well as the polaron to molecule transition. By including one particle-hole excitation in the molecular state, we find significant correction to the transition point. This transition point moves toward the BCS side for increasing particle densities, which suggests that the corresponding many-body physics is similar to a narrow resonance.

  15. A self-consistent theory of the magnetic polaron

    International Nuclear Information System (INIS)

    Marvakov, D.I.; Kuzemsky, A.L.; Vlahov, J.P.

    1984-10-01

    A finite temperature self-consistent theory of magnetic polaron in the s-f model of ferromagnetic semiconductors is developed. The calculations are based on the novel approach of the thermodynamic two-time Green function methods. This approach consists in the introduction of the ''irreducible'' Green functions (IGF) and derivation of the exact Dyson equation and exact self-energy operator. It is shown that IGF method gives a unified and natural approach for a calculation of the magnetic polaron states by taking explicitly into account the damping effects and finite lifetime. (author)

  16. Al-bound hole polarons in TiO2

    International Nuclear Information System (INIS)

    Stashans, Arvids; Bermeo, Sthefano

    2009-01-01

    Changes in the structural and electronic properties of TiO 2 (anatase and rutile) due to the Al-doping are studied using a quantum-chemical approach based on the Hartree-Fock theory. The formation of hole polarons trapped at oxygen sites near the Al impurity has been discovered and their spatial configuration are discussed. The occurrence of well-localized one-center hole polarons in rutile may influence its photocatalytic activity. Optical absorption energy for this hole center is obtained, 0.4 eV, using the ΔSCF approach.

  17. A partial Hamiltonian approach for current value Hamiltonian systems

    Science.gov (United States)

    Naz, R.; Mahomed, F. M.; Chaudhry, Azam

    2014-10-01

    We develop a partial Hamiltonian framework to obtain reductions and closed-form solutions via first integrals of current value Hamiltonian systems of ordinary differential equations (ODEs). The approach is algorithmic and applies to many state and costate variables of the current value Hamiltonian. However, we apply the method to models with one control, one state and one costate variable to illustrate its effectiveness. The current value Hamiltonian systems arise in economic growth theory and other economic models. We explain our approach with the help of a simple illustrative example and then apply it to two widely used economic growth models: the Ramsey model with a constant relative risk aversion (CRRA) utility function and Cobb Douglas technology and a one-sector AK model of endogenous growth are considered. We show that our newly developed systematic approach can be used to deduce results given in the literature and also to find new solutions.

  18. Global stability and quadratic Hamiltonian structure in Lotka-Volterra and quasi-polynomial systems

    Energy Technology Data Exchange (ETDEWEB)

    Szederkenyi, Gabor; Hangos, Katalin M

    2004-04-26

    We show that the global stability of quasi-polynomial (QP) and Lotka-Volterra (LV) systems with the well-known logarithmic Lyapunov function is equivalent to the existence of a local generalized dissipative Hamiltonian description of the LV system with a diagonal quadratic form as a Hamiltonian function. The Hamiltonian function can be calculated and the quadratic dissipativity neighborhood of the origin can be estimated by solving linear matrix inequalities.

  19. Global stability and quadratic Hamiltonian structure in Lotka-Volterra and quasi-polynomial systems

    Science.gov (United States)

    Szederkényi, Gábor; Hangos, Katalin M.

    2004-04-01

    We show that the global stability of quasi-polynomial (QP) and Lotka-Volterra (LV) systems with the well-known logarithmic Lyapunov function is equivalent to the existence of a local generalized dissipative Hamiltonian description of the LV system with a diagonal quadratic form as a Hamiltonian function. The Hamiltonian function can be calculated and the quadratic dissipativity neighborhood of the origin can be estimated by solving linear matrix inequalities.

  20. Global stability and quadratic Hamiltonian structure in Lotka-Volterra and quasi-polynomial systems

    International Nuclear Information System (INIS)

    Szederkenyi, Gabor; Hangos, Katalin M.

    2004-01-01

    We show that the global stability of quasi-polynomial (QP) and Lotka-Volterra (LV) systems with the well-known logarithmic Lyapunov function is equivalent to the existence of a local generalized dissipative Hamiltonian description of the LV system with a diagonal quadratic form as a Hamiltonian function. The Hamiltonian function can be calculated and the quadratic dissipativity neighborhood of the origin can be estimated by solving linear matrix inequalities

  1. Hamiltonian description of the ideal fluid

    International Nuclear Information System (INIS)

    Morrison, P.J.

    1998-01-01

    The Hamiltonian viewpoint of fluid mechanical systems with few and infinite number of degrees of freedom is described. Rudimentary concepts of finite-degree-of-freedom Hamiltonian dynamics are reviewed, in the context of the passive advection of a scalar or tracer field by a fluid. The notions of integrability, invariant-tori, chaos, overlap criteria, and invariant-tori breakup are described in this context. Preparatory to the introduction of field theories, systems with an infinite number of degrees of freedom, elements of functional calculus and action principles of mechanics are reviewed. The action principle for the ideal compressible fluid is described in terms of Lagrangian or material variables. Hamiltonian systems in terms of noncanonical variables are presented, including several examples of Eulerian or inviscid fluid dynamics. Lie group theory sufficient for the treatment of reduction is reviewed. The reduction from Lagrangian to Eulerian variables is treated along with Clebsch variable decompositions. Stability in the canonical and noncanonical Hamiltonian contexts is described. Sufficient conditions for stability, such as Rayleigh-like criteria, are seen to be only sufficient in the general case because of the existence of negative-energy modes, which are possessed by interesting fluid equilibria. Linearly stable equilibria with negative energy modes are argued to be unstable when nonlinearity or dissipation is added. The energy-Casimir method is discussed and a variant of it that depends upon the notion of dynamical accessibility is described. The energy content of a perturbation about a general fluid equilibrium is calculated using three methods. copyright 1998 The American Physical Society

  2. Trapping, self-trapping and the polaron family

    International Nuclear Information System (INIS)

    Stoneham, A M; Gavartin, J; Shluger, A L; Kimmel, A V; Ramo, D Munoz; Roennow, H M; Aeppli, G; Renner, C

    2007-01-01

    The earliest ideas of the polaron recognized that the coupling of an electron to ionic vibrations would affect its apparent mass and could effectively immobilize the carrier (self-trapping). We discuss how these basic ideas have been generalized to recognize new materials and new phenomena. First, there is an interplay between self-trapping and trapping associated with defects or with fluctuations in an amorphous solid. In high dielectric constant oxides, like HfO 2 , this leads to oxygen vacancies having as many as five charge states. In colossal magnetoresistance manganites, this interplay makes possible the scanning tunnelling microscopy (STM) observation of polarons. Second, excitons can self-trap and, by doing so, localize energy in ways that can modify the material properties. Third, new materials introduce new features, with polaron-related ideas emerging for uranium dioxide, gate dielectric oxides, Jahn-Teller systems, semiconducting polymers and biological systems. The phonon modes that initiate self-trapping can be quite different from the longitudinal optic modes usually assumed to dominate. Fourth, there are new phenomena, like possible magnetism in simple oxides, or with the evolution of short-lived polarons, like muons or excitons. The central idea remains that of a particle whose properties are modified by polarizing or deforming its host solid, sometimes profoundly. However, some of the simpler standard assumptions can give a limited, indeed misleading, description of real systems, with qualitative inconsistencies. We discuss representative cases for which theory and experiment can be compared in detail

  3. Localized polarons and doorway vibrons in finite quantum structures

    Czech Academy of Sciences Publication Activity Database

    Fehske, H.; Wellein, G.; Loos, Jan; Bishop, A. R.

    2008-01-01

    Roč. 77, č. 8 (2008), 085117/1-085117/6 ISSN 1098-0121 Institutional research plan: CEZ:AV0Z10100521 Keywords : quantum dots * electron - phonon interaction * polarons Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 3.322, year: 2008

  4. Ground state energy of a polaron in a superlattice

    International Nuclear Information System (INIS)

    Mensah, S.Y.; Allotey, F.K.A.; Nkrumah, G.; Mensah, N.G.

    2000-10-01

    The ground state energy of a polaron in a superlattice was calculated using the double-time Green functions. The effective mass of the polaron along the planes perpendicular to the superlattice axis was also calculated. The dependence of the ground state energy and the effective mass along the planes perpendicular to the superlattice axis on the electron-phonon coupling constant α and on the superlattice parameters (i.e. the superlattice period d and the bandwidth Δ) were studied. It was observed that if an infinite square well potential is assumed, the ground state energy of the polaron decreases (i.e. becomes more negative) with increasing α and d, but increases with increasing Δ. For small values of α, the polaron ground state energy varies slowly with Δ, becoming approximately constant for large Δ. The effective mass along the planes perpendicular to the superlattice axis was found to be approximately equal to the mass of an electron for all typical values of α, d and Δ. (author)

  5. Alternative Hamiltonian representation for gravity

    Energy Technology Data Exchange (ETDEWEB)

    Rosas-RodrIguez, R [Instituto de Fisica, Universidad Autonoma de Puebla, Apdo. Postal J-48, 72570, Puebla, Pue. (Mexico)

    2007-11-15

    By using a Hamiltonian formalism for fields wider than the canonical one, we write the Einstein vacuum field equations in terms of alternative variables. This variables emerge from the Ashtekar's formalism for gravity.

  6. Alternative Hamiltonian representation for gravity

    International Nuclear Information System (INIS)

    Rosas-RodrIguez, R

    2007-01-01

    By using a Hamiltonian formalism for fields wider than the canonical one, we write the Einstein vacuum field equations in terms of alternative variables. This variables emerge from the Ashtekar's formalism for gravity

  7. Effective Hamiltonians for phosphorene and silicene

    DEFF Research Database (Denmark)

    Voon, L. C. Lew Yan; Lopez-Bezanilla, A.; Wang, J.

    2015-01-01

    We derived the effective Hamiltonians for silicene and phosphorene with strain, electric field andmagnetic field using the method of invariants. Our paper extends the work of Geissler et al 2013 (NewJ. Phys. 15 085030) on silicene, and Li and Appelbaum 2014 (Phys. Rev. B 90, 115439) on phosphorene.......For phosphorene, it is shown that the bands near the Brillouin zone center only have terms ineven powers of the wave vector. We predict that the energies change quadratically in the presence of aperpendicular external electric field but linearly in a perpendicular magnetic field, as opposed to thosefor silicene...

  8. Scattering theory for Stark Hamiltonians

    International Nuclear Information System (INIS)

    Jensen, Arne

    1994-01-01

    An introduction to the spectral and scattering theory for Schroedinger operators is given. An abstract short range scattering theory is developed. It is applied to perturbations of the Laplacian. Particular attention is paid to the study of Stark Hamiltonians. The main result is an explanation of the discrepancy between the classical and the quantum scattering theory for one-dimensional Stark Hamiltonians. (author). 47 refs

  9. Full-counting statistics of energy transport of molecular junctions in the polaronic regime

    International Nuclear Information System (INIS)

    Tang, Gaomin; Yu, Zhizhou; Wang, Jian

    2017-01-01

    We investigate the full-counting statistics (FCS) of energy transport carried by electrons in molecular junctions for the Anderson–Holstein model in the polaronic regime. Using the two-time quantum measurement scheme, the generating function (GF) for the energy transport is derived and expressed as a Fredholm determinant in terms of Keldysh nonequilibrium Green’s function in the time domain. Dressed tunneling approximation is used in decoupling the phonon cloud operator in the polaronic regime. This formalism enables us to analyze the time evolution of energy transport dynamics after a sudden switch-on of the coupling between the dot and the leads towards the stationary state. The steady state energy current cumulant GF in the long time limit is obtained in the energy domain as well. Universal relations for steady state energy current FCS are derived under a finite temperature gradient with zero bias and this enabled us to express the equilibrium energy current cumulant by a linear combination of lower order cumulants. The behaviors of energy current cumulants in steady state under temperature gradient and external bias are numerically studied and explained. The transient dynamics of energy current cumulants is numerically calculated and analyzed. Universal scaling of normalized transient energy cumulants is found under both temperature gradient and external bias. (paper)

  10. Hamiltonian quantum simulation with bounded-strength controls

    International Nuclear Information System (INIS)

    Bookatz, Adam D; Wocjan, Pawel; Viola, Lorenza

    2014-01-01

    We propose dynamical control schemes for Hamiltonian simulation in many-body quantum systems that avoid instantaneous control operations and rely solely on realistic bounded-strength control Hamiltonians. Each simulation protocol consists of periodic repetitions of a basic control block, constructed as a modification of an ‘Eulerian decoupling cycle,’ that would otherwise implement a trivial (zero) target Hamiltonian. For an open quantum system coupled to an uncontrollable environment, our approach may be employed to engineer an effective evolution that simulates a target Hamiltonian on the system while suppressing unwanted decoherence to the leading order, thereby allowing for dynamically corrected simulation. We present illustrative applications to both closed- and open-system simulation settings, with emphasis on simulation of non-local (two-body) Hamiltonians using only local (one-body) controls. In particular, we provide simulation schemes applicable to Heisenberg-coupled spin chains exposed to general linear decoherence, and show how to simulate Kitaev's honeycomb lattice Hamiltonian starting from Ising-coupled qubits, as potentially relevant to the dynamical generation of a topologically protected quantum memory. Additional implications for quantum information processing are discussed. (papers)

  11. Hamiltonian description of the ideal fluid

    International Nuclear Information System (INIS)

    Morrison, P.J.

    1994-01-01

    Fluid mechanics is examined from a Hamiltonian perspective. The Hamiltonian point of view provides a unifying framework; by understanding the Hamiltonian perspective, one knows in advance (within bounds) what answers to expect and what kinds of procedures can be performed. The material is organized into five lectures, on the following topics: rudiments of few-degree-of-freedom Hamiltonian systems illustrated by passive advection in two-dimensional fluids; functional differentiation, two action principles of mechanics, and the action principle and canonical Hamiltonian description of the ideal fluid; noncanonical Hamiltonian dynamics with examples; tutorial on Lie groups and algebras, reduction-realization, and Clebsch variables; and stability and Hamiltonian systems

  12. Effective Hamiltonians for phosphorene and silicene

    International Nuclear Information System (INIS)

    Lew Yan Voon, L C; Lopez-Bezanilla, A; Wang, J; Zhang, Y; Willatzen, M

    2015-01-01

    We derived the effective Hamiltonians for silicene and phosphorene with strain, electric field and magnetic field using the method of invariants. Our paper extends the work of Geissler et al 2013 (New J. Phys. 15 085030) on silicene, and Li and Appelbaum 2014 (Phys. Rev. B 90, 115439) on phosphorene. Our Hamiltonians are compared to an equivalent one for graphene. For silicene, the expression for band warping is obtained analytically and found to be of different order than for graphene. We prove that a uniaxial strain does not open a gap, resolving contradictory numerical results in the literature. For phosphorene, it is shown that the bands near the Brillouin zone center only have terms in even powers of the wave vector. We predict that the energies change quadratically in the presence of a perpendicular external electric field but linearly in a perpendicular magnetic field, as opposed to those for silicene which vary linearly in both cases. Preliminary ab initio calculations for the intrinsic band structures have been carried out in order to evaluate some of the k⋅p parameters. (paper)

  13. First principles of Hamiltonian medicine.

    Science.gov (United States)

    Crespi, Bernard; Foster, Kevin; Úbeda, Francisco

    2014-05-19

    We introduce the field of Hamiltonian medicine, which centres on the roles of genetic relatedness in human health and disease. Hamiltonian medicine represents the application of basic social-evolution theory, for interactions involving kinship, to core issues in medicine such as pathogens, cancer, optimal growth and mental illness. It encompasses three domains, which involve conflict and cooperation between: (i) microbes or cancer cells, within humans, (ii) genes expressed in humans, (iii) human individuals. A set of six core principles, based on these domains and their interfaces, serves to conceptually organize the field, and contextualize illustrative examples. The primary usefulness of Hamiltonian medicine is that, like Darwinian medicine more generally, it provides novel insights into what data will be productive to collect, to address important clinical and public health problems. Our synthesis of this nascent field is intended predominantly for evolutionary and behavioural biologists who aspire to address questions directly relevant to human health and disease.

  14. Variational identities and Hamiltonian structures

    International Nuclear Information System (INIS)

    Ma Wenxiu

    2010-01-01

    This report is concerned with Hamiltonian structures of classical and super soliton hierarchies. In the classical case, basic tools are variational identities associated with continuous and discrete matrix spectral problems, targeted to soliton equations derived from zero curvature equations over general Lie algebras, both semisimple and non-semisimple. In the super case, a supertrace identity is presented for constructing Hamiltonian structures of super soliton equations associated with Lie superalgebras. We illustrate the general theories by the KdV hierarchy, the Volterra lattice hierarchy, the super AKNS hierarchy, and two hierarchies of dark KdV equations and dark Volterra lattices. The resulting Hamiltonian structures show the commutativity of each hierarchy discussed and thus the existence of infinitely many commuting symmetries and conservation laws.

  15. Dynamical decoupling of unbounded Hamiltonians

    Science.gov (United States)

    Arenz, Christian; Burgarth, Daniel; Facchi, Paolo; Hillier, Robin

    2018-03-01

    We investigate the possibility to suppress interactions between a finite dimensional system and an infinite dimensional environment through a fast sequence of unitary kicks on the finite dimensional system. This method, called dynamical decoupling, is known to work for bounded interactions, but physical environments such as bosonic heat baths are usually modeled with unbounded interactions; hence, here, we initiate a systematic study of dynamical decoupling for unbounded operators. We develop a sufficient decoupling criterion for arbitrary Hamiltonians and a necessary decoupling criterion for semibounded Hamiltonians. We give examples for unbounded Hamiltonians where decoupling works and the limiting evolution as well as the convergence speed can be explicitly computed. We show that decoupling does not always work for unbounded interactions and we provide both physically and mathematically motivated examples.

  16. Painlevé IV Hamiltonian systems and coherent states

    International Nuclear Information System (INIS)

    Bermudez, D; Contreras-Astorga, A; Fernández C, D J

    2015-01-01

    Schrödinger Hamiltonians with third-order differential ladder operators are linked to the Painlevé IV equation. Some of these appear from applying SUSY QM to the harmonic oscillator. Departing from them, we will build coherent states as eigenstates of the annihilation operator, then as displaced versions of the extremal states, both involving the third-order ladder operators, and finally as displaced extremal states using linearized ladder operators. To each Hamiltonian corresponds two families of coherent states for fixed ladder operators: one in the infinite dimension subspace associated with the oscillator spectrum and another in the finite dimension one generated by the eigenstates created by SUSY QM. (paper)

  17. Bound magnetic polaron in a semimagnetic double quantum well

    Science.gov (United States)

    Kalpana, P.; Jayakumar, K.

    2017-09-01

    The effect of different combinations of the concentration of Mn2+ ion in the Quantum well Cd1-xinMnxin Te and the barrier Cd1-xoutMnxout Te on the Bound Magnetic Polaron (BMP) in a Diluted Magnetic Semiconductors (DMS) Double Quantum Well (DQW) has been investigated. The Schrodinger equation is solved variationally in the effective mass approximation through which the Spin Polaronic Shift (SPS) due to the formation of BMP has been estimated for various locations of the donor impurity in the DQW. The results show that the effect of the increase of Mn2+ ion composition with different combinations on SPS is predominant for On Centre Well (OCW) impurity when compared to all other impurity locations when there is no application of magnetic field (γ = 0), γ being a dimensionless parameter for the magnetic field, and the same is predominant for On Centre Barrier (OCB) impurity with the application of external magnetic field (γ = 0.15).

  18. Optical Detection of Polarons in High - Tc Cuprate

    International Nuclear Information System (INIS)

    Calvani, P.; Capizzi, M.; Lupi, S.; Maselli, P.; Paolone, A.; Roy LURE, P.; Berger, H.

    1995-01-01

    The optical conductivity σ (ω) of slightly e-doped single-crystals of (Nd,Gd) 2 CuO 4-y shows local modes in the far-infrared as well as a broad infrared absorption centered at ∼ 0.1 eV (d-band). This latter shows a fine structure, in agreement with recent calculations of Alexandrov et al., which is made up by intense overtones of the local modes observed in the far-infrared. Similar polaronic structures are shown to exist in the normal metallic phase of Nd 2-x Ce x CuO 4-y and even in the σ (ω ) of YBCO crystals, measured by different authors. The present observations provide evidence for the existence of small polarons in all materials with a Cu-O plane

  19. Invariant metrics for Hamiltonian systems

    International Nuclear Information System (INIS)

    Rangarajan, G.; Dragt, A.J.; Neri, F.

    1991-05-01

    In this paper, invariant metrics are constructed for Hamiltonian systems. These metrics give rise to norms on the space of homeogeneous polynomials of phase-space variables. For an accelerator lattice described by a Hamiltonian, these norms characterize the nonlinear content of the lattice. Therefore, the performance of the lattice can be improved by minimizing the norm as a function of parameters describing the beam-line elements in the lattice. A four-fold increase in the dynamic aperture of a model FODO cell is obtained using this procedure. 7 refs

  20. Thermoelectric power of small polarons in magnetic semiconductors

    International Nuclear Information System (INIS)

    Liu, N.H.; Emin, D.

    1984-01-01

    The thermoelectric power (Seebeck coefficient) α of a small polaron in both ferromagnetic and antiferromagnetic semiconductors and insulators is calculated for the first time. In particular, we obtain the contribution to the Seebeck coefficient arising from exchange interactions between the severely localized carrier (i.e., small polaron) of charge q and the spins of the host lattice. In essence, we study the heat transported along with a carrier. This heat, the Peltier heat, Pi, is related to the Seebeck coefficient by the Kelvin relation: Pi = qTα, where T is the temperature. The heat per carrier is simply the product of the temperature and the change of the entropy of the system when a small polaron is added to it. The magnetic contribution to the Seebeck coefficient is therefore directly related to the change of the magnetic entropy of the system upon introduction of a charge carrier. We explicitly treat the intrasite and intersite exchange interactions between a small polaron and the spins of a spin-1/2 system. These magnetic interactions produce two competing contributions to the Seebeck coefficient. First, adding the carrier tends to provide extra spin freedom (e.g., spin up or spin down of the carrier). This effect augments the entropy of the system, thereby producing a positive contribution to the Peltier heat. Second, however, the additional exchange between the carrier and the sites about it enhances the exchange binding among these sites. This generally reduces the energetically allowable spin configurations. The concomitant reduction of the system's entropy provides a negative contribution to the Peltier heat. At the highest of temperatures, when kT exceeds the intrasite exchange energy, the first effect dominates. Then, the Peltier heat is simply augmented by kT ln2

  1. Electron localization, polarons and clustered states in manganites

    International Nuclear Information System (INIS)

    Mannella, N.

    2004-01-01

    Full text: A recent multi-spectroscopic study of prototypical colossal magnetoresistance (CMR) compounds La 1-x Sr x MnO 3 (LSMO, x = 0.3, 0.4) using photoemission (PE), x-ray absorption (XAS), x-ray emission (XES) and extended x-ray absorption e structure (EXAFS) has exposed a dramatic change in the electronic structure on crossing the ferromagnetic-to-paramagnetic transition temperature (T C ). In particular, this investigation revealed an increase of the Mn magnetic moment by ca. 1 Bohr magneton and charge transfer to the Mn atom on crossing T C concomitant with the presence of Jahn-Teller distortions, thus providing direct evidence of lattice polaron formation. These results thus challenge the belief of some authors that the LSMO compounds are canonical double-exchange (DE) systems in which polaron formation is unimportant, and thus help to unify the theoretical description of the CMR oxides. The relationship of these data to other recent work suggesting electron localization, polarons and phase separation, along with additional measurements of magnetic susceptibility indicating the formation of ferromagnetic clusters in the metallic paramagnetic state above T C will be discussed

  2. Absolute instability of polaron mode in semiconductor magnetoplasma

    Science.gov (United States)

    Paliwal, Ayushi; Dubey, Swati; Ghosh, S.

    2018-01-01

    Using coupled mode theory under hydrodynamic regime, a compact dispersion relation is derived for polaron mode in semiconductor magnetoplasma. The propagation and amplification characteristics of the wave are explored in detail. The analysis deals with the behaviour of anomalous threshold and amplification derived from dispersion relation, as function of external parameters like doping concentration and applied magnetic field. The results of this investigation are hoped to be useful in understanding electron-longitudinal optical phonon interplay in polar n-type semiconductor plasmas under the influence of coupled collective cyclotron excitations. The best results in terms of smaller threshold and higher gain of polaron mode could be achieved by choosing moderate doping concentration in the medium at higher magnetic field. For numerical appreciation of the results, relevant data of III-V n-GaAs compound semiconductor at 77 K is used. Present study provides a qualitative picture of polaron mode in magnetized n-type polar semiconductor medium duly shined by a CO2 laser.

  3. Existence of infinitely many periodic solutions for second-order nonautonomous Hamiltonian systems

    Directory of Open Access Journals (Sweden)

    Wen Guan

    2015-04-01

    Full Text Available By using minimax methods and critical point theory, we obtain infinitely many periodic solutions for a second-order nonautonomous Hamiltonian systems, when the gradient of potential energy does not exceed linear growth.

  4. Hamiltonian formulation of the supermembrane

    International Nuclear Information System (INIS)

    Bergshoeff, E.; Sezgin, E.; Tanii, Y.

    1987-06-01

    The Hamiltonian formulation of the supermembrane theory in eleven dimensions is given. The covariant split of the first and second class constraints is exhibited, and their Dirac brackets are computed. Gauge conditions are imposed in such a way that the reparametrizations of the membrane with divergence free 2-vectors are unfixed. (author). 10 refs

  5. Relativistic non-Hamiltonian mechanics

    International Nuclear Information System (INIS)

    Tarasov, Vasily E.

    2010-01-01

    Relativistic particle subjected to a general four-force is considered as a nonholonomic system. The nonholonomic constraint in four-dimensional space-time represents the relativistic invariance by the equation for four-velocity u μ u μ + c 2 = 0, where c is the speed of light in vacuum. In the general case, four-forces are non-potential, and the relativistic particle is a non-Hamiltonian system in four-dimensional pseudo-Euclidean space-time. We consider non-Hamiltonian and dissipative systems in relativistic mechanics. Covariant forms of the principle of stationary action and the Hamilton's principle for relativistic mechanics of non-Hamiltonian systems are discussed. The equivalence of these principles is considered for relativistic particles subjected to potential and non-potential forces. We note that the equations of motion which follow from the Hamilton's principle are not equivalent to the equations which follow from the variational principle of stationary action. The Hamilton's principle and the principle of stationary action are not compatible in the case of systems with nonholonomic constraint and the potential forces. The principle of stationary action for relativistic particle subjected to non-potential forces can be used if the Helmholtz conditions are satisfied. The Hamilton's principle and the principle of stationary action are equivalent only for a special class of relativistic non-Hamiltonian systems.

  6. Mathematical Modeling of Constrained Hamiltonian Systems

    NARCIS (Netherlands)

    Schaft, A.J. van der; Maschke, B.M.

    1995-01-01

    Network modelling of unconstrained energy conserving physical systems leads to an intrinsic generalized Hamiltonian formulation of the dynamics. Constrained energy conserving physical systems are directly modelled as implicit Hamiltonian systems with regard to a generalized Dirac structure on the

  7. Geometric Hamiltonian structures and perturbation theory

    International Nuclear Information System (INIS)

    Omohundro, S.

    1984-08-01

    We have been engaged in a program of investigating the Hamiltonian structure of the various perturbation theories used in practice. We describe the geometry of a Hamiltonian structure for non-singular perturbation theory applied to Hamiltonian systems on symplectic manifolds and the connection with singular perturbation techniques based on the method of averaging

  8. Notch filters for port-Hamiltonian systems

    NARCIS (Netherlands)

    Dirksz, D.A.; Scherpen, J.M.A.; van der Schaft, A.J.; Steinbuch, M.

    2012-01-01

    In this paper a standard notch filter is modeled in the port-Hamiltonian framework. By having such a port-Hamiltonian description it is proven that the notch filter is a passive system. The notch filter can then be interconnected with another (nonlinear) port-Hamiltonian system, while preserving the

  9. Constructing Dense Graphs with Unique Hamiltonian Cycles

    Science.gov (United States)

    Lynch, Mark A. M.

    2012-01-01

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

  10. The Hamiltonian of QED. Zero mode

    International Nuclear Information System (INIS)

    Zastavenko, L.G.

    1990-01-01

    We start with the standard QED Lagrangian. New derivation of the spinor QED Hamiltonian is given. We have taken into account the zero mode. Our derivation is faultless from the point of view of gauge invariance. It gives important corrections to the standard QED Hamiltonian. Our derivation of the Hamiltonian can be generalized to the case of QCD. 5 refs

  11. Hamiltonian indices and rational spectral densities

    Science.gov (United States)

    Byrnes, C. I.; Duncan, T. E.

    1980-01-01

    Several (global) topological properties of various spaces of linear systems, particularly symmetric, lossless, and Hamiltonian systems, and multivariable spectral densities of fixed McMillan degree are announced. The study is motivated by a result asserting that on a connected but not simply connected manifold, it is not possible to find a vector field having a sink as its only critical point. In the scalar case, this is illustrated by showing that only on the space of McMillan degree = /Cauchy index/ = n, scalar transfer functions can one define a globally convergent vector field. This result holds both in discrete-time and for the nonautonomous case. With these motivations in mind, theorems of Bochner and Fogarty are used in showing that spaces of transfer functions defined by symmetry conditions are, in fact, smooth algebraic manifolds.

  12. A Hamiltonian five-field gyrofluid model

    Energy Technology Data Exchange (ETDEWEB)

    Keramidas Charidakos, I.; Waelbroeck, F. L.; Morrison, P. J. [Institute for Fusion Studies and Department of Physics, The University of Texas at Austin, Austin, TX 78712 (United States)

    2015-11-15

    A Lie-Poisson bracket is presented for a five-field gyrofluid model, thereby showing the model to be Hamiltonian. The model includes the effects of magnetic field curvature and describes the evolution of the electron and ion gyro-center densities, the parallel component of the ion and electron velocities, and the ion temperature. The quasineutrality property and Ampère's law determine, respectively, the electrostatic potential and magnetic flux. The Casimir invariants are presented, and shown to be associated with five Lagrangian invariants advected by distinct velocity fields. A linear, local study of the model is conducted both with and without Landau and diamagnetic resonant damping terms. Stability criteria and dispersion relations for the electrostatic and the electromagnetic cases are derived and compared with their analogs for fluid and kinetic models.

  13. Effective hamiltonian calculations using incomplete model spaces

    International Nuclear Information System (INIS)

    Koch, S.; Mukherjee, D.

    1987-01-01

    It appears that the danger of encountering ''intruder states'' is substantially reduced if an effective hamiltonian formalism is developed for incomplete model spaces (IMS). In a Fock-space approach, the proof a ''connected diagram theorem'' is fairly straightforward with exponential-type of ansatze for the wave-operator W, provided the normalization chosen for W is separable. Operationally, one just needs a suitable categorization of the Fock-space operators into ''diagonal'' and ''non-diagonal'' parts that is generalization of the corresponding procedure for the complete model space. The formalism is applied to prototypical 2-electron systems. The calculations have been performed on the Cyber 205 super-computer. The authors paid special attention to an efficient vectorization for the construction and solution of the resulting coupled non-linear equations

  14. Weak KAM for commuting Hamiltonians

    International Nuclear Information System (INIS)

    Zavidovique, M

    2010-01-01

    For two commuting Tonelli Hamiltonians, we recover the commutation of the Lax–Oleinik semi-groups, a result of Barles and Tourin (2001 Indiana Univ. Math. J. 50 1523–44), using a direct geometrical method (Stoke's theorem). We also obtain a 'generalization' of a theorem of Maderna (2002 Bull. Soc. Math. France 130 493–506). More precisely, we prove that if the phase space is the cotangent of a compact manifold then the weak KAM solutions (or viscosity solutions of the critical stationary Hamilton–Jacobi equation) for G and for H are the same. As a corollary we obtain the equality of the Aubry sets and of the Peierls barrier. This is also related to works of Sorrentino (2009 On the Integrability of Tonelli Hamiltonians Preprint) and Bernard (2007 Duke Math. J. 136 401–20)

  15. Hamiltonian dynamics of extended objects

    Science.gov (United States)

    Capovilla, R.; Guven, J.; Rojas, E.

    2004-12-01

    We consider relativistic extended objects described by a reparametrization-invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the dynamics of such higher derivative models which is motivated by the ADM formulation of general relativity. The canonical momenta are identified by looking at boundary behaviour under small deformations of the action; the relationship between the momentum conjugate to the embedding functions and the conserved momentum density is established. The canonical Hamiltonian is constructed explicitly; the constraints on the phase space, both primary and secondary, are identified and the role they play in the theory is described. The multipliers implementing the primary constraints are identified in terms of the ADM lapse and shift variables and Hamilton's equations are shown to be consistent with the Euler Lagrange equations.

  16. A Hamiltonian approach to Thermodynamics

    Energy Technology Data Exchange (ETDEWEB)

    Baldiotti, M.C., E-mail: baldiotti@uel.br [Departamento de Física, Universidade Estadual de Londrina, 86051-990, Londrina-PR (Brazil); Fresneda, R., E-mail: rodrigo.fresneda@ufabc.edu.br [Universidade Federal do ABC, Av. dos Estados 5001, 09210-580, Santo André-SP (Brazil); Molina, C., E-mail: cmolina@usp.br [Escola de Artes, Ciências e Humanidades, Universidade de São Paulo, Av. Arlindo Bettio 1000, CEP 03828-000, São Paulo-SP (Brazil)

    2016-10-15

    In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic Mechanics. Our proposal is constructed on top of a usual symplectic manifold, where phase space is even dimensional and one has well-defined Poisson brackets. The main idea is the introduction of an extended phase space where thermodynamic equations of state are realized as constraints. We are then able to apply the canonical transformation toolkit to thermodynamic problems. Throughout this development, Dirac’s theory of constrained systems is extensively used. To illustrate the formalism, we consider paradigmatic examples, namely, the ideal, van der Waals and Clausius gases. - Highlights: • A strictly Hamiltonian approach to Thermodynamics is proposed. • Dirac’s theory of constrained systems is extensively used. • Thermodynamic equations of state are realized as constraints. • Thermodynamic potentials are related by canonical transformations.

  17. Hamiltonian description of bubble dynamics

    International Nuclear Information System (INIS)

    Maksimov, A. O.

    2008-01-01

    The dynamics of a nonspherical bubble in a liquid is described within the Hamiltonian formalism. Primary attention is focused on the introduction of the canonical variables into the computational algorithm. The expansion of the Dirichlet-Neumann operator in powers of the displacement of a bubble wall from an equilibrium position is obtained in the explicit form. The first three terms (more specifically, the second-, third-, and fourth-order terms) in the expansion of the Hamiltonian in powers of the canonical variables are determined. These terms describe the spectrum and interaction of three essentially different modes, i.e., monopole oscillations (pulsations), dipole oscillations (translational motions), and surface oscillations. The cubic nonlinearity is analyzed for the problem associated with the generation of Faraday ripples on the wall of a bubble in an acoustic field. The possibility of decay processes occurring in the course of interaction of surface oscillations for the first fifteen (experimentally observed) modes is investigated.

  18. Hamiltonian dynamics of extended objects

    International Nuclear Information System (INIS)

    Capovilla, R; Guven, J; Rojas, E

    2004-01-01

    We consider relativistic extended objects described by a reparametrization-invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the dynamics of such higher derivative models which is motivated by the ADM formulation of general relativity. The canonical momenta are identified by looking at boundary behaviour under small deformations of the action; the relationship between the momentum conjugate to the embedding functions and the conserved momentum density is established. The canonical Hamiltonian is constructed explicitly; the constraints on the phase space, both primary and secondary, are identified and the role they play in the theory is described. The multipliers implementing the primary constraints are identified in terms of the ADM lapse and shift variables and Hamilton's equations are shown to be consistent with the Euler-Lagrange equations

  19. Hamiltonian dynamics of extended objects

    Energy Technology Data Exchange (ETDEWEB)

    Capovilla, R [Departamento de FIsica, Centro de Investigacion y de Estudios Avanzados del IPN, Apdo Postal 14-740, 07000 Mexico, DF (Mexico); Guven, J [School of Theoretical Physics, Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 4 (Ireland); Rojas, E [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apdo Postal 70-543, 04510 Mexico, DF (Mexico)

    2004-12-07

    We consider relativistic extended objects described by a reparametrization-invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the dynamics of such higher derivative models which is motivated by the ADM formulation of general relativity. The canonical momenta are identified by looking at boundary behaviour under small deformations of the action; the relationship between the momentum conjugate to the embedding functions and the conserved momentum density is established. The canonical Hamiltonian is constructed explicitly; the constraints on the phase space, both primary and secondary, are identified and the role they play in the theory is described. The multipliers implementing the primary constraints are identified in terms of the ADM lapse and shift variables and Hamilton's equations are shown to be consistent with the Euler-Lagrange equations.

  20. A Hamiltonian approach to Thermodynamics

    International Nuclear Information System (INIS)

    Baldiotti, M.C.; Fresneda, R.; Molina, C.

    2016-01-01

    In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic Mechanics. Our proposal is constructed on top of a usual symplectic manifold, where phase space is even dimensional and one has well-defined Poisson brackets. The main idea is the introduction of an extended phase space where thermodynamic equations of state are realized as constraints. We are then able to apply the canonical transformation toolkit to thermodynamic problems. Throughout this development, Dirac’s theory of constrained systems is extensively used. To illustrate the formalism, we consider paradigmatic examples, namely, the ideal, van der Waals and Clausius gases. - Highlights: • A strictly Hamiltonian approach to Thermodynamics is proposed. • Dirac’s theory of constrained systems is extensively used. • Thermodynamic equations of state are realized as constraints. • Thermodynamic potentials are related by canonical transformations.

  1. On the domain of the Nelson Hamiltonian

    Science.gov (United States)

    Griesemer, M.; Wünsch, A.

    2018-04-01

    The Nelson Hamiltonian is unitarily equivalent to a Hamiltonian defined through a closed, semibounded quadratic form, the unitary transformation being explicitly known and due to Gross. In this paper, we study the mapping properties of the Gross-transform in order to characterize the regularity properties of vectors in the form domain of the Nelson Hamiltonian. Since the operator domain is a subset of the form domain, our results apply to vectors in the domain of the Hamiltonian as well. This work is a continuation of our previous work on the Fröhlich Hamiltonian.

  2. Hamiltonian systems in accelerator physics

    International Nuclear Information System (INIS)

    Laslett, L.J.

