Light-Front Hamiltonian Approach to the Bound-State Problem in Quantum Electrodynamics
Jones, Billy D.
1997-10-01
Why is the study of the Lamb shift in hydrogen, which at the level of detail found in this paper was largely completed by Bethe in 1947, of any real interest today? While completing such a calculation using new techniques may be very interesting for formal and academic reasons, our primary motivation is to lay groundwork for precision bound-state calculations in QCD. The Lamb shift provides an excellent pedagogical tool for illustrating light-front Hamiltonian techniques, which are not widely known; but more importantly it presents three of the central dynamical and computational problems that we must face to make these techniques useful for solving QCD: How does a constituent picture emerge in a gauge field theory? How do bound-state energy scales emerge non-perturbatively? How does rotational symmetry emerge in a non-perturbative light-front calculation?
Charmonium spectrum and diffractive production in a light-front Hamiltonian approach
Chen, Guangyao; Li, Yang; Maris, Pieter; Tuchin, Kirill; Vary, James P.
2017-08-01
We study exclusive charmonium production in diffractive deep inelastic scattering and ultra-peripheral heavy-ion collisions within the dipole picture. The mass spectrum and light-front wavefunctions of charmonium are obtained from the basis light-front quantization approach, using the one-gluon exchange interaction plus a confining potential inspired by light-front holography. We apply these light-front wavefunctions to exclusive charmonium production. The resulting cross sections are in reasonable agreement with electron-proton collision data at HERA and ultra-peripheral nucleus collision measurements at RHIC and LHC. The charmonium cross-section has model dependence on the dipole model. We observe that the cross-section ratio of excited states to the ground state has a weaker dependence than the cross-section itself. We suggest that measurements of excited states of heavy quarkonium production in future electron-ion collision experiments will impose rigorous constraints on heavy quarkonium light-front wave-functions, thus improving our understanding of meson structure, which eventually will help us develop a precise description of the gluon distribution function in the small-x regime.
Pauli-Villars regularization in nonperturbative Hamiltonian approach on the light front
Energy Technology Data Exchange (ETDEWEB)
Malyshev, M. Yu., E-mail: mimalysh@yandex.ru; Paston, S. A.; Prokhvatilov, E. V.; Zubov, R. A.; Franke, V. A. [Saint Petersburg State University, Saint Petersburg (Russian Federation)
2016-01-22
The advantage of Pauli-Villars regularization in quantum field theory quantized on the light front is explained. Simple examples of scalar λφ{sup 4} field theory and Yukawa-type model are used. We give also an example of nonperturbative calculation in the theory with Pauli-Villars fields, using for that a model of anharmonic oscillator modified by inclusion of ghost variables playing the role similar to Pauli-Villars fields.
The light-front vacuum and dynamics
Polyzou, W. N.
2004-01-01
I give a quantum theoretical description of kinematically invariant vacuua on the algebra of free fields restricted to a light front and discuss the relation between the light-front Hamiltonian, P-, the vacuum, and Poincare invariance. This provides a quantum theoretical description of zero modes.
Light-Front Holography and the Light-Front Schrodinger Equation
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.; de Teramond, Guy
2012-08-15
One of the most important nonperturbative methods for solving QCD is quantization at fixed light-front time {tau} = t+z=c - Dirac's 'Front Form'. The eigenvalues of the light-front QCD Hamiltonian predict the hadron spectrum and the eigensolutions provide the light-front wavefunctions which describe hadron structure. More generally, we show that the valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a single-variable relativistic equation of motion, analogous to the nonrelativistic radial Schrodinger equation, with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. We outline a method for computing the required potential from first principles in QCD. The holographic mapping of gravity in AdS space to QCD, quantized at fixed light-front time, yields the same light front Schrodinger equation; in fact, the soft-wall AdS/QCD approach provides a model for the light-front potential which is color-confining and reproduces well the light-hadron spectrum. One also derives via light-front holography a precise relation between the bound-state amplitudes in the fifth dimension of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. The elastic and transition form factors of the pion and the nucleons are found to be well described in this framework. The light-front AdS/QCD holographic approach thus gives a frame-independent first approximation of the color-confining dynamics, spectroscopy, and excitation spectra of relativistic light-quark bound states in QCD.
Energy Technology Data Exchange (ETDEWEB)
Brodsky, S.
2004-11-30
In these lectures, I survey a number of applications of light-front methods to hadron and nuclear physics phenomenology and dynamics, including light-front statistical physics. Light-front Fock-state wavefunctions provide a frame-independent representation of hadrons in terms of their fundamental quark and gluon degrees of freedom. Nonperturbative methods for computing LFWFs in QCD are discussed, including string/gauge duality which predicts the power-law fall-off at high momentum transfer of light-front Fock-state hadronic wavefunctions with an arbitrary number of constituents and orbital angular momentum. The AdS/CFT correspondence has important implications for hadron phenomenology in the conformal limit, including an all-orders derivation of counting rules for exclusive processes. One can also compute the hadronic spectrum of near-conformal QCD assuming a truncated AdS/CFT space. Given the LFWFs, one can compute form factors, heavy hadron decay amplitudes, hadron distribution amplitudes, and the generalized parton distributions underlying deeply virtual Compton scattering. The quantum fluctuations represented by the light-front Fock expansion leads to novel QCD phenomena such as color transparency, intrinsic heavy quark distributions, diffractive dissociation, and hidden-color components of nuclear wavefunctions. A new test of hidden color in deuteron photodisintegration is proposed. The origin of leading-twist phenomena such as the diffractive component of deep inelastic scattering, single-spin asymmetries, nuclear shadowing and antishadowing is also discussed; these phenomena cannot be described by light-front wavefunctions of the target computed in isolation. Part of the anomalous NuTeV results for the weak mixing angle {theta}{sub W} could be due to the non-universality of nuclear antishadowing for charged and neutral currents.
Light-front holography: a first approximation to QCD.
de Téramond, Guy F; Brodsky, Stanley J
2009-02-27
Starting from the Hamiltonian equation of motion in QCD, we identify an invariant light-front coordinate zeta which allows the separation of the dynamics of quark and gluon binding from the kinematics of constituent spin and internal orbital angular momentum. The result is a single-variable light-front Schrödinger equation for QCD which determines the eigenspectrum and the light-front wave functions of hadrons for general spin and orbital angular momentum. This light-front wave equation is equivalent to the equations of motion which describe the propagation of spin-J modes on anti-de Sitter (AdS) space.
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.; de Teramond, Guy F.; /SLAC /Southern Denmark U., CP3-Origins /Costa Rica U.
2011-01-10
AdS/QCD, the correspondence between theories in a dilaton-modified five-dimensional anti-de Sitter space and confining field theories in physical space-time, provides a remarkable semiclassical model for hadron physics. Light-front holography allows hadronic amplitudes in the AdS fifth dimension to be mapped to frame-independent light-front wavefunctions of hadrons in physical space-time. The result is a single-variable light-front Schroedinger equation which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum. The coordinate z in AdS space is uniquely identified with a Lorentz-invariant coordinate {zeta} which measures the separation of the constituents within a hadron at equal light-front time and determines the off-shell dynamics of the bound state wavefunctions as a function of the invariant mass of the constituents. The hadron eigenstates generally have components with different orbital angular momentum; e.g., the proton eigenstate in AdS/QCD with massless quarks has L = 0 and L = 1 light-front Fock components with equal probability. Higher Fock states with extra quark-anti quark pairs also arise. The soft-wall model also predicts the form of the nonperturbative effective coupling and its {beta}-function. The AdS/QCD model can be systematically improved by using its complete orthonormal solutions to diagonalize the full QCD light-front Hamiltonian or by applying the Lippmann-Schwinger method to systematically include QCD interaction terms. Some novel features of QCD are discussed, including the consequences of confinement for quark and gluon condensates. A method for computing the hadronization of quark and gluon jets at the amplitude level is outlined.
Light-Front Holography: A First Approximation to QCD
Energy Technology Data Exchange (ETDEWEB)
de Teramond, Guy F.; Brodsky, Stanley J.
2008-10-03
Starting from the Hamiltonian equation of motion in QCD, we identify an invariant light-front coordinate {zeta} which allows the separation of the dynamics of quark and gluon binding from the kinematics of constituent spin and internal orbital angular momentum. The result is a single variable light-front Schroedinger equation for QCD which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum. This light-front wave equation is equivalent to the equations of motion which describe the propagation of spin-J modes on anti-de Sitter (AdS) space. This allows us to establish formally a gauge/gravity correspondence between an effective gravity theory defined on AdS5 and light front QCD.
Quarkonium as a relativistic bound state on the light front
Li, Yang; Maris, Pieter; Vary, James P.
2017-07-01
We study charmonium and bottomonium as relativistic bound states in a light-front quantized Hamiltonian formalism. The effective Hamiltonian is based on light-front holography. We use a recently proposed longitudinal confinement to complete the soft-wall holographic potential for the heavy flavors. The spin structure is generated from the one-gluon exchange interaction with a running coupling. The adoption of asymptotic freedom improves the spectroscopy compared with previous light-front results. Within this model, we compute the mass spectroscopy, decay constants and the r.m.s. radii. We also present a detailed study of the obtained light-front wave functions and use the wave functions to compute the light-cone distributions, specifically the distribution amplitudes and parton distribution functions. Overall, our model provides a reasonable description of the heavy quarkonia.
QCD Phenomenology and Light-Front Wavefunctions
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.
2001-11-21
A natural calculus for describing the bound-state structure of relativistic composite systems in quantum field theory is the light-front Fock expansion which encodes the properties of a hadrons in terms of a set of frame-independent n-particle wavefunctions. Light-front quantization in the doubly-transverse light-cone gauge has a number of remarkable advantages, including explicit unitarity, a physical Fock expansion, the absence of ghost degrees of freedom, and the decoupling properties needed to prove factorization theorems in high momentum transfer inclusive and exclusive reactions. A number of applications are discussed in these lectures, including semileptonic B decays, two-photon exclusive reactions, diffractive dissociation into jets, and deeply virtual Compton scattering. The relation of the intrinsic sea to the light-front wavefunctions is discussed. Light-front quantization can also be used in the Hamiltonian form to construct an event generator for high energy physics reactions at the amplitude level. The light-cone partition function, summed over exponentially weighted light-cone energies, has simple boost properties which may be useful for studies in heavy ion collisions. I also review recent work which shows that the structure functions measured in deep inelastic lepton scattering are affected by final-state rescattering, thus modifying their connection to light-front probability distributions. In particular, the shadowing of nuclear structure functions is due to destructive interference effects from leading-twist diffraction of the virtual photon, physics not included in the nuclear light-cone wavefunctions.
QCD and Light-Front Holography
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.; /SLAC /Southern Denmark U., CP3-Origins; de Teramond, Guy F.; /Costa Rica U.
2010-10-27
The soft-wall AdS/QCD model, modified by a positive-sign dilaton metric, leads to a remarkable one-parameter description of nonperturbative hadron dynamics. The model predicts a zero-mass pion for zero-mass quarks and a Regge spectrum of linear trajectories with the same slope in the leading orbital angular momentum L of hadrons and the radial quantum number N. Light-Front Holography maps the amplitudes which are functions of the fifth dimension variable z of anti-de Sitter space to a corresponding hadron theory quantized on the light front. The resulting Lorentz-invariant relativistic light-front wave equations are functions of an invariant impact variable {zeta} which measures the separation of the quark and gluonic constituents within the hadron at equal light-front time. The result is to a semi-classical frame-independent first approximation to the spectra and light-front wavefunctions of meson and baryon light-quark bound states, which in turn predict the behavior of the pion and nucleon form factors. The theory implements chiral symmetry in a novel way: the effects of chiral symmetry breaking increase as one goes toward large interquark separation, consistent with spectroscopic data, and the the hadron eigenstates generally have components with different orbital angular momentum; e.g., the proton eigenstate in AdS/QCD with massless quarks has L = 0 and L = 1 light-front Fock components with equal probability. The soft-wall model also predicts the form of the non-perturbative effective coupling {alpha}{sub s}{sup AdS} (Q) and its {beta}-function which agrees with the effective coupling {alpha}{sub g1} extracted from the Bjorken sum rule. The AdS/QCD model can be systematically improved by using its complete orthonormal solutions to diagonalize the full QCD light-front Hamiltonian or by applying the Lippmann-Schwinger method in order to systematically include the QCD interaction terms. A new perspective on quark and gluon condensates is also reviewed.
Fermions in light front transverse lattice quantum chromodynamics
Indian Academy of Sciences (India)
boost invariant wave functions. Furthermore, rotations in the transverse plane remains kinematical. Since vacuum processes receive contributions only from k· =0, Fock vacuum becomes an eigenstate of the light front Hamiltonian in the interacting theory (with the exception of theories with spontaneous symmetry breaking) ...
Light-Front Holography, Light-Front Wavefunctions, and Novel QCD Phenomena
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.; /SLAC /Southern Denmark U., CP3-Origins; de Teramond, Guy F.; /Costa Rica U.
2012-02-16
Light-Front Holography is one of the most remarkable features of the AdS/CFT correspondence. In spite of its present limitations it provides important physical insights into the nonperturbative regime of QCD and its transition to the perturbative domain. This novel framework allows hadronic amplitudes in a higher dimensional anti-de Sitter (AdS) space to be mapped to frame-independent light-front wavefunctions of hadrons in physical space-time. The model leads to an effective confining light-front QCD Hamiltonian and a single-variable light-front Schroedinger equation which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum. The coordinate z in AdS space is uniquely identified with a Lorentz-invariant coordinate {zeta} which measures the separation of the constituents within a hadron at equal light-front time and determines the off-shell dynamics of the bound-state wavefunctions, and thus the fall-off as a function of the invariant mass of the constituents. The soft-wall holographic model modified by a positive-sign dilaton metric, leads to a remarkable one-parameter description of nonperturbative hadron dynamics - a semi-classical frame-independent first approximation to the spectra and light-front wavefunctions of meson and baryons. The model predicts a Regge spectrum of linear trajectories with the same slope in the leading orbital angular momentum L of hadrons and the radial quantum number n. The hadron eigensolutions projected on the free Fock basis provides the complete set of valence and non-valence light-front Fock state wavefunctions {Psi}{sub n/H} (x{sub i}, k{sub {perpendicular}i}, {lambda}{sub i}) which describe the hadron's momentum and spin distributions needed to compute the direct measures of hadron structure at the quark and gluon level, such as elastic and transition form factors, distribution amplitudes, structure functions, generalized parton distributions and transverse
Light-Front Holography and Non-Perturbative QCD
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.; /SLAC; de Teramond, Guy F.; /Costa Rica U.
2009-12-09
The combination of Anti-de Sitter space (AdS) methods with light-front holography leads to a semi-classical first approximation to the spectrum and wavefunctions of meson and baryon light-quark bound states. Starting from the bound-state Hamiltonian equation of motion in QCD, we derive relativistic light-front wave equations in terms of an invariant impact variable {zeta} which measures the separation of the quark and gluonic constituents within the hadron at equal light-front time. These equations of motion in physical space-time are equivalent to the equations of motion which describe the propagation of spin-J modes in anti-de Sitter (AdS) space. Its eigenvalues give the hadronic spectrum, and its eigenmodes represent the probability distribution of the hadronic constituents at a given scale. Applications to the light meson and baryon spectra are presented. The predicted meson spectrum has a string-theory Regge form M{sup 2} = 4{kappa}{sup 2}(n + L + S = 2); i.e., the square of the eigenmass is linear in both L and n, where n counts the number of nodes of the wavefunction in the radial variable {zeta}. The space-like pion form factor is also well reproduced. One thus obtains a remarkable connection between the description of hadronic modes in AdS space and the Hamiltonian formulation of QCD in physical space-time quantized on the light-front at fixed light-front time {tau}. The model can be systematically improved by using its complete orthonormal solutions to diagonalize the full QCD light-front Hamiltonian or by applying the Lippmann-Schwinger method in order to systematically include the QCD interaction terms.
Chiral symmetry in light-front QCD
Wu, Menh-Hsiu; Zhang, Wei-Min
2004-04-01
The definition of chiral transformations in light-front field theory is very different from the conventional form in equal-time formalism. We study the consistency of chiral transformations and chiral symmetry in light-front QCD and derive a complete new light-front axial-vector current for QCD. The breaking of chiral symmetry in light-front QCD is only associated with helicity flip interaction between quarks and gluons. Remarkably, the new axial-vector current does not contain the pion pole part so that the associate chiral charge smoothly describes pion transitions for various hadronic processes.
Chiral Symmetry in Light-front QCD
Wu, Meng-Hsiu; Zhang, Wei-Min
2003-01-01
The definition of chiral transformations in light-front field theory is very different from the conventional form in equal-time formalism. We study the consistency of chiral transformations and chiral symmetry in light-front QCD and derive a complete new light-front axial-vector current for QCD. The breaking of chiral symmetry in light-front QCD is only associated with helicity flip interaction between quarks and gluons. Remarkably, the new axial-vector current does not contain the pion pole ...
Light front quantum chromodynamics: Towards phenomenology
Indian Academy of Sciences (India)
We briefly review the application of light front QCD to inclusive deep inelastic scattering. Keywords. Light front dynamics .... longitudinal gluon structure function and to a new sum rule. К. dmFД/m = 4M¾/Q¾. , which ... For the transversely polarized structure function g¾, if the twist three contributions are ignored, one gets an ...
Applications of AdS/QCD and Light-Front Holography to Baryon Physics
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.; /SLAC; de Teramond, Guy F.; /Costa Rica U.
2011-08-22
The correspondence between theories in anti-de Sitter space and field theories in physical space-time leads to an analytic, semiclassical model for strongly-coupled QCD which has scale invariance at short distances and color confinement at large distances. These equations, for both mesons and baryons, give a very good representation of the observed hadronic spectrum, including a zero mass pion. Light-front holography allows hadronic amplitudes in the AdS fifth dimension to be mapped to frame-independent light-front wavefunctions of hadrons in physical space-time, thus providing a relativistic description of hadrons at the amplitude level. The meson and baryon wavefunctions derived from light-front holography and AdS/QCD also have remarkable phenomenological features, including predictions for the electromagnetic form factors and decay constants. The approach can be systematically improved using light-front Hamiltonian methods. Some novel features of QCD for baryon physics are also discussed.
Light front distribution of the chiral condensate
National Research Council Canada - National Science Library
Chang, Lei; Roberts, Craig D; Schmidt, Sebastian M
2013-01-01
The pseudoscalar projection of the pionE1/4s Poincare-covariant Bethe-Salpeter amplitude onto the light-front may be understood to provide the probability distribution of the chiral condensate within the pion...
Light-Front Quantization Approach to the Gauge Gravity Correspondence and Hadron Spectroscopy
Energy Technology Data Exchange (ETDEWEB)
de Teramond, Guy F.; /Costa Rica U.; Brodsky, Stanley J.; /SLAC
2010-05-26
We find a correspondence between semiclassical QCD quantized on the light-front and a dual gravity model in anti-de Sitter (AdS) space, thus providing an initial approximation to QCD in its strongly coupled regime. This correspondence - light-front holography - leads to a light-front Hamiltonian and relativistic bound-state wave equations that are functions of an invariant impact variable {zeta} which measures the separation of the quark and gluonic constituents within hadrons at equal lightfront time. The eigenvalues of the resulting light-front Schrodinger and Dirac equations are consistent with the observed light meson and baryon spectrum, and the eigenmodes provide the light-front wavefunctions, the probability amplitudes describing the dynamics of the hadronic constituents. The light-front equations of motion, which are dual to an effective classical gravity theory, possess remarkable algebraic and integrability properties which are dictated by the underlying conformal properties of the theory. We extend the algebraic construction to include a confining potential while preserving the integrability of the mesonic and baryonic bound-state equations.
AdS/QCD and Light Front Holography: A New Approximation to QCD
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.; de Teramond, Guy
2010-02-15
The combination of Anti-de Sitter space (AdS) methods with light-front holography leads to a semi-classical first approximation to the spectrum and wavefunctions of meson and baryon light-quark bound states. Starting from the bound-state Hamiltonian equation of motion in QCD, we derive relativistic light-front wave equations in terms of an invariant impact variable {zeta} which measures the separation of the quark and gluonic constituents within the hadron at equal light-front time. These equations of motion in physical space-time are equivalent to the equations of motion which describe the propagation of spin-J modes in anti-de Sitter (AdS) space. Its eigenvalues give the hadronic spectrum, and its eigenmodes represent the probability distribution of the hadronic constituents at a given scale. Applications to the light meson and baryon spectra are presented. The predicted meson spectrum has a string-theory Regge form M{sup 2} = 4{kappa}{sup 2}(n+L+S/2); i.e., the square of the eigenmass is linear in both L and n, where n counts the number of nodes of the wavefunction in the radial variable {zeta}. The space-like pion form factor is also well reproduced. One thus obtains a remarkable connection between the description of hadronic modes in AdS space and the Hamiltonian formulation of QCD in physical space-time quantized on the light-front at fixed light-front time {tau}. The model can be systematically improved by using its complete orthonormal solutions to diagonalize the full QCD light-front Hamiltonian or by applying the Lippmann-Schwinger method in order to systematically include the QCD interaction terms.
Light-Front Dynamics in Hadron Physics
Ji, C.R.; Bakker, B.L.G.; Choi, H.M.
2013-01-01
Light-front dynamics(LFD) plays an important role in the analyses of relativistic few-body systems. As evidenced from the recent studies of generalized parton distributions (GPDs) in hadron physics, a natural framework for a detailed study of hadron structures is LFD due to its direct application in
Light-Front Holography, Light-Front Wavefunctions, and Novel QCD Phenomena
DEFF Research Database (Denmark)
Brodsky, S. J.; de Teramond, G. F.
2012-01-01
-classical frame-independent first approximation to the spectra and light-front wavefunctions of meson and baryons. The model predicts a Regge spectrum of linear trajectories with the same slope in the leading orbital angular momentum L of hadrons and the radial quantum number n. The hadron eigensolutions...... the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum. The coordinate z in AdS space is uniquely identified with a Lorentz-invariant coordinate zeta which measures the separation of the constituents within a hadron at equal light-front time and determines...
Light-Front Quantization and AdS/QCD: An Overview
Energy Technology Data Exchange (ETDEWEB)
de Teramond, Guy F.; /Costa Rica U.; Brodsky, Stanley J.; /SLAC /Stanford U., Phys. Dept.
2011-08-19
We give an overview of the light-front holographic approach to strongly coupled QCD, whereby a confining gauge theory, quantized on the light front, is mapped to a higher-dimensional anti de Sitter (AdS) space. The framework is guided by the AdS/CFT correspondence incorporating a gravitational background asymptotic to AdS space which encodes the salient properties of QCD, such as the ultraviolet conformal limit at the AdS boundary at z {yields} 0, as well as modifications of the geometry in the large z infrared region to describe confinement and linear Regge behavior. There are two equivalent procedures for deriving the AdS/QCD equations of motion: one can start from the Hamiltonian equation of motion in physical space time by studying the off-shell dynamics of the bound state wavefunctions as a function of the invariant mass of the constituents. To a first semiclassical approximation, where quantum loops and quark masses are not included, this leads to a light-front Hamiltonian equation which describes the bound state dynamics of light hadrons in terms of an invariant impact variable {zeta} which measures the separation of the partons within the hadron at equal light-front time. Alternatively, one can start from the gravity side by studying the propagation of hadronic modes in a fixed effective gravitational background. Both approaches are equivalent in the semiclassical approximation. This allows us to identify the holographic variable z in AdS space with the impact variable {zeta}. Light-front holography thus allows a precise mapping of transition amplitudes from AdS to physical space-time. The internal structure of hadrons is explicitly introduced and the angular momentum of the constituents plays a key role.
Light-Front Holography and Gauge/Gravity Duality: The Light Meson and Baryon Spectra
Energy Technology Data Exchange (ETDEWEB)
de Teramond, Guy F.; /Costa Rica U.; Brodsky, Stanley J.; /SLAC
2009-12-09
Starting from the bound state Hamiltonian equation of motion in QCD, we derive relativistic light-front wave equations in terms of an invariant impact variable {zeta} which measures the separation of the quark and gluonic constituents within the hadron at equal light-front time. These equations of motion in physical space-time are equivalent to the equations of motion which describe the propagation of spin-J modes in anti-de Sitter (AdS) space. Its eigenvalues give the hadronic spectrum, and its eigenmodes represent the probability amplitudes of the hadronic constituents at a given scale. An effective classical gravity description in a positive-sign dilaton background exp(+{kappa}{sup 2}z{sup 2}) is given for the phenomenologically successful soft-wall model which naturally encodes the internal structure of hadrons and their orbital angular momentum. Applications to the light meson and baryon spectrum are presented.
Spectrum and structure of Bc mesons on the light-front
Tang, Shuo; Li, Yang; Maris, Pieter; Vary, James
2017-09-01
Recent measurements at LHC have renewed the theoretical interest in the production, spectrum and decay of charm-beauty (Bc) mesons. We solve for the low-lying (b c) states using a light-front Hamiltonian with a confining interaction based on AdS/QCD holography plus one-gluon exchange that gives a good description of charmonium and botomonium. Without adjusting any parameters we find good agreement for the ground state Bc mass compared to experiment. We also discuss the spectrum below threshold, and compare our results with quark model calculations. The corresponding light-front wave functions can be used to calculate other observables such as the decays constants, distribution amplitudes, and GPDs. DOE-FG02-87ER40371.
AdS/QCD, Light-Front Holography, and Sublimated Gluons
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.; /SLAC; de Teramond, Guy F.; /Costa Rica U.
2012-02-16
The gauge/gravity duality leads to a simple analytical and phenomenologically compelling nonperturbative approximation to the full light-front QCD Hamiltonian - 'Light-Front Holography', which provides a Lorentz-invariant first-approximation to QCD, and successfully describes the spectroscopy of light-quark meson and baryons, their elastic and transition form factors, and other hadronic properties. The bound-state Schroedinger and Dirac equations of the soft-wall AdS/QCD model predict linear Regge trajectories which have the same slope in orbital angular momentum L and radial quantum number n for both mesons and baryons. Light-front holography connects the fifth-dimensional coordinate of AdS space z to an invariant impact separation variable {zeta} in 3+1 space at fixed light-front time. A key feature is the determination of the frame-independent light-front wavefunctions of hadrons - the relativistic analogs of the Schroedinger wavefunctions of atomic physics which allow one to compute form factors, transversity distributions, spin properties of the valence quarks, jet hadronization, and other hadronic observables. One thus obtains a one-parameter color-confining model for hadron physics at the amplitude level. AdS/QCD also predicts the form of the non-perturbative effective coupling {alpha}{sub s}{sup AdS} (Q) and its {beta}-function with an infrared fixed point which agrees with the effective coupling a{sub g1} (Q{sup 2}) extracted from measurements of the Bjorken sum rule below Q{sup 2} < 1 GeV{sup 2}. This is consistent with a flux-tube interpretation of QCD where soft gluons with virtualities Q{sup 2} < 1 GeV{sup 2} are sublimated into a color-confining potential for quarks. We discuss a number of phenomenological hadronic properties which support this picture.
Novel Perspectives from Light-Front QCD, Super-Conformal Algebra, and Light-Front Holography
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-12-01
Light-Front Quantization – Dirac’s “Front Form” – provides a physical, frame-independent formalism for hadron dynamics and structure. Observables such as structure functions, transverse momentum distributions, and distribution amplitudes are defined from the hadronic LFWFs. One obtains new insights into the hadronic mass scale, the hadronic spectrum, and the functional form of the QCD running coupling in the nonperturbative domain using light-front holography. In addition, superconformal algebra leads to remarkable supersymmetric relations between mesons and baryons. I also discuss evidence that the antishadowing of nuclear structure functions is nonuniversal; i.e., flavor dependent, and why shadowing and antishadowing phenomena may be incompatible with the momentum and other sum rules for the nuclear parton distribution functions.
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J. [SLAC National Accelerator Lab., Menlo Park, CA (United States); de Teramond, Guy F. [Univ. of Costa Rica, San Pedro (Costa Rica); Deur, Alexandre P. [Jefferson La.b, Newport News, VA (United States); Dosch, Hans G. [Institut fur Theoretische Physik, Heidelberg (Germany)
2015-09-01
The valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a relativistic equation of motion with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. If one requires that the effective action which underlies the QCD Lagrangian remains conformally invariant and extends the formalism of de Alfaro, Fubini and Furlan to light front Hamiltonian theory, the potential U has a unique form of a harmonic oscillator potential, and a mass gap arises. The result is a nonperturbative relativistic light-front quantum mechanical wave equation which incorporates color confinement and other essential spectroscopic and dynamical features of hadron physics, including a massless pion for zero quark mass and linear Regge trajectories with the same slope in the radial quantum number n and orbital angular momentum L. Only one mass parameter κ appears. Light-front holography thus provides a precise relation between the bound-state amplitudes in the fifth dimension of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. We also show how the mass scale κ underlying confinement and hadron masses determines the scale Λ_{{ovr MS}} controlling the evolution of the perturbative QCD coupling. The relation between scales is obtained by matching the nonperturbative dynamics, as described by an effective conformal theory mapped to the light-front and its embedding in AdS space, to the perturbative QCD regime computed to four-loop order. The result is an effective coupling defined at all momenta. The predicted value Λ_{{ovr MS}}=0.328±0.034 GeV is in agreement with the world average 0.339±0.010 GeV. The analysis applies to any renormalization scheme.
Spin-1 particles with light-front approach
Directory of Open Access Journals (Sweden)
de Melo J.P.B.C.
2014-06-01
Full Text Available For the vector sector, i.e, mesons with spin-1, the electromagnetic form factors and anothers observables are calculated with the light-front approach. However, the light-front quantum field theory have some problems, for example, the rotational symmetry breaking. We solve that problem added the zero modes contribuition to the matrix elements of the electromagnetic current, besides the valence contribuition. We found that among the four independent matrix elements of the plus component in the light-front helicity basis only the 0 → 0 one carries zero mode contributions.
Nucleon parton distributions in a light-front quark model
National Research Council Canada - National Science Library
Gutsche, Thomas; Lyubovitskij, Valery E; Schmidt, Ivan
2017-01-01
Continuing our analysis of parton distributions in the nucleon, we extend our light-front quark model in order to obtain both the helicity-independent and the helicity-dependent parton distributions...
Light-Front Holography and AdS/QCD Correspondence
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.; de Teramond, Guy F.
2008-04-23
Light-Front Holography is a remarkable consequence of the correspondence between string theory in AdS space and conformal field theories in physical-space time. It allows string modes {Phi}(z) in the AdS fifth dimension to be precisely mapped to the light-front wavefunctions of hadrons in terms of a specific light-front impact variable {zeta} which measures the separation of the quark and gluonic constituents within the hadron. This mapping was originally obtained by matching the exact expression for electromagnetic current matrix elements in AdS space with the corresponding exact expression for the current matrix element using light-front theory in physical space-time. More recently we have shown that one obtains the identical holographic mapping using matrix elements of the energy-momentum tensor, thus providing an important consistency test and verification of holographic mapping from AdS to physical observables defined on the light-front. The resulting light-front Schrodinger equations predicted from AdS/QCD give a good representation of the observed meson and baryon spectra and give excellent phenomenological predictions for amplitudes such as electromagnetic form factors and decay constants.
Brodsky, S. J.
2017-07-01
A fundamental problem in hadron physics is to obtain a relativistic color-confining, first approximation to QCD which can predict both hadron spectroscopy and the frame-independent light-front (LF) wavefunctions underlying hadron dynamics. The QCD Lagrangian with zero quark mass has no explicit mass scale; the classical theory is conformally invariant. Thus, a fundamental problem is to understand how the mass gap and ratios of masses - such as m ρ/ m p - can arise in chiral QCD. De Alfaro, Fubini, and Furlan have made an important observation that a mass scale can appear in the equations of motion without affecting the conformal invariance of the action if one adds a term to the Hamiltonian proportional to the dilatation operator or the special conformal operator and rescales the time variable. If one applies the same procedure to the light-front Hamiltonian, it leads uniquely to a confinement potential κ 4 ζ 2 for mesons, where ζ 2 is the LF radial variable conjugate to the q\\overline{q} invariant mass squared. The same result, including spin terms, is obtained using light-front holography - the duality between light-front dynamics and AdS5, the space of isometries of the conformal group if one modifies the action of AdS5 by the dilaton {e}^{κ^2}{z}^2 in the fifth dimension z . When one generalizes this procedure using superconformal algebra, the resulting light-front eigensolutions predict unified Regge spectroscopy of meson, baryon, and tetraquarks, including remarkable supersymmetric relations between the masses of mesons and baryons of the same parity. One also predicts observables such as hadron structure functions, transverse momentum distributions, and the distribution amplitudes defined from the hadronic light-front wavefunctions. The mass scale κ underlying confinement and hadron masses can be connected to the parameter {Λ}_{\\overline{MS}} in the QCD running coupling by matching the nonperturbative dynamics to the perturbative QCD regime. The
Covariance of light-front models: pair current
Melo, J.P.B.C. de; Frederico, T.; Naus, H.W.L.; Sauer, P.U.
1999-01-01
We compute the + component, i.e., j+ = j0 + j3, of the electromagnetic current of a composite spin-one two-fermion system for vanishing momentum transfer component q+ = q0 + q3. In particular, we extract the nonvanishing pair production amplitude on the light-front. It is a consequence of the
Chiral Boson Theory on the Light-Front
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Srivastava, Prem P.
1999-09-16
The framework for describing the quantized theory of chiral boson is discussed. It avoids the conflict with the requirement of the principle of microcausality as is found in the conventional treatment. The discussion of the Floreanini-Jackiw model and its modified version for describing the chiral boson becomes very transparent on the light-front.
Nucleon parton distributions in a light-front quark model
Energy Technology Data Exchange (ETDEWEB)
Gutsche, Thomas [Universitaet Tuebingen, Institut fuer Theoretische Physik, Kepler Center for Astro and Particle Physics, Tuebingen (Germany); Lyubovitskij, Valery E. [Universitaet Tuebingen, Institut fuer Theoretische Physik, Kepler Center for Astro and Particle Physics, Tuebingen (Germany); Tomsk State University, Department of Physics, Tomsk (Russian Federation); Tomsk Polytechnic University, Laboratory of Particle Physics, Mathematical Physics Department, Tomsk (Russian Federation); Universidad Tecnica Federico Santa Maria, Departamento de Fisica y Centro Cientifico Tecnologico de Valparaiso (CCTVal), Valparaiso (Chile); Schmidt, Ivan [Universidad Tecnica Federico Santa Maria, Departamento de Fisica y Centro Cientifico Tecnologico de Valparaiso (CCTVal), Valparaiso (Chile)
2017-02-15
Continuing our analysis of parton distributions in the nucleon, we extend our light-front quark model in order to obtain both the helicity-independent and the helicity-dependent parton distributions, analytically matching the results of global fits at the initial scale μ∝ 1 GeV; they also contain the correct Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution. We also calculate the transverse parton, Wigner and Husimi distributions from a unified point of view, using our light-front wave functions and expressing them in terms of the parton distributions q{sub v}(x) and δq{sub v}(x). Our results are very relevant for the current and future program of the COMPASS experiment at SPS (CERN). (orig.)
The 3He spectral function in light-front dynamics
Directory of Open Access Journals (Sweden)
Rinaldi Matteo
2016-01-01
Full Text Available A distorted spin-dependent spectral function for 3He is considered for the extraction of the transverse-momentum dependent parton distributions in the neutron from semi-inclusive deep inelastic electron scattering off polarized 3He at finite momentum transfers, where final state interactions are taken into account. The generalization of the analysis to a Poincaré covariant framework within the light-front dynamics is outlined.
Light-front interpretation of proton generalized polarizabilities.
Gorchtein, M; Lorcé, C; Pasquini, B; Vanderhaeghen, M
2010-03-19
We extend the recently developed formalism to extract light-front quark charge densities from nucleon form factor data to the deformations of these quark charge densities when applying an external electric field. We show that the resulting induced polarizations can be extracted from proton generalized polarizabilities. The available data for the generalized electric polarizability of the proton yield a pronounced structure in its induced polarization at large transverse distances, which will be pinned down by forthcoming high precision virtual Compton scattering experiments.
Meson Transition Form Factors in Light-Front Holographic QCD
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.; /SLAC; Cao, Fu-Guang; /Massey U.; de Teramond, Guy F.; /Costa Rica U.
2011-06-22
We study the photon-to-meson transition form factors (TFFs) F{sub M{gamma}}(Q{sup 2}) for {gamma}{gamma}* {yields} M using light-front holographic methods. The Chern-Simons action, which is a natural form in 5-dimensional anti-de Sitter (AdS) space, leads directly to an expression for the photon-to-pion TFF for a class of confining models. Remarkably, the predicted pion TFF is identical to the leading order QCD result where the distribution amplitude has asymptotic form. The Chern-Simons form is local in AdS space and is thus somewhat limited in its predictability. It only retains the q{bar q} component of the pion wavefunction, and further, it projects out only the asymptotic form of the meson distribution amplitude. It is found that in order to describe simultaneously the decay process {pi}{sup 0} {yields} {gamma}{gamma} and the pion TFF at the asymptotic limit, a probability for the q{bar q} component of the pion wavefunction P{sub q{bar q}} = 0.5 is required; thus giving indication that the contributions from higher Fock states in the pion light-front wavefunction need to be included in the analysis. The probability for the Fock state containing four quarks (anti-quarks) which follows from analyzing the hadron matrix elements, P{sub q{bar q}q{bar q}} {approx} 10%, agrees with the analysis of the pion elastic form factor using light-front holography including higher Fock components in the pion wavefunction. The results for the TFFs for the {eta} and {eta}{prime} mesons are also presented. The rapid growth of the pion TFF exhibited by the BABAR data at high Q{sup 2} is not compatible with the models discussed in this article, whereas the theoretical calculations are in agreement with the experimental data for the {eta} and {eta}{prime} TFFs.
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.; de Teramond, Guy F.
2008-02-04
The AdS/CFT correspondence between string theory in AdS space and conformal field theories in physical space-time leads to an analytic, semi-classical model for strongly-coupled QCD which has scale invariance and dimensional counting at short distances and color confinement at large distances. The AdS/CFT correspondence also provides insights into the inherently nonperturbative aspects of QCD such as the orbital and radial spectra of hadrons and the form of hadronic wavefunctions. In particular, we show that there is an exact correspondence between the fifth-dimensional coordinate of AdS space z and a specific impact variable {zeta} which measures the separation of the quark and gluonic constituents within the hadron in ordinary space-time. This connection leads to AdS/CFT predictions for the analytic form of the frame-independent light-front wavefunctions (LFWFs) of mesons and baryons, the fundamental entities which encode hadron properties. The LFWFs in turn predict decay constants and spin correlations, as well as dynamical quantities such as form factors, structure functions, generalized parton distributions, and exclusive scattering amplitudes. Relativistic light-front equations in ordinary space-time are found which reproduce the results obtained using the fifth-dimensional theory and have remarkable algebraic structures and integrability properties. As specific examples we describe the behavior of the pion form factor in the space and time-like regions and determine the Dirac nucleon form factors in the space-like region. An extension to nonzero quark mass is used to determine hadronic distribution amplitudes of all mesons, heavy and light. We compare our results with the moments of the distribution amplitudes which have recently been computed from lattice gauge theory.
Quantum Field Theory in Two Dimensions: Light-front Versus Space-like Solutions
Martinovic̆, L'ubomír
2017-07-01
A few non-perturbative topics of quantum field theory in D=1+1 are studied in both the conventional (SL) and light-front (LF) versions. First, we give a concise review of the recently proposed quantization of the two-dimensional massless LF fields. The LF version of bosonization follows in a simple and natural way including the bosonized form of the Thirring model. As a further application, we demonstrate the closeness of the 2D massless LF quantum fields to conformal field theory (CFT). We calculate several correlation functions including those between the components of the LF energy-momentum tensor and derive the LF version of the Virasoro algebra. Using the Euclidean time variable, we can immediately transform calculated quantities to the (anti)holomorphic form. The results found are in agreement with those from CFT. Finally, we show that the proposed framework provides us with the elements needed for an independent LF study of exactly solvable models. We compute the non-perturbative correlation functions from the exact operator solution of the LF Thirring model and compare it to the analogous results in the SL theory. While the vacuum effects are automatically taken into account in the LF case, the non-trivial vacuum structure has to be incorported by an explicit diagonalization of the SL Hamiltonians, to obtain the equivalently complete solution.