    1985-06-01

    General features of the design of annular particle accelerators or storage rings are outlined and the Hamiltonian character of individual-ion motion is indicated. Examples of phase plots are presented, for the motion in one spatial degree of freedom, of an ion subject to a periodic nonlinear focusing force. A canonical transformation describing coupled nonlinear motion also is given, and alternative types of graphical display are suggested for the investigation of long-term stability in such cases. 7 figs

  3. Asymptotic dependence of Gross–Tulub polaron ground-state energy in the strong coupling region

    Directory of Open Access Journals (Sweden)

    N.I. Kashirina

    2017-12-01

    Full Text Available The properties of translationally invariant polaron functional have been investigated in the region of strong and extremely strong coupling. It has been shown that the Gross–Tulub polaron functional obtained earlier using the methods of field theory was derived only for the region , where is the Fröhlich constant of the electron-phonon coupling. Various representations of exact and approximate polaron functionals have been considered. Asymptotic dependences of the polaron energy have been obtained using a functional extending the Gross–Tulub functional to the region of extremely strong coupling. The asymptotic dependence of polaron energies for an extremely strong coupling are (for the one-parameter variational function fk, and (for a two-parameter function . It has been shown that the virial theorem 1:3:4 holds for the two-parameter function . Minimization of the approximate functional obtained by expanding the exact Gross–Tulub functional in a series on leads to a quadratic dependence of the polaron energy. This approximation is justified for . For a two-parameter function , the corresponding dependence has the form . However, the use of approximate functionals, in contrast to the strict variational procedure, when the exact polaron functional varies, does not guarantee obtaining the upper limit for the polaron energy.

  4. Effect of interchain coupling on the excited polaron in conjugated polymers

    International Nuclear Information System (INIS)

    Li, Xiao-xue; Chen, Gang

    2017-01-01

    Based on the one-dimensional extended Su–Schrieffer–Heeger model, we theoretically investigate the effect of interchain coupling on the formation and polarization of the single-excited state of polaron in conjugated polymers. It is found that there exists a turnover value of the coupling strength, over which the excited polaron could not be formed in either of the two coupled chains. Instead, a polaron-like particle is localized at the center of each chain. In addition, we also find that the reverse polarization of the excited polaron could be enhanced for some cases in polymer when the interchain coupling becomes strong until it exceeds the critical value. - Highlights: • Effect of interchain coupling on the single-excited state of polaron is studied. • When coupling strength exceeds critical value, the excited polaron is dissociated. • Soliton pair could be dissociated into polaron-like particle with strong coupling. • Reverse polarization of excited polaron is enhanced by weak interchain coupling. • Reverse polarization is obtained more easily in solid film of polymer molecules.

  5. Effect of interchain coupling on the excited polaron in conjugated polymers

    Energy Technology Data Exchange (ETDEWEB)

    Li, Xiao-xue, E-mail: sps_lixx@ujn.edu.cn; Chen, Gang, E-mail: ss_cheng@ujn.edu.cn

    2017-02-05

    Based on the one-dimensional extended Su–Schrieffer–Heeger model, we theoretically investigate the effect of interchain coupling on the formation and polarization of the single-excited state of polaron in conjugated polymers. It is found that there exists a turnover value of the coupling strength, over which the excited polaron could not be formed in either of the two coupled chains. Instead, a polaron-like particle is localized at the center of each chain. In addition, we also find that the reverse polarization of the excited polaron could be enhanced for some cases in polymer when the interchain coupling becomes strong until it exceeds the critical value. - Highlights: • Effect of interchain coupling on the single-excited state of polaron is studied. • When coupling strength exceeds critical value, the excited polaron is dissociated. • Soliton pair could be dissociated into polaron-like particle with strong coupling. • Reverse polarization of excited polaron is enhanced by weak interchain coupling. • Reverse polarization is obtained more easily in solid film of polymer molecules.

  6. Contact symmetries and Hamiltonian thermodynamics

    International Nuclear Information System (INIS)

    Bravetti, A.; Lopez-Monsalvo, C.S.; Nettel, F.

    2015-01-01

    It has been shown that contact geometry is the proper framework underlying classical thermodynamics and that thermodynamic fluctuations are captured by an additional metric structure related to Fisher’s Information Matrix. In this work we analyse several unaddressed aspects about the application of contact and metric geometry to thermodynamics. We consider here the Thermodynamic Phase Space and start by investigating the role of gauge transformations and Legendre symmetries for metric contact manifolds and their significance in thermodynamics. Then we present a novel mathematical characterization of first order phase transitions as equilibrium processes on the Thermodynamic Phase Space for which the Legendre symmetry is broken. Moreover, we use contact Hamiltonian dynamics to represent thermodynamic processes in a way that resembles the classical Hamiltonian formulation of conservative mechanics and we show that the relevant Hamiltonian coincides with the irreversible entropy production along thermodynamic processes. Therefore, we use such property to give a geometric definition of thermodynamically admissible fluctuations according to the Second Law of thermodynamics. Finally, we show that the length of a curve describing a thermodynamic process measures its entropy production

  7. Generic Local Hamiltonians are Gapless

    Science.gov (United States)

    Movassagh, Ramis

    2017-12-01

    We prove that generic quantum local Hamiltonians are gapless. In fact, we prove that there is a continuous density of states above the ground state. The Hamiltonian can be on a lattice in any spatial dimension or on a graph with a bounded maximum vertex degree. The type of interactions allowed for include translational invariance in a disorder (i.e., probabilistic) sense with some assumptions on the local distributions. Examples include many-body localization and random spin models. We calculate the scaling of the gap with the system's size when the local terms are distributed according to a Gaussian β orthogonal random matrix ensemble. As a corollary, there exist finite size partitions with respect to which the ground state is arbitrarily close to a product state. When the local eigenvalue distribution is discrete, in addition to the lack of an energy gap in the limit, we prove that the ground state has finite size degeneracies. The proofs are simple and constructive. This work excludes the important class of truly translationally invariant Hamiltonians where the local terms are all equal.

  8. Hamiltonian dynamics of preferential attachment

    International Nuclear Information System (INIS)

    Zuev, Konstantin; Papadopoulos, Fragkiskos; Krioukov, Dmitri

    2016-01-01

    Prediction and control of network dynamics are grand-challenge problems in network science. The lack of understanding of fundamental laws driving the dynamics of networks is among the reasons why many practical problems of great significance remain unsolved for decades. Here we study the dynamics of networks evolving according to preferential attachment (PA), known to approximate well the large-scale growth dynamics of a variety of real networks. We show that this dynamics is Hamiltonian, thus casting the study of complex networks dynamics to the powerful canonical formalism, in which the time evolution of a dynamical system is described by Hamilton’s equations. We derive the explicit form of the Hamiltonian that governs network growth in PA. This Hamiltonian turns out to be nearly identical to graph energy in the configuration model, which shows that the ensemble of random graphs generated by PA is nearly identical to the ensemble of random graphs with scale-free degree distributions. In other words, PA generates nothing but random graphs with power-law degree distribution. The extension of the developed canonical formalism for network analysis to richer geometric network models with non-degenerate groups of symmetries may eventually lead to a system of equations describing network dynamics at small scales. (paper)

  9. Repulsive polarons and itinerant ferromagnetism in strongly polarized Fermi gases

    DEFF Research Database (Denmark)

    Massignan, Pietro; Bruun, Georg

    2011-01-01

    We analyze the properties of a single impurity immersed in a Fermi sea. At positive energy and scattering lengths, we show that the system possesses a well-defined but metastable excitation, the repulsive polaron, and we calculate its energy, quasiparticle residue and effective mass. From...... polarized (ferromagnetic) domains are then examined for a binary mixture of atoms with a general mass ratio. Our results indicate that mass imbalance lowers the critical interaction strength for phase-separation, but that very short quasiparticle decay times will complicate the experimental observation...

  10. Quantum transition and decoherence of levitating polaron on helium film thickness under an electromagnetic field

    Science.gov (United States)

    Kenfack, S. C.; Fotue, A. J.; Fobasso, M. F. C.; Djomou, J.-R. D.; Tiotsop, M.; Ngouana, K. S. L.; Fai, L. C.

    2017-12-01

    We have studied the transition probability and decoherence time of levitating polaron in helium film thickness. By using a variational method of Pekar type, the ground and the first excited states of polaron are calculated above the liquid-helium film placed on the polar substrate. It is shown that the polaron transits from the ground to the excited state in the presence of an external electromagnetic field in the plane. We have seen that, in the helium film, the effects of the magnetic and electric fields on the polaron are opposite. It is also shown that the energy, transition probability and decoherence time of the polaron depend sensitively on the helium film thickness. We found that decoherence time decreases as a function of increasing electron-phonon coupling strength and the helium film thickness. It is seen that the film thickness can be considered as a new confinement in our system and can be adjusted in order to reduce decoherence.

  11. Observation of Spin-Polarons in a strongly interacting Fermi liquid

    Science.gov (United States)

    Zwierlein, Martin

    2009-03-01

    We have observed spin-polarons in a highly imbalanced mixture of fermionic atoms using tomographic RF spectroscopy. Feshbach resonances allow to freely tune the interactions between the two spin states involved. A single spin down atom immersed in a Fermi sea of spin up atoms can do one of two things: For strong attraction, it can form a molecule with exactly one spin up partner, but for weaker interaction it will spread its attraction and surround itself with a collection of majority atoms. This spin down atom ``dressed'' with a spin up cloud constitutes the spin-polaron. We have observed a striking spectroscopic signature of this quasi-particle for various interaction strengths, a narrow peak in the spin down spectrum that emerges above a broad background. The narrow width signals a long lifetime of the spin-polaron, much longer than the collision rate with spin up atoms, as it must be for a proper quasi-particle. The peak position allows to directly measure the polaron energy. The broad pedestal at high energies reveals physics at short distances and is thus ``molecule-like'': It is exactly matched by the spin up spectra. The comparison with the area under the polaron peak allows to directly obtain the quasi-particle weight Z. We observe a smooth transition from polarons to molecules. At a critical interaction strength of 1/kFa = 0.7, the polaron peak vanishes and spin up and spin down spectra exactly match, signalling the formation of molecules. This is the same critical interaction strength found earlier to separate a normal Fermi mixture from a superfluid molecular Bose-Einstein condensate. The spin-polarons determine the low-temperature phase diagram of imbalanced Fermi mixtures. In principle, polarons can interact with each other and should, at low enough temperatures, form a superfluid of p-wave pairs. We will present a first indication for interactions between polarons.

  12. Relativistic Many-Body Hamiltonian Approach to Mesons

    OpenAIRE

    Llanes-Estrada, Felipe J.; Cotanch, Stephen R.

    2001-01-01

    We represent QCD at the hadronic scale by means of an effective Hamiltonian, $H$, formulated in the Coulomb gauge. As in the Nambu-Jona-Lasinio model, chiral symmetry is explicity broken, however our approach is renormalizable and also includes confinement through a linear potential with slope specified by lattice gauge theory. This interaction generates an infrared integrable singularity and we detail the computationally intensive procedure necessary for numerical solution. We focus upon app...

  13. Peltier heat of a small polaron in a magnetic semiconductor

    International Nuclear Information System (INIS)

    Liu, N.H.; Emin, D.

    1985-01-01

    For the first time the heat transported with a small polaron in both antiferromagnetic and ferromagnetic semiconductors is calculated. This heat, the Peltier heat, π, is obtained from the change of the entropy of the total system upon introduction of a charge carrier. We explicitly consider both the intrasite and intersite exchange interactions between a small polaron and the interacting spins of a spin-1/2 magnet. There are two competing magnetic contributions to the Peltier heat. First, adding the carrier increases the spin entropy of the system. This provides a positive contribution to π. Second, the exchange between the carrier and the sites about it enhances the exchange binding between these sites. This reduces the energetically allowable spin configurations and provides a negative contribution to π. At extremely high temperatures when kT exceeds the intrasite exchange energy, the first effect dominates. Then π is simply augmented by kT ln 2. However, well below the magnetic transition temperature the second effect dominates. In the experimentally accessible range between these limits both effects are comparable and sizable. The net magnetic contribution to the Peltier heat rises with temperature. Thus, a carrier's interactions with its magnetic environment produces a significant and distinctive contribution to its Peltier heat

  14. Peltier heat of a small polaron in a magnetic semiconductor

    International Nuclear Information System (INIS)

    Liu, N.L.H.; Emin, D.

    1984-01-01

    The heat transported with a small polaron in both antiferromagnetic and ferromagnetic semiconductors is calculated. This heat, the Peltier heat, π, is obtained from the change of the entropy of the total system upon introduction of a charge carrier. We explicitly consider both the intrasite and intersite exchange interactions between a small polaron and the interacting spins of a spin-1/2 magnet. There are two competing magnetic contributions to the Peltier heat. First, adding the carrier increases the spin entropy of the system. This provides a positive contribution to π. Second, the exchange between the carrier and the sites about it enhances the exchange binding between these sites. This reduces the energetically allowable spin configurations and provides a negative contribution to π. At extremely high temperature when kT exceeds the intrasite exchange energy, the first effect dominates. Then π is simply augmented by kTln2. However, well below the magnetic transition temperature the second effect dominates. In the experimentally accessible range between these limits both effects are comparable and sizable. The net magnetic contribution to the Peltier heat rises with temperature. Thus, a carrier's interactions with its magnetic environment produces a significant and distinctive contribution to its Peltier heat

  15. Evidence for polaron conduction in nanostructured manganese ferrite

    International Nuclear Information System (INIS)

    Gopalan, E Veena; Anantharaman, M R; Malini, K A; Saravanan, S; Kumar, D Sakthi; Yoshida, Yasuhiko

    2008-01-01

    Nanoparticles of manganese ferrite were prepared by the chemical co-precipitation technique. The dielectric parameters, namely, real and imaginary dielectric permittivity (ε' and ε-prime), ac conductivity (σ ac ) and dielectric loss tangent (tanδ), were measured in the frequency range of 100 kHz-8 MHz at different temperatures. The variations of dielectric dispersion (ε') and dielectric absorption (ε-prime) with frequency and temperature were also investigated. The variation of dielectric permittivity with frequency and temperature followed the Maxwell-Wagner model based on interfacial polarization in consonance with Koops phenomenological theory. The dielectric loss tangent and hence ε-prime exhibited a relaxation at certain frequencies and at relatively higher temperatures. The dispersion of dielectric permittivity and broadening of the dielectric absorption suggest the possibility of a distribution of relaxation time and the existence of multiple equilibrium states in manganese ferrite. The activation energy estimated from the dielectric relaxation is found to be high and is characteristic of polaron conduction in the nanosized manganese ferrite. The ac conductivity followed a power law dependence σ ac = Bω n typical of charge transport assisted by a hopping or tunnelling process. The observed minimum in the temperature dependence of the frequency exponent n strongly suggests that tunnelling of the large polarons is the dominant transport process

  16. Hamiltonian theory of vacuum helical torus lines of magnetic force

    International Nuclear Information System (INIS)

    Gnudi, Giovanni; Hatori, Tadatsugu

    1994-01-01

    For making plasma into equilibrium state, the lines of magnetic force must have magnetic surfaces. However in a helical system, space is divided into the region having magnetic surface structure and the region that does not have it. Accordingly, it is an important basic research for the plasma confinement in a helical system to examine where is the boundary of both regions and how is the large area structure of the lines of magnetic force in the boundary region. The lines of magnetic force can be treated as a Hamilton mechanics system, and it has been proved that the Hamiltonian for the lines of magnetic force can be expressed by a set of canonical variables and the function of time. In this research, the Hamiltonian that describes the lines of magnetic force of helical system torus coordination in vacuum was successfully determined concretely. Next, the development of new linear symplectic integration method was carried out. The important supports for the theory of determining Hamiltonian are Lie transformation and paraxial expansion. The procedure is explained. In Appendix, Lie transformation, Hamiltonian for the lines of magnetic force, magnetic potential, Taylor expansion of the potential, cylindrical limit approximation, helical toroidal potential and integrable model are described. (K.I.)

  17. Quantum finance Hamiltonian for coupon bond European and barrier options.

    Science.gov (United States)

    Baaquie, Belal E

    2008-03-01

    Coupon bond European and barrier options are financial derivatives that can be analyzed in the Hamiltonian formulation of quantum finance. Forward interest rates are modeled as a two-dimensional quantum field theory and its Hamiltonian and state space is defined. European and barrier options are realized as transition amplitudes of the time integrated Hamiltonian operator. The double barrier option for a financial instrument is "knocked out" (terminated with zero value) if the price of the underlying instrument exceeds or falls below preset limits; the barrier option is realized by imposing boundary conditions on the eigenfunctions of the forward interest rates' Hamiltonian. The price of the European coupon bond option and the zero coupon bond barrier option are calculated. It is shown that, is general, the constraint function for a coupon bond barrier option can -- to a good approximation -- be linearized. A calculation using an overcomplete set of eigenfunctions yields an approximate price for the coupon bond barrier option, which is given in the form of an integral of a factor that results from the barrier condition times another factor that arises from the payoff function.

  18. Hamiltonian Chaos and Fractional Dynamics

    International Nuclear Information System (INIS)

    Combescure, M

    2005-01-01

    This book provides an introduction and discussion of the main issues in the current understanding of classical Hamiltonian chaos, and of its fractional space-time structure. It also develops the most complex and open problems in this context, and provides a set of possible applications of these notions to some fundamental questions of dynamics: complexity and entropy of systems, foundation of classical statistical physics on the basis of chaos theory, and so on. Starting with an introduction of the basic principles of the Hamiltonian theory of chaos, the book covers many topics that can be found elsewhere in the literature, but which are collected here for the readers' convenience. In the last three parts, the author develops topics which are not typically included in the standard textbooks; among them are: - the failure of the traditional description of chaotic dynamics in terms of diffusion equations; - he fractional kinematics, its foundation and renormalization group analysis; - 'pseudo-chaos', i.e. kinetics of systems with weak mixing and zero Lyapunov exponents; - directional complexity and entropy. The purpose of this book is to provide researchers and students in physics, mathematics and engineering with an overview of many aspects of chaos and fractality in Hamiltonian dynamical systems. In my opinion it achieves this aim, at least provided researchers and students (mainly those involved in mathematical physics) can complement this reading with comprehensive material from more specialized sources which are provided as references and 'further reading'. Each section contains introductory pedagogical material, often illustrated by figures coming from several numerical simulations which give the feeling of what's going on, and thus is very useful to the reader who is not very familiar with the topics presented. Some problems are included at the end of most sections to help the reader to go deeper into the subject. My one regret is that the book does not

  19. Coherent states for quadratic Hamiltonians

    International Nuclear Information System (INIS)

    Contreras-Astorga, Alonso; Fernandez C, David J; Velazquez, Mercedes

    2011-01-01

    The coherent states for a set of quadratic Hamiltonians in the trap regime are constructed. A matrix technique which allows us to directly identify the creation and annihilation operators will be presented. Then, the coherent states as simultaneous eigenstates of the annihilation operators will be derived, and will be compared with those attained through the displacement operator method. The corresponding wavefunction will be found, and a general procedure for obtaining several mean values involving the canonical operators in these states will be described. The results will be illustrated through the asymmetric Penning trap.

  20. Perturbation theory of effective Hamiltonians

    International Nuclear Information System (INIS)

    Brandow, B.H.

    1975-01-01

    This paper constitutes a review of the many papers which have used perturbation theory to derive ''effective'' or ''model'' Hamiltonians. It begins with a brief review of nondegenerate and non-many-body perturbation theory, and then considers the degenerate but non-many-body problem in some detail. It turns out that the degenerate perturbation problem is not uniquely defined, but there are some practical criteria for choosing among the various possibilities. Finally, the literature dealing with the linked-cluster aspects of open-shell many-body systems is reviewed. (U.S.)

  1. The Hamiltonian structures of the super KP hierarchy associated with an even parity superlax operator

    International Nuclear Information System (INIS)

    Barcelos Neto, J.; Ghosh, S.; Roy, S.

    1993-07-01

    We consider the even parity superLax operator for the supersymmetric KP hierarchy of the form L = D 2 + Σ ∞ i=0 u i-2 D -i+1 and obtain the two Hamiltonian structures following the standard method of Gelfand and Dikii. We observe that the first Hamiltonian structure is local and linear whereas the second Hamiltonian structure is non-local and nonlinear among the superfields appearing in the Lax operator. We discuss briefly on their connections with the super ω ∞ algebra. (author). 23 refs

  2. Perspective: Quantum Hamiltonians for optical interactions

    Science.gov (United States)

    Andrews, David L.; Jones, Garth A.; Salam, A.; Woolley, R. Guy

    2018-01-01

    The multipolar Hamiltonian of quantum electrodynamics is extensively employed in chemical and optical physics to treat rigorously the interaction of electromagnetic fields with matter. It is also widely used to evaluate intermolecular interactions. The multipolar version of the Hamiltonian is commonly obtained by carrying out a unitary transformation of the Coulomb gauge Hamiltonian that goes by the name of Power-Zienau-Woolley (PZW). Not only does the formulation provide excellent agreement with experiment, and versatility in its predictive ability, but also superior physical insight. Recently, the foundations and validity of the PZW Hamiltonian have been questioned, raising a concern over issues of gauge transformation and invariance, and whether observable quantities obtained from unitarily equivalent Hamiltonians are identical. Here, an in-depth analysis of theoretical foundations clarifies the issues and enables misconceptions to be identified. Claims of non-physicality are refuted: the PZW transformation and ensuing Hamiltonian are shown to rest on solid physical principles and secure theoretical ground.

  3. Polaron-mediated surface reconstruction in the reduced Rutile TiO2 (110) surface

    Science.gov (United States)

    Reticcioli, Michele; Setvin, Martin; Hao, Xianfeng; Diebold, Ulrike; Franchini, Cesare

    The role of polarons is of key importance for the understanding of the fundamental properties and functionalities of TiO2. We use density functional theory with an on-site Coulomb interaction and molecular dynamics to study the formation and dynamics of small polarons in the reduced rutile (110) surface. We show that excess electrons donated by oxygen-vacancies (VO) form mobile small polarons that hop easily in subsurface and surface Ti-sites. The polaron formation becomes more favorable by increasing the VO concentration level (up to 20%) due to the progressively lower energy cost needed to distort the lattice. However, at higher VO concentration the shortening of the averaged polaron-polaron distance leads to an increased Coulomb repulsion among the trapped charges at the Ti-sites, which weakens this trend. This instability is overtaken by means of a structural 1 × 2 surface reconstruction, characterized by a distinctively more favorable polaron distribution. The calculations are validated by a direct comparison with experimental AFM and STM data. Our study identifies a fundamentally novel mechanism to drive surface reconstructions and resolves a long standing issue on the origin of the reconstruction in rutile (110) surface.

  4. Generalized oscillator representations for Calogero Hamiltonians

    International Nuclear Information System (INIS)

    Tyutin, I V; Voronov, B L

    2013-01-01

    This paper is a natural continuation of the previous paper (Gitman et al 2011 J. Phys. A: Math. Theor. 44 425204), where oscillator representations for nonnegative Calogero Hamiltonians with coupling constant α ⩾ − 1/4 were constructed. In this paper, we present generalized oscillator representations for all Calogero Hamiltonians with α ⩾ − 1/4. These representations are generally highly nonunique, but there exists an optimum representation for each Hamiltonian. (comment)

  5. The iteration formula of the Maslov-type index theory with applications to nonlinear Hamiltonian systems

    International Nuclear Information System (INIS)

    Di Dong; Yiming Long.

    1994-10-01

    In this paper, the iteration formula of the Maslov-type index theory for linear Hamiltonian systems with continuous periodic and symmetric coefficients is established. This formula yields a new method to determine the minimality of the period for solutions of nonlinear autonomous Hamiltonian systems via their Maslov-type indices. Applications of this formula give new results on the existence of periodic solutions with prescribed minimal period for such systems. (author). 40 refs

  6. Hamiltonian formulation of reduced magnetohydrodynamics

    International Nuclear Information System (INIS)

    Morrison, P.J.; Hazeltine, R.D.

    1983-07-01

    Reduced magnetohydrodynamics (RMHD) has become a principal tool for understanding nonlinear processes, including disruptions, in tokamak plasmas. Although analytical studies of RMHD turbulence have been useful, the model's impressive ability to simulate tokamak fluid behavior has been revealed primarily by numerical solution. The present work describes a new analytical approach, not restricted to turbulent regimes, based on Hamiltonian field theory. It is shown that the nonlinear (ideal) RMHD system, in both its high-beta and low-beta versions, can be expressed in Hanmiltonian form. Thus a Poisson bracket, [ , ], is constructed such that each RMHD field quantitity, xi/sub i/, evolves according to xi/sub i/ = [xi/sub i/,H], where H is the total field energy. The new formulation makes RMHD accessible to the methodology of Hamiltonian mechanics; it has lead, in particular, to the recognition of new RMHD invariants and even exact, nonlinear RMHD solutions. A canonical version of the Poisson bracket, which requires the introduction of additional fields, leads to a nonlinear variational principle for time-dependent RMHD

  7. General technique to produce isochronous Hamiltonians

    International Nuclear Information System (INIS)

    Calogero, F; Leyvraz, F

    2007-01-01

    We introduce a new technique-characterized by an arbitrary positive constant Ω, with which we associate the period T = 2π/Ω-to 'Ω-modify' a Hamiltonian so that the new Hamiltonian thereby obtained is entirely isochronous, namely it yields motions all of which (except possibly for a lower dimensional set of singular motions) are periodic with the same fixed period T in all their degrees of freedom. This technique transforms real autonomous Hamiltonians into Ω-modified Hamiltonians which are also real and autonomous, and it is widely applicable, for instance, to the most general many-body problem characterized by Newtonian equations of motion ('acceleration equal force') provided it is translation invariant. The Ω-modified Hamiltonians are of course not translation invariant, but for Ω = 0 they reduce (up to marginal changes) to the unmodified Hamiltonians they were obtained from. Hence, when this technique is applied to translation-invariant Hamiltonians yielding, in their center-of-mass systems, chaotic motions with a natural time scale much smaller than T, the corresponding Ω-modified Hamiltonians shall display a chaotic behavior for quite some time before the isochronous character of the motions takes over. We moreover show that the quantized versions of these Ω-modified Hamiltonians feature equispaced spectra

  8. Collective Hamiltonians for dipole giant resonances

    International Nuclear Information System (INIS)

    Weiss, L.I.

    1991-07-01

    The collective hamiltonian for the Giant Dipole resonance (GDR), in the Goldhaber-Teller-Model, is analytically constructed using the semiclassical and generator coordinates method. Initially a conveniently parametrized set of many body wave functions and a microscopic hamiltonian, the Skyrme hamiltonian - are used. These collective Hamiltonians are applied to the investigation of the GDR, in He 4 , O 16 and Ca 40 nuclei. Also the energies and spectra of the GDR are obtained in these nuclei. The two sets of results are compared, and the zero point energy effects analysed. (author)

  9. Canonical transformations and hamiltonian path integrals

    International Nuclear Information System (INIS)

    Prokhorov, L.V.

    1982-01-01

    Behaviour of the Hamiltonian path integrals under canonical transformations produced by a generator, is investigated. An exact form is determined for the kernel of the unitary operator realizing the corresponding quantum transformation. Equivalence rules are found (the Hamiltonian formalism, one-dimensional case) enabling one to exclude non-standard terms from the action. It is shown that the Hamiltonian path integral changes its form under cononical transformations: in the transformed expression besides the classical Hamiltonian function there appear some non-classical terms

  10. Identity of the SU(3) model phenomenological hamiltonian and the hamiltonian of nonaxial rotator

    International Nuclear Information System (INIS)

    Filippov, G.F.; Avramenko, V.I.; Sokolov, A.M.

    1984-01-01

    Interpretation of nonspheric atomic nuclei spectra on the basis of phenomenological hamiltonians of SU(3) model showed satisfactory agreement of simulation calculations with experimental data. Meanwhile physical sense of phenomenological hamiltonians was not yet discussed. It is shown that phenomenological hamiltonians of SU(3) model are reduced to hamiltonian of nonaxial rotator but with additional items of the third and fourth powers angular momentum operator of rotator

  11. Polarons induced electronic transport, dielectric relaxation and magnetodielectric coupling in spin frustrated Ba{sub 2}FeWO{sub 6}

    Energy Technology Data Exchange (ETDEWEB)

    Pezhumkattil Palakkal, Jasnamol [Academy of Scientific and Innovative Research (AcSIR), CSIR—National Institute for Interdisciplinary Science and Technology (CSIR-NIIST) Campus, Trivandrum 695 019 (India); Materials Science and Technology Division, National Institute for Interdisciplinary Science and Technology, CSIR, Trivandrum 695 019 (India); Lekshmi, P. Neenu; Thomas, Senoy [Materials Science and Technology Division, National Institute for Interdisciplinary Science and Technology, CSIR, Trivandrum 695 019 (India); Valant, Matjaz [Materials Research Laboratory, University of Nova Gorica, Nova Gorica 5000 (Slovenia); Suresh, K.G. [Department of Physics, Indian Institute of Technology Bombay, Mumbai 400 076 (India); Varma, Manoj Raama, E-mail: manoj@niist.res.in [Academy of Scientific and Innovative Research (AcSIR), CSIR—National Institute for Interdisciplinary Science and Technology (CSIR-NIIST) Campus, Trivandrum 695 019 (India); Materials Science and Technology Division, National Institute for Interdisciplinary Science and Technology, CSIR, Trivandrum 695 019 (India)

    2016-04-15

    Highlights: • Ordered double perovskite Ba{sub 2}FeWO{sub 6} synthesized in reducing atmosphere possess a tetragonal I4/m crystal structure with mixed valent Fe/W cations. • Ba{sub 2}FeWO{sub 6} has an antiferromagnetic structure with T{sub N} at 19 K. • Insulating Ba{sub 2}FeWO{sub 6} shows different conducting mechanisms at different temperature regions and dielectric relaxation. • The polarons invoked by the mixed valence state of cations and their disordered arrangements are solely responsible for the various physical phenomena observed in Ba{sub 2}FeWO{sub 6}. - Abstract: Mixed valent double perovskite Ba{sub 2}FeWO{sub 6}, with tetragonal crystal structure, synthesized in a highly controlled reducing atmosphere, shows antiferromagnetic transition at T{sub N} = 19 K. A cluster glass-like transition is observed around 30 K arising from the competing interactions between inhomogeneous magnetic states. The structural distortion leads to the formation of polarons that are not contributing to DC conduction below charge ordering temperature, T{sub CO} = 279 K. Above T{sub CO}, small polarons will start to hop by exploiting thermal energy and participate in the conduction mechanism. The polarons are also responsible for the dielectric relaxor behavior, in which the dielectric relaxation time follows non-linearity in temperature as proposed by Fulcher. The material also exhibits a small room temperature magnetoresistance of 1.7% at 90 kOe. An intrinsic magnetodielectric coupling of ∼4% near room temperature and at lower temperatures, as well as an extrinsic magnetodielectric coupling change from +4% to −6% at around 210 K are reported.

  12. Hamiltonian closures in fluid models for plasmas

    Science.gov (United States)

    Tassi, Emanuele

    2017-11-01

    This article reviews recent activity on the Hamiltonian formulation of fluid models for plasmas in the non-dissipative limit, with emphasis on the relations between the fluid closures adopted for the different models and the Hamiltonian structures. The review focuses on results obtained during the last decade, but a few classical results are also described, in order to illustrate connections with the most recent developments. With the hope of making the review accessible not only to specialists in the field, an introduction to the mathematical tools applied in the Hamiltonian formalism for continuum models is provided. Subsequently, we review the Hamiltonian formulation of models based on the magnetohydrodynamics description, including those based on the adiabatic and double adiabatic closure. It is shown how Dirac's theory of constrained Hamiltonian systems can be applied to impose the incompressibility closure on a magnetohydrodynamic model and how an extended version of barotropic magnetohydrodynamics, accounting for two-fluid effects, is amenable to a Hamiltonian formulation. Hamiltonian reduced fluid models, valid in the presence of a strong magnetic field, are also reviewed. In particular, reduced magnetohydrodynamics and models assuming cold ions and different closures for the electron fluid are discussed. Hamiltonian models relaxing the cold-ion assumption are then introduced. These include models where finite Larmor radius effects are added by means of the gyromap technique, and gyrofluid models. Numerical simulations of Hamiltonian reduced fluid models investigating the phenomenon of magnetic reconnection are illustrated. The last part of the review concerns recent results based on the derivation of closures preserving a Hamiltonian structure, based on the Hamiltonian structure of parent kinetic models. Identification of such closures for fluid models derived from kinetic systems based on the Vlasov and drift-kinetic equations are presented, and

  13. A polaronic model of superconductivity in doped fulleride systems

    International Nuclear Information System (INIS)

    Tiwari, S.C.

    2007-01-01

    Full text: A polaronic model of superconductivity in doped fulleride systems is presented. The normal and anomalous one-particle Green's functions are derived for a system with strong electron phonon coupling. The study of collapse of the electron band and the phonon vacuum is presented within the mean-field approximation. Self consistent equation for the superconducting order parameter is derived using Green's function technique and following Lang and Firsov transformations. Expressions for specific heat, density of states, free energy and critical field based on this model have been derived. The theory is applied to explain the experimental results in the systems K 3 C 60 and Rb 3 C 6 O. These results are in good agreement with the available experimental data. (authors)

  14. Study of spin-polaron formation in 1D systems

    Energy Technology Data Exchange (ETDEWEB)

    Arredondo, Y.; Navarro, O. [Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, Apartado Postal 70-360, 04510 México D.F. (Mexico); Vallejo, E. [Facultad de Ingeniería Mecánica y Eléctrica, Universidad Autónoma de Coahuila, Carretera Torreón-Matamoros Km. 7.5 Ciudad Universitaria, 27276 Torreón, Coahuila (Mexico)

    2014-05-15

    We study numerically the formation of spin-polarons in low-dimensional systems. We consider a ferromagnetic Kondo lattice model with Hund coupling J{sub H} and localized spins interacting antiferromagnetically with coupling constant J. We investigate the ground state phase diagram as a function of the exchange couplings J{sub H} and J and as a function of the band filling, since it has been observed that doping either on the ferromagnetic or antiferromagnetic regime lead to formation of magnetic domains [1]. We explore the quasi-particle formation and phase separation using the density-matrix renormalization group method, which is a highly efficient method to investigate quasi-one-dimensional strongly correlated systems.

  15. Study of spin-polaron formation in 1D systems

    International Nuclear Information System (INIS)

    Arredondo, Y.; Navarro, O.; Vallejo, E.

    2014-01-01

    We study numerically the formation of spin-polarons in low-dimensional systems. We consider a ferromagnetic Kondo lattice model with Hund coupling J H and localized spins interacting antiferromagnetically with coupling constant J. We investigate the ground state phase diagram as a function of the exchange couplings J H and J and as a function of the band filling, since it has been observed that doping either on the ferromagnetic or antiferromagnetic regime lead to formation of magnetic domains [1]. We explore the quasi-particle formation and phase separation using the density-matrix renormalization group method, which is a highly efficient method to investigate quasi-one-dimensional strongly correlated systems

  16. Proton impurity in the neutron matter: a nuclear polaron problem

    Energy Technology Data Exchange (ETDEWEB)

    Kutschera, M [Institute of Nuclear Physics, Cracow (Poland); Wojcik, W [Politechnika Krakowska, Cracow (Poland)

    1992-10-01

    We study interactions of a proton impurity with density oscillations of the neutron matter in a Debye approximation. The proton-phonon coupling is of the deformation-potential type at long wavelengths. It is weak at low density and increases with the neutron matter density. We calculate the proton`s effective mass perturbatively for a weak coupling, and use a canonical transformation technique for stronger couplings. The proton`s effective mass grows significantly with density, and at higher densities the proton impurity can be localized. This behaviour is similar to that of the polaron in solids. We obtain properties of the localized proton in the strong coupling regime from variational calculations, treating the neutron in the Thomas-Fermi approximation. (author). 14 refs, 8 figs.

  17. Hamiltonian analysis of Plebanski theory

    International Nuclear Information System (INIS)

    Buffenoir, E; Henneaux, M; Noui, K; Roche, Ph

    2004-01-01

    We study the Hamiltonian formulation of Plebanski theory in both the Euclidean and Lorentzian cases. A careful analysis of the constraints shows that the system is non-regular, i.e., the rank of the Dirac matrix is non-constant on the non-reduced phase space. We identify the gravitational and topological sectors which are regular subspaces of the non-reduced phase space. The theory can be restricted to the regular subspace which contains the gravitational sector. We explicitly identify first- and second-class constraints in this case. We compute the determinant of the Dirac matrix and the natural measure for the path integral of the Plebanski theory (restricted to the gravitational sector). This measure is the analogue of the Leutwyler-Fradkin-Vilkovisky measure of quantum gravity

  18. Metastable states in parametrically excited multimode Hamiltonian systems

    CERN Document Server

    Kirr, E

    2003-01-01

    Consider a linear autonomous Hamiltonian system with time periodic bound state solutions. In this paper we study their dynamics under time almost periodic perturbations which are small, localized and Hamiltonian. The analysis proceeds through a reduction of the original infinite dimensional dynamical system to the dynamics of two coupled subsystems: a dominant m-dimensional system of ordinary differential equations (normal form), governing the projections onto the bound states and an infinite dimensional dispersive wave equation. The present work generalizes previous work of the authors, where the case of a single bound state is considered. Here, the interaction picture is considerably more complicated and requires deeper analysis, due to a multiplicity of bound states and the very general nature of the perturbation's time dependence. Parametric forcing induces coupling of bound states to continuum radiation modes, bound states directly to bound states, as well as coupling among bound states, which is mediate...

  19. From Hamiltonian chaos to complex systems a nonlinear physics approach

    CERN Document Server

    Leonetti, Marc

    2013-01-01

    From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach collects contributions on recent developments in non-linear dynamics and statistical physics with an emphasis on complex systems. This book provides a wide range of state-of-the-art research in these fields. The unifying aspect of this book is a demonstration of how similar tools coming from dynamical systems, nonlinear physics, and statistical dynamics can lead to a large panorama of  research in various fields of physics and beyond, most notably with the perspective of application in complex systems. This book also: Illustrates the broad research influence of tools coming from dynamical systems, nonlinear physics, and statistical dynamics Adopts a pedagogic approach to facilitate understanding by non-specialists and students Presents applications in complex systems Includes 150 illustrations From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach is an ideal book for graduate students and researchers working in applied...

  20. Quantum Statistical Operator and Classically Chaotic Hamiltonian ...

    African Journals Online (AJOL)

    Quantum Statistical Operator and Classically Chaotic Hamiltonian System. ... Journal of the Nigerian Association of Mathematical Physics ... In a Hamiltonian system von Neumann Statistical Operator is used to tease out the quantum consequence of (classical) chaos engendered by the nonlinear coupling of system to its ...

  1. A Direct Method of Hamiltonian Structure

    International Nuclear Information System (INIS)

    Li Qi; Chen Dengyuan; Su Shuhua

    2011-01-01

    A direct method of constructing the Hamiltonian structure of the soliton hierarchy with self-consistent sources is proposed through computing the functional derivative under some constraints. The Hamiltonian functional is related with the conservation densities of the corresponding hierarchy. Three examples and their two reductions are given. (general)

  2. Port Hamiltonian modeling of Power Networks

    NARCIS (Netherlands)

    van Schaik, F.; van der Schaft, Abraham; Scherpen, Jacquelien M.A.; Zonetti, Daniele; Ortega, R

    2012-01-01

    In this talk a full nonlinear model for the power network in port–Hamiltonian framework is derived to study its stability properties. For this we use the modularity approach i.e., we first derive the models of individual components in power network as port-Hamiltonian systems and then we combine all

  3. Hamiltonian representation of divergence-free fields

    International Nuclear Information System (INIS)

    Boozer, A.H.

    1984-11-01

    Globally divergence-free fields, such as the magnetic field and the vorticity, can be described by a two degree of freedom Hamiltonian. The Hamiltonian function provides a complete topological description of the field lines. The formulation also separates the dissipative and inertial time scale evolution of the magnetic and the vorticity fields

  4. Momentum and hamiltonian in complex action theory

    DEFF Research Database (Denmark)

    Nagao, Keiichi; Nielsen, Holger Frits Bech

    2012-01-01

    $-parametrized wave function, which is a solution to an eigenvalue problem of a momentum operator $\\hat{p}$, in FPI with a starting Lagrangian. Solving the eigenvalue problem, we derive the momentum and Hamiltonian. Oppositely, starting from the Hamiltonian we derive the Lagrangian in FPI, and we are led...

  5. A parcel formulation for Hamiltonian layer models

    NARCIS (Netherlands)

    Bokhove, Onno; Oliver, M.

    Starting from the three-dimensional hydrostatic primitive equations, we derive Hamiltonian N-layer models with isentropic tropospheric and isentropic or isothermal stratospheric layers. Our construction employs a new parcel Hamiltonian formulation which describes the fluid as a continuum of

  6. On Distributed Port-Hamiltonian Process Systems

    NARCIS (Netherlands)

    Lopezlena, Ricardo; Scherpen, Jacquelien M.A.

    2004-01-01

    In this paper we use the term distributed port-Hamiltonian Process Systems (DPHPS) to refer to the result of merging the theory of distributed Port-Hamiltonian systems (DPHS) with the theory of process systems (PS). Such concept is useful for combining the systematic interconnection of PHS with the

  7. Relativistic magnetohydrodynamics as a Hamiltonian system

    International Nuclear Information System (INIS)

    Holm, D.D.; Kupershmidt, A.

    1985-01-01

    The equations of ideal relativistic magnetohydrodynamics in the laboratory frame form a noncanonical Hamiltonian system with the same Poisson bracket as for the nonrelativistic system, but with dynamical variables and Hamiltonian obtained via a regular deformation of their nonrelativistic counterparts [fr

  8. Hamiltonian Cycles on Random Eulerian Triangulations

    DEFF Research Database (Denmark)

    Guitter, E.; Kristjansen, C.; Nielsen, Jakob Langgaard

    1998-01-01

    . Considering the case n -> 0, this implies that the system of random Eulerian triangulations equipped with Hamiltonian cycles describes a c=-1 matter field coupled to 2D quantum gravity as opposed to the system of usual random triangulations equipped with Hamiltonian cycles which has c=-2. Hence, in this case...

  9. Almost periodic Hamiltonians: an algebraic approach

    International Nuclear Information System (INIS)

    Bellissard, J.

    1981-07-01

    We develop, by analogy with the study of periodic potential, an algebraic theory for almost periodic hamiltonians, leading to a generalized Bloch theorem. This gives rise to results concerning the spectral measures of these operators in terms of those of the corresponding Bloch hamiltonians

  10. Nested Sampling with Constrained Hamiltonian Monte Carlo

    OpenAIRE

    Betancourt, M. J.

    2010-01-01

    Nested sampling is a powerful approach to Bayesian inference ultimately limited by the computationally demanding task of sampling from a heavily constrained probability distribution. An effective algorithm in its own right, Hamiltonian Monte Carlo is readily adapted to efficiently sample from any smooth, constrained distribution. Utilizing this constrained Hamiltonian Monte Carlo, I introduce a general implementation of the nested sampling algorithm.

  11. Polaron self-localization in white-light emitting hybrid perovskites

    KAUST Repository

    Cortecchia, Daniele; Yin, Jun; Bruno, Annalisa; Lo, Shu Zee Alencious; Gurzadyan, Gagik G.; Mhaisalkar, Subodh; Bredas, Jean-Luc; Soci, Cesare

    2017-01-01

    within the inorganic perovskite framework. Due to strong Coulombic interactions, these species retain their original excitonic character and form self-trapped polaron-excitons acting as radiative colour centres. These findings are expected to be relevant

  12. Excitonic and Polaronic Properties of 2D Hybrid Organic–Inorganic Perovskites

    KAUST Repository

    Yin, Jun

    2017-01-20

    We theoretically characterize the unusual white-light emission properties of two-dimensional (2D) hybrid organic inorganic perovskites with an APbX(4) structure (where A is a bidentate organic cation and X = Cl, Br). In addition to band structure calculations including corrections due to spin orbit couplings and electron hole interactions, a computationally intensive molecular cluster approach is exploited to describe the excitonic and polaronic properties of these 2D perovskites at the atomistic level. Upon adding or removing an electron from the neutral systems, we find that strongly localized small polarons form in the 2D clusters. The polaron charge density is distributed over just lattice sites, which is consistent with the calculated large polaron binding energies, on the order of similar to 0.4-1.2 eV.

  13. Excitonic and Polaronic Properties of 2D Hybrid Organic–Inorganic Perovskites

    KAUST Repository

    Yin, Jun; Li, Hong; Cortecchia, Daniele; Soci, Cesare; Bredas, Jean-Luc

    2017-01-01

    calculations including corrections due to spin orbit couplings and electron hole interactions, a computationally intensive molecular cluster approach is exploited to describe the excitonic and polaronic properties of these 2D perovskites at the atomistic level

  14. A possible method for non-Hermitian and Non-PT-symmetric Hamiltonian systems.

    Directory of Open Access Journals (Sweden)

    Jun-Qing Li

    Full Text Available A possible method to investigate non-Hermitian Hamiltonians is suggested through finding a Hermitian operator η+ and defining the annihilation and creation operators to be η+ -pseudo-Hermitian adjoint to each other. The operator η+ represents the η+ -pseudo-Hermiticity of Hamiltonians. As an example, a non-Hermitian and non-PT-symmetric Hamiltonian with imaginary linear coordinate and linear momentum terms is constructed and analyzed in detail. The operator η+ is found, based on which, a real spectrum and a positive-definite inner product, together with the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution, are obtained for the non-Hermitian and non-PT-symmetric Hamiltonian. Moreover, this Hamiltonian turns out to be coupled when it is extended to the canonical noncommutative space with noncommutative spatial coordinate operators and noncommutative momentum operators as well. Our method is applicable to the coupled Hamiltonian. Then the first and second order noncommutative corrections of energy levels are calculated, and in particular the reality of energy spectra, the positive-definiteness of inner products, and the related properties (the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution are found not to be altered by the noncommutativity.

  15. Compact invariant sets of the Bianchi VIII and Bianchi IX Hamiltonian systems

    International Nuclear Information System (INIS)

    Starkov, Konstantin E.

    2011-01-01

    In this Letter we prove that all compact invariant sets of the Bianchi VIII Hamiltonian system are contained in the set described by several simple linear equalities and inequalities. Moreover, we describe invariant domains in which the phase flow of this system has no recurrence property and show that there are no periodic orbits and neither homoclinic, nor heteroclinic orbits contained in the zero level set of its Hamiltonian. Similar results are obtained for the Bianchi IX Hamiltonian system. -- Highlights: → Zero level set of Hamiltonian of Bianchi VIII/IX systems contains no periodic orbits. → Similar conditions for homoclinic/heteroclinic orbits are given. → General nonexistence conditions of compact invariant sets are got.

  16. Compact invariant sets of the Bianchi VIII and Bianchi IX Hamiltonian systems

    Energy Technology Data Exchange (ETDEWEB)

    Starkov, Konstantin E., E-mail: konst@citedi.mx [CITEDI-IPN, Av. del Parque 1310, Mesa de Otay, Tijuana, BC (Mexico)

    2011-08-22

    In this Letter we prove that all compact invariant sets of the Bianchi VIII Hamiltonian system are contained in the set described by several simple linear equalities and inequalities. Moreover, we describe invariant domains in which the phase flow of this system has no recurrence property and show that there are no periodic orbits and neither homoclinic, nor heteroclinic orbits contained in the zero level set of its Hamiltonian. Similar results are obtained for the Bianchi IX Hamiltonian system. -- Highlights: → Zero level set of Hamiltonian of Bianchi VIII/IX systems contains no periodic orbits. → Similar conditions for homoclinic/heteroclinic orbits are given. → General nonexistence conditions of compact invariant sets are got.

  17. Nonstandard conserved Hamiltonian structures in dissipative/damped systems: Nonlinear generalizations of damped harmonic oscillator

    International Nuclear Information System (INIS)

    Pradeep, R. Gladwin; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.

    2009-01-01

    In this paper we point out the existence of a remarkable nonlocal transformation between the damped harmonic oscillator and a modified Emden-type nonlinear oscillator equation with linear forcing, xe+αxx+βx 3 +γx=0, which preserves the form of the time independent integral, conservative Hamiltonian, and the equation of motion. Generalizing this transformation we prove the existence of nonstandard conservative Hamiltonian structure for a general class of damped nonlinear oscillators including Lienard-type systems. Further, using the above Hamiltonian structure for a specific example, namely, the generalized modified Emden equation xe+αx q x+βx 2q+1 =0, where α, β, and q are arbitrary parameters, the general solution is obtained through appropriate canonical transformations. We also present the conservative Hamiltonian structure of the damped Mathews-Lakshmanan oscillator equation. The associated Lagrangian description for all the above systems is also briefly discussed.

  18. First-principles supercell calculations of small polarons with proper account for long-range polarization effects

    Science.gov (United States)

    Kokott, Sebastian; Levchenko, Sergey V.; Rinke, Patrick; Scheffler, Matthias

    2018-03-01

    We present a density functional theory (DFT) based supercell approach for modeling small polarons with proper account for the long-range elastic response of the material. Our analysis of the supercell dependence of the polaron properties (e.g., atomic structure, binding energy, and the polaron level) reveals long-range electrostatic effects and the electron–phonon (el–ph) interaction as the two main contributors. We develop a correction scheme for DFT polaron calculations that significantly reduces the dependence of polaron properties on the DFT exchange-correlation functional and the size of the supercell in the limit of strong el–ph coupling. Using our correction approach, we present accurate all-electron full-potential DFT results for small polarons in rocksalt MgO and rutile TiO2.

  19. Indirect quantum tomography of quadratic Hamiltonians

    Energy Technology Data Exchange (ETDEWEB)

    Burgarth, Daniel [Institute for Mathematical Sciences, Imperial College London, London SW7 2PG (United Kingdom); Maruyama, Koji; Nori, Franco, E-mail: daniel@burgarth.de, E-mail: kmaruyama@riken.jp [Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198 (Japan)

    2011-01-15

    A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few resources. We found that almost all the properties of the Hamiltonian are determined by its surface and that these properties can be measured even if the system can only be initialized to a mixed state. Therefore, our method can be applied to various physical models, with important examples including coupled nano-mechanical oscillators, hopping fermions in optical lattices and transverse Ising chains.

  20. Incomplete Dirac reduction of constrained Hamiltonian systems

    Energy Technology Data Exchange (ETDEWEB)

    Chandre, C., E-mail: chandre@cpt.univ-mrs.fr

    2015-10-15

    First-class constraints constitute a potential obstacle to the computation of a Poisson bracket in Dirac’s theory of constrained Hamiltonian systems. Using the pseudoinverse instead of the inverse of the matrix defined by the Poisson brackets between the constraints, we show that a Dirac–Poisson bracket can be constructed, even if it corresponds to an incomplete reduction of the original Hamiltonian system. The uniqueness of Dirac brackets is discussed. The relevance of this procedure for infinite dimensional Hamiltonian systems is exemplified.

  1. Quantum entangling power of adiabatically connected Hamiltonians

    International Nuclear Information System (INIS)

    Hamma, Alioscia; Zanardi, Paolo

    2004-01-01

    The space of quantum Hamiltonians has a natural partition in classes of operators that can be adiabatically deformed into each other. We consider parametric families of Hamiltonians acting on a bipartite quantum state space. When the different Hamiltonians in the family fall in the same adiabatic class, one can manipulate entanglement by moving through energy eigenstates corresponding to different values of the control parameters. We introduce an associated notion of adiabatic entangling power. This novel measure is analyzed for general dxd quantum systems, and specific two-qubit examples are studied

  2. Quantum Hamiltonian Physics with Supercomputers

    International Nuclear Information System (INIS)

    Vary, James P.

    2014-01-01

    The vision of solving the nuclear many-body problem in a Hamiltonian framework with fundamental interactions tied to QCD via Chiral Perturbation Theory is gaining support. The goals are to preserve the predictive power of the underlying theory, to test fundamental symmetries with the nucleus as laboratory and to develop new understandings of the full range of complex quantum phenomena. Advances in theoretical frameworks (renormalization and many-body methods) as well as in computational resources (new algorithms and leadership-class parallel computers) signal a new generation of theory and simulations that will yield profound insights into the origins of nuclear shell structure, collective phenomena and complex reaction dynamics. Fundamental discovery opportunities also exist in such areas as physics beyond the Standard Model of Elementary Particles, the transition between hadronic and quark–gluon dominated dynamics in nuclei and signals that characterize dark matter. I will review some recent achievements and present ambitious consensus plans along with their challenges for a coming decade of research that will build new links between theory, simulations and experiment. Opportunities for graduate students to embark upon careers in the fast developing field of supercomputer simulations is also discussed

  3. Quantum Hamiltonian Physics with Supercomputers

    Energy Technology Data Exchange (ETDEWEB)

    Vary, James P.

    2014-06-15

    The vision of solving the nuclear many-body problem in a Hamiltonian framework with fundamental interactions tied to QCD via Chiral Perturbation Theory is gaining support. The goals are to preserve the predictive power of the underlying theory, to test fundamental symmetries with the nucleus as laboratory and to develop new understandings of the full range of complex quantum phenomena. Advances in theoretical frameworks (renormalization and many-body methods) as well as in computational resources (new algorithms and leadership-class parallel computers) signal a new generation of theory and simulations that will yield profound insights into the origins of nuclear shell structure, collective phenomena and complex reaction dynamics. Fundamental discovery opportunities also exist in such areas as physics beyond the Standard Model of Elementary Particles, the transition between hadronic and quark–gluon dominated dynamics in nuclei and signals that characterize dark matter. I will review some recent achievements and present ambitious consensus plans along with their challenges for a coming decade of research that will build new links between theory, simulations and experiment. Opportunities for graduate students to embark upon careers in the fast developing field of supercomputer simulations is also discussed.

  4. Small polaron conduction in lead modified lanthanum ferrite ceramics

    Energy Technology Data Exchange (ETDEWEB)

    Bhargav, K.K.; Ram, S.; Majumder, S.B., E-mail: subhasish@matsc.iitkgp.ernet.in

    2015-07-25

    Highlights: • La{sub 0.8}Pb{sub 0.2}FeO{sub 3} (ε{sub r} ∼ 30,000) shows higher dielectric constant than LaFeO{sub 3} (∼14,000). • Lower A-site dopant content, the dielectric maxima shift to higher temperature. • The frequency dependence of ε{sub r} and tan δ vs. temperature exhibit CDC like behavior. • R{sub g} and R{sub gb} of Pb modified LaFeO{sub 3} follow small polaron hopping conduction model. - Abstract: In the present work we have illustrated the physics of the electrical characteristics of nanocrystalline La{sub 1−x}Pb{sub x}FeO{sub 3,} (0 ⩽ x ⩽ 0.2) powder prepared using auto-combustion synthesis. The effect of lead doping on the dielectric, impedance and ac conductivity characteristics of lanthanum ferrite has systematically been investigated. The synthesized powders were phase pure and crystallized into centro-symmetric Pnma space group. As compared to pure LaFeO{sub 3} ceramics (dielectric constant ∼ 14,000), the dielectric constant is grossly increased (∼30,000) in Pb doped LaFeO{sub 3}. The temperature dependence of dielectric constant of 10.0 at.% Pb doped LaFeO{sub 3} exhibits dielectric maxima similar to that observed in ferroelectric ceramics with non-centrosymmetric point group. For La{sub 0.8}Pb{sub 0.2}FeO{sub 3} ceramics, the frequency dependence of the dielectric constant and loss tangent at various temperatures (300–450 K) exhibit typical colossal dielectric constant (CDC) like behavior. From the impedance spectroscopy we have estimated the grain and grain boundary resistance and capacitance of Pb doped LaFeO{sub 3} that follow a small polaron hopping conduction model. Long range movement of the charge carriers govern the CDC behavior.

  5. Jacobi fields of completely integrable Hamiltonian systems

    International Nuclear Information System (INIS)

    Giachetta, G.; Mangiarotti, L.; Sardanashvily, G.

    2003-01-01

    We show that Jacobi fields of a completely integrable Hamiltonian system of m degrees of freedom make up an extended completely integrable system of 2m degrees of freedom, where m additional first integrals characterize a relative motion

  6. Quantum Hamiltonian reduction in superspace formalism

    International Nuclear Information System (INIS)

    Madsen, J.O.; Ragoucy, E.

    1994-02-01

    Recently the quantum Hamiltonian reduction was done in the case of general sl(2) embeddings into Lie algebras and superalgebras. The results are extended to the quantum Hamiltonian reduction of N=1 affine Lie superalgebras in the superspace formalism. It is shown that if we choose a gauge for the supersymmetry, and consider only certain equivalence classes of fields, then our quantum Hamiltonian reduction reduces to quantum Hamiltonian reduction of non-supersymmetric Lie superalgebras. The super energy-momentum tensor is constructed explicitly as well as all generators of spin 1 (and 1/2); thus all generators in the superconformal, quasi-superconformal and Z 2 *Z 2 superconformal algebras are constructed. (authors). 21 refs

  7. Integrable Hamiltonian systems and spectral theory

    CERN Document Server

    Moser, J

    1981-01-01

    Classical integrable Hamiltonian systems and isospectral deformations ; geodesics on an ellipsoid and the mechanical system of C. Neumann ; the Schrödinger equation for almost periodic potentials ; finite band potentials ; limit cases, Bargmann potentials.

  8. Spectral properties of almost-periodic Hamiltonians

    International Nuclear Information System (INIS)

    Lima, R.

    1983-12-01

    We give a description of some spectral properties of almost-periodic hamiltonians. We put the stress on some particular points of the proofs of the existence of absolutely continuous or pure point spectrum [fr

  9. Air parcels and air particles: Hamiltonian dynamics

    NARCIS (Netherlands)

    Bokhove, Onno; Lynch, Peter

    We present a simple Hamiltonian formulation of the Euler equations for fluid flow in the Lagrangian framework. In contrast to the conventional formulation, which involves coupled partial differential equations, our "innovative'' mathematical formulation involves only ordinary differential equations

  10. Discrete Hamiltonian evolution and quantum gravity

    International Nuclear Information System (INIS)

    Husain, Viqar; Winkler, Oliver

    2004-01-01

    We study constrained Hamiltonian systems by utilizing general forms of time discretization. We show that for explicit discretizations, the requirement of preserving the canonical Poisson bracket under discrete evolution imposes strong conditions on both allowable discretizations and Hamiltonians. These conditions permit time discretizations for a limited class of Hamiltonians, which does not include homogeneous cosmological models. We also present two general classes of implicit discretizations which preserve Poisson brackets for any Hamiltonian. Both types of discretizations generically do not preserve first class constraint algebras. Using this observation, we show that time discretization provides a complicated time gauge fixing for quantum gravity models, which may be compared with the alternative procedure of gauge fixing before discretization

  11. Classical mechanics Hamiltonian and Lagrangian formalism

    CERN Document Server

    Deriglazov, Alexei

    2016-01-01

    This account of the fundamentals of Hamiltonian mechanics also covers related topics such as integral invariants and the Noether theorem. With just the elementary mathematical methods used for exposition, the book is suitable for novices as well as graduates.

  12. Hamiltonian cycle problem and Markov chains

    CERN Document Server

    Borkar, Vivek S; Filar, Jerzy A; Nguyen, Giang T

    2014-01-01

    This book summarizes a line of research that maps certain classical problems of discrete mathematics and operations research - such as the Hamiltonian cycle and the Travelling Salesman problems - into convex domains where continuum analysis can be carried out.

  13. Variable Delay in port-Hamiltonian Telemanipulation

    NARCIS (Netherlands)

    Secchi, C; Stramigioli, Stefano; Fantuzzi, C.

    2006-01-01

    In several applications involving bilateral telemanipulation, master and slave act at different power scales. In this paper a strategy for passively dealing with variable communication delay in scaled port-Hamiltonian based telemanipulation over packet switched networks is proposed.

  14. The pairing theory of polarons in real- and impulse spaces

    International Nuclear Information System (INIS)

    Dzhumanov, S.; Abboudy, S.; Baratov, A.A.

    1995-07-01

    A consistent pairing theory of carriers in real- and impulse spaces is developed. The pairing of different free (F), delocalized (D) and self-trapped (S) carriers in real-space, leading to the formation of various bipolaronic states are considered within the continuum model and adiabatic approximation taking into account the combined effect of the short- and long-range components of electron-lattice interaction with and without electron correlation. The formation possibility of D- and S-bipolarons as a function of ε ∞ /ε 0 are shown. The pairing scenarios of carriers in k-space leading to the formation of different bipolarons (including also Cooper pairs dynamic bipolarons) are considered within the generalized BCS-like model taking into account the combined phonon and polaron-bag mediated processes. It is shown that the pure BCS pairing picture is the particular case of the general BCS-like one. The possible relevance of the obtained results to high-T c superconductors is discussed in details in the framework of a novel two-stage Fermi-Bose-liquid scenarios of superconductivity which is caused by single particle and pair condensation of an attracting bipolarons. (author). 51 refs, 6 figs

  15. Effects of compositional defects on small polaron hopping in micas.

    Science.gov (United States)

    Rosso, Kevin M; Ilton, Eugene S

    2005-06-22

    Hartree-Fock calculations and electron transfer (ET) theory were used to model the effects of compositional defects on ET in the brucite-like octahedral sheet of mica. ET was modeled as an Fe(IIIII) valence interchange reaction across shared octahedral edges of the M2-M2 iron sublattice. The model entails the hopping of localized electrons and small polaron behavior. Hartree-Fock calculations indicate that substitution of F for structural OH bridges increases the reorganization energy lambda, decreases the electronic coupling matrix element V(AB), and thereby substantially decreases the hopping rate. The lambda increase arises from modification of the metal-ligand bond force constants, and the V(AB) decrease arises from reduction of superexchange interaction through anion bridges. Deprotonation of an OH bridge, consistent with a possible mechanism of maintaining charge neutrality during net oxidation, yields a net increase in the ET rate. Although substitution of Al or Mg for Fe in M1 sites distorts the structure of adjacent Fe-occupied M2 sites, the distortion has little net impact on ET rates through these M2 sites. Hence the main effect of Al or Mg substitution for Fe, should it occur in the M2 sublattice, is to block ET pathways. Collectively, these findings pave the way for larger-scale oxidation/reduction models to be constructed for realistic, compositionally diverse micas.

  16. Systems of conservation laws with third-order Hamiltonian structures

    Science.gov (United States)

    Ferapontov, Evgeny V.; Pavlov, Maxim V.; Vitolo, Raffaele F.

    2018-02-01

    We investigate n-component systems of conservation laws that possess third-order Hamiltonian structures of differential-geometric type. The classification of such systems is reduced to the projective classification of linear congruences of lines in P^{n+2} satisfying additional geometric constraints. Algebraically, the problem can be reformulated as follows: for a vector space W of dimension n+2 , classify n-tuples of skew-symmetric 2-forms A^{α } \\in Λ ^2(W) such that φ _{β γ }A^{β }\\wedge A^{γ }=0, for some non-degenerate symmetric φ.

  17. On local Hamiltonians and dissipative systems

    Energy Technology Data Exchange (ETDEWEB)

    Castagnino, M. [CONICET-Institutos de Fisica Rosario y de Astronomia y Fisica del Espacio Casilla de Correos 67, Sucursal 28, 1428, Buenos Aires (Argentina); Gadella, M. [Facultad de Ciencias Exactas, Ingenieria y Agrimensura UNR, Rosario (Argentina) and Departamento de Fisica Teorica, Facultad de Ciencias c. Real de Burgos, s.n., 47011 Valladolid (Spain)]. E-mail: manuelgadella@yahoo.com.ar; Lara, L.P. [Facultad de Ciencias Exactas, Ingenieria y Agrimensura UNR, Rosario (Argentina)

    2006-11-15

    We study a type of one-dimensional dynamical systems on the corresponding two-dimensional phase space. By using arguments related to the existence of integrating factors for Pfaff equations, we show that some one-dimensional non-Hamiltonian systems like dissipative systems, admit a Hamiltonian description by sectors on the phase plane. This picture is not uniquely defined and is coordinate dependent. A simple example is exhaustively discussed. The method, is not always applicable to systems with higher dimensions.

  18. Generalized Hubbard Hamiltonian: renormalization group approach

    International Nuclear Information System (INIS)

    Cannas, S.A.; Tamarit, F.A.; Tsallis, C.

    1991-01-01

    We study a generalized Hubbard Hamiltonian which is closed within the framework of a Quantum Real Space Renormalization Group, which replaces the d-dimensional hypercubic lattice by a diamond-like lattice. The phase diagram of the generalized Hubbard Hamiltonian is analyzed for the half-filled band case in d = 2 and d = 3. Some evidence for superconductivity is presented. (author). 44 refs., 12 figs., 2 tabs

  19. Polaron binding energy and effective mass in the GaAs film

    International Nuclear Information System (INIS)

    Wu Zhenhua; Yan Liangxing; Tian Qiang; Li Hua; Liu Bingcan

    2012-01-01

    The binding energy and effective mass of a polaron in a GaAs film deposited on the Al 0.3 Ga 0.7 As substrate are studied theoretically by using the fractional-dimensional space approach. Our calculations show that the polaron binding energy and mass shift decrease monotonously with increasing the film thickness. For the film thicknesses with L w ≤ 70Å and the substrate thicknesses with L b ≤ 200Å, the different values of the substrate thickness influence the polaron binding energy and mass shift in the GaAs film. The polaron binding energy and mass shift increase monotonously with increasing the substrate thickness. For the film thickness with L w ≥ 70Å or the substrate thicknesses with L b ≤ 200Å, the different values of the substrate thickness have no significant influence on the polaron binding energy and mass shift in the GaAs film deposited on the Al 0.3 Ga 0.7 As substrate.

  20. Observation of Spin Polarons in a Tunable Fermi Liquid of Ultracold Atoms

    Science.gov (United States)

    Zwierlein, Martin

    2009-05-01

    We have observed spin polarons, dressed spin down impurities in a spin up Fermi sea of ultracold atoms via tomographic RF spectroscopy. Feshbach resonances allow to freely tune the interactions between the two spin states involved. A single spin down atom immersed in a Fermi sea of spin up atoms can do one of two things: For strong attraction, it can form a molecule with exactly one spin up partner, but for weaker interaction it will spread its attraction and surround itself with a collection of majority atoms. This spin down atom dressed with a spin up cloud constitutes the spin- or Fermi polaron. We have observed a striking spectroscopic signature of this quasi-particle for various interaction strengths, a narrow peak in the spin down spectrum that emerges above a broad background. The spectra allow us to directly measure the polaron energy and the quasi-particle residue Z. The polarons are found to be only weakly interacting with each other, and can thus be identified with the quasi-particles of Landau's Fermi liquid theory. At a critical interaction strength, we observe a transition from spin one-half polarons to spin zero molecules. At this point the Fermi liquid undergoes a phase transition into a superfluid Bose liquid.

  1. Small polaron hopping conduction mechanism in LiFePO4 glass and crystal

    Science.gov (United States)

    Banday, Azeem; Murugavel, Sevi

    2017-01-01

    The optimization of a cathode material is the most important criterion of lithium ion battery technology, which decides the power density. In order to improve the rate capability, a cathode material must possess high electronic and ionic conductivities. Therefore, it is important to understand the charge transport mechanism in such an advanced cathode material in its intrinsic state before modifying it by various means. In this work, we report the thermal, structural, and electrical conductivity studies on lithium iron phosphate, LiFePO4, both in its polycrystalline (LFPC) and glassy (LFPG) counterpart states. The vibrational spectroscopic measurements reveal the characteristic vibrational modes, which are the intrinsic part of LFPC, whereas in LFPG, the phonon modes become broader and overlap with each other due to the lattice disorder. The electrical conductivity measurements reveal that LFPG exhibits a higher polaronic conductivity of 1.6 orders than the LFPC sample. The temperature dependent dc conductivity has been analyzed with the Mott model of polarons and reveals the origin of enhanced polaronic conductivity in LFPG. Based on the analysis, the enhanced polaronic conductivity in LFPG has been attributed to the combined effect of reduced hopping length, decreased activation energy, and enhanced polaron concentration.

  2. Influence of Coherent Tunneling and Incoherent Hopping on the Charge Transfer Mechanism in Linear Donor-Bridge-Acceptor Systems.

    Science.gov (United States)

    Li, Guangqi; Govind, Niranjan; Ratner, Mark A; Cramer, Christopher J; Gagliardi, Laura

    2015-12-17

    The mechanism of charge transfer has been observed to change from tunneling to hopping with increasing numbers of DNA base pairs in polynucleotides and with the length of molecular wires. The aim of this paper is to investigate this transition by examining the population dynamics using a tight-binding Hamiltonian with model parameters to describe a linear donor-bridge-acceptor (D-B-A) system. The model includes a primary vibration and an electron-vibration coupling at each site. A further coupling of the primary vibration with a secondary phonon bath allows the system to dissipate energy to the environment and reach a steady state. We apply the quantum master equation (QME) approach, based on second-order perturbation theory in a quantum dissipative system, to examine the dynamical processes involved in charge-transfer and follow the population transfer rate at the acceptor, ka, to shed light on the transition from tunneling to hopping. With a small tunneling parameter, V, the on-site population tends to localize and form polarons, and the hopping mechanism dominates the transfer process. With increasing V, the population tends to be delocalized and the tunneling mechanism dominates. The competition between incoherent hopping and coherent tunneling governs the mechanism of charge transfer. By varying V and the total number of sites, we also examine the onset of the transition from tunneling to hopping with increasing length.

  3. Giant Optical Polarization Rotation Induced by Spin-Orbit Coupling in Polarons

    Science.gov (United States)

    Casals, Blai; Cichelero, Rafael; García Fernández, Pablo; Junquera, Javier; Pesquera, David; Campoy-Quiles, Mariano; Infante, Ingrid C.; Sánchez, Florencio; Fontcuberta, Josep; Herranz, Gervasi

    2016-07-01

    We have uncovered a giant gyrotropic magneto-optical response for doped ferromagnetic manganite La2 /3Ca1 /3MnO3 around the near room-temperature paramagnetic-to-ferromagnetic transition. At odds with current wisdom, where this response is usually assumed to be fundamentally fixed by the electronic band structure, we point to the presence of small polarons as the driving force for this unexpected phenomenon. We explain the observed properties by the intricate interplay of mobility, Jahn-Teller effect, and spin-orbit coupling of small polarons. As magnetic polarons are ubiquitously inherent to many strongly correlated systems, our results provide an original, general pathway towards the generation of magnetic-responsive gigantic gyrotropic responses that may open novel avenues for magnetoelectric coupling beyond the conventional modulation of magnetization.

  4. Polaron effects on nonlinear optical rectification in asymmetrical Gaussian potential quantum wells with applied electric fields

    International Nuclear Information System (INIS)

    Wu, Jinghe; Guo, Kangxian; Liu, Guanghui

    2014-01-01

    Polaron effects on nonlinear optical rectification in asymmetrical Gaussian potential quantum wells are studied by the effective mass approximation and the perturbation theory. The numerical results show that nonlinear optical rectification coefficients are strongly dependent on the barrier hight V 0 of the Gaussian potential quantum wells, the range L of the confinement potential and the electric field F. Besides, the numerical results show that no matter how V 0 , L and F change, taking into consideration polaron effects, the optical rectification coefficients χ 0 (2) get greatly enhanced.

  5. Stability and Polaronic Motion of Self-Trapped Holes in Silver Halides

    DEFF Research Database (Denmark)

    Loftager, Simon; Garcia-Fernandez, P.; Aramburu, J. A.

    2016-01-01

    Polarons and their associated transport properties are a field of great current interest both in chemistry and physics. To further our understanding of these quasi-particles, we have carried out first-principles calculations of self-trapped holes (STHs) in the model compounds AgCl and AgBr, for w......Polarons and their associated transport properties are a field of great current interest both in chemistry and physics. To further our understanding of these quasi-particles, we have carried out first-principles calculations of self-trapped holes (STHs) in the model compounds AgCl and Ag...

  6. Quantum Monte Carlo simulations of the Fermi-polaron problem and bosons with Gaussian interactions

    Energy Technology Data Exchange (ETDEWEB)

    Kroiss, Peter Michael

    2017-02-01

    This thesis deals with the application of current Quantum Monte Carlo algorithms to many-body systems of fermionic and bosonic species. The first part applies the diagrammatic Monte Carlo method to the Fermi polaron problem, a system of an impurity interacting resonantly with a homogeneous Fermi bath. It is numerically shown that the three particle-hole diagrams do not contribute significantly to the final answer in a quasi-two-dimensional setup, thus demonstrating a nearly perfect destructive interference of contributions in subspaces with higher-order particle-hole lines. Consequently, for strong-enough confinement in the third direction, the transition between the polaron and the molecule ground state is found to be in good agreement with the pure two-dimensional case and agrees very well with the one found by the wave-function approach in the two-particle-hole subspace. In three-dimensional Fermi-polaron systems with mass imbalance of impurity and bath atoms, polaron energy and quasiparticle residue can be accurately determined over a broad range of impurity masses. Furthermore, the spectral function of an imbalanced polaron demonstrates the stability of the quasiparticle and also allows us to locate the repulsive polaron as an excited state. The quantitative exactness of two-particle-hole wave functions is investigated, resulting in a relative lowering of polaronic energies in the mass-imbalance phase diagram. Tan's contact coefficient for the mass-balanced polaron system is found to be in good agreement with variational methods. Mass-imbalanced systems can be studied experimentally by ultracold atom mixtures such as {sup 6}Li-{sup 40}K. In the second part of the thesis, the ground state of a two-dimensional system of Bose particles of spin zero, interacting via a repulsive Gaussian-Core potential, is investigated by means of path integral Monte Carlo simulations. The quantum phase diagram is qualitatively identical to that of two-dimensional Yukawa

  7. Al-bound hole polarons in TiO{sub 2}

    Energy Technology Data Exchange (ETDEWEB)

    Stashans, Arvids, E-mail: arvids@utpl.edu.ec [Grupo de Fisicoquimica de Materiales, Instituto de Quimica Aplicada, Universidad Tecnica Particular de Loja, Apartado 11-01-608, Loja (Ecuador); Bermeo, Sthefano [Grupo de Fisicoquimica de Materiales, Instituto de Quimica Aplicada, Universidad Tecnica Particular de Loja, Apartado 11-01-608, Loja (Ecuador)] [Escuela de Electronica y Telecomunicaciones, Universidad Tecnica Particular de Loja, Apartado 11-01-608, Loja (Ecuador)

    2009-09-18

    Changes in the structural and electronic properties of TiO{sub 2} (anatase and rutile) due to the Al-doping are studied using a quantum-chemical approach based on the Hartree-Fock theory. The formation of hole polarons trapped at oxygen sites near the Al impurity has been discovered and their spatial configuration are discussed. The occurrence of well-localized one-center hole polarons in rutile may influence its photocatalytic activity. Optical absorption energy for this hole center is obtained, 0.4 eV, using the {Delta}SCF approach.

  8. Inapplicability of small-polaron model for the explanation of infrared absorption spectrum in acetanilide.

    Science.gov (United States)

    Zeković, Slobodan; Ivić, Zoran

    2009-01-01

    The applicability of small-polaron model for the interpretation of infrared absorption spectrum in acetanilide has been critically reexamined. It is shown that the energy difference between the normal and anomalous peak, calculated by means of small-polaron theory, displays pronounced temperature dependence which is in drastic contradiction with experiment. It is demonstrated that self-trapped states, which are recently suggested to explain theoretically the experimental absorption spectrum in protein, cannot cause the appearance of the peaks in absorption spectrum for acetanilide.

  9. Polaron mobility obtained by a variational approach for lattice Fröhlich models

    Science.gov (United States)

    Kornjača, Milan; Vukmirović, Nenad

    2018-04-01

    Charge carrier mobility for a class of lattice models with long-range electron-phonon interaction was investigated. The approach for mobility calculation is based on a suitably chosen unitary transformation of the model Hamiltonian which transforms it into the form where the remaining interaction part can be treated as a perturbation. Relevant spectral functions were then obtained using Matsubara Green's functions technique and charge carrier mobility was evaluated using Kubo's linear response formula. Numerical results were presented for a wide range of electron-phonon interaction strengths and temperatures in the case of one-dimensional version of the model. The results indicate that the mobility decreases with increasing temperature for all electron-phonon interaction strengths in the investigated range, while longer interaction range leads to more mobile carriers.

  10. Gravitational surface Hamiltonian and entropy quantization

    Directory of Open Access Journals (Sweden)

    Ashish Bakshi

    2017-02-01

    Full Text Available The surface Hamiltonian corresponding to the surface part of a gravitational action has xp structure where p is conjugate momentum of x. Moreover, it leads to TS on the horizon of a black hole. Here T and S are temperature and entropy of the horizon. Imposing the hermiticity condition we quantize this Hamiltonian. This leads to an equidistant spectrum of its eigenvalues. Using this we show that the entropy of the horizon is quantized. This analysis holds for any order of Lanczos–Lovelock gravity. For general relativity, the area spectrum is consistent with Bekenstein's observation. This provides a more robust confirmation of this earlier result as the calculation is based on the direct quantization of the Hamiltonian in the sense of usual quantum mechanics.