Theory and Experiment for Hadrons on the Light-Front
Salme, Giovanni
2016-01-01
LC2015 belongs to a Conference series that started in 1991 under the supervision of the International Light Cone Advisory Committee (ILCAC), with the aim of promoting the research towards a rigorous description of hadrons and nuclei, based on Light-Cone quantization methods. A strong relation with the experimental activity was always pursued and it will be emphasized in the next edition, in order to meet one of the main goals of the whole Light-Cone community "to assist in the development of crucial experimental tests of hadron facilities". The scientific program will feature invited as well as contributed talks, selected in collaboration with the Scientific Advisory Committee and the ILCAC. The main topics to be addressed are: * Hadron physics at present and future facilities; * Nonperturbative methods in quantum field theory * AdS/CFT: theory and applications * Light-front theories in QCD and QED * Relativistic methods for nuclear and hadronic structures * Few-body problems onto the Light cone * Lattice gau...
Double parton correlations in Light-Front constituent quark models
Directory of Open Access Journals (Sweden)
Rinaldi Matteo
2015-01-01
Full Text Available Double parton distribution functions (dPDF represent a tool to explore the 3D proton structure. They can be measured in high energy proton-proton and proton nucleus collisions and encode information on how partons inside a proton are correlated among each other. dPFDs are studied here in the valence quark region, by means of a constituent quark model, where two particle correlations are present without any additional prescription. This framework allows to understand the dynamical origin of the correlations and to clarify which, among the features of the results, are model independent. Use will be made of a relativistic light-front scheme, able to overcome some drawbacks of the previous calculation. Transverse momentum correlations, due to the exact treatment of the boosts, are predicted and analyzed. The role of spin correlations is also shown. Due to the covariance of the approach, some symmetries of the dPDFs are seen unambigously. For the valence sector, also the study of the QCD evolution of the model results, which can be performed safely thanks to the property of good support, has been also completed.
Electromagnetic form factors for spin-1 particles with the light-front
Energy Technology Data Exchange (ETDEWEB)
Mello, Clayton S. [Laboratório de Física Teórica e Computacional (LFTC), Universidade Cruzeiro do Sul, 01506-000, São Paulo (Brazil); Departamento de Física, Instituto Tecnológico de Aeronáutica, 12.228-900 São José dos Campos, São Paulo (Brazil); Nunes da Silva, Anacé; Melo, J.P.B.C. de [Laboratório de Física Teórica e Computacional (LFTC), Universidade Cruzeiro do Sul, 01506-000, São Paulo (Brazil); Frederico, T. [Departamento de Física, Instituto Tecnológico de Aeronáutica, 12.228-900 São José dos Campos, São Paulo (Brazil)
2014-06-15
This work is dedicate to investigate the spin-1 electromagnetic form factors with the light-front quantum field theory approach. All prescriptions with the light-front approach are contamined by the zero-modes contribuitions to the electromagnetic matrix elements of the electromagnetic current with the plus component of the current; however, the Inna Grach prescriptions it is immune for the zero modes contribuitions. We show numerically the contribution of zero-modes for the electromagnetic current in the case of the vector particles in the light-front quantum field theory. Also the electromagnetic observables, like electromagnetic form factors, radius and the decay constant are presented.
AdS/QCD and Applications of Light-Front Holography
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.; /SLAC /Southern Denmark U., CP3-Origins; Cao, Fu-Guang; /Massey U.; de Teramond, Guy F.; /Costa Rica U.
2012-02-16
Light-Front Holography leads to a rigorous connection between hadronic amplitudes in a higher dimensional anti-de Sitter (AdS) space and frame-independent light-front wavefunctions of hadrons in 3 + 1 physical space-time, thus providing a compelling physical interpretation of the AdS/CFT correspondence principle and AdS/QCD, a useful framework which describes the correspondence between theories in a modified AdS5 background and confining field theories in physical space-time. To a first semiclassical approximation, where quantum loops and quark masses are not included, this approach leads to a single-variable light-front Schroedinger equation which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum. The coordinate z in AdS space is uniquely identified with a Lorentz-invariant coordinate {zeta} which measures the separation of the constituents within a hadron at equal light-front time. The internal structure of hadrons is explicitly introduced and the angular momentum of the constituents plays a key role. We give an overview of the light-front holographic approach to strongly coupled QCD. In particular, we study the photon-to-meson transition form factors (TFFs) F{sub M{gamma}}(Q{sup 2}) for {gamma}{gamma}* {yields} M using light-front holographic methods. The results for the TFFs for the {eta} and {eta}' mesons are also presented. Some novel features of QCD are discussed, including the consequences of confinement for quark and gluon condensates. A method for computing the hadronization of quark and gluon jets at the amplitude level is outlined.
Energy Technology Data Exchange (ETDEWEB)
Orsucci, Davide [Scuola Normale Superiore, I-56126 Pisa (Italy); Burgarth, Daniel [Department of Mathematics, Aberystwyth University, Aberystwyth SY23 3BZ (United Kingdom); Facchi, Paolo; Pascazio, Saverio [Dipartimento di Fisica and MECENAS, Università di Bari, I-70126 Bari (Italy); INFN, Sezione di Bari, I-70126 Bari (Italy); Nakazato, Hiromichi; Yuasa, Kazuya [Department of Physics, Waseda University, Tokyo 169-8555 (Japan); Giovannetti, Vittorio [NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa (Italy)
2015-12-15
The problem of Hamiltonian purification introduced by Burgarth et al. [Nat. Commun. 5, 5173 (2014)] is formalized and discussed. Specifically, given a set of non-commuting Hamiltonians (h{sub 1}, …, h{sub m}) operating on a d-dimensional quantum system ℋ{sub d}, the problem consists in identifying a set of commuting Hamiltonians (H{sub 1}, …, H{sub m}) operating on a larger d{sub E}-dimensional system ℋ{sub d{sub E}} which embeds ℋ{sub d} as a proper subspace, such that h{sub j} = PH{sub j}P with P being the projection which allows one to recover ℋ{sub d} from ℋ{sub d{sub E}}. The notions of spanning-set purification and generator purification of an algebra are also introduced and optimal solutions for u(d) are provided.
Light Cone 2017 : Frontiers in Light Front Hadron Physics : Theory and Experiment.
2018-01-01
LC2017 belongs to a series of Light-Cone conferences, which started in 1991. Light Cone conferences are held each year under the auspices of the International Light Cone Advisory Committee (ILCAC) (http://www.ilcacinc.org). The main objective of the Light Cone conference series is to provide a timely update of the progress in light-front theory and its phenomenological applications. Light-front theory provides a suitable framework to calculate observables such as scattering amplitudes, decay rates, spin effects, parton distributions, and other hadronic observables. One of the themes of the conference will be the interface between theory and experiment in hadron physics. The main topics of the program are: o Hadron Physics at present and future colliders o Light Front Field Theory in QED and QCD o AdS/QCD, D Branes and Strings o Hadron Structure : TMDs, GPDs and PDFs o Lattice QCD o QCD at high temperature and density o Higher order QCD corrections
Light-front projection of spin-1 electromagnetic current and zero-modes
Energy Technology Data Exchange (ETDEWEB)
Melo, J.P.B.C. de [Laboratorio de Fisica Teorica e Computacao Cientifica - LFTC, Universidade Cruzeiro do Sul, 01506-000 Sao Paulo, SP (Brazil); Frederico, T., E-mail: tobias@ita.br [Instituto Tecnologico de Aeronautica, DCTA, 12.228-900 Sao Jose dos Campos, SP (Brazil)
2012-02-14
The issue of the contribution of zero-modes to the light-front projection of the electromagnetic current of phenomenological models of vector particles vertices is addressed in the Drell-Yan frame. Our analytical model of the Bethe-Salpeter amplitude of a spin-1 fermion-antifermion composite state gives a physically motivated light-front wave function symmetric by the exchange of the fermion and antifermion, as in the {rho}-meson case. We found that among the four independent matrix elements of the plus component in the light-front helicity basis only the 0{yields}0 one carries zero-mode contributions. Our derivation generalizes to symmetric models, important for applications, the above conclusion found for a simplified non-symmetrical form of the spin-1 Bethe-Salpeter amplitude with photon-fermion point-like coupling and also for a smeared fermion-photon vertex model.
Nucleon-generalized parton distributions in the light-front quark model
Indian Academy of Sciences (India)
2016-01-12
Jan 12, 2016 ... We calculate the generalized parton distributions (GPDs) for the up- and downquarks in nucleon using the effective light-front wavefunction. The results obtained for GPDs in momentum and impact parameter space are comparable with phenomenological parametrization methods.
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
Angular momentum conservation law in light-front quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Chiu, Kelly Yu-Ju; Brodsky, Stanley J.; /SLAC /Stanford U.
2017-03-01
We prove the Lorentz invariance of the angular momentum conservation law and the helicity sum rule for relativistic composite systems in the light-front formulation. We explicitly show that j 3 , the z -component of the angular momentum remains unchanged under Lorentz transformations generated by the light-front kinematical boost operators. The invariance of j 3 under Lorentz transformations is a feature unique to the front form. Applying the Lorentz invariance of the angular quantum number in the front form, we obtain a selection rule for the orbital angular momentum which can be used to eliminate certain interaction vertices in QED and QCD. We also generalize the selection rule to any renormalizable theory and show that there exists an upper bound on the change of orbital angular momentum in scattering processes at any fixed order in perturbation theory.
In-medium pion valence distributions in a light-front model
Energy Technology Data Exchange (ETDEWEB)
Melo, J.P.B.C. de, E-mail: joao.mello@cruzeirodosul.edu.br [Laboratório de Física Teórica e Computacional – LFTC, Universidade Cruzeiro do Sul, 01506-000 São Paulo (Brazil); Tsushima, K. [Laboratório de Física Teórica e Computacional – LFTC, Universidade Cruzeiro do Sul, 01506-000 São Paulo (Brazil); Ahmed, I. [Laboratório de Física Teórica e Computacional – LFTC, Universidade Cruzeiro do Sul, 01506-000 São Paulo (Brazil); National Center for Physics, Quaidi-i-Azam University Campus, Islamabad 45320 (Pakistan)
2017-03-10
Pion valence distributions in nuclear medium and vacuum are studied in a light-front constituent quark model. The in-medium input for studying the pion properties is calculated by the quark-meson coupling model. We find that the in-medium pion valence distribution, as well as the in-medium pion valence wave function, are substantially modified at normal nuclear matter density, due to the reduction in the pion decay constant.
Pesudoscalar transition form factors within the light-front quark model
Geng, Chao-Qiang; Lih, Chong-Chung
2012-09-01
We study the transition form factors of the pesudoscalar mesons (π,η, and η') as functions of the momentum transfer Q2 within the light-front quark model. We compare our results with the recent experimental data by CELLO, CLEO, BaBar and Belle collaborations. By considering the possible uncertainties from the quark masses, we illustrate that our predicted form factors can fit with all the data, including those at the large Q2 regions.
AdS/QCD and Applications of Light-Front Holography
DEFF Research Database (Denmark)
Brodsky, S. J.; Cao, F. G.; de Teramond, G. F.
2012-01-01
-to-meson transition form factors (TFFs) F-M gamma (Q(2)) for gamma* -> M using light-front holographic methods. The results for the TFFs for the eta and eta' mesons are also presented. Some novel features of QCD are discussed, including the consequences of confinement for quark and gluon condensates. A method...... for computing the hadronization of quark and gluon jets at the amplitude level is outlined....
Electromagnetic structure and weak decay of meson K in a light-front QCD-inspired
Pereira, Fabiano P; Frederico, T; Tomio, Lauro
2007-01-01
The kaon electromagnetic (e.m.) form factor is reviewed considering a light-front constituent quark model. In this approach, it is discussed the relevance of the quark-antiquark pair terms for the full covariance of the e.m. current. It is also verified, by considering a QCD dynamical model, that a good agreement with experimental data can be obtained for the kaon weak decay constant once a probability of about 80% of the valence component is taken into account.
Recursion relations for multi-gluon off-shell amplitudes on the light-front and Wilson lines
Directory of Open Access Journals (Sweden)
C. Cruz-Santiago
2015-06-01
Full Text Available We analyze the off-shell scattering amplitudes in the framework of the light-front perturbation theory. It is shown that the previously derived recursion relation between tree level off-shell amplitudes in this formalism actually resums whole classes of graphs into a Wilson line. More precisely, we establish a correspondence between the light-front methods for the computation of the off-shell amplitudes and the approach which makes use of the matrix elements of straight infinite Wilson lines, which are manifestly gauge invariant objects. Furthermore, since it is needed to explicitly verify the gauge invariance of light-front amplitudes, it is demonstrated that the Ward identities in this framework need additional instantaneous terms in the light-front graphs.
Hamiltonian systems with discontinuities
Tulczyjew, Wlodzimierz M.
2006-01-01
Standandard Hamiltonian mechanics in its homogeneous formulation is applied to the study of discontinuities representing rapid changes of Hamiltonians. Different formulations of Hamiltonian mechanics are reviewed. An original representation of a positive homogeneous Hamiltonian system by an outer oriented coisotropic submanifold of the phase space is proposed.
Maji, Tanmay; Chakrabarti, Dipankar; Mukherjee, Asmita
2018-01-01
The spin asymmetries in SIDIS associated with T -odd TMDs are presented in a light-front quark-diquark model of a proton. To incorporate the effects of the final-state interaction, the light front wave functions are modified to have a phase factor which is essential to have Sivers or Boer-Mulders functions. The Sivers and Boer-Mulder asymmetries are compared with HERMES and COMPASS data.
Unpolarized and polarized densities based on a light-front quark-diquark model
Nikkhoo, Negin Sattary; Shojaei, Mohammad Reza
2017-06-01
In this paper, we calculate the proton and neutron unpolarized and transversely polarized densities. We use the light-front wave function (LFWF), which at an initial scale is constrained by the soft-wall anti-de Sitter (AdS) QCD model, for calculating the Dirac and Pauli form factors which transverse densities are in terms of these form factors. Also, we use these form factors for calculating the flavor separated results for the proton and neutron electromagnetic form factors and calculate u and d quark unpolarized and transversely polarized densities. Finally, we compare our results with other previous parametrizations.
Imaging dynamical chiral-symmetry breaking: pion wave function on the light front.
Chang, Lei; Cloët, I C; Cobos-Martinez, J J; Roberts, C D; Schmidt, S M; Tandy, P C
2013-03-29
We project onto the light front the pion's Poincaré-covariant Bethe-Salpeter wave function obtained using two different approximations to the kernels of quantum chromodynamics' Dyson-Schwinger equations. At an hadronic scale, both computed results are concave and significantly broader than the asymptotic distribution amplitude, φ(π)(asy)(x)=6x(1-x); e.g., the integral of φ(π)(x)/φ(π)(asy)(x) is 1.8 using the simplest kernel and 1.5 with the more sophisticated kernel. Independent of the kernels, the emergent phenomenon of dynamical chiral-symmetry breaking is responsible for hardening the amplitude.
Radiative Decays of Scalar Mesons in Light-Front Quark Model
Dewitt, Martin; Choi, Ho-Meoyng; Ji, Chueng-Ryong
2003-04-01
It is currently thought that the difficulty in experimentally identifying the light scalar glueball results from the fact that it tends to mix with nearby conventional scalar mesons. Therefore, the glueball's presence can only be inferred from the behavior of the experimentally observed (mixed) scalar states. Here, we present relativistic light-front quark model calculations of absolute widths for the radiative decay processes Scalar[0^++] → γγ, Scalar[0^++]→γ Vector[1^-], and Vector[1^-]→γ Scalar[0^++] which incorporate the effects of glueball-q barq mixing. The mixed physical states are assumed to be the f_0(1370), the f_0(1500), and the f_0(1710). The n barn, s bars, and gg content of each of the physical states is taken from the mass mixing matrix calculations of other works. These flavor/glue wavefunctions are then used in conjunction with light-front spin-space wavefunctions to compute transition form factors for the decay processes mentioned above. In the q^2→ 0 limit the form factors are used to determine the corresponding decay widths. Our results are compared with available experimental data as well as the results of a recent non-relativistic model calculation of the process Scalar[0^++]→γ Vector[1^-].
Symmetric multivariate polynomials as a basis for three-boson light-front wave functions.
Chabysheva, Sophia S; Elliott, Blair; Hiller, John R
2013-12-01
We develop a polynomial basis to be used in numerical calculations of light-front Fock-space wave functions. Such wave functions typically depend on longitudinal momentum fractions that sum to unity. For three particles, this constraint limits the two remaining independent momentum fractions to a triangle, for which the three momentum fractions act as barycentric coordinates. For three identical bosons, the wave function must be symmetric with respect to all three momentum fractions. Therefore, as a basis, we construct polynomials in two variables on a triangle that are symmetric with respect to the interchange of any two barycentric coordinates. We find that, through the fifth order, the polynomial is unique at each order, and, in general, these polynomials can be constructed from products of powers of the second- and third-order polynomials. The use of such a basis is illustrated in a calculation of a light-front wave function in two-dimensional ϕ(4) theory; the polynomial basis performs much better than the plane-wave basis used in discrete light-cone quantization.
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.
Bravetti, Alessandro; Cruz, Hans; Tapias, Diego
2016-01-01
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.
Hamiltonian Algorithm Sound Synthesis
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.
ρ meson unpolarized generalized parton distributions with a light-front constituent quark model
Sun, Bao-Dong; Dong, Yu-Bing
2017-08-01
We study ρ meson unpolarized generalized parton distributions based on a light-front constituent quark model where the quark-antiquark-meson vertex is constructed under the symmetric loop momentum convention. The form factors and some other low-energy observables of the ρ meson are calculated. Moreover, the contributions to the form factors and generalized parton distributions from the valence and nonvalence regimes are discussed and analyzed in detail. In the forward limit, the usual structure functions are estimated as well. In addition, by evolving the moments of the obtained structure functions to the scale of the lattice calculation, we give the factorization scale of our quark model. It is found that the present phenomenological model is reasonable to describe the general properties of ρ meson.
Basis of symmetric polynomials for many-boson light-front wave functions.
Chabysheva, Sophia S; Hiller, John R
2014-12-01
We provide an algorithm for the construction of orthonormal multivariate polynomials that are symmetric with respect to the interchange of any two coordinates on the unit hypercube and are constrained to the hyperplane where the sum of the coordinates is one. These polynomials form a basis for the expansion of bosonic light-front momentum-space wave functions, as functions of longitudinal momentum, where momentum conservation guarantees that the fractions are on the interval [0,1] and sum to one. This generalizes earlier work on three-boson wave functions to wave functions for arbitrarily many identical bosons. A simple application in two-dimensional ϕ(4) theory illustrates the use of these polynomials.
Maxwell's equations instantaneous Hamiltonian
Kulyabov, D. S.; Korolkova, A. V.; Sevastianov, L. A.; Eferina, E. G.; Velieva, T. R.; Zaryadov, I. S.
2017-04-01
The Hamiltonian formalism is extremely elegant and convenient to mechanics problems. However, its application to the classical field theories is a difficult task. In fact, you can set one to one correspondence between the Lagrangian and Hamiltonian in the case of hyperregular Lagrangian. It is impossible to do the same in field theories. In the case of irregular Lagrangian the Dirac-Bergman Hamiltonian formalism with constraints is usually used, and this leads to a number of certain difficulties. The paper proposes a reformulation of the problem to the case of a field without sources. This allows to use a instantaneous (symplectic) Hamiltonian formalism.
Bayesian analysis of light-front models and the nucleon's charmed sigma term
Hobbs, T. J.; Alberg, Mary; Miller, Gerald A.
2017-10-01
We present the results of a recent analysis to study the nucleon's charm sigma term, σc c ¯. We construct a minimal model in terms of light-front variables and constrain the range of possibilities using extant knowledge from deeply inelastic scattering (DIS) and Bayesian parameter estimation, ultimately computing σc c ¯ in an explicitly covariant manner. We find a close correlation between a possible nonperturbative component of the charm structure function, F2,IC c c ¯ , and σc c ¯. Independent of the prescription for the covariant relativistic quark-nucleon vertex, we determine σc c ¯ under several different scenarios for the magnitude of intrinsic charm in DIS, namely ⟨x ⟩c+c ¯=0.1 %, 0.35%, and 1%, obtaining for these σc c ¯=4 ±4 , 12 ±13 , and 32 ±34 MeV , respectively. These results imply the existence of a reciprocity between the intrinsic charm parton distribution function and σc c ¯ such that new information from either DIS or improved determinations of σc c ¯ could significantly impact constraints to the charm sector of the proton wave function.
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 ...
Perspectives of Light-Front Quantized Field Theory: Some New Results
Energy Technology Data Exchange (ETDEWEB)
Srivastava, Prem P.
1999-08-13
A review of some basic topics in the light-front (LF) quantization of relativistic field theory is made. It is argued that the LF quantization is equally appropriate as the conventional one and that they lead, assuming the microcausality principle, to the same physical content. This is confirmed in the studies on the LF of the spontaneous symmetry breaking (SSB), of the degenerate vacua in Schwinger model (SM) and Chiral SM (CSM), of the chiral boson theory, and of the QCD in covariant gauges among others. The discussion on the LF is more economical and more transparent than that found in the conventional equal-time quantized theory. The removal of the constraints on the LF phase space by following the Dirac method, in fact, results in a substantially reduced number of independent dynamical variables. Consequently, the descriptions of the physical Hilbert space and the vacuum structure, for example, become more tractable. In the context of the Dyson-Wick perturbation theory the relevant propagators in the front form theory are causal. The Wick rotation can then be performed to employ the Euclidean space integrals in momentum space. The lack of manifest covariance becomes tractable, and still more so if we employ, as discussed in the text, the Fourier transform of the fermionic field based on a special construction of the LF spinor. The fact that the hyperplanes x{sup {+-}} = 0 constitute characteristic surfaces of the hyperbolic partial differential equation is found irrelevant in the quantized theory; it seems sufficient to quantize the theory on one of the characteristic hyperplanes.
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.; /SLAC; Gardner, Susan; /Kentucky U.; Hwang, Dae Sung; /Sejong U.
2006-01-11
We consider the electric dipole form factor, F{sub 3}(q{sup 2}), as well as the Dirac and Pauli form factors, F{sub 1}(q{sup 2}) and F{sub 2}(q{sup 2}), of the nucleon in the light-front formalism. We derive an exact formula for F{sub 3}(q{sup 2}) to complement those known for F{sub 1}(q{sup 2}) and F{sub 2}(q{sup 2}). We derive the light-front representation of the discrete symmetry transformations and show that time-reversal- and parity-odd effects are captured by phases in the light-front wave functions. We thus determine that the contributions to F{sub 2}(q{sup 2}) and F{sub 3}(q{sup 2}), Fock-state by Fock-state, are related, independent of the fundamental mechanism through which CP violation is generated. Our relation is not specific to the nucleon, but, rather, is true of spin-1/2 systems in general, be they lepton or baryon. The empirical values of the anomalous magnetic moments, in concert with empirical bounds on the associated electric dipole moments, can better constrain theories of CP violation. In particular, we find that the neutron and proton electric dipole moments echo the isospin structure of the anomalous magnetic moments, {kappa}{sup n} {approx} -{kappa}{sup p}.
Miskovic, O; Miskovic, Olivera; Zanelli, Jorge
2003-01-01
Hamiltonian systems with linearly dependent constraints (irregular systems), are classified according to their behavior in the vicinity of the constraint surface. For these systems, the standard Dirac procedure is not directly applicable. However, Dirac's treatment can be slightly modified to obtain, in some cases, a Hamiltonian description completely equivalent to the Lagrangian one. A recipe to deal with the different cases is provided, along with a few pedagogical examples.
Energy Technology Data Exchange (ETDEWEB)
Bengtsson, Anders K.H. [Academy of Textiles, Engineering and Economics, University of Borås,Allégatan 1, SE-50190 Borås (Sweden)
2016-12-27
The dynamical commutators of the light-front Poincaré algebra yield first order differential equations in the p{sup +} momenta for the interaction vertex operators. The homogeneous solution to the equation for the quartic vertex is studied. Consequences as regards the constructibility assumption of quartic higher spin amplitudes from cubic amplitudes are discussed. The existence of quartic contact interactions unrelated to cubic interactions by Poincaré symmetry indicates that the higher spin S-matrix is not constructible. Thus quartic amplitude based no-go results derived by BCFW recursion for Minkowski higher spin massless fields may be circumvented.
Lagrangian and Hamiltonian dynamics
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...
Remarks on hamiltonian digraphs
DEFF Research Database (Denmark)
Gutin, Gregory; Yeo, Anders
2001-01-01
This note is motivated by A.Kemnitz and B.Greger, Congr. Numer. 130 (1998)127-131. We show that the main result of the paper by Kemnitz and Greger is an easy consequence of the characterization of hamiltonian out-locally semicomplete digraphs by Bang-Jensen, Huang, and Prisner, J. Combin. Theory ...
Hamiltonian paths on Platonic graphs
Directory of Open Access Journals (Sweden)
Brian Hopkins
2004-07-01
Full Text Available We develop a combinatorial method to show that the dodecahedron graph has, up to rotation and reflection, a unique Hamiltonian cycle. Platonic graphs with this property are called topologically uniquely Hamiltonian. The same method is used to demonstrate topologically distinct Hamiltonian cycles on the icosahedron graph and to show that a regular graph embeddable on the 2-holed torus is topologically uniquely Hamiltonian.
An electromechanical Ising Hamiltonian.
Mahboob, Imran; Okamoto, Hajime; Yamaguchi, Hiroshi
2016-06-01
Solving intractable mathematical problems in simulators composed of atoms, ions, photons, or electrons has recently emerged as a subject of intense interest. We extend this concept to phonons that are localized in spectrally pure resonances in an electromechanical system that enables their interactions to be exquisitely fashioned via electrical means. We harness this platform to emulate the Ising Hamiltonian whose spin 1/2 particles are replicated by the phase bistable vibrations from the parametric resonances of multiple modes. The coupling between the mechanical spins is created by generating two-mode squeezed states, which impart correlations between modes that can imitate a random, ferromagnetic state or an antiferromagnetic state on demand. These results suggest that an electromechanical simulator could be built for the Ising Hamiltonian in a nontrivial configuration, namely, for a large number of spins with multiple degrees of coupling.
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...
Quantum Hamiltonian Complexity
Gharibian, Sevag; Huang, Yichen; Landau, Zeph; Shin, Seung Woo
2014-01-01
Constraint satisfaction problems are a central pillar of modern computational complexity theory. This survey provides an introduction to the rapidly growing field of Quantum Hamiltonian Complexity, which includes the study of quantum constraint satisfaction problems. Over the past decade and a half, this field has witnessed fundamental breakthroughs, ranging from the establishment of a "Quantum Cook-Levin Theorem" to deep insights into the structure of 1D low-temperature quantum systems via s...
Energy Technology Data Exchange (ETDEWEB)
Mondal, Chandan; Chakrabarti, Dipankar [Indian Institute of Technology Kanpur, Department of Physics, Kanpur (India)
2015-06-15
We present a study of the generalized parton distributions (GPDs) for the quarks in a proton in both momentum and position spaces using the light-front wave functions (LFWFs) of a quark-diquark model for the nucleon predicted by the soft-wall model of AdS/QCD. The results are compared with the soft-wall AdS/QCD model of proton GPDs for zero skewness. We also calculate the GPDs for nonzero skewness. We observe that the GPDs have a diffraction pattern in longitudinal position space, as seen before in other models. Then we present a comparative study of the nucleon charge and anomalous magnetization densities in the transverse plane. Flavor decompositions of the form factors and transverse densities are also discussed. (orig.)
Branching fractions of semileptonic D and D_s decays from the covariant light-front quark model
Cheng, Hai-Yang; Kang, Xian-Wei
2017-09-01
Based on the predictions of the relevant form factors from the covariant light-front quark model, we show the branching fractions for the D (D_s) → (P, S, V, A) ℓ ν _ℓ (ℓ =e or μ ) decays, where P denotes the pseudoscalar meson, S the scalar meson with a mass above 1 GeV, V the vector meson and A the axial-vector one. Comparison with the available experimental results are made, and we find an excellent agreement. The predictions for other decay modes can be tested in a charm factory, e.g., the BESIII detector. The future measurements will definitely further enrich our knowledge of the hadronic transition form factors as well as the inner structure of the even-parity mesons ( S and A).
Double parton scattering: A study of the effective cross section within a Light-Front quark model
Directory of Open Access Journals (Sweden)
Matteo Rinaldi
2016-01-01
Full Text Available We present a calculation of the effective cross section σeff, an important ingredient in the description of double parton scattering in proton–proton collisions. Our theoretical approach makes use of a Light-Front quark model as a framework to calculate the double parton distribution functions at low-resolution scale. QCD evolution is implemented to reach the experimental scale. The obtained values of σeff in the valence region are consistent with the present experimental scenario, in particular with the sets of data which include the same kinematical range. However the result of the complete calculation shows a dependence of σeff on xi, a feature not easily seen in the available data, probably because of their low accuracy. Measurements of σeff in restricted xi regions are addressed to obtain indications on double parton correlations, a novel and interesting aspect of the three dimensional structure of the nucleon.
Branching fractions of semileptonic D and D{sub s} decays from the covariant light-front quark model
Energy Technology Data Exchange (ETDEWEB)
Cheng, Hai-Yang; Kang, Xian-Wei [Academia Sinica, Institute of Physics, Taipei (China)
2017-09-15
Based on the predictions of the relevant form factors from the covariant light-front quark model, we show the branching fractions for the D(D{sub s}) → (P, S, V, A) lν{sub l} (l = e or μ) decays, where P denotes the pseudoscalar meson, S the scalar meson with a mass above 1 GeV, V the vector meson and A the axial-vector one. Comparison with the available experimental results are made, and we find an excellent agreement. The predictions for other decay modes can be tested in a charm factory, e.g., the BESIII detector. The future measurements will definitely further enrich our knowledge of the hadronic transition form factors as well as the inner structure of the even-parity mesons (S and A). (orig.)
Analytic parametrizations of the γ*N →N (1440 ) form factors inspired by light-front holography
Ramalho, G.
2017-09-01
We present analytic parametrizations for the γ*N →N (1440 ) form factors derived from light-front holography in leading twist approximation. The new parametrizations describe the electromagnetic form factors using analytic functions dependent on the masses of the ρ meson and respective radial excitations, as well as the masses of the nucleon and the resonance N (1440 ). The free parameters of the model, associated with three independent couplings, are interpreted as bare couplings, and are fixed by the nucleon data for large Q2. The proposed parametrizations compare remarkably well with the empirical data for Q2>2 GeV2 , corroborating the dominant role of the valence quark degrees of freedom in the γ*N →N (1440 ) transition.
Globally superintegrable Hamiltonian systems
Kurov, A. V.; Sardanashvily, G. A.
2017-06-01
The generalization of the Mishchenko-Fomenko theorem for symplectic superintegrable systems to the case of an arbitrary, not necessarily compact, invariant submanifold allows giving a global description of a superintegrable Hamiltonian system, which can be split into several nonequivalent globally superintegrable systems on nonoverlapping open submanifolds of the symplectic phase manifold having both compact and noncompact invariant submanifolds. A typical example of such a composition of globally superintegrable systems is motion in a centrally symmetric field, in particular, the two-dimensional Kepler problem.
Zezyulin, Dmitry A.; Konotop, Vladimir V.
2018-01-01
We introduce a nonlinear parity-time-symmetric dispersive coupler which admits Hamiltonian and Lagrangian formulations. We show that, in spite of the gain and dissipation, the model has several conservation laws. The system also supports a variety of exact solutions. We focus on exact bright solitons and demonstrate numerically that they are dynamically stable in a wide parameter range and undergo elastic interactions, thus manifesting nearly-integrable dynamics. Physical applications of the introduced model in the theory of Bose–Einstein condensates in nonlinear lattices are discussed.
Optimal control of effective Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Verdeny Vilalta, Albert; Mintert, Florian [Freiburg Institute for Advanced Studies, Albert-Ludwigs University of Freiburg, Freiburg 79104 (Germany); Mueller, Cord A. [Centre for Quantum Technologies, National University of Singapore, Singapore 117543 (Singapore)
2013-07-01
Periodically driven Hamiltonians can be approximately described by a time-independent effective Hamiltonian if the driving is sufficiently fast. There exist, however, many different drivings that result in the same effective Hamiltonian. Using optimal control techniques, we investigate which driving yields the best approximation to the dynamics induced by a desired effective Hamiltonian. The viability of our approach is proven for the simplest example of a driven three-level Lambda system, and shall ultimately help to improve the precision of quantum simulations.
Simulating highly nonlocal Hamiltonians with less nonlocal Hamiltonians
Subasi, Yigit; Jarzynski, Christopher
The need for Hamiltonians with many-body interactions arises in various applications of quantum computing. However, interactions beyond two-body are difficult to realize experimentally. Perturbative gadgets were introduced to obtain arbitrary many-body effective interactions using Hamiltonians with two-body interactions only. Although valid for arbitrary k-body interactions, their use is limited to small k because the strength of interaction is k'th order in perturbation theory. Here we develop a nonperturbative technique for obtaining effective k-body interactions using Hamiltonians consisting of at most l-body interactions with l gadgets to embed Hamiltonians of considerable complexity in proper subspaces of two-local Hamiltonians. We describe how our technique can be implemented in a hybrid (gate-based and adiabatic) as well as solely adiabatic quantum computing scheme. We gratefully acknowledge financial support from the Lockheed Martin Corporation under Contract U12001C.
Memristive port-Hamiltonian Systems
Jeltsema, Dimitri; Schaft, Arjan J. van der
2010-01-01
The port-Hamiltonian modelling framework is extended to a class of systems containing memristive elements and phenomena. First, the concept of memristance is generalised to the same generic level as the port-Hamiltonian framework. Second, the underlying Dirac structure is augmented with a memristive
HAMILTONIAN FORMALISM ON CHARACTERISTIC SURFACES.
The problem of the construction of a Hamiltonian formalism suitable for propagation of a field off characteristic or null surfaces is considered. In...is developed on characteristic surfaces. A Hamiltonian for gravitation (general relativity) is constructed, first on null surfaces described only by
Implicit Hamiltonian Systems with Symmetry
Schaft, A.J. van der
1998-01-01
Implicit Hamiltonian systems with symmetry are treated by exploiting the notion of symmetry of Dirac structures. It is shown how Dirac structures can be reduced to Dirac structures on the orbit space of the symmetry group, leading to a reduced implicit (generalized) Hamiltonian system. The approach
Implicit Hamiltonian systems with symmetry
van der Schaft, Arjan
1998-01-01
Implicit Hamiltonian systems with symmetry are treated by exploiting the notion of symmetry of Dirac structures. It is shown how Dirac structures can be reduced to Dirac structures on the orbit space of the symmetry group, leading to a reduced implicit (generalized) Hamiltonian system. The approach
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...
A partial Hamiltonian approach for current value Hamiltonian systems
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.
Simulating highly nonlocal Hamiltonians with less nonlocal Hamiltonians
Subasi, Yigit; Jarzynski, Christopher
2016-01-01
The need for Hamiltonians with many-body interactions arises in various applications of quantum computing. However, interactions beyond two-body are difficult to realize experimentally. Perturbative gadgets were introduced to obtain arbitrary many-body effective interactions using Hamiltonians with two-body interactions only. Although valid for arbitrary $k$-body interactions, their use is limited to small $k$ because the strength of interaction is $k$'th order in perturbation theory. In this...
Hamiltonian Structure of PI Hierarchy
Directory of Open Access Journals (Sweden)
Kanehisa Takasaki
2007-03-01
Full Text Available The string equation of type (2,2g+1 may be thought of as a higher order analogue of the first Painlevé equation that corresponds to the case of g = 1. For g > 1, this equation is accompanied with a finite set of commuting isomonodromic deformations, and they altogether form a hierarchy called the PI hierarchy. This hierarchy gives an isomonodromic analogue of the well known Mumford system. The Hamiltonian structure of the Lax equations can be formulated by the same Poisson structure as the Mumford system. A set of Darboux coordinates, which have been used for the Mumford system, can be introduced in this hierarchy as well. The equations of motion in these Darboux coordinates turn out to take a Hamiltonian form, but the Hamiltonians are different from the Hamiltonians of the Lax equations (except for the lowest one that corresponds to the string equation itself.
Hamiltonian cycles in polyhedral maps
Indian Academy of Sciences (India)
Dipendu Maity
2017-08-24
contractible separating Hamiltonian cycles; proper graphs in polyhedral maps. Mathematics Subject Classification. 57M20, 57N05, 05C38. 1. Introduction and definitions. By a topological graph we mean a representation of a graph in ...
Hamiltonian analysis of interacting fluids
Energy Technology Data Exchange (ETDEWEB)
Banerjee, Rabin; Mitra, Arpan Krishna [S. N. Bose National Centre for Basic Sciences, Kolkata (India); Ghosh, Subir [Indian Statistical Institute, Kolkata (India)
2015-05-15
Ideal fluid dynamics is studied as a relativistic field theory with particular stress on its hamiltonian structure. The Schwinger condition, whose integrated version yields the stress tensor conservation, is explicitly verified both in equal-time and light-cone coordinate systems. We also consider the hamiltonian formulation of fluids interacting with an external gauge field. The complementary roles of the canonical (Noether) stress tensor and the symmetric one obtained by metric variation are discussed. (orig.)
Hamiltonian description of the ideal fluid
Energy Technology Data Exchange (ETDEWEB)
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.
Effective Hamiltonian of strained graphene
Linnik, T. L.
2012-05-01
Based on the symmetry properties of the graphene lattice, we derive the effective Hamiltonian of graphene under spatially nonuniform acoustic and optical strains. Comparison with the published results of the first-principles calculations allows us to determine the values of some Hamiltonian parameters, and suggests the validity of the derived Hamiltonian for acoustical strain up to 10%. The results are generalized for the case of graphene with broken plane reflection symmetry, which corresponds, for example, to the case of graphene placed on a substrate. Here, essential modifications to the Hamiltonian give rise, in particular, to the gap opening in the spectrum in the presence of the out-of-plane component of optical strain, which is shown to be due to the lifting of the sublattice symmetry. The developed effective Hamiltonian can be used as a convenient tool for analysis of a variety of strain-related effects, including electron-phonon interaction or pseudo-magnetic fields induced by the nonuniform strain.
First principles of Hamiltonian medicine.
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.
Hamiltonians defined by biorthogonal sets
Bagarello, Fabio; Bellomonte, Giorgia
2017-04-01
In some recent papers, studies on biorthogonal Riesz bases have found renewed motivation because of their connection with pseudo-Hermitian quantum mechanics, which deals with physical systems described by Hamiltonians that are not self-adjoint but may still have real point spectra. Also, their eigenvectors may form Riesz, not necessarily orthonormal, bases for the Hilbert space in which the model is defined. Those Riesz bases allow a decomposition of the Hamiltonian, as already discussed in some previous papers. However, in many physical models, one has to deal not with orthonormal bases or with Riesz bases, but just with biorthogonal sets. Here, we consider the more general concept of G -quasi basis, and we show a series of conditions under which a definition of non-self-adjoint Hamiltonian with purely point real spectra is still possible.
Electroproduction of lightest nucleon resonances up to Q*2=12 GeV*2 in quark models at light front
Directory of Open Access Journals (Sweden)
Obukhovsky I.T.
2017-01-01
Full Text Available The lightest nucleon resonances are described at light front as mixed states of the 3q cluster (“quark core” possessing a definite value of the inner orbital momentum L = 0,1 and a hadron molecular state, N+σ or Λ+K. Helicity amplitudes of the resonance electroproduction off the proton are calculated at large Q2 up to 12 GeV2 and compared to the last CLAS data. At this basis we have estimated the probability of quark core in lightest nucleon resonances and predicted the high Q2 behaviour of the resonance electrocoupling.
EXTENDED LUCAS TUBE: GRAF HAMILTONIAN BARU
Directory of Open Access Journals (Sweden)
Ernastuti .