  11. Effective Hamiltonian for travelling discrete breathers

    Science.gov (United States)

    MacKay, Robert S.; Sepulchre, Jacques-Alexandre

    2002-05-01

    Hamiltonian chains of oscillators in general probably do not sustain exact travelling discrete breathers. However solutions which look like moving discrete breathers for some time are not difficult to observe in numerics. In this paper we propose an abstract framework for the description of approximate travelling discrete breathers in Hamiltonian chains of oscillators. The method is based on the construction of an effective Hamiltonian enabling one to describe the dynamics of the translation degree of freedom of moving breathers. Error estimate on the approximate dynamics is also studied. The concept of the Peierls-Nabarro barrier can be made clear in this framework. We illustrate the method with two simple examples, namely the Salerno model which interpolates between the Ablowitz-Ladik lattice and the discrete nonlinear Schrödinger system, and the Fermi-Pasta-Ulam chain.

  12. Noncanonical Hamiltonian methods in plasma dynamics

    International Nuclear Information System (INIS)

    Kaufman, A.N.

    1982-01-01

    A Hamiltonian approach to plasma dynamics is described. The Poisson bracket of two observables g 1 and g 2 is given by using an antisymmetric tensor J, and must satisfy the Jacobi condition. The J can be obtained by elementary tensor analysis. The evolution in time of an observable g is given in terms of the Poisson bracket and a Hamiltonian H(Z). The guiding-center description of particle motion was presented by Littlejohn. The ponderomotive drift and force, the wave-induced oscillation-center velocity, and the gyrofrequency shift are obtained. The Lie transform yields the wave-induced increment to the gyromomentum. In the coulomb model for a Vlasov system, the dynamical variable is the Vlasov distribution f(z). The Hamiltonian functional and the Poisson bracket are obtained. The coupling of f(z) to the Maxwell field appears in the Poisson bracket. The evolution equation yields the Vlasov-Maxwell system. (Kato, T.)

  13. Hamiltonian boundary term and quasilocal energy flux

    International Nuclear Information System (INIS)

    Chen, C.-M.; Nester, James M.; Tung, R.-S.

    2005-01-01

    The Hamiltonian for a gravitating region includes a boundary term which determines not only the quasilocal values but also, via the boundary variation principle, the boundary conditions. Using our covariant Hamiltonian formalism, we found four particular quasilocal energy-momentum boundary term expressions; each corresponds to a physically distinct and geometrically clear boundary condition. Here, from a consideration of the asymptotics, we show how a fundamental Hamiltonian identity naturally leads to the associated quasilocal energy flux expressions. For electromagnetism one of the four is distinguished: the only one which is gauge invariant; it gives the familiar energy density and Poynting flux. For Einstein's general relativity two different boundary condition choices correspond to quasilocal expressions which asymptotically give the ADM energy, the Trautman-Bondi energy and, moreover, an associated energy flux (both outgoing and incoming). Again there is a distinguished expression: the one which is covariant

  14. A real nonlinear integrable couplings of continuous soliton hierarchy and its Hamiltonian structure

    International Nuclear Information System (INIS)

    Yu Fajun

    2011-01-01

    Some integrable coupling systems of existing papers are linear integrable couplings. In the Letter, beginning with Lax pairs from special non-semisimple matrix Lie algebras, we establish a scheme for constructing real nonlinear integrable couplings of continuous soliton hierarchy. A direct application to the AKNS spectral problem leads to a novel nonlinear integrable couplings, then we consider the Hamiltonian structures of nonlinear integrable couplings of AKNS hierarchy with the component-trace identity. - Highlights: → We establish a scheme to construct real nonlinear integrable couplings. → We obtain a novel nonlinear integrable couplings of AKNS hierarchy. → Hamiltonian structure of nonlinear integrable couplings AKNS hierarchy is presented.

  15. Hamiltonian dynamics for complex food webs

    Science.gov (United States)

    Kozlov, Vladimir; Vakulenko, Sergey; Wennergren, Uno

    2016-03-01

    We investigate stability and dynamics of large ecological networks by introducing classical methods of dynamical system theory from physics, including Hamiltonian and averaging methods. Our analysis exploits the topological structure of the network, namely the existence of strongly connected nodes (hubs) in the networks. We reveal new relations between topology, interaction structure, and network dynamics. We describe mechanisms of catastrophic phenomena leading to sharp changes of dynamics and hence completely altering the ecosystem. We also show how these phenomena depend on the structure of interaction between species. We can conclude that a Hamiltonian structure of biological interactions leads to stability and large biodiversity.

  16. Convergence to equilibrium under a random Hamiltonian

    Science.gov (United States)

    Brandão, Fernando G. S. L.; Ćwikliński, Piotr; Horodecki, Michał; Horodecki, Paweł; Korbicz, Jarosław K.; Mozrzymas, Marek

    2012-09-01

    We analyze equilibration times of subsystems of a larger system under a random total Hamiltonian, in which the basis of the Hamiltonian is drawn from the Haar measure. We obtain that the time of equilibration is of the order of the inverse of the arithmetic average of the Bohr frequencies. To compute the average over a random basis, we compute the inverse of a matrix of overlaps of operators which permute four systems. We first obtain results on such a matrix for a representation of an arbitrary finite group and then apply it to the particular representation of the permutation group under consideration.

  17. Ostrogradski Hamiltonian approach for geodetic brane gravity

    International Nuclear Information System (INIS)

    Cordero, Ruben; Molgado, Alberto; Rojas, Efrain

    2010-01-01

    We present an alternative Hamiltonian description of a branelike universe immersed in a flat background spacetime. This model is named geodetic brane gravity. We set up the Regge-Teitelboim model to describe our Universe where such field theory is originally thought as a second order derivative theory. We refer to an Ostrogradski Hamiltonian formalism to prepare the system to its quantization. This approach comprize the manage of both first- and second-class constraints and the counting of degrees of freedom follows accordingly.

  18. Supersymmetric Extension of Non-Hermitian su(2 Hamiltonian and Supercoherent States

    Directory of Open Access Journals (Sweden)

    Omar Cherbal

    2010-12-01

    Full Text Available A new class of non-Hermitian Hamiltonians with real spectrum, which are written as a real linear combination of su(2 generators in the form H=ωJ_3+αJ_−+βJ_+, α≠β, is analyzed. The metrics which allows the transition to the equivalent Hermitian Hamiltonian is established. A pseudo-Hermitian supersymmetic extension of such Hamiltonians is performed. They correspond to the pseudo-Hermitian supersymmetric systems of the boson-phermion oscillators. We extend the supercoherent states formalism to such supersymmetic systems via the pseudo-unitary supersymmetric displacement operator method. The constructed family of these supercoherent states consists of two dual subfamilies that form a bi-overcomplete and bi-normal system in the boson-phermion Fock space. The states of each subfamily are eigenvectors of the boson annihilation operator and of one of the two phermion lowering operators.

  19. Quantitative measurements of magnetic polaron binding on acceptors in CdMnTe alloys

    Science.gov (United States)

    Nhung, Tran Hong; Planel, R.

    1983-03-01

    The acceptor binding energy is measured as a function of Temperature and composition in Cd1-x Mnx Te alloys, by time resolved spectroscopy. The Bound magnetic polaron effect is measured and compared with a theory accouting for magnetic saturation and fluctuations.

  20. Formation time of a small electron polaron in LiNbO3: measurements and interpretation

    International Nuclear Information System (INIS)

    Qiu, Yong; Ucer, K.B.; Williams, R.T.

    2005-01-01

    Infrared optical absorption attributed to the electron polaron on a non-defective site in LiNbO 3 and KNbO 3 has previously been observed using pulsed electron and laser techniques. With subpicosecond laser excitation and spectroscopy, it is possible to measure a rise time of the infrared absorption, which may be interpreted as the time for a band-state conduction electron to cool by phonon scattering, collapse its wavefunction around a site made attractive by thermal disorder, and relax vibrationally to a small polaron. This is a process which is of fundamental interest, involving dynamics of self-localization from band states and vibrational relaxation of a localized electron in an otherwise non-defective lattice. For example, Gavartin and Shluger have recently performed calculations on the role of thermal fluctuations in self-trapping of holes in MgO. We report initial measurements on the rise time of infrared absorption at 0.95 eV (Mg-perturbed polaron) in LiNbO 3 :Mg to be τ R ∼230 fs at T=20 K and τ R ∼110 fs at T=296 K. We discuss 2 stages that together may account for the delay and its temperature dependence: free-electron cooling and vibrational relaxation of a ''defect'' (small polaron) in a host. (copyright 2005 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

  1. Impact of morphology on polaron delocalization in a semicrystalline conjugated polymer

    KAUST Repository

    Steyrleuthner, Robert; Zhang, Yuexing; Zhang, Lei; Kraffert, Felix; Cherniawski, Benjamin P.; Bittl, Robert; Briseno, Alejandro L.; Bredas, Jean-Luc; Behrends, Jan

    2016-01-01

    We investigate the delocalization of holes in the semicrystalline conjugated polymer poly(2,5-bis(3-alkylthiophene-2-yl)thieno[3,2-b]thiophene) (PBTTT) by directly measuring the hyperfine coupling between photogenerated polarons and bound nuclear

  2. Decay of Polarons and Molecules in a Strongly Polarized Fermi Gas

    DEFF Research Database (Denmark)

    Bruun, Georg; Massignan, P.

    2010-01-01

    , and that it vanishes much faster than the energy difference between the two states, thereby confirming the first order nature of the polaron-molecule transition. In the regime where each state is metastable, we find quasiparticle lifetimes which are much longer than what is expected for a usual Fermi liquid. Our...

  3. Effect of doping Ca on polaron hopping in LaSr 2 Mn 2 O 7

    Indian Academy of Sciences (India)

    ... Lecture Workshops · Refresher Courses · Symposia · Live Streaming. Home; Journals; Pramana – Journal of Physics; Volume 58; Issue 5-6. Effect of doping Ca on polaron hopping in LaSr2Mn2O7. S N Bhatia Osama A Yassin. Colossal Magnetoresistance & Other Materials Volume 58 Issue 5-6 May-June 2002 pp 1061- ...

  4. A new polaronic order-disorder phase transition in magnetite as observed through μSR

    International Nuclear Information System (INIS)

    Boekema, C.; Lichti, R.L.; Denison, A.B.; Brabers, V.A.M.; Cooke, D.W.; Heffner, R.H.; Hutson, R.L.; Schillaci, M.E.

    1986-01-01

    Recent μSr measurements on the Mott-Wigner glass magnetite, as a function of temperature and external magnetic field have shown the existence of two inequivalent magnetic sites below T A = 247 K. These data are being interpreted in terms of the onset or destruction of local order manifested as local atomic correlations (molecular polarons). (orig.)

  5. Time Domain View of Liquid-like Screening and Large Polaron Formation in Lead Halide Perovskites

    Science.gov (United States)

    Joshi, Prakriti Pradhan; Miyata, Kiyoshi; Trinh, M. Tuan; Zhu, Xiaoyang

    The structural softness and dynamic disorder of lead halide perovskites contributes to their remarkable optoelectronic properties through efficient charge screening and large polaron formation. Here we provide a direct time-domain view of the liquid-like structural dynamics and polaron formation in single crystal CH3NH3PbBr3 and CsPbBr3 using femtosecond optical Kerr effect spectroscopy in conjunction with transient reflectance spectroscopy. We investigate structural dynamics as function of pump energy, which enables us to examine the dynamics in the absence and presence of charge carriers. In the absence of charge carriers, structural dynamics are dominated by over-damped picosecond motions of the inorganic PbBr3- sub-lattice and these motions are strongly coupled to band-gap electronic transitions. Carrier injection from across-gap optical excitation triggers additional 0.26 ps dynamics in CH3NH3PbBr3 that can be attributed to the formation of large polarons. In comparison, large polaron formation is slower in CsPbBr3 with a time constant of 0.6 ps. We discuss how such dynamic screening protects charge carriers in lead halide perovskites. US Department of Energy, Office of Science - Basic Energy Sciences.

  6. On the relationship between modifications to the Raychaudhuri equation and the canonical Hamiltonian structures

    International Nuclear Information System (INIS)

    Singh, Parampreet; Soni, S K

    2016-01-01

    The problem of obtaining canonical Hamiltonian structures from the equations of motion, without any knowledge of the action, is studied in the context of the spatially flat Friedmann, ‘Robertson’, and Walker models. Modifications to the Raychaudhuri equation are implemented independently as quadratic and cubic terms of energy density without introducing additional degrees of freedom. Depending on their sign, modifications make gravity repulsive above a curvature scale for matter satisfying strong energy conditions, or more attractive than in the classical theory. The canonical structure of the modified theories is determined by demanding that the total Hamiltonian be a linear combination of gravity and matter Hamiltonians. In the quadratic repulsive case, the modified canonical phase space of gravity is a polymerized phase space with canonical momentum as inverse a trigonometric function of the Hubble rate; the canonical Hamiltonian can be identified with the effective Hamiltonian in loop quantum cosmology. The repulsive cubic modification results in a ‘generalized polymerized’ canonical phase space. Both the repulsive modifications are found to yield singularity avoidance. In contrast, the quadratic and cubic attractive modifications result in a canonical phase space in which canonical momentum is nontrigonometric and singularities persist. Our results hint at connections between the repulsive/attractive nature of modifications to gravity arising from the gravitational sector and polymerized/non polymerized gravitational phase space. (paper)

  7. Adaptive control of port-Hamiltonian systems

    NARCIS (Netherlands)

    Dirksz, D.A.; Scherpen, J.M.A.; Edelmayer, András

    2010-01-01

    In this paper an adaptive control scheme is presented for general port-Hamiltonian systems. Adaptive control is used to compensate for control errors that are caused by unknown or uncertain parameter values of a system. The adaptive control is also combined with canonical transformation theory for

  8. Iterated Hamiltonian type systems and applications

    Science.gov (United States)

    Tiba, Dan

    2018-04-01

    We discuss, in arbitrary dimension, certain Hamiltonian type systems and prove existence, uniqueness and regularity properties, under the independence condition. We also investigate the critical case, define a class of generalized solutions and prove existence and basic properties. Relevant examples and counterexamples are also indicated. The applications concern representations of implicitly defined manifolds and their perturbations, motivated by differential systems involving unknown geometries.

  9. Symmetry and resonance in Hamiltonian systems

    NARCIS (Netherlands)

    Tuwankotta, J.M.; Verhulst, F.

    2000-01-01

    In this paper we study resonances in two degrees of freedom, autonomous, hamiltonian systems. Due to the presence of a symmetry condition on one of the degrees of freedom, we show that some of the resonances vanish as lower order resonances. After giving a sharp estimate of the resonance domain, we

  10. Symmetry and resonance in Hamiltonian systems

    NARCIS (Netherlands)

    Tuwankotta, J.M.; Verhulst, F.

    1999-01-01

    In this paper we study resonances in two degrees of freedom, autonomous, hamiltonian systems. Due to the presence of a symmetry condition on one of the degrees of freedom, we show that some of the resonances vanish as lower order resonances. After determining the size of the resonance domain, we

  11. Hamiltonian evolutions of twisted polygons in RPn

    International Nuclear Information System (INIS)

    Beffa, Gloria Marì; Wang, Jing Ping

    2013-01-01

    In this paper we find a discrete moving frame and their associated invariants along projective polygons in RP n , and we use them to describe invariant evolutions of projective N-gons. We then apply a reduction process to obtain a natural Hamiltonian structure on the space of projective invariants for polygons, establishing a close relationship between the projective N-gon invariant evolutions and the Hamiltonian evolutions on the invariants of the flow. We prove that any Hamiltonian evolution is induced on invariants by an invariant evolution of N-gons—what we call a projective realization—and both evolutions are connected explicitly in a very simple way. Finally, we provide a completely integrable evolution (the Boussinesq lattice related to the lattice W 3 -algebra), its projective realization in RP 2 and its Hamiltonian pencil. We generalize both structures to n-dimensions and we prove that they are Poisson, defining explicitly the n-dimensional generalization of the planar evolution (a discretization of the W n -algebra). We prove that the generalization is completely integrable, and we also give its projective realization, which turns out to be very simple. (paper)

  12. Discrete variable representation for singular Hamiltonians

    DEFF Research Database (Denmark)

    Schneider, B. I.; Nygaard, Nicolai

    2004-01-01

    We discuss the application of the discrete variable representation (DVR) to Schrodinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based...

  13. The hamiltonian structures of the KP hierarchy

    International Nuclear Information System (INIS)

    Das, A.; Panda, S.; Huang Wenjui

    1991-01-01

    We obtain the two hamiltonian structures of the KP hierarchy following the method of Drinfeld and Sokolov. We point out how the second structure of Drinfeld and Sokolov needs to be modified in the present case. We briefly comment on the connection between these structures and the W 1+∞ algebra. (orig.)

  14. Hamiltonian structure for rescaled integrable Lorenz systems

    International Nuclear Information System (INIS)

    Haas, F.; Goedert, J.

    1993-01-01

    It is shown that three among the known invariants for the Lorenz system recast the original equations into a Hamiltonian form. This is made possible by an appropriate time-dependent rescaling and the use of a generalized formalism with non-trivial structure functions. (author)

  15. Singularities of Poisson structures and Hamiltonian bifurcations

    NARCIS (Netherlands)

    Meer, van der J.C.

    2010-01-01

    Consider a Poisson structure on C8(R3,R) with bracket {, } and suppose that C is a Casimir function. Then {f, g} =<¿C, (¿g x ¿f) > is a possible Poisson structure. This confirms earlier observations concerning the Poisson structure for Hamiltonian systems that are reduced to a one degree of freedom

  16. Transparency in port-Hamiltonian based telemanipulation

    NARCIS (Netherlands)

    Secchi, C; Stramigioli, Stefano; Fantuzzi, C.

    2005-01-01

    After stability, transparency is the major issue in the design of a telemanipulation system. In this paper we exploit a behavioral approach in order to provide an index for the evaluation of transparency in port-Hamiltonian based teleoperators. Furthermore we provide a transparency analysis of

  17. Transparency in Port-Hamiltonian-Based Telemanipulation

    NARCIS (Netherlands)

    Secchi, Cristian; Stramigioli, Stefano; Fantuzzi, Cesare

    After stability, transparency is the major issue in the design of a telemanipulation system. In this paper, we exploit the behavioral approach in order to provide an index for the evaluation of transparency in port-Hamiltonian-based teleoperators. Furthermore, we provide a transparency analysis of

  18. Equivalence of Lagrangian and Hamiltonian BRST quantizations

    International Nuclear Information System (INIS)

    Grigoryan, G.V.; Grigoryan, R.P.; Tyutin, I.V.

    1992-01-01

    Two approaches to the quantization of gauge theories using BRST symmetry are widely used nowadays: the Lagrangian quantization, developed in (BV-quantization) and Hamiltonian quantization, formulated in (BFV-quantization). For all known examples of field theory (Yang-Mills theory, gravitation etc.) both schemes give equivalent results. However the equivalence of these approaches in general wasn't proved. The main obstacle in comparing of these formulations consists in the fact, that in Hamiltonian approach the number of ghost fields is equal to the number of all first-class constraints, while in the Lagrangian approach the number of ghosts is equal to the number of independent gauge symmetries, which is equal to the number of primary first-class constraints only. This paper is devoted to the proof of the equivalence of Lagrangian and Hamiltonian quantizations for the systems with first-class constraints only. This is achieved by a choice of special gauge in the Hamiltonian approach. It's shown, that after integration over redundant variables on the functional integral we come to effective action which is constructed according to rules for construction of the effective action in Lagrangian quantization scheme

  19. Hamiltonian formulation of anomaly free chiral bosons

    International Nuclear Information System (INIS)

    Abdalla, E.; Abdalla, M.C.B.; Devecchi, F.P.; Zadra, A.

    1988-01-01

    Starting out of an anomaly free Lagrangian formulation for chiral scalars, which a Wess-Zumino Term (to cancel the anomaly), we formulate the corresponding hamiltonian problem. Ther we use the (quantum) Siegel invariance to choose a particular, which turns out coincide with the obtained by Floreanini and Jackiw. (author) [pt

  20. Hamiltonian structure of gravitational field theory

    International Nuclear Information System (INIS)

    Rayski, J.

    1992-01-01

    Hamiltonian generalizations of Einstein's theory of gravitation introducing a laminar structure of spacetime are discussed. The concepts of general relativity and of quasi-inertial coordinate systems are extended beyond their traditional scope. Not only the metric, but also the coordinate system, if quantized, undergoes quantum fluctuations

  1. Port-Hamiltonian Systems on Open Graphs

    NARCIS (Netherlands)

    Schaft, A.J. van der; Maschke, B.M.

    2010-01-01

    In this talk we discuss how to define in an intrinsic manner port-Hamiltonian dynamics on open graphs. Open graphs are graphs where some of the vertices are boundary vertices (terminals), which allow interconnection with other systems. We show that a directed graph carries two natural Dirac

  2. Gauge theories of infinite dimensional Hamiltonian superalgebras

    International Nuclear Information System (INIS)

    Sezgin, E.

    1989-05-01

    Symplectic diffeomorphisms of a class of supermanifolds and the associated infinite dimensional Hamiltonian superalgebras, H(2M,N) are discussed. Applications to strings, membranes and higher spin field theories are considered: The embedding of the Ramond superconformal algebra in H(2,1) is obtained. The Chern-Simons gauge theory of symplectic super-diffeomorphisms is constructed. (author). 29 refs

  3. The Hamiltonian structures of the KP hierarchy

    International Nuclear Information System (INIS)

    Das, A.; Panda, S.; Huang Wenjui

    1991-08-01

    We obtain the two Hamiltonian structures of the KP hierarchy following the method of Drinfeld and Sokolov. We point out how the second structure of Drinfeld and Sokolov needs to be modified in the present case. We briefly comment on the connection between these structures and the W 1+∞ algebra. (author). 18 refs

  4. Quasi exact solution of the Rabi Hamiltonian

    CERN Document Server

    Koç, R; Tuetuencueler, H

    2002-01-01

    A method is suggested to obtain the quasi exact solution of the Rabi Hamiltonian. It is conceptually simple and can be easily extended to other systems. The analytical expressions are obtained for eigenstates and eigenvalues in terms of orthogonal polynomials. It is also demonstrated that the Rabi system, in a particular case, coincides with the quasi exactly solvable Poeschl-Teller potential.

  5. Edge-disjoint Hamiltonian cycles in hypertournaments

    DEFF Research Database (Denmark)

    Thomassen, Carsten

    2006-01-01

    We introduce a method for reducing k-tournament problems, for k >= 3, to ordinary tournaments, that is, 2-tournaments. It is applied to show that a k-tournament on n >= k + 1 + 24d vertices (when k >= 4) or on n >= 30d + 2 vertices (when k = 3) has d edge-disjoint Hamiltonian cycles if and only...

  6. Hamiltonian constraint in polymer parametrized field theory

    International Nuclear Information System (INIS)

    Laddha, Alok; Varadarajan, Madhavan

    2011-01-01

    Recently, a generally covariant reformulation of two-dimensional flat spacetime free scalar field theory known as parametrized field theory was quantized using loop quantum gravity (LQG) type ''polymer'' representations. Physical states were constructed, without intermediate regularization structures, by averaging over the group of gauge transformations generated by the constraints, the constraint algebra being a Lie algebra. We consider classically equivalent combinations of these constraints corresponding to a diffeomorphism and a Hamiltonian constraint, which, as in gravity, define a Dirac algebra. Our treatment of the quantum constraints parallels that of LQG and obtains the following results, expected to be of use in the construction of the quantum dynamics of LQG: (i) the (triangulated) Hamiltonian constraint acts only on vertices, its construction involves some of the same ambiguities as in LQG and its action on diffeomorphism invariant states admits a continuum limit, (ii) if the regulating holonomies are in representations tailored to the edge labels of the state, all previously obtained physical states lie in the kernel of the Hamiltonian constraint, (iii) the commutator of two (density weight 1) Hamiltonian constraints as well as the operator correspondent of their classical Poisson bracket converge to zero in the continuum limit defined by diffeomorphism invariant states, and vanish on the Lewandowski-Marolf habitat, (iv) the rescaled density 2 Hamiltonian constraints and their commutator are ill-defined on the Lewandowski-Marolf habitat despite the well-definedness of the operator correspondent of their classical Poisson bracket there, (v) there is a new habitat which supports a nontrivial representation of the Poisson-Lie algebra of density 2 constraints.

  7. The group of Hamiltonian automorphisms of a star product

    OpenAIRE

    La Fuente-Gravy, Laurent

    2015-01-01

    We deform the group of Hamiltonian diffeomorphisms into the group of Hamiltonian automorphisms of a formal star product on a symplectic manifold. We study the geometry of that group and deform the Flux morphism in the framework of deformation quantization.

  8. QCD string with quarks. 2. Light cone Hamiltonian

    International Nuclear Information System (INIS)

    Dubin, A.Yu.; Kaidalov, A.B.; Simonov, Yu.A.

    1994-01-01

    The light-cone Hamiltonian is derived from the general gauge - and Lorentz - invariant expression for the qq-bar Green function. The resulting Hamiltonian contains in a non-additive way contributions from quark and string degrees of freedom

  9. On integrable Hamiltonians for higher spin XXZ chain

    International Nuclear Information System (INIS)

    Bytsko, Andrei G.

    2003-01-01

    Integrable Hamiltonians for higher spin periodic XXZ chains are constructed in terms of the spin generators; explicit examples for spins up to (3/2) are given. Relations between Hamiltonians for some U q (sl 2 )-symmetric and U(1)-symmetric universal r-matrices are studied; their properties are investigated. A certain modification of the higher spin periodic chain Hamiltonian is shown to be an integrable U q (sl 2 )-symmetric Hamiltonian for an open chain

  10. Numerical determination of the magnetic field line Hamiltonian

    International Nuclear Information System (INIS)

    Kuo-Petravic, G.; Boozer, A.H.

    1986-03-01

    The structure of a magnetic field is determined by a one-degree of freedom, time-dependent Hamiltonian. This Hamiltonian is evaluated for a given field in a perturbed action-angle form. The location and the size of magnetic islands in the given field are determined from Hamiltonian perturbation theory and from an ordinary Poincare plot of the field line trajectories

  11. Effective Hamiltonians in quantum physics: resonances and geometric phase

    International Nuclear Information System (INIS)

    Rau, A R P; Uskov, D

    2006-01-01

    Effective Hamiltonians are often used in quantum physics, both in time-dependent and time-independent contexts. Analogies are drawn between the two usages, the discussion framed particularly for the geometric phase of a time-dependent Hamiltonian and for resonances as stationary states of a time-independent Hamiltonian

  12. Hamiltonian formalism of the Skyrme model with ω mesons

    International Nuclear Information System (INIS)

    Adami, C.

    1988-07-01

    We have in this thesis presented the semiclassical quantum theory of the Skyrme model with coupling to an isoscalar gauge field. For the quantization of the classical theory we used the Hamiltonian formalism. Furthermore we have studied the consequences of the canonical treatment, whereby we found the explicite πN vertex of the theory, as well as presented the correct treatment of the spatial contribution of the ω field. Furthermore we indicated that a consistent treatment requires the summation of all tree diagrams of the theory with internal π and ω lines. Such a calculation contains the explicite construction of solutions for the coupled πω field equations. A further result of this thesis concerns the application of the linear πN vertex to the calculation of the Δ decay width via the process Δ→Nπ. (orig./HSI) [de

  13. Hamiltonian lattice studies of chiral meson field theories

    International Nuclear Information System (INIS)

    Chin, S.A.

    1998-01-01

    The latticization of the non-linear sigma model reduces a chiral meson field theory to an O(4) spin lattice system with quantum fluctuations. The result is an interesting marriage between quantum many-body theory and classical spin systems. By solving the resulting lattice Hamiltonian by Monte Carlo methods, the dynamics and thermodynamics of pions can be determined non-perturbatively. In a variational 16 3 lattice study, the ground state chiral phase transition is shown to be first order. Moreover, as the chiral phase transition is approached, the mass gap of pionic collective modes with quantum number of the ω vector meson drops toward zero. (Copyright (1998) World Scientific Publishing Co. Pte. Ltd)

  14. Coherent states of systems with quadratic Hamiltonians

    Energy Technology Data Exchange (ETDEWEB)

    Bagrov, V.G., E-mail: bagrov@phys.tsu.ru [Department of Physics, Tomsk State University, Tomsk (Russian Federation); Gitman, D.M., E-mail: gitman@if.usp.br [Tomsk State University, Tomsk (Russian Federation); Pereira, A.S., E-mail: albertoufcg@hotmail.com [Universidade de Sao Paulo (USP), Sao Paulo, SP (Brazil). Instituto de Fisica

    2015-06-15

    Different families of generalized coherent states (CS) for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. In principle, all known CS of systems with quadratic Hamiltonian are members of these families. Some of the constructed generalized CS are close enough to the well-known due to Schroedinger and Glauber CS of a harmonic oscillator; we call them simply CS. However, even among these CS, there exist different families of complete sets of CS. These families differ by values of standard deviations at the initial time instant. According to the values of these initial standard deviations, one can identify some of the families with semiclassical CS. We discuss properties of the constructed CS, in particular, completeness relations, minimization of uncertainty relations and so on. As a unknown application of the general construction, we consider different CS of an oscillator with a time dependent frequency. (author)

  15. Coherent states of systems with quadratic Hamiltonians

    International Nuclear Information System (INIS)

    Bagrov, V.G.; Gitman, D.M.; Pereira, A.S.

    2015-01-01

    Different families of generalized coherent states (CS) for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. In principle, all known CS of systems with quadratic Hamiltonian are members of these families. Some of the constructed generalized CS are close enough to the well-known due to Schroedinger and Glauber CS of a harmonic oscillator; we call them simply CS. However, even among these CS, there exist different families of complete sets of CS. These families differ by values of standard deviations at the initial time instant. According to the values of these initial standard deviations, one can identify some of the families with semiclassical CS. We discuss properties of the constructed CS, in particular, completeness relations, minimization of uncertainty relations and so on. As a unknown application of the general construction, we consider different CS of an oscillator with a time dependent frequency. (author)

  16. Effective Hamiltonian for high Tc Cu oxides

    International Nuclear Information System (INIS)

    Fukuyama, H.; Matsukawa, H.

    1989-01-01

    Effective Hamiltonian has been derived for CuO 2 layers in the presence of extra holes doped mainly into O-sites by taking both on-site and intersite Coulomb interaction into account. A special case with a single hole has been examined in detail. It is found that there exist various types of bound states, singlet and triplet with different spatial symmetry, below the hole bank continuum. The spatial extent of the Zhang-Rice singlet state, which is most stabilized, and the effective transfer integral between these singlet states are seen to be very sensitive to the relative magnitude of the direct and the indirect transfer integrals between O-sites. Effective Hamiltonian for the case of electron doping has also been derived

  17. Partial quantization of Lagrangian-Hamiltonian systems

    International Nuclear Information System (INIS)

    Amaral, C.M. do; Soares Filho, P.C.

    1979-05-01

    A classical variational principle is constructed in the Weiss form, for dynamical systems with support spaces of the configuration-phase kind. This extended principle rules the dynamics of classical systems, partially Hamiltonian, in interaction with Lagrangean parameterized subsidiary dynamics. The variational family of equations obtained, consists of an equation of the Hamilton-Jacobi type, coupled to a family of differential equations of the Euler-Lagrange form. The basic dynamical function appearing in the equations is a function of the Routh kind. By means of an ansatz induced by the variationally obtained family, a generalized set of equation, is proposed constituted by a wave equation of Schroedinger type, coupled to a family of equations formaly analog to those Euler-Lagrange equations. A basic operator of Routh type appears in our generalized set of equations. This operator describes the interaction between a quantized Hamiltonian dynamics, with a parameterized classical Lagrangean dynamics in semi-classical closed models. (author) [pt

  18. Quadratic hamiltonians and relativistic quantum mechanics

    International Nuclear Information System (INIS)

    Razumov, A.V.; Solov'ev, V.O.; Taranov, A.Yu.

    1981-01-01

    For the case of a charged scalar field described by a quadratic hamiltonian the equivalent relativistic quantum mechanics is constructed in one-particle sector. Complete investigation of a charged relativistic particle motion in the Coulomb field is carried out. Subcritical as well as supercritical cases are considered. In the course of investigation of the charged scalar particle in the Coulomb field the diagonalization of the quadratic hamiltonian describing the charged scalar quantized field interaction with the external Coulomb field has taken place. Mathematically this problem is bound to the construction of self-conjugated expansions of the symmetric operator. The construction of such expansion is necessary at any small external field magnitude [ru

  19. Hamiltonian mechanics and divergence-free fields

    International Nuclear Information System (INIS)

    Boozer, A.H.

    1986-08-01

    The field lines, or integral curves, of a divergence-free field in three dimensions are shown to be topologically equivalent to the trajectories of a Hamiltonian with two degrees of freedom. The consideration of fields that depend on a parameter allow the construction of a canonical perturbation theory which is valid even if the perturbation is large. If the parametric dependence of the magnetic, or the vorticity field is interpreted as time dependence, evolution equations are obtained which give Kelvin's theorem or the flux conservation theorem for ideal fluids and plasmas. The Hamiltonian methods prove especially useful for study of fields in which the field lines must be known throughout a volume of space

  20. Quantum mechanical Hamiltonian models of discrete processes

    International Nuclear Information System (INIS)

    Benioff, P.

    1981-01-01

    Here the results of other work on quantum mechanical Hamiltonian models of Turing machines are extended to include any discrete process T on a countably infinite set A. The models are constructed here by use of scattering phase shifts from successive scatterers to turn on successive step interactions. Also a locality requirement is imposed. The construction is done by first associating with each process T a model quantum system M with associated Hilbert space H/sub M/ and step operator U/sub T/. Since U/sub T/ is not unitary in general, M, H/sub M/, and U/sub T/ are extended into a (continuous time) Hamiltonian model on a larger space which satisfies the locality requirement. The construction is compared with the minimal unitary dilation of U/sub T/. It is seen that the model constructed here is larger than the minimal one. However, the minimal one does not satisfy the locality requirement

  1. Boundary Hamiltonian Theory for Gapped Topological Orders

    Science.gov (United States)

    Hu, Yuting; Wan, Yidun; Wu, Yong-Shi

    2017-06-01

    We report our systematic construction of the lattice Hamiltonian model of topological orders on open surfaces, with explicit boundary terms. We do this mainly for the Levin-Wen string-net model. The full Hamiltonian in our approach yields a topologically protected, gapped energy spectrum, with the corresponding wave functions robust under topology-preserving transformations of the lattice of the system. We explicitly present the wavefunctions of the ground states and boundary elementary excitations. The creation and hopping operators of boundary quasi-particles are constructed. It is found that given a bulk topological order, the gapped boundary conditions are classified by Frobenius algebras in its input data. Emergent topological properties of the ground states and boundary excitations are characterized by (bi-) modules over Frobenius algebras.

  2. Hamiltonian reduction of Kac-Moody algebras

    International Nuclear Information System (INIS)

    Kimura, Kazuhiro

    1991-01-01

    Feigin-Fucks construction provides us methods to treat rational conformal theories in terms of free fields. This formulation enables us to describe partition functions and correlation functions in the Fock space of free fields. There are several attempt extending to supersymmetric theories. In this report authors present an explicit calculation of the Hamiltonian reduction based on the free field realization. In spite of the results being well-known, the relations can be clearly understood in the language of bosons. Authors perform the hamiltonian reduction by imposing a constraint with appropriate gauge transformations which preserve the constraint. This approaches enables us to gives the geometric interpretation of super Virasoro algebras and relations of the super gravity. In addition, author discuss the properties of quantum groups by using the explicit form of the group element. It is also interesting to extend to super Kac-Moody algebras. (M.N.)

  3. Phase transitions in the Hubbard Hamiltonian

    International Nuclear Information System (INIS)

    Chaves, C.M.; Lederer, P.; Gomes, A.A.

    1977-05-01

    Phase transition in the isotropic non-degenerate Hubbard Hamiltonian within the renormalization group techniques is studied, using the epsilon = 4 - d expansion to first order in epsilon. The functional obtained from the Hubbard Hamiltonian displays full rotation symmetry and describes two coupled fields: a vector spin field, with n components and a non-soft scalar charge field. This coupling is pure imaginary, which has interesting consequences on the critical properties of this coupled field system. The effect of simple constraints imposed on the charge field is considered. The relevance of the coupling between the fields in producing Fisher renormalization of the critical exponents is discussed. The possible singularities introduced in the charge-charge correlation function by the coupling are also discussed

  4. Hamiltonian partial differential equations and applications

    CERN Document Server

    Nicholls, David; Sulem, Catherine

    2015-01-01

    This book is a unique selection of work by world-class experts exploring the latest developments in Hamiltonian partial differential equations and their applications. Topics covered within are representative of the field’s wide scope, including KAM and normal form theories, perturbation and variational methods, integrable systems, stability of nonlinear solutions as well as applications to cosmology, fluid mechanics and water waves. The volume contains both surveys and original research papers and gives a concise overview of the above topics, with results ranging from mathematical modeling to rigorous analysis and numerical simulation. It will be of particular interest to graduate students as well as researchers in mathematics and physics, who wish to learn more about the powerful and elegant analytical techniques for Hamiltonian partial differential equations.

  5. Gauge fixing and the Hamiltonian for cylindrical spacetimes

    Science.gov (United States)

    Mena Marugán, Guillermo A.

    2001-01-01

    We introduce a complete gauge fixing for cylindrical spacetimes in vacuo that, in principle, do not contain the axis of symmetry. By cylindrically symmetric we understand spacetimes that possess two commuting spacelike Killing vectors, one of them rotational and the other one translational. The result of our gauge fixing is a constraint-free model whose phase space has four field-like degrees of freedom and that depends on three constant parameters. Two of these constants determine the global angular momentum and the linear momentum in the axis direction, while the third parameter is related with the behavior of the metric around the axis. We derive the explicit expression of the metric in terms of the physical degrees of freedom, calculate the reduced equations of motion and obtain the Hamiltonian that generates the reduced dynamics. We also find upper and lower bounds for this reduced Hamiltonian that provides the energy per unit length contained in the system. In addition, we show that the reduced formalism constructed is well defined and consistent at least when the linear momentum in the axis direction vanishes. Furthermore, in that case we prove that there exists an infinite number of solutions in which all physical fields are constant both in the surroundings of the axis and at sufficiently large distances from it. If the global angular momentum is different from zero, the isometry group of these solutions is generally not orthogonally transitive. Such solutions generalize the metric of a spinning cosmic string in the region where no closed timelike curves are present.

  6. A diagrammatic construction of formal E-independent model hamiltonian

    International Nuclear Information System (INIS)

    Kvasnicka, V.

    1977-01-01

    A diagrammatic construction of formal E-independent model interaction (i.e., without second-quantization formalism) is suggested. The construction starts from the quasi-degenerate Brillouin-Wigner perturbation theory, in the framework of which an E-dependent model Hamiltonian is simply constructed. Applying the ''E-removing'' procedure to this E-dependent model Hamiltonian, the E-independent formal model Hamiltonian either Hermitian or non-Hermitian can diagrammatically be easily derived. For the formal E-independent model Hamiltonian the separability theorem is proved, which can be profitably used for a rather ''formalistic ''construction of a many-body E-independent model Hamiltonian

  7. Boson mapping and the microscopic collective nuclear Hamiltonian

    International Nuclear Information System (INIS)

    Dobes, J.; Ivanova, S.P.; Dzholos, R.V.; Pedrosa, R.