2012-06-01
Full Text Available A Hamiltonian cycle in a connected graph G is defined as a closed walk that traverses every vertex of G exactly once, except the starting vertex at which the walk also terminates. If an edge from a Hamiltonian cycle is removed, it forms a path calleda Hamiltonian path. A graph G is called Hamiltonian if there is a Hamiltonian cyclein G. It is known that every hypercube graph is Hamiltonian. But when one or more vertices are removed from a hypercube graph, will it still be Hamiltonian? Some induced subgraphs of a hypercube graph such as the Fibonacci cube (FC, the extended Fibonaccicube (EFC, and the Lucas cube (LC have been introduced and their Hamiltonicities have been investigated. Research results showed that less than a third of FC graphs are Hamiltonian although all of them have Hamiltonian path. All EFC graphs are Hamiltonian and none of LC graphs is Hamiltonian although some still have Hamiltonian paths.This paper introduces another subgraph of a hypercube graph called the Extended Lucas Cube (ELC. The ELC is shown to be Hamiltonian by using the approach of k-Gray Code and Bipartition Property.
Integrable Hamiltonian systems with swallowtails
Efstathiou, K.; Sugny, D.
2010-01-01
We consider two-degree-of-freedom integrable Hamiltonian systems with bifurcation diagrams containing swallowtail structures. The global properties of the action coordinates in such systems together with the parallel transport of the period lattice and corresponding quantum cells in the joint
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.
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 ...
On Hamiltonian formulation of cosmologies
Indian Academy of Sciences (India)
matter era for some cosmological models. It is argued that these solutions appear to hint at their possible relevance in the early phase of cosmological evolution. Keywords. Hamiltonian formulation; some cosmologies. PACS No. 98.80. Hw. It has been shown by Novelloet al [1,2] that it is possible to study perturbations in the ...
Hamiltonian formulation of the supermembrane
Bergshoeff, E.; Sezgin, E.; Tanii, Y.
1988-01-01
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
Mathematical Modeling of Constrained Hamiltonian Systems
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
Simplifying quantum double Hamiltonians using perturbative gadgets
Koenig, Robert
2009-01-01
Perturbative gadgets were originally introduced to generate effective k-local interactions in the low-energy sector of a 2-local Hamiltonian. Extending this idea, we present gadgets which are specifically suited for realizing Hamiltonians exhibiting non-abelian anyonic excitations. At the core of our construction is a perturbative analysis of a widely used hopping-term Hamiltonian. We show that in the low-energy limit, this Hamiltonian can be approximated by a certain ordered p...
Noether's first theorem in Hamiltonian mechanics
Sardanashvily, G.
2015-01-01
Non-autonomous non-relativistic mechanics is formulated as Lagrangian and Hamiltonian theory on fibre bundles over the time axis R. Hamiltonian mechanics herewith can be reformulated as particular Lagrangian theory on a momentum phase space. This facts enable one to apply Noether's first theorem both to Lagrangian and Hamiltonian mechanics. By virtue of Noether's first theorem, any symmetry defines a symmetry current which is an integral of motion in Lagrangian and Hamiltonian mechanics. The ...
Notch filters for port-Hamiltonian systems
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
Port-Hamiltonian systems: an introductory survey
van der Schaft, Arjan; Sanz-Sole, M.; Soria, J.; Varona, J.L.; Verdera, J.
2006-01-01
The theory of port-Hamiltonian systems provides a framework for the geometric description of network models of physical systems. It turns out that port-based network models of physical systems immediately lend themselves to a Hamiltonian description. While the usual geometric approach to Hamiltonian
Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories
Tronko, Natalia
2015-01-01
A consistent guiding-center Hamiltonian theory is derived by Lie-transform perturbation method, with terms up to second order in magnetic-field nonuniformity. Consistency is demonstrated by showing that the guiding-center transformation presented here satisfies separate Jacobian and Lagrangian constraints that have not been explored before. A new first-order term appearing in the guiding-center phase-space Lagrangian is identified through a calculation of the guiding-center polarization. It is shown that this new polarization term also yields a simpler expression of the guiding-center toroidal canonical momentum, which satisfies an exact conservation law in axisymmetric magnetic geometries. Lastly, an application of the guiding-center Lagrangian constraint on the guiding-center Hamiltonian yields a natural interpretation for its higher-order corrections.
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.
Hamiltonian mechanics of stochastic acceleration.
Burby, J W; Zhmoginov, A I; Qin, H
2013-11-08
We show how to find the physical Langevin equation describing the trajectories of particles undergoing collisionless stochastic acceleration. These stochastic differential equations retain not only one-, but two-particle statistics, and inherit the Hamiltonian nature of the underlying microscopic equations. This opens the door to using stochastic variational integrators to perform simulations of stochastic interactions such as Fermi acceleration. We illustrate the theory by applying it to two example problems.
Generic Local Hamiltonians are Gapless
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.
Hamiltonian theory of stochastic acceleration.
Makhnovskii, Yurii A; Pollak, Eli
2006-04-01
Stochastic acceleration, defined in terms of a stochastic equation of motion for the acceleration, is derived from a Hamiltonian model. A free particle is coupled bilinearly to a harmonic bath through the particle's momentum and coordinate. Under appropriate conditions, momentum coupling induces velocity diffusion which is not destroyed by the spatial coupling. Spatial-momentum coupling may induce spatial subdiffusion. The thermodynamic equilibrium theory presented in this paper does not violate the second law of thermodynamics, although the average velocity squared of the particle may increase in time without bound.
Elements of (super-)Hamiltonian Formalism
Nersessian, Armen
2005-01-01
In these lectures we discuss some basic aspects of Hamiltonian formalism, which usually do not appear in standard texbooks on classical mechanics for physicists. We pay special attention to the procedure of Hamiltonian reduction illustrating it by the examples related to Hopf maps. Then we briefly discuss the supergeneralisation(s) of the Hamiltonian formalism and present some simple models of supersymmetric mechanics on K\\"ahler manifolds.
Hamiltonian closures in fluid models for plasmas
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
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 ...
A parcel formulation for Hamiltonian layer models
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
A parcel formulation for Hamiltonian layer models
Bokhove, Onno; Oliver, M.
2009-01-01
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
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...
Nonperturbative embedding for highly nonlocal Hamiltonians
Subaşı, Yiǧit; Jarzynski, Christopher
2016-07-01
The need for Hamiltonians with many-body interactions arises in various applications of quantum computing. However, interactions beyond two-body are difficult to realize experimentally. Perturbative gadgets were introduced to obtain arbitrary many-body effective interactions using Hamiltonians with at most two-body interactions. Although valid for arbitrary k -body interactions, their use is limited to small k because the strength of interaction is k th order in perturbation theory. In this paper we develop a nonperturbative technique for obtaining effective k -body interactions using Hamiltonians consisting of at most l -body interactions with l gadgets to embed Hamiltonians of considerable complexity in proper subspaces of two-local Hamiltonians. We describe how our technique can be implemented in a hybrid (gate-based and adiabatic) as well as solely adiabatic quantum computing scheme.
B_c→ B_{sJ} form factors and B_c decays into B_{sJ} in covariant light-front approach
Shi, Yu-Ji; Wang, Wei; Zhao, Zhen-Xing
2016-10-01
We suggest to study the Bs and its excitations B_{sJ} in the B_c decays. We calculate the B_c→ B_{sJ} and B_c→ BJ form factors within the covariant light-front quark model, where the B_{sJ} and BJ denote an s-wave or p-wave bar{b}s and bar{b}d meson, respectively. The form factors at q^2=0 are directly computed while their q^2-distributions are obtained by extrapolation. The derived form factors are then used to study semileptonic B_c→ (B_{sJ},BJ)bar{ℓ }ν decays, and nonleptonic B_c→ B_{sJ}π . Branching fractions and polarizations are predicted in the standard model. We find that the branching fractions are sizable and might be accessible at the LHC experiment and future high-energy e^+e^- colliders with a high luminosity at the Z-pole. The future experimental measurements are helpful to study the nonperturbative QCD dynamics in the presence of a heavy spectator and also of great value for the study of spectroscopy.
Choi, Ho-Meoyng; Ryu, Hui-Young; Ji, Chueng-Ryong
2017-09-01
We investigate the (π0,η ,η')→γ*γ transitions both for the spacelike region and the timelike region using the light-front quark model (LFQM). In particular, we present the new direct method to explore the timelike region without resorting to mere analytic continuation from the spacelike region to the timelike region. Our direct calculation in timelike region shows the complete agreement not only with the analytic continuation result from the spacelike region but also with the result from the dispersion relation between the real and imaginary parts of the form factor. For the low energy regime, we compare our LFQM results of the transition form factors (TFFs) for the low timelike momentum transfer region and the slope parameters at q2=0 with the recent experimental data from the Dalitz decays of (π0,η ,η'). For the high energy regime, we incorporate the QCD factorization in our LFQM to examine the asymptotic behavior of TFFs both for the spacelike region and the timelike region. We compare our results with the available experimental data.
Quantum adiabatic protocols using emergent local Hamiltonians.
Modak, Ranjan; Vidmar, Lev; Rigol, Marcos
2017-10-01
We present two applications of emergent local Hamiltonians to speed up quantum adiabatic protocols for isolated noninteracting and weakly interacting fermionic systems in one-dimensional lattices. We demonstrate how to extract maximal work from initial band-insulating states, and how to adiabatically transfer systems from linear and harmonic traps into box traps. Our protocols consist of two stages. The first one involves a free expansion followed by a quench to an emergent local Hamiltonian. In the second stage, the emergent local Hamiltonian is "turned off" quasistatically. For the adiabatic transfer from a harmonic trap, we consider both zero- and nonzero-temperature initial states.
Extended Hamiltonian approach to continuous tempering.
Gobbo, Gianpaolo; Leimkuhler, Benedict J
2015-06-01
We introduce an enhanced sampling simulation technique based on continuous tempering, i.e., on continuously varying the temperature of the system under investigation. Our approach is mathematically straightforward, being based on an extended Hamiltonian formulation in which an auxiliary degree of freedom, determining the effective temperature, is coupled to the physical system. The physical system and its temperature evolve continuously in time according to the equations of motion derived from the extended Hamiltonian. Due to the Hamiltonian structure, it is easy to show that a particular subset of the configurations of the extended system is distributed according to the canonical ensemble for the physical system at the correct physical temperature.
Improved Sufficient Conditions for Hamiltonian Properties
Directory of Open Access Journals (Sweden)
Bode Jens-P.
2015-05-01
Full Text Available In 1980 Bondy [2] proved that a (k+s-connected graph of order n ≥ 3 is traceable (s = −1 or Hamiltonian (s = 0 or Hamiltonian-connected (s = 1 if the degree sum of every set of k+1 pairwise nonadjacent vertices is at least ((k+1(n+s−1+1/2. It is shown in [1] that one can allow exceptional (k+ 1-sets violating this condition and still implying the considered Hamiltonian property. In this note we generalize this result for s = −1 and s = 0 and graphs that fulfill a certain connectivity condition.
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.
Classical mechanics Hamiltonian and Lagrangian formalism
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.
Hamiltonian cycle problem and Markov chains
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.
Non-Hamiltonian commutators in quantum mechanics.
Sergi, Alessandro
2005-12-01
The symplectic structure of quantum commutators is first unveiled and then exploited to describe generalized non-Hamiltonian brackets in quantum mechanics. It is easily recognized that quantum-classical systems are described by a particular realization of such a bracket. In light of previous work, this paper explains a unified approach to classical and quantum-classical non-Hamiltonian dynamics. In order to illustrate the use of non-Hamiltonian commutators, it is shown how to define thermodynamic constraints in quantum-classical systems. In particular, quantum-classical Nosé-Hoover equations of motion and the associated stationary density matrix are derived. The non-Hamiltonian commutators for both Nosé-Hoover chains and Nosé-Andersen (constant-pressure, constant-temperature) dynamics are also given. Perspectives of the formalism are discussed.
Integrable Hamiltonian systems and spectral theory
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.
Supersymmetric analysis of a spin Hamiltonian model
Energy Technology Data Exchange (ETDEWEB)
Demircioglu, B. [Saraykoey Nuclear Research and Training Center, Saraykoey /Ankara (Turkey); Bilge Ocak, S. [Saraykoey Nuclear Research and Training Center, Saraykoey/Ankara (Turkey)]. E-mail: semamuzo@yahoo.com; Kuru, S. [Department of Physics, Ankara University, Faculty of Science, 06100 Tandogan/Ankara (Turkey)
2006-04-17
The intertwining method has been applied to the effective potential of the spin Hamiltonian H=-{gamma}S{sub z}{sup 2}-BS{sub x}. The supersymmetric partner potentials, some of which are singular, are obtained by using low-lying states of this potential. Applying the intertwining method successively, hierarchy of effective potentials has been established. Supersymmetric partner of the transformed spin Hamiltonian's effective potential has also been constructed.
Electronic Structure Calculations and the Ising Hamiltonian.
Xia, Rongxin; Bian, Teng; Kais, Sabre
2017-11-20
Obtaining exact solutions to the Schrödinger equation for atoms, molecules, and extended systems continues to be a "Holy Grail" problem which the fields of theoretical chemistry and physics have been striving to solve since inception. Recent breakthroughs have been made in the development of hardware-efficient quantum optimizers and coherent Ising machines capable of simulating hundreds of interacting spins with an Ising-type Hamiltonian. One of the most vital questions pertaining to these new devices is, "Can these machines be used to perform electronic structure calculations?" Within this work, we review the general procedure used by these devices and prove that there is an exact mapping between the electronic structure Hamiltonian and the Ising Hamiltonian. Additionally, we provide simulation results of the transformed Ising Hamiltonian for H2 , He2 , HeH+, and LiH molecules, which match the exact numerical calculations. This demonstrates that one can map the molecular Hamiltonian to an Ising-type Hamiltonian which could easily be implemented on currently available quantum hardware. This is an early step in developing generalized methods on such devices for chemical physics.
The Hamiltonian approach in classification and integrability of hydrodynamic chains
Pavlov, Maxim V.
2006-01-01
New approach in classification of integrable hydrodynamic chains is established. This is the method of the Hamiltonian hydrodynamic reductions. Simultaneously, this approach yields explicit Hamiltonian hydrodynamic reductions of the Hamiltonian hydrodynamic chains. The concept of reducible Poisson brackets is established. Also this approach is useful for non-Hamiltonian hydrodynamic chains. The deformed Benney hydrodynamic chain is considered.
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.
Integrability Of Non-KAM Hamiltonians
Salat, A.
1984-09-01
The integrability of Hamiltonians of the type H(P1, P2, Q1, Q2) = ? Pi ·Gi (Q1, Q2), Gi 2 π-periodic in Q1, Q2, is investigated numerically and analytically. With Gi = ωi + Fi (Q1, Q2) and = H0 = ? ωi + Pi, the unperturbed frequencies ωi = ∂H0/∂Pi, are independent of the momenta, and KAM theory cannot be applied. Surface of section plots and Fourier analysis of orbits reveal that "most" Hamiltonians are integrable. Possibly non-integrable Hamiltonians do not show "island plus ergodic region" structure but sequences which tend towards infinity. No theory is available to distinguish completely the classes of integrable and non-integrable functions Gi(Q1,Q2). In such a theory the problem of "small denominators" would play an essential role just as in KAM theory.
Gravitational surface Hamiltonian and entropy quantization
Bakshi, Ashish; Samanta, Saurav
2016-01-01
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.
Gravitational surface Hamiltonian and entropy quantization
Energy Technology Data Exchange (ETDEWEB)
Bakshi, Ashish, E-mail: ashishbakshi@outlook.com [Indian Statistical Institute, 203 B.T. Road, Kolkata-700108 (India); Majhi, Bibhas Ranjan, E-mail: bibhas.majhi@iitg.ernet.in [Department of Physics, Indian Institute of Technology Guwahati, Guwahati 781039, Assam (India); Samanta, Saurav, E-mail: srvsmnt@gmail.com [Narasinha Dutt College, 129, Belilious Road, Howrah-711101 (India)
2017-02-10
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.
Polynomial entropies for Bott nondegenerate Hamiltonian systems
Labrousse, Clémence; Marco, Jean-Pierre
2012-01-01
In this paper, we study the entropy of a Hamiltonian flow in restriction to an enregy level where it admits a first integral which is nondegenerate in the Bott sense. It is easy to see that for such a flow, the topological entropy vanishes. We focus on the polynomial and the weak polynomial entropies. We prove that, under conditions on the critical level of the Bott first integral and dynamical conditions on the hamiltonian function, the weak polynomial entropy belongs to {0,1} and the polyno...
Numerical bifurcation of Hamiltonian relative periodic orbits
DEFF Research Database (Denmark)
Wulff, Claudia; Schilder, Frank
2009-01-01
Relative periodic orbits (RPOs) are ubiquitous in symmetric Hamiltonian systems and occur, for example, in celestial mechanics, molecular dynamics, and the motion of rigid bodies. RPOs are solutions which are periodic orbits of the symmetry-reduced system. In this paper we analyze certain symmetry...
Quasi exact solution of the Rabi Hamiltonian
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.
Global Properties of Integrable Hamiltonian Systems
Lukina, O.V.; Takens, F.; Broer, H.W.
2008-01-01
This paper deals with Lagrangian bundles which are symplectic torus bundles that occur in integrable Hamiltonian systems. We review the theory of obstructions to triviality, in particular monodromy, as well as the ensuing classification problems which involve the Chern and Lagrange class. Our
Notch filters for port-Hamiltonian systems
Dirksz, Daniel; Scherpen, Jacquelien M.A.; van der Schaft, Abraham; Steinbuch, M.
2012-01-01
Network modeling of lumped-parameter physical systems naturally leads to a geometrically defined class of systems, i.e., port-Hamiltonian (PH) systems [4, 6]. The PH modeling framework describes a large class of (nonlinear) systems including passive mechanical systems, electrical systems,
The HELP inequality for Hamiltonian systems
Directory of Open Access Journals (Sweden)
Evans WD
1999-01-01
Full Text Available We extend the Hardy–Everitt–Littlewood–Polya inequality, hitherto established for 2nth order formally selfadjoint ordinary differential equations, to a wide class of linear Hamiltonian systems. The method follows Dias (Ph.D. thesis, Cardiff: University of Wales, 1994 but without the Hilbert space setting which he uses.
Valence band effective Hamiltonians in nitride semiconductors
Punya, Atchara; Schwertfager, Nucharee; Lambrecht, Walter
2012-02-01
Valence band effective Hamiltonians are useful to determine the electronic states of shallow impurities, quantum wells, quantum wires and quantum dots within the effective mass approximation. Although significant experimental and theoretical work has been performed, basic parameters such as the Rashba Sheka Pikus (RSP) Hamiltonian parameters are still uncertain. In this work, the electronic band structures of AlN, GaN and InN, all in the wurtzite crystal structure, as well as the RSP Hamiltonian parameters are determined by using the QSGW approximation in a FP-LMTO implementation. The corrections offered by this approach beyond the LDA are important to obtain the splittings and effective masses accurately. The present GW implementation, which allows for a real space representation of the self-energy, enables us to interpolate exactly to a fine k-mesh and hence to obtain accurate effective masses. We find the crystal field splitting in GaN (12 meV) in much closer agreement with experiment than previous work and obtain a negative SO coupling for InN. Moreover, we have generalized the method of invariants to crystals with orthorombic symmetry, such as ZnSiN2 ZnGeN2, ZnSnN2 and CdGeN2 and determined the corresponding Hamiltonian parameters.
Effective Hamiltonian approach to periodically perturbed quantum optical systems
Energy Technology Data Exchange (ETDEWEB)
Sainz, I. [Centro Universitario de los Lagos, Universidad de Guadalajara, Enrique Diaz de Leon, 47460 Lagos de Moreno, Jal. (Mexico)]. E-mail: isa@culagos.udg.mx; Klimov, A.B. [Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, 44410 Guadalajara, Jal. (Mexico)]. E-mail: klimov@cencar.udg.mx; Saavedra, C. [Center for Quantum Optics and Quantum Information, Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion (Chile)]. E-mail: csaaved@udec.cl
2006-02-20
We apply the method of Lie-type transformations to Floquet Hamiltonians for periodically perturbed quantum systems. Some typical examples of driven quantum systems are considered in the framework of this approach and corresponding effective time dependent Hamiltonians are found.
Hamiltonian gadgets with reduced resource requirements
Cao, Yudong; Babbush, Ryan; Biamonte, Jacob; Kais, Sabre
2015-01-01
Application of the adiabatic model of quantum computation requires efficient encoding of the solution to computational problems into the lowest eigenstate of a Hamiltonian that supports universal adiabatic quantum computation. Experimental systems are typically limited to restricted forms of two-body interactions. Therefore, universal adiabatic quantum computation requires a method for approximating quantum many-body Hamiltonians up to arbitrary spectral error using at most two-body interactions. Hamiltonian gadgets, introduced around a decade ago, offer the only current means to address this requirement. Although the applications of Hamiltonian gadgets have steadily grown since their introduction, little progress has been made in overcoming the limitations of the gadgets themselves. In this experimentally motivated theoretical study, we introduce several gadgets which require significantly more realistic control parameters than similar gadgets in the literature. We employ analytical techniques which result in a reduction of the resource scaling as a function of spectral error for the commonly used subdivision, three- to two-body and k -body gadgets. Accordingly, our improvements reduce the resource requirements of all proofs and experimental proposals making use of these common gadgets. Next, we numerically optimize these gadgets to illustrate the tightness of our analytical bounds. Finally, we introduce a gadget that simulates a Y Y interaction term using Hamiltonians containing only {X ,Z ,X X ,Z Z } terms. Apart from possible implications in a theoretical context, this work could also be useful for a first experimental implementation of these key building blocks by requiring less control precision without introducing extra ancillary qubits.
Algebraic aspects of Tremblay-Turbiner-Winternitz Hamiltonian systems
Calzada, J. A.; Celeghini, E.; del Olmo, M. A.; Velasco, M. A.
2012-02-01
Using the factorization method we find a hierarchy of Tremblay-Turbiner-Winternitz Hamiltonians labeled by discrete indices. The shift operators (those connecting eigenfunctions of different Hamiltonians of the hierarchy) as well the ladder operators (they connect eigenstates of a determined Hamiltonian) obtained in this way close different algebraic structures that are presented here.
On Hamiltonian cycles of power graphs of abelian groups
Mukherjee, Himadri
2015-01-01
In this article we discuss the question of presence of Hamiltonian cycle in the un-directed power graph of a group. In the process we develop weighted Hamiltonian cycle concept and prove a few general results regarding the Hamiltonian question.
Effective Floquet Hamiltonian for spin = 1 in magic angle spinning ...
Indian Academy of Sciences (India)
Contact transformation is an operator transformation method in time-independent perturbation theory which is used successfully in molecular spectroscopy to obtain an effective Hamiltonian. Floquet theory is used to transform the periodic time-dependent Hamiltonian, to a time-independent Floquet Hamiltonian. In this ...
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.......Our Hamiltonians are compared to an equivalent one for graphene. For silicene, the expressionfor band warping is obtained analytically and found to be of different order than for graphene. Weprove 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 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...
An Underlying Geometrical Manifold for Hamiltonian Mechanics
Horwitz, L P; Levitan, J; Lewkowicz, M
2015-01-01
We show that there exists an underlying manifold with a conformal metric and compatible connection form, and a metric type Hamiltonian (which we call the geometrical picture) that can be put into correspondence with the usual Hamilton-Lagrange mechanics. The requirement of dynamical equivalence of the two types of Hamiltonians, that the momenta generated by the two pictures be equal for all times, is sufficient to determine an expansion of the conformal factor, defined on the geometrical coordinate representation, in its domain of analyticity with coefficients to all orders determined by functions of the potential of the Hamilton-Lagrange picture, defined on the Hamilton-Lagrange coordinate representation, and its derivatives. Conversely, if the conformal function is known, the potential of a Hamilton-Lagrange picture can be determined in a similar way. We show that arbitrary local variations of the orbits in the Hamilton-Lagrange picture can be generated by variations along geodesics in the geometrical pictu...
Hamiltonian partial differential equations and applications
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.
Hamiltonian deformations of Gabor frames: First steps.
de Gosson, Maurice A
2015-03-01
Gabor frames can advantageously be redefined using the Heisenberg-Weyl operators familiar from harmonic analysis and quantum mechanics. Not only does this redefinition allow us to recover in a very simple way known results of symplectic covariance, but it immediately leads to the consideration of a general deformation scheme by Hamiltonian isotopies (i.e. arbitrary paths of non-linear symplectic mappings passing through the identity). We will study in some detail an associated weak notion of Hamiltonian deformation of Gabor frames, using ideas from semiclassical physics involving coherent states and Gaussian approximations. We will thereafter discuss possible applications and extensions of our method, which can be viewed - as the title suggests - as the very first steps towards a general deformation theory for Gabor frames.
Non-Hamiltonian equilibrium statistical mechanics.
Sergi, Alessandro
2003-02-01
In this paper the equilibrium statistical mechanics of non-Hamiltonian systems is formulated introducing an algebraic bracket. The latter defines non-Hamiltonian equations of motion in classical phase space according to the approach introduced in Phys. Rev. E 64, 056125 (2001). The Jacobi identity is no longer satisfied by the generalized bracket and as a result the algebra of phase space functions is not time translation invariant. The presence of a nonzero phase space compressibility spoils also the time-reversal invariance of the dynamics. The general Liouville equation is rederived and the properties of statistical averages are accounted for. The features of time correlation functions and linear response theory are also discussed.
Hamiltonian methods in the theory of solitons
Faddeev, Ludwig
1987-01-01
The main characteristic of this classic exposition of the inverse scattering method and its applications to soliton theory is its consistent Hamiltonian approach to the theory. The nonlinear Schrodinger equation is considered as a main example, forming the first part of the book. The second part examines such fundamental models as the sine-Gordon equation and the Heisenberg equation, the classification of integrable models and methods for constructing their solutions.
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.
The Effective Hamiltonian in the Scalar Electrodynamics
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.
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 i......) 2005 Wiley Periodicals, Inc....
Hamiltonian gyrokinetic Vlasov-Maxwell system
Burby, J. W.; Brizard, A. J.; Morrison, P. J.; Qin, H.
2015-09-01
A new formulation of electromagnetic gyrokinetics that possesses Hamiltonian form is constructed. The new formulation replaces Poisson-like equations by hyperbolic equations for the electromagnetic field with the speed of light slowed to that of the gyrokinetic vacuum, thereby significantly reducing computational cost. An energy principle is derived using the field-theoretic noncanonical Poisson bracket formulation of the theory. The energy principle is used to prove stability of the thermal equilibrium state in a uniform background magnetic field.
Diffusion in a weakly random Hamiltonian flow
Komorowski, T.; Ryzhik, L.
2005-01-01
We consider the motion of a particle governed by a weakly random Hamiltonian flow. We identify temporal and spatial scales on which the particle trajectory converges to a spatial Brownian motion. The main technical issue in the proof is to obtain error estimates for the convergence of the solution of the stochastic acceleration problem to a momentum diffusion. We also apply our results to the system of random geometric acoustics equations and show that the energy density of the acoustic waves...
Optimal Hamiltonian Simulation by Quantum Signal Processing.
Low, Guang Hao; Chuang, Isaac L
2017-01-06
The physics of quantum mechanics is the inspiration for, and underlies, quantum computation. As such, one expects physical intuition to be highly influential in the understanding and design of many quantum algorithms, particularly simulation of physical systems. Surprisingly, this has been challenging, with current Hamiltonian simulation algorithms remaining abstract and often the result of sophisticated but unintuitive constructions. We contend that physical intuition can lead to optimal simulation methods by showing that a focus on simple single-qubit rotations elegantly furnishes an optimal algorithm for Hamiltonian simulation, a universal problem that encapsulates all the power of quantum computation. Specifically, we show that the query complexity of implementing time evolution by a d-sparse Hamiltonian H[over ^] for time-interval t with error ε is O[td∥H[over ^]∥_{max}+log(1/ε)/loglog(1/ε)], which matches lower bounds in all parameters. This connection is made through general three-step "quantum signal processing" methodology, comprised of (i) transducing eigenvalues of H[over ^] into a single ancilla qubit, (ii) transforming these eigenvalues through an optimal-length sequence of single-qubit rotations, and (iii) projecting this ancilla with near unity success probability.
Continuum balances from extended Hamiltonian dynamics.
Giusteri, Giulio G; Podio-Guidugli, Paolo; Fried, Eliot
2017-06-14
The classical procedure devised by Irving and Kirkwood in 1950 and completed slightly later by Noll produces counterparts of the basic balance laws of standard continuum mechanics starting from an ordinary Hamiltonian description of the dynamics of a system of material points. Post-1980 molecular dynamics simulations of the time evolution of such systems use extended Hamiltonians such as those introduced by Andersen, Nosé, and Parrinello and Rahman. The additional terms present in these extensions affect the statistical properties of the system so as to capture certain target phenomenologies that would otherwise be beyond reach. We here propose a physically consistent application of the Irving-Kirkwood-Noll procedure to the extended Hamiltonian systems of material points. Our procedure produces balance equations at the continuum level featuring non-standard terms because the presence of auxiliary degrees of freedom gives rise to additional fluxes and sources that influence the thermodynamic and transport properties of the continuum model. Being aware of the additional contributions may prove crucial when designing multiscale computational schemes in which information is exchanged between the atomistic and continuum levels.
Hamiltonian approach to the magnetostatic equilibrium problem
Energy Technology Data Exchange (ETDEWEB)
Tessarotto, M.; Zheng, Lin Jin [Universita di Trieste (Italy); Johnson, J.L. [Princeton Univ., NJ (United States). Plasma Physics Lab.
1995-02-01
The purpose of this paper is to investigate the classical scalar-pressure magnetostatic equilibrium problem for non-symmetric configurations in the framework of a Hamiltonian approach. Requiring that the equilibrium admits locally, in a suitable subdomain, a family of nested toroidal magnetic surfaces, the Hamiltonian equations describing the magnetic flux lines in such a subdomain are obtained for general curvilinear coordinate systems. The properties of such Hamiltonian system are investigated. A representation of the magnetic field in terms of arbitrary general curvilinear coordinates is thus obtained. Its basic feature is that the magnetic field must fulfill suitable periodicity constraints to be imposed on arbitrary rational magnetic surfaces for general non-symmetric toroidal equilibria, i.e., it is quasi-symmetric. Implications for the existence of magnetostatic equilibria are pointed out. In particular, it is proven that a generalized equilibrium equation exists for such quasi-symmetric equilibria, which extends the Grad-Shafranov equation to fully three-dimensional configurations. As an application, the case is considered of quasi-helical equilibria, i.e., displaying a magnetic field magnitude depending on the poloidal ({chi}) and toroidal ({var_theta}) angles only in terms of {alpha}={chi}-N{theta} with N an arbitrary integer.
Action-minimizing methods in Hamiltonian dynamics
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
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...
Statistical mechanics of Hamiltonian adaptive resolution simulations.
Español, P; Delgado-Buscalioni, R; Everaers, R; Potestio, R; Donadio, D; Kremer, K
2015-02-14
The Adaptive Resolution Scheme (AdResS) is a hybrid scheme that allows to treat a molecular system with different levels of resolution depending on the location of the molecules. The construction of a Hamiltonian based on the this idea (H-AdResS) allows one to formulate the usual tools of ensembles and statistical mechanics. We present a number of exact and approximate results that provide a statistical mechanics foundation for this simulation method. We also present simulation results that illustrate the theory.
Fractal boundaries in chaotic hamiltonian systems
Viana, R. L.; Mathias, A. C.; Marcus, F. A.; Kroetz, T.; Caldas, I. L.
2017-10-01
Fractal structures are typically present in the dynamics of chaotic orbits in non-integrable open Hamiltonian systems and result from the extremely complicated nature of the invariant manifolds of unstable periodic orbits. Exit basins, the set of initial conditions leading to orbits escaping through a given exit, have very frequently fractal boundaries. In this work we analyze exit basin boundaries in a dynamical system of physical interest, namely the motion of charged particles in a magnetized plasma subjected to electrostatic drift waves, and characterize in a quantitative way the fractality of these structures and their observable consequences, as the final-state uncertainty.
Model Hamiltonians for atomic and molecular systems
Carlson, J.; Moskowitz, Jules W.; Schmidt, K. E.
1989-01-01
A model Hamiltonian, designed to allow larger systems to be treated with the Green's function Monte Carlo method, is introduced for atomic and molecular systems. The model reduces the statistical variance associated with Green's function Monte Carlo calculations by reducing potential energy fluctuations in the core regions. By performing calculations of Li, LiH, and Li2 we show that this method can be used to obtain energy differences with much less computer time than required for the complete interaction. Increases in efficiency for larger systems will be even greater.
Reducing the generalised Sudoku problem to the Hamiltonian cycle problem
Directory of Open Access Journals (Sweden)
Michael Haythorpe
2016-12-01
Full Text Available The generalised Sudoku problem with N symbols is known to be NP-complete, and hence is equivalent to any other NP-complete problem, even for the standard restricted version where N is a perfect square. In particular, generalised Sudoku is equivalent to the, classical, Hamiltonian cycle problem. A constructive algorithm is given that reduces generalised Sudoku to the Hamiltonian cycle problem, where the resultant instance of Hamiltonian cycle problem is sparse, and has O(N3 vertices. The Hamiltonian cycle problem instance so constructed is a directed graph, and so a (known conversion to undirected Hamiltonian cycle problem is also provided so that it can be submitted to the best heuristics. A simple algorithm for obtaining the valid Sudoku solution from the Hamiltonian cycle is provided. Techniques to reduce the size of the resultant graph are also discussed.
CPT and effective Hamiltonians for neutral kaon and similar complexes
Urbanowski, K.
2002-01-01
We begin with a discussion of the general form and general CP-- and CPT-- transformation properties of the Lee--Oehme--Yang (LOY) effective Hamiltonian for the neutral kaon complex. Next, the properties of the exact effective Hamiltonian for this complex are discussed. Using the Khalfin Theorem we show that the diagonal matrix elements of the effective Hamiltonian governing the time evolution in the subspace of states of an unstable particle and its antiparticle need not be equal at for t > t...
SUSY approach to Pauli Hamiltonians with an axial symmetry
Energy Technology Data Exchange (ETDEWEB)
Ioffe, M V; Kuru, S; Negro, J; Nieto, L M [Departamento de Fisica Teorica, Atomica y Optica, Universidad de Valladolid, 47071 Valladolid (Spain)
2006-06-02
A two-dimensional Pauli Hamiltonian describing the interaction of a neutral spin-1/2 particle with a magnetic field having axial and second-order symmetries is considered. After separation of variables, the one-dimensional matrix Hamiltonian is analysed from the point of view of supersymmetric quantum mechanics. Attention is paid to the discrete symmetries of the Hamiltonian and also to the Hamiltonian hierarchies generated by intertwining operators. The spectrum is studied by means of the associated matrix shape invariance. The relation between the intertwining operators and the second-order symmetries is established, and the full set of ladder operators that complete the dynamical algebra is constructed.
An effective Hamiltonian approach to quantum random walk
Indian Academy of Sciences (India)
In this article we present an effective Hamiltonian approach for discrete time quantum random walk. A form of the Hamiltonian ... TARUN KANTI GHOSH2. Inter-University Centre for Astronomy and Astrophysics, Ganeshkhind, Pune 411 007, India; Department of Physics, Indian Institute of Technology, Kanpur 208 016, India ...
Spectral analysis of the direct sum Hamiltonian operators ...
African Journals Online (AJOL)
... the Sz.-Nagy-Foias characteristic function, we prove that all root (eigen and associated) vectors of the maximal dissipative extensions of the minimal symmetric direct sum Hamiltonian operators are complete in the Hilbert spaces. Keywords: Hamiltonian system, dissipative operator, characteristic function, scattering matrix, ...
Bifurcations in Hamiltonian systems with a reflecting symmetry
Bosschaert, M.; Hanssmann, H.
2011-01-01
A reflecting symmetry q 7→ −q of a Hamiltonian system does not leave the symplectic structure dq∧dp invariant and is therefore usually asso- ciated with a reversible Hamiltonian system. However, if q 7→ −q leads to H 7→ −H, then the equations of motion are invariant under the re- flection. This
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.
Some sufficient conditions for Hamiltonian property in terms of ...
Indian Academy of Sciences (India)
... v ) ) for various choices of the function (), where (, ) is the distance between vertices and in . In this paper, we give some sufficient conditions for a connected graph to be Hamiltonian, a connected graph to be traceable, and a connected bipartite graph to be Hamiltonian in terms of the Wiener-type invariants ...
HAMILTONIAN INCLUSIONS WITH CONVEX DISSIPATION WITH A VIEW TOWARDS APPLICATIONS
Directory of Open Access Journals (Sweden)
Marius Buliga
2010-01-01
Full Text Available We propose a generalization of Hamiltonian mechanics, as a Hamiltonian inclusion with convex dissipation function. We obtain a dynamical version of the approach of Mielke to quasistatic rate-independent processes. Then we show that a class of models of dynamical brittle damage can be formulated in this setting.
Periodic Hamiltonian hierarchies and non-uniqueness of ...
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 88; Issue 1. Periodic Hamiltonian hierarchies and ... ABHIJIT BANERJEE. Regular Volume 88 Issue 1 January 2017 Article ID 1 ... Abstract. In this article, a family of periodic quantum Hamiltonians, that is subject to a closure condition is considered. In the context of the ...
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.
On the minimization of Hamiltonians over pure Gaussian states
DEFF Research Database (Denmark)
Derezinski, Jan; Napiorkowski, Marcin; Solovej, Jan Philip
2013-01-01
A Hamiltonian defined as a polynomial in creation and annihilation operators is considered. After a minimization of its expectation value over pure Gaussian states, the Hamiltonian is Wick-ordered in creation and annihillation operators adapted to the minimizing state. It is shown that this proce...
Symmetry and reduction in implicit generalized Hamiltonian systems
Blankenstein, G.; van der Schaft, Arjan
In this paper we study the notion of symmetry for implicit generalized Hamiltonian systems, which are Hamiltonian systems with respect to a generalized Dirac structure. We investigate the reduction of these systems admitting a symmetry Lie group with corresponding quantities. Main features in this
Symmetry and Reduction in Implicit Generalized Hamiltonian Systems
Blankenstein, G.; Schaft, A.J. van der
2001-01-01
In this paper we study the notion of symmetry for implicit generalized Hamiltonian systems, which are Hamiltonian systems with respect to a generalized Dirac structure. We investigate the reduction of these systems admitting a symmetry Lie group with corresponding conserved quantities. Main features
Distributed port-Hamiltonian formulation of infinite dimensional systems
Macchelli, Alessandro; Macchelli, A.; van der Schaft, Arjan; Melchiorri, Claudio
2004-01-01
In this paper, some new results concerning the modeling and control 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
Distributed Port-Hamiltonian Formulation of Innite Dimensional Systems
Macchelli, Alessandro; Schaft, Arjan J. van der; Melchiorri, Claudio
2004-01-01
In this paper, some new results concerning the modeling and control 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
A Hamiltonian approach to stabilization of nonholonomic mechanical systems
Maschke, B.M.; Schaft, A.J. van der
1994-01-01
A simple procedure is provided to write the equations of motion of controlled mechanical systems with constraints as controlled Hamiltonian equations with respect to a "Poisson" bracket which does not necessarily satisfy the Jacobi-identity. Based on the Hamiltonian form a stabilization procedure is
g Algebra and two-dimensional quasiexactly solvable Hamiltonian ...
Indian Academy of Sciences (India)
In this article, we write the general form of the quasiexactly solvable Hamiltonian of g2 algebra via one special ... In general, there are two types of problems in such systems: the quasiexactly solvable (QES) models .... we should not consider writing the general form of the QES Hamiltonian of g2 algebra. If we take the whole ...
Using Hamiltonian control to desynchronize Kuramoto oscillators
Gjata, Oltiana; Asllani, Malbor; Barletti, Luigi; Carletti, Timoteo
2017-02-01
Many coordination phenomena are based on a synchronization process, whose global behavior emerges from the interactions among the individual parts. Often in nature, such self-organized mechanism allows the system to behave as a whole and thus grounding its very first existence, or expected functioning, on such process. There are, however, cases where synchronization acts against the stability of the system; for instance in some neurodegenerative diseases or epilepsy or the famous case of Millennium Bridge where the crowd synchronization of the pedestrians seriously endangered the stability of the structure. In this paper we propose an innovative control method to tackle the synchronization process based on the application of the Hamiltonian control theory, by adding a small control term to the system we are able to impede the onset of the synchronization. We present our results on a generalized class of the paradigmatic Kuramoto model.
Boundary Liouville Theory: Hamiltonian Description and Quantization
Directory of Open Access Journals (Sweden)
Harald Dorn
2007-01-01
Full Text Available The paper is devoted to the Hamiltonian treatment of classical and quantum properties of Liouville field theory on a timelike strip in 2d Minkowski space. We give a complete description of classical solutions regular in the interior of the strip and obeying constant conformally invariant conditions on both boundaries. Depending on the values of the two boundary parameters these solutions may have different monodromy properties and are related to bound or scattering states. By Bohr-Sommerfeld quantization we find the quasiclassical discrete energy spectrum for the bound states in agreement with the corresponding limit of spectral data obtained previously by conformal bootstrap methods in Euclidean space. The full quantum version of the special vertex operator $e^varphi$ in terms of free field exponentials is constructed in the hyperbolic sector.
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.
Classical Mechanics Hamiltonian and Lagrangian Formalism
Deriglazov, Alexei
2010-01-01
Formalism of classical mechanics underlies a number of powerful mathematical methods that are widely used in theoretical and mathematical physics. This book considers the basics facts of Lagrangian and Hamiltonian mechanics, as well as related topics, such as canonical transformations, integral invariants, potential motion in geometric setting, symmetries, the Noether theorem and systems with constraints. While in some cases the formalism is developed beyond the traditional level adopted in the standard textbooks on classical mechanics, only elementary mathematical methods are used in the exposition of the material. The mathematical constructions involved are explicitly described and explained, so the book can be a good starting point for the undergraduate student new to this field. At the same time and where possible, intuitive motivations are replaced by explicit proofs and direct computations, preserving the level of rigor that makes the book useful for the graduate students intending to work in one of the...
Asymptotic freedom in the Hamiltonian approach to binding of color
Directory of Open Access Journals (Sweden)
Gómez-Rocha María
2017-01-01
Full Text Available We derive asymptotic freedom and the SU(3 Yang-Mills β-function using the renormalization group procedure for effective particles. In this procedure, the concept of effective particles of size s is introduced. Effective particles in the Fock space build eigenstates of the effective Hamiltonian Hs, which is a matrix written in a basis that depend on the scale (or size parameter s. The effective Hamiltonians Hs and the (regularized canonical Hamiltonian H0 are related by a similarity transformation. We calculate the effective Hamiltonian by solving its renormalization-group equation perturbatively up to third order and calculate the running coupling from the three-gluon-vertex function in the effective Hamiltonian operator.
Asymptotic freedom in the Hamiltonian approach to binding of color
Gómez-Rocha, María
2017-03-01
We derive asymptotic freedom and the SU(3) Yang-Mills β-function using the renormalization group procedure for effective particles. In this procedure, the concept of effective particles of size s is introduced. Effective particles in the Fock space build eigenstates of the effective Hamiltonian Hs, which is a matrix written in a basis that depend on the scale (or size) parameter s. The effective Hamiltonians Hs and the (regularized) canonical Hamiltonian H0 are related by a similarity transformation. We calculate the effective Hamiltonian by solving its renormalization-group equation perturbatively up to third order and calculate the running coupling from the three-gluon-vertex function in the effective Hamiltonian operator.
A Hamiltonian Formulation On Tsunami Over Swell
TIAN, M.; Sheremet, A.; Kaihatu, J. M.
2012-12-01
Tsunami induced by earthquakes typically evolves shore-ward with a significant amplification of amplitude during the last stages of shoaling. This study focuses on tsunami evolution in shallow water under the effects of the oceanographic environment such as breaking and tsunami- swell interaction. One generally describes wave breaking directly with a discontinuity in the solution to the classical nonlinear shallow water equations (NLSW) (e.g., Stoker 1985). This wave-front steepness calculation, however, has the potential problem that for the case of the single wave defined by solitary wave, breaking occurs much closer to the wave crest so that the method is formally invalid (Madsen et. al. 2008). Li and Raichlen (2002) applied a weighted essentially non-oscillatory (WENO) shock-capturing scheme in the numerical NSWE model to capture the wave breaking process. The problem arises that a convenient hamiltonian formalism is lacking to describe wave breaking. One wants to evaluate breaking by deducing the decay of the tsunami energy in a straightforward manner. The linear effect of the tsunami background circulation on swell is well known (e.g., Madsen et. al. 2008). However, Kaihatu and El Safty(2011) hypothesized that this is only one "half" of the mutual interaction between the tsunami and the overlying swell field, which might have subtle effects on the tsunami front-face steepness and breaking process. These effects were observed in a laboratory experiments (Kaihatu and El Safty 2011). It was observed that the presence of swell affects the maximum surface amplitude of overall wave field and produces significant energy shifts to high frequencies, thus promoting tsunami breaking. The theoretical study for tsunami-swell interaction requires a phase-resolving wave-wave interaction model. In this study, we derive a Hamiltonian formulation for the tsunami-swell interaction using the quasi stream-function formulation. This formalism is better able to handle uneven
Enhancing sensitivity in quantum metrology by Hamiltonian extensions
Fraïsse, Julien Mathieu Elias; Braun, Daniel
2017-06-01
A well-studied scenario in quantum parameter estimation theory arises when the parameter to be estimated is imprinted on the initial state by a Hamiltonian of the form θ G . For such "phase-shift Hamiltonians" it has been shown that one cannot improve the channel quantum Fisher information by adding ancillas and letting the system interact with them. Here we investigate the general case, where the Hamiltonian is not necessarily a phase shift, and show that in this case in general it is possible to increase the quantum channel information and to reach an upper bound. This can be done by adding a term proportional to the derivative of the Hamiltonian, or by subtracting a term from the original Hamiltonian. Neither method makes use of any ancillas, which shows that, for quantum channel estimation with an arbitrary parameter-dependent Hamiltonian, entanglement with an ancillary system is not necessary to reach the best possible sensitivity. By adding an operator to the Hamiltonian we can also modify the time scaling of the channel quantum Fisher information. We illustrate our techniques with nitrogen vacancy center magnetometry and the estimation of the direction of a magnetic field in a given plane using a single spin-1 as probe.
Nonunitary quantum computation in the ground space of local Hamiltonians
Usher, Naïri; Hoban, Matty J.; Browne, Dan E.
2017-09-01
A central result in the study of quantum Hamiltonian complexity is that the k -local Hamiltonian problem is quantum-Merlin-Arthur-complete. In that problem, we must decide if the lowest eigenvalue of a Hamiltonian is bounded below some value, or above another, promised one of these is true. Given the ground state of the Hamiltonian, a quantum computer can determine this question, even if the ground state itself may not be efficiently quantum preparable. Kitaev's proof of QMA-completeness encodes a unitary quantum circuit in QMA into the ground space of a Hamiltonian. However, we now have quantum computing models based on measurement instead of unitary evolution; furthermore, we can use postselected measurement as an additional computational tool. In this work, we generalize Kitaev's construction to allow for nonunitary evolution including postselection. Furthermore, we consider a type of postselection under which the construction is consistent, which we call tame postselection. We consider the computational complexity consequences of this construction and then consider how the probability of an event upon which we are postselecting affects the gap between the ground-state energy and the energy of the first excited state of its corresponding Hamiltonian. We provide numerical evidence that the two are not immediately related by giving a family of circuits where the probability of an event upon which we postselect is exponentially small, but the gap in the energy levels of the Hamiltonian decreases as a polynomial.
Unconstrained Hamiltonian formulation of low energy QCD
Directory of Open Access Journals (Sweden)
Pavel Hans-Peter
2014-04-01
Full Text Available Using a generalized polar decomposition of the gauge fields into gaugerotation and gauge-invariant parts, which Abelianises the Non-Abelian Gauss-law constraints to be implemented, a Hamiltonian formulation of QCD in terms of gauge invariant dynamical variables can be achieved. The exact implementation of the Gauss laws reduces the colored spin-1 gluons and spin-1/2 quarks to unconstrained colorless spin-0, spin-1, spin-2 and spin-3 glueball fields and colorless Rarita-Schwinger fields respectively. The obtained physical Hamiltonian naturally admits a systematic strongcoupling expansion in powers of λ = g−2/3, equivalent to an expansion in the number of spatial derivatives. The leading-order term corresponds to non-interacting hybridglueballs, whose low-lying spectrum can be calculated with high accuracy by solving the Schrödinger-equation of the Dirac-Yang-Mills quantum mechanics of spatially constant fields (at the moment only for the 2-color case. The discrete glueball excitation spectrum shows a universal string-like behaviour with practically all excitation energy going in to the increase of the strengths of merely two fields, the “constant Abelian fields” corresponding to the zero-energy valleys of the chromomagnetic potential. Inclusion of the fermionic degrees of freedom significantly lowers the spectrum and allows for the study of the sigma meson. Higher-order terms in λ lead to interactions between the hybridglueballs and can be taken into account systematically using perturbation theory in λ, allowing for the study of IR-renormalisation and Lorentz invarianz. The existence of the generalized polar decomposition used, the position of the zeros of the corresponding Jacobian (Gribov horizons, and the ranges of the physical variables can be investigated by solving a system of algebraic equations. Its exact solution for the case of one spatial dimension and first numerical solutions for two and three spatial dimensions indicate
A cohomological obstruction for global quasi-bi-Hamiltonian fields
Energy Technology Data Exchange (ETDEWEB)
Rakotondralambo, Joseph, E-mail: joseph.rakotondralambo@unimes.f [Departement de Mathematiques et Informatique, Faculte des Sciences, Universite d' Antananarivo (Madagascar)
2011-02-14
We introduce the notion of integrating factor for a 1-form which is an inner product of a vector fields and a 2-form, and the notion of weakly bi-Hamiltonian field also, which is locally quasi-bi-Hamiltonian. A cohomological class in some first cohomology space is associated to such vector fields when this is weakly bi-Hamiltonian and defined relatively to the above 1-form. This class is a cohomological obstruction to the existence of a global integrating factor for the 1-form.
The Tremblay-Turbiner-Winternitz system as extended Hamiltonian
Chanu, Claudia Maria; Degiovanni, Luca; Rastelli, Giovanni
2014-12-01
We generalize the idea of "extension of Hamiltonian systems"—developed in a series of previous articles—which allows the explicit construction of Hamiltonian systems with additional non-trivial polynomial first integrals of arbitrarily high degree, as well as the determination of new superintegrable systems from old ones. The present generalization, that we call "modified extension of Hamiltonian systems," produces the third independent first integral for the (complete) Tremblay-Turbiner-Winternitz system, as well as for the caged anisotropic oscillator in dimension two.
Linear Quantum Entropy and Non-Hermitian Hamiltonians
Directory of Open Access Journals (Sweden)
Alessandro Sergi
2016-12-01
Full Text Available We consider the description of open quantum systems with probability sinks (or sources in terms of general non-Hermitian Hamiltonians. Within such a framework, we study novel possible definitions of the quantum linear entropy as an indicator of the flow of information during the dynamics. Such linear entropy functionals are necessary in the case of a partially Wigner-transformed non-Hermitian Hamiltonian (which is typically useful within a mixed quantum-classical representation. Both the case of a system represented by a pure non-Hermitian Hamiltonian as well as that of the case of non-Hermitian dynamics in a classical bath are explicitly considered.
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.
Phase space flows for non-Hamiltonian systems with constraints.
Sergi, Alessandro
2005-09-01
In this paper, non-Hamiltonian systems with holonomic constraints are treated by a generalization of Dirac's formalism. Non-Hamiltonian phase space flows can be described by generalized antisymmetric brackets or by general Liouville operators which cannot be derived from brackets. Both situations are treated. In the first case, a Nosé-Dirac bracket is introduced as an example. In the second one, Dirac's recipe for projecting out constrained variables from time translation operators is generalized and then applied to non-Hamiltonian linear response. Dirac's formalism avoids spurious terms in the response function of constrained systems. However, corrections coming from phase space measure must be considered for general perturbations.
Covariant Hamiltonian tetrad approach to numerical relativity
Hamilton, Andrew J. S.
2017-12-01
A Hamiltonian approach to the equations of general relativity is proposed using the powerful mathematical language of multivector-valued differential forms. In the approach, the gravitational coordinates are the 12 spatial components of the line interval (the vierbein) including their antisymmetric parts, and their 12 conjugate momenta. A feature of the proposed formalism is that it allows Lorentz gauge freedoms to be imposed on the Lorentz connections rather than on the vierbein, which may facilitate numerical integration in some challenging problems. The 40 Hamilton's equations comprise 12 +12 =24 equations of motion, ten constraint equations (first class constraints, which must be arranged on the initial hypersurface of constant time, but which are guaranteed thereafter by conservation laws), and six identities (second class constraints). The six identities define a trace-free spatial tensor that is the gravitational analog of the magnetic field of electromagnetism. If the gravitational magnetic field is promoted to an independent field satisfying its own equation of motion, then the system becomes the Wahlquist-Estabrook-Buchman-Bardeen (WEBB) system, which is known to be strongly hyperbolic. Some other approaches, including Arnowitt-Deser-Misner, Baumgarte-Shapiro-Shibata-Nakamura, WEBB, and loop quantum gravity, are translated into the language of multivector-valued forms, bringing out their underlying mathematical structure.
Mixing Properties of Stochastic Quantum Hamiltonians
Onorati, E.; Buerschaper, O.; Kliesch, M.; Brown, W.; Werner, A. H.; Eisert, J.
2017-11-01
Random quantum processes play a central role both in the study of fundamental mixing processes in quantum mechanics related to equilibration, thermalisation and fast scrambling by black holes, as well as in quantum process design and quantum information theory. In this work, we present a framework describing the mixing properties of continuous-time unitary evolutions originating from local Hamiltonians having time-fluctuating terms, reflecting a Brownian motion on the unitary group. The induced stochastic time evolution is shown to converge to a unitary design. As a first main result, we present bounds to the mixing time. By developing tools in representation theory, we analytically derive an expression for a local k-th moment operator that is entirely independent of k, giving rise to approximate unitary k-designs and quantum tensor product expanders. As a second main result, we introduce tools for proving bounds on the rate of decoupling from an environment with random quantum processes. By tying the mathematical description closely with the more established one of random quantum circuits, we present a unified picture for analysing local random quantum and classes of Markovian dissipative processes, for which we also discuss applications.
On the Edge-Hyper-Hamiltonian Laceability of Balanced Hypercubes
Directory of Open Access Journals (Sweden)
Cao Jianxiang
2016-11-01
Full Text Available The balanced hypercube BHn, defined by Wu and Huang, is a variant of the hypercube network Qn, and has been proved to have better properties than Qn with the same number of links and processors. For a bipartite graph G = (V0 ∪ V1,E, we say G is edge-hyper-Hamiltonian laceable if it is Hamiltonian laceable, and for any vertex v ∈ Vi, i ∈ {0, 1}, any edge e ∈ E(G − v, there is a Hamiltonian path containing e in G − v between any two vertices of V1−i. In this paper, we prove that BHn is edge-hy per- Hamiltonian laceable.
A Lagrangian for Hamiltonian vector fields on singular Poisson manifolds
Turki, Yahya
2015-04-01
On a manifold equipped with a bivector field, we introduce for every Hamiltonian a Lagrangian on paths valued in the cotangent space whose stationary points project onto Hamiltonian vector fields. We show that the remaining components of those stationary points tell whether the bivector field is Poisson or at least defines an integrable distribution-a class of bivector fields generalizing twisted Poisson structures that we study in detail.
Discrete-Time Models for Implicit Port-Hamiltonian Systems
Castaños, Fernando; Michalska, Hannah; Gromov, Dmitry; Hayward, Vincent
2015-01-01
Implicit representations of finite-dimensional port-Hamiltonian systems are studied from the perspective of their use in numerical simulation and control design. Implicit representations arise when a system is modeled in Cartesian coordinates and when the system constraints are applied in the form of additional algebraic equations (the system model is in a DAE form). Such representations lend themselves better to sample-data approximations. An implicit representation of a port-Hamiltonian sys...
Quadratic fermionic interactions yield effective Hamiltonians for adiabatic quantum computing
O'Hara, Michael J.; O'Leary, Dianne P.
2008-01-01
Polynomially-large ground-state energy gaps are rare in many-body quantum systems, but useful for adiabatic quantum computing. We show analytically that the gap is generically polynomially-large for quadratic fermionic Hamiltonians. We then prove that adiabatic quantum computing can realize the ground states of Hamiltonians with certain random interactions, as well as the ground states of one, two, and three-dimensional fermionic interaction lattices, in polynomial time. Finally, we use the J...
Applications of Noether conservation theorem to Hamiltonian systems
Energy Technology Data Exchange (ETDEWEB)
Mouchet, Amaury, E-mail: mouchet@phys.univ-tours.fr
2016-09-15
The Noether theorem connecting symmetries and conservation laws can be applied directly in a Hamiltonian framework without using any intermediate Lagrangian formulation. This requires a careful discussion about the invariance of the boundary conditions under a canonical transformation and this paper proposes to address this issue. Then, the unified treatment of Hamiltonian systems offered by Noether’s approach is illustrated on several examples, including classical field theory and quantum dynamics.
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)
Some sufficient conditions for Hamiltonian property in terms of ...
Indian Academy of Sciences (India)
In this section, we will give a sufficient condition of a connected graph to be Hamiltonian by means of the Wiener-type index. First we introduce the following Chvátal condition for a connected graph to be Hamiltonian. Lemma 1 [2]. Let G be a nontrivial graph of order n, n ≥ 3, with degree sequence (d1, d2,...,dn), where d1 ...
Exactly solvable PT-symmetric Hamiltonian having no Hermitian counterpart
Bender, Carl M.; Mannheim, Philip D.
2008-07-01
In a recent paper Bender and Mannheim showed that the unequal-frequency fourth-order derivative Pais-Uhlenbeck oscillator model has a realization in which the energy eigenvalues are real and bounded below, the Hilbert-space inner product is positive definite, and time evolution is unitary. Central to that analysis was the recognition that the Hamiltonian HPU of the model is PT symmetric. This Hamiltonian was mapped to a conventional Dirac-Hermitian Hamiltonian via a similarity transformation whose form was found exactly. The present paper explores the equal-frequency limit of the same model. It is shown that in this limit the similarity transform that was used for the unequal-frequency case becomes singular and that HPU becomes a Jordan-block operator, which is nondiagonalizable and has fewer energy eigenstates than eigenvalues. Such a Hamiltonian has no Hermitian counterpart. Thus, the equal-frequency PT theory emerges as a distinct realization of quantum mechanics. The quantum mechanics associated with this Jordan-block Hamiltonian can be treated exactly. It is shown that the Hilbert space is complete with a set of nonstationary solutions to the Schrödinger equation replacing the missing stationary ones. These nonstationary states are needed to establish that the Jordan-block Hamiltonian of the equal-frequency Pais-Uhlenbeck model generates unitary time evolution.
Extended Hamiltonians and shift, ladder functions and operators
Chanu, Claudia Maria; Rastelli, Giovanni
2017-11-01
In recent years, many natural Hamiltonian systems, classical and quantum, with constants of motion of high degree, or symmetry operators of high order, have been found and studied. Most of these Hamiltonians, in the classical case, can be included in the family of extended Hamiltonians, geometrically characterized by the structure of warped manifold of their configuration manifold. For the extended Hamiltonians, the characteristic constants of motion of high degree are polynomial in the momenta of determined form. We consider here a different form of the constants of motion, based on the factorization procedure developed for systems of two degrees of freedom by S. Kuru, J. Negro and others. We show that an important subclass of the extended Hamiltonians, with arbitrary dimension, admits factorized constants of motion and we determine their expression. The classical constants can be polynomial or non-polynomial in the momenta, but the factorization procedure allows, in a type of extended Hamiltonians, their quantization via shift and ladder operators, for systems of any finite dimension.
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)
Efficient Quantum Pseudorandomness with Nearly Time-Independent Hamiltonian Dynamics
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Yoshifumi Nakata
2017-04-01
Full Text Available Quantum randomness is an essential key to understanding the dynamics of complex many-body systems and also a powerful tool for quantum engineering. However, exact realizations of quantum randomness take an extremely long time and are infeasible in many-body systems, leading to the notion of quantum pseudorandomness, also known as unitary designs. Here, to explore microscopic dynamics of generating quantum pseudorandomness in many-body systems, we provide new efficient constructions of unitary designs and propose a design Hamiltonian, a random Hamiltonian of which dynamics always forms a unitary design after a threshold time. The new constructions are based on the alternate applications of random potentials in the generalized position and momentum spaces, and we provide explicit quantum circuits generating quantum pseudorandomness significantly more efficient than previous ones. We then provide a design Hamiltonian in disordered systems with periodically changing spin-glass-type interactions. The design Hamiltonian generates quantum pseudorandomness in a constant time even in the system composed of a large number of spins. We also point out the close relationship between the design Hamiltonian and quantum chaos.
Magnetic field lines, Hamiltonian dynamics, and nontwist systems
Energy Technology Data Exchange (ETDEWEB)
Morrison, P. J. [Department of Physics and Institute for Fusion Studies, University of Texas at Austin, Austin, Texas 78712 (United States)
2000-06-01
Magnetic field lines typically do not behave as described in the symmetrical situations treated in conventional physics textbooks. Instead, they behave in a chaotic manner; in fact, magnetic field lines are trajectories of Hamiltonian systems. Consequently the quest for fusion energy has interwoven, for 50 years, the study of magnetic field configurations and Hamiltonian systems theory. The manner in which invariant tori breakup in symplectic twist maps, maps that embody one and a half degree-of-freedom Hamiltonian systems in general and describe magnetic field lines in tokamaks in particular, will be reviewed, including symmetry methods for finding periodic orbits and Greene's residue criterion. In nontwist maps, which describe, e.g., reverse shear tokamaks and zonal flows in geophysical fluid dynamics, a new theory is required for describing tori breakup. The new theory is discussed and comments about renormalization are made. (c) 2000 American Institute of Physics.
Lanting, Trevor; King, Andrew D.; Evert, Bram; Hoskinson, Emile
2017-10-01
Perturbative anticrossings have long been identified as a potential computational bottleneck for quantum annealing. This bottleneck can appear, for example, when a uniform transverse driver Hamiltonian is applied to each qubit. Previous theoretical research sought to alleviate such anticrossings by adjusting the transverse driver Hamiltonians on individual qubits according to a perturbative approximation. Here we apply this principle to a physical implementation of quantum annealing in a D-Wave 2000Q system. We use samples from the quantum annealing hardware and per-qubit anneal offsets to produce nonuniform driver Hamiltonians. On small instances with severe perturbative anticrossings, our algorithm yields an increase in minimum eigengaps, ground-state success probabilities, and escape rates from metastable valleys. We also demonstrate that the same approach can mitigate biased sampling of degenerate ground states.
NATO Advanced Study Institute on Hamiltonian Dynamical Systems and Applications
2008-01-01
Physical laws are for the most part expressed in terms of differential equations, and natural classes of these are in the form of conservation laws or of problems of the calculus of variations for an action functional. These problems can generally be posed as Hamiltonian systems, whether dynamical systems on finite dimensional phase space as in classical mechanics, or partial differential equations (PDE) which are naturally of infinitely many degrees of freedom. This volume is the collected and extended notes from the lectures on Hamiltonian dynamical systems and their applications that were given at the NATO Advanced Study Institute in Montreal in 2007. Many aspects of the modern theory of the subject were covered at this event, including low dimensional problems as well as the theory of Hamiltonian systems in infinite dimensional phase space; these are described in depth in this volume. Applications are also presented to several important areas of research, including problems in classical mechanics, continu...
Extended Hamiltonian learning on Riemannian manifolds: numerical aspects.
Fiori, Simone
2012-01-01
This paper is the second part of a study initiated with the paper S. Fiori, "Extended Hamiltonian learning on Riemannian manifolds: Theoretical aspects," IEEE Trans. Neural Netw., vol. 22, no. 5, pp. 687-700, May 2011, which aimed at introducing a general framework to develop a theory of learning on differentiable manifolds by extended Hamiltonian stationary-action principle. This paper discusses the numerical implementation of the extended Hamiltonian learning paradigm by making use of notions from geometric numerical integration to numerically solve differential equations on manifolds. The general-purpose integration schemes and the discussion of several cases of interest show that the implementation of the dynamical learning equations exhibits a rich structure. The behavior of the discussed learning paradigm is illustrated via several numerical examples and discussions of case studies. The numerical examples confirm the theoretical developments presented in this paper as well as in its first part.
On the Hamiltonian formalism of the tetrad-connection gravity
Lagraa, M. H.; Lagraa, M.; Touhami, N.
2017-06-01
We present a detailed analysis of the Hamiltonian constraints of the d-dimensional tetrad-connection gravity where the non-dynamic part of the spatial connection is fixed to zero by an adequate gauge transformation. This new action leads to a coherent Hamiltonian formalism where the Lorentz, scalar and vectorial first-class constraints obey a closed algebra in terms of Poisson brackets. This algebra closes with structure constants instead of structure functions resulting from the Hamiltonian formalisms based on the A.D.M. decomposition. The same algebra of the reduced first-class constraints, where the second-class constraints are eliminated as strong equalities, is obtained in terms of Dirac brackets. These first-class constraints lead to the same physical degrees of freedom of the general relativity.
Hamiltonian approach to second order gauge invariant cosmological perturbations
Domènech, Guillem; Sasaki, Misao
2018-01-01
In view of growing interest in tensor modes and their possible detection, we clarify the definition of tensor modes up to 2nd order in perturbation theory within the Hamiltonian formalism. Like in gauge theory, in cosmology the Hamiltonian is a suitable and consistent approach to reduce the gauge degrees of freedom. In this paper we employ the Faddeev-Jackiw method of Hamiltonian reduction. An appropriate set of gauge invariant variables that describe the dynamical degrees of freedom may be obtained by suitable canonical transformations in the phase space. We derive a set of gauge invariant variables up to 2nd order in perturbation expansion and for the first time we reduce the 3rd order action without adding gauge fixing terms. In particular, we are able to show the relation between the uniform-ϕ and Newtonian slicings, and study the difference in the definition of tensor modes in these two slicings.
Cluster expansion for ground states of local Hamiltonians
Directory of Open Access Journals (Sweden)
Alvise Bastianello
2016-08-01
Full Text Available A central problem in many-body quantum physics is the determination of the ground state of a thermodynamically large physical system. We construct a cluster expansion for ground states of local Hamiltonians, which naturally incorporates physical requirements inherited by locality as conditions on its cluster amplitudes. Applying a diagrammatic technique we derive the relation of these amplitudes to thermodynamic quantities and local observables. Moreover we derive a set of functional equations that determine the cluster amplitudes for a general Hamiltonian, verify the consistency with perturbation theory and discuss non-perturbative approaches. Lastly we verify the persistence of locality features of the cluster expansion under unitary evolution with a local Hamiltonian and provide applications to out-of-equilibrium problems: a simplified proof of equilibration to the GGE and a cumulant expansion for the statistics of work, for an interacting-to-free quantum quench.
Directory of Open Access Journals (Sweden)
Rudowicz Czesław
2015-07-01
Full Text Available The interface between optical spectroscopy, electron magnetic resonance (EMR, and magnetism of transition ions forms the intricate web of interrelated notions. Major notions are the physical Hamiltonians, which include the crystal field (CF (or equivalently ligand field (LF Hamiltonians, and the effective spin Hamiltonians (SH, which include the zero-field splitting (ZFS Hamiltonians as well as to a certain extent also the notion of magnetic anisotropy (MA. Survey of recent literature has revealed that this interface, denoted CF (LF ↔ SH (ZFS, has become dangerously entangled over the years. The same notion is referred to by three names that are not synonymous: CF (LF, SH (ZFS, and MA. In view of the strong need for systematization of nomenclature aimed at bringing order to the multitude of different Hamiltonians and the associated quantities, we have embarked on this systematization. In this article, we do an overview of our efforts aimed at providing a deeper understanding of the major intricacies occurring at the CF (LF ↔ SH (ZFS interface with the focus on the EMR-related problems for transition ions.
Lagrangian and Hamiltonian formulation of classical electrodynamics without potentials
Vollick, Dan N.
2017-10-01
In the standard Lagrangian and Hamiltonian approach to Maxwell's theory the potentials A^{μ} are taken as the dynamical variables. In this paper I take the electric field \\overrightarrow{E} and the magnetic field \\overrightarrow{B} as the dynamical variables. I find a Lagrangian that gives the dynamical Maxwell equations and include the constraint equations by using Lagrange multipliers. In passing to the Hamiltonian one finds that the canonical momenta \\overrightarrow{Π}E and \\overrightarrow{Π}B are constrained giving 6 second class constraints at each point in space. Gauss's law and \\overrightarrow{\
Modified Hamiltonian Formalism for Regge-Teitelboim Cosmology
Directory of Open Access Journals (Sweden)
Pinaki Patra
2014-01-01
Full Text Available The Ostrogradski approach for the Hamiltonian formalism of higher derivative theory is not satisfactory because the Lagrangian cannot be viewed as a function on the tangent bundle to coordinate manifold. In this paper, we have used an alternative approach which leads directly to the Lagrangian which, being a function on the tangent manifold, gives correct equation of motion; no new coordinate variables need to be added. This approach can be used directly to the singular (in Ostrogradski sense Lagrangian. We have used this method for the Regge-Teitelboim (RT minisuperspace cosmological model. We have obtained the Hamiltonian of the dynamical equation of the scale factor of RT model.
Hamiltonian LGT in the complete Fourier analysis basis
Energy Technology Data Exchange (ETDEWEB)
Burgio, G.; De Pietri, R.; Morales-Tecotl, H.A.; Urrutia, L.F.; Vergara, J.D
2000-03-01
The main problem in the Hamiltonian formulation of Lattice Gauge Theories is the determination of an appropriate basis avoiding the over-completeness arising from Mandelstam relations. We short-cut this problem using Harmonic analysis on Lie-Groups and intertwining operators formalism to explicitly construct a basis of the Hilbert space. Our analysis is based only on properties of the tensor category of Lie-Group representations. The Hamiltonian of such theories is calculated yielding a sparse matrix whose spectrum and eigenstates could be exactly derived as functions of the coupling g{sup 2}.
Hamiltonian and Godunov structures of the Grad hierarchy.
Grmela, Miroslav; Hong, Liu; Jou, David; Lebon, Georgy; Pavelka, Michal
2017-03-01
The time evolution governed by the Boltzmann kinetic equation is compatible with mechanics and thermodynamics. The former compatibility is mathematically expressed in the Hamiltonian and Godunov structures, the latter in the structure of gradient dynamics guaranteeing the growth of entropy and consequently the approach to equilibrium. We carry all three structures to the Grad reformulation of the Boltzmann equation (to the Grad hierarchy). First, we recognize the structures in the infinite Grad hierarchy and then in several examples of finite hierarchies representing extended hydrodynamic equations. In the context of Grad's hierarchies, we also investigate relations between Hamiltonian and Godunov structures.
Bubble interaction dynamics in Lagrangian and Hamiltonian mechanics.
Ilinskii, Yurii A; Hamilton, Mark F; Zabolotskaya, Evgenia A
2007-02-01
Two models of interacting bubble dynamics are presented, a coupled system of second-order differential equations based on Lagrangian mechanics, and a first-order system based on Hamiltonian mechanics. Both account for pulsation and translation of an arbitrary number of spherical bubbles. For large numbers of interacting bubbles, numerical solution of the Hamiltonian equations provides greater stability. The presence of external acoustic sources is taken into account explicitly in the derivation of both sets of equations. In addition to the acoustic pressure and its gradient, it is found that the particle velocity associated with external sources appears in the dynamical equations.
Noether symmetries and integrability in time-dependent Hamiltonian mechanics
Directory of Open Access Journals (Sweden)
Jovanović Božidar
2016-01-01
Full Text Available We consider Noether symmetries within Hamiltonian setting as transformations that preserve Poincaré-Cartan form, i.e., as symmetries of characteristic line bundles of nondegenerate 1-forms. In the case when the Poincaré-Cartan form is contact, the explicit expression for the symmetries in the inverse Noether theorem is given. As examples, we consider natural mechanical systems, in particular the Kepler problem. Finally, we prove a variant of the theorem on complete (non-commutative integrability in terms of Noether symmetries of time-dependent Hamiltonian systems.
Hamiltonian Monte Carlo with Constrained Molecular Dynamics as Gibbs Sampling.
Spiridon, Laurentiu; Minh, David D L
2017-10-10
Compared to fully flexible molecular dynamics, simulations of constrained systems can use larger time steps and focus kinetic energy on soft degrees of freedom. Achieving ergodic sampling from the Boltzmann distribution, however, has proven challenging. Using recent generalizations of the equipartition principle and Fixman potential, here we implement Hamiltonian Monte Carlo based on constrained molecular dynamics as a Gibbs sampling move. By mixing Hamiltonian Monte Carlo based on fully flexible and torsional dynamics, we are able to reproduce free energy landscapes of simple model systems and enhance sampling of macrocycles.
Fring, Andreas; Frith, Thomas
2017-01-01
We propose a procedure to obtain exact analytical solutions to the time-dependent Schrödinger equations involving explicit time-dependent Hermitian Hamiltonians from solutions to time-independent non-Hermitian Hamiltonian systems and the time-dependent Dyson relation, together with the time-dependent quasi-Hermiticity relation. We illustrate the working of this method for a simple Hermitian Rabi-type model by relating it to a non-Hermitian time-independent system corresponding to the one-site lattice Yang-Lee model.
The Electromagnetic Dipole Radiation Field through the Hamiltonian Approach
Likar, A.; Razpet, N.
2009-01-01
The dipole radiation from an oscillating charge is treated using the Hamiltonian approach to electrodynamics where the concept of cavity modes plays a central role. We show that the calculation of the radiation field can be obtained in a closed form within this approach by emphasizing the role of coherence between the cavity modes, which is…
Generalized Hamiltonian biodynamics and topology invariants of humanoid robots
Vladimir Ivancevic
2002-01-01
Humanoid robots are anthropomorphic mechanisms with biodynamics that resembles human musculo-skeletal dynamics. This paper proposes a new generalized (dissipative, muscle-driven, stochastic) Hamiltonian model of humanoid biodynamics. Also, (co)homological analysis is performed on its Lie-group based configuration and momentum phase-space manifolds.
Many-body Hamiltonian with screening parameter and ionization ...
Indian Academy of Sciences (India)
Yukawa-type potential; ionization and excitation energies; many-body. Hamiltonian; spin-orbit coupling; energy-level splitting. PACS Nos 71.10.-w; 31.10.+z; 03.65.Ca. 1. Introduction. Finding even an approximate but an accurate solution to a Coulombian many-body problem (many-electron atoms and solids) is no doubt, ...
Effect of three-body transformed Hamiltonian ( ) using full connected ...
Indian Academy of Sciences (India)
KALIPADA ADHIKARI
2018-02-13
Feb 13, 2018 ... Indian Academy of Sciences https://doi.org/10.1007/s12043-018-1523-3. Effect of three-body transformed Hamiltonian ( ˜H3) using full connected triple excitation coupled cluster operators on valence ionisation potentials of Cl2 and F2 computed via. EIP-VUMRCCSDτ scheme. KALIPADA ADHIKARI.
Coupled Higgs field equation and Hamiltonian amplitude equation ...
Indian Academy of Sciences (India)
... involving parameters of the coupled Higgs equation and Hamiltonian amplitude equation using (′/)-expansion methodc, where = () satisfies a second-order linear ordinary differential equation (ODE). The travelling wave solutions expressed by hyperbolic, trigonometric and the rational functions are obtained.
Theoretical studies of the spin-Hamiltonian parameters for the ...
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 70; Issue 4. Theoretical studies of the spin-Hamiltonian parameters for the orthorhombic Pr4+ centers in Sr2CeO4 ... Author Affiliations. Wen-Lin Feng1. Department of Applied Physics, Chongqing Institute of Technology, Chongqing 400050, People Republic of China ...
Matrix factorization method for the Hamiltonian structure of ...
Indian Academy of Sciences (India)
S Ghosh, B Talukdar and S Chakraborti. The Hamiltonian structure of non-linear evolution equations solvable by the inverse spectral method was discovered in 1971 by Zakharov and Faddeev [2] and by Gardner [3] who interpreted the Kortweg-de Vries (KdV) equation as a completely integrable Hamilto- nian system in an ...
Matrix factorization method for the Hamiltonian structure of ...
Indian Academy of Sciences (India)
We demonstrate that the process of matrix factorization provides a systematic mathematical method to investigate the Hamiltonian structure of non-linear evolution equations characterized by hereditary operators with Nijenhuis property. Author Affiliations. S Ghosh1 B Talukdar1 S Chakraborti2. Department of Physics ...
Translation-Invariant Parent Hamiltonians of Valence Bond Crystals
Huerga, Daniel; Greco, Andrés; Gazza, Claudio; Muramatsu, Alejandro
2017-04-01
We present a general method to construct translation-invariant and SU(2) symmetric antiferromagnetic parent Hamiltonians of valence bond crystals (VBCs). The method is based on a canonical mapping transforming S =1 /2 spin operators into a bilinear form of a new set of dimer fermion operators. We construct parent Hamiltonians of the columnar and the staggered VBCs on the square lattice, for which the VBC is an eigenstate in all regimes and the exact ground state in some region of the phase diagram. We study the departure from the exact VBC regime upon tuning the anisotropy by means of the hierarchical mean field theory and exact diagonalization on finite clusters. In both Hamiltonians, the VBC phase extends over the exact regime and transits to a columnar antiferromagnet (CAFM) through a window of intermediate phases, revealing an intriguing competition of correlation lengths at the VBC-CAFM transition. The method can be readily applied to construct other VBC parent Hamiltonians in different lattices and dimensions.
Classical and quantum mechanics of complex Hamiltonian systems ...
Indian Academy of Sciences (India)
Certain aspects of classical and quantum mechanics of complex Hamiltonian systems in one dimension ... collected by a conscious observer (for example, as is the case in the quantum mea- surement problem or the ..... property of a function is bound to break down, say for an open system or in the presence of subjectivity.
Conservation Laws and Symmetries for Hamiltonian Systems with Inputs
Schaft, A.J. van der
1984-01-01
After a brief introduction to Hamiltonian Systems with external forces (inputs) we define symmetries and conservations laws for such systems, and prove a generalization of Soether's theorem. Finally we show how this theory can be applied to the solution of optimal control problems.
Bohr Hamiltonian with deformation-dependent mass term
Energy Technology Data Exchange (ETDEWEB)
Bonatsos, Dennis, E-mail: bonat@inp.demokritos.g [Institute of Nuclear Physics, N.C.S.R. ' Demokritos' , GR-15310 Aghia Paraskevi, Attiki (Greece); Georgoudis, P.; Lenis, D. [Institute of Nuclear Physics, N.C.S.R. ' Demokritos' , GR-15310 Aghia Paraskevi, Attiki (Greece); Minkov, N. [Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tzarigrad Road, 1784 Sofia (Bulgaria); Quesne, C. [Physique Nucleaire Theorique et Physique Mathematique, Universite Libre de Bruxelles, Campus de la Plaine CP229, Boulevard du Triomphe, B-1050 Brussels (Belgium)
2010-01-25
The Bohr Hamiltonian describing the collective motion of atomic nuclei is modified by allowing the mass to depend on the nuclear deformation. Exact analytical expressions are derived for spectra and wave functions in the case of a gamma-unstable Davidson potential, using techniques of supersymmetric quantum mechanics. Numerical results in the Xe-Ba region are discussed.
Horizontal circulation and jumps in Hamiltonian wave models
Gagarina, Elena; van der Vegt, Jacobus J.W.; Bokhove, Onno
We are interested in the numerical modeling of wave-current interactions around surf zones at beaches. Any model that aims to predict the onset of wave breaking at the breaker line needs to capture both the nonlinearity of the wave and its dispersion. We have therefore formulated the Hamiltonian
Horizontal circulation and jumps in Hamiltonian wave models
Gagarina, Elena; van der Vegt, Jacobus J.W.; Bokhove, Onno
2013-01-01
We are interested in the numerical modeling of wave-current interactions around surf zones at beaches. Any model that aims to predict the onset of wave breaking at the breaker line needs to capture both the nonlinearity of the wave and its dispersion. We have therefore formulated the Hamiltonian
Algebra and two-dimensional quasiexactly solvable Hamiltonian ...
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 83; Issue 1. 2 Algebra and two-dimensional ... Then, by choosing an appropriate set of coefficients and making a gauge rotation, we show that this Hamiltonian leads to the solvable Poschl–Teller model on an open infinite strip. Finally, we assign 2 hidden algebra ...
Approximate first integrals of a chaotic Hamiltonian system | Unal ...
African Journals Online (AJOL)
Approximate first integrals (conserved quantities) of a Hamiltonian dynamical system with two-degrees of freedom which arises in the modeling of galaxy have been obtained based on the approximate Noether symmetries for the resonance ω1 = ω2. Furthermore, Kolmogorov-Arnold-Moser (KAM) curves have been ...