    1990-01-01

    Starting with the mapping of the quadrupole collective states in the fermion space onto the boson space, the fermion nuclear problem is transformed into the boson one. The boson images of the bifermion operators and of the fermion Hamiltonian are found. Recurrence relations are used to obtain approximately the norm matrix which appears in the boson-fermion mapping. The resulting boson Hamiltonian contains terms which go beyond the ordinary SU(6) symmetry Hamiltonian of the interacting boson model. Calculations, however, suggest that on the phenomenological level the differences between the mapped Hamiltonian and the SU(6) Hamiltonian are not too important. 18 refs.; 2 figs

  8. Non-canonical distribution and non-equilibrium transport beyond weak system-bath coupling regime: A polaron transformation approach

    Science.gov (United States)

    Xu, Dazhi; Cao, Jianshu

    2016-08-01

    The concept of polaron, emerged from condense matter physics, describes the dynamical interaction of moving particle with its surrounding bosonic modes. This concept has been developed into a useful method to treat open quantum systems with a complete range of system-bath coupling strength. Especially, the polaron transformation approach shows its validity in the intermediate coupling regime, in which the Redfield equation or Fermi's golden rule will fail. In the polaron frame, the equilibrium distribution carried out by perturbative expansion presents a deviation from the canonical distribution, which is beyond the usual weak coupling assumption in thermodynamics. A polaron transformed Redfield equation (PTRE) not only reproduces the dissipative quantum dynamics but also provides an accurate and efficient way to calculate the non-equilibrium steady states. Applications of the PTRE approach to problems such as exciton diffusion, heat transport and light-harvesting energy transfer are presented.

  9. Effect of base-pair inhomogeneities on charge transport along the DNA molecule, mediated by twist and radial polarons

    International Nuclear Information System (INIS)

    Palmero, F; Archilla, J F R; Hennig, D; Romero, F R

    2004-01-01

    Some recent results for a three-dimensional, semi-classical, tight-binding model for DNA show that there are two types of polarons, namely radial and twist polarons, which can transport charge along the DNA molecule. However, the existence of two types of base pairs in real DNA makes it crucial to find out if charge transport also exists in DNA chains with different base pairs. In this paper, we address this problem in its simple case, a homogeneous chain except for a single different base pair, which we call a base-pair inhomogeneity, and its effect on charge transport. Radial polarons experience either reflection or trapping. However, twist polarons are good candidates for charge transport along real DNA. This transport is also very robust with respect to weak parametric and diagonal disorder

  10. Zero-Magnetic-Field Spin Splitting of Polaron's Ground State Energy Induced by Rashba Spin-Orbit Interaction

    International Nuclear Information System (INIS)

    Liu Jia; Xiao Jingling

    2006-01-01

    We study theoretically the ground state energy of a polaron near the interface of a polar-polar semiconductor by considering the Rashba spin-orbit (SO) coupling with the Lee-Low-Pines intermediate coupling method. Our numerical results show that the Rashba SO interaction originating from the inversion asymmetry in the heterostructure splits the ground state energy of the polaron. The electron areal density and vector dependence of the ratio of the SO interaction to the total ground state energy or other energy composition are obvious. One can see that even without any external magnetic field, the ground state energy can be split by the Rashba SO interaction, and this split is not a single but a complex one. Since the presents of the phonons, whose energy gives negative contribution to the polaron's, the spin-splitting states of the polaron are more stable than electron's.

  11. Recursive tridiagonalization of infinite dimensional Hamiltonians

    International Nuclear Information System (INIS)

    Haydock, R.; Oregon Univ., Eugene, OR

    1989-01-01

    Infinite dimensional, computable, sparse Hamiltonians can be numerically tridiagonalized to finite precision using a three term recursion. Only the finite number of components whose relative magnitude is greater than the desired precision are stored at any stage in the computation. Thus the particular components stored change as the calculation progresses. This technique avoids errors due to truncation of the orbital set, and makes terminators unnecessary in the recursion method. (orig.)

  12. Hamiltonian theory of guiding-center motion

    International Nuclear Information System (INIS)

    Littlejohn, R.G.

    1980-05-01

    A Hamiltonian treatment of the guiding center problem is given which employs noncanonical coordinates in phase space. Separation of the unperturbed system from the perturbation is achieved by using a coordinate transformation suggested by a theorem of Darboux. As a model to illustrate the method, motion in the magnetic field B=B(x,y)z is studied. Lie transforms are used to carry out the perturbation expansion

  13. Symplectic Geometric Algorithms for Hamiltonian Systems

    CERN Document Server

    Feng, Kang

    2010-01-01

    "Symplectic Geometry Algorithms for Hamiltonian Systems" will be useful not only for numerical analysts, but also for those in theoretical physics, computational chemistry, celestial mechanics, etc. The book generalizes and develops the generating function and Hamilton-Jacobi equation theory from the perspective of the symplectic geometry and symplectic algebra. It will be a useful resource for engineers and scientists in the fields of quantum theory, astrophysics, atomic and molecular dynamics, climate prediction, oil exploration, etc. Therefore a systematic research and development

  14. The Effective Hamiltonian in the Scalar Electrodynamics

    CERN Document Server

    Dineykhan, M D; Zhaugasheva, S A; Sakhyev, S K

    2002-01-01

    On the basis of an investigation of the asymptotic behaviour of the polarization loop for the scalar particles in the external electromagnetic field the relativistic corrections to the Hamiltonian are determined. The constituent mass of the particles in the bound state is analytically derived. It is shown that the constituent mass of the particles differs from the mass of the particles in the free state. The corrections connected with the Thomas precession have been calculated.

  15. Symplectic topology of integrable Hamiltonian systems

    International Nuclear Information System (INIS)

    Nguyen Tien Zung.

    1993-08-01

    We study the topology of integrable Hamiltonian systems, giving the main attention to the affine structure of their orbit spaces. In particular, we develop some aspects of Fomenko's theory about topological classification of integrable non-degenerate systems, and consider some relations between such systems and ''pure'' contact and symplectic geometry. We give a notion of integrable surgery and use it to obtain some interesting symplectic structures. (author). Refs, 10 figs

  16. Hamiltonian description and quantization of dissipative systems

    Science.gov (United States)

    Enz, Charles P.

    1994-09-01

    Dissipative systems are described by a Hamiltonian, combined with a “dynamical matrix” which generalizes the simplectic form of the equations of motion. Criteria for dissipation are given and the examples of a particle with friction and of the Lotka-Volterra model are presented. Quantization is first introduced by translating generalized Poisson brackets into commutators and anticommutators. Then a generalized Schrödinger equation expressed by a dynamical matrix is constructed and discussed.

  17. Hamiltonian theory of guiding-center motion

    Energy Technology Data Exchange (ETDEWEB)

    Littlejohn, R.G.

    1980-05-01

    A Hamiltonian treatment of the guiding center problem is given which employs noncanonical coordinates in phase space. Separation of the unperturbed system from the perturbation is achieved by using a coordinate transformation suggested by a theorem of Darboux. As a model to illustrate the method, motion in the magnetic field B=B(x,y)z is studied. Lie transforms are used to carry out the perturbation expansion.

  18. Large-scale stochasticity in Hamiltonian systems

    International Nuclear Information System (INIS)

    Escande, D.F.

    1982-01-01

    Large scale stochasticity (L.S.S.) in Hamiltonian systems is defined on the paradigm Hamiltonian H(v,x,t) =v 2 /2-M cos x-P cos k(x-t) which describes the motion of one particle in two electrostatic waves. A renormalization transformation Tsub(r) is described which acts as a microscope that focusses on a given KAM (Kolmogorov-Arnold-Moser) torus in phase space. Though approximate, Tsub(r) yields the threshold of L.S.S. in H with an error of 5-10%. The universal behaviour of KAM tori is predicted: for instance the scale invariance of KAM tori and the critical exponent of the Lyapunov exponent of Cantori. The Fourier expansion of KAM tori is computed and several conjectures by L. Kadanoff and S. Shenker are proved. Chirikov's standard mapping for stochastic layers is derived in a simpler way and the width of the layers is computed. A simpler renormalization scheme for these layers is defined. A Mathieu equation for describing the stability of a discrete family of cycles is derived. When combined with Tsub(r), it allows to prove the link between KAM tori and nearby cycles, conjectured by J. Greene and, in particular, to compute the mean residue of a torus. The fractal diagrams defined by G. Schmidt are computed. A sketch of a methodology for computing the L.S.S. threshold in any two-degree-of-freedom Hamiltonian system is given. (Auth.)

  19. NLO renormalization in the Hamiltonian truncation

    Science.gov (United States)

    Elias-Miró, Joan; Rychkov, Slava; Vitale, Lorenzo G.

    2017-09-01

    Hamiltonian truncation (also known as "truncated spectrum approach") is a numerical technique for solving strongly coupled quantum field theories, in which the full Hilbert space is truncated to a finite-dimensional low-energy subspace. The accuracy of the method is limited only by the available computational resources. The renormalization program improves the accuracy by carefully integrating out the high-energy states, instead of truncating them away. In this paper, we develop the most accurate ever variant of Hamiltonian Truncation, which implements renormalization at the cubic order in the interaction strength. The novel idea is to interpret the renormalization procedure as a result of integrating out exactly a certain class of high-energy "tail states." We demonstrate the power of the method with high-accuracy computations in the strongly coupled two-dimensional quartic scalar theory and benchmark it against other existing approaches. Our work will also be useful for the future goal of extending Hamiltonian truncation to higher spacetime dimensions.

  20. Redesign of the DFT/MRCI Hamiltonian

    Energy Technology Data Exchange (ETDEWEB)

    Lyskov, Igor; Kleinschmidt, Martin; Marian, Christel M., E-mail: Christel.Marian@hhu.de [Institute of Theoretical and Computational Chemistry, Heinrich-Heine-University Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf (Germany)

    2016-01-21

    The combined density functional theory and multireference configuration interaction (DFT/MRCI) method of Grimme and Waletzke [J. Chem. Phys. 111, 5645 (1999)] is a well-established semi-empirical quantum chemical method for efficiently computing excited-state properties of organic molecules. As it turns out, the method fails to treat bi-chromophores owing to the strong dependence of the parameters on the excitation class. In this work, we present an alternative form of correcting the matrix elements of a MRCI Hamiltonian which is built from a Kohn-Sham set of orbitals. It is based on the idea of constructing individual energy shifts for each of the state functions of a configuration. The new parameterization is spin-invariant and incorporates less empirism compared to the original formulation. By utilizing damping techniques together with an algorithm of selecting important configurations for treating static electron correlation, the high computational efficiency has been preserved. The robustness of the original and redesigned Hamiltonians has been tested on experimentally known vertical excitation energies of organic molecules yielding similar statistics for the two parameterizations. Besides that, our new formulation is free from artificially low-lying doubly excited states, producing qualitatively correct and consistent results for excimers. The way of modifying matrix elements of the MRCI Hamiltonian presented here shall be considered as default choice when investigating photophysical processes of bi-chromophoric systems such as singlet fission or triplet-triplet upconversion.

  1. A new DFT approach to model small polarons in oxides with proper account for long-range polarization

    Science.gov (United States)

    Kokott, Sebastian; Levchenko, Sergey V.; Scheffler, Matthias; Theory Department Team

    In this work, we address two important challenges in the DFT description of small polarons (excess charges localized within one unit cell): sensitivity to the errors in exchange-correlation (XC) treatment and finite-size effects in supercell calculations. The polaron properties are obtained using a modified neutral potential-energy surface (PES). Using the hybrid HSE functional and considering the whole range 0 Deutsche Forschungsgemeinschaft).

  2. Multi-Hamiltonian formulations and stability of higher-derivative extensions of 3d Chern-Simons

    Energy Technology Data Exchange (ETDEWEB)

    Abakumova, V.A.; Kaparulin, D.S.; Lyakhovich, S.L. [Tomsk State University, Physics Faculty, Tomsk (Russian Federation)

    2018-02-15

    Most general third-order 3d linear gauge vector field theory is considered. The field equations involve, besides the mass, two dimensionless constant parameters. The theory admits two-parameter series of conserved tensors with the canonical energy-momentum being a particular representative of the series. For a certain range of the model parameters, the series of conserved tensors include bounded quantities. This makes the dynamics classically stable, though the canonical energy is unbounded in all the instances. The free third-order equations are shown to admit constrained multi-Hamiltonian form with the 00-components of conserved tensors playing the roles of corresponding Hamiltonians. The series of Hamiltonians includes the canonical Ostrogradski's one, which is unbounded. The Hamiltonian formulations with different Hamiltonians are not connected by canonical transformations. This means, the theory admits inequivalent quantizations at the free level. Covariant interactions are included with spinor fields such that the higher-derivative dynamics remains stable at interacting level if the bounded conserved quantity exists in the free theory. In the first-order formalism, the interacting theory remains Hamiltonian and therefore it admits quantization, though the vertices are not necessarily Lagrangian in the third-order field equations. (orig.)

  3. Hall effect driven by non-collinear magnetic polarons in diluted magnetic semiconductors

    Science.gov (United States)

    Denisov, K. S.; Averkiev, N. S.

    2018-04-01

    In this letter, we develop the theory of Hall effect driven by non-collinear magnetic textures (topological Hall effect—THE) in diluted magnetic semiconductors (DMSs). We show that a carrier spin-orbit interaction induces a chiral magnetic ordering inside a bound magnetic polaron (BMP). The inner structure of non-collinear BMP is controlled by the type of spin-orbit coupling, allowing us to create skyrmion- (Rashba) or antiskyrmion-like (Dresselhaus) configurations. The asymmetric scattering of itinerant carriers on polarons leads to the Hall response which exists in weak external magnetic fields and at low temperatures. We point out that DMS-based systems allow one to investigate experimentally the dependence of THE both on a carrier spin polarization and on a non-collinear magnetic texture shape.

  4. One dimensional polaron effects and current inhomogeneities in sequential phonon emission

    Energy Technology Data Exchange (ETDEWEB)

    Hellman, E.S.; Harris, J.S.; Hanna, C.; Laughlin, R.B.

    1985-07-01

    We have constructed a physical model to explain the tunneling current oscillations reported by Hickmott et al., for GaAs/AlGaAs heterostructures in high magnetic fields. We propose that the periodic structure observed is due to space charge which builds up in the undepleted layer when electrons enter it with energy just below the phonon emission threshold. Such electrons interact with the lattice to form polarons whose energy is pinned to the phonon energy, and thus has a very small group velocity. The polaron effect is strongly enhanced by the confinement of the electrons by the strong magnetic field. We infer from the current-voltage data that most of the tunneling current flows through a small area of the sample. The combined model gives reasonable quantitative agreement with experiment. 6 refs., 6 figs.

  5. Impact of morphology on polaron delocalization in a semicrystalline conjugated polymer

    KAUST Repository

    Steyrleuthner, Robert

    2016-12-20

    We investigate the delocalization of holes in the semicrystalline conjugated polymer poly(2,5-bis(3-alkylthiophene-2-yl)thieno[3,2-b]thiophene) (PBTTT) by directly measuring the hyperfine coupling between photogenerated polarons and bound nuclear spins using electron nuclear double resonance spectroscopy. An extrapolation of the corresponding oligomer spectra reveals that charges tend to delocalize over 4.0-4.8 nm with delocalization strongly dependent on molecular order and crystallinity of the PBTTT polymer thin films. Density functional theory calculations of hyperfine couplings confirm that long-range corrected functionals appropriately describe the change in coupling strength with increasing oligomer size and agree well with the experimentally measured polymer limit. Our discussion presents general guidelines illustrating the various pitfalls and opportunities when deducing polaron localization lengths from hyperfine coupling spectra of conjugated polymers.

  6. Two Impurities in a Bose-Einstein Condensate: From Yukawa to Efimov Attracted Polarons

    Science.gov (United States)

    Naidon, Pascal

    2018-04-01

    The well-known Yukawa and Efimov potentials are two different mediated interaction potentials. The first one arises in quantum field theory from the exchange of virtual particles. The second one is mediated by a real particle resonantly interacting with two other particles. This Letter shows how two impurities immersed in a Bose-Einstein condensate can exhibit both phenomena. For a weak attraction with the condensate, the two impurities form two polarons that interact through a weak Yukawa attraction mediated by virtual excitations. For a resonant attraction with the condensate, the exchanged excitation becomes a real boson and the mediated interaction changes to a strong Efimov attraction that can bind the two polarons. The resulting bipolarons turn into in-medium Efimov trimers made of the two impurities and one boson. Evidence of this physics could be seen in ultracold mixtures of atoms.

  7. Transport and ordering of polarons in CER manganites PrCaMnO

    International Nuclear Information System (INIS)

    Schramm, S; Hoffmann, J; Jooss, Ch

    2008-01-01

    The temperature-dependent resistivity and the colossal resistance effect induced by strong electric fields of the small-band Pr 1-x Ca x MnO 3 (PCMO) manganites are analysed with respect to the influence of the Ca doping, post-annealing, the prehistory of the electric stimulation, and the physical dimensions of the sample. Despite the phase separation between charge and orbital ordered and disordered phases, PCMO reveals the properties of a homogeneous medium with a conductivity governed by the hopping of small polarons if the electric field is not too strong. In contrast, high electric fields induce a structural transition which gives rise to a glassy behaviour in the transient regime. In the low resistance state the small activation energy of charge carrier hopping implies a transition to large polaron hopping

  8. One dimensional polaron effects and current inhomogeneities in sequential phonon emission

    International Nuclear Information System (INIS)

    Hellman, E.S.; Harris, J.S.; Hanna, C.; Laughlin, R.B.

    1985-07-01

    We have constructed a physical model to explain the tunneling current oscillations reported by Hickmott et al., for GaAs/AlGaAs heterostructures in high magnetic fields. We propose that the periodic structure observed is due to space charge which builds up in the undepleted layer when electrons enter it with energy just below the phonon emission threshold. Such electrons interact with the lattice to form polarons whose energy is pinned to the phonon energy, and thus has a very small group velocity. The polaron effect is strongly enhanced by the confinement of the electrons by the strong magnetic field. We infer from the current-voltage data that most of the tunneling current flows through a small area of the sample. The combined model gives reasonable quantitative agreement with experiment. 6 refs., 6 figs

  9. Small polaron formation and motion of holes in a-SiO2

    International Nuclear Information System (INIS)

    Hughes, R.C.; Emin, D.

    1978-01-01

    X-ray generated holes in SiO 2 are observed to be reduced to low mobility in times of the order of vibrational periods, 10 -12 s. The temperature dependence, electric field dependence and magnitude of this mobility for times up to about 100 ns are consistent with those of hole-like small polarons. The circumstances which favor the occurrence of rapid small polaron formation are a large effective mass (narrow valence band), the presence of the long-range hole-lattice interaction characteristic of an ionic material and the presence of disorder, all of which are found in amorphous SiO 2 . An alternative explanation involving trapping requires an extremely large localized state density and fortuitous temperature and field dependences of the hopping rates

  10. Generalized formula for electron emission taking account of the polaron effect

    Science.gov (United States)

    Barengolts, Yu A.; Beril, S. I.; Barengolts, S. A.

    2018-01-01

    A generalized formula is derived for the electron emission current as a function of temperature, field, and electron work function in a metal-dielectric system that takes account of the quantum nature of the image forces. In deriving the formula, the Fermi-Dirac distribution for electrons in a metal and the quantum potential of the image obtained in the context of electron polaron theory are used.

  11. Dynamics of the optically-induced properties of a small-polaronic glass

    International Nuclear Information System (INIS)

    Emin, D.

    1979-01-01

    The relaxation and recombination of an electronic excitation created by the absorption of a super-band-gap photon is considered for a system in which excitons and charge carriers find it energetically favorable to self-trap. The notions of a barrier to self-trapping, a short-range repulsion between electrons and holes, and the electromodulation of the small-polaron absorption band play a central role in this discussion. The results are consistent with experiments on chalcogenide glasses

  12. Quantum fluctuations of D5d polarons on C60 molecules

    International Nuclear Information System (INIS)

    Wang Chui-Lin; Wang Wenzheng; Liu Yuliang; Su Zhaobin; Yu Lu.

    1994-06-01

    The dynamic Jahn-Teller splitting of the six equivalent D 5d polarons due to quantum fluctuations is studied in the framework of the Bogoliubov-de Gennes formalism. The tunneling induced level splittings are determined to be 2 T 1u + 2 T 2u and 1 A g + 1 H g for C 1- 60 and C -2 60 , respectively, which should give rise to observable effects in experiments. (author). 17 refs, 2 tabs

  13. Spectral Signatures of Polarons in Conjugated Co-polymers

    NARCIS (Netherlands)

    Wiebeler, Christian; Tautz, Raphael; Feldmann, Jochen; von Hauff, Elizabeth; Da Como, Enrico; Schumacher, Stefan

    2013-01-01

    We study electronic and optical properties of the low-bandgap co-polymer PCPDT-BT (poly-cyclopentadithiophene-co-benzothiadiazole) and compare it with the corresponding homo-polymer PCPDT (poly-cyclopentadithiophene). We investigate the linear absorptivity in these systems for neutral molecules and

  14. Polaron self-localization in white-light emitting hybrid perovskites

    KAUST Repository

    Cortecchia, Daniele

    2017-02-03

    Two-dimensional (2D) perovskites with the general formula APbX are attracting increasing interest as solution processable, white-light emissive materials. Recent studies have shown that their broadband emission is related to the formation of intra-gap colour centres. Here, we provide an in-depth description of the charge localization sites underlying the generation of such radiative centres and their corresponding decay dynamics, highlighting the formation of small polarons trapped within their lattice distortion field. Using a combination of spectroscopic techniques and first-principles calculations to study the white-light emitting 2D perovskites (EDBE)PbCl and (EDBE)PbBr, we infer the formation of Pb , Pb, and X (where X = Cl or Br) species confined within the inorganic perovskite framework. Due to strong Coulombic interactions, these species retain their original excitonic character and form self-trapped polaron-excitons acting as radiative colour centres. These findings are expected to be relevant for a broad class of white-light emitting perovskites with large polaron relaxation energy.

  15. Holstein polaron in a valley-degenerate two-dimensional semiconductor.

    Science.gov (United States)

    Kang, Mingu; Jung, Sung Won; Shin, Woo Jong; Sohn, Yeongsup; Ryu, Sae Hee; Kim, Timur K; Hoesch, Moritz; Kim, Keun Su

    2018-05-28

    Two-dimensional (2D) crystals have emerged as a class of materials with tunable carrier density 1 . Carrier doping to 2D semiconductors can be used to modulate many-body interactions 2 and to explore novel composite particles. The Holstein polaron is a small composite particle of an electron that carries a cloud of self-induced lattice deformation (or phonons) 3-5 , which has been proposed to play a key role in high-temperature superconductivity 6 and carrier mobility in devices 7 . Here we report the discovery of Holstein polarons in a surface-doped layered semiconductor, MoS 2 , in which a puzzling 2D superconducting dome with the critical temperature of 12 K was found recently 8-11 . Using a high-resolution band mapping of charge carriers, we found strong band renormalizations collectively identified as a hitherto unobserved spectral function of Holstein polarons 12-18 . The short-range nature of electron-phonon (e-ph) coupling in MoS 2 can be explained by its valley degeneracy, which enables strong intervalley coupling mediated by acoustic phonons. The coupling strength is found to increase gradually along the superconducting dome up to the intermediate regime, which suggests a bipolaronic pairing in the 2D superconductivity.

  16. DFT +U Modeling of Hole Polarons in Organic Lead Halide Perovskites

    Science.gov (United States)

    Welch, Eric; Erhart, Paul; Scolfaro, Luisa; Zakhidov, Alex

    Due to the ever present drive towards improved efficiencies in solar cell technology, new and improved materials are emerging rapidly. Organic halide perovskites are a promising prospect, yet a fundamental understanding of the organic perovskite structure and electronic properties is missing. Particularly, explanations of certain physical phenomena, specifically a low recombination rate and high mobility of charge carriers still remain controversial. We theoretically investigate possible formation of hole polarons adopting methodology used for oxide perovskites. The perovskite studied here is the ABX3structure, with A being an organic cation, B lead and C a halogen; the combinations studied allow for A1,xA2 , 1 - xBX1,xX2 , 3 - xwhere the alloy convention is used to show mixtures of the organic cations and/or the halogens. Two organic cations, methylammonium and formamidinium, and three halogens, iodine, chlorine and bromine are studied. Electronic structures and polaron behavior is studied through first principle density functional theory (DFT) calculations using the Vienna Ab Initio Simulation Package (VASP). Local density approximation (LDA) pseudopotentials are used and a +U Hubbard correction of 8 eV is added; this method was shown to work with oxide perovskites. It is shown that a localized state is realized with the Hubbard correction in systems with an electron removed, residing in the band gap of each different structure. Thus, hole polarons are expected to be seen in these perovskites.

  17. Influence of quasi-particle density over polaron mobility in armchair graphene nanoribbons.

    Science.gov (United States)

    Silva, Gesiel Gomes; da Cunha, Wiliam Ferreira; de Sousa Junior, Rafael Timóteo; Almeida Fonseca, Antonio Luciano; Ribeiro Júnior, Luiz Antônio; E Silva, Geraldo Magela

    2018-06-20

    An important aspect concerning the performance of armchair graphene nanoribbons (AGNRs) as materials for conceiving electronic devices is related to the mobility of charge carriers in these systems. When several polarons are considered in the system, a quasi-particle wave function can be affected by that of its neighbor provided the two are close enough. As the overlap may affect the transport of the carrier, the question concerning how the density of polarons affect its mobility arises. In this work, we investigate such dependence for semiconducting AGNRs in the scope of nonadiabatic molecular dynamics. Our results unambiguously show an impact of the density on both the stability and average velocity of the quasi-particles. We have found a phase transition between regimes where increasing density stops inhibiting and starts promoting mobility; densities higher than 7 polarons per 45 Å present increasing mean velocity with increasing density. We have also established three different regions relating electric field and average velocity. For the lowest electric field regime, surpassing the aforementioned threshold results in overcoming the 0.3 Å fs-1 limit, thus representing a transition between subsonic and supersonic regimes. For the highest of the electric fields, density effects alone are responsible for a stunning difference of 1.5 Å fs-1 in the mean carrier velocity.

  18. Finite temperature dynamics of a Holstein polaron: The thermo-field dynamics approach

    Science.gov (United States)

    Chen, Lipeng; Zhao, Yang

    2017-12-01

    Combining the multiple Davydov D2 Ansatz with the method of thermo-field dynamics, we study finite temperature dynamics of a Holstein polaron on a lattice. It has been demonstrated, using the hierarchy equations of motion method as a benchmark, that our approach provides an efficient, robust description of finite temperature dynamics of the Holstein polaron in the simultaneous presence of diagonal and off-diagonal exciton-phonon coupling. The method of thermo-field dynamics handles temperature effects in the Hilbert space with key numerical advantages over other treatments of finite-temperature dynamics based on quantum master equations in the Liouville space or wave function propagation with Monte Carlo importance sampling. While for weak to moderate diagonal coupling temperature increases inhibit polaron mobility, it is found that off-diagonal coupling induces phonon-assisted transport that dominates at high temperatures. Results on the mean square displacements show that band-like transport features dominate the diagonal coupling cases, and there exists a crossover from band-like to hopping transport with increasing temperature when including off-diagonal coupling. As a proof of concept, our theory provides a unified treatment of coherent and incoherent transport in molecular crystals and is applicable to any temperature.

  19. Energy Migration in Organic Thin Films--From Excitons to Polarons

    Science.gov (United States)

    Mullenbach, Tyler K.

    The rise of organic photovoltaic devices (OPVs) and organic light-emitting devices has generated interest in the physics governing exciton and polaron dynamics in thin films. Energy transfer has been well studied in dilute solutions, but there are emergent properties in thin films and greater complications due to complex morphologies which must be better understood. Despite the intense interest in energy transport in thin films, experimental limitations have slowed discoveries. Here, a new perspective of OPV operation is presented where photovoltage, instead of photocurrent, plays the fundamental role. By exploiting this new vantage point the first method of measuring the diffusion length (LD) of dark (non-luminescent) excitons is developed, a novel photodetector is invented, and the ability to watch exciton arrival, in real-time, at the donor-acceptor heterojunction is presented. Using an enhanced understanding of exciton migration in thin films, paradigms for enhancing LD by molecular modifications are discovered, and the first exciton gate is experimentally and theoretically demonstrated. Generation of polarons from exciton dissociation represents a second phase of energy migration in OPVs that remains understudied. Current approaches are capable of measuring the rate of charge carrier recombination only at open-circuit. To enable a better understanding of polaron dynamics in thin films, two new approaches are presented which are capable of measuring both the charge carrier recombination and transit rates at any OPV operating voltage. These techniques pave the way for a more complete understanding of charge carrier kinetics in molecular thin films.

  20. Structural correlations in the generation of polaron pairs in low-bandgap polymers for photovoltaics

    Science.gov (United States)

    Tautz, Raphael; da Como, Enrico; Limmer, Thomas; Feldmann, Jochen; Egelhaaf, Hans-Joachim; von Hauff, Elizabeth; Lemaur, Vincent; Beljonne, David; Yilmaz, Seyfullah; Dumsch, Ines; Allard, Sybille; Scherf, Ullrich

    2012-07-01

    Polymeric semiconductors are materials where unique optical and electronic properties often originate from a tailored chemical structure. This allows for synthesizing conjugated macromolecules with ad hoc functionalities for organic electronics. In photovoltaics, donor-acceptor co-polymers, with moieties of different electron affinity alternating on the chain, have attracted considerable interest. The low bandgap offers optimal light-harvesting characteristics and has inspired work towards record power conversion efficiencies. Here we show for the first time how the chemical structure of donor and acceptor moieties controls the photogeneration of polaron pairs. We show that co-polymers with strong acceptors show large yields of polaron pair formation up to 24% of the initial photoexcitations as compared with a homopolymer (η=8%). π-conjugated spacers, separating the donor and acceptor centre of masses, have the beneficial role of increasing the recombination time. The results provide useful input into the understanding of polaron pair photogeneration in low-bandgap co-polymers for photovoltaics.

  1. Optical Characterization of the Hole Polaron in a Series of Diketopyrrolopyrrole Polymers Used for Organic Photovoltaics

    Directory of Open Access Journals (Sweden)

    Evan L. Williams

    2014-12-01

    Full Text Available A strategy that is often used for designing low band gap polymers involves the incorporation of electron-rich (donor and electron-deficient (acceptor conjugated segments within the polymer backbone. In this paper we investigate such a series of Diketopyrrolopyrrole (DPP-based co-polymers. The co-polymers consisted of a DPP unit attached to a phenylene, naphthalene, or anthracene unit. Additionally, polymers utilizing either the thiophene-flanked DPP or the furan-flanked DPP units paired with the naphthalene comonomer were compared. As these polymers have been used as donor materials and subsequent hole transporting materials in organic solar cells, we are specifically interested in characterizing the optical absorption of the hole polaron of these DPP based copolymers. We employ chemical doping, electrochemical doping, and photoinduced absorption (PIA studies to probe the hole polaron absorption spectra. While some donor-acceptor polymers have shown an appreciable capacity to generate free charge carriers upon photoexcitation, no polaron signal was observed in the PIA spectrum of the polymers in this study. The relations between molecular structure and optical properties are discussed.

  2. Photoelectron spectroscopy on the charge reorganization energy and small polaron binding energy of molecular film

    Energy Technology Data Exchange (ETDEWEB)

    Kera, Satoshi, E-mail: kera@ims.ac.jp [Institute for Molecular Science, Myodaiji, Okazaki 444-8585 (Japan); Department of Nanomaterial Science, Graduate School of Advanced Integration Science, Chiba University, Inage-ku, Chiba 263-8522 (Japan); Ueno, Nobuo [Department of Nanomaterial Science, Graduate School of Advanced Integration Science, Chiba University, Inage-ku, Chiba 263-8522 (Japan)

    2015-10-01

    Understanding of electron-phonon coupling as well as intermolecular interaction is required to discuss the mobility of charge carrier in functional molecular solids. This article summarizes recent progress in direct measurements of valence hole-vibration coupling in ultrathin films of organic semiconductors by using ultraviolet photoelectron spectroscopy (UPS). The experimental study of hole-vibration coupling of the highest occupied molecular orbital (HOMO) state in ordered monolayer film by UPS is essential to comprehend hole-hopping transport and small-polaron related transport in organic semiconductors. Only careful measurements can attain the high-resolution spectra and provide key parameters in hole-transport dynamics, namely the charge reorganization energy and small polaron binding energy. Analyses methods of the UPS HOMO fine feature and resulting charge reorganization energy and small polaron binding energy are described for pentacene and perfluoropentacene films. Difference between thin-film and gas-phase results is discussed by using newly measured high-quality gas-phase spectra of pentacene. Methodology for achieving high-resolution UPS measurements for molecular films is also described.

  3. First-principles lattice-gas Hamiltonian revisited: O-Pd(100)

    OpenAIRE

    Kappus, Wolfgang

    2016-01-01

    The methodology of deriving an adatom lattice-gas Hamiltonian (LGH) from first principles (FP) calculations is revisited. Such LGH cluster expansions compute a large set of lateral pair-, trio-, quarto interactions by solving a set of linear equations modelling regular adatom configurations and their FP energies. The basic assumption of truncating interaction terms beyond fifth nearest neighbors does not hold when adatoms show longer range interactions, e.g. substrate mediated elastic interac...

  4. A novel hierarchy of differential—integral equations and their generalized bi-Hamiltonian structures

    International Nuclear Information System (INIS)

    Zhai Yun-Yun; Geng Xian-Guo; He Guo-Liang

    2014-01-01

    With the aid of the zero-curvature equation, a novel integrable hierarchy of nonlinear evolution equations associated with a 3 × 3 matrix spectral problem is proposed. By using the trace identity, the bi-Hamiltonian structures of the hierarchy are established with two skew-symmetric operators. Based on two linear spectral problems, we obtain the infinite many conservation laws of the first member in the hierarchy

  5. On the asymptotic form of the recursion method basis vectors for periodic Hamiltonians

    International Nuclear Information System (INIS)

    O'Reilly, E.P.; Weaire, D.

    1984-01-01

    The authors present the first detailed study of the recursion method basis vectors for the case of a periodic Hamiltonian. In the examples chosen, the probability density scales linearly with n as n → infinity, whenever the local density of states is bounded. Whenever it is unbounded and the recursion coefficients diverge, different scaling behaviour is found. These findings are explained and a scaling relationship between the asymptotic forms of the recursion coefficients and basis vectors is proposed. (author)

  6. Interpolation approach to Hamiltonian-varying quantum systems and the adiabatic theorem

    International Nuclear Information System (INIS)

    Pan, Yu; James, Matthew R.; Miao, Zibo; Amini, Nina H.; Ugrinovskii, Valery

    2015-01-01

    Quantum control could be implemented by varying the system Hamiltonian. According to adiabatic theorem, a slowly changing Hamiltonian can approximately keep the system at the ground state during the evolution if the initial state is a ground state. In this paper we consider this process as an interpolation between the initial and final Hamiltonians. We use the mean value of a single operator to measure the distance between the final state and the ideal ground state. This measure resembles the excitation energy or excess work performed in thermodynamics, which can be taken as the error of adiabatic approximation. We prove that under certain conditions, this error can be estimated for an arbitrarily given interpolating function. This error estimation could be used as guideline to induce adiabatic evolution. According to our calculation, the adiabatic approximation error is not linearly proportional to the average speed of the variation of the system Hamiltonian and the inverse of the energy gaps in many cases. In particular, we apply this analysis to an example in which the applicability of the adiabatic theorem is questionable. (orig.)

  7. Extension of the CPT theorem to non-Hermitian Hamiltonians and unstable states

    Energy Technology Data Exchange (ETDEWEB)

    Mannheim, Philip D., E-mail: philip.mannheim@uconn.edu

    2016-02-10

    We extend the CPT theorem to quantum field theories with non-Hermitian Hamiltonians and unstable states. Our derivation is a quite minimal one as it requires only the time-independent evolution of scalar products, invariance under complex Lorentz transformations, and a non-standard but nonetheless perfectly legitimate interpretation of charge conjugation as an antilinear operator. The first of these requirements does not force the Hamiltonian to be Hermitian. Rather, it forces its eigenvalues to either be real or to appear in complex conjugate pairs, forces the eigenvectors of such conjugate pairs to be conjugates of each other, and forces the Hamiltonian to admit of an antilinear symmetry. The latter two requirements then force this antilinear symmetry to be CPT, while forcing the Hamiltonian to be real rather than Hermitian. Our work justifies the use of the CPT theorem in establishing the equality of the lifetimes of unstable particles that are charge conjugates of each other. We show that the Euclidean time path integrals of a CPT-symmetric theory must always be real. In the quantum-mechanical limit the key results of the PT symmetry program of Bender and collaborators are recovered, with the C-operator of the PT symmetry program being identified with the linear component of the charge conjugation operator.

  8. Quantum Hamiltonian reduction and conformal field theories

    International Nuclear Information System (INIS)

    Bershadsky, M.

    1991-01-01

    It is proved that irreducible representation of the Virasoro algebra can be extracted from an irreducible representation space of the SL (2, R) current algebra by putting a constraint on the latter using the BRST formalism. Thus there is a SL(2, R) symmetry in the Virasoro algebra which is gauged and hidden. This construction of the Virasoro algebra is the quantum analog of the Hamiltonian reduction. The author then naturally leads to consider an SL(2, R) Wess-Zumino-Witten model. This system is related to the quantum field theory of the coadjoint orbit of the Virasoro group. Based on this result he presents the canonical derivation of the SL(2, R) current algebra in Polyakov's theory of two dimensional gravity; it is manifestation of the SL(2, R) symmetry in the conformal field theory hidden by the quantum Hamiltonian reduction. He discusses the quantum Hamiltonian reduction of the SL(n, R) current algebra for the general type of constraints labeled by index 1 ≤ l ≤ (n - 1) and claim that it leads to the new extended conformal algebras W n l . For l = 1 he recovers the well known W n algebra introduced by A. Zamolodchikov. For SL(3, R) Wess-Zumino-Witten model there are two different possibilities of constraining it. The first possibility gives the W 3 algebra, while the second leads to the new chiral algebra W 3 2 generated by the stress-energy tensor, two bosonic supercurrents with spins 3/2 and the U(1) current. He conjectures a Kac formula that describes the highly reducible representation for this algebra. He also makes some speculations concerning the structure of W gravity

  9. Classical effective Hamiltonians, Wigner functions, and the sign problem

    International Nuclear Information System (INIS)

    Samson, J.H.

    1995-01-01

    In the functional-integral technique an auxiliary field, coupled to appropriate operators such as spins, linearizes the interaction term in a quantum many-body system. The partition function is then averaged over this time-dependent stochastic field. Quantum Monte Carlo methods evaluate this integral numerically, but suffer from the sign (or phase) problem: the integrand may not be positive definite (or not real). It is shown that, in certain cases that include the many-band Hubbard model and the Heisenberg model, the sign problem is inevitable on fundamental grounds. Here, Monte Carlo simulations generate a distribution of incompatible operators---a Wigner function---from which expectation values and correlation functions are to be calculated; in general no positive-definite distribution of this form exists. The distribution of time-averaged auxiliary fields is the convolution of this operator distribution with a Gaussian of variance proportional to temperature, and is interpreted as a Boltzmann distribution exp(-βV eff ) in classical configuration space. At high temperatures and large degeneracies this classical effective Hamiltonian V eff tends to the static approximation as a classical limit. In the low-temperature limit the field distribution becomes a Wigner function, the sign problem occurs, and V eff is complex. Interpretations of the distributions, and a criterion for their positivity, are discussed. The theory is illustrated by an exact evaluation of the Wigner function for spin s and the effective classical Hamiltonian for the spin-1/2 van der Waals model. The field distribution can be negative here, more noticeably if the number of spins is odd

  10. Integrable Time-Dependent Quantum Hamiltonians

    Science.gov (United States)

    Sinitsyn, Nikolai A.; Yuzbashyan, Emil A.; Chernyak, Vladimir Y.; Patra, Aniket; Sun, Chen

    2018-05-01

    We formulate a set of conditions under which the nonstationary Schrödinger equation with a time-dependent Hamiltonian is exactly solvable analytically. The main requirement is the existence of a non-Abelian gauge field with zero curvature in the space of system parameters. Known solvable multistate Landau-Zener models satisfy these conditions. Our method provides a strategy to incorporate time dependence into various quantum integrable models while maintaining their integrability. We also validate some prior conjectures, including the solution of the driven generalized Tavis-Cummings model.

  11. Discrete variable representation for singular Hamiltonians

    DEFF Research Database (Denmark)

    Schneider, B. I.; Nygaard, Nicolai

    2004-01-01

    We discuss the application of the discrete variable representation (DVR) to Schrodinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based...... solely on an orthogonal polynomial basis is adequate, provided the Gauss-Lobatto or Gauss-Radau quadrature rule is used. This ensures that the mesh contains the singular points and by simply discarding the DVR functions corresponding to those points, all matrix elements become well behaved. the boundary...

  12. Resonant driving of a nonlinear Hamiltonian system

    International Nuclear Information System (INIS)

    Palmisano, Carlo; Gervino, Gianpiero; Balma, Massimo; Devona, Dorina; Wimberger, Sandro

    2013-01-01

    As a proof of principle, we show how a classical nonlinear Hamiltonian system can be driven resonantly over reasonably long times by appropriately shaped pulses. To keep the parameter space reasonably small, we limit ourselves to a driving force which consists of periodic pulses additionally modulated by a sinusoidal function. The main observables are the average increase of kinetic energy and of the action variable (of the non-driven system) with time. Applications of our scheme aim for driving high frequencies of a nonlinear system with a fixed modulation signal.

  13. Nonabelian N=2 superstrings: Hamiltonian structure

    International Nuclear Information System (INIS)

    Isaev, A.P.; Ivanov, E.A.

    1991-04-01

    We examine the Hamiltonian structure of nonabelian N=2 superstring models which are the supergroup manifold extensions of N=2 Green-Schwarz superstring. We find the Kac-Moody and Virasoro type superalgebras of the relevant constraints and present elements of the corresponding quantum theory. A comparison with the type IIA Green-Schwarz superstring moving in a general curved 10-d supergravity background is also given. We find that nonabelian superstrings (for d=10) present a particular case of this general system corresponding to a special choice of the background. (author). 22 refs

  14. Hamiltonian Description of Convective-cell Generation

    International Nuclear Information System (INIS)

    Krommes, J.A.; Kolesnikov, R.A.

    2004-01-01

    The nonlinear statistical growth rate eq for convective cells driven by drift-wave (DW) interactions is studied with the aid of a covariant Hamiltonian formalism for the gyrofluid nonlinearities. A statistical energy theorem is proven that relates eq to a second functional tensor derivative of the DW energy. This generalizes to a wide class of systems of coupled partial differential equations a previous result for scalar dynamics. Applications to (i) electrostatic ion-temperature-gradient-driven modes at small ion temperature, and (ii) weakly electromagnetic collisional DW's are noted

  15. Eigenfunctions of quadratic hamiltonians in Wigner representation

    International Nuclear Information System (INIS)

    Akhundova, Eh.A.; Dodonov, V.V.; Man'ko, V.I.

    1984-01-01

    Exact solutions of the Schroedinger equation in Wigner representation are obtained for an arbitrary non-stationary N-dimensional quadratic Hamiltonian. It is shown that the complete system of the solutions can always be chosen in the form of the products of Laguerre polynomials, the arguments of which are the quadratic integrals of motion of the corresponding classical problem. The generating function is found for the transition probabilities between Fock states which represent a many-dimensional generatization of a well-known Husimi formula for the oscillator of variable frequency. As an example, the motion of a charged particle in an uniform alternate electromagnetic field is considered in detail

  16. Action-minimizing methods in Hamiltonian dynamics

    CERN Document Server

    Sorrentino, Alfonso

    2015-01-01

    John Mather's seminal works in Hamiltonian dynamics represent some of the most important contributions to our understanding of the complex balance between stable and unstable motions in classical mechanics. His novel approach-known as Aubry-Mather theory-singles out the existence of special orbits and invariant measures of the system, which possess a very rich dynamical and geometric structure. In particular, the associated invariant sets play a leading role in determining the global dynamics of the system. This book provides a comprehensive introduction to Mather's theory, and can serve as a

  17. A new perturbative treatment of pentadiagonal Hamiltonians

    International Nuclear Information System (INIS)

    Znojil, M.

    1987-01-01

    A new formulation of the Rayleich - Schroedinger perturbation theory is proposed. It is inspired by a recurent construction of propagators, and its main idea lies in a replacement of the auxiliary matrix elements (generalized continued fractions) by their non-numerical approximants. In a test of convergence (the anharmonic oscillator), the asymptotic fixed-point approximation scheme is used. The results indicate a good applicability of this fixed-point version of our formalism to systems with a band-matrix structure of the Hamiltonian

  18. First-Principles Modeling of Polaron Formation in TiO2 Polymorphs.

    Science.gov (United States)

    Elmaslmane, A R; Watkins, M B; McKenna, K P

    2018-06-21

    We present a computationally efficient and predictive methodology for modeling the formation and properties of electron and hole polarons in solids. Through a nonempirical and self-consistent optimization of the fraction of Hartree-Fock exchange (α) in a hybrid functional, we ensure the generalized Koopmans' condition is satisfied and self-interaction error is minimized. The approach is applied to model polaron formation in known stable and metastable phases of TiO 2 including anatase, rutile, brookite, TiO 2 (H), TiO 2 (R), and TiO 2 (B). Electron polarons are predicted to form in rutile, TiO 2 (H), and TiO 2 (R) (with trapping energies ranging from -0.02 eV to -0.35 eV). In rutile the electron localizes on a single Ti ion, whereas in TiO 2 (H) and TiO 2 (R) the electron is distributed across two neighboring Ti sites. Hole polarons are predicted to form in anatase, brookite, TiO 2 (H), TiO 2 (R), and TiO 2 (B) (with trapping energies ranging from -0.16 eV to -0.52 eV). In anatase, brookite, and TiO 2 (B) holes localize on a single O ion, whereas in TiO 2 (H) and TiO 2 (R) holes can also be distributed across two O sites. We find that the optimized α has a degree of transferability across the phases, with α = 0.115 describing all phases well. We also note the approach yields accurate band gaps, with anatase, rutile, and brookite within six percent of experimental values. We conclude our study with a comparison of the alignment of polaron charge transition levels across the different phases. Since the approach we describe is only two to three times more expensive than a standard density functional theory calculation, it is ideally suited to model charge trapping at complex defects (such as surfaces and interfaces) in a range of materials relevant for technological applications but previously inaccessible to predictive modeling.

  19. Lennard-Jones triple-point bulk and shear viscosities. Green-Kubo theory, Hamiltonian mechanics, and nonequilibrium molecular dynamics

    International Nuclear Information System (INIS)

    Hoover, W.G.; Evans, D.J.; Hickman, R.B.; Ladd, A.J.C.; Ashurst, W.T.; Moran, B.

    1980-01-01

    A new Hamiltonian method for deformation simulations is related to the Green-Kubo fluctuation theory through perturbation theory and linear-response theory. Numerical results for the bulk and shear viscosity coefficients are compared to corresponding Green-Kubo calculations. Both viscosity coefficients depend similarly on frequency, in a way consistent with enhanced ''long-time tails.''

  20. Effective hamiltonian within the microscopic unitary nuclear model

    International Nuclear Information System (INIS)

    Avramenko, V.I.; Blokhin, A.L.

    1989-01-01

    Within the microscopic version of the unitary collective model with the horizontal mixing the effective Hamiltonian for 18 O and 18 Ne nuclei is constructed. The algebraic structure of the Hamiltonian is compared to the familiar phenomenological ones with the SU(3)-mixing terms which describe the coupled rotational and vibrational spectra. The Hamiltonian, including central nuclear and Coulomb interaction, is diagonalized on the basis of three SU(3) irreducible representations with two orbital symmetries. 32 refs.; 2 figs.; 4 tabs

  1. Introduction to thermodynamics of spin models in the Hamiltonian limit

    Energy Technology Data Exchange (ETDEWEB)

    Berche, Bertrand [Groupe M, Laboratoire de Physique des Materiaux, UMR CNRS No 7556, Universite Henri Poincare, Nancy 1, BP 239, F-54506 Vandoeuvre les Nancy, (France); Lopez, Alexander [Instituto Venezolano de Investigaciones CientIficas, Centro de Fisica, Carr. Panamericana, km 11, Altos de Pipe, Aptdo 21827, 1020-A Caracas, (Venezuela)

    2006-01-01

    A didactic description of the thermodynamic properties of classical spin systems is given in terms of their quantum counterpart in the Hamiltonian limit. Emphasis is on the construction of the relevant Hamiltonian and the calculation of thermal averages is explicitly done in the case of small systems described, in Hamiltonian field theory, by small matrices. The targeted students are those of a graduate statistical physics course.

  2. Hamiltonian structure of the Lotka-Volterra equations

    Science.gov (United States)

    Nutku, Y.

    1990-03-01

    The Lotka-Volterra equations governing predator-prey relations are shown to admit Hamiltonian structure with respect to a generalized Poisson bracket. These equations provide an example of a system for which the naive criterion for the existence of Hamiltonian structure fails. We show further that there is a three-component generalization of the Lotka-Volterra equations which is a bi-Hamiltonian system.

  3. Geometry and Hamiltonian mechanics on discrete spaces

    International Nuclear Information System (INIS)

    Talasila, V; Clemente-Gallardo, J; Schaft, A J van der

    2004-01-01

    Numerical simulation is often crucial for analysing the behaviour of many complex systems which do not admit analytic solutions. To this end, one either converts a 'smooth' model into a discrete (in space and time) model, or models systems directly at a discrete level. The goal of this paper is to provide a discrete analogue of differential geometry, and to define on these discrete models a formal discrete Hamiltonian structure-in doing so we try to bring together various fundamental concepts from numerical analysis, differential geometry, algebraic geometry, simplicial homology and classical Hamiltonian mechanics. For example, the concept of a twisted derivation is borrowed from algebraic geometry for developing a discrete calculus. The theory is applied to a nonlinear pendulum and we compare the dynamics obtained through a discrete modelling approach with the dynamics obtained via the usual discretization procedures. Also an example of an energy-conserving algorithm on a simple harmonic oscillator is presented, and its effect on the Poisson structure is discussed

  4. Thermalization Time Bounds for Pauli Stabilizer Hamiltonians

    Science.gov (United States)

    Temme, Kristan

    2017-03-01

    We prove a general lower bound to the spectral gap of the Davies generator for Hamiltonians that can be written as the sum of commuting Pauli operators. These Hamiltonians, defined on the Hilbert space of N-qubits, serve as one of the most frequently considered candidates for a self-correcting quantum memory. A spectral gap bound on the Davies generator establishes an upper limit on the life time of such a quantum memory and can be used to estimate the time until the system relaxes to thermal equilibrium when brought into contact with a thermal heat bath. The bound can be shown to behave as {λ ≥ O(N^{-1} exp(-2β overline{ɛ}))}, where {overline{ɛ}} is a generalization of the well known energy barrier for logical operators. Particularly in the low temperature regime we expect this bound to provide the correct asymptotic scaling of the gap with the system size up to a factor of N -1. Furthermore, we discuss conditions and provide scenarios where this factor can be removed and a constant lower bound can be proven.

  5. Normal form for mirror machine Hamiltonians

    International Nuclear Information System (INIS)

    Dragt, A.J.; Finn, J.M.

    1979-01-01

    A systematic algorithm is developed for performing canonical transformations on Hamiltonians which govern particle motion in magnetic mirror machines. These transformations are performed in such a way that the new Hamiltonian has a particularly simple normal form. From this form it is possible to compute analytic expressions for gyro and bounce frequencies. In addition, it is possible to obtain arbitrarily high order terms in the adiabatic magnetic moment expansion. The algorithm makes use of Lie series, is an extension of Birkhoff's normal form method, and has been explicitly implemented by a digital computer programmed to perform the required algebraic manipulations. Application is made to particle motion in a magnetic dipole field and to a simple mirror system. Bounce frequencies and locations of periodic orbits are obtained and compared with numerical computations. Both mirror systems are shown to be insoluble, i.e., trajectories are not confined to analytic hypersurfaces, there is no analytic third integral of motion, and the adiabatic magnetic moment expansion is divergent. It is expected also that the normal form procedure will prove useful in the study of island structure and separatrices associated with periodic orbits, and should facilitate studies of breakdown of adiabaticity and the onset of ''stochastic'' behavior

  6. Nonextensive formalism and continuous Hamiltonian systems

    International Nuclear Information System (INIS)

    Boon, Jean Pierre; Lutsko, James F.

    2011-01-01

    A recurring question in nonequilibrium statistical mechanics is what deviation from standard statistical mechanics gives rise to non-Boltzmann behavior and to nonlinear response, which amounts to identifying the emergence of 'statistics from dynamics' in systems out of equilibrium. Among several possible analytical developments which have been proposed, the idea of nonextensive statistics introduced by Tsallis about 20 years ago was to develop a statistical mechanical theory for systems out of equilibrium where the Boltzmann distribution no longer holds, and to generalize the Boltzmann entropy by a more general function S q while maintaining the formalism of thermodynamics. From a phenomenological viewpoint, nonextensive statistics appeared to be of interest because maximization of the generalized entropy S q yields the q-exponential distribution which has been successfully used to describe distributions observed in a large class of phenomena, in particular power law distributions for q>1. Here we re-examine the validity of the nonextensive formalism for continuous Hamiltonian systems. In particular we consider the q-ideal gas, a model system of quasi-particles where the effect of the interactions are included in the particle properties. On the basis of exact results for the q-ideal gas, we find that the theory is restricted to the range q<1, which raises the question of its formal validity range for continuous Hamiltonian systems.

  7. Hamiltonian Anomalies from Extended Field Theories

    Science.gov (United States)

    Monnier, Samuel

    2015-09-01

    We develop a proposal by Freed to see anomalous field theories as relative field theories, namely field theories taking value in a field theory in one dimension higher, the anomaly field theory. We show that when the anomaly field theory is extended down to codimension 2, familiar facts about Hamiltonian anomalies can be naturally recovered, such as the fact that the anomalous symmetry group admits only a projective representation on the Hilbert space, or that the latter is really an abelian bundle gerbe over the moduli space. We include in the discussion the case of non-invertible anomaly field theories, which is relevant to six-dimensional (2, 0) superconformal theories. In this case, we show that the Hamiltonian anomaly is characterized by a degree 2 non-abelian group cohomology class, associated to the non-abelian gerbe playing the role of the state space of the anomalous theory. We construct Dai-Freed theories, governing the anomalies of chiral fermionic theories, and Wess-Zumino theories, governing the anomalies of Wess-Zumino terms and self-dual field theories, as extended field theories down to codimension 2.

  8. Phase space eigenfunctions of multidimensional quadratic Hamiltonians

    International Nuclear Information System (INIS)

    Dodonov, V.V.; Man'ko, V.I.

    1986-01-01

    We obtain the explicit expressions for phace space eigenfunctions (PSE),i.e. Weyl's symbols of dyadic operators like vertical stroken> ,vertical strokem>, being the solution of the Schroedinger equation with the Hamiltonian which is a quite arbitrary multidimensional quadratic form of the operators of Cartesian coordinates and conjugated to them momenta with time-dependent coefficients. It is shown that for an arbitrary quadratic Hamiltonian one can always construct the set of completely factorized PSE which are products of N factors, each factor being dependent only on two arguments for nnot=m and on a single argument for n=m. These arguments are nothing but constants of motion of the correspondent classical system. PSE are expressed in terms of the associated Laguerre polynomials in the case of a discrete spectrum and in terms of the Airy functions in the continuous spectrum case. Three examples are considered: a harmonic oscillator with a time-dependent frequency, a charged particle in a nonstationary uniform magnetic field, and a particle in a time-dependent uniform potential field. (orig.)

  9. Diffeomorphism invariance in the Hamiltonian formulation of General Relativity

    International Nuclear Information System (INIS)

    Kiriushcheva, N.; Kuzmin, S.V.; Racknor, C.; Valluri, S.R.

    2008-01-01

    It is shown that when the Einstein-Hilbert Lagrangian is considered without any non-covariant modifications or change of variables, its Hamiltonian formulation leads to results consistent with principles of General Relativity. The first-class constraints of such a Hamiltonian formulation, with the metric tensor taken as a canonical variable, allow one to derive the generator of gauge transformations, which directly leads to diffeomorphism invariance. The given Hamiltonian formulation preserves general covariance of the transformations derivable from it. This characteristic should be used as the crucial consistency requirement that must be met by any Hamiltonian formulation of General Relativity

  10. Matchings Extend to Hamiltonian Cycles in 5-Cube

    Directory of Open Access Journals (Sweden)

    Wang Fan

    2018-02-01

    Full Text Available Ruskey and Savage asked the following question: Does every matching in a hypercube Qn for n ≥ 2 extend to a Hamiltonian cycle of Qn? Fink confirmed that every perfect matching can be extended to a Hamiltonian cycle of Qn, thus solved Kreweras’ conjecture. Also, Fink pointed out that every matching can be extended to a Hamiltonian cycle of Qn for n ∈ {2, 3, 4}. In this paper, we prove that every matching in Q5 can be extended to a Hamiltonian cycle of Q5.

  11. Squeezed states from a quantum deformed oscillator Hamiltonian

    Energy Technology Data Exchange (ETDEWEB)

    Ramírez, R. [IFLP, CONICET–Department of Mathematics, University of La Plata c.c. 67 1900, La Plata (Argentina); Reboiro, M., E-mail: marta.reboiro@gmail.com [IFLP, CONICET–Department of Physics, University of La Plata c.c. 67 1900, La Plata (Argentina)

    2016-03-11

    The spectrum and the time evolution of a system, which is modeled by a non-hermitian quantum deformed oscillator Hamiltonian, is analyzed. The proposed Hamiltonian is constructed from a non-standard realization of the algebra of Heisenberg. We show that, for certain values of the coupling constants and for a range of values of the deformation parameter, the deformed Hamiltonian is a pseudo-hermitic Hamiltonian. We explore the conditions under which the Hamiltonian is similar to a Swanson Hamiltonian. Also, we show that the lowest eigenstate of the system is a squeezed state. We study the time evolution of the system, for different initial states, by computing the corresponding Wigner functions. - Highlights: • A generalization of the squeezed harmonic oscillator is constructed from a non-standard realization of the Heisenberg algebra. • It is proved that, for certain values of the parameters of the model, the Hamiltonian is a pseudo-hermitian Hamiltonian. • It is shown that the lowest eigenstate of the Hamiltonian is a squeezed state. • The squeezing behavior of the associated Gazeau–Klauder state, as a function of time, is discussed.

  12. Spectral and resonance properties of the Smilansky Hamiltonian

    Energy Technology Data Exchange (ETDEWEB)

    Exner, Pavel [Department of Theoretical Physics, Nuclear Physics Institute, Czech Academy of Sciences, 25068 Řež near Prague (Czech Republic); Doppler Institute for Mathematical Physics and Applied Mathematics, Czech Technical University, Břehová 7, 11519 Prague (Czech Republic); Lotoreichik, Vladimir [Department of Theoretical Physics, Nuclear Physics Institute, Czech Academy of Sciences, 25068 Řež near Prague (Czech Republic); Tater, Miloš, E-mail: tater@ujf.cas.cz [Department of Theoretical Physics, Nuclear Physics Institute, Czech Academy of Sciences, 25068 Řež near Prague (Czech Republic)

    2017-02-26

    We analyze the Hamiltonian proposed by Smilansky to describe irreversible dynamics in quantum graphs and studied further by Solomyak and others. We derive a weak-coupling asymptotics of the ground state and add new insights by finding the discrete spectrum numerically in the subcritical case. Furthermore, we show that the model then has a rich resonance structure. - Highlights: • We derive conditions on bound states and on resonances of the Smilansky Hamiltonian. • Using these conditions we find numerically discrete spectrum and resonances of this Hamiltonian. • Our numerical tests confirm known properties of the Hamiltonian and allow us to conjecture new ones.

  13. A Hamiltonian approach to model and analyse networks of ...

    Indian Academy of Sciences (India)

    2015-09-24

    Sep 24, 2015 ... Gyroscopes; energy harvesters; synchronization; Hamiltonian mechanics. ... ideas and methods from nonlinear dynamics system theory, in particular, ... deploy highly sensitive, lowpower, magnetic and electric field sensors.

  14. Mechanism of small-polaron formation in the biferroic YCrO{sub 3} doped with calcium

    Energy Technology Data Exchange (ETDEWEB)

    Duran, A., E-mail: dural@cnyn.unam.mx [Universidad Nacional Autonoma de Mexico, Centro de Nanociencias y Nanotecnologia, Apartado Postal 41, C.P. 22800, Ensenada, B.C. (Mexico); Verdin, E. [Universidad de Sonora, Departamento de Fisica, Apartado Postal 1626, Hermosillo, Sonora C.P. 8300 (Mexico); Escamilla, R.; Morales, F.; Escudero, R. [Universidad Nacional Autonoma de Mexico, Instituto de Investigaciones en Materiales, Apartado Postal 70-360, Mexico D.F. 04510 (Mexico)

    2012-04-16

    Highlights: Black-Right-Pointing-Pointer The Ca doped in the YCrO3 matrix was analyzed by means of complete structural, magnetic and electric properties. Black-Right-Pointing-Pointer E{sub act} deduced by Arrhenius' Law suggests small-polarons as conduction mechanisms in pristine and doped sample. Black-Right-Pointing-Pointer Local non-centrosymmetry in pristine sample is proposed as responsible of small polarons formation. Black-Right-Pointing-Pointer A mechanism of formation of small polarons is proposed supported by experimental evidence. Black-Right-Pointing-Pointer The structural distortion caused by the Ca doped in the YCrO3 matrix is harmful to the Ferroic properties. - Abstract: The effects of Ca substitutions on the structure, magnetism and electrical properties of YCrO{sub 3} ceramics are investigated by X-ray diffraction, magnetic susceptibility and electrical conductivity measurements. The cell volume decrease occurs through the change from Cr(III) to Cr(IV) as a result of the charge compensation of the Ca doping. No changes are observed in the antiferromagnetic transition temperature while strong changes are observed in the transport measurements due to Ca content. The increase of the electrical conductivity as well as the decrease of the activation energy is caused by the formation of the small-polarons localized in the O-Cr-O lattice distortion. The origin of small-polarons in the undoped sample is different in nature from the calcium doped. 'Local non-centrosymmetry' is the source of the small-polaron formation in undoped sample, while the change from Cr(III) to Cr(IV) through the charge compensation of Ca(II) in the Y(III) site is the source of small-polarons formations. The decrease of the average bond length Cr-O as well as effective moments in the paramagnetic state and the increase of the electrical conductivity are clear evidence that the Ca doping induces localized polarons, which in turn, these quasiparticles move from site to

  15. Hamiltonians and variational principles for Alfvén simple waves

    International Nuclear Information System (INIS)

    Webb, G M; Hu, Q; Roux, J A le; Dasgupta, B; Zank, G P

    2012-01-01

    The evolution equations for the magnetic field induction B with the wave phase for Alfvén simple waves are expressed as variational principles and in the Hamiltonian form. The evolution of B with the phase (which is a function of the space and time variables) depends on the generalized Frenet–Serret equations, in which the wave normal n (which is a function of the phase) is taken to be tangent to a curve X, in a 3D Cartesian geometry vector space. The physical variables (the gas density, fluid velocity, gas pressure and magnetic field induction) in the wave depend only on the phase. Three approaches are developed. One approach exploits the fact that the Frenet equations may be written as a 3D Hamiltonian system, which can be described using the Nambu bracket. It is shown that B as a function of the phase satisfies a modified version of the Frenet equations, and hence the magnetic field evolution equations can be expressed in the Hamiltonian form. A second approach develops an Euler–Poincaré variational formulation. A third approach uses the Frenet frame formulation, in which the hodograph of B moves on a sphere of constant radius and uses a stereographic projection transformation due to Darboux. The equations for the projected field components reduce to a complex Riccati equation. By using a Cole–Hopf transformation, the Riccati equation reduces to a linear second order differential equation for the new variable. A Hamiltonian formulation of the second order differential equation then allows the system to be written in the Hamiltonian form. Alignment dynamics equations for Alfvén simple waves give rise to a complex Riccati equation or, equivalently, to a quaternionic Riccati equation, which can be mapped onto the Riccati equation obtained by stereographic projection. (paper)

  16. Crossover from Polaronic to Magnetically Phase-Separated Behavior in La1-xSrxCoO3

    Science.gov (United States)

    Phelan, D.; El Khatib, S.; Wang, S.; Barker, J.; Zhao, J.; Zheng, H.; Mitchell, J. F.; Leighton, C.

    2013-03-01

    Dilute hole-doping in La1-xSrxCoO3 leads to the formation of ``spin-state polarons'' where a non-zero spin-state is stabilized on the nearest Co3+ ions surrounding a hole. Here, we discuss the development of electronic/magnetic properties of this system from non-magnetic x=0, through the regime of spin-state polarons, and into the region where longer-range spin correlations and phase separation develop. We present magnetometry, transport, heat capacity, and small-angle neutron scattering (SANS) on single crystals. Magnetometry indicates a crossover with x from Langevin-like behavior (polaronic) to a state with a freezing temperature and finite coercivity. Fascinating correlations with this behavior are seen in transport measurements, the evolution from polaronic to clustered states being accompanied by a crossover from Mott variable range hopping to intercluster hopping. SANS data shows Lorentzian scattering from short-range ferromagnetic clusters first emerging around x = 0.03 with correlation lengths of order two unit cells. We argue that this system provides a unique opportunity to understand in detail the crossover from polaronic to truly phase-separated states.

  17. A new hierarchy of generalized derivative nonlinear Schroedinger equations, its bi-Hamiltonian structure and finite-dimensional involutive system

    International Nuclear Information System (INIS)

    Yan, Z.; Zhang, H.

    2001-01-01

    In this paper, an isospectral problem and one associated with a new hierarchy of nonlinear evolution equations are presented. As a reduction, a representative system of new generalized derivative nonlinear Schroedinger equations in the hierarchy is given. It is shown that the hierarchy possesses bi-Hamiltonian structures by using the trace identity method and is Liouville integrable. The spectral problem is non linearized as a finite-dimensional completely integrable Hamiltonian system under a constraint between the potentials and spectral functions. Finally, the involutive solutions of the hierarchy of equations are obtained. In particular, the involutive solutions of the system of new generalized derivative nonlinear Schroedinger equations are developed

  18. Geometric solitons of Hamiltonian flows on manifolds

    Energy Technology Data Exchange (ETDEWEB)

    Song, Chong, E-mail: songchong@xmu.edu.cn [School of Mathematical Sciences, Xiamen University, Xiamen 361005 (China); Sun, Xiaowei, E-mail: sunxw@cufe.edu.cn [School of Applied Mathematics, Central University of Finance and Economics, Beijing 100081 (China); Wang, Youde, E-mail: wyd@math.ac.cn [Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190 (China)

    2013-12-15

    It is well-known that the LIE (Locally Induction Equation) admit soliton-type solutions and same soliton solutions arise from different and apparently irrelevant physical models. By comparing the solitons of LIE and Killing magnetic geodesics, we observe that these solitons are essentially decided by two families of isometries of the domain and the target space, respectively. With this insight, we propose the new concept of geometric solitons of Hamiltonian flows on manifolds, such as geometric Schrödinger flows and KdV flows for maps. Moreover, we give several examples of geometric solitons of the Schrödinger flow and geometric KdV flow, including magnetic curves as geometric Schrödinger solitons and explicit geometric KdV solitons on surfaces of revolution.

  19. Betatron coupling: Merging Hamiltonian and matrix approaches

    Directory of Open Access Journals (Sweden)

    R. Calaga

    2005-03-01

    Full Text Available Betatron coupling is usually analyzed using either matrix formalism or Hamiltonian perturbation theory. The latter is less exact but provides a better physical insight. In this paper direct relations are derived between the two formalisms. This makes it possible to interpret the matrix approach in terms of resonances, as well as use results of both formalisms indistinctly. An approach to measure the complete coupling matrix and its determinant from turn-by-turn data is presented. Simulations using methodical accelerator design MAD-X, an accelerator design and tracking program, were performed to validate the relations and understand the scope of their application to real accelerators such as the Relativistic Heavy Ion Collider.

  20. Hamiltonian circuited simulations in reactor physics

    International Nuclear Information System (INIS)

    Rio Hirowati Shariffudin

    2002-01-01

    In the assessment of suitability of reactor designs and in the investigations into reactor safety, the steady state of a nuclear reactor has to be studied carefully. The analysis can be done through mockup designs but this approach costs a lot of money and consumes a lot of time. A less expensive approach is via simulations where the reactor and its neutron interactions are modelled mathematically. Finite difference discretization of the diffusion operator has been used to approximate the steady state multigroup neutron diffusion equations. The steps include the outer scheme which estimates the resulting right hand side of the matrix equation, the group scheme which calculates the upscatter problem and the inner scheme which solves for the flux for a particular group. The Hamiltonian circuited simulations for the inner iterations of the said neutron diffusion equation enable the effective use of parallel computing, especially where the solutions of multigroup neutron diffusion equations involving two or more space dimensions are required. (Author)

  1. Hamiltonian inclusive fitness: a fitter fitness concept.

    Science.gov (United States)

    Costa, James T

    2013-01-01

    In 1963-1964 W. D. Hamilton introduced the concept of inclusive fitness, the only significant elaboration of Darwinian fitness since the nineteenth century. I discuss the origin of the modern fitness concept, providing context for Hamilton's discovery of inclusive fitness in relation to the puzzle of altruism. While fitness conceptually originates with Darwin, the term itself stems from Spencer and crystallized quantitatively in the early twentieth century. Hamiltonian inclusive fitness, with Price's reformulation, provided the solution to Darwin's 'special difficulty'-the evolution of caste polymorphism and sterility in social insects. Hamilton further explored the roles of inclusive fitness and reciprocation to tackle Darwin's other difficulty, the evolution of human altruism. The heuristically powerful inclusive fitness concept ramified over the past 50 years: the number and diversity of 'offspring ideas' that it has engendered render it a fitter fitness concept, one that Darwin would have appreciated.

  2. Renormalized semiclassical quantization for rescalable Hamiltonians

    International Nuclear Information System (INIS)

    Takahashi, Satoshi; Takatsuka, Kazuo

    2004-01-01

    A renormalized semiclassical quantization method for rescalable Hamiltonians is proposed. A classical Hamilton system having a potential function that consists of homogeneous polynomials like the Coulombic potential can have a scale invariance in its extended phase space (phase space plus time). Consequently, infinitely many copies of a single trajectory constitute a one-parameter family that is characterized in terms of a scaling factor. This scaling invariance in classical dynamics is lost in quantum mechanics due to the presence of the Planck constant. It is shown that in a system whose classical motions have a self-similarity in the above sense, classical trajectories adopted in the semiclassical scheme interact with infinitely many copies of their own that are reproduced by the relevant scaling procedure, thereby undergoing quantum interference among themselves to produce a quantized spectrum

  3. Integrable time-dependent Hamiltonians, solvable Landau-Zener models and Gaudin magnets

    Science.gov (United States)

    Yuzbashyan, Emil A.

    2018-05-01

    We solve the non-stationary Schrödinger equation for several time-dependent Hamiltonians, such as the BCS Hamiltonian with an interaction strength inversely proportional to time, periodically driven BCS and linearly driven inhomogeneous Dicke models as well as various multi-level Landau-Zener tunneling models. The latter are Demkov-Osherov, bow-tie, and generalized bow-tie models. We show that these Landau-Zener problems and their certain interacting many-body generalizations map to Gaudin magnets in a magnetic field. Moreover, we demonstrate that the time-dependent Schrödinger equation for the above models has a similar structure and is integrable with a similar technique as Knizhnik-Zamolodchikov equations. We also discuss applications of our results to the problem of molecular production in an atomic Fermi gas swept through a Feshbach resonance and to the evaluation of the Landau-Zener transition probabilities.

  4. Consistency of the Hamiltonian formulation of the lowest-order effective action of the complete Horava theory

    International Nuclear Information System (INIS)

    Bellorin, Jorge; Restuccia, Alvaro

    2011-01-01

    We perform the Hamiltonian analysis for the lowest-order effective action, up to second order in derivatives, of the complete Horava theory. The model includes the invariant terms that depend on ∂ i lnN proposed by Blas, Pujolas, and Sibiryakov. We show that the algebra of constraints closes. The Hamiltonian constraint is of second-class behavior and it can be regarded as an elliptic partial differential equation for N. The linearized version of this equation is a Poisson equation for N that can be solved consistently. The preservation in time of the Hamiltonian constraint yields an equation that can be consistently solved for a Lagrange multiplier of the theory. The model has six propagating degrees of freedom in the phase space, corresponding to three even physical modes. When compared with the λR model studied by us in a previous paper, it lacks two second-class constraints, which leads to the extra even mode.

  5. Non-self-adjoint hamiltonians defined by Riesz bases

    Energy Technology Data Exchange (ETDEWEB)

    Bagarello, F., E-mail: fabio.bagarello@unipa.it [Dipartimento di Energia, Ingegneria dell' Informazione e Modelli Matematici, Facoltà di Ingegneria, Università di Palermo, I-90128 Palermo, Italy and INFN, Università di Torino, Torino (Italy); Inoue, A., E-mail: a-inoue@fukuoka-u.ac.jp [Department of Applied Mathematics, Fukuoka University, Fukuoka 814-0180 (Japan); Trapani, C., E-mail: camillo.trapani@unipa.it [Dipartimento di Matematica e Informatica, Università di Palermo, I-90123 Palermo (Italy)

    2014-03-15

    We discuss some features of non-self-adjoint Hamiltonians with real discrete simple spectrum under the assumption that the eigenvectors form a Riesz basis of Hilbert space. Among other things, we give conditions under which these Hamiltonians can be factorized in terms of generalized lowering and raising operators.

  6. The Group of Hamiltonian Automorphisms of a Star Product

    Energy Technology Data Exchange (ETDEWEB)

    La Fuente-Gravy, Laurent, E-mail: lfuente@ulg.ac.be [Université de Liège, Département de Mathématique (Belgium)

    2016-09-15

    We deform the group of Hamiltonian diffeomorphisms into a group of Hamiltonian automorphisms, Ham(M,∗), of a formal star product ∗ on a symplectic manifold (M,ω). We study the geometry of that group and deform the Flux morphism in the framework of deformation quantization.

  7. Hamiltonian formulation for the Martin-Taylor model

    International Nuclear Information System (INIS)

    Vasconcelos, D.B.; Viana, R.L.

    1993-01-01

    Locally stochastic layer and its optimization are studied. In order to accomplish this task, it is employed a Hamiltonian formulation of magnetic field line flow with a subsequent application of Escande-Doveil renormalization method which have been extensively used to obtain accurate estimates of stochasticity thresholds in systems exhibiting Hamiltonian chaos. (author)

  8. Formulation of Hamiltonian mechanics with even and odd Poisson brackets

    International Nuclear Information System (INIS)

    Khudaverdyan, O.M.; Nersesyan, A.P.

    1987-01-01

    A possibility is studied as to constrict the odd Poisson bracket and odd Hamiltonian by the given dynamics in phase superspace - the even Poisson bracket and even Hamiltonian so the transition to the new structure does not change the equations of motion. 9 refs

  9. Effective Hamiltonian within the microscopic unitary nuclear model

    International Nuclear Information System (INIS)

    Filippov, G.F.; Blokhin, A.L.

    1989-01-01

    A technique of projecting the microscopic nuclear Hamiltonian on the SU(3)-group enveloping algebra is developed. The approach proposed is based on the effective Hamiltonian restored from the matrix elements between the coherent states of the SU(3) irreducible representations. The technique is displayed for almost magic nuclei within the mixed representation basis, and for arbitrary nuclei within the single representation. 40 refs

  10. Classical and quantum mechanics of complex Hamiltonian systems ...

    Indian Academy of Sciences (India)

    Vol. 73, No. 2. — journal of. August 2009 physics pp. 287–297. Classical and quantum mechanics of complex. Hamiltonian systems: An extended complex phase space ... 1Department of Physics, Ramjas College (University Enclave), University of Delhi,. Delhi 110 ... 1.1 Motivation behind the study of complex Hamiltonians.

  11. Local Hamiltonians for maximally multipartite-entangled states

    Science.gov (United States)

    Facchi, P.; Florio, G.; Pascazio, S.; Pepe, F.

    2010-10-01

    We study the conditions for obtaining maximally multipartite-entangled states (MMESs) as nondegenerate eigenstates of Hamiltonians that involve only short-range interactions. We investigate small-size systems (with a number of qubits ranging from 3 to 5) and show some example Hamiltonians with MMESs as eigenstates.

  12. Local Hamiltonians for maximally multipartite-entangled states

    International Nuclear Information System (INIS)

    Facchi, P.; Florio, G.; Pascazio, S.; Pepe, F.

    2010-01-01

    We study the conditions for obtaining maximally multipartite-entangled states (MMESs) as nondegenerate eigenstates of Hamiltonians that involve only short-range interactions. We investigate small-size systems (with a number of qubits ranging from 3 to 5) and show some example Hamiltonians with MMESs as eigenstates.