Classical and quantum mechanics of complex Hamiltonian systems ...
Indian Academy of Sciences (India)
Certain aspects of classical and quantum mechanics of complex Hamiltonian systems in one dimension investigated within the framework of an extended complex phase space approach, characterized by the transformation = 1 + 2, = 1 + 2, are revisited. It is argued that Carl Bender inducted P T symmetry in ...
Spectral Results on Some Hamiltonian Properties of Graphs
Directory of Open Access Journals (Sweden)
Rao Li
2014-10-01
Full Text Available Using Lotker’s interlacing theorem on the Laplacian eigenvalues of a graph in [5] and Wang and Belardo’s interlacing theorem on the signless Laplacian eigenvalues of a graph in [6], we in this note obtain spectral conditions for some Hamiltonian properties of graphs
Port-Hamiltonian discretization for open channel flows
Pasumarthy, R.; Ambati, V.R.; Schaft, A.J. van der
A finite-dimensional Port-Hamiltonian formulation for the presented. A numerical scheme based on this formulation is shallow water equations. The scheme is verified against conservation of mass and energy to the discrete level. dynamics of smooth open channel flows is developed for both the linear
Conditional Reducibility of Certain Unbounded Nonnegative Hamiltonian Operator Functions
Azizov, T.Ya.; Dijksma, A.; Gridneva, I.V.
Let and be operators on a Hilbert space which are both self-adjoint and unitary and satisfy . We consider an operator function on [0, 1] of the form , , where is a closed densely defined Hamiltonian ( -skew-self-adjoint) operator on with and is a function on [0, 1] whose values are bounded operators
Symplectic Hamiltonian HDG methods for wave propagation phenomena
Sánchez, M. A.; Ciuca, C.; Nguyen, N. C.; Peraire, J.; Cockburn, B.
2017-12-01
We devise the first symplectic Hamiltonian hybridizable discontinuous Galerkin (HDG) methods for the acoustic wave equation. We discretize in space by using a Hamiltonian HDG scheme, that is, an HDG method which preserves the Hamiltonian structure of the wave equation, and in time by using symplectic, diagonally implicit and explicit partitioned Runge-Kutta methods. The fundamental feature of the resulting scheme is that the conservation of a discrete energy, which is nothing but a discrete version of the original Hamiltonian, is guaranteed. We present numerical experiments which indicate that the method achieves optimal approximations of order k + 1 in the L2-norm when polynomials of degree k ≥ 0 and Runge-Kutta time-marching methods of order k + 1 are used. In addition, by means of post-processing techniques and by increasing the order of the Runge-Kutta method to k + 2, we obtain superconvergent approximations of order k + 2 in the L2-norm for the displacement and the velocity. We also present numerical examples that corroborate that the methods conserve energy and that they compare favorably with dissipative HDG schemes, of similar accuracy properties, for long-time simulations.
Measure synchronization in a coupled Hamiltonian associated with ...
African Journals Online (AJOL)
We report here, the existence of measure synchronization (MS) in a coupled Hamiltonian system associated with the motion of particles in a periodic potential of the pendulum type. We show that the oscillators can assume chaotic MS stares vis quasiperiodic measure desynchrononized state. In the chaotic MS state, the ...
The Quaternions and Bott Periodicity Are Quantum Hamiltonian Reductions
Johnson-Freyd, Theo
2016-12-01
We show that the Morita equivalences Cliff(4) ≃ H, Cliff(7) ≃ Cliff(-1), and Cliff(8) ≃ R arise from quantizing the Hamiltonian reductions R^{0|4} // Spin(3), R^{0|7} // G_2, and R^{0|8} // Spin(7), respectively.
On self-adjointness of singular Floquet Hamiltonians
DEFF Research Database (Denmark)
Duclos, Pierre; Jensen, Arne
2010-01-01
Schrödinger equations with time-dependent interactions are studied. We investigate how to define the Floquet Hamiltonian as a self-adjoint operator, when the interaction is singular in time or space. Using these results we establish the existence of a bounded propagator, by applying a result given...
Contact Hamiltonian Dynamics: The Concept and Its Use
Directory of Open Access Journals (Sweden)
Alessandro Bravetti
2017-10-01
Full Text Available We give a short survey on the concept of contact Hamiltonian dynamics and its use in several areas of physics, namely reversible and irreversible thermodynamics, statistical physics and classical mechanics. Some relevant examples are provided along the way. We conclude by giving insights into possible future directions.
Steiner systems and large non-Hamiltonian hypergraphs
Directory of Open Access Journals (Sweden)
Zsolt Tuza
2006-10-01
Full Text Available From Steiner systems S(k − 2, 2k − 3, v, we construct k-uniform hyper- graphs of large size without Hamiltonian cycles. This improves previous estimates due to G. Y. Katona and H. Kierstead [J. Graph Theory 30 (1999, pp. 205–212].
Structure Preserving Adaptive Control of Port-Hamiltonian Systems
Dirksz, Daniel A.; Scherpen, Jacquelien M. A.
2012-01-01
In this technical note, 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
Many-body Hamiltonian with screening parameter and ionization ...
Indian Academy of Sciences (India)
We prove the existence of a Hamiltonian with ionization energy as part of the eigenvalue, which can be used to study strongly correlated matter. This eigenvalue consists of total energy at zero temperature (0) and the ionization energy (). We show that the existence of this total energy eigenvalue, 0 ± , does not violate ...
Port-Hamiltonian modeling for soft-finger manipulation
Ficuciello, F.; Carloni, R.; Visser, L. C.; Stramigioli, S.
2010-01-01
In this paper, we present a port-Hamiltonian model of a multi-fingered robotic hand, with soft-pads, while grasping and manipulating an object. The algebraic constraints of the interconnected systems are represented by a geometric object, called Dirac structure. This provides a powerful way to
Geometry and topology in hamiltonian dynamics and statistical mechanics
Pettini, Marco
2007-01-01
Explores the foundations of hamiltonian dynamical systems and statistical mechanics, in particular phase transitions, from the point of view of geometry and topology. This book provides an overview of the research in the area. Using geometrical thinking to solve fundamental problems in these areas could be highly productive
Geometry of KAM tori for nearly integrable Hamiltonian systems
Broer, Hendrik; Cushman, Richard; Fassò, Francesco; Takens, Floris
We obtain a global version of the Hamiltonian KAM theorem for invariant Lagrangian tori by gluing together local KAM conjugacies with the help of a partition of unity. In this way we find a global Whitney smooth conjugacy between a nearly integrable system and an integrable one. This leads to the
Geometry of torus bundles in integrable Hamiltonian systems
Lukina, Olga
2008-01-01
Thesis is concerned with global properties of Lagrangian bundles, i.e. symplectic n-torus bundles, as these occur in integrable Hamiltonian systems. It treats obstructions to triviality and concerns with classification of such bundles, as well as with manifestations of global invariants in
Hamiltonian systems, Titchmarsh-Weyl coefficients, and models
Dijksma, A.
1996-01-01
This note concerns an eigenvalue problem for a Hamiltonian system of ordinary differential equations in an L(2)-space with a boundary condition depending linearly on the eigenvalue parameter. We show that the spectral properties (in particular, the embedded eigenvalues) of this problem can be
On the Hamiltonian Formulation of Nonholonomic Mechanical Systems
Schaft, A.J. van der; Maschke, B.M.
1994-01-01
A simple procedure is provided to write the equations of motion of mechanical systems with constraints as Hamiltonian equations with respect to a “Poisson” bracket on the constrained state space, which does not necessarily satisfy the Jacobi identity. It is shown that the Jacobi identity is
On the Hamiltonian formulation of nonholonomic mechanical systems
van der Schaft, Arjan; Maschke, B.M.
1994-01-01
A simple procedure is provided to write the equations of motion of mechanical systems with constraints as Hamiltonian equations with respect to a ¿Poisson¿ bracket on the constrained state space, which does not necessarily satisfy the Jacobi identity. It is shown that the Jacobi identity is
On the Curvature and Heat Flow on Hamiltonian Systems
Directory of Open Access Journals (Sweden)
Ohta Shin-ichi
2014-01-01
Full Text Available We develop the differential geometric and geometric analytic studies of Hamiltonian systems. Key ingredients are the curvature operator, the weighted Laplacian, and the associated Riccati equation.We prove appropriate generalizations of the Bochner-Weitzenböck formula and Laplacian comparison theorem, and study the heat flow.
Bohr Hamiltonian with different mass parameters applied to band ...
Indian Academy of Sciences (India)
pp. 1055–1066. Bohr Hamiltonian with different mass parameters applied to band structures of Eu isotopes built on Nilsson orbitals. M J ERMAMATOV1,∗, H YÉPEZ-MARTÍNEZ2 and P C SRIVASTAVA3. 1Institute of Nuclear Physics, Ulughbek, Tashkent 100214, Uzbekistan. 2Universidad Autónoma de la Ciudad de México ...
When a local Hamiltonian must be frustration-free.
Sattath, Or; Morampudi, Siddhardh C; Laumann, Chris R; Moessner, Roderich
2016-06-07
A broad range of quantum optimization problems can be phrased as the question of whether a specific system has a ground state at zero energy, i.e., whether its Hamiltonian is frustration-free. Frustration-free Hamiltonians, in turn, play a central role for constructing and understanding new phases of matter in quantum many-body physics. Unfortunately, determining whether this is the case is known to be a complexity-theoretically intractable problem. This makes it highly desirable to search for efficient heuristics and algorithms to, at least, partially answer this question. Here we prove a general criterion-a sufficient condition-under which a local Hamiltonian is guaranteed to be frustration-free by lifting Shearer's theorem from classical probability theory to the quantum world. Remarkably, evaluating this condition proceeds via a fully classical analysis of a hardcore lattice gas at negative fugacity on the Hamiltonian's interaction graph, which, as a statistical mechanics problem, is of interest in its own right. We concretely apply this criterion to local Hamiltonians on various regular lattices, while bringing to bear the tools of spin glass physics that permit us to obtain new bounds on the satisfiable to unsatisfiable transition in random quantum satisfiability. We are then led to natural conjectures for when such bounds will be tight, as well as to a novel notion of universality for these computer science problems. Besides providing concrete algorithms leading to detailed and quantitative insights, this work underscores the power of marrying classical statistical mechanics with quantum computation and complexity theory.
Urbanowski, K.
2003-01-01
We start from a discussion of the general form and general CP-- and CPT-- transformation properties of the Lee--Oehme--Yang (LOY) effective Hamiltonian for the neutral kaon complex. Next we show that there exists an approximation which is more accurate than the LOY, and which leads to an effective Hamiltonian whose diagonal matrix elements posses CPT transformation properties, which differ from those of the LOY effective Hamiltonian. These properties of the mentioned effective Hamiltonians ar...
Effective Floquet Hamiltonian for spin I = 1 in magic angle spinning ...
Indian Academy of Sciences (India)
WINTEC
S S H. = +. −. (5). The diagonal part of the above Hamiltonian gives diagonal correction of order λ2 to the zeroth order. Hamiltonian in addition to the diagonal term of H2. Thus the Hamiltonian (1). (1). 2. (1). 0. 1. 2 d d. H. H. H λ λ. +. + is more effective than the Hamiltonian. 2. 0. 1. 2 . d d. H. H. H λ λ. +. +. The general term (1).
Interconnection of port-Hamiltonian systems and composition of Dirac structures
Cervera, J.; van der Schaft, Arjan; Baños, A.
2007-01-01
Port-based network modeling of physical systems leads to a model class of nonlinear systems known as port-Hamiltonian systems. Port-Hamiltonian systems are defined with respect to a geometric structure on the state space, called a Dirac structure. Interconnection of port-Hamiltonian systems results
Interconnection of port-Hamiltonian systems and composition of Dirac structures
Cervera, J.; Schaft, A.J. van der; Baños, A.
Port-based network modeling of physical systems leads to a model class of nonlinear systems known as port-Hamiltonian systems. Port-Hamiltonian systems are defined with respect to a geometric structure on the state space, called a Dirac structure. Interconnection of port-Hamiltonian systems results
Quadratic time dependent Hamiltonians and separation of variables
Anzaldo-Meneses, A.
2017-06-01
Time dependent quantum problems defined by quadratic Hamiltonians are solved using canonical transformations. The Green's function is obtained and a comparison with the classical Hamilton-Jacobi method leads to important geometrical insights like exterior differential systems, Monge cones and time dependent Gaussian metrics. The Wei-Norman approach is applied using unitary transformations defined in terms of generators of the associated Lie groups, here the semi-direct product of the Heisenberg group and the symplectic group. A new explicit relation for the unitary transformations is given in terms of a finite product of elementary transformations. The sequential application of adequate sets of unitary transformations leads naturally to a new separation of variables method for time dependent Hamiltonians, which is shown to be related to the Inönü-Wigner contraction of Lie groups. The new method allows also a better understanding of interacting particles or coupled modes and opens an alternative way to analyze topological phases in driven systems.
Witnessing eigenstates for quantum simulation of Hamiltonian spectra
Santagati, Raffaele; Wang, Jianwei; Gentile, Antonio A.; Paesani, Stefano; Wiebe, Nathan; McClean, Jarrod R.; Morley-Short, Sam; Shadbolt, Peter J.; Bonneau, Damien; Silverstone, Joshua W.; Tew, David P.; Zhou, Xiaoqi; O’Brien, Jeremy L.; Thompson, Mark G.
2018-01-01
The efficient calculation of Hamiltonian spectra, a problem often intractable on classical machines, can find application in many fields, from physics to chemistry. We introduce the concept of an “eigenstate witness” and, through it, provide a new quantum approach that combines variational methods and phase estimation to approximate eigenvalues for both ground and excited states. This protocol is experimentally verified on a programmable silicon quantum photonic chip, a mass-manufacturable platform, which embeds entangled state generation, arbitrary controlled unitary operations, and projective measurements. Both ground and excited states are experimentally found with fidelities >99%, and their eigenvalues are estimated with 32 bits of precision. We also investigate and discuss the scalability of the approach and study its performance through numerical simulations of more complex Hamiltonians. This result shows promising progress toward quantum chemistry on quantum computers. PMID:29387796
Hamiltonian Dynamics of Doubly-Foliable Space-Times
Directory of Open Access Journals (Sweden)
Cecília Gergely
2018-01-01
Full Text Available The 2 + 1 + 1 decomposition of space-time is useful in monitoring the temporal evolution of gravitational perturbations/waves in space-times with a spatial direction singled-out by symmetries. Such an approach based on a perpendicular double foliation has been employed in the framework of dark matter and dark energy-motivated scalar-tensor gravitational theories for the discussion of the odd sector perturbations of spherically-symmetric gravity. For the even sector, however, the perpendicularity has to be suppressed in order to allow for suitable gauge freedom, recovering the 10th metric variable. The 2 + 1 + 1 decomposition of the Einstein–Hilbert action leads to the identification of the canonical pairs, the Hamiltonian and momentum constraints. Hamiltonian dynamics is then derived via Poisson brackets.
Anyons are not energy eigenspaces of quantum double Hamiltonians
Kómár, Anna; Landon-Cardinal, Olivier
2017-11-01
Kitaev's quantum double models, including the toric code, are canonical examples of quantum topological models on a two-dimensional spin lattice. Their Hamiltonian defines the ground space by imposing an energy penalty to any nontrivial flux or charge, but does not distinguish among those. We generalize this construction by introducing a family of Hamiltonians made of commuting four-body projectors that provide an intricate splitting of the Hilbert space by discriminating among nontrivial charges and fluxes. Our construction highlights that anyons are not in one-to-one correspondence with energy eigenspaces, a feature already present in Kitaev's construction. This discrepancy is due to the presence of local degrees of freedom in addition to topological ones on a lattice.
From Hamiltonian chaos to complex systems a nonlinear physics approach
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...
Fluctuations in a Spin Chain and the Entanglement Hamiltonian
Turner, Ari; Demler, Eugene
2014-03-01
How are quantum fluctuations and thermal fluctuations different in many-body systems? I will compare the variance of the fluctuations of spin in a segment of a spin chain in the ground state and at a finite temperature, showing that fluctuations in the ground state are much more correlated than in the thermal state. The full distribution function of spin can also be determined, and is non-Gaussian. These effects could possibly be measured in a chain of sodium atoms in an optical lattice. The method involves mapping the system to an imaginary thermal system called the ``entanglement Hamiltonian.'' Measuring the ground state fluctuations of the spin chain gives an indirect way of measuring the entanglement Hamiltonian.
Applications of the trilinear Hamiltonian with three trapped ions
Hablutzel Marrero, Roland Esteban; Ding, Shiqian; Maslennikov, Gleb; Gan, Jaren; Nimmrichter, Stefan; Roulet, Alexandre; Dai, Jibo; Scarani, Valerio; Matsukevich, Dzmitry
2017-04-01
The trilinear Hamiltonian a† bc + ab†c† , which describes a nonlinear interaction between harmonic oscillators, can be implemented to study different phenomena ranging from simple quantum models to quantum thermodynamics. We engineer this coupling between three modes of motion of three trapped 171Yb+ ions, where the interaction arises naturally from their mutual (anharmonic) Coulomb repulsion. By tuning our trapping parameters we are able to turn on / off resonant exchange of energy between the modes on demand. We present applications of this Hamiltonian for simulations of the parametric down conversion process in the regime of depleted pump, a simple model of Hawking radiation, and the Tavis-Cummings model. We also discuss the implementation of the quantum absorption refrigerator in such system and experimentally study effects of quantum coherence on its performance. This research is supported by the National Research Foundation, Prime Minister's Office, Singapore and the Ministry of Education, Singapore under the Research Centres of Excellence programme.
RG-Whitham dynamics and complex Hamiltonian systems
Directory of Open Access Journals (Sweden)
A. Gorsky
2015-06-01
Full Text Available Inspired by the Seiberg–Witten exact solution, we consider some aspects of the Hamiltonian dynamics with the complexified phase space focusing at the renormalization group (RG-like Whitham behavior. We show that at the Argyres–Douglas (AD point the number of degrees of freedom in Hamiltonian system effectively reduces and argue that anomalous dimensions at AD point coincide with the Berry indexes in classical mechanics. In the framework of Whitham dynamics AD point turns out to be a fixed point. We demonstrate that recently discovered Dunne–Ünsal relation in quantum mechanics relevant for the exact quantization condition exactly coincides with the Whitham equation of motion in the Ω-deformed theory.
Metastable states in parametrically excited multimode Hamiltonian systems
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...
Extended hamiltonian formalism and Lorentz-violating lagrangians
Colladay, Don
2017-09-01
A new perspective on the classical mechanical formulation of particle trajectories in Lorentz-violating theories is presented. Using the extended hamiltonian formalism, a Legendre Transformation between the associated covariant lagrangian and hamiltonian varieties is constructed. This approach enables calculation of trajectories using Hamilton's equations in momentum space and the Euler-Lagrange equations in velocity space away from certain singular points that arise in the theory. Singular points are naturally de-singularized by requiring the trajectories to be smooth functions of both velocity and momentum variables. In addition, it is possible to identify specific sheets of the dispersion relations that correspond to specific solutions for the lagrangian. Examples corresponding to bipartite Finsler functions are computed in detail. A direct connection between the lagrangians and the field-theoretic solutions to the Dirac equation is also established for a special case.
An application of Hamiltonian neurodynamics using Pontryagin's Maximum (Minimum) Principle.
Koshizen, T; Fulcher, J
1995-12-01
Classical optimal control methods, notably Pontryagin's Maximum (Minimum) Principle (PMP) can be employed, together with Hamiltonians, to determine optimal system weights in Artificial Neural dynamical systems. A new learning rule based on weight equations derived using PMP is shown to be suitable for both discrete- and continuous-time systems, and moreover, can also be applied to feedback networks. Preliminary testing shows that this PMP learning rule compares favorably with Standard BackPropagations (SBP) on the XOR problem.
Tsunami generation by ocean floor rupture front propagation: Hamiltonian description
Directory of Open Access Journals (Sweden)
V. I. Pavlov
2009-02-01
Full Text Available The Hamiltonian method is applied to the problem of tsunami generation caused by a propagating rupture front and deformation of the ocean floor. The method establishes an alternative framework for analyzing the tsunami generation process and produces analytical expressions for the power and directivity of tsunami radiation (in the far-field for two illustrative cases, with constant and gradually varying speeds of rupture front propagation.
Chaos and Exponentially Localized Eigenstates in Smooth Hamiltonian Systems
Santhanam, M S; Lakshminarayan, A
1998-01-01
We present numerical evidence to show that the wavefunctions of smooth classically chaotic Hamiltonian systems scarred by certain simple periodic orbits are exponentially localized in the space of unperturbed basis states. The degree of localization, as measured by the information entropy, is shown to be correlated with the local phase space structure around the scarring orbit; indicating sharp localization when the orbit undergoes a pitchfork bifurcation and loses stability.
Non-Hamiltonian perturbation theory for deformable fast rotators
Varadi, F.; Moore, W. B.
2005-05-01
Deformable fast rotators, such as the Earth and Mars, change both their rotational states (spin axis direction) and shapes due to external forces and internal material motions. The standard approach to rigid-body dynamics is Hamiltonian perturbation theory in canonical action-angle (Andoyer) variables which incorporate the moments of inertia form the outset. Dealing with deformations is usually based on linear perturbation theory around rigid-body reference solutions which yields transfer functions from the rigid to the deformable case. We present the elements of a general, non-Hamiltonian perturbation theory in non-canonical variables based on Lie series. First, we present general results on non-Hamiltonian perturbation theory and averaging, such as a coordinate-free formula for the solution of the homological equation of the Lie series in the case of perturbed periodic orbits. In general, the averaged system does not fully Lie-commute with the unperturbed system and the reduction of the averaged system to the orbit space of unperturbed system has to allow for drift along the unperturbed orbits. In the case of a fast rotator, we start with rotation around the spin axis as the unperturbed system. The orientation of the body is represented as a rotation matrix and we derive the appropriate Lie bracket. After averaging over the rotation period, we reduce the system by eliminating the phase variable associated with pure rotation around the spin axis. The reduced system is expressed in terms of the spin axis in both inertial and body frames. We compare our results to those of traditional Hamiltonian theories and numerical simulations. This work is supported by NSF Planetary Astronomy.
Hamiltonian ODE's on a Space of Deficient Measures
Chayes, L.; Gangbo, W.; Lei, H. K.
2011-01-01
We continue the study (initiated in [1]) of Borel measures whose time evolution is provided by an interacting Hamiltonian structure. Here, the principal focus is the development and advancement of deficency in the measure caused by displacement of mass to infinity in finite time. We introduce - and study in its own right - a regularization scheme based on a dissipative mechanism which naturally degrades mass according to distance traveled (in phase space). Our principal results are obtained b...
Hamiltonian ODEs on a space of deficient measures
Chayes, L.; Gangbo, W.; Lei, H. K
2013-01-01
We continue the study (initiated in [1]) of Borel measures whose time evolution is provided by an interacting Hamiltonian structure. Here, the principal focus is the development and advancement of deficency in the measure caused by displacement of mass to infinity in finite time. We introduce - and study in its own right - a regularization scheme based on a dissipative mechanism which naturally degrades mass according to distance traveled (in phase space). Our principal results are obtained b...
H∞ control strategy for a class of switched Hamiltonian systems
Zhu, Huawei; Zhang, Zhisen; Zhao, Quanjun; Tu, Pu
2017-02-01
Using multiple Lyapunov function method, the H∞ control theory of switched Hamiltonian systems is discussed. The sufficient conditions in the form of linear matrix inequality (LMI) are presented to guarantee stability of switched Hamilton system. At the same time, an switching law based on switching dwell time is constructed. In order to prove the effectiveness of this conclusion, a numerical simulation example is given, in which the corresponding parameters are calculated by LMI.
Escapes in Hamiltonian systems with multiple exit channels: Part II
Zotos, Euaggelos E.
2015-01-01
We explore the escape dynamics in open Hamiltonian systems with multiple channels of escape continuing the work initiated in Part I. A thorough numerical investigation is conducted distinguishing between trapped (ordered and chaotic) and escaping orbits. The determination of the location of the basins of escape towards the different escape channels and their correlations with the corresponding escape periods of the orbits is undoubtedly an issue of paramount importance. We consider four diffe...
Theoretical studies of the spin-Hamiltonian parameters for the ...
Indian Academy of Sciences (India)
Theoretical studies of spin-Hamiltonian (SH) parameters associated with. Pr4+ in Sr2CeO4 single crystals have been made by ... other is the perturbation theory method (PTM) [7,8]. As suggested in previous studies [7–10], the PTM ... k (θj,φj) can be obtained from the local lattice struc- tural parameters of the studied system.
Noether symmetries and integrability in time-dependent Hamiltonian mechanics
Jovanović Božidar
2016-01-01
We consider Noether symmetries within Hamiltonian setting as transformations that preserve Poincaré-Cartan form, i.e., as symmetries of characteristic line bundles of nondegenerate 1-forms. In the case when the Poincaré-Cartan form is contact, the explicit expression for the symmetries in the inverse Noether theorem is given. As examples, we consider natural mechanical systems, in particular the Kepler problem. Finally, we prove a variant of the theorem on ...
Hydrodynamic Covariant Symplectic Structure from Bilinear Hamiltonian Functions
Directory of Open Access Journals (Sweden)
Capozziello S.
2005-07-01
Full Text Available Starting from generic bilinear Hamiltonians, constructed by covariant vector, bivector or tensor fields, it is possible to derive a general symplectic structure which leads to holonomic and anholonomic formulations of Hamilton equations of motion directly related to a hydrodynamic picture. This feature is gauge free and it seems a deep link common to all interactions, electromagnetism and gravity included. This scheme could lead toward a full canonical quantization.
Entanglement Entropy of Eigenstates of Quadratic Fermionic Hamiltonians.
Vidmar, Lev; Hackl, Lucas; Bianchi, Eugenio; Rigol, Marcos
2017-07-14
In a seminal paper [D. N. Page, Phys. Rev. Lett. 71, 1291 (1993)PRLTAO0031-900710.1103/PhysRevLett.71.1291], Page proved that the average entanglement entropy of subsystems of random pure states is S_{ave}≃lnD_{A}-(1/2)D_{A}^{2}/D for 1≪D_{A}≤sqrt[D], where D_{A} and D are the Hilbert space dimensions of the subsystem and the system, respectively. Hence, typical pure states are (nearly) maximally entangled. We develop tools to compute the average entanglement entropy ⟨S⟩ of all eigenstates of quadratic fermionic Hamiltonians. In particular, we derive exact bounds for the most general translationally invariant models lnD_{A}-(lnD_{A})^{2}/lnD≤⟨S⟩≤lnD_{A}-[1/(2ln2)](lnD_{A})^{2}/lnD. Consequently, we prove that (i) if the subsystem size is a finite fraction of the system size, then ⟨S⟩
Production and transfer of energy and information in Hamiltonian systems.
Antonopoulos, Chris G; Bianco-Martinez, Ezequiel; Baptista, Murilo S
2014-01-01
We present novel results that relate energy and information transfer with sensitivity to initial conditions in chaotic multi-dimensional Hamiltonian systems. We show the relation among Kolmogorov-Sinai entropy, Lyapunov exponents, and upper bounds for the Mutual Information Rate calculated in the Hamiltonian phase space and on bi-dimensional subspaces. Our main result is that the net amount of transfer from kinetic to potential energy per unit of time is a power-law of the upper bound for the Mutual Information Rate between kinetic and potential energies, and also a power-law of the Kolmogorov-Sinai entropy. Therefore, transfer of energy is related with both transfer and production of information. However, the power-law nature of this relation means that a small increment of energy transferred leads to a relatively much larger increase of the information exchanged. Then, we propose an "experimental" implementation of a 1-dimensional communication channel based on a Hamiltonian system, and calculate the actual rate with which information is exchanged between the first and last particle of the channel. Finally, a relation between our results and important quantities of thermodynamics is presented.
Production and transfer of energy and information in Hamiltonian systems.
Directory of Open Access Journals (Sweden)
Chris G Antonopoulos
Full Text Available We present novel results that relate energy and information transfer with sensitivity to initial conditions in chaotic multi-dimensional Hamiltonian systems. We show the relation among Kolmogorov-Sinai entropy, Lyapunov exponents, and upper bounds for the Mutual Information Rate calculated in the Hamiltonian phase space and on bi-dimensional subspaces. Our main result is that the net amount of transfer from kinetic to potential energy per unit of time is a power-law of the upper bound for the Mutual Information Rate between kinetic and potential energies, and also a power-law of the Kolmogorov-Sinai entropy. Therefore, transfer of energy is related with both transfer and production of information. However, the power-law nature of this relation means that a small increment of energy transferred leads to a relatively much larger increase of the information exchanged. Then, we propose an "experimental" implementation of a 1-dimensional communication channel based on a Hamiltonian system, and calculate the actual rate with which information is exchanged between the first and last particle of the channel. Finally, a relation between our results and important quantities of thermodynamics is presented.
Trojan dynamics well approximated by a new Hamiltonian normal form
Páez, Rocío Isabel; Locatelli, Ugo
2015-10-01
We revisit a classical perturbative approach to the Hamiltonian related to the motions of Trojan bodies, in the framework of the planar circular restricted three-body problem, by introducing a number of key new ideas in the formulation. In some sense, we adapt the approach of Garfinkel to the context of the normal form theory and its modern techniques. First, we make use of Delaunay variables for a physically accurate representation of the system. Therefore, we introduce a novel manipulation of the variables so as to respect the natural behaviour of the model. We develop a normalization procedure over the fast angle which exploits the fact that singularities in this model are essentially related to the slow angle. Thus, we produce a new normal form, i.e. an integrable approximation to the Hamiltonian. We emphasize some practical examples of the applicability of our normalizing scheme, e.g. the estimation of the stable libration region. Finally, we compare the level curves produced by our normal form with surfaces of section provided by the integration of the non-normalized Hamiltonian, with very good agreement. Further precision tests are also provided. In addition, we give a step-by-step description of the algorithm, allowing for extensions to more complicated models.
Runtime of unstructured search with a faulty Hamiltonian oracle
Temme, Kristan
2014-08-01
We show that it is impossible to obtain a quantum speedup for a faulty Hamiltonian oracle. The effect of dephasing noise to this continuous-time oracle model has first been investigated by Shenvi, Brown, and Whaley [Phys. Rev. A 68, 052313 (2003)., 10.1103/PhysRevA.68.052313]. The authors consider a faulty oracle described by a continuous-time master equation that acts as dephasing noise in the basis determined by the marked item. The analysis focuses on the implementation with a particular driving Hamiltonian. A universal lower bound for this oracle model, which rules out a better performance with a different driving Hamiltonian, has so far been lacking. Here, we derive an adversary-type lower bound which shows that the evolution time T has to be at least in the order of N, i.e., the size of the search space, when the error rate of the oracle is constant. This means that quadratic quantum speedup vanishes and the runtime assumes again the classical scaling. For the standard quantum oracle model this result was first proven by Regev and Schiff [in Automata, Languages and Programming, Lecture Notes in Computer Science Vol. 5125 (Springer, Berlin, 2008), pp. 773-781]. Here, we extend this result to the continuous-time setting.
Optimized t-expansion method for the Rabi Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Travenec, Igor, E-mail: fyzitrav@savba.sk [Institute of Physics, Slovak Academy of Sciences, Dubravska cesta 9, 845 11 Bratislava (Slovakia); Samaj, Ladislav [Institute of Physics, Slovak Academy of Sciences, Dubravska cesta 9, 845 11 Bratislava (Slovakia)
2011-10-31
A polemic arose recently about the applicability of the t-expansion method to the calculation of the ground state energy E{sub 0} of the Rabi model. For specific choices of the trial function and very large number of involved connected moments, the t-expansion results are rather poor and exhibit considerable oscillations. In this Letter, we formulate the t-expansion method for trial functions containing two free parameters which capture two exactly solvable limits of the Rabi Hamiltonian. At each order of the t-series, E{sub 0} is assumed to be stationary with respect to the free parameters. A high accuracy of E{sub 0} estimates is achieved for small numbers (5 or 6) of involved connected moments, the relative error being smaller than 10{sup -4} (0.01%) within the whole parameter space of the Rabi Hamiltonian. A special symmetrization of the trial function enables us to calculate also the first excited energy E{sub 1}, with the relative error smaller than 10{sup -2} (1%). -- Highlights: → We study the ground state energy of the Rabi Hamiltonian. → We use the t-expansion method with an optimized trial function. → High accuracy of estimates is achieved, the relative error being smaller than 0.01%. → The calculation of the first excited state energy is made. The method has a general applicability.
On Critical Behaviour in Systems of Hamiltonian Partial Differential Equations.
Dubrovin, Boris; Grava, Tamara; Klein, Christian; Moro, Antonio
2015-01-01
We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components. We argue that near the critical point of gradient catastrophe of the dispersionless system, the solutions to a suitable initial value problem for the perturbed equations are approximately described by particular solutions to the Painlevé-I (P[Formula: see text]) equation or its fourth-order analogue P[Formula: see text]. As concrete examples, we discuss nonlinear Schrödinger equations in the semiclassical limit. A numerical study of these cases provides strong evidence in support of the conjecture.
Third derivatives of the integrable part of an asteroid Hamiltonian
Directory of Open Access Journals (Sweden)
Pavlović R.
2007-01-01
Full Text Available To apply the theorem of Nekhoroshev (1977 to asteroids, one first has to check whether a necessary geometrical condition is fulfilled: either convexity, or quasi-convexity, or only a 3-jet non-degeneracy. This requires computation of the derivatives of the integrable part of the corresponding Hamiltonian up to the third order over actions and a thorough analysis of their properties. In this paper we describe in detail the procedure of derivation and we give explicit expressions for the obtained derivatives. .
Chaotic dynamics in Hamiltonian systems with applications to celestial mechanics
Dankowicz, Harry
1997-01-01
In the past hundred years investigators have learned the significance of complex behavior in deterministic systems. The potential applications of this discovery are as numerous as they are encouraging.This text clearly presents the mathematical foundations of chaotic dynamics, including methods and results at the forefront of current research. The book begins with a thorough introduction to dynamical systems and their applications. It goes on to develop the theory of regular and stochastic behavior in higher-degree-of-freedom Hamiltonian systems, covering topics such as homoclinic chaos, KAM t
Relativistic tidal heating of Hamiltonian quasi-local boundary expressions
So, Lau Loi
2015-01-01
Purdue and Favata calculate the tidal heating used certain classical pseudotensors. Booth and Creighton employed the quasi-local mass formalism of Brown and York to demonstrate the same subject. All of them give the result matched with the Newtonian theory. Here we present another Hamiltonian quasi-local boundary expressions and all give the same desired value. This indicates that the tidal heating is unique as Thorne predicted. Moreover, we discovered that the pseudo-tensor method and quasi-local method are fundamentally different.
Quantum mechanics of non-Hamiltonian and dissipative systems
Tarasov, Vasily
2008-01-01
Quantum Mechanics of Non-Hamiltonian and Dissipative Systems is self-contained and can be used by students without a previous course in modern mathematics and physics. The book describes the modern structure of the theory, and covers the fundamental results of last 15 years. The book has been recommended by Russian Ministry of Education as the textbook for graduate students and has been used for graduate student lectures from 1998 to 2006. Requires no preliminary knowledge of graduate and advanced mathematics Discusses the fundamental results of last 15 years in this theory Suitable for cours
Modular Hamiltonian for Excited States in Conformal Field Theory.
Lashkari, Nima
2016-07-22
We present a novel replica trick that computes the relative entropy of two arbitrary states in conformal field theory. Our replica trick is based on the analytic continuation of partition functions that break the Z_{n} replica symmetry. It provides a method for computing arbitrary matrix elements of the modular Hamiltonian corresponding to excited states in terms of correlation functions. We show that the quantum Fisher information in vacuum can be expressed in terms of two-point functions on the replica geometry. We perform sample calculations in two-dimensional conformal field theories.
Periodic Solutions of Hamiltonian Systems of 3-Body Type
1989-08-01
As has been noted earlier. a(C) < 4(4 + C2) - 1 implies this is impossible. Thus I has no critical points in this region and there does not exist a...unstable manifolds for Z 12 in the region e1 <- J 1 2(q) -< M + 1 have a transversal intersection. Points on the unstable manifold between levels ci...Hamiltonian systems, Nonlinear Analysis: TMA, 12, (1988), 259-270. [7] Marino, A. and G. Prodi, Metodi perturbativi nella teoria di Morse, Boll. Un. Mat
Adiabatic dynamics of one-dimensional classical Hamiltonian dissipative systems
Pritula, G. M.; Petrenko, E. V.; Usatenko, O. V.
2018-02-01
A linearized plane pendulum with the slowly varying mass and length of string and the suspension point moving at a slowly varying speed is presented as an example of a simple 1D mechanical system described by the generalized harmonic oscillator equation, which is a basic model in discussion of the adiabatic dynamics and geometric phase. The expression for the pendulum geometric phase is obtained by three different methods. The pendulum is shown to be canonically equivalent to the damped harmonic oscillator. This supports the mathematical conclusion, not widely accepted in physical community, of no difference between the dissipative and Hamiltonian 1D systems.
15th International Conference on Non-Hermitian Hamiltonians in Quantum Physics
Passante, Roberto; Trapani, Camillo
2016-01-01
This book presents the Proceedings of the 15th International Conference on Non-Hermitian Hamiltonians in Quantum Physics, held in Palermo, Italy, from 18 to 23 May 2015. Non-Hermitian operators, and non-Hermitian Hamiltonians in particular, have recently received considerable attention from both the mathematics and physics communities. There has been a growing interest in non-Hermitian Hamiltonians in quantum physics since the discovery that PT-symmetric Hamiltonians can have a real spectrum and thus a physical relevance. The main subjects considered in this book include: PT-symmetry in quantum physics, PT-optics, Spectral singularities and spectral techniques, Indefinite-metric theories, Open quantum systems, Krein space methods, and Biorthogonal systems and applications. The book also provides a summary of recent advances in pseudo-Hermitian Hamiltonians and PT-symmetric Hamiltonians, as well as their applications in quantum physics and in the theory of open quantum systems.
Structure-preserving tangential interpolation for model reduction of port-Hamiltonian Systems
Gugercin, Serkan; Polyuga, Rostyslav V.; Beattie, Christopher; van der Schaft, Arjan
2011-01-01
Port-Hamiltonian systems result from port-based network modeling of physical systems and are an important example of passive state-space systems. In this paper, we develop the framework for model reduction of large-scale multi-input/multi-output port-Hamiltonian systems via tangential rational interpolation. The resulting reduced-order model not only is a rational tangential interpolant but also retains the port-Hamiltonian structure; hence is passive. This reduction methodology is described ...
Keshtkar, F.; Erjaee, G.; Boutefnouchet, M.
2014-01-01
In this article, a brief stability analysis of equilibrium points in nonlinear fractional order dynamical systems is given. Then, based on the first integral concept, a definition of planar Hamiltonian systems with fractional order introduced. Some interesting properties of these fractional Hamiltonian systems are also presented. Finally, we illustrate two examples to see the differences between fractional Hamiltonian systems with their classical order counterparts. NPRP . Grant Number: NP...
Recursion operators and bi-Hamiltonian structure of the general heavenly equation
Sheftel, M. B.; Yazıcı, D.; Malykh, A. A.
2017-06-01
We discover two additional Lax pairs and three nonlocal recursion operators for symmetries of the general heavenly equation introduced by Doubrov and Ferapontov. Converting the equation to a two-component form, we obtain Lagrangian and Hamiltonian structures of the two-component general heavenly system. We study all point symmetries of the two-component system and, using the inverse Noether theorem in the Hamiltonian form, obtain all the integrals of motion corresponding to each variational (Noether) symmetry. We discover that in the two-component form we have only a single nonlocal recursion operator. Composing the recursion operator with the first Hamiltonian operator we obtain second Hamiltonian operator. We check the Jacobi identities for the second Hamiltonian operator and compatibility of the two Hamiltonian structures using P. Olver's theory of functional multi-vectors. Our well-founded conjecture is that P. Olver's method works fine for nonlocal operators. We show that the general heavenly equation in the two-component form is a bi-Hamiltonian system integrable in the sense of Magri. We demonstrate how to obtain nonlocal Hamiltonian flows generated by local Hamiltonians by using formal adjoint recursion operator.
Quantum gates by inverse engineering of a Hamiltonian
Santos, Alan C.