  13. On the physical applications of hyper-Hamiltonian dynamics

    International Nuclear Information System (INIS)

    Gaeta, Giuseppe; Rodriguez, Miguel A

    2008-01-01

    An extension of Hamiltonian dynamics, defined on hyper-Kahler manifolds ('hyper-Hamiltonian dynamics') and sharing many of the attractive features of standard Hamiltonian dynamics, was introduced in previous work. In this paper, we discuss applications of the theory to physically interesting cases, dealing with the dynamics of particles with spin 1/2 in a magnetic field, i.e. the Pauli and the Dirac equations. While the free Pauli equation corresponds to a hyper-Hamiltonian flow, it turns out that the hyper-Hamiltonian description of the Dirac equation, and of the full Pauli one, is in terms of two commuting hyper-Hamiltonian flows. In this framework one can use a factorization principle discussed here (which is a special case of a general phenomenon studied by Walcher) and provide an explicit description of the resulting flow. On the other hand, by applying the familiar Foldy-Wouthuysen and Cini-Tousheck transformations (and the one recently introduced by Mulligan) which separate-in suitable limits-the Dirac equation into two equations, each of these turn out to be described by a single hyper-Hamiltonian flow. Thus the hyper-Hamiltonian construction is able to describe the fundamental dynamics for particles with spin

  14. The Group of Hamiltonian Automorphisms of a Star Product

    International Nuclear Information System (INIS)

    La Fuente-Gravy, Laurent

    2016-01-01

    We deform the group of Hamiltonian diffeomorphisms into a group of Hamiltonian automorphisms, Ham(M,∗), of a formal star product ∗ on a symplectic manifold (M,ω). We study the geometry of that group and deform the Flux morphism in the framework of deformation quantization.

  15. Hamiltonian reduction of SU(2) Yang-Mills field theory

    International Nuclear Information System (INIS)

    Khvedelidze, A.M.; Pavel, H.-P.

    1998-01-01

    The unconstrained system equivalent to SU (2) Yang-Mills field theory is obtained in the framework of the generalized Hamiltonian formalism using the method of Hamiltonian reduction. The reduced system is expressed in terms of fields with 'nonrelativistic' spin-0 and spin-2

  16. An effective Hamiltonian approach to quantum random walk

    Indian Academy of Sciences (India)

    2017-02-09

    Feb 9, 2017 ... Abstract. In this article we present an effective Hamiltonian approach for discrete time quantum random walk. A form of the Hamiltonian for one-dimensional quantum walk has been prescribed, utilizing the fact that Hamil- tonians are generators of time translations. Then an attempt has been made to ...

  17. Model reduction of port-Hamiltonian systems as structured systems

    NARCIS (Netherlands)

    Polyuga, R.V.; Schaft, van der A.J.

    2010-01-01

    The goal of this work is to demonstrate that a specific projection-based model reduction method, which provides an H2 error bound, turns out to be applicable to port-Hamiltonian systems, preserving the port-Hamiltonian structure for the reduced order model, and, as a consequence, passivity.

  18. Port Hamiltonian Formulation of Infinite Dimensional Systems I. Modeling

    NARCIS (Netherlands)

    Macchelli, Alessandro; Schaft, Arjan J. van der; Melchiorri, Claudio

    2004-01-01

    In this paper, some new results concerning the modeling of distributed parameter systems in port Hamiltonian form are presented. The classical finite dimensional port Hamiltonian formulation of a dynamical system is generalized in order to cope with the distributed parameter and multi-variable case.

  19. Port-Hamiltonian approaches to motion generation for mechanical systems

    NARCIS (Netherlands)

    Sakai, Satoru; Stramigioli, Stefano

    This paper gives new motion generation methods for mechanical port-Hamiltonian systems. First, we propose a generation method based on an asymptotic stabilization method without damping assignment. This asymptotic stabilization method preserves the Hamiltonian structure in the closed-loop system

  20. Structure preserving port-Hamiltonian model reduction of electrical circuits

    NARCIS (Netherlands)

    Polyuga, R.; Schaft, van der A.J.; Benner, P.; Hinze, M.; Maten, ter E.J.W.

    2011-01-01

    This paper discusses model reduction of electrical circuits based on a port-Hamiltonian representation. It is shown that by the use of the Kalman decomposition an uncontrollable and/or unobservable port-Hamiltonian system is reduced to a controllable/observable system that inherits the

  1. Residual gauge invariance of Hamiltonian lattice gauge theories

    International Nuclear Information System (INIS)

    Ryang, S.; Saito, T.; Shigemoto, K.

    1984-01-01

    The time-independent residual gauge invariance of Hamiltonian lattice gauge theories is considered. Eigenvalues and eigenfunctions of the unperturbed Hamiltonian are found in terms of Gegengauer's polynomials. Physical states which satisfy the subsidiary condition corresponding to Gauss' law are constructed systematically. (orig.)

  2. Spectrally resolved hyperfine interactions between polaron and nuclear spins in organic light emitting diodes: Magneto-electroluminescence studies

    Energy Technology Data Exchange (ETDEWEB)

    Crooker, S. A.; Kelley, M. R.; Martinez, N. J. D.; Nie, W.; Mohite, A.; Nayyar, I. H.; Tretiak, S.; Smith, D. L. [Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Liu, F.; Ruden, P. P. [University of Minnesota, Minneapolis, Minnesota 55455 (United States)

    2014-10-13

    We use spectrally resolved magneto-electroluminescence (EL) measurements to study the energy dependence of hyperfine interactions between polaron and nuclear spins in organic light-emitting diodes. Using layered devices that generate bright exciplex emission, we show that the increase in EL emission intensity I due to small applied magnetic fields of order 100 mT is markedly larger at the high-energy blue end of the EL spectrum (ΔI/I ∼ 11%) than at the low-energy red end (∼4%). Concurrently, the widths of the magneto-EL curves increase monotonically from blue to red, revealing an increasing hyperfine coupling between polarons and nuclei and directly providing insight into the energy-dependent spatial extent and localization of polarons.

  3. Local modular Hamiltonians from the quantum null energy condition

    Science.gov (United States)

    Koeller, Jason; Leichenauer, Stefan; Levine, Adam; Shahbazi-Moghaddam, Arvin

    2018-03-01

    The vacuum modular Hamiltonian K of the Rindler wedge in any relativistic quantum field theory is given by the boost generator. Here we investigate the modular Hamiltonian for more general half-spaces which are bounded by an arbitrary smooth cut of a null plane. We derive a formula for the second derivative of the modular Hamiltonian with respect to the coordinates of the cut which schematically reads K''=Tv v . This formula can be integrated twice to obtain a simple expression for the modular Hamiltonian. The result naturally generalizes the standard expression for the Rindler modular Hamiltonian to this larger class of regions. Our primary assumptions are the quantum null energy condition—an inequality between the second derivative of the von Neumann entropy of a region and the stress tensor—and its saturation in the vacuum for these regions. We discuss the validity of these assumptions in free theories and holographic theories to all orders in 1 /N .

  4. Sdg interacting boson hamiltonian in the seniority scheme

    Energy Technology Data Exchange (ETDEWEB)

    Yoshinaga, N.

    1989-03-06

    The sdg interacting boson hamiltonian is derived in the seniority scheme. We use the method of Otsuka, Arima and Iachello in order to derive the boson hamiltonian from the fermion hamiltonian. To examine how good is the boson approximation in the zeroth-order, we carry out the exact shell model calculations in a single j-shell. It is found that almost all low-lying levels are reproduced quite well by diagonalizing the sdg interacting boson hamiltonian in the vibrational case. In the deformed case the introduction of g-bosons improves the reproduction of the spectra and of the binding energies which are obtained by diagnoalizing the exact shell model hamiltonian. In particular the sdg interacting boson model reproduces well-developed rotational bands.

  5. sdg Interacting boson hamiltonian in the seniority scheme

    Science.gov (United States)

    Yoshinaga, N.

    1989-03-01

    The sdg interacting boson hamiltonian is derived in the seniority scheme. We use the method of Otsuka, Arima and Iachello in order to derive the boson hamiltonian from the fermion hamiltonian. To examine how good is the boson approximation in the zeroth-order, we carry out the exact shell model calculations in a single j-shell. It is found that almost all low-lying levels are reproduced quite well by diagonalizing the sdg interacting boson hamiltonian in the vibrational case. In the deformed case the introduction of g-bosons improves the reproduction of the spectra and of the binding energies which are obtained by diagonalizing the exact shell model hamiltonian. In particular the sdg interacting boson model reproduces well-developed rotational bands.

  6. Frustration-free Hamiltonians supporting Majorana zero edge modes

    International Nuclear Information System (INIS)

    Jevtic, Sania; Barnett, Ryan

    2017-01-01

    A one-dimensional fermionic system, such as a superconducting wire, may host Majorana zero-energy edge modes (MZMs) at its edges when it is in the topological phase. MZMs provide a path to realising fault-tolerant quantum computation, and so are the focus of intense experimental and theoretical studies. However, given a Hamiltonian, determining whether MZMs exist is a daunting task as it relies on knowing the spectral properties of the Hamiltonian in the thermodynamic limit. The Kitaev chain is a paradigmatic non-interacting model that supports MZMs and the Hamiltonian can be fully diagonalised. However, for interacting models, the situation is far more complex. Here we consider a different classification of models, namely, ones with frustration-free Hamiltonians. Within this class of models, interacting and non-interacting systems are treated on an equal footing, and we identify exactly which Hamiltonians can realise MZMs. (paper)

  7. Frustration-free Hamiltonians supporting Majorana zero edge modes

    Science.gov (United States)

    Jevtic, Sania; Barnett, Ryan

    2017-10-01

    A one-dimensional fermionic system, such as a superconducting wire, may host Majorana zero-energy edge modes (MZMs) at its edges when it is in the topological phase. MZMs provide a path to realising fault-tolerant quantum computation, and so are the focus of intense experimental and theoretical studies. However, given a Hamiltonian, determining whether MZMs exist is a daunting task as it relies on knowing the spectral properties of the Hamiltonian in the thermodynamic limit. The Kitaev chain is a paradigmatic non-interacting model that supports MZMs and the Hamiltonian can be fully diagonalised. However, for interacting models, the situation is far more complex. Here we consider a different classification of models, namely, ones with frustration-free Hamiltonians. Within this class of models, interacting and non-interacting systems are treated on an equal footing, and we identify exactly which Hamiltonians can realise MZMs.

  8. Polaron Hopping in Nano-scale Poly(dA–Poly(dT DNA

    Directory of Open Access Journals (Sweden)

    Singh Mahi

    2010-01-01

    Full Text Available Abstract We investigate the current–voltage relationship and the temperature-dependent conductance of nano-scale samples of poly(dA–poly(dT DNA molecules. A polaron hopping model has been used to calculate the I–V characteristic of nano-scale samples of DNA. This model agrees with the data for current versus voltage at temperatures greater than 100 K. The quantities G 0 , i 0 , and T 1d are determined empirically, and the conductivity is estimated for samples of poly(dA–poly(dT.

  9. Polaron Self-localization in White-light Emitting Hybrid Perovskites

    OpenAIRE

    Cortecchia, Daniele; Yin, Jun; Bruno, Annalisa; Lo, Shu-Zee Alencious; Gurzadyan, Gagik G.; Mhaisalkar, Subodh; Brédas, Jean-Luc; Soci, Cesare

    2016-01-01

    Two-dimensional (2D) perovskites with general formula $APbX_4$ are attracting increasing interest as solution processable, white-light emissive materials. Recent studies have shown that their broadband emission is related to the formation of intra-gap color centers; however, the nature and dynamics of the emissive species have remained elusive. Here we show that the broadband photoluminescence of the 2D perovskites $(EDBE)PbCl_4$ and $(EDBE)PbBr_4$ stems from the localization of small polaron...

  10. The ground state energy of a bound polaron in the presence of a magnetic field

    Energy Technology Data Exchange (ETDEWEB)

    Zorkani, I [International Centre for Theoretical Physics, Trieste (Italy); Belhissi, R [Faculte des Sciences Dhar Mahraz, Fes (Morocco). Dept. de Physique

    1995-09-01

    A theoretical calculation for the ground state energy of a bound polaron as a function of the magnetic field is presented. The theory is based on a variational approach using a trial wave function proposed by Devreese et al. in the absence of the magnetic field. It was shown that his function is adequate for all electron - phonon coupling {alpha} and all parameter {gamma}{sub 0} which is the ratio between the L.O. phonon energy and the Colombian one. Analytical results are obtained in the weak coupling limit. (author). 27 refs, 4 figs, 1 tab.

  11. A variational study of the self-trapped magnetic polaron formation in double-exchange model

    International Nuclear Information System (INIS)

    Liu Tao; Feng Mang; Wang Kelin

    2005-01-01

    We study the formation of self-trapped magnetic polaron (STMP) in an antiferro/ferromagnetic double-exchange model semi-analytically by variational solutions. It is shown that the Jahn-Teller effect is not essential to the STMP formation and the STMP forms in the antiferromagnetic material within the region of the order of the lattice constant. We also confirm that no ground state STMP exists in the ferromagnetic background, but the ground state bound MP could appear due to the impurity potential

  12. Breakdown of the lattice polaron picture in La0.7Ca0.3MnO3 single crystals

    International Nuclear Information System (INIS)

    Chun, S. H.; Salamon, M. B.; Tomioka, Y.; Tokura, Y.

    2000-01-01

    When heated through the magnetic transition at T C , La 0.7 Ca 0.3 MnO 3 changes from a band metal to a polaronic insulator. The Hall constant R H , through its activated behavior and sign anomaly, provides key evidence for polaronic behavior. We use R H and the Hall mobility to demonstrate the breakdown of the polaron phase. Above 1.4T C , the polaron picture holds in detail, while below, the activation energies of both R H and the mobility deviate strongly from their polaronic values. These changes reflect the presence of metallic, ferromagnetic fluctuations, in the volume of which the Hall effect develops additional contributions tied to quantal phases. (c) 2000 The American Physical Society

  13. Hamiltonian analysis of fast wave current drive in tokamak plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Becoulet, A; Fraboulet, D; Giruzzi, G; Moreau, D; Saoutic, B [Association Euratom-CEA, Centre d` Etudes de Cadarache, 13 - Saint-Paul-lez-Durance (France). Dept. de Recherches sur la Fusion Controlee; Chinardet, J [CISI Ingenierie, Centre d` Etudes de Cadarache, 13 - Saint-Paul-lez-Durance (France)

    1993-12-01

    The Hamiltonian formalism is used to analyze the direct resonant interaction between the fast magnetosonic wave and the electrons in a tokamak plasma. The intrinsic stochasticity of the electron phase space trajectories is derived, and together with extrinsic de-correlation processes, assesses the validity of the quasilinear approximation for the kinetic studies of fast wave current drive (FWCD). A full-wave resolution of the Maxwell-Vlasov set of equations provides the exact pattern of the wave fields in a complete tokamak geometry, for a realistic antenna spectrum. The local quasilinear diffusion tensor is derived from the wave fields, and is used for a computation of the driven current and deposited power profiles, the current drive efficiency, including possible non-linear effects in the kinetic equation. Several applications of FWCD on existing and future machines are given, as well as results concerning combination of FWCD with other non inductive current drive methods. An analytical expression for the current drive efficiency is given in the high single-pass absorption regimes. (authors). 20 figs., 1 tab., 26 refs.

  14. Hamiltonian analysis of fast wave current drive in tokamak plasmas

    International Nuclear Information System (INIS)

    Becoulet, A.; Fraboulet, D.; Giruzzi, G.; Moreau, D.; Saoutic, B.

    1993-12-01

    The Hamiltonian formalism is used to analyze the direct resonant interaction between the fast magnetosonic wave and the electrons in a tokamak plasma. The intrinsic stochasticity of the electron phase space trajectories is derived, and together with extrinsic de-correlation processes, assesses the validity of the quasilinear approximation for the kinetic studies of fast wave current drive (FWCD). A full-wave resolution of the Maxwell-Vlasov set of equations provides the exact pattern of the wave fields in a complete tokamak geometry, for a realistic antenna spectrum. The local quasilinear diffusion tensor is derived from the wave fields, and is used for a computation of the driven current and deposited power profiles, the current drive efficiency, including possible non-linear effects in the kinetic equation. Several applications of FWCD on existing and future machines are given, as well as results concerning combination of FWCD with other non inductive current drive methods. An analytical expression for the current drive efficiency is given in the high single-pass absorption regimes. (authors). 20 figs., 1 tab., 26 refs

  15. Singlet and triplet polaron relaxation in doubly charged self-assembled quantum dots

    International Nuclear Information System (INIS)

    Grange, T; Zibik, E A; Ferreira, R; Bastard, G; Carpenter, B A; Phillips, P J; Stehr, D; Winnerl, S; Helm, M; Steer, M J; Hopkinson, M; Cockburn, J W; Skolnick, M S; Wilson, L R

    2007-01-01

    Polaron relaxation in self-assembled InAs/GaAs quantum dot samples containing 2 electrons per dot is studied using far-infrared, time-resolved pump-probe measurements for transitions between the s-like ground and p-like first excited conduction band states. Spin-flip transitions between singlet and triplet states are observed experimentally in the decay of the absorption bleaching, which shows a clear biexponential dependence. The initial fast decay (∼30 ps) is associated with the singlet polaron decay, while the decay component with the longer time constant (∼5 ns) corresponds to the excited state triplet lifetime. The results are explained by considering the intrinsic Dresselhaus spin-orbit interaction, which induces spin-flip transitions by acoustic phonon emission or phonon anharmonicity. We have calculated the spin-flip decay times, and good agreement is obtained between the experiment and the simulation of the pump-probe signal. Our results demonstrate the importance of spin-mixing effects for intraband energy relaxation in InAs/GaAs quantum dots

  16. Anisotropic small-polaron hopping in W:BiVO4 single crystals

    International Nuclear Information System (INIS)

    Rettie, Alexander J. E.; Chemelewski, William D.; Zhou, Jianshi; Lindemuth, Jeffrey; McCloy, John S.; Marshall, Luke G.; Emin, David; Mullins, C. Buddie

    2015-01-01

    DC electrical conductivity, Seebeck and Hall coefficients are measured between 300 and 450 K on single crystals of monoclinic bismuth vanadate that are doped n-type with 0.3% tungsten donors (W:BiVO 4 ). Strongly activated small-polaron hopping is implied by the activation energies of the Arrhenius conductivities (about 300 meV) greatly exceeding the energies characterizing the falls of the Seebeck coefficients' magnitudes with increasing temperature (about 50 meV). Small-polaron hopping is further evidenced by the measured Hall mobility in the ab-plane (10 −1  cm 2  V −1  s −1 at 300 K) being larger and much less strongly activated than the deduced drift mobility (about 5 × 10 −5  cm 2  V −1  s −1 at 300 K). The conductivity and n-type Seebeck coefficient is found to be anisotropic with the conductivity larger and the Seebeck coefficient's magnitude smaller and less temperature dependent for motion within the ab-plane than that in the c-direction. These anisotropies are addressed by considering highly anisotropic next-nearest-neighbor (≈5 Å) transfers in addition to the somewhat shorter (≈4 Å), nearly isotropic nearest-neighbor transfers

  17. Appearance of small polaron hopping conduction in iron modified cobalt lithium bismuth borate glasses

    Energy Technology Data Exchange (ETDEWEB)

    Dahiya, M. S.; Khasa, S., E-mail: skhasa@yahoo.com; Yadav, Arti [Physics Department, Deenbandhu Chhotu Ram University of Science and Technology, Murthal, India-131039 (India); Agarwal, A. [Applied Physics Department, Guru Jambheshwara University of Science and Technology, Hisar, India-125001 (India)

    2016-05-23

    Lithium bismuth borate glasses containing different amounts of cobalt and iron oxides having chemical composition xFe{sub 2}O{sub 3}•(20-x)CoO•30Li{sub 2}O•10Bi{sub 2}O{sub 3}•40B{sub 2}O{sub 3} (x = 0, 5, 10, 15 and 20 mol% abbreviated as CFLBB1-5 respectively) prepared via melt quench technique have been investigated for their dc electrical conductivity. The amorphous nature of prepared glasses has been confirmed through X-ray diffraction measurements. The dc electrical conductivity has been analyzed by applying Mott’s small polaron hopping model. Activation energies corresponding to lower and higher temperature region have been evaluated. The iron ion concentration (N), mean spacing between iron ions (R) and polaron radius (R{sub p}) has been evaluated using the values of phonon radius (R{sub ph}) and Debye temperature (θ{sub D}). The glass sample without iron (CFLBB1) shows ionic conductivity but the incorporation of iron in the glass matrix results in the appearance of electronic conductivity.

  18. Polaron effects on the dc- and ac-tunneling characteristics of molecular Josephson junctions

    Science.gov (United States)

    Wu, B. H.; Cao, J. C.; Timm, C.

    2012-07-01

    We study the interplay of polaronic effect and superconductivity in transport through molecular Josephson junctions. The tunneling rates of electrons are dominated by vibronic replicas of the superconducting gap, which show up as prominent features in the differential conductance for the dc and ac current. For relatively large molecule-lead coupling, a features that appears when the Josephson frequency matches the vibron frequency can be identified with an over-the-gap structure observed by Marchenkov [Nat. Nanotech. 1748-338710.1038/nnano.2007.2182, 481 (2007)]. However, we are more concerned with the weak-coupling limit, where resonant tunneling through the molecular level dominates. We find that certain features involving both Andreev reflection and vibron emission show an unusual shift of the bias voltage V at their maximum with the gate voltage Vg as V˜(2/3)Vg. Moreover, due to the polaronic effect, the ac Josephson current shows a phase shift of π when the bias eV is increased by one vibronic energy quantum ℏωv. This distinctive even-odd effect is explained in terms of the different sign of the coupling to vibrons of electrons and of Andreev-reflected holes.

  19. Density functional theory + U modeling of polarons in organohalide lead perovskites

    Directory of Open Access Journals (Sweden)

    Eric Welch

    2016-12-01

    Full Text Available We investigate the possible formation of polarons in four organic perovskites (CH3NH3PbI3, CH3NH3PbBr3, CH3NH3PbCl3, and CH3NH3PbI2Cl1 using a density functional theory (DFT calculations with local potentials and hybrid functionals. We show that DFT+U method with U = 8 eV predicts a correct band-gap and matches the forces on ions from hybrid calculations. We then use the DFT + U approach to study the effect of polarons, i.e. to search the configuration space and locate the lowest energy localized band gap state self-trapped hole (STH. STH configurations were found for three pure halides and one mixed halide system. Spin orbit coupling (SOC was also taken into account and the results may be found in the supplementary material. This study focuses on the +U method; however, SOC corrections added to the DFT+U calculations also resulted in STH states in all four systems.

  20. Madelung and Hubbard interactions in polaron band model of doped organic semiconductors

    Science.gov (United States)

    Png, Rui-Qi; Ang, Mervin C.Y.; Teo, Meng-How; Choo, Kim-Kian; Tang, Cindy Guanyu; Belaineh, Dagmawi; Chua, Lay-Lay; Ho, Peter K.H.

    2016-01-01

    The standard polaron band model of doped organic semiconductors predicts that density-of-states shift into the π–π* gap to give a partially filled polaron band that pins the Fermi level. This picture neglects both Madelung and Hubbard interactions. Here we show using ultrahigh workfunction hole-doped model triarylamine–fluorene copolymers that Hubbard interaction strongly splits the singly-occupied molecular orbital from its empty counterpart, while Madelung (Coulomb) interactions with counter-anions and other carriers markedly shift energies of the frontier orbitals. These interactions lower the singly-occupied molecular orbital band below the valence band edge and give rise to an empty low-lying counterpart band. The Fermi level, and hence workfunction, is determined by conjunction of the bottom edge of this empty band and the top edge of the valence band. Calculations are consistent with the observed Fermi-level downshift with counter-anion size and the observed dependence of workfunction on doping level in the strongly doped regime. PMID:27582355

  1. Multi-impurity polarons in a dilute Bose-Einstein condensate

    International Nuclear Information System (INIS)

    Santamore, D H; Timmermans, Eddy

    2011-01-01

    We describe the ground state of a large, dilute, neutral atom Bose-Einstein condensate (BEC) doped with N strongly coupled mutually indistinguishable, bosonic neutral atoms (referred to as ‘impurity’) in the polaron regime where the BEC density response to the impurity atoms remains significantly smaller than the average density of the surrounding BEC. We find that N impurity atoms with N ≠ 1 can self-localize at a lower value of the impurity-boson interaction strength than a single impurity atom. When the ‘bare’ short-range impurity-impurity repulsion does not play a significant role, the self-localization of multiple bosonic impurity atoms into the same single particle orbital (which we call co-self-localization) is the nucleation process of the phase separation transition. When the short-range impurity-impurity repulsion successfully competes with co-self-localization, the system may form a stable liquid of self-localized single impurity polarons. (paper)

  2. Observation of magnetic polarons in the magnetoresistive pyrochlore Lu2V2O7

    International Nuclear Information System (INIS)

    Storchak, Vyacheslav G; Brewer, Jess H; Eshchenko, Dmitry G; Mengyan, Patrick W; Zhou Haidong; Wiebe, Christopher R

    2013-01-01

    Materials that exhibit colossal magnetoresistance (CMR) have attracted much attention due to their potential technological applications. One particularly interesting model for the magnetoresistance of low-carrier-density ferromagnets involves mediation by magnetic polarons (MP)—electrons localized in nanoscale ferromagnetic ‘droplets’ by their exchange interaction. However, MP have not previously been directly detected and their size has been difficult to determine from macroscopic measurements. In order to provide this crucial information, we have carried out muon spin rotation measurements on the magnetoresistive semiconductor Lu 2 V 2 O 7 in the temperature range from 2 to 300 K and in magnetic fields up to 7 T. Magnetic polarons with characteristic radius R ≈ 0.4 nm are detected below about 100 K, where Lu 2 V 2 O 7 exhibits CMR; at higher temperature, where the magnetoresistance vanishes, these MP also disappear. This observation confirms the MP-mediated model of CMR and reveals the microscopic size of the MP in magnetoresistive pyrochlores. (paper)

  3. New Hamiltonian constraint operator for loop quantum gravity

    Directory of Open Access Journals (Sweden)

    Jinsong Yang

    2015-12-01

    Full Text Available A new symmetric Hamiltonian constraint operator is proposed for loop quantum gravity, which is well defined in the Hilbert space of diffeomorphism invariant states up to non-planar vertices with valence higher than three. It inherits the advantage of the original regularization method to create new vertices to the spin networks. The quantum algebra of this Hamiltonian is anomaly-free on shell, and there is less ambiguity in its construction in comparison with the original method. The regularization procedure for this Hamiltonian constraint operator can also be applied to the symmetric model of loop quantum cosmology, which leads to a new quantum dynamics of the cosmological model.

  4. Greenberger-Horne-Zeilinger States and Few-Body Hamiltonians

    Science.gov (United States)

    Facchi, Paolo; Florio, Giuseppe; Pascazio, Saverio; Pepe, Francesco V.

    2011-12-01

    The generation of Greenberger-Horne-Zeilinger (GHZ) states is a crucial problem in quantum information. We derive general conditions for obtaining GHZ states as eigenstates of a Hamiltonian. We find that a necessary condition for an n-qubit GHZ state to be a nondegenerate eigenstate of a Hamiltonian is the presence of m-qubit couplings with m≥[(n+1)/2]. Moreover, we introduce a Hamiltonian with a GHZ eigenstate and derive sufficient conditions for the removal of the degeneracy.

  5. Homotopical Dynamics IV: Hopf invariants and hamiltonian flows

    OpenAIRE

    Cornea, Octavian

    2001-01-01

    In a non-compact context the first natural step in the search for periodic orbits of a hamiltonian flow is to detect bounded ones. In this paper we show that, in a non-compact setting, certain algebraic topological constraints imposed to a gradient flow of the hamiltonian function $f$ imply the existence of bounded orbits for the hamiltonian flow of $f$. Once the existence of bounded orbits is established, under favorable circumstances, application of the $C^{1}$-closing lemma leads to period...

  6. New Hamiltonian constraint operator for loop quantum gravity

    Energy Technology Data Exchange (ETDEWEB)

    Yang, Jinsong, E-mail: yangksong@gmail.com [Department of Physics, Guizhou university, Guiyang 550025 (China); Institute of Physics, Academia Sinica, Taiwan (China); Ma, Yongge, E-mail: mayg@bnu.edu.cn [Department of Physics, Beijing Normal University, Beijing 100875 (China)

    2015-12-17

    A new symmetric Hamiltonian constraint operator is proposed for loop quantum gravity, which is well defined in the Hilbert space of diffeomorphism invariant states up to non-planar vertices with valence higher than three. It inherits the advantage of the original regularization method to create new vertices to the spin networks. The quantum algebra of this Hamiltonian is anomaly-free on shell, and there is less ambiguity in its construction in comparison with the original method. The regularization procedure for this Hamiltonian constraint operator can also be applied to the symmetric model of loop quantum cosmology, which leads to a new quantum dynamics of the cosmological model.

  7. Remarks on Hamiltonian structures in G2-geometry

    International Nuclear Information System (INIS)

    Cho, Hyunjoo; Salur, Sema; Todd, A. J.

    2013-01-01

    In this article, we treat G 2 -geometry as a special case of multisymplectic geometry and make a number of remarks regarding Hamiltonian multivector fields and Hamiltonian differential forms on manifolds with an integrable G 2 -structure; in particular, we discuss existence and make a number of identifications of the spaces of Hamiltonian structures associated to the two multisymplectic structures associated to an integrable G 2 -structure. Along the way, we prove some results in multisymplectic geometry that are generalizations of results from symplectic geometry

  8. Hamiltonian reduction and supersymmetric mechanics with Dirac monopole

    International Nuclear Information System (INIS)

    Bellucci, Stefano; Nersessian, Armen; Yeranyan, Armen

    2006-01-01

    We apply the technique of Hamiltonian reduction for the construction of three-dimensional N=4 supersymmetric mechanics specified by the presence of a Dirac monopole. For this purpose we take the conventional N=4 supersymmetric mechanics on the four-dimensional conformally-flat spaces and perform its Hamiltonian reduction to three-dimensional system. We formulate the final system in the canonical coordinates, and present, in these terms, the explicit expressions of the Hamiltonian and supercharges. We show that, besides a magnetic monopole field, the resulting system is specified by the presence of a spin-orbit coupling term. A comparision with previous work is also carried out

  9. Toric codes and quantum doubles from two-body Hamiltonians

    Energy Technology Data Exchange (ETDEWEB)

    Brell, Courtney G; Bartlett, Stephen D; Doherty, Andrew C [Centre for Engineered Quantum Systems, School of Physics, University of Sydney, Sydney (Australia); Flammia, Steven T, E-mail: cbrell@physics.usyd.edu.au [Perimeter Institute for Theoretical Physics, Waterloo (Canada)

    2011-05-15

    We present here a procedure to obtain the Hamiltonians of the toric code and Kitaev quantum double models as the low-energy limits of entirely two-body Hamiltonians. Our construction makes use of a new type of perturbation gadget based on error-detecting subsystem codes. The procedure is motivated by a projected entangled pair states (PEPS) description of the target models, and reproduces the target models' behavior using only couplings that are natural in terms of the original Hamiltonians. This allows our construction to capture the symmetries of the target models.

  10. Greenberger-Horne-Zeilinger states and few-body Hamiltonians.

    Science.gov (United States)

    Facchi, Paolo; Florio, Giuseppe; Pascazio, Saverio; Pepe, Francesco V

    2011-12-23

    The generation of Greenberger-Horne-Zeilinger (GHZ) states is a crucial problem in quantum information. We derive general conditions for obtaining GHZ states as eigenstates of a Hamiltonian. We find that a necessary condition for an n-qubit GHZ state to be a nondegenerate eigenstate of a Hamiltonian is the presence of m-qubit couplings with m≥[(n+1)/2]. Moreover, we introduce a Hamiltonian with a GHZ eigenstate and derive sufficient conditions for the removal of the degeneracy.

  11. Quantum bootstrapping via compressed quantum Hamiltonian learning

    International Nuclear Information System (INIS)

    Wiebe, Nathan; Granade, Christopher; Cory, D G

    2015-01-01

    A major problem facing the development of quantum computers or large scale quantum simulators is that general methods for characterizing and controlling are intractable. We provide a new approach to this problem that uses small quantum simulators to efficiently characterize and learn control models for larger devices. Our protocol achieves this by using Bayesian inference in concert with Lieb–Robinson bounds and interactive quantum learning methods to achieve compressed simulations for characterization. We also show that the Lieb–Robinson velocity is epistemic for our protocol, meaning that information propagates at a rate that depends on the uncertainty in the system Hamiltonian. We illustrate the efficiency of our bootstrapping protocol by showing numerically that an 8 qubit Ising model simulator can be used to calibrate and control a 50 qubit Ising simulator while using only about 750 kilobits of experimental data. Finally, we provide upper bounds for the Fisher information that show that the number of experiments needed to characterize a system rapidly diverges as the duration of the experiments used in the characterization shrinks, which motivates the use of methods such as ours that do not require short evolution times. (fast track communication)

  12. Relativistic and separable classical hamiltonian particle dynamics

    International Nuclear Information System (INIS)

    Sazdjian, H.

    1981-01-01

    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

  13. Superconformal gravity in Hamiltonian form: another approach to the renormalization of gravitation

    International Nuclear Information System (INIS)

    Kaku, M.

    1983-01-01

    We reexpress superconformal gravity in Hamiltonian form, explicitly displaying all 24 generators of the group as Dirac constraints on the Hilbert space. From this, we can establish a firm foundation for the canonical quantization of superconformal gravity. The purpose of writing down the Hamiltonian form of the theory is to reexamine the question of renormalization and unitarity. Usually, we start with unitary theories of gravity, such as the Einstein-Hilbert action or supergravity, both of which are probably not renormalizable. In this series of papers, we take the opposite approach and start with a theory which is renormalizable but has problems with unitarity. Conformal and superconformal gravity are both plagued with dipole ghosts when we use perturbation theory to quantize the theories. It is difficult to interpret the results of perturbation theory because the asymptotic states have zero norm and the potential between particles grows linearly with the separation distance. The purpose of writing the Hamiltonian form of these theories is to approach the question of unitarity from a different point of view. For example, a strong-coupling approach to these theories may yield a totally different perturbation expansion. We speculate that canonically quantizing the theory by power expanding in the strong-coupling regime may yield a different set of asymptotic states, somewhat similar to the situation in gauge theories. In this series of papers, we wish to reopen the question of the unitarity of conformal theories. We conjecture that ghosts are ''confined.''

  14. Weak form of Stokes-Dirac structures and geometric discretization of port-Hamiltonian systems

    Science.gov (United States)

    Kotyczka, Paul; Maschke, Bernhard; Lefèvre, Laurent

    2018-05-01

    We present the mixed Galerkin discretization of distributed parameter port-Hamiltonian systems. On the prototypical example of hyperbolic systems of two conservation laws in arbitrary spatial dimension, we derive the main contributions: (i) A weak formulation of the underlying geometric (Stokes-Dirac) structure with a segmented boundary according to the causality of the boundary ports. (ii) The geometric approximation of the Stokes-Dirac structure by a finite-dimensional Dirac structure is realized using a mixed Galerkin approach and power-preserving linear maps, which define minimal discrete power variables. (iii) With a consistent approximation of the Hamiltonian, we obtain finite-dimensional port-Hamiltonian state space models. By the degrees of freedom in the power-preserving maps, the resulting family of structure-preserving schemes allows for trade-offs between centered approximations and upwinding. We illustrate the method on the example of Whitney finite elements on a 2D simplicial triangulation and compare the eigenvalue approximation in 1D with a related approach.

  15. Electrostatics of proteins in dielectric solvent continua. II. Hamiltonian reaction field dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Bauer, Sebastian; Tavan, Paul; Mathias, Gerald, E-mail: gerald.mathias@physik.uni-muenchen.de [Lehrstuhl für BioMolekulare Optik, Ludig-Maximilians Universität München, Oettingenstr. 67, 80538 München (Germany)

    2014-03-14

    In Paper I of this work [S. Bauer, G. Mathias, and P. Tavan, J. Chem. Phys. 140, 104102 (2014)] we have presented a reaction field (RF) method, which accurately solves the Poisson equation for proteins embedded in dielectric solvent continua at a computational effort comparable to that of polarizable molecular mechanics (MM) force fields. Building upon these results, here we suggest a method for linearly scaling Hamiltonian RF/MM molecular dynamics (MD) simulations, which we call “Hamiltonian dielectric solvent” (HADES). First, we derive analytical expressions for the RF forces acting on the solute atoms. These forces properly account for all those conditions, which have to be self-consistently fulfilled by RF quantities introduced in Paper I. Next we provide details on the implementation, i.e., we show how our RF approach is combined with a fast multipole method and how the self-consistency iterations are accelerated by the use of the so-called direct inversion in the iterative subspace. Finally we demonstrate that the method and its implementation enable Hamiltonian, i.e., energy and momentum conserving HADES-MD, and compare in a sample application on Ac-Ala-NHMe the HADES-MD free energy landscape at 300 K with that obtained in Paper I by scanning of configurations and with one obtained from an explicit solvent simulation.

  16. Equivalent Hermitian Hamiltonian for the non-Hermitian -x4 potential

    International Nuclear Information System (INIS)

    Jones, H.F.; Mateo, J.

    2006-01-01

    The potential V(x)=-x 4 , which is unbounded below on the real line, can give rise to a well-posed bound state problem when x is taken on a contour in the lower-half complex plane. It is then PT-symmetric rather than Hermitian. Nonetheless it has been shown numerically to have a real spectrum, and a proof of reality, involving the correspondence between ordinary differential equations and integrable systems, was subsequently constructed for the general class of potentials -(ix) N . For such Hamiltonians the natural PT metric is not positive definite, but a dynamically-defined positive-definite metric can be defined, depending on an operator Q. Further, with the help of this operator an equivalent Hermitian Hamiltonian h can be constructed. This programme has been carried out exactly for a few soluble models, and the first few terms of a perturbative expansion have been found for the potential m 2 x 2 +igx 3 . However, until now, the -x 4 potential has proved intractable. In the present paper we give explicit, closed form expressions for Q and h, which are made possible by a particular parametrization of the contour in the complex plane on which the problem is defined. This constitutes an explicit proof of the reality of the spectrum. The resulting equivalent Hamiltonian has a potential with a positive quartic term together with a linear term

  17. Effect of defects on the small polaron formation and transport properties of hematite from first-principles calculations.

    Science.gov (United States)

    Smart, Tyler J; Ping, Yuan

    2017-10-04

    Hematite (α-Fe 2 O 3 ) is a promising candidate as a photoanode material for solar-to-fuel conversion due to its favorable band gap for visible light absorption, its stability in an aqueous environment and its relatively low cost in comparison to other prospective materials. However, the small polaron transport nature in α-Fe 2 O 3 results in low carrier mobility and conductivity, significantly lowering its efficiency from the theoretical limit. Experimentally, it has been found that the incorporation of oxygen vacancies and other dopants, such as Sn, into the material appreciably enhances its photo-to-current efficiency. Yet no quantitative explanation has been provided to understand the role of oxygen vacancy or Sn-doping in hematite. We employed density functional theory to probe the small polaron formation in oxygen deficient hematite, N-doped as well as Sn-doped hematite. We computed the charged defect formation energies, the small polaron formation energy and hopping activation energies to understand the effect of defects on carrier concentration and mobility. This work provides us with a fundamental understanding regarding the role of defects on small polaron formation and transport properties in hematite, offering key insights into the design of new dopants to further improve the efficiency of transition metal oxides for solar-to-fuel conversion.

  18. Multiphonon contribution to the polaron formation in cuprates with strong electron correlations and strong electron-phonon interaction

    Science.gov (United States)

    Ovchinnikov, Sergey G.; Makarov, Ilya A.; Kozlov, Peter A.

    2017-03-01

    In this work dependences of the electron band structure and spectral function in the HTSC cuprates on magnitude of electron-phonon interaction (EPI) and temperature are investigated. We use three-band p-d model with diagonal and offdiagonal EPI with breathing and buckling phonon mode in the frameworks of polaronic version of the generalized tight binding (GTB) method. The polaronic quasiparticle excitation in the system with EPI within this approach is formed by a hybridization of the local multiphonon Franck-Condon excitations with lower and upper Hubbard bands. Increasing EPI leads to transfer of spectral weight to high-energy multiphonon excitations and broadening of the spectral function. Temperature effects are taken into account by occupation numbers of local excited polaronic states and variations in the magnitude of spin-spin correlation functions. Increasing the temperature results in band structure reconstruction, spectral weight redistribution, broadening of the spectral function peak at the top of the valence band and the decreasing of the peak intensity. The effect of EPI with two phonon modes on the polaron spectral function is discussed.

  19. Raman and optical spectroscopic studies of small-to-large polaron crossover in the perovskite manganese oxides

    International Nuclear Information System (INIS)

    Yoon, S.; Liu, H.L.; Schollerer, G.; Cooper, S.L.; Han, P.D.; Payne, D.A.; Cheong, S.; Fisk, Z.

    1998-01-01

    We present an optical reflectance and Raman-scattering study of the A 1-x A ' x MnO 3 system as a function of temperature and doping (0.2≤x≤0.5). The metal-semiconductor transition in the A 1-x A ' x MnO 3 system is characterized by a change from a diffusive electronic Raman-scattering response in the high-temperature paramagnetic phase, to a flat continuum scattering response in the low-temperature ferromagnetic phase. We interpret this change in the scattering response as a crossover from a small-polaron-dominated regime at high temperatures to a large-polaron-dominated low-temperature regime. Interestingly, we observe evidence for the coexistence of large and small polarons in the low-temperature ferromagnetic phase. We contrast these results with those obtained for EuB 6 , which is a low-T c magnetic semiconductor with similar properties to the manganites, but with a substantially reduced carrier density and polaron energy. copyright 1998 The American Physical Society

  20. Direct observation of anisotropic small-hole polarons in an orthorhombic structure of BiV O4 films

    Science.gov (United States)

    Chaudhuri, A.; Mandal, L.; Chi, X.; Yang, M.; Scott, M. C.; Motapothula, M.; Yu, X. J.; Yang, P.; Shao-Horn, Y.; Venkatesan, T.; Wee, A. T. S.; Rusydi, A.

    2018-05-01

    Here, we report an anisotropic small-hole polaron in an orthorhombic structure of BiV O4 films grown by pulsed-laser deposition on yttrium-doped zirconium oxide substrate. The polaronic state and electronic structure of BiV O4 films are revealed using a combination of polarization-dependent x-ray absorption spectroscopy at V L3 ,2 edges, spectroscopic ellipsometry, x-ray photoemission spectroscopies, and high-resolution x-ray diffraction with the support of first-principles calculations. We find that in the orthorhombic phase, which is slightly different from the conventional pucherite structure, the unoccupied V 3d orbitals and charge inhomogeneities lead to an anisotropic small-hole polaron state. Our result shows the importance of the interplay of charge and lattice for the formation of a hole polaronic state, which has a significant impact in the electrical conductivity of BiV O4 , hence its potential use as a photoanode for water splitting.

  1. DFT+U study of polaronic conduction in Li2O2 and Li2CO3

    DEFF Research Database (Denmark)

    García Lastra, Juan Maria; Myrdal, J.S.G.; Christensen, Rune

    2013-01-01

    The main discharge products formed at the cathode of nonaqueous Li-air batteries are known to be Li2O2 and residual Li2CO3. Recent experiments indicate that the charge transport through these materials is the main limiting factor for the battery performance. It has been also shown...... that the performance of the battery decreases drastically when the amount of Li2CO3 at the cathode increases with respect to Li2O2. In this work, we study the formation and transport of hole and electron polarons in Li2O2 and Li2CO3 using density functional theory (DFT) within the PBE+U approximation. For both...... materials, we find that the formation of polarons (both hole and electron) is stabilized with respect to the delocalized states for all physically relevant values of U. We find a much higher mobility for hole polarons than for the electron polarons, and we show that the poor charge transport in Li2CO3...

  2. Shallow trapping vs. deep polarons in a hybrid lead halide perovskite, CH3NH3PbI3.

    Science.gov (United States)

    Kang, Byungkyun; Biswas, Koushik

    2017-10-18

    There has been considerable speculation over the nature of charge carriers in organic-inorganic hybrid perovskites, i.e., whether they are free and band-like, or they are prone to self-trapping via short range deformation potentials. Unusually long minority-carrier diffusion lengths and moderate-to-low mobilities, together with relatively few deep defects add to their intrigue. Here we implement density functional methods to investigate the room-temperature, tetragonal phase of CH 3 NH 3 PbI 3 . We compare charge localization behavior at shallow levels and associated lattice relaxation versus those at deep polaronic states. The shallow level originates from screened Coulomb interaction between the perturbed host and an excited electron or hole. The host lattice has a tendency towards forming these shallow traps where the electron or hole is localized not too far from the band edge. In contrast, there is a considerable potential barrier that must be overcome in order to initiate polaronic hole trapping. The formation of a hole polaron (I 2 - center) involves strong lattice relaxation, including large off-center displacement of the organic cation, CH 3 NH 3 + . This type of deep polaron is energetically unfavorable, and active shallow traps are expected to shape the carrier dynamics in this material.

  3. Determining a hopping polaron's bandwidth from its Seebeck coefficient: Measuring the disorder energy of a non-crystalline semiconductor

    International Nuclear Information System (INIS)

    Emin, David

    2016-01-01

    Charge carriers that execute multi-phonon hopping generally interact strongly enough with phonons to form polarons. A polaron's sluggish motion is linked to slowly shifting atomic displacements that severely reduce the intrinsic width of its transport band. Here a means to estimate hopping polarons' bandwidths from Seebeck-coefficient measurements is described. The magnitudes of semiconductors' Seebeck coefficients are usually quite large (>k/|q| = 86 μV/K) near room temperature. However, in accord with the third law of thermodynamics, Seebeck coefficients must vanish at absolute zero. Here, the transition of the Seebeck coefficient of hopping polarons to its low-temperature regime is investigated. The temperature and sharpness of this transition depend on the concentration of carriers and on the width of their transport band. This feature provides a means of estimating the width of a polaron's transport band. Since the intrinsic broadening of polaron bands is very small, less than the characteristic phonon energy, the net widths of polaron transport bands in disordered semiconductors approach the energetic disorder experienced by their hopping carriers, their disorder energy

  4. The Hamiltonian of Einstein affine-metric formulation of general relativity

    International Nuclear Information System (INIS)

    Kiriushcheva, N.; Kuzmin, S.V.

    2010-01-01

    It is shown that the Hamiltonian of the Einstein affine-metric (first-order) formulation of General Relativity (GR) leads to a constraint structure that allows the restoration of its unique gauge invariance, four-diffeomorphism, without the need of any field dependent redefinition of gauge parameters as in the case of the second-order formulation. In the second-order formulation of ADM gravity the need for such a redefinition is the result of the non-canonical change of variables (Xiv:0809.0097). For the first-order formulation, the necessity of such a redefinition ''to correspond to diffeomorphism invariance'' (reported by Ghalati, arXiv:0901.3344) is just an artifact of using the Henneaux-Teitelboim-Zanelli ansatz (Nucl. Phys. B 332:169, 1990), which is sensitive to the choice of linear combination of tertiary constraints. This ansatz cannot be used as an algorithm for finding a gauge invariance, which is a unique property of a physical system, and it should not be affected by different choices of linear combinations of non-primary first class constraints. The algorithm of Castellani (Ann. Phys. 143:357, 1982) is free from such a deficiency and it leads directly to four-diffeomorphism invariance for first, as well as for second-order Hamiltonian formulations of GR. The distinct role of primary first class constraints, the effect of considering different linear combinations of constraints, the canonical transformations of phase-space variables, and their interplay are discussed in some detail for Hamiltonians of the second- and first-order formulations of metric GR. The first-order formulation of Einstein-Cartan theory, which is the classical background of Loop Quantum Gravity, is also discussed. (orig.)

  5. Integrable Hamiltonian systems and interactions through quadratic constraints

    International Nuclear Information System (INIS)

    Pohlmeyer, K.

    1975-08-01

    Osub(n)-invariant classical relativistic field theories in one time and one space dimension with interactions that are entirely due to quadratic constraints are shown to be closely related to integrable Hamiltonian systems. (orig.) [de

  6. Towards practical characterization of quantum systems with quantum Hamiltonian learning

    NARCIS (Netherlands)

    Santagati, R.; Wang, J.; Paesani, S.; Knauer, S.; Gentile, A. A.; Wiebe, N.; Petruzzella, M.; O'Brien, J. L.; Rarity, J. G.; Laing, A.; Thompson, M. G.

    2017-01-01

    Here we show the first experimental implementation of quantum Hamiltonian Learning, where a silicon-on-insulator quantum photonic simulator is used to learn the dynamics of an electron-spin in an NV center in diamond.

  7. On the quantization of sectorially Hamiltonian dissipative systems

    Energy Technology Data Exchange (ETDEWEB)

    Castagnino, M. [Instituto de Fisica de Rosario, 2000 Rosario (Argentina); Instituto de Astronomia y Fisica del Espacio, Casilla de Correos 67, Sucursal 28, 1428 Buenos Aires (Argentina); Gadella, M. [Instituto de Fisica de Rosario, 2000 Rosario (Argentina); Departamento de Fisica Teorica, Atomica y Optica, Facultad de Ciencias, Universidad de Valladolid, 47005 Valladolid (Spain)], E-mail: manuelgadella@yahoo.com.ar; Lara, L.P. [Instituto de Fisica de Rosario, 2000 Rosario (Argentina); Facultad Regional Rosario, UTN, 2000 Rosario (Argentina)

    2009-10-15

    We present a theoretical discussion showing that, although some dissipative systems may have a sectorial Hamiltonian description, this description does not allow for canonical quantization. However, a quantum Liouville counterpart of these systems is possible, although it is not unique.

  8. On the quantization of sectorially Hamiltonian dissipative systems

    International Nuclear Information System (INIS)

    Castagnino, M.; Gadella, M.; Lara, L.P.

    2009-01-01

    We present a theoretical discussion showing that, although some dissipative systems may have a sectorial Hamiltonian description, this description does not allow for canonical quantization. However, a quantum Liouville counterpart of these systems is possible, although it is not unique.

  9. Hamiltonian formalisms and symmetries of the Pais–Uhlenbeck oscillator

    Directory of Open Access Journals (Sweden)

    Krzysztof Andrzejewski

    2014-12-01

    Full Text Available The study of the symmetry of Pais–Uhlenbeck oscillator initiated in Andrzejewski et al. (2014 [24] is continued with special emphasis put on the Hamiltonian formalism. The symmetry generators within the original Pais and Uhlenbeck Hamiltonian approach as well as the canonical transformation to the Ostrogradski Hamiltonian framework are derived. The resulting algebra of generators appears to be the central extension of the one obtained on the Lagrangian level; in particular, in the case of odd frequencies one obtains the centrally extended l-conformal Newton–Hooke algebra. In this important case the canonical transformation to an alternative Hamiltonian formalism (related to the free higher derivatives theory is constructed. It is shown that all generators can be expressed in terms of the ones for the free theory and the result agrees with that obtained by the orbit method.

  10. Experimental Hamiltonian identification for controlled two-level systems

    International Nuclear Information System (INIS)

    Schirmer, S.G.; Kolli, A.; Oi, D.K.L.

    2004-01-01

    We present a strategy to empirically determine the internal and control Hamiltonians for an unknown two-level system (black box) subject to various (piecewise constant) control fields when direct readout by measurement is limited to a single, fixed observable

  11. A local inverse spectral theorem for Hamiltonian systems

    International Nuclear Information System (INIS)

    Langer, Matthias; Woracek, Harald

    2011-01-01

    We consider (2 × 2)-Hamiltonian systems of the form y'(x) = zJH(x)y(x), x in [s − , s + ). If a system of this form is in the limit point case, an analytic function is associated with it, namely its Titchmarsh–Weyl coefficient q H . The (global) uniqueness theorem due to de Branges says that the Hamiltonian H is (up to reparameterization) uniquely determined by the function q H . In this paper we give a local uniqueness theorem; if the Titchmarsh–Weyl coefficients q H 1 and q H 2 corresponding to two Hamiltonian systems are exponentially close, then the Hamiltonians H 1 and H 2 coincide (up to reparameterization) up to a certain point of their domain, which depends on the quantitative degree of exponential closeness of the Titchmarsh–Weyl coefficients

  12. Hamiltonian Approach to 2+1 Dimensional Gravity

    Science.gov (United States)

    Cantini, L.; Menotti, P.; Seminara, D.

    2002-12-01

    It is shown that the reduced particle dynamics of 2+1 dimensional gravity in the maximally slicing gauge has hamiltonian form. We give the exact diffeomorphism which transforms the spinning cone metric in the Deser, Jackiw, 't Hooft gauge to the maximally slicing gauge. It is explicitly shown that the boundary term in the action, written in hamiltonian form gives the hamiltonian for the reduced particle dynamics. The quantum mechanical translation of the two particle hamiltonian gives rise to the logarithm of the Laplace-Beltrami operator on a cone whose angular deficit is given by the total energy of the system irrespective of the masses of the particles thus proving at the quantum level a conjecture by 't Hooft on the two particle dynamics.

  13. Diffusion Monte Carlo approach versus adiabatic computation for local Hamiltonians

    Science.gov (United States)

    Bringewatt, Jacob; Dorland, William; Jordan, Stephen P.; Mink, Alan

    2018-02-01

    Most research regarding quantum adiabatic optimization has focused on stoquastic Hamiltonians, whose ground states can be expressed with only real non-negative amplitudes and thus for whom destructive interference is not manifest. This raises the question of whether classical Monte Carlo algorithms can efficiently simulate quantum adiabatic optimization with stoquastic Hamiltonians. Recent results have given counterexamples in which path-integral and diffusion Monte Carlo fail to do so. However, most adiabatic optimization algorithms, such as for solving MAX-k -SAT problems, use k -local Hamiltonians, whereas our previous counterexample for diffusion Monte Carlo involved n -body interactions. Here we present a 6-local counterexample which demonstrates that even for these local Hamiltonians there are cases where diffusion Monte Carlo cannot efficiently simulate quantum adiabatic optimization. Furthermore, we perform empirical testing of diffusion Monte Carlo on a standard well-studied class of permutation-symmetric tunneling problems and similarly find large advantages for quantum optimization over diffusion Monte Carlo.

  14. Compact versus noncompact quantum dynamics of time-dependent su(1,1)-valued Hamiltonians

    International Nuclear Information System (INIS)

    Penna, V.

    1996-01-01

    We consider the Schroedinger problem for time-dependent (TD) Hamiltonians represented by a linear combination of the compact generator and the hyperbolic generator of su(1,1). Several types of transitions, characterized by different time initial conditions on the generator coefficients, are analyzed by resorting to the harmonic oscillator model with a frequency vanishing for t→+∞. We provide examples that point out how the TD states of the transitions can be constructed either by the compact eigenvector basis or by the noncompact eigenvector basis depending on the initial conditions characterizing the frequency time behavior. Copyright copyright 1996 Academic Press, Inc

  15. The quadratic-form identity for constructing the Hamiltonian structure of integrable systems

    International Nuclear Information System (INIS)

    Guo Fukui; Zhang Yufeng

    2005-01-01

    A usual loop algebra, not necessarily the matrix form of the loop algebra A-tilde n-1 , is also made use of for constructing linear isospectral problems, whose compatibility conditions exhibit a zero-curvature equation from which integrable systems are derived. In order to look for the Hamiltonian structure of such integrable systems, a quadratic-form identity is created in the present paper whose special case is just the trace identity; that is, when taking the loop algebra A-tilde 1 , the quadratic-form identity presented in this paper is completely consistent with the trace identity

  16. Time and a physical Hamiltonian for quantum gravity.

    Science.gov (United States)

    Husain, Viqar; Pawłowski, Tomasz

    2012-04-06

    We present a nonperturbative quantization of general relativity coupled to dust and other matter fields. The dust provides a natural time variable, leading to a physical Hamiltonian with spatial diffeomorphism symmetry. The surprising feature is that the Hamiltonian is not a square root. This property, together with the kinematical structure of loop quantum gravity, provides a complete theory of quantum gravity, and puts applications to cosmology, quantum gravitational collapse, and Hawking radiation within technical reach. © 2012 American Physical Society

  17. A hierarchy of Liouville integrable discrete Hamiltonian equations

    Energy Technology Data Exchange (ETDEWEB)

    Xu Xixiang [College of Science, Shandong University of Science and Technology, Qingdao 266510 (China)], E-mail: xixiang_xu@yahoo.com.cn

    2008-05-12

    Based on a discrete four-by-four matrix spectral problem, a hierarchy of Lax integrable lattice equations with two potentials is derived. Two Hamiltonian forms are constructed for each lattice equation in the resulting hierarchy by means of the discrete variational identity. A strong symmetry operator of the resulting hierarchy is given. Finally, it is shown that the resulting lattice equations are all Liouville integrable discrete Hamiltonian systems.

  18. On the topological entropy of an optical Hamiltonian flow

    OpenAIRE

    Niche, Cesar J.

    2000-01-01

    In this article we prove two formulas for the topological entropy of an F-optical Hamiltonian flow induced by a C^{\\infty} Hamiltonian, where F is a Lagrangian distribution. In these formulas, we calculate the topological entropy as the exponential growth rate of the average of the determinant of the differential of the flow, restricted to the Lagrangian distribution or to a proper modification.

  19. SOLVING THE HAMILTONIAN CYCLE PROBLEM USING SYMBOLIC DETERMINANTS

    OpenAIRE

    Ejov, V.; Filar, J. A.; Lucas, S. K.; Nelson, J. L.

    2006-01-01

    In this note we show how the Hamiltonian Cycle problem can be reduced to solving a system of polynomial equations related to the adjacency matrix of a graph. This system of equations can be solved using the method of Gröbner bases, but we also show how a symbolic determinant related to the adjacency matrix can be used to directly decide whether a graph has a Hamiltonian cycle.

  20. Noncanonical Hamiltonian density formulation of hydrodynamics and ideal MHD

    International Nuclear Information System (INIS)

    Morrison, P.J.; Greene, J.M.

    1980-04-01

    A new Hamiltonian density formulation of a perfect fluid with or without a magnetic field is presented. Contrary to previous work the dynamical variables are the physical variables, rho, v, B, and s, which form a noncanonical set. A Poisson bracket which satisfies the Jacobi identity is defined. This formulation is transformed to a Hamiltonian system where the dynamical variables are the spatial Fourier coefficients of the fluid variables

  1. Families of superintegrable Hamiltonians constructed from exceptional polynomials

    International Nuclear Information System (INIS)

    Post, Sarah; Tsujimoto, Satoshi; Vinet, Luc

    2012-01-01

    We introduce a family of exactly-solvable two-dimensional Hamiltonians whose wave functions are given in terms of Laguerre and exceptional Jacobi polynomials. The Hamiltonians contain purely quantum terms which vanish in the classical limit leaving only a previously known family of superintegrable systems. Additional, higher-order integrals of motion are constructed from ladder operators for the considered orthogonal polynomials proving the quantum system to be superintegrable. (paper)

  2. Construction of alternative Hamiltonian structures for field equations

    Energy Technology Data Exchange (ETDEWEB)

    Herrera, Mauricio [Departamento de Fisica, Facultad de Ciencias Fisicas y Matematicas, Universidad de Chile, Santiago (Chile); Hojman, Sergio A. [Departamento de Fisica, Facultad de Ciencias, Universidad de Chile, Santiago (Chile); Facultad de Educacion, Universidad Nacional Andres Bello, Santiago (Chile); Centro de Recursos Educativos Avanzados, CREA, Santiago (Chile)

    2001-08-10

    We use symmetry vectors of nonlinear field equations to build alternative Hamiltonian structures. We construct such structures even for equations which are usually believed to be non-Hamiltonian such as heat, Burger and potential Burger equations. We improve on a previous version of the approach using recursion operators to increase the rank of the Poisson bracket matrices. Cole-Hopf and Miura-type transformations allow the mapping of these structures from one equation to another. (author)

  3. Orbits and variational principles for conservative Hamiltonian systems

    International Nuclear Information System (INIS)

    Torres del Castillo, G.F.

    1989-01-01

    It is shown that for any Hamiltonian system whose Hamiltonian is time-independent the equations that determine the orbits followed by the system, without making reference to time, have the form of Hamilton's equations in a phase space of dimension two units smaller than that of the original phase space. By considering the cases of classical mechanics and of geometrical optics, it is shown that this result amounts, respectively, to Maupertuis' least action principle and to Fermat's principle. (Author)

  4. Parton Theory of Magnetic Polarons: Mesonic Resonances and Signatures in Dynamics

    Science.gov (United States)

    Grusdt, F.; Kánasz-Nagy, M.; Bohrdt, A.; Chiu, C. S.; Ji, G.; Greiner, M.; Greif, D.; Demler, E.

    2018-01-01

    When a mobile hole is moving in an antiferromagnet it distorts the surrounding Néel order and forms a magnetic polaron. Such interplay between hole motion and antiferromagnetism is believed to be at the heart of high-temperature superconductivity in cuprates. In this article, we study a single hole described by the t -Jz model with Ising interactions between the spins in two dimensions. This situation can be experimentally realized in quantum gas microscopes with Mott insulators of Rydberg-dressed bosons or fermions, or using polar molecules. We work at strong couplings, where hole hopping is much larger than couplings between the spins. In this regime we find strong theoretical evidence that magnetic polarons can be understood as bound states of two partons, a spinon and a holon carrying spin and charge quantum numbers, respectively. Starting from first principles, we introduce a microscopic parton description which is benchmarked by comparison with results from advanced numerical simulations. Using this parton theory, we predict a series of excited states that are invisible in the spectral function and correspond to rotational excitations of the spinon-holon pair. This is reminiscent of mesonic resonances observed in high-energy physics, which can be understood as rotating quark-antiquark pairs carrying orbital angular momentum. Moreover, we apply the strong-coupling parton theory to study far-from-equilibrium dynamics of magnetic polarons observable in current experiments with ultracold atoms. Our work supports earlier ideas that partons in a confining phase of matter represent a useful paradigm in condensed-matter physics and in the context of high-temperature superconductivity in particular. While direct observations of spinons and holons in real space are impossible in traditional solid-state experiments, quantum gas microscopes provide a new experimental toolbox. We show that, using this platform, direct observations of partons in and out of equilibrium are

  5. Oscillator representations for self-adjoint Calogero Hamiltonians

    Energy Technology Data Exchange (ETDEWEB)

    Gitman, D M [Institute of Physics, University of Sao Paulo (Brazil); Tyutin, I V; Voronov, B L, E-mail: gitman@dfn.if.usp.br, E-mail: tyutin@lpi.ru, E-mail: voronov@lpi.ru [Lebedev Physical Institute, Moscow (Russian Federation)

    2011-10-21

    In Gitman et al (2010 J. Phys. A: Math. Theor. 43 145205), we presented a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential V(x) = {alpha}x{sup -2}. We described all possible self-adjoint (s.a.) operators (s.a. Hamiltonians) associated with the differential operation H=-d{sub x}{sup 2}+{alpha}x{sup -2} for the Calogero Hamiltonian. Here, we discuss a new aspect of the problem, the so-called oscillator representations for the Calogero Hamiltonians. As is known, operators of the form N-hat = a-hat{sup +} a-hat and A-hat = a-hat a-hat{sup +} are called operators of oscillator type. Oscillator-type operators possess a number of useful properties in the case when the elementary operators a-hat are closed. It turns out that some s.a. Calogero Hamiltonians allow oscillator-type representations. We describe such Hamiltonians and find the corresponding mutually adjoint elementary operators a-hat and a-hat{sup +}. An oscillator-type representation for a given Hamiltonian is generally not unique. (paper)

  6. Oscillator representations for self-adjoint Calogero Hamiltonians

    International Nuclear Information System (INIS)

    Gitman, D M; Tyutin, I V; Voronov, B L

    2011-01-01

    In Gitman et al (2010 J. Phys. A: Math. Theor. 43 145205), we presented a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential V(x) = αx -2 . We described all possible self-adjoint (s.a.) operators (s.a. Hamiltonians) associated with the differential operation H=-d x 2 +αx -2 for the Calogero Hamiltonian. Here, we discuss a new aspect of the problem, the so-called oscillator representations for the Calogero Hamiltonians. As is known, operators of the form N-hat = a-hat + a-hat and A-hat = a-hat a-hat + are called operators of oscillator type. Oscillator-type operators possess a number of useful properties in the case when the elementary operators a-hat are closed. It turns out that some s.a. Calogero Hamiltonians allow oscillator-type representations. We describe such Hamiltonians and find the corresponding mutually adjoint elementary operators a-hat and a-hat + . An oscillator-type representation for a given Hamiltonian is generally not unique. (paper)

  7. A current value Hamiltonian Approach for Discrete time Optimal Control Problems arising in Economic Growth

    OpenAIRE

    Naz, Rehana

    2018-01-01

    Pontrygin-type maximum principle is extended for the present value Hamiltonian systems and current value Hamiltonian systems of nonlinear difference equations for uniform time step $h$. A new method termed as a discrete time current value Hamiltonian method is established for the construction of first integrals for current value Hamiltonian systems of ordinary difference equations arising in Economic growth theory.

  8. Hamiltonian formalism at light front for two-dimensional quantum electrodynamics equivalent to lorentz-covariant approach

    CERN Document Server

    Paston, S A; Prokhvatilov, E V

    2002-01-01

    The Hamiltonian, reproducing the results of the two-dimensional quantum electrodynamics in the Lorentz coordinates, is constructed on the light front. The procedure of bosonization and analysis of the boson perturbation theory in all the orders by the fermions mass are applied for this purpose. Besides the common terms, originating by the naive quantization on the light front, the obtained Hamiltonian contains an additional counterterm. It is proportional to the linear combination of the fermion zero modes (multiplied by a certain factor compensating the charge and fermion number). The coefficient before this counterterm has no ultraviolet divergence, depends on the value of the fermion condensate in the theta-vacuum and by the small fermion mass is linear by it

  9. Formation of spin-polarons in the ferromagnetic Kondo lattice model away from half-filling

    International Nuclear Information System (INIS)

    Arredondo, Y; Navarro, O; Vallejo, E; Avignon, M

    2012-01-01

    Even though realistic one-dimensional experiments in the field of half-metallic semiconductors are not at hand yet, we are interested in the underlying fundamental physics. In this regard we study a one-dimensional ferromagnetic Kondo lattice model, a model in which a conduction band is coupled ferromagnetically to a background of localized d moments with coupling constant J H , and investigate the T = 0 phase diagram as a function of the antiferromagnetic interaction J between the localized moments and the band-filling n, since it has been observed that doping of the compounds has led to formation of magnetic domains. We explore the spin-polaron formation by looking at the nearest-neighbour correlation functions in the spin and charge regimes for which we use the density matrix renormalization group method, which is a highly efficient method to investigate quasi-one-dimensional strongly correlated systems. (paper)

  10. Two pairs of Lie algebras and the integrable couplings as well as the Hamiltonian structure of the Yang hierarchy

    International Nuclear Information System (INIS)

    Zhang Yufeng; Guo Fukui

    2007-01-01

    Two types of Lie algebras, which are the subalgebras of the Lie algebra A 2 , A 3 respectively, are presented. The resulting loop algebras are following. As their applications, two different integrable couplings of the Yang hierarchy are obtained, called them the double integrable couplings. The Hamiltonian structure of one of them is worked out by a proper linear isomorphic transformation and the quadratic-form identity

  11. Numerical study on a canonized Hamiltonian system representing reduced magnetohydrodynamics and its comparison with two-dimensional Euler system

    OpenAIRE

    Kaneko, Yuta; Yoshida, Zensho

    2014-01-01

    Introducing a Clebsch-like parameterization, we have formulated a canonical Hamiltonian system on a symplectic leaf of reduced magnetohydrodynamics. An interesting structure of the equations is in that the Lorentz-force, which is a quadratic nonlinear term in the conventional formulation, appears as a linear term -{\\Delta}Q, just representing the current density (Q is a Clebsch variable, and {\\Delta} is the two-dimensional Laplacian); omitting this term reduces the system into the two-dimensi...

  12. Hamiltonian derivation of a gyrofluid model for collisionless magnetic reconnection

    International Nuclear Information System (INIS)

    Tassi, E

    2014-01-01

    We consider a simple electromagnetic gyrokinetic model for collisionless plasmas and show that it possesses a Hamiltonian structure. Subsequently, from this model we derive a two-moment gyrofluid model by means of a procedure which guarantees that the resulting gyrofluid model is also Hamiltonian. The first step in the derivation consists of imposing a generic fluid closure in the Poisson bracket of the gyrokinetic model, after expressing such bracket in terms of the gyrofluid moments. The constraint of the Jacobi identity, which every Poisson bracket has to satisfy, selects then what closures can lead to a Hamiltonian gyrofluid system. For the case at hand, it turns out that the only closures (not involving integro/differential operators or an explicit dependence on the spatial coordinates) that lead to a valid Poisson bracket are those for which the second order parallel moment, independently for each species, is proportional to the zero order moment. In particular, if one chooses an isothermal closure based on the equilibrium temperatures and derives accordingly the Hamiltonian of the system from the Hamiltonian of the parent gyrokinetic model, one recovers a known Hamiltonian gyrofluid model for collisionless reconnection. The proposed procedure, in addition to yield a gyrofluid model which automatically conserves the total energy, provides also, through the resulting Poisson bracket, a way to derive further conservation laws of the gyrofluid model, associated with the so called Casimir invariants. We show that a relation exists between Casimir invariants of the gyrofluid model and those of the gyrokinetic parent model. The application of such Hamiltonian derivation procedure to this two-moment gyrofluid model is a first step toward its application to more realistic, higher-order fluid or gyrofluid models for tokamaks. It also extends to the electromagnetic gyrokinetic case, recent applications of the same procedure to Vlasov and drift- kinetic systems

  13. Effects of Polaron and Quantum Confinement on the Nonlinear Optical Properties in a GaAs/Ga1-xAlxAs Quantum Well Wire

    Directory of Open Access Journals (Sweden)

    L. Caroline Sugirtham

    2014-01-01

    Full Text Available The binding energy of a polaron confined in a GaAs/Ga1-xAlxAs quantum well wire is calculated within the framework of the variational technique and Lee-Low Pines approach. The polaron-induced photoionization cross section as a function of normalized photon energy for a on-centre donor impurity in the quantum wire is investigated. The oscillator strength with the geometrical effect is studied taking into account the polaron effects in a GaAs/Ga0.8Al0.2As quantum well wire. The effect of polaron on the third-order susceptibility of third harmonic generation is studied. Our theoretical results are shown to be in good agreement with previous investigations.

  14. Notch Filters for Port-Hamiltonian Systems

    NARCIS (Netherlands)

    Dirksz, Danny; Scherpen, Jacquelien M.A.; van der Schaft, Abraham J.; Steinbuch, Maarten

    Many powerful tools exist for control design in the frequency domain, but are theoretically only justified for linear systems. On the other hand, nonlinear control deals with control design methodologies that are theoretically justified for a larger and more realistic class of systems, but primarily

  15. An extended discrete gradient formula for oscillatory Hamiltonian systems

    International Nuclear Information System (INIS)

    Liu Kai; Shi Wei; Wu Xinyuan

    2013-01-01

    In this paper, incorporating the idea of the discrete gradient method into the extended Runge–Kutta–Nyström integrator, we derive and analyze an extended discrete gradient formula for the oscillatory Hamiltonian system with the Hamiltonian H(p,q)= 1/2 p T p+ 1/2 q T Mq+U(q), where q:R→R d represents generalized positions, p:R→R d represents generalized momenta and M is an element of R dxd is a symmetric and positive semi-definite matrix. The solution of this system is a nonlinear oscillator. Basically, many nonlinear oscillatory mechanical systems with a partitioned Hamiltonian function lend themselves to this approach. The extended discrete gradient formula presented in this paper exactly preserves the energy H(p, q). We derive some properties of the new formula. The convergence is analyzed for the implicit schemes based on the discrete gradient formula, and it turns out that the convergence of the implicit schemes based on the extended discrete gradient formula is independent of ‖M‖, which is a significant property for the oscillatory Hamiltonian system. Thus, it transpires that a larger step size can be chosen for the new energy-preserving schemes than that for the traditional discrete gradient methods when applied to the oscillatory Hamiltonian system. Illustrative examples show the competence and efficiency of the new schemes in comparison with the traditional discrete gradient methods in the scientific literature. (paper)

  16. Multivector field formulation of Hamiltonian field theories: equations and symmetries

    Energy Technology Data Exchange (ETDEWEB)

    Echeverria-Enriquez, A.; Munoz-Lecanda, M.C.; Roman-Roy, N. [Departamento de Matematica Aplicada y Telematica, Edificio C-3, Campus Norte UPC, Barcelona (Spain)

    1999-12-03

    We state the intrinsic form of the Hamiltonian equations of first-order classical field theories in three equivalent geometrical ways: using multivector fields, jet fields and connections. Thus, these equations are given in a form similar to that in which the Hamiltonian equations of mechanics are usually given. Then, using multivector fields, we study several aspects of these equations, such as the existence and non-uniqueness of solutions, and the integrability problem. In particular, these problems are analysed for the case of Hamiltonian systems defined in a submanifold of the multimomentum bundle. Furthermore, the existence of first integrals of these Hamiltonian equations is considered, and the relation between Cartan-Noether symmetries and general symmetries of the system is discussed. Noether's theorem is also stated in this context, both the 'classical' version and its generalization to include higher-order Cartan-Noether symmetries. Finally, the equivalence between the Lagrangian and Hamiltonian formalisms is also discussed. (author)

  17. Non-stoquastic Hamiltonians in quantum annealing via geometric phases

    Science.gov (United States)

    Vinci, Walter; Lidar, Daniel A.

    2017-09-01

    We argue that a complete description of quantum annealing implemented with continuous variables must take into account the non-adiabatic Aharonov-Anandan geometric phase that arises when the system Hamiltonian changes during the anneal. We show that this geometric effect leads to the appearance of non-stoquasticity in the effective quantum Ising Hamiltonians that are typically used to describe quantum annealing with flux qubits. We explicitly demonstrate the effect of this geometric non-stoquasticity when quantum annealing is performed with a system of one and two coupled flux qubits. The realization of non-stoquastic Hamiltonians has important implications from a computational complexity perspective, since it is believed that in many cases quantum annealing with stoquastic Hamiltonians can be efficiently simulated via classical algorithms such as Quantum Monte Carlo. It is well known that the direct implementation of non-stoquastic Hamiltonians with flux qubits is particularly challenging. Our results suggest an alternative path for the implementation of non-stoquasticity via geometric phases that can be exploited for computational purposes.

  18. Polaron variable range hopping in TiO2-δ(-0.04=<δ=<0.2) thin films

    International Nuclear Information System (INIS)

    Heluani, S.P.; Comedi, D.; Villafuerte, M.; Juarez, G.

    2007-01-01

    The mechanisms of electrical conduction in TiO 2-δ (-0.04= 2 +Ar gas atmospheres where changes in δ and film structure had been achieved by varying the O 2 flow rate and the substrate temperature. The electrical transport properties of these samples were investigated by measuring the conductivity as a function of temperature between 17K and room temperature. At the temperature range between 200 and 290K the best fit to the experimental data was obtained assuming a dependence characteristic of adiabatic variable range hopping. At lower temperature the activation energy for the conductivity tends to zero. The results suggest that the conduction mechanism is adiabatic small polaron hopping, which switches to conduction in a polaron band at low temperatures

  19. Construction of exact invariants of time-dependent linear nonholonomic dynamical systems

    International Nuclear Information System (INIS)

    Fu Jingli; Jimenez, Salvador; Tang Yifa; Vazquez, Luis

    2008-01-01

    In this work, we build exact dynamical invariants for time-dependent, linear, nonholonomic Hamiltonian systems in two dimensions. Our aim is to obtain an additional insight into the theoretical understanding of generalized Hamilton canonical equations. In particular, we investigate systems represented by a quadratic Hamiltonian subject to linear nonholonomic constraints. We use a Lie algebraic method on the systems to build the invariants. The role and scope of these invariants is pointed out

  20. Construction of exact invariants of time-dependent linear nonholonomic dynamical systems

    Energy Technology Data Exchange (ETDEWEB)

    Fu Jingli [Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018 (China)], E-mail: sqfujingli@163.com; Jimenez, Salvador [Departamento de Matematica Aplicada TTII, E.T.S.I. Telecomunicacion, Universidad Politecnica de Madrid, 28040 Madrid (Spain); Tang Yifa [State Key Laboratory of Scientific and Engineering Computing, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, PO Box 2719, Beijing 100080 (China); Vazquez, Luis [Departamento de Matematica Aplicada Facultad de Informatica, Universidad Complutense de Madrid, 28040 Madrid (Spain); Centro de Astrobiologia (CSIC-INTA), Torrejon de Ardoz, 28850 Madrid (Spain)

    2008-03-03

    In this work, we build exact dynamical invariants for time-dependent, linear, nonholonomic Hamiltonian systems in two dimensions. Our aim is to obtain an additional insight into the theoretical understanding of generalized Hamilton canonical equations. In particular, we investigate systems represented by a quadratic Hamiltonian subject to linear nonholonomic constraints. We use a Lie algebraic method on the systems to build the invariants. The role and scope of these invariants is pointed out.