2018-01-01
Inverse engineering of a Hamiltonian (IEH) from an evolution operator is a useful technique for the protocol of quantum control with potential applications in quantum information processing. In this paper we introduce a particular protocol to perform IEH and we show how this scheme can be used to implement a set of quantum gates by using minimal quantum resources (such as entanglement, interactions between more than two qubits or auxiliary qubits). Remarkably, while previous protocols request three-qubit interactions and/or auxiliary qubits to implement such gates, our protocol requires just two-qubit interactions and no auxiliary qubits. By using this approach we can obtain a large class of Hamiltonians that allow us to implement single and two-qubit gates necessary for quantum computation. To conclude this article we analyze the performance of our scheme against systematic errors related to amplitude noise, where we show that the free parameters introduced in our scheme can be useful for enhancing the robustness of the protocol against such errors.
L\\'eon Rosenfeld's invention of constrained Hamiltonian dynamics
Salisbury, Donald
2016-01-01
This commentary reflects on the 1930 discoveries of L\\'eon Rosenfeld in the domain of phase-space constraints. We start with a short biography of Rosenfeld and his motivation for this article in the context of ideas pursued by W. Pauli, F. Klein, E. Noether. We then comment on Rosenfeld's General Theory dealing with symmetries and constraints, symmetry generators, conservation laws and the construction of a Hamiltonian in the case of phase-space constraints. It is remarkable that he was able to derive expressions for all phase space symmetry generators without making explicit reference to the generator of time evolution. In his Applications, Rosenfeld treated the general relativistic example of Einstein-Maxwell-Dirac theory. We show, that although Rosenfeld refrained from fully applying his general findings to this example, he could have obtained the Hamiltonian. Many of Rosenfeld's discoveries were re-developed or re-discovered by others two decades later, yet as we show there remain additional firsts that a...
Quantum Hamiltonian daemons: Unitary analogs of combustion engines
Thesing, Eike P.; Gilz, Lukas; Anglin, James R.
2017-07-01
Hamiltonian daemons have recently been defined classically as small, closed Hamiltonian systems which can exhibit secular energy transfer from high-frequency to low-frequency degrees of freedom (steady downconversion), analogous to the steady transfer of energy in a combustion engine from the high terahertz frequencies of molecular excitations to the low kilohertz frequencies of piston motion [L. Gilz, E. P. Thesing, and J. R. Anglin, Phys. Rev. E 94, 042127 (2016), 10.1103/PhysRevE.94.042127]. Classical daemons achieve downconversion within a small, closed system by exploiting nonlinear resonances; the adiabatic theorem permits their operation but imposes nontrivial limitations on their efficiency. Here we investigate a simple example of a quantum mechanical daemon. In the correspondence regime it obeys similar efficiency limits to its classical counterparts, but in the strongly quantum mechanical regime the daemon operates in an entirely different manner. It maintains an engine-like behavior in a distinctly quantum mechanical form: a weight is lifted at a steady average speed through a long sequence of quantum jumps in momentum, at each of which a quantum of fuel is consumed. The quantum daemon can cease downconversion at any time through nonadiabatic Landau-Zener transitions, and continuing operation of the quantum daemon is associated with steadily growing entanglement between fast and slow degrees of freedom.
Hamiltonian approach to Ehrenfest expectation values and Gaussian quantum states.
Bonet-Luz, Esther; Tronci, Cesare
2016-05-01
The dynamics of quantum expectation values is considered in a geometric setting. First, expectation values of the canonical observables are shown to be equivariant momentum maps for the action of the Heisenberg group on quantum states. Then, the Hamiltonian structure of Ehrenfest's theorem is shown to be Lie-Poisson for a semidirect-product Lie group, named the Ehrenfest group. The underlying Poisson structure produces classical and quantum mechanics as special limit cases. In addition, quantum dynamics is expressed in the frame of the expectation values, in which the latter undergo canonical Hamiltonian motion. In the case of Gaussian states, expectation values dynamics couples to second-order moments, which also enjoy a momentum map structure. Eventually, Gaussian states are shown to possess a Lie-Poisson structure associated with another semidirect-product group, which is called the Jacobi group. This structure produces the energy-conserving variant of a class of Gaussian moment models that have previously appeared in the chemical physics literature.
Interest rates in quantum finance: the Wilson expansion and Hamiltonian.
Baaquie, Belal E
2009-10-01
Interest rate instruments form a major component of the capital markets. The Libor market model (LMM) is the finance industry standard interest rate model for both Libor and Euribor, which are the most important interest rates. The quantum finance formulation of the Libor market model is given in this paper and leads to a key generalization: all the Libors, for different future times, are imperfectly correlated. A key difference between a forward interest rate model and the LMM lies in the fact that the LMM is calibrated directly from the observed market interest rates. The short distance Wilson expansion [Phys. Rev. 179, 1499 (1969)] of a Gaussian quantum field is shown to provide the generalization of Ito calculus; in particular, the Wilson expansion of the Gaussian quantum field A(t,x) driving the Libors yields a derivation of the Libor drift term that incorporates imperfect correlations of the different Libors. The logarithm of Libor phi(t,x) is defined and provides an efficient and compact representation of the quantum field theory of the Libor market model. The Lagrangian and Feynman path integrals of the Libor market model of interest rates are obtained, as well as a derivation given by its Hamiltonian. The Hamiltonian formulation of the martingale condition provides an exact solution for the nonlinear drift of the Libor market model. The quantum finance formulation of the LMM is shown to reduce to the industry standard Bruce-Gatarek-Musiela-Jamshidian model when the forward interest rates are taken to be exactly correlated.
New Hamiltonians for loop quantum cosmology with arbitrary spin representations
Ben Achour, Jibril; Brahma, Suddhasattwa; Geiller, Marc
2017-04-01
In loop quantum cosmology, one has to make a choice of SU(2) irreducible representation in which to compute holonomies and regularize the curvature of the connection. The systematic choice made in the literature is to work in the fundamental representation, and very little is known about the physics associated with higher spin labels. This constitutes an ambiguity of which the understanding, we believe, is fundamental for connecting loop quantum cosmology to full theories of quantum gravity like loop quantum gravity, its spin foam formulation, or cosmological group field theory. We take a step in this direction by providing here a new closed formula for the Hamiltonian of flat Friedmann-Lemaître-Robertson-Walker models regularized in a representation of arbitrary spin. This expression is furthermore polynomial in the basic variables which correspond to well-defined operators in the quantum theory, takes into account the so-called inverse-volume corrections, and treats in a unified way two different regularization schemes for the curvature. After studying the effective classical dynamics corresponding to single and multiple-spin Hamiltonians, we study the behavior of the critical density when the number of representations is increased and the stability of the difference equations in the quantum theory.
Léon Rosenfeld's general theory of constrained Hamiltonian dynamics
Salisbury, Donald; Sundermeyer, Kurt
2017-04-01
This commentary reflects on the 1930 general theory of Léon Rosenfeld dealing with phase-space constraints. We start with a short biography of Rosenfeld and his motivation for this article in the context of ideas pursued by W. Pauli, F. Klein, E. Noether. We then comment on Rosenfeld's General Theory dealing with symmetries and constraints, symmetry generators, conservation laws and the construction of a Hamiltonian in the case of phase-space constraints. It is remarkable that he was able to derive expressions for all phase space symmetry generators without making explicit reference to the generator of time evolution. In his Applications, Rosenfeld treated the general relativistic example of Einstein-Maxwell-Dirac theory. We show, that although Rosenfeld refrained from fully applying his general findings to this example, he could have obtained the Hamiltonian. Many of Rosenfeld's discoveries were re-developed or re-discovered by others two decades later, yet as we show there remain additional firsts that are still not recognized in the community.
Negative-energy {P} {T}-symmetric Hamiltonians
Bender, Carl M.; Hook, Daniel W.; Klevansky, S. P.
2012-11-01
The non-Hermitian {P} {T}-symmetric quantum-mechanical Hamiltonian H = p2 + x2(ix)ɛ has real, positive and discrete eigenvalues for all ɛ ⩾ 0. These eigenvalues are analytic continuations of the harmonic-oscillator eigenvalues En = 2n + 1 (n = 0, 1, 2, 3, …) at ɛ = 0. However, the harmonic oscillator also has negative eigenvalues En = -2n - 1 (n = 0, 1, 2, 3, …), and one may ask whether it is equally possible to continue analytically from these eigenvalues. It is shown in this paper that for appropriate {P} {T}-symmetric boundary conditions the Hamiltonian H = p2 + x2(ix)ɛ also has real and negative discrete eigenvalues. The negative eigenvalues fall into classes labeled by the integer N (N = 1, 2, 3, …). For the Nth class of eigenvalues, ɛ lies in the range (4N - 6)/3 article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’.
Optimized t-expansion method for the Rabi Hamiltonian
Travěnec, Igor; Šamaj, Ladislav
2011-10-01
A polemic arose recently about the applicability of the t-expansion method to the calculation of the ground state energy E0 of the Rabi model. For specific choices of the trial function and very large number of involved connected moments, the t-expansion results are rather poor and exhibit considerable oscillations. In this Letter, we formulate the t-expansion method for trial functions containing two free parameters which capture two exactly solvable limits of the Rabi Hamiltonian. At each order of the t-series, E0 is assumed to be stationary with respect to the free parameters. A high accuracy of E0 estimates is achieved for small numbers (5 or 6) of involved connected moments, the relative error being smaller than 10 (0.01%) within the whole parameter space of the Rabi Hamiltonian. A special symmetrization of the trial function enables us to calculate also the first excited energy E1, with the relative error smaller than 10 (1%).
Optimal adaptive control for quantum metrology with time-dependent Hamiltonians
Pang, Shengshi; Jordan, Andrew N.
2017-01-01
Quantum metrology has been studied for a wide range of systems with time-independent Hamiltonians. For systems with time-dependent Hamiltonians, however, due to the complexity of dynamics, little has been known about quantum metrology. Here we investigate quantum metrology with time-dependent Hamiltonians to bridge this gap. We obtain the optimal quantum Fisher information for parameters in time-dependent Hamiltonians, and show proper Hamiltonian control is generally necessary to optimize the Fisher information. We derive the optimal Hamiltonian control, which is generally adaptive, and the measurement scheme to attain the optimal Fisher information. In a minimal example of a qubit in a rotating magnetic field, we find a surprising result that the fundamental limit of T2 time scaling of quantum Fisher information can be broken with time-dependent Hamiltonians, which reaches T4 in estimating the rotation frequency of the field. We conclude by considering level crossings in the derivatives of the Hamiltonians, and point out additional control is necessary for that case. PMID:28276428
Toward Protein Tertiary Structure Recognition by means of Associative Memory Hamiltonians
Friedrichs, Mark S.; Wolynes, Peter G.
1989-10-01
The statistical mechanics of associative memories and spin glasses suggests ways to design Hamiltonians for protein folding. An associative memory Hamiltonian based on hydrophobicity patterns is shown to have a large capacity for recall and to be capable of recognizing tertiary structure for moderately variant sequences.
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....
Structure-preserving tangential interpolation for model reduction of port-Hamiltonian systems
Gugercin, Serkan; Polyuga, Rostyslav V.; Beattie, Christopher; Schaft, Arjan van der
Port-Hamiltonian systems result from port-based network modeling of physical systems and are an important example of passive state-space systems. In this paper, we develop a framework for model reduction of large-scale multi-input/multi-output port-Hamiltonian systems via tangential rational
Divide and conquer method for proving gaps of frustration free Hamiltonians
DEFF Research Database (Denmark)
Kastoryano, Michael J.; Lucia, Angelo
2017-01-01
Providing system-size independent lower bounds on the spectral gap of local Hamiltonian is in general a hard problem. For the case of finite-range, frustration free Hamiltonians on a spin lattice of arbitrary dimension, we show that a property of the ground state space is sufficient to obtain suc...
Composition of Dirac structures and control of Port-Hamiltonian systems
van der Schaft, Arjan; Cervera, J.; Gilliam, D.S.; Rosenthal, J.
2002-01-01
Key feature of Dirac structures (as opposed to Poisson or symplectic structures) is the fact that the standard composition of two Dirac structures is again a Dirac structure. In particular this implies that any power-conserving interconnection of port-Hamiltonian systems is a port-Hamiltonian system
Symplectic Hamiltonian Formulation of Transmission Line Systems with Boundary Energy Flow
Jeltsema, Dimitri; Schaft, Arjan van der
2008-01-01
The classical Lagrangian and Hamiltonian formulation of an electrical transmission line is reviewed and extended to allow for varying boundary conditions. This extension is based on the definition of an infinite-dimensional analogue of the affine Lagrangian and Hamiltonian input-output systems
Lagrangian and Hamiltonian Formulation of Transmission Line Systems with Boundary Energy Flow
Jeltsema, Dimitri; Schaft, Arjan J. van der
The classical Lagrangian and Hamiltonian formulation of an electrical transmission line is reviewed and extended to allow for varying boundary conditions, The method is based on the definition of an infinite-dimensional analogue of the affine Lagrangian and Hamiltonian input-output systems
Self-adjoint Hamiltonians with a mass jump: General matching conditions
Energy Technology Data Exchange (ETDEWEB)
Gadella, M. [Departamento de Fisica Teorica, Atomica y Optica, Facultad de Ciencias, Universidad de Valladolid, 47005 Valladolid (Spain)]. E-mail: manuelgadella@yahoo.com.ar; Kuru, S. [Departamento de Fisica Teorica, Atomica y Optica, Facultad de Ciencias, Universidad de Valladolid, 47005 Valladolid (Spain); Department of Physics, Faculty of Science, Ankara University, 06100 Ankara (Turkey); Negro, J. [Departamento de Fisica Teorica, Atomica y Optica, Facultad de Ciencias, Universidad de Valladolid, 47005 Valladolid (Spain)
2007-03-05
The simplest position-dependent mass Hamiltonian in one dimension, where the mass has the form of a step function with a jump discontinuity at one point, is considered. The most general matching conditions at the jumping point for the solutions of the Schroedinger equation that provide a self-adjoint Hamiltonian are characterized.
Schaft, Arjan van der
1981-01-01
The definitions of symmetries and conservation laws for autonomous (i.e. without external forces) Hamiltonian systems are generalized to Hamiltonian systems with inputs and outputs. It is shown that a symmetry implies the existence of a conservation law and vice versa; thereby generalizing Noether's
van Oers, A.M.; Maas, L.R.M.; Bokhove, O.
2017-01-01
The linear equations governing internal gravity waves in a stratified ideal fluid possess a Hamiltonian structure. A discontinuous Galerkin finite element method has been developed in which this Hamiltonian structure is discretized, resulting in conservation of discrete analogs of phase space and
Optimal adaptive control for quantum metrology with time-dependent Hamiltonians.
Pang, Shengshi; Jordan, Andrew N
2017-03-09
Quantum metrology has been studied for a wide range of systems with time-independent Hamiltonians. For systems with time-dependent Hamiltonians, however, due to the complexity of dynamics, little has been known about quantum metrology. Here we investigate quantum metrology with time-dependent Hamiltonians to bridge this gap. We obtain the optimal quantum Fisher information for parameters in time-dependent Hamiltonians, and show proper Hamiltonian control is generally necessary to optimize the Fisher information. We derive the optimal Hamiltonian control, which is generally adaptive, and the measurement scheme to attain the optimal Fisher information. In a minimal example of a qubit in a rotating magnetic field, we find a surprising result that the fundamental limit of T2 time scaling of quantum Fisher information can be broken with time-dependent Hamiltonians, which reaches T4 in estimating the rotation frequency of the field. We conclude by considering level crossings in the derivatives of the Hamiltonians, and point out additional control is necessary for that case.
A port-Hamiltonian approach to visual servo control of a pick and place system
Dirksz, Daniel A.; Scherpen, Jacquelien M.A.
2012-01-01
In this paper we take a port-Hamiltonian approach to address the problem of image-based visual servo control of a pick and place system. We realize a closed-loop system, including the nonlinear camera dynamics, which is port-Hamiltonian. Although the closed-loop system is nonlinear, the resulting
Port Hamiltonian Formulation of Infinite Dimensional Systems II. Boundary Control by Interconnection
Macchelli, Alessandro; Schaft, Arjan J. van der; Melchiorri, Claudio
2004-01-01
In this paper, some new results concerning the boundary control of distributed parameter systems in port Hamiltonian form are presented. The classical finite dimensional port Hamiltonian formulation of a dynamical system has been generalized to the distributed parameter and multi-variable case by
Entanglement Entropy of Eigenstates of Quantum Chaotic Hamiltonians.
Vidmar, Lev; Rigol, Marcos
2017-12-01
In quantum statistical mechanics, it is of fundamental interest to understand how close the bipartite entanglement entropy of eigenstates of quantum chaotic Hamiltonians is to maximal. For random pure states in the Hilbert space, the average entanglement entropy is known to be nearly maximal, with a deviation that is, at most, a constant. Here we prove that, in a system that is away from half filling and divided in two equal halves, an upper bound for the average entanglement entropy of random pure states with a fixed particle number and normally distributed real coefficients exhibits a deviation from the maximal value that grows with the square root of the volume of the system. Exact numerical results for highly excited eigenstates of a particle number conserving quantum chaotic model indicate that the bound is saturated with increasing system size.
Hamiltonian and action formalisms for two-dimensional gyroviscous magnetohydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Morrison, P. J., E-mail: morrison@physics.utexas.edu; Lingam, M., E-mail: manasvi@physics.utexas.edu [Department of Physics and Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712 (United States); Acevedo, R., E-mail: raul-ace60@yahoo.com [3311 Black Locust Dr., Sugar Land, Texas 77479 (United States)
2014-08-15
A general procedure for constructing action principles for continuum models via a generalization of Hamilton's principle of mechanics is described. Through the procedure, an action principle for a gyroviscous magnetohydrodynamics model is constructed. The model is shown to agree with a reduced version of Braginskii's fluid equations. The construction reveals the origin of the gyromap, a device used to derive previous gyrofluid models. Also, a systematic reduction procedure is presented for obtaining the Hamiltonian structure in terms of the noncanonical Poisson bracket. The construction procedure yields a class of Casimir invariants, which are then used to construct variational principles for equilibrium equations with flow and gyroviscosity. The procedure for obtaining reduced fluid models with gyroviscosity is also described.
Concomitant Hamiltonian and topological structures of extended magnetohydrodynamics
Lingam, Manasvi; Morrison, Philip J
2016-01-01
The paper describes the unique geometric properties of ideal magnetohydrodynamics (MHD), and demonstrates how such features are inherited by extended MHD models, which incorporate two-fluid effects. The helicities and other geometric expressions for these models are presented in a topological context, emphasizing their universal features. Some of the results presented include: the generalized Kelvin circulation theorems, the existence of two Lie-dragged 2-forms, and two concomitant helicities (which can be studied via the Jones polynomial from Chern-Simons theory). The ensuing commonality is traced to the existence of an underlying Hamiltonian structure for all the extended MHD models, exemplified by the presence of a unique noncanonical Poisson bracket, and its associated energy.
Hamiltonian Evolution of Monokinetic Measures with Rough Momentum Profile
Bardos, Claude W.
2014-12-27
Consider a monokinetic probability measure on the phase space (Formula presented.) , i.e. (Formula presented.) where Uin is a vector field on RN and ρin a probability density on RN. Let Φt be a Hamiltonian flow on RN × RN. In this paper, we study the structure of the transported measure (Formula presented.) and of its integral in the ξ variable denoted ρ(t). In particular, we give estimates on the number of folds in (Formula presented.) , on which μ(t) is concentrated. We explain how our results can be applied to investigate the classical limit of the Schrödinger equation by using the formalism of Wigner measures. Our formalism includes initial momentum profiles Uin with much lower regularity than required by the WKB method. Finally, we discuss a few examples showing that our results are sharp.
Gravitational Modification of the Coulomb-Breit Hamiltonian
Caicedo, José Alexander; Urrutia, Luis Fernando
2009-04-01
In the poster session we presented a short review of our first results in the construction of the Coulomb-Breit Hamiltonian for a pair of fermions immersed in a background gravitational field which is described by General Relativity. Here we present a resume of that construction. We make a special stress on the objectives and the hypothesis used, but there is no special attention on the explicit form of the results because actually there is an updated and optimised version of our work in the edition process for publication; however we mention some special characteristics of the effect of the background gravitational field on the quantum nature of the system composed by fermions and its electromagnetic field, particularly the possibility of the observation of centre of mass effects in matter interferometry experiments.
Hamiltonian Dynamics of Spider-Type Multirotor Rigid Bodies Systems
Doroshin, Anton V.
2010-03-01
This paper sets out to develop a spider-type multiple-rotor system which can be used for attitude control of spacecraft. The multirotor system contains a large number of rotor-equipped rays, so it was called a ``Spider-type System,'' also it can be called ``Rotary Hedgehog.'' These systems allow using spinups and captures of conjugate rotors to perform compound attitude motion of spacecraft. The paper describes a new method of spacecraft attitude reorientation and new mathematical model of motion in Hamilton form. Hamiltonian dynamics of the system is investigated with the help of Andoyer-Deprit canonical variables. These variables allow obtaining exact solution for hetero- and homoclinic orbits in phase space of the system motion, which are very important for qualitative analysis.
Mesh-free Hamiltonian implementation of two dimensional Darwin model
Siddi, Lorenzo; Lapenta, Giovanni; Gibbon, Paul
2017-08-01
A new approach to Darwin or magnetoinductive plasma simulation is presented, which combines a mesh-free field solver with a robust time-integration scheme avoiding numerical divergence errors in the solenoidal field components. The mesh-free formulation employs an efficient parallel Barnes-Hut tree algorithm to speed up the computation of fields summed directly from the particles, avoiding the necessity of divergence cleaning procedures typically required by particle-in-cell methods. The time-integration scheme employs a Hamiltonian formulation of the Lorentz force, circumventing the development of violent numerical instabilities associated with time differentiation of the vector potential. It is shown that a semi-implicit scheme converges rapidly and is robust to further numerical instabilities which can develop from a dominant contribution of the vector potential to the canonical momenta. The model is validated by various static and dynamic benchmark tests, including a simulation of the Weibel-like filamentation instability in beam-plasma interactions.
Exact solution of the two-axis countertwisting Hamiltonian
Pan, Feng; Zhang, Yao-Zhong; Draayer, Jerry P.
2017-01-01
It is shown that the two-axis countertwisting Hamiltonian is exactly solvable when the quantum number of the total angular momentum of the system is an integer after the Jordan-Schwinger (differential) boson realization of the SU(2) algebra. Algebraic Bethe ansatz is used to get the exact solution with the help of the SU(1,1) algebraic structure, from which a set of Bethe ansatz equations of the problem is derived. It is shown that solutions of the Bethe ansatz equations can be obtained as zeros of the Heine-Stieltjes polynomials. The total number of the four sets of the zeros equals exactly 2 J + 1 for a given integer angular momentum quantum number J, which proves the completeness of the solutions. It is also shown that double degeneracy in level energies may also occur in the J → ∞ limit for integer J case except a unique non-degenerate level with zero excitation energy.
Hamiltonian truncation approach to quenches in the Ising field theory
Rakovszky, Tibor; Collura, Mario; Kormos, Márton; Takács, Gábor
2016-01-01
In contrast to lattice systems where powerful numerical techniques such as matrix product state based methods are available to study the non-equilibrium dynamics, the non-equilibrium behaviour of continuum systems is much harder to simulate. We demonstrate here that Hamiltonian truncation methods can be efficiently applied to this problem, by studying the quantum quench dynamics of the 1+1 dimensional Ising field theory using a truncated free fermionic space approach. After benchmarking the method with integrable quenches corresponding to changing the mass in a free Majorana fermion field theory, we study the effect of an integrability breaking perturbation by the longitudinal magnetic field. In both the ferromagnetic and paramagnetic phases of the model we find persistent oscillations with frequencies set by the low-lying particle excitations even for moderate size quenches. In the ferromagnetic phase these particles are the various non-perturbative confined bound states of the domain wall excitations, while...
Higher-Order Hamiltonian Model for Unidirectional Water Waves
Bona, J. L.; Carvajal, X.; Panthee, M.; Scialom, M.
2017-10-01
Formally second-order correct, mathematical descriptions of long-crested water waves propagating mainly in one direction are derived. These equations are analogous to the first-order approximations of KdV- or BBM-type. The advantage of these more complex equations is that their solutions corresponding to physically relevant initial perturbations of the rest state may be accurate on a much longer timescale. The initial value problem for the class of equations that emerges from our derivation is then considered. A local well-posedness theory is straightforwardly established by a contraction mapping argument. A subclass of these equations possess a special Hamiltonian structure that implies the local theory can be continued indefinitely.
Evolution of multiple quantum coherences with scaled dipolar Hamiltonian
Sánchez, Claudia M.; Buljubasich, Lisandro; Pastawski, Horacio M.; Chattah, Ana K.
2017-08-01
In this article, we introduce a pulse sequence which allows the monitoring of multiple quantum coherences distribution of correlated spin states developed with scaled dipolar Hamiltonian. The pulse sequence is a modification of our previous Proportionally Refocused Loschmidt echo (PRL echo) with phase increment, in order to verify the accuracy of the weighted coherent quantum dynamics. The experiments were carried out with different scaling factors to analyze the evolution of the total magnetization, the time dependence of the multiple quantum coherence orders, and the development of correlated spins clusters. In all cases, a strong dependence between the evolution rate and the weighting factor is observed. Remarkably, all the curves appeared overlapped in a single trend when plotted against the self-time, a new time scale that includes the scaling factor into the evolution time. In other words, the spin system displayed always the same quantum evolution, slowed down as the scaling factor decreases, confirming the high performance of the new pulse sequence.
Nonautonomous linear Hamiltonian systems oscillation, spectral theory and control
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...
IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence
Borisov, Alexey V; Mamaev, Ivan S; Sokolovskiy, Mikhail A; IUTAM BOOKSERIES : Volume 6
2008-01-01
This work brings together previously unpublished notes contributed by participants of the IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence (Moscow, 25-30 August 2006). The study of vortex motion is of great interest to fluid and gas dynamics: since all real flows are vortical in nature, applications of the vortex theory are extremely diverse, many of them (e.g. aircraft dynamics, atmospheric and ocean phenomena) being especially important. The last few decades have shown that serious possibilities for progress in the research of real turbulent vortex motions are essentially related to the combined use of mathematical methods, computer simulation and laboratory experiments. These approaches have led to a series of interesting results which allow us to study these processes from new perspectives. Based on this principle, the papers collected in this proceedings volume present new results on theoretical and applied aspects of the processes of formation and evolution of various flows, wave a...
Open quantum systems, effective Hamiltonians, and device characterization
Duffus, S. N. A.; Dwyer, V. M.; Everitt, M. J.
2017-10-01
High fidelity models, which are able to both support accurate device characterization and correctly account for environmental effects, are crucial to the engineering of scalable quantum technologies. As it ensures positivity of the density matrix, one preferred model of open systems describes the dynamics with a master equation in Lindblad form. In practice, Linblad operators are rarely derived from first principles, and often a particular form of annihilator is assumed. This results in dynamical models that miss those additional terms which must generally be added for the master equation to assume the Lindblad form, together with the other concomitant terms that must be assimilated into an effective Hamiltonian to produce the correct free evolution. In first principles derivations, such additional terms are often canceled (or countered), frequently in a somewhat ad hoc manner, leading to a number of competing models. Whilst the implications of this paper are quite general, to illustrate the point we focus here on an example anharmonic system; specifically that of a superconducting quantum interference device (SQUID) coupled to an Ohmic bath. The resulting master equation implies that the environment has a significant impact on the system's energy; we discuss the prospect of keeping or canceling this impact and note that, for the SQUID, monitoring the magnetic susceptibility under control of the capacitive coupling strength and the externally applied flux results in experimentally measurable differences between a number of these models. In particular, one should be able to determine whether a squeezing term of the form X ̂P ̂+P ̂X ̂ should be present in the effective Hamiltonian or not. If model generation is not performed correctly, device characterization will be prone to systemic errors.
Intrinsic origin of the high order angular momentum terms in a nuclear rotation Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Minkov, N [Institute of Nuclear Research and Nuclear Energy, 72 Tzarigrad Road, Sofia 1784 (Bulgaria); Yotov, P [Institute of Nuclear Research and Nuclear Energy, 72 Tzarigrad Road, Sofia 1784 (Bulgaria); Jolos, R V [Joint Institute for Nuclear Research, 141980 Dubna (Russian Federation); Scheid, W [Institut fuer Theoretische Physik der Justus-Liebig-Universitaet, Heinrich-Buff-Ring 16, D-35392 Giessen (Germany)
2007-02-15
A nuclear Hamiltonian with high order terms in the collective angular momentum operators is constructed by applying the method of contact transformations to a Hamiltonian including intrinsic particle motion and Coriolis interaction. In the space of intrinsic variables, the coefficients of the transformed Hamiltonian appear as matrix elements depending on the intrinsic angular momentum. Their transformation properties under the time reversal assure the time-reversal invariance of the Hamiltonian in the collective space. It is shown that the intrinsic matrix elements correspond to the coefficients in the point-symmetry-based quadrupole-octupole rotation Hamiltonian. In this framework, the developed formalism gives an insight into the intrinsic origin of the high order effects in the rotation motion of complex-deformed nuclei.
Chou, Chia-Chun; Kouri, Donald J
2013-04-25
We show that there exist spurious states for the sector two tensor Hamiltonian in multidimensional supersymmetric quantum mechanics. For one-dimensional supersymmetric quantum mechanics on an infinite domain, the sector one and two Hamiltonians have identical spectra with the exception of the ground state of the sector one. For tensorial multidimensional supersymmetric quantum mechanics, there exist normalizable spurious states for the sector two Hamiltonian with energy equal to the ground state energy of the sector one. These spurious states are annihilated by the adjoint charge operator, and hence, they do not correspond to physical states for the original Hamiltonian. The Hermitian property of the sector two Hamiltonian implies the orthogonality between spurious and physical states. In addition, we develop a method for construction of a specific form of the spurious states for any quantum system and also generate several spurious states for a two-dimensional anharmonic oscillator system and for the hydrogen atom.
Four-band Hamiltonian for fast calculations in intermediate-band solar cells
Luque, Antonio; Panchak, Aleksandr; Vlasov, Alexey; Martí, Antonio; Andreev, Viacheslav
2016-02-01
The 8-dimensional Luttinger-Kohn-Pikus-Bir Hamiltonian matrix may be made up of four 4-dimensional blocks. A 4-band Hamiltonian is presented, obtained from making the non-diagonal blocks zero. The parameters of the new Hamiltonian are adjusted to fit the calculated effective masses and strained QD bandgap with the measured ones. The 4-dimensional Hamiltonian thus obtained agrees well with measured quantum efficiency of a quantum dot intermediate band solar cell and the full absorption spectrum can be calculated in about two hours using Mathematica© and a notebook. This is a hundred times faster than with the commonly-used 8-band Hamiltonian and is considered suitable for helping design engineers in the development of nanostructured solar cells.
Kleiner, Isabelle; Hougen, Jon T.
2017-06-01
In this talk we report on our progress in trying to make the hybrid Hamiltonian competitive with the pure-tunneling Hamiltonian for treating large-amplitude motions in methylamine. A treatment using the pure-tunneling model has the advantages of: (i) requiring relatively little computer time, (ii) working with relatively uncorrelated fitting parameters, and (iii) yielding in the vast majority of cases fits to experimental measurement accuracy. These advantages are all illustrated in the work published this past year on a gigantic v_{t} = 1 data set for the torsional fundamental band in methyl amine. A treatment using the hybrid model has the advantages of: (i) being able to carry out a global fit involving both v_{t} = 0 and v_{t} = 1 energy levels and (ii) working with fitting parameters that have a clearer physical interpretation. Unfortunately, a treatment using the hybrid model has the great disadvantage of requiring a highly correlated set of fitting parameters to achieve reasonable fitting accuracy, which complicates the search for a good set of molecular fitting parameters and a fit to experimental accuracy. At the time of writing this abstract, we have been able to carry out a fit with J up to 15 that includes all available infrared data in the v_{t} = 1-0 torsional fundamental band, all ground-state microwave data with K up to 10 and J up to 15, and about a hundred microwave lines within the v_{t} = 1 torsional state, achieving weighted root-mean-square (rms) deviations of about 1.4, 2.8, and 4.2 for these three categories of data. We will give an update of this situation at the meeting. I. Gulaczyk, M. Kreglewski, V.-M. Horneman, J. Mol. Spectrosc., in Press (2017).
Energy Technology Data Exchange (ETDEWEB)
Shikakhwa, M.S., E-mail: mohammad@metu.edu.tr [Department of Physics, The University of Jordan, Amman 11942 (Jordan); Middle East Technical University Northern Cyprus Campus, Kalkanlı, Güzelyurt, via Mersin 10 (Turkey); Chair, N. [Department of Physics, The University of Jordan, Amman 11942 (Jordan)
2016-08-19
The Schrödinger Hamiltonian of a spin-less particle as well as the Pauli Hamiltonian with spin–orbit coupling included of a spin one-half particle in electromagnetic fields that are confined to a curved surface embedded in a three-dimensional space spanned by a general Orthogonal Curvilinear Coordinate are constructed. A new approach, based on the physical argument that upon squeezing the particle to the surface by a potential, then it is the physical gauge-covariant kinematical momentum operator (velocity operator) transverse to the surface that should be dropped from the Hamiltonian(s). In both cases, the resulting Hermitian gauge-invariant Hamiltonian on the surface is free from any reference to the component of the vector potential transverse to the surface, and the approach is completely gauge-independent. In particular, for the Pauli Hamiltonian these results are obtained exactly without any further assumptions or approximations. Explicit covariant plug-and-play formulae for the Schrödinger Hamiltonians on the surfaces of a cylinder, a sphere and a torus are derived. - Highlights: • New physical approach to confine particles to curved surfaces. • Confinement of a particle in a magnetic field to a surface is gauge-independent. • Spin one-half particle with SO coupling confined to a surface.
The mathematics of a quantum Hamiltonian computing half adder Boolean logic gate.
Dridi, G; Julien, R; Hliwa, M; Joachim, C
2015-08-28
The mathematics behind the quantum Hamiltonian computing (QHC) approach of designing Boolean logic gates with a quantum system are given. Using the quantum eigenvalue repulsion effect, the QHC AND, NAND, OR, NOR, XOR, and NXOR Hamiltonian Boolean matrices are constructed. This is applied to the construction of a QHC half adder Hamiltonian matrix requiring only six quantum states to fullfil a half Boolean logical truth table. The QHC design rules open a nano-architectronic way of constructing Boolean logic gates inside a single molecule or atom by atom at the surface of a passivated semi-conductor.
Energy Technology Data Exchange (ETDEWEB)
Khodel, V.A.; Saperstein, E.E.; Zverev, M.V.
1987-04-13
Different effects of the mass operator energy dependence are discussed. They are calculated within the framework of the Hartree-Fock (HF) method with effective forces as RPA corrections to the HF ground state. In the quasiparticle Lagrange method (QLM) they arise naturally and are taken into account in the self-consistent procedure itself. Approaches with the quasiparticle lagrangian and quasiparticle hamiltonian are compared. It is shown that the QLM can also be formulated with the help of the hamiltonian, but a simple lagrangian corresponds to a very complicated hamiltonian. Arguments in favour of the simple lagrangian are presented.
Extremal Density Matrices for the Expectation Value of a Qudit Hamiltonian
Castaños, O.; Figueroa, A.; López, J.; López-Peña, R.
2017-05-01
An algebraic procedure to find extremal density matrices for the expectation value of a finite Hamiltonian matrix is established. The extremal density matrices for pure states provide a complete description of the system, that is, its corresponding energy spectrum and projectors. For density matrices representing mixed states, one gets the most probable eigenstates that yield extremal mean values of the energy. The procedure uses mainly the stationary solutions of the von Neumann equation of motion, the orbits of the Hamiltonian, and the positivity conditions of the density matrix. The method is illustrated for matrix Hamiltonians of dimensions d = 2 and d = 3.
Lagrangian-Hamiltonian unified formalism for autonomous higher order dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Prieto-Martinez, Pedro Daniel; Roman-Roy, Narciso, E-mail: peredaniel@ma4.upc.edu, E-mail: nrr@ma4.upc.edu [Departamento de Matematica Aplicada IV, Edificio C-3, Campus Norte UPC, C/ Jordi Girona 1, 08034 Barcelona (Spain)
2011-09-23
The Lagrangian-Hamiltonian unified formalism of Skinner and Rusk was originally stated for autonomous dynamical systems in classical mechanics. It has been generalized for non-autonomous first-order mechanical systems, as well as for first-order and higher order field theories. However, a complete generalization to higher order mechanical systems is yet to be described. In this work, after reviewing the natural geometrical setting and the Lagrangian and Hamiltonian formalisms for higher order autonomous mechanical systems, we develop a complete generalization of the Lagrangian-Hamiltonian unified formalism for these kinds of systems, and we use it to analyze some physical models from this new point of view. (paper)
van Oers, Alexander M.; Maas, Leo R. M.; Bokhove, Onno
2017-02-01
The linear equations governing internal gravity waves in a stratified ideal fluid possess a Hamiltonian structure. A discontinuous Galerkin finite element method has been developed in which this Hamiltonian structure is discretized, resulting in conservation of discrete analogs of phase space and energy. This required (i) the discretization of the Hamiltonian structure using alternating flux functions and symplectic time integration, (ii) the discretization of a divergence-free velocity field using Dirac's theory of constraints and (iii) the handling of large-scale computational demands due to the 3-dimensional nature of internal gravity waves and, in confined, symmetry-breaking fluid domains, possibly its narrow zones of attraction.
Hamiltonian analysis of an on-shell U(1) gauge field theory
Lin, Chunshan; Sasaki, Misao
2017-11-01
We perform the Hamiltonian analysis of an on-shell U (1) gauge field theory, in which the action is not invariant under local U (1) transformations but recovers the invariance when the equations of motion are imposed. We firstly apply Dirac's method of Hamiltonian analysis. We find one first-class constraint and two second-class constraints in the vector sector. It implies the photons have only two polarisations, at least at the classical level, although the standard U (1) symmetry is explicitly broken. The reduced Hamiltonian is bounded from below and the on-shell U (1) gauge field theory is free from ghosts at the classical level.
Hamiltonian reductions of the one-dimensional Vlasov equation using phase-space moments
Chandre, C.; Perin, M.
2016-03-01
We consider Hamiltonian closures of the Vlasov equation using the phase-space moments of the distribution function. We provide some conditions on the closures imposed by the Jacobi identity. We completely solve some families of examples. As a result, we show that imposing that the resulting reduced system preserves the Hamiltonian character of the parent model shapes its phase space by creating a set of Casimir invariants as a direct consequence of the Jacobi identity. We exhibit three main families of Hamiltonian models with two, three, and four degrees of freedom aiming at modeling the complexity of the bunch of particles in the Vlasov dynamics.
Confinement and fermion doubling problem in Dirac-like Hamiltonians
Messias de Resende, B.; de Lima, F. Crasto; Miwa, R. H.; Vernek, E.; Ferreira, G. J.
2017-10-01
We investigate the interplay between confinement and the fermion doubling problem in Dirac-like Hamiltonians. Individually, both features are well known. First, simple electrostatic gates do not confine electrons due to the Klein tunneling. Second, a typical lattice discretization of the first-order derivative k →-i ∂x skips the central point and allow spurious low-energy, highly oscillating solutions known as fermion doublers. While a no-go theorem states that the doublers cannot be eliminated without artificially breaking a symmetry, here we show that the symmetry broken by the Wilson's mass approach is equivalent to the enforcement of hard-wall boundary conditions, thus making the no-go theorem irrelevant when confinement is foreseen. We illustrate our arguments by calculating the following: (i) the band structure and transport properties across thin films of the topological insulator Bi2Se3 , for which we use ab initio density functional theory calculations to justify the model; and (ii) the band structure of zigzag graphene nanoribbons.
Numerical Studies of Disordered Tight-Binding Hamiltonians
Scalettar, R. T.
2007-06-01
These are notes used for a set of lectures delivered at the Vietri summer school on Condensed Matter Physics in Fall 2006. They concern the general problem of the interplay of interactions and disorder in two dimensional electronic systems, as realized in the specific context of Quantum Monte Carlo simulations of the Anderson-Hubbard Hamiltonian. I wish to thank the organizers of this school for their hospitality during my visit, and their work in general in providing this educational opportunity for students over the years. It is a pleasure also to acknowledge the collaborators together with whom I have learned much of the physics and numerics presented in these notes: Zhaojun Bai, Andrew Baldwin, George Batrouni, Karim Bouadim, Wenbin Chen, Peter Denteneer, Fred Hébert, Norman Paris, Matt Schram, Nandini Trivedi, Martin Ulmke, Ichitaro Yamazaki and Gergely Zimanyi. This work was supported by the National Science Foundation (NSF-DMR-0312261 and NSF-ITR-0313390), and China Special Funds for Major State Basic Research Projects under contract 2005CB321700.
Subthreshold dynamics of a single neuron from a Hamiltonian perspective.
Wilson, M T; Steyn-Ross, D A
2008-12-01
We use Hamilton's equations of classical mechanics to investigate the behavior of a cortical neuron on the approach to an action potential. We use a two-component dynamic model of a single neuron, due to Wilson, with added noise inputs. We derive a Lagrangian for the system, from which we construct Hamilton's equations. The conjugate momenta are found to be linear combinations of the noise input to the system. We use this approach to consider theoretically and computationally the most likely manner in which such a modeled neuron approaches a firing event. We find that the firing of a neuron is a result of a drop in inhibition, due to a temporary increase in negative bias of the mean noise input to the inhibitory control equation. Moreover, we demonstrate through theory and simulation that, on average, the bias in the noise increases in an exponential manner on the approach to an action potential. In the Hamiltonian description, an action potential can therefore be considered a result of the exponential growth of the conjugate momenta variables pulling the system away from its equilibrium state, into a nonlinear regime.
Quantum mechanics/molecular mechanics dual Hamiltonian free energy perturbation.
Polyak, Iakov; Benighaus, Tobias; Boulanger, Eliot; Thiel, Walter
2013-08-14
The dual Hamiltonian free energy perturbation (DH-FEP) method is designed for accurate and efficient evaluation of the free energy profile of chemical reactions in quantum mechanical/molecular mechanical (QM/MM) calculations. In contrast to existing QM/MM FEP variants, the QM region is not kept frozen during sampling, but all degrees of freedom except for the reaction coordinate are sampled. In the DH-FEP scheme, the sampling is done by semiempirical QM/MM molecular dynamics (MD), while the perturbation energy differences are evaluated from high-level QM/MM single-point calculations at regular intervals, skipping a pre-defined number of MD sampling steps. After validating our method using an analytic model potential with an exactly known solution, we report a QM/MM DH-FEP study of the enzymatic reaction catalyzed by chorismate mutase. We suggest guidelines for QM/MM DH-FEP calculations and default values for the required computational parameters. In the case of chorismate mutase, we apply the DH-FEP approach in combination with a single one-dimensional reaction coordinate and with a two-dimensional collective coordinate (two individual distances), with superior results for the latter choice.
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.
Hamiltonian truncation approach to quenches in the Ising field theory
Rakovszky, T.; Mestyán, M.; Collura, M.; Kormos, M.; Takács, G.
2016-10-01
In contrast to lattice systems where powerful numerical techniques such as matrix product state based methods are available to study the non-equilibrium dynamics, the non-equilibrium behaviour of continuum systems is much harder to simulate. We demonstrate here that Hamiltonian truncation methods can be efficiently applied to this problem, by studying the quantum quench dynamics of the 1 + 1 dimensional Ising field theory using a truncated free fermionic space approach. After benchmarking the method with integrable quenches corresponding to changing the mass in a free Majorana fermion field theory, we study the effect of an integrability breaking perturbation by the longitudinal magnetic field. In both the ferromagnetic and paramagnetic phases of the model we find persistent oscillations with frequencies set by the low-lying particle excitations not only for small, but even for moderate size quenches. In the ferromagnetic phase these particles are the various non-perturbative confined bound states of the domain wall excitations, while in the paramagnetic phase the single magnon excitation governs the dynamics, allowing us to capture the time evolution of the magnetisation using a combination of known results from perturbation theory and form factor based methods. We point out that the dominance of low lying excitations allows for the numerical or experimental determination of the mass spectra through the study of the quench dynamics.
Realizing the classical XY Hamiltonian in polariton simulators
Berloff, Natalia G.; Silva, Matteo; Kalinin, Kirill; Askitopoulos, Alexis; Töpfer, Julian D.; Cilibrizzi, Pasquale; Langbein, Wolfgang; Lagoudakis, Pavlos G.
2017-11-01
The vast majority of real-life optimization problems with a large number of degrees of freedom are intractable by classical computers, since their complexity grows exponentially fast with the number of variables. Many of these problems can be mapped into classical spin models, such as the Ising, the XY or the Heisenberg models, so that optimization problems are reduced to finding the global minimum of spin models. Here, we propose and investigate the potential of polariton graphs as an efficient analogue simulator for finding the global minimum of the XY model. By imprinting polariton condensate lattices of bespoke geometries we show that we can engineer various coupling strengths between the lattice sites and read out the result of the global minimization through the relative phases. Besides solving optimization problems, polariton graphs can simulate a large variety of systems undergoing the U(1) symmetry-breaking transition. We realize various magnetic phases, such as ferromagnetic, anti-ferromagnetic, and frustrated spin configurations on a linear chain, the unit cells of square and triangular lattices, a disordered graph, and demonstrate the potential for size scalability on an extended square lattice of 45 coherently coupled polariton condensates. Our results provide a route to study unconventional superfluids, spin liquids, Berezinskii-Kosterlitz-Thouless phase transition, and classical magnetism, among the many systems that are described by the XY Hamiltonian.
Punchets: nonlinear transport in Hamiltonian pump-ratchet hybrids
Dittrich, Thomas; Medina Sánchez, Nicolás
2018-02-01
‘Punchets’ are hybrids between ratchets and pumps, combining a spatially periodic static potential, typically asymmetric under space inversion, with a local driving that breaks time-reversal invariance, and are intended to model metal or semiconductor surfaces irradiated by a collimated laser beam. Their crucial feature is irregular driven scattering between asymptotic regions supporting periodic (as opposed to free) motion. With all binary spatio-temporal symmetries broken, scattering in punchets typically generates directed currents. We here study the underlying nonlinear transport mechanisms, from chaotic scattering to the parameter dependence of the currents, in three types of Hamiltonian models, (i) with spatially periodic potentials where only in the driven scattering region, spatial and temporal symmetries are broken, and (ii), spatially asymmetric (ratchet) potentials with a driving that only breaks time-reversal invariance. As more realistic models of laser-irradiated surfaces, we consider (iii), a driving in the form of a running wave confined to a compact region by a static envelope. In this case, the induced current can even run against the direction of wave propagation, drastically evidencing its nonlinear nature. Quantizing punchets is indicated as a viable research perspective.
Multi-Hamiltonian Structures on Beauville's Integrable System and Its Variant
Directory of Open Access Journals (Sweden)
Rei Inoue
2007-01-01
Full Text Available We study Beauville's completely integrable system and its variant from a viewpoint of multi-Hamiltonian structures. We also relate our result to the previously known Poisson structures on the Mumford system and the even Mumford system.
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.
Spontaneous symmetry breaking and neutral stability in the noncanonical Hamiltonian formalism
Energy Technology Data Exchange (ETDEWEB)
Morrison, P.J.; Eliezer, S.
1985-10-01
The noncanonical Hamiltonian formalism is based upon a generalization of the Poisson bracket, a particular form of which is possessed by continuous media fields. Associated with this generalization are special constants of motion called Casimirs. These are constants that can be viewed as being built into the phase space, for they are invariant for all Hamiltonians. Casimirs are important because when added to the Hamiltonian they yield an effective Hamiltonian that produces equilibrium states upon variation. The stability of these states can be ascertained by a second variation. Goldstone's theorem, in its usual context, determines zero eigenvalues of the mass matrix for a given vacuum state, the equilibrium with minimum energy. Here, since for fluids and plasmas the vacuum state is uninteresting, we examine symmetry breaking for general equilibria. Broken symmetries imply directions of neutral stability. Two examples are presented: the nonlinear Alfven wave of plasma physics and the Korteweg-de Vries soliton. 46 refs.
Spontaneous symmetry breaking and neutral stability in the noncanonical Hamiltonian formalism
Energy Technology Data Exchange (ETDEWEB)
Morrison, P.J.; Eliezer, S.
1986-06-01
The noncanonical Hamiltonian formalism is based upon a generalization of the Poisson bracket, a particular form of which is possessed by continuous media fields. Associated with this generalization are special constants of motion called Casimir invariants. These are constants that can be viewed as being built into the phase space, for they are invariant for all Hamiltonians. Casimir invariants are important because when added to the Hamiltonian they yield an effective Hamiltonian that produces equilibrium states upon variation. The stability of these states can be ascertained by a second variation. Goldstone's theorem, in its usual context, determines zero eigenvalues of the mass matrix for a given vacuum state, the equilibrium with minimum energy. Here, since for fluids and plasmas the vacuum state is uninteresting, we examine symmetry breaking for general equilibria. Broken symmetries imply directions of neutral stability. Two examples are presented: the nonlinear Alfven wave of plasma physics and the Korteweg-de Vries soliton.
Xie, Yu; Jiang, Shengshi; Zheng, Jie; Lan, Zhenggang
2017-12-21
Photoinduced excited-state electron and energy transfer processes are crucial in biological photoharvesting systems and organic photovoltaic devices. We discuss the construction of a diabatic vibronic Hamiltonian for the proper treatment of these processes involving the projection approach acting on both electronic wave functions and vibrational modes. In the electronic part, the wave function projection approach is used to construct the diabatic Hamiltonian in which both local excited states and charge-transfer states are included on the same footing. For the vibrational degrees of freedom, the vibronic couplings in the diabatic Hamiltonian are obtained in the basis of the pseudonormal modes localized on each monomer site by applying delocalized-to-localized mode projection. This systematic approach allows us to construct the vibronic diabatic Hamiltonian in molecular aggregates.
Nandi, Debottam
2016-01-01
In this work, we present a consistent Hamiltonian analysis of cosmological perturbations for generalized non-canonical scalar fields. In order to do so, we introduce a new phase-space variable that is uniquely defined for different non-canonical scalar fields. We also show that this is the simplest and efficient way of expressing the Hamiltonian. We extend the Hamiltonian approach of [arXiv:1512.02539] to non-canonical scalar field and obtain a new definition of speed of sound in phase-space. In order to invert generalized phase-space Hamilton's equations to Euler-Lagrange equations of motion, we prescribe a general inversion formulae and show that our approach for non-canonical scalar field is consistent. We also obtain the third and fourth order interaction Hamiltonian for generalized non-canonical scalar fields and briefly discuss the extension of our method to generalized Galilean scalar fields.
Ohzeki, Masayuki
2017-01-23
Quantum annealing is a generic solver of the optimization problem that uses fictitious quantum fluctuation. Its simulation in classical computing is often performed using the quantum Monte Carlo simulation via the Suzuki-Trotter decomposition. However, the negative sign problem sometimes emerges in the simulation of quantum annealing with an elaborate driver Hamiltonian, since it belongs to a class of non-stoquastic Hamiltonians. In the present study, we propose an alternative way to avoid the negative sign problem involved in a particular class of the non-stoquastic Hamiltonians. To check the validity of the method, we demonstrate our method by applying it to a simple problem that includes the anti-ferromagnetic XX interaction, which is a typical instance of the non-stoquastic Hamiltonians.
Samsonov, Boris F
2013-04-28
One of the simplest non-Hermitian Hamiltonians, first proposed by Schwartz in 1960, that may possess a spectral singularity is analysed from the point of view of the non-Hermitian generalization of quantum mechanics. It is shown that the η operator, being a second-order differential operator, has supersymmetric structure. Asymptotic behaviour of the eigenfunctions of a Hermitian Hamiltonian equivalent to the given non-Hermitian one is found. As a result, the corresponding scattering matrix and cross section are given explicitly. It is demonstrated that the possible presence of a spectral singularity in the spectrum of the non-Hermitian Hamiltonian may be detected as a resonance in the scattering cross section of its Hermitian counterpart. Nevertheless, just at the singular point, the equivalent Hermitian Hamiltonian becomes undetermined.
Effective Hamiltonian for surface states of topological insulator thin films with hexagonal warping
Energy Technology Data Exchange (ETDEWEB)
Siu, Zhuo Bin; Jalil, Mansoor B. A. [Computational Nanoelectronics and Nanodevices Laboratory, Electrical and Computer Engineering Department, National University of Singapore (Singapore); Tan, Seng Ghee [Data Storage Institute, Agency for Science, Technology and Research - A*STAR (Singapore)
2016-05-15
The effective Hamiltonian of the surface states on semi-infinite slabs of the topological insulators (TI) Bi{sub 2}Te{sub 3} and Bi{sub 2}Se{sub 3} require the addition of a cubic momentum hexagonal warping term on top of the usual Dirac fermion Hamiltonian in order to reproduce the experimentally measured constant energy contours at intermediate values of Fermi energy. In this work, we derive the effective Hamiltonian for the surface states of a Bi{sub 2}Se{sub 3} thin film incorporating the corresponding hexagonal warping terms. We then calculate the dispersion relation of the effective Hamiltonian and show that the hexagonal warping leads distorts the equal energy contours from the circular cross sections of the Dirac cones.
New Exact Solutions of the New Hamiltonian Amplitude-Equation and Fokas Lenells Equation
Directory of Open Access Journals (Sweden)
Seyma Tuluce Demiray
2015-08-01
Full Text Available In this paper, exact solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation are successfully obtained. The extended trial equation method (ETEM and generalized Kudryashov method (GKM are applied to find several exact solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation. Primarily, we seek some exact solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation by using ETEM. Then, we research dark soliton solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation by using GKM. Lastly, according to the values of some parameters, we draw two and three dimensional graphics of imaginary and real values of certain solutions found by utilizing both methods.
Ohzeki, Masayuki
2017-01-01
Quantum annealing is a generic solver of the optimization problem that uses fictitious quantum fluctuation. Its simulation in classical computing is often performed using the quantum Monte Carlo simulation via the Suzuki–Trotter decomposition. However, the negative sign problem sometimes emerges in the simulation of quantum annealing with an elaborate driver Hamiltonian, since it belongs to a class of non-stoquastic Hamiltonians. In the present study, we propose an alternative way to avoid the negative sign problem involved in a particular class of the non-stoquastic Hamiltonians. To check the validity of the method, we demonstrate our method by applying it to a simple problem that includes the anti-ferromagnetic XX interaction, which is a typical instance of the non-stoquastic Hamiltonians. PMID:28112244
Homoclinic orbits at infinity for second-order Hamiltonian systems with fixed energy
Directory of Open Access Journals (Sweden)
Dong-Lun Wu
2015-06-01
Full Text Available We obtain the existence of homoclinic orbits at infinity for a class of second-order Hamiltonian systems with fixed energy. We use the limit for a sequence of approximate solutions which are obtained by variational methods.
Hamiltonian positivity of massive spin-2 particles via a rank-2 tensor
Benndorf, D.; Dalmazi, D.; dos Santos, A. L. R.
2017-02-01
There are three families of Lagrangians describing massive spin-2 particles via a general (nonsymmetric) rank-2 tensor. Each of those families depends on an arbitrary real parameter, one of them includes the paradigmatic Fierz-Pauli theory whose Hamiltonian positivity is known and reviewed here. Here we apply the plain Dirac-Bergmann procedure in the two remaining families. We identify all Hamiltonian constraints and prove both positivity of the reduced Hamiltonian and correct counting of degrees of freedom. The positivity of each spin mode contribution is demonstrated by using spin projection operators. The massless cases are also examined. In particular, we prove positivity of the reduced Hamiltonian and correct counting of degrees of freedom of a Weyl invariant description of massless spin-2 particles.
Higher-rank discrete symmetries in the IBM I. Octahedral shapes: General Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Van Isacker, P., E-mail: isacker@ganil.fr [Grand Accélérateur National d' Ions Lourds, CEA/DSM–CNRS/IN2P3, Bd Henri Becquerel, BP 55027, F-14076 Caen Cedex 5 (France); Bouldjedri, A.; Zerguine, S. [Department of Physics, PRIMALAB Laboratory, University of Batna, Avenue Boukhelouf M El Hadi, 05000 Batna (Algeria)
2015-06-15
In the context of the interacting boson model with s, d and g bosons, the conditions for obtaining an intrinsic shape with octahedral symmetry are derived for a general Hamiltonian with up to two-body interactions.
The GL(n,Fp)invariance of the Potts Hamiltonian
Mihai Caragiu; Mellita Caragiu
1997-01-01
After defining a meanfield by arithmetic means, using multiplicative characters of finite fields, its Potts Hamiltonian is exactly computed. Moreover, it proves to be invariant with respect to every change of basis in Fq over the prime field Fp.
Ground State Properties of the 1/2 Flux Harper Hamiltonian
Kennedy, Colin; Burton, William Cody; Chung, Woo Chang; Ketterle, Wolfgang
2015-05-01
The Harper Hamiltonian describes the motion of charged particles in an applied magnetic field - the spectrum of which exhibits the famed Hofstadter's butterfly. Recent advances in driven optical lattices have made great strides in simulating nontrivial Hamiltonians, such as the Harper model, in the time-averaged sense. We report on the realization of the ground state of bosons in the Harper Hamiltonian for 1/2 flux per plaquette utilizing a tilted two-dimensional lattice with laser assisted tunneling. We detail progress in studying various ground state properties of the 1/2 flux Harper Hamiltonian including ground state degeneracies, gauge-dependent observables, effects of micromotion, adiabatic loading schemes, and emergence and decay of coherence. Additionally, we describe prospects for flux rectification using a period-tripled superlattice and generalizations to three dimensions. MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, Department of Physics, Massachusetts Institute of Technology.
An optimum Hamiltonian for non-Hermitian quantum evolution and the complex Bloch sphere
Energy Technology Data Exchange (ETDEWEB)
Nesterov, Alexander I., E-mail: nesterov@cencar.udg.m [Departamento de Fisica, CUCEI, Universidad de Guadalajara, Av. Revolucion 1500, Guadalajara, CP 44420, Jalisco (Mexico)
2009-09-28
For a quantum system governed by a non-Hermitian Hamiltonian, we studied the problem of obtaining an optimum Hamiltonian that generates nonunitary transformations of a given initial state into a certain final state in the smallest time tau. The analysis is based on the relationship between the states of the two-dimensional subspace of the Hilbert space spanned by the initial and final states and the points of the two-dimensional complex Bloch sphere.
Explicit symplectic approximation of nonseparable Hamiltonians: algorithm and long time performance
Tao, Molei
2016-01-01
Explicit symplectic integrators have been important tools for accurate and efficient approximations of mechanical systems with separable Hamiltonians. For the first time, the article proposes for arbitrary Hamiltonians similar integrators, which are explicit, of any even order, symplectic in an extended phase space, and with pleasant long time properties. They are based on a mechanical restraint that binds two copies of phase space together. Using backward error analysis, KAM theory, and addi...
Adiabatic and Hamiltonian computing on a 2D lattice with simple two-qubit interactions
Lloyd, Seth; Terhal, Barbara
2016-01-01
We show how to perform universal Hamiltonian and adiabatic computing using a time-independent Hamiltonian on a 2D grid describing a system of hopping particles which string together and interact to perform the computation. In this construction, the movement of one particle is controlled by the presence or absence of other particles, an effective quantum field effect transistor that allows the construction of controlled-NOT and controlled-rotation gates. The construction translates into a mode...
Reshetnyak, A. A.
2003-01-01
In the framework of started in Ref.[1] construction procedure of the general superfield quantization method for gauge theories in Lagrangian formalism the rules for Hamiltonian formulation of general superfield theory of fields (GSTF) are introduced and are on the whole considered. Mathematical means developed in [1] for Lagrangian formulation of GSTF are extended to use in Hamiltonian one. Hamiltonization for Lagrangian formulation of GSTF via Legendre transform of superfunction $S_{L}\\bigl(...
Mass segregation phenomena using the Hamiltonian Mean Field model
Steiner, J. R.; Zolacir, T. O.
2018-02-01
Mass segregation problem is thought to be entangled with the dynamical evolution of young stellar clusters (Olczak, 2011 [1]). This is a common sense in the astrophysical community. In this work, the Hamiltonian Mean Field (HMF) model with different masses is studied. A mass segregation phenomenon (MSP) arises from this study as a dynamical feature. The MSP in the HMF model is a consequence of the Landau damping (LD) and it appears in systems that the interactions belongs to a long range regime. Actually HMF is a toy model known to show up the main characteristics of astrophysical systems due to the mean field character of the potential and for different masses, as stellar and galaxies clusters, also exhibits MSP. It is in this sense that computational simulations focusing in what happens over the mass distribution in the phase space are performed for this system. What happens through the violent relaxation period and what stands for the quasi-stationary states (QSS) of this dynamics is analyzed. The results obtained support the fact that MSP is observed already in the violent relaxation time and is maintained during the QSS. Some structures in the mass distribution function are observed. As a result of this study the mass distribution is determined by the system dynamics and is independent of the dimensionality of the system. MSP occurs in a one dimensional system as a result of the long range forces that acts in the system. In this approach MSP emerges as a dynamical feature. We also show that for HMF with different masses, the dynamical time scale is N.
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.
Adiabatic and Hamiltonian computing on a 2D lattice with simple two-qubit interactions
Lloyd, Seth; Terhal, Barbara M.
2016-02-01
We show how to perform universal Hamiltonian and adiabatic computing using a time-independent Hamiltonian on a 2D grid describing a system of hopping particles which string together and interact to perform the computation. In this construction, the movement of one particle is controlled by the presence or absence of other particles, an effective quantum field effect transistor that allows the construction of controlled-NOT and controlled-rotation gates. The construction translates into a model for universal quantum computation with time-independent two-qubit ZZ and XX+YY interactions on an (almost) planar grid. The effective Hamiltonian is arrived at by a single use of first-order perturbation theory avoiding the use of perturbation gadgets. The dynamics and spectral properties of the effective Hamiltonian can be fully determined as it corresponds to a particular realization of a mapping between a quantum circuit and a Hamiltonian called the space-time circuit-to-Hamiltonian construction. Because of the simple interactions required, and because no higher-order perturbation gadgets are employed, our construction is potentially realizable using superconducting or other solid-state qubits.
Modification of logarithmic Hamiltonians and application of explicit symplectic-like integrators
Li, Dan; Wu, Xin
2017-08-01
We modify the logarithmic Hamiltonian of Mikkola and Tanikawa by adding a constant (or function) to both the kinetic energy and the force function. Explicit symplectic algorithms are available when the logarithmic Hamiltonian has two separable parts of coordinates and momenta. However, they are not if the logarithmic Hamiltonian is inseparable. Fortunately, they are still efficient by manipulating the logarithmic Hamiltonian as a new separable Hamiltonian in an extended phase space. In fact, they belong to symplectic-like integrators. The choice of mixing maps affects the performance of the considered symplectic-like integrators. It is shown that two maps about sequent permutations of coordinates and momenta are inferior to a map with mid-point permutations in some cases. The choice of the constant (or function) added also exerts some influence on the performance of the algorithms. As a result, with the help of the mid-point permutations and a suitable choice for the constant (or function) included, the logarithmic Hamiltonian methods bring an increase in accuracy compared to the non-logarithmic ones, particularly for highly eccentric orbits.
On the exactness of effective Floquet Hamiltonians employed in solid-state NMR spectroscopy
Garg, Rajat; Ramachandran, Ramesh
2017-05-01
Development of theoretical models based on analytic theory has remained an active pursuit in molecular spectroscopy for its utility both in the design of experiments as well as in the interpretation of spectroscopic data. In particular, the role of "Effective Hamiltonians" in the evolution of theoretical frameworks is well known across all forms of spectroscopy. Nevertheless, a constant revalidation of the approximations employed in the theoretical frameworks is necessitated by the constant improvements on the experimental front in addition to the complexity posed by the systems under study. Here in this article, we confine our discussion to the derivation of effective Floquet Hamiltonians based on the contact transformation procedure. While the importance of the effective Floquet Hamiltonians in the qualitative description of NMR experiments has been realized in simpler cases, its extension in quantifying spectral data deserves a cautious approach. With this objective, the validity of the approximations employed in the derivation of the effective Floquet Hamiltonians is re-examined through a comparison with exact numerical methods under differing experimental conditions. The limitations arising from the existing analytic methods are outlined along with remedial measures for improving the accuracy of the derived effective Floquet Hamiltonians.
A Class of Hamiltonians for a Three-Particle Fermionic System at Unitarity
Energy Technology Data Exchange (ETDEWEB)
Correggi, M., E-mail: michele.correggi@gmail.com [Università degli Studi Roma Tre, Largo San Leonardo Murialdo 1, Dipartimento di Matematica e Fisica (Italy); Dell’Antonio, G. [“Sapienza” Università di Roma, P.le A. Moro 5, Dipartimento di Matematica (Italy); Finco, D. [Università Telematica Internazionale Uninettuno, Corso V. Emanuele II 39, Facoltà di Ingegneria (Italy); Michelangeli, A. [Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265 (Italy); Teta, A. [“Sapienza” Università di Roma, P.le A. Moro 5, Dipartimento di Matematica (Italy)
2015-12-15
We consider a quantum mechanical three-particle system made of two identical fermions of mass one and a different particle of mass m, where each fermion interacts via a zero-range force with the different particle. In particular we study the unitary regime, i.e., the case of infinite two-body scattering length. The Hamiltonians describing the system are, by definition, self-adjoint extensions of the free Hamiltonian restricted on smooth functions vanishing at the two-body coincidence planes, i.e., where the positions of two interacting particles coincide. It is known that for m larger than a critical value m{sup ∗} ≃ (13.607){sup −1} a self-adjoint and lower bounded Hamiltonian H{sub 0} can be constructed, whose domain is characterized in terms of the standard point-interaction boundary condition at each coincidence plane. Here we prove that for m ∈ (m{sup ∗},m{sup ∗∗}), where m{sup ∗∗} ≃ (8.62){sup −1}, there is a further family of self-adjoint and lower bounded Hamiltonians H{sub 0,β}, β ∈ ℝ, describing the system. Using a quadratic form method, we give a rigorous construction of such Hamiltonians and we show that the elements of their domains satisfy a further boundary condition, characterizing the singular behavior when the positions of all the three particles coincide.
A geometric approach to the Lagrangian and Hamiltonian formalism of electrodynamics
Kulyabov, D. S.; Korolkova, A. V.; Sevastianov, L. A.; Eferina, E. G.; Velieva, T. R.
2017-04-01
In solving field problems, for example problems of electrodynamics, we commonly use the Lagrangian and Hamiltonian formalisms. Hamiltonian formalism of field theory has the advantage over the Lagrangian, which inherently contains a gauge condition. While the gauge condition is introduced ad hoc from some external reasons in the Lagrangian formalism. However, the use of the Hamiltonian formalism in the field theory is difficult due to the non-regularity of the field Lagrangian. We must use such variant of the Lagrangian and the Hamiltonian formalism, which would allow us to work with the field models, in particular, to solve the problem of electrodynamics. We suggest to use the modern differential geometry and the algebraic topology, in particular the theory of fiber bundles, as a mathematical apparatus. This apparatus leads to greater clarity in the understanding of mathematical structures, associated with physical and technical models. The usage the fiber bundles theory allows us to deepen and expand both the Lagrangian and the Hamiltonian formalism. We can detect a wide range of these formalisms. Also we can select the most appropriate formalism. Actually just using the fiber bundles formalism we can adequately solve the problems of the field theory, in particular the problems of electrodynamics.
Hamiltonian solutions of the 3-body problem in (2+1) gravity
Energy Technology Data Exchange (ETDEWEB)
Ciafaloni, M [Dipartimento di Fisica, Universita di Firenze and INFN, Sezione di Firenze, 50019 Sesto Fiorentino (Italy); Munier, S [Centre de Physique Theorique, Ecole Polytechnique, CNRS, 91128 Palaiseau (France)
2011-10-01
We present a full study of the 3-body problem in gravity in a flat (2+1)-dimensional spacetime, and in the nonrelativistic limit of small velocities. We provide an explicit form of the Arnowitt-Deser-Misner Hamiltonian in a regular coordinate system and we set up all the ingredients for canonical quantization. We emphasize the role of a U(2) symmetry under which the Hamiltonian is invariant and which should generalize to a U(N - 1) symmetry for N bodies. This symmetry seems to stem from a braid group structure in the operations of looping of particles around each other, and guarantees the single valuedness of the Hamiltonian. Its role for the construction of single-valued energy eigenfunctions is also discussed.
Chiral super-Tremblay-Turbiner-Winternitz Hamiltonians and their dynamical superalgebra
Quesne, C.
2010-12-01
The family of Tremblay-Turbiner-Winternitz (TTW) Hamiltonians Hk on a plane, corresponding to any positive real value of k, is shown to admit another {\\cal N} = 2 supersymmetric extension than that previously introduced by the present author. This new extension is of the same kind as that considered by D'Hoker and Vinet in the study of magnetic monopoles and is characterized by the fact that all the irreducible representations of the corresponding osp(2/2, \\ {R}) dynamical superalgebra are atypical lowest-weight state ones. The new supersymmetric Hamiltonians may be referred to as chiral super-TTW Hamiltonians, the role of chirality being played here by the fermion number parity operator.
Curvature in Hamiltonian mechanics and the Einstein-Maxwell-dilaton action
Rajeev, S. G.
2017-05-01
Riemannian geometry is a particular case of Hamiltonian mechanics: the orbits of the Hamiltonian H =1/2 gi jpipj are the geodesics. Given a symplectic manifold (Γ ,ω ) , a Hamiltonian H :Γ →ℝ , and a Lagrangian sub-manifold M ⊂Γ , we find a generalization of the notion of curvature. The particular case H =1/2 gi j[pi-Ai ] [pj-Aj ] +ϕ of a particle moving in gravitational, electromagnetic, and scalar fields is studied in more detail. The integral of the generalized Ricci tensor with respect to the Boltzmann weight reduces to the action principle ∫[R +1/4 Fi kFj lgk lgi j -gi j∂iϕ ∂jϕ ] e-ϕ√{g }dnq for the scalar, vector and tensor fields.
Relativistic two-body Coulomb-Breit Hamiltonian in an external weak gravitational field
Caicedo, J. A.; Urrutia, L. F.
2011-11-01
A construction of the Coulomb-Breit Hamiltonian for a pair of fermions, considered as a quantum two-body system, immersed in an arbitrary background gravitational field described by Einstein's General Relativity is presented. Working with Fermi normal coordinates for a freely falling observer in a spacetime region where there are no background sources and ignoring the gravitational back-reaction of the system, the effective Coulomb-Breit Hamiltonian is obtained starting from the S-matrix element corresponding to the one-photon exchange between the charged fermionic currents. The contributions due to retardation are considered up to order (v / c) 2 and they are subsequently written as effective operators in the relativistic quantum mechanical Hilbert space of the system. The final Hamiltonian includes effects linear in the curvature and up to order (v / c) 2.
Relativistic two-body Coulomb-Breit Hamiltonian in an external weak gravitational field
Energy Technology Data Exchange (ETDEWEB)
Caicedo, J.A. [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, A. Postal 70-543, 04510 Mexico D.F. (Mexico); Urrutia, L.F., E-mail: urrutia@nucleares.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, A. Postal 70-543, 04510 Mexico D.F. (Mexico)
2011-11-03
A construction of the Coulomb-Breit Hamiltonian for a pair of fermions, considered as a quantum two-body system, immersed in an arbitrary background gravitational field described by Einstein's General Relativity is presented. Working with Fermi normal coordinates for a freely falling observer in a spacetime region where there are no background sources and ignoring the gravitational back-reaction of the system, the effective Coulomb-Breit Hamiltonian is obtained starting from the S-matrix element corresponding to the one-photon exchange between the charged fermionic currents. The contributions due to retardation are considered up to order (v/c){sup 2} and they are subsequently written as effective operators in the relativistic quantum mechanical Hilbert space of the system. The final Hamiltonian includes effects linear in the curvature and up to order (v/c){sup 2}.
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.
A unified theoretical framework for mapping models for the multi-state Hamiltonian.
Liu, Jian
2016-11-28
We propose a new unified theoretical framework to construct equivalent representations of the multi-state Hamiltonian operator and present several approaches for the mapping onto the Cartesian phase space. After mapping an F-dimensional Hamiltonian onto an F+1 dimensional space, creation and annihilation operators are defined such that the F+1 dimensional space is complete for any combined excitation. Commutation and anti-commutation relations are then naturally derived, which show that the underlying degrees of freedom are neither bosons nor fermions. This sets the scene for developing equivalent expressions of the Hamiltonian operator in quantum mechanics and their classical/semiclassical counterparts. Six mapping models are presented as examples. The framework also offers a novel way to derive such as the well-known Meyer-Miller model.
An Energy-Work Relationship Integration Scheme for Nonconservative Hamiltonian Systems
Directory of Open Access Journals (Sweden)
Fu Jingli
2008-01-01
Full Text Available This letter focuses on studying a new energy-work relationship numerical integration scheme of nonconservative Hamiltonian systems. The signal-stage, multistage, and parallel composition numerical integration schemes are presented for this system. The high-order energy-work relation scheme of the system is constructed by a parallel connection of n multistage scheme of order 2 which its order of accuracy is 2n. The connection, which is discrete analog of usual case, between the change of energy and work of nonconservative force is obtained for nonconservative Hamiltonian systems.This letter also shows that the more the stages of the schemes are, the less the error rate of the scheme is for nonconservative Hamiltonian systems. Finally, an applied example is discussed to illustrate these results.
Barnes, George L; Kellman, Michael E
2010-09-14
We present a two-dimensional potential surface for the isomerization in the hydroperoxyl radical HO(2) and calculate the vibrational spectrum. We then show that a simple effective spectroscopic fitting Hamiltonian is capable of reproducing large scale vibrational spectral structure above the isomerization barrier. Polyad breaking with multiple resonances is necessary to adequately describe the spectral features of the system. Insight into the dynamical nature of isomerization related to the effective Hamiltonian is gained through classical trajectories on the model potential. Contrary to physical intuition, the bend mode is not a "reaction mode," but rather isomerization requires excitation in both stretch and bend. The dynamics reveals a Farey tree formed from the 2:1 and 3:1 resonances, corresponding to the resonance coupling terms in the effective Hamiltonian, with the prominent 5:2 (2:1+3:1) feature dividing the tree into parts that we call the 3:1 and 2:1 portions.
Cariglia, Marco
2015-01-01
This work originates from part of a final year undergraduate research project on the Eisenhart lift for Hamiltonian systems. The Eisenhart lift is a procedure to describe trajectories of a classical natural Hamiltonian system as geodesics in an enlarged space. We point out that it can be easily obtained from basic principles of Hamiltonian dynamics, and as such it represents a useful didactical way to introduce graduate students to several modern concepts of geometry applied to physics: curved spaces, both Riemannian and Lorentzian, conformal transformations, geometrisation of interactions and extra dimensions, geometrisation of dynamical symmetries. For all these concepts the Eisenhart lift can be used as a theoretical tool that provides easily achievable examples, with the added benefit of also being a topic of current research with several applications, among which the study of dynamical systems and non-relativistic holography.
Bayne, Mike; Chakraborty, Arindam
2013-01-01
A resolution of identity approach to explicitly correlated congruent transformed Hamiltonian (CTH) is presented. One of the principle challenges associated with the congruent transformation of the many-electron Hamiltonian is the generation of three, four, five, and six particle operators. Successful application of the congruent transformation requires efficient implementation of the many-particle operators. In this work, we present the resolution of identity congruent transformed Hamiltonian (RI-CTH) method to handle many-particle operators. The resolution of identity was used to project the explicitly correlated operator in a N-particle finite basis to avoid explicit computation of the many-particle operators. Single-particle states were obtained by performing Hartee-Fock calculations, which were then used for construction of many-particle states. The limitation of the finite nature of the resolution of identity was addressed by developing partial infinite order (PIOS) diagrammatic summation technique. In t...
Diagonalizing the Hamiltonian of λϕ4 theory in 2 space-time dimensions
Christensen, Neil
2018-01-01
We propose a new non-perturbative technique for calculating the scattering amplitudes of field-theory directly from the eigenstates of the Hamiltonian. Our method involves a discretized momentum space and a momentum cutoff, thereby truncating the Hilbert space and making numerical diagonalization of the Hamiltonian achievable. We show how to do this in the context of a simplified λϕ4 theory in two space-time dimensions. We present the results of our diagonalization, its dependence on time, its dependence on the parameters of the theory and its renormalization.
{\\cal N}=2 supersymmetric extension of the Tremblay-Turbiner-Winternitz Hamiltonians on a plane
Quesne, C.
2010-07-01
The family of Tremblay-Turbiner-Winternitz Hamiltonians Hk on a plane, corresponding to any positive real value of k, is shown to admit an {\\cal N} = 2 supersymmetric extension of the same kind as that introduced by Freedman and Mende for the Calogero problem and based on an {osp}(2/2, \\mathbb {R}) \\sim {su}(1,1/1) superalgebra. The irreducible representations of the latter are characterized by the quantum number specifying the eigenvalues of the first integral of motion Xk of Hk. Bases for them are explicitly constructed. The ground state of each supersymmetrized Hamiltonian is shown to belong to an atypical lowest-weight state irreducible representation.
Resolutions of Identity for Some Non-Hermitian Hamiltonians. II. Proofs
Directory of Open Access Journals (Sweden)
Andrey V. Sokolov
2011-12-01
Full Text Available This part is a continuation of the Part I where we built resolutions of identity for certain non-Hermitian Hamiltonians constructed of biorthogonal sets of their eigen- and associated functions for the spectral problem defined on entire axis. Non-Hermitian Hamiltonians under consideration are taken with continuous spectrum and the following cases are examined: an exceptional point of arbitrary multiplicity situated on a boundary of continuous spectrum and an exceptional point situated inside of continuous spectrum. In the present work the rigorous proofs are given for the resolutions of identity in both cases.
Ground-State Analysis for an Exactly Solvable Coupled-Spin Hamiltonian
Directory of Open Access Journals (Sweden)
Eduardo Mattei
2013-11-01
Full Text Available We introduce a Hamiltonian for two interacting su(2 spins. We use a mean-field analysis and exact Bethe ansatz results to investigate the ground-state properties of the system in the classical limit, defined as the limit of infinite spin (or highest weight. Complementary insights are provided through investigation of the energy gap, ground-state fidelity, and ground-state entanglement, which are numerically computed for particular parameter values. Despite the simplicity of the model, a rich array of ground-state features are uncovered. Finally, we discuss how this model may be seen as an analogue of the exactly solvable p+ip pairing Hamiltonian.
Kinetic energy in the collective quadrupole Hamiltonian from the experimental data
Directory of Open Access Journals (Sweden)
R.V. Jolos
2017-06-01
Full Text Available Dependence of the kinetic energy term of the collective nuclear Hamiltonian on collective momentum is considered. It is shown that the fourth order in collective momentum term of the collective quadrupole Hamiltonian generates a sizable effect on the excitation energies and the matrix elements of the quadrupole moment operator. It is demonstrated that the results of calculation are sensitive to the values of some matrix elements of the quadrupole moment. It stresses the importance for a concrete nucleus to have the experimental data for the reduced matrix elements of the quadrupole moment operator taken between all low lying states with the angular momenta not exceeding 4.
k centre dot p Hamiltonians for quantum dots in a magnetic field
Planelles, J
2003-01-01
The problem of multiband k centre dot p Hamiltonians describing the hole energy structure of semiconductor nanosystems in a magnetic field is addressed. The approximate formulation given previously by Luttinger is revisited. We show that interaction with a magnetic field enters into the multiband equations for the envelope function components through the usual quadratic term and two linear Zeeman terms. The first linear term corresponds to the envelope angular momentum, while the other corresponds to the Bloch band-edge angular momentum. Several approximate ways of including the magnetic field in a four-band valence Hamiltonian are discussed and numerically compared. (letter to the editor)
On Reductions and Real Hamiltonian Forms of Affine Toda Field Theories
Gerdjikov, Vladimir S.; Grahovski, Georgi G.
2006-01-01
A family of real Hamiltonian forms (RHF) for the special class of affine 1+1 - dimensional Toda field theories is constructed. Thus the method, proposed in [Mikhailov;1981] for systems with finite number of degrees of freedom is generalized to infinite-dimensional Hamiltonian systems. We show that each of these RHF is related to a special Z_2-symmetry of the system of roots for the relevant Kac-Moody algebra. A number of explicit nontrivial examples of RHF of ATFT are presented.
Real Hamiltonian Forms of Affine Toda Models Related to Exceptional Lie Algebras
Directory of Open Access Journals (Sweden)
Vladimir S. Gerdjikov
2006-02-01
Full Text Available The construction of a family of real Hamiltonian forms (RHF for the special class of affine 1+1-dimensional Toda field theories (ATFT is reported. Thus the method, proposed in [1] for systems with finite number of degrees of freedom is generalized to infinite-dimensional Hamiltonian systems. The construction method is illustrated on the explicit nontrivial example of RHF of ATFT related to the exceptional algebras E_6 and E_7. The involutions of the local integrals of motion are proved by means of the classical R-matrix approach.
Recursion Operators and Tri-Hamiltonian Structure of the First Heavenly Equation of Plebański
Sheftel, Mikhail; Yazıcı, Devrim
2016-09-01
We present first heavenly equation of Plebański in a two-component evolutionary form and obtain Lagrangian and Hamiltonian representations of this system. We study all point symmetries of the two-component system and, using the inverse Noether theorem in the Hamiltonian form, obtain all the integrals of motion corresponding to each variational (Noether) symmetry. We derive two linearly independent recursion operators for symmetries of this system related by a discrete symmetry of both the two-component system and its symmetry condition. Acting by these operators on the first Hamiltonian operator J_0 we obtain second and third Hamiltonian operators. However, we were not able to find Hamiltonian densities corresponding to the latter two operators. Therefore, we construct two recursion operators, which are either even or odd, respectively, under the above-mentioned discrete symmetry. Acting with them on J_0, we generate another two Hamiltonian operators J_+ and J_- and find the corresponding Hamiltonian densities, thus obtaining second and third Hamiltonian representations for the first heavenly equation in a two-component form. Using P. Olver's theory of the functional multi-vectors, we check that the linear combination of J_0, J_+ and J_- with arbitrary constant coefficients satisfies Jacobi identities. Since their skew symmetry is obvious, these three operators are compatible Hamiltonian operators and hence we obtain a tri-Hamiltonian representation of the first heavenly equation. Our well-founded conjecture applied here is that P. Olver's method works fine for nonlocal operators and our proof of the Jacobi identities and bi-Hamiltonian structures crucially depends on the validity of this conjecture.
Quantum phase transitions in an effective Hamiltonian: fast and slow systems
Energy Technology Data Exchange (ETDEWEB)
Sainz, I [School of Information and Communication Technology, Royal Institute of Technology (KTH), Electrum 229, SE-164 40 Kista (Sweden); Klimov, A B [Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, 44420 Guadalajara, Jalisco (Mexico); Roa, L [Center for Quantum Optics and Quantum Information, Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion (Chile)], E-mail: klimov@cencar.udg.mx
2008-09-05
An effective Hamiltonian describing interaction between generic fast and slow systems is obtained in the strong interaction limit. The result is applied for studying the effect of quantum phase transition as a bifurcation of the ground state of the slow subsystem. Examples such as atom-field and atom-atom interactions are analyzed in detail.
Hamiltonian approach to GR - Part 2: covariant theory of quantum gravity
Cremaschini, Claudio; Tessarotto, Massimo
2017-05-01
A non-perturbative quantum field theory of General Relativity is presented which leads to a new realization of the theory of covariant quantum gravity (CQG-theory). The treatment is founded on the recently identified Hamiltonian structure associated with the classical space-time, i.e., the corresponding manifestly covariant Hamilton equations and the related Hamilton-Jacobi theory. The quantum Hamiltonian operator and the CQG-wave equation for the corresponding CQG-state and wave function are realized in 4-scalar form. The new quantum wave equation is shown to be equivalent to a set of quantum hydrodynamic equations which warrant the consistency with the classical GR Hamilton-Jacobi equation in the semiclassical limit. A perturbative approximation scheme is developed, which permits the adoption of the harmonic oscillator approximation for the treatment of the Hamiltonian potential. As an application of the theory, the stationary vacuum CQG-wave equation is studied, yielding a stationary equation for the CQG-state in terms of the 4-scalar invariant-energy eigenvalue associated with the corresponding approximate quantum Hamiltonian operator. The conditions for the existence of a discrete invariant-energy spectrum are pointed out. This yields a possible estimate for the graviton mass together with a new interpretation about the quantum origin of the cosmological constant.
Directory of Open Access Journals (Sweden)
Luis Mello
2017-11-01
Full Text Available In this article we study the existence and positions of limit cycles in piecewise smooth perturbations of planar Hamiltonian centers. By using the regularization method we provide an analytical expression for the first order Melnikov function frequently used in the literature directly from the original non-smooth problem.
Towards Ocean Grazer's Modular Power Take-Off System Modeling : A Port-Hamiltonian Approach
Barradas-Berglind, J. J.; Muñoz Arias, M.; Wei, Y.; Prins, W.A.; Vakis, A.I.; Jayawardhana, B.; Dochain, Denis; Henrion, Didier; Peaucelle, Dimitri
This paper presents a modular modeling framework for the Ocean Grazer's Power Take-Off (PTO) system, which operates as an array of point-absorber type devices connected to a hydraulic system. The modeling is based on the port-Hamiltonian (PH) framework that enables energy-based analysis and control
Hamiltonian approach to GR. Pt. 2. Covariant theory of quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Cremaschini, Claudio [Faculty of Philosophy and Science, Silesian University in Opava, Institute of Physics and Research Center for Theoretical Physics and Astrophysics, Opava (Czech Republic); Tessarotto, Massimo [University of Trieste, Department of Mathematics and Geosciences, Trieste (Italy); Faculty of Philosophy and Science, Silesian University in Opava, Institute of Physics, Opava (Czech Republic)
2017-05-15
A non-perturbative quantum field theory of General Relativity is presented which leads to a new realization of the theory of covariant quantum gravity (CQG-theory). The treatment is founded on the recently identified Hamiltonian structure associated with the classical space-time, i.e., the corresponding manifestly covariant Hamilton equations and the related Hamilton-Jacobi theory. The quantum Hamiltonian operator and the CQG-wave equation for the corresponding CQG-state and wave function are realized in 4-scalar form. The new quantum wave equation is shown to be equivalent to a set of quantum hydrodynamic equations which warrant the consistency with the classical GR Hamilton-Jacobi equation in the semiclassical limit. A perturbative approximation scheme is developed, which permits the adoption of the harmonic oscillator approximation for the treatment of the Hamiltonian potential. As an application of the theory, the stationary vacuum CQG-wave equation is studied, yielding a stationary equation for the CQG-state in terms of the 4-scalar invariant-energy eigenvalue associated with the corresponding approximate quantum Hamiltonian operator. The conditions for the existence of a discrete invariant-energy spectrum are pointed out. This yields a possible estimate for the graviton mass together with a new interpretation about the quantum origin of the cosmological constant. (orig.)
Port-Hamiltonian formulation of shallow water equations with Coriolis force and topography
Ramkrishna Pasumarthy, R.P.; Ambati, V.R.; van der Schaft, Arjan
2008-01-01
We look into the problem of approximating the shallow water equations with Coriolis forces and topography. We model the system as an in��?nite-dimensional port-Hamiltonian system which is represented by a non-constant Stokes-Dirac structure. We here employ the idea of using diﬀerent ��?nite elements
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.
Darboux integrability of 2-dimensional Hamiltonian systems with homogenous potentials of degree 3
Energy Technology Data Exchange (ETDEWEB)
Llibre, Jaume, E-mail: jllibre@mat.uab.cat [Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia (Spain); Valls, Claudia, E-mail: cvalls@math.ist.utl.pt [Departamento de Matemática, Instituto Superior Técnico, Universidade Técnica de Lisboa, Av. Rovisco Pais 1049-001, Lisboa (Portugal)
2014-03-15
We provide a characterization of all Hamiltonian systems of the form H=(p{sub 1}{sup 2}+p{sub 2}{sup 2})/2+V(q{sub 1},q{sub 2}), where V is a homogenous polynomial of degree 3 which are completely integrable with Darboux first integrals.
The Hourglass - Consequences of Pure Hamiltonian Evolution of a Radiating System
McCartor, Donald
2007-01-01
Hourglass is the name given here to a formal isolated quantum system that can radiate. Starting from a time when it defines the system it represents clearly and no radiation is present, it is given straightforward Hamiltonian evolution. The question of what significance hourglasses have is raised, and this question is proposed to be more consequential than the measurement problem.
Non-Hermitian Hamiltonians with a real spectrum and their physical ...
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 73; Issue 2 ... attempts to understand the role of pseudo-Hermitian and P T -symmetric Hamiltonians in modelling unitary quantum systems and elaborate on a particular physical phenomenon whose discovery originated in the study of complex scattering potentials.
Energy Shaping of Port-Hamiltonian Systems by Using Alternate Passive Input-Output Pairs
Venkatraman, A.; Schaft, A. van der
2010-01-01
We consider port-Hamiltonian systems with dissipation (PHSD) whose underlying geometric structure is represented as the composition of a Dirac and a resistive structure. We show how the choice of a new passive input-output pair for a PHSD is reflected in a new Dirac structure. We define a general
Doria-Cerezo, A.; van der Heijden, L.; Scherpen, J. M. A.
2013-01-01
This paper presents the use of the memristor as a new element for designing passivity-based controllers. From the port-Hamiltonian description of the electrical circuits with memristors, a target dynamics is assigned to the matching equation proposed by the methodology known as Interconnection and
Strictly convex loss functions for port-Hamiltonian based optimization algorithm for MTDC networks
Benedito, Ernest; del Puerto Flores, Dunstano; Doria-Cerezo, A.; van der Feltz, Olivier; Scherpen, Jacquelien M.A.
2016-01-01
In this work we propose a primal-dual method that can be cast in a port-Hamiltonian framework for minimizing the power losses in a multi-terminal DC network. The main contribution consists of proposing an alternative power loss function by means of a change of variables that translates the convex
Modelling very-high-eccentricity asteroidal librations with the Andoyer Hamiltonian.
Simula, A.; Ferraz-Mello, S.; Giordano, C.
High eccentricity asteroidal librations are modelled using a tailored Hamiltonian which is built from the high eccentricity non planar asymmetric expansion (Roig et al. 1998). We show that, using the reducing Sessin's rotation, the Hamiltonian of the pseudo circular model is actually a first order Andoyer Hamiltonian. This Hamiltonian has already been used by Henrard, at least for a numerical study, as a second fundamental model for resonance. A different approach was followed by Ferraz-Mello, who carried on the integration of the equations of motion in formal way by the use of the Jacobian elliptic functions. This second approach permits an explicit description of the asteroidal dynamics combined with a very precise analytical computation of the frequencies. We use this analytical approach for the study of asteroidal librations. Secular perturbations of the perturber's orbit can also be considered in the dynamics, together with the short periodic variations of Jupiter's orbit associated to the 5/2 near-commensurability between Jupiter and Saturn. Some preliminary results are shown.
Broer, H.W.; Lunter, G.A; Vegter, G.
1998-01-01
We consider Hamiltonian systems near equilibrium that can be (formally) reduced to one degree of freedom. Spatiotemporal symmetries play a key role. The planar reduction is studied by equivariant singularity theory with distinguished parameters. The method is illustrated on the conservative
Directory of Open Access Journals (Sweden)
Alexander A. Andrianov
2011-12-01
Full Text Available Resolutions of identity for certain non-Hermitian Hamiltonians constructed from biorthogonal sets of their eigen- and associated functions are given for the spectral problem defined on entire axis. Non-Hermitian Hamiltonians under consideration possess the continuous spectrum and the following peculiarities are investigated: (1 the case when there is an exceptional point of arbitrary multiplicity situated on a boundary of continuous spectrum; (2 the case when there is an exceptional point situated inside of continuous spectrum. The reductions of the derived resolutions of identity under narrowing of the classes of employed test functions are revealed. It is shown that in the case (1 some of associated functions included into the resolution of identity are normalizable and some of them may be not and in the case (2 the bounded associated function corresponding to the exceptional point does not belong to the physical state space. Spectral properties of a SUSY partner Hamiltonian for the Hamiltonian with an exceptional point are examined.
Wang, Kai; Yang, Yanzhi; Chodera, John D.; Shirts, Michael R.
2014-01-01
We present a method to identify small molecule ligand binding sites and orientations to a given protein crystal structure using GPU-accelerated Hamiltonian replica exchange molecular dynamics simulations. The Hamiltonians used vary from the physical end state of protein interacting with the ligand to a unphysical end state where the ligand does not interact with the protein. As replicas explore the space of Hamiltonians interpolating between these states the ligand can rapidly escape local minima and explore potential binding sites. Geometric restraints keep the ligands within the protein volume, and a potential energy pathway designed to increase phase space overlap between intermediates ensures good mixing. Because of the rigorous statistical mechanical nature of the Hamiltonian exchange framework, we can also extract binding free energy estimates at all putative binding sites, which agree well with free energies computed from occupation probabilities. We present results of this methodology on the T4 lysozyme L99A model system with four ligands, including one non-binder as a control. We find that our methodology identifies the crystallographic binding sites consistently and accurately for the small number of ligands considered here and gives free energies consistent with experiment. We are also able to analyze the contribution of individual binding sites on the overall binding affinity. Our methodology points to near term potential applications in early-stage drug discovery. PMID:24297454
Hamiltonian formulation of the conservative self-force dynamics in the Kerr geometry
Fujita, Ryuichi; Isoyama, Soichiro; Le Tiec, Alexandre; Nakano, Hiroyuki; Sago, Norichika; Tanaka, Takahiro
2017-07-01
We formulate a Hamiltonian description of the orbital motion of a point particle in Kerr spacetime for generic (eccentric, inclined) orbits, which accounts for the effects of the conservative part of the gravitational self-force. This formulation relies on a description of the particle’s motion as geodesic in a certain smooth effective spacetime, in terms of (generalized) action-angle variables. Clarifying the role played by the gauge freedom in the Hamiltonian dynamics, we extract the gauge-invariant information contained in the conservative self-force. We also propose a possible gauge choice for which the orbital dynamics can be described by an effective Hamiltonian, written solely in terms of the action variables. As an application of our Hamiltonian formulation in this gauge, we derive the conservative self-force correction to the orbital frequencies of Kerr innermost stable spherical (inclined or circular) orbits. This gauge choice also allows us to establish a ‘first law of mechanics’ for black-hole-particle binary systems, at leading order beyond the test-mass approximation.
On integrals, Hamiltonian and metriplectic formulations of polynomial systems in 3D
Directory of Open Access Journals (Sweden)
Esen Oğul
2017-01-01
Full Text Available The first integrals of the reduced three-wave interaction problem, the Rabinovich system, the Hindmarsh-Rose model, and the Oregonator model are derived using the method of Darboux polynomials. It is shown that, the reduced three-wave interaction problem, the Rabinovich system, the Hindmarsh-Rose model can be written in a bi-Hamiltonian/Nambu metriplectic form.
Hamiltonian approach to GR - Part 1: covariant theory of classical gravity
Cremaschini, Claudio
2016-01-01
A challenging issue in General Relativity concerns the determination of the manifestly-covariant continuum Hamiltonian structure underlying the Einstein field equations and the related formulation of the corresponding covariant Hamilton-Jacobi theory. The task is achieved by adopting a synchronous variational principle requiring distinction between the prescribed deterministic metric tensor $\\hat{g}(r)\\equiv \\left\\{ \\hat{g}_{\\mu \
Eckart ro-vibrational Hamiltonians via the gateway Hamilton operator: Theory and practice
Szalay, Viktor
2017-03-01
Recently, a general expression for Eckart-frame Hamilton operators has been obtained by the gateway Hamiltonian method [V. Szalay, J. Chem. Phys. 142, 174107 (2015) and V. Szalay, J. Chem. Phys. 143, 064104 (2015)]. The kinetic energy operator in this general Hamiltonian is nearly identical to that of the Eckart-Watson operator even when curvilinear vibrational coordinates are employed. Its different realizations correspond to different methods of calculating Eckart displacements. There are at least two different methods for calculating such displacements: rotation and projection. In this communication, the application of Eckart Hamiltonian operators constructed by rotation and projection, respectively, is numerically demonstrated in calculating vibrational energy levels. The numerical examples confirm that there is no need for rotation to construct an Eckart ro-vibrational Hamiltonian. The application of the gateway method is advantageous even when rotation is used since it obviates the need for differentiation of the matrix rotating into the Eckart frame. Simple geometrical arguments explain that there are infinitely many different methods for calculating Eckart displacements. The geometrical picture also suggests that a unique Eckart displacement vector may be defined as the shortest (mass-weighted) Eckart displacement vector among Eckart displacement vectors corresponding to configurations related by rotation. Its length, as shown analytically and demonstrated by numerical examples, is equal to or less than that of the Eckart displacement vector one can obtain by rotation to the Eckart frame.
Subharmonic solutions of planar Hamiltonian systems via the Poincaré́-Birkhoff theorem
Directory of Open Access Journals (Sweden)
Alberto Boscaggin
2011-06-01
Full Text Available We revisit some recent results obtained in [1] about the existence of subharmonic solutions for a class of (nonautonomous planar Hamiltonian systems, and we compare them with the existing literature. New applications to undamped second order equations are discussed, as well.
Franck-Condon Factors for Diatomics: Insights and Analysis Using the Fourier Grid Hamiltonian Method
Ghosh, Supriya; Dixit, Mayank Kumar; Bhattacharyya, S. P.; Tembe, B. L.
2013-01-01
Franck-Condon factors (FCFs) play a crucial role in determining the intensities of the vibrational bands in electronic transitions. In this article, a relatively simple method to calculate the FCFs is illustrated. An algorithm for the Fourier Grid Hamiltonian (FGH) method for computing the vibrational wave functions and the corresponding energy…
A time-dependent Fourier grid Hamiltonian-based formulation of ...
Indian Academy of Sciences (India)
A large number of time-dependent quantum mechanical methods are currently avail- able in literature for handling a wide variety of dynamical problems [1,2]. One of these methods is the time-dependent Fourier grid Hamiltonian (TDFGH) method which evolved naturally as the time-dependent generalization [3,4] of the time ...
Polynomial integrability of Hamiltonian systems with homogeneous potentials of degree −k
Energy Technology Data Exchange (ETDEWEB)
Oliveira, Regilene, E-mail: regilene@icmc.usp.br [Departamento de Matemática, Instituto de Ciências Matemáticas e Computação, Universidade de São Paulo, Avenida Trabalhador São-carlense, 400, 13566-590, São Carlos, SP (Brazil); Valls, Claudia, E-mail: cvalls@math.ist.utl.pt [Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa (Portugal)
2016-12-01
In this paper we shall answer positively two open problems proposed by Llibre–Mahdi–Valls (2011) in [9]. More precisely, we characterize the polynomial integrability of Hamiltonian system with potentials given by the inverse of a homogeneous potential of degree k.
A convenient criterion under which Z{sub 2}-graded operators are Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Hussin, Veronique [Departement de Mathematiques et de Statistique, Universite de Montreal, C.P. 6128, succ. Centre-ville, Montreal, Quebec H3C 3J7 (Canada); Kiselev, Arthemy V, E-mail: hussin@dms.umontreal.ca, E-mail: A.V.Kiselev@rug.nl [Mathematical Institute, University of Utrecht, PO Box 80.010, 3508 TA Utrecht (Netherlands)
2011-03-01
We formulate a simple and convenient criterion under which skew-adjoint Z{sub 2}-graded total differential operators are Hamiltonian, provided that their images are closed under commutation in the Lie algebras of evolutionary vector fields on the infinite jet spaces for vector bundles over smooth manifolds.
Experimental Determination of the Hamiltonian for Synchrotron Motion with RF Phase Modulation
Energy Technology Data Exchange (ETDEWEB)
Minty, Michiko
2003-07-11
Synchrotron motion with rf phase modulation was studied experimentally. Poincare maps in the resonant processing frame were obtained from the experimental data and compared with the tori of the resonant Hamiltonian. The experimental data revealed island structure in longitudinal phase space. Experimental results for synchrotron motion excited by phase modulation at the third harmonic of the synchrotron frequency are also reported.
Statistical relevance of vorticity conservation with the Hamiltonian particle-mesh method
S. Dubinkina (Svetlana); J.E. Frank (Jason)
2009-01-01
htmlabstractWe conduct long simulations with a Hamiltonian particle-mesh method for ideal fluid flow, to determine the statistical mean vorticity field. Lagrangian and Eulerian statistical models are proposed for the discrete dynamics, and these are compared against numerical experiments. The
Efficient certification and simulation of local quantum many-body Hamiltonians
Holzäpfel, Milan; Plenio, Martin B.
2017-01-01
We discuss efficient simulation and certification of the dynamics induced by a quantum many-body Hamiltonian with short-ranged interactions, extending prior results for one-dimensional systems [Osborne, Phys. Rev. Lett. 97, 157202 (2006) and Lanyon, Maier et al, Nat. Phys. 13, 1158 (2017)] to lattices in arbitrary spatial dimensions.
Generalized Jaynes-Cummings Hamiltonians by shape-invariant hierarchies and their SUSY partners
Energy Technology Data Exchange (ETDEWEB)
Hussin, V [Centre de recherches mathematiques et Departement de mathematiques et de statistique, Universite de Montreal, C P 6128, succ. Centre-ville, Montreal (Quebec), H3C 3J7 (Canada); Kuru, S [Departamento de Fisica Teorica, Atomica y Optica, Universidad de Valladolid, 47071 Valladolid (Spain); Negro, J [Departamento de Fisica Teorica, Atomica y Optica, Universidad de Valladolid, 47071 Valladolid (Spain)
2006-09-08
A generalization of the matrix Jaynes-Cummings model in the rotating wave approximation is proposed by means of the shape-invariant hierarchies of scalar factorized Hamiltonians. A class of Darboux transformations (sometimes called SUSY transformations in this context) suitable for these generalized Jaynes-Cummings models is constructed. Finally one example is worked out using the methods developed.
Non-Hermitian Hamiltonians with a real spectrum and their physical ...
Indian Academy of Sciences (India)
physics pp. 269–277. Non-Hermitian Hamiltonians with a real spectrum and their physical applications. ALI MOSTAFAZADEH. Department of Mathematics, Koç University, 34450 Sariyer, Istanbul, Turkey. E-mail: amostafazadeh@ku.edu.tr. Abstract. We present an evaluation of some recent attempts to understand the role of.
Asymptotic Stabilization of Non-holonomic Port-controlled Hamiltonian Systems
DEFF Research Database (Denmark)
Sørensen, Mathias Jesper; Bendtsen, Jan Dimon; Andersen, Palle
2004-01-01
A novel method for asymptotic stabilization of a class of non-holonomic systems is presented. The method is based on the port-controlled Hamiltonian description of electro-mechanical systems. The general system is augmented with so-called kinematic inputs, thus representing a special class of mob...
Eckart ro-vibrational Hamiltonians via the gateway Hamilton operator: Theory and practice.
Szalay, Viktor
2017-03-28
Recently, a general expression for Eckart-frame Hamilton operators has been obtained by the gateway Hamiltonian method [V. Szalay, J. Chem. Phys. 142, 174107 (2015) and V. Szalay, J. Chem. Phys. 143, 064104 (2015)]. The kinetic energy operator in this general Hamiltonian is nearly identical to that of the Eckart-Watson operator even when curvilinear vibrational coordinates are employed. Its different realizations correspond to different methods of calculating Eckart displacements. There are at least two different methods for calculating such displacements: rotation and projection. In this communication, the application of Eckart Hamiltonian operators constructed by rotation and projection, respectively, is numerically demonstrated in calculating vibrational energy levels. The numerical examples confirm that there is no need for rotation to construct an Eckart ro-vibrational Hamiltonian. The application of the gateway method is advantageous even when rotation is used since it obviates the need for differentiation of the matrix rotating into the Eckart frame. Simple geometrical arguments explain that there are infinitely many different methods for calculating Eckart displacements. The geometrical picture also suggests that a unique Eckart displacement vector may be defined as the shortest (mass-weighted) Eckart displacement vector among Eckart displacement vectors corresponding to configurations related by rotation. Its length, as shown analytically and demonstrated by numerical examples, is equal to or less than that of the Eckart displacement vector one can obtain by rotation to the Eckart frame.
The solution of the Schroedinger equation for complex Hamiltonian systems in two dimensions
Energy Technology Data Exchange (ETDEWEB)
Chand, Fakir [Department of Physics, Kurukshetra University, Kurukshetra-136 119, Haryana (India); Singh, Ram Mehar [Department of Physics, Haryana College of Technology and Management, Kaithal-136 027, Haryana (India); Kumar, Narender [Department of Physics, Kurukshetra University, Kurukshetra-136 119, Haryana (India); Mishra, S C [Department of Physics, Kurukshetra University, Kurukshetra-136 119, Haryana (India)
2007-08-17
We investigate the ground state solutions of the Schroedinger equation for complex (non-Hermitian) Hamiltonian systems in two dimensions within the framework of an extended complex phase-space approach. The eigenvalues and eigenfunctions of some two-dimensional complex potentials are found.
Control by Interconnection and Standard Passivity-Based Control of Port-Hamiltonian Systems
Ortega, Romeo; Schaft, Arjan van der; Castaños, Fernando; Astolfi, Alessandro
2008-01-01
The dynamics of many physical processes can be suitably described by Port-Hamiltonian (PH) models, where the importance of the energy function, the interconnection pattern and the dissipation of the system is underscored. To regulate the behavior of PH systems it is natural to adopt a
Hamiltonian description of the topology of drift orbits of relativistic particles in a tokamak
de Rover, M.; Cardozo, N. J. L.; Montvai, A.
1996-01-01
Using classical perturbation theory, a Hamiltonian description of the guiding center motion of relativistic electrons in a torus with an axially symmetric magnetic field is derived. The magnetic field itself generates concentric circular flux surfaces. This description enables us to assess the
Rath, Biswanath; Mallick, P.
2014-01-01
A new method for generating analytical expression of quantum Hamiltonian from non-linear differential equation with stationary energy level has been formulated.Further calculation of energy levels have been carried out analytically using and numerically using matrix diagonalisation method.
Regulation and input disturbance suppression for port-controlled Hamiltonian systems
Gentili, L.; Astolfi, A.; van der Schaft, Arjan; Gordillo, F.
2003-01-01
In this paper the output feedback regulation problem for port-controlled Hamiltonian systems (PCHS) is addressed. Following the nonlinear output regulation theory, the regulator which solves the problem is given by a parallel connection of two subcontrollers: an internal model unit and a regulator
Change in Hamiltonian general relativity from the lack of a time-like Killing vector field
Pitts, J. Brian
2014-08-01
In General Relativity in Hamiltonian form, change has seemed to be missing, defined only asymptotically, or otherwise obscured at best, because the Hamiltonian is a sum of first-class constraints and a boundary term and thus supposedly generates gauge transformations. Attention to the gauge generator G of Rosenfeld, Anderson, Bergmann, Castellani et al., a specially tuned sum of first-class constraints, facilitates seeing that a solitary first-class constraint in fact generates not a gauge transformation, but a bad physical change in electromagnetism (changing the electric field) or General Relativity. The change spoils the Lagrangian constraints, Gauss's law or the Gauss-Codazzi relations describing embedding of space into space-time, in terms of the physically relevant velocities rather than auxiliary canonical momenta. While Maudlin and Healey have defended change in GR much as G. E. Moore resisted skepticism, there remains a need to exhibit the technical flaws in the no-change argument. Insistence on Hamiltonian-Lagrangian equivalence, a theme emphasized by Mukunda, Castellani, Sugano, Pons, Salisbury, Shepley and Sundermeyer among others, holds the key. Taking objective change to be ineliminable time dependence, one recalls that there is change in vacuum GR just in case there is no time-like vector field ξα satisfying Killing's equation £ξgμν = 0, because then there exists no coordinate system such that everything is independent of time. Throwing away the spatial dependence of GR for convenience, one finds explicitly that the time evolution from Hamilton's equations is real change just when there is no time-like Killing vector. The inclusion of a massive scalar field is simple. No obstruction is expected in including spatial dependence and coupling more general matter fields. Hence change is real and local even in the Hamiltonian formalism. The considerations here resolve the Earman-Maudlin standoff over change in Hamiltonian General Relativity: the
Giese, Timothy John
This work describes the development and validation of many-body force fields and semiempirical Hamiltonians as part of a multi-scale modeling effort by the York Group targeted at biological applications. Basic science effort is spent towards the testing of existing polarizable force field functional forms in the areas of charge transfer and the coupling of polarization with many-body exchange. A new semiempirical model (MNDO/d+CPE) is developed by a novel combination of the modified neglect of diatomic overlap with extension to d-orbitals (MNDO/d) semiempirical Hamiltonian with a set of charge-dependent, atom-centered, density response dipole functions. It is shown that existing semiempirical Hamiltonians severely under-predict the polarizability of atoms and molecules whereas the MNDO/d+CPE model reduces the errors across a wide range of charge states (2- to 2+) by an order of magnitude. Another semiempirical Hamiltonian (PM3 BP) is created through a reparametrization of the PM3 Hamiltonian to model hydrogen bonded nucleic acid base pairs. A large database of molecules (on-line at http://theory.chem.umn.edu/QCRNA) for the purpose of parametrizing future models is described. Semiempirical methods lack treatment for long-range London dispersion forces. Therefore, basic science work is performed on van der Waals systems with a large emphasis on rare gas dimers. The accurate calculation of dispersion interactions from ab initio is very computationally intensive. Therefore, a new multicoefficient correlation method is developed to decrease the computational effort required to obtain a large collection of van der Waals interaction energy reference data.
Magnetic Hamiltonian and phase diagram of the quantum spin liquid Ca10Cr7O28
Balz, Christian; Lake, Bella; Nazmul Islam, A. T. M.; Singh, Yogesh; Rodriguez-Rivera, Jose A.; Guidi, Tatiana; Wheeler, Elisa M.; Simeoni, Giovanna G.; Ryll, Hanjo
2017-05-01
A spin liquid is a new state of matter with topological order where the spin moments continue to fluctuate coherently down to the lowest temperatures rather than develop static long-range magnetic order as found in conventional magnets. For spin liquid behavior to arise in a material the magnetic Hamiltonian must be "frustrated", where the combination of lattice geometry, interactions, and anisotropies gives rise to competing spin arrangements in the ground state. Theoretical Hamiltonians which produce spin liquids are spin ice, the Kitaev honeycomb model, and the kagome antiferromagnet. Spin liquid behavior, however, in real materials is rare because they can only approximate these Hamiltonians and often have weak higher-order terms that destroy the spin liquid state. Ca10Cr7O28 is a new quantum spin liquid candidate with magnetic Cr5 + ions that possess quantum spin number S =½ . The spins are entirely dynamic in the ground state and the excitation spectrum is broad and diffuse, as is typical of spinons which are the excitations of a spin liquid. In this paper we determine the Hamiltonian of Ca10Cr7O28 using inelastic neutron scattering under high magnetic field to induce a field-polarized paramagnetic ground state and spin-wave excitations that can be fitted to extract the interactions. We further explore the phase diagram by using inelastic neutron scattering and heat capacity measurements and establish the boundaries of the spin liquid phase as a function of magnetic field and temperature. Our results show that Ca10Cr7O28 consists of distorted kagome bilayers with several isotropic ferromagnetic and antiferromagnetic interactions where, unexpectedly, the ferromagnetic interactions are stronger than the antiferromagnetic ones. This complex Hamiltonian does not correspond to any known spin liquid model and points to new directions in the search for quantum spin liquid behavior.
A Hamiltonian Approach to Fault Isolation in a Planar Vertical Take–Off and Landing Aircraft Model
Directory of Open Access Journals (Sweden)
Rodriguez-Alfaro Luis H.
2015-03-01
Full Text Available The problem of fault detection and isolation in a class of nonlinear systems having a Hamiltonian representation is considered. In particular, a model of a planar vertical take-off and landing aircraft with sensor and actuator faults is studied. A Hamiltonian representation is derived from an Euler-Lagrange representation of the system model considered. In this form, nonlinear decoupling is applied in order to obtain subsystems with (as much as possible specific fault sensitivity properties. The resulting decoupled subsystem is represented as a Hamiltonian system and observer-based residual generators are designed. The results are presented through simulations to show the effectiveness of the proposed approach.
Hamiltonian approach to QCD in Coulomb gauge: Gribov’s confinement scenario at work*
Directory of Open Access Journals (Sweden)
Reinhardt H.
2017-01-01
Full Text Available I will review essential features of the Hamiltonian approach to QCD in Coulomb gauge showing that Gribov's confinement scenario is realized in this gauge. For this purpose I will discuss in detail the emergence of the horizon condition and the Coulomb string tension. I will show that both are induced by center vortex gauge field configurations, which establish the connection between Gribov’s confinement scenario and the center vortex picture of confinement. I will then extend the Hamiltonian approach to QCD in Coulomb gauge to finite temperatures, first by the usual grand canonical ensemble and second by the compactification of a spatial dimension. I will present results for the pressure, energy density and interaction measure as well as for the Polyakov loop.
Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space.
Poulin, David; Qarry, Angie; Somma, Rolando; Verstraete, Frank
2011-04-29
We consider the manifold of all quantum many-body states that can be generated by arbitrary time-dependent local Hamiltonians in a time that scales polynomially in the system size, and show that it occupies an exponentially small volume in Hilbert space. This implies that the overwhelming majority of states in Hilbert space are not physical as they can only be produced after an exponentially long time. We establish this fact by making use of a time-dependent generalization of the Suzuki-Trotter expansion, followed by a well-known counting argument. This also demonstrates that a computational model based on arbitrarily rapidly changing Hamiltonians is no more powerful than the standard quantum circuit model.
Introduction to Hamiltonian dynamical systems and the N-body problem
Meyer, Kenneth R
2017-01-01
This third edition text provides expanded material on the restricted three body problem and celestial mechanics. With each chapter containing new content, readers are provided with new material on reduction, orbifolds, and the regularization of the Kepler problem, all of which are provided with applications. The previous editions grew out of graduate level courses in mathematics, engineering, and physics given at several different universities. The courses took students who had some background in differential equations and lead them through a systematic grounding in the theory of Hamiltonian mechanics from a dynamical systems point of view. This text provides a mathematical structure of celestial mechanics ideal for beginners, and will be useful to graduate students and researchers alike. Reviews of the second edition: "The primary subject here is the basic theory of Hamiltonian differential equations studied from the perspective of differential dynamical systems. The N-body problem is used as the primary exa...
Chen, Yongpin P; Jiang, Li Jun; Meng, Min; Wu, Yu Mao; Chew, Weng Cho
2016-01-01
A novel unified Hamiltonian approach is proposed to solve Maxwell-Schrodinger equation for modeling the interaction between classical electromagnetic (EM) fields and particles. Based on the Hamiltonian of electromagnetics and quantum mechanics, a unified Maxwell-Schrodinger system is derived by the variational principle. The coupled system is well-posed and symplectic, which ensures energy conserving property during the time evolution. However, due to the disparity of wavelengths of EM waves and that of electron waves, a numerical implementation of the finite-difference time-domain (FDTD) method to the multiscale coupled system is extremely challenging. To overcome this difficulty, a reduced eigenmode expansion technique is first applied to represent the wave function of the particle. Then, a set of ordinary differential equations (ODEs) governing the time evolution of the slowly-varying expansion coefficients are derived to replace the original Schrodinger equation. Finally, Maxwell's equations represented b...
Resistance of a 1D random chain: Hamiltonian version of the transfer matrix approach
Dossetti-Romero, V.; Izrailev, F. M.; Krokhin, A. A.
2004-01-01
We study some mesoscopic properties of electron transport by employing one-dimensional chains and Anderson tight-binding model. Principal attention is paid to the resistance of finite-length chains with disordered white-noise potential. We develop a new version of the transfer matrix approach based on the equivalency of a discrete Schrödinger equation and a two-dimensional Hamiltonian map describing a parametric kicked oscillator. In the two limiting cases of ballistic and localized regime we demonstrate how analytical results for the mean resistance and its second moment can be derived directly from the averaging over classical trajectories of the Hamiltonian map. We also discuss the implication of the single parameter scaling hypothesis to the resistance.
Hamiltonian models for the propagation of irrotational surface gravity waves over a variable bottom.
Compelli, A; Ivanov, R; Todorov, M
2018-01-28
A single incompressible, inviscid, irrotational fluid medium bounded by a free surface and varying bottom is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the surface waves are presented in Hamiltonian form. Specific scaling of the variables is selected which leads to approximations of Boussinesq and Korteweg-de Vries (KdV) types, taking into account the effect of the slowly varying bottom. The arising KdV equation with variable coefficients is studied numerically when the initial condition is in the form of the one-soliton solution for the initial depth.This article is part of the theme issue 'Nonlinear water waves'. © 2017 The Author(s).
DEFF Research Database (Denmark)
Zhang, N.G.; Henley, C.L.; Rischel, C.
2002-01-01
We study the low-lying eigenenergy clustering patterns of quantum antiferromagnets with p sublattices (in particular p = 4). We treat each sublattice as a large spin, and using second-order degenerate perturbation theory, we derive the effective (biquadratic) Hamiltonian coupling the p large spins....... In order to compare with exact diagonalizations, the Hamiltonian is explicitly written for a finite-size lattice, and it contains information on energies of excited states as well as the ground state. The result is applied to the face-centered-cubic Type-I antiferromagnet of spin 1/2, including second......-neighbor interactions. A 32-site system is exactly diagonalized, and the energy spectrum of the low-lying singlets follows the analytically predicted clustering pattern....
Al-Refaie, Ahmed F.; Tennyson, Jonathan
2017-12-01
Construction and diagonalization of the Hamiltonian matrix is the rate-limiting step in most low-energy electron - molecule collision calculations. Tennyson (1996) implemented a novel algorithm for Hamiltonian construction which took advantage of the structure of the wavefunction in such calculations. This algorithm is re-engineered to make use of modern computer architectures and the use of appropriate diagonalizers is considered. Test calculations demonstrate that significant speed-ups can be gained using multiple CPUs. This opens the way to calculations which consider higher collision energies, larger molecules and / or more target states. The methodology, which is implemented as part of the UK molecular R-matrix codes (UKRMol and UKRMol+) can also be used for studies of bound molecular Rydberg states, photoionization and positron-molecule collisions.
Directory of Open Access Journals (Sweden)
Karim P. Y. Thébault
2011-03-01
Full Text Available Hamiltonian constraints feature in the canonical formulation of general relativity. Unlike typical constraints they cannot be associated with a reduction procedure leading to a non-trivial reduced phase space and this means the physical interpretation of their quantum analogues is ambiguous. In particular, can we assume that “quantisation commutes with reduction” and treat the promotion of these constraints to operators annihilating the wave function, according to a Dirac type procedure, as leading to a Hilbert space equivalent to that reached by quantisation of the problematic reduced space? If not, how should we interpret Hamiltonian constraints quantum mechanically? And on what basis do we assert that quantisation and reduction commute anyway? These questions will be refined and explored in the context of modern approaches to the quantisation of canonical general relativity.
Exact Hamiltonians with Rashba and cubic Dresselhaus spin-orbit couplings on a curved surface
Chang, Jian-Yuan; Wu, Jhih-Sheng; Chang, Ching-Ray
2013-05-01
The exact Hamiltonians for Rashba and cubic Dresselhaus spin-orbit couplings on a curved surface with an arbitrary shape are rigorously derived. Two orthogonal principal curvatures dominate the electronic spin transport, and the asymptotic behavior of the normal confined potential on a curved surface is insignificant. For a curved surface with a large curvature, the higher order momentum terms play an important role in controlling spin transport. The Rashba spin-orbit coupling on a curved surface only induces the extra pseudopotential term, and the cubic Dresselhaus spin-orbit coupling on a curved surface can induce the extra pseudokinetic and pseudomomentum terms. Because of the extra curvature-induced terms and the associated pseudomagnetic fields, spin transport on a curved surface is very different from that on a flat surface. The Hamiltonians on both cylindrical and spherical surfaces are explicitly derived here, and the associated physical properties of electrons are studied in detail.
PREFACE: 6th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics
Fring, Andreas; Jones, Hugh; Znojil, Miloslav
2008-06-01
Attempts to understand the quantum mechanics of non-Hermitian Hamiltonian systems can be traced back to the early days, one example being Heisenberg's endeavour to formulate a consistent model involving an indefinite metric. Over the years non-Hermitian Hamiltonians whose spectra were believed to be real have appeared from time to time in the literature, for instance in the study of strong interactions at high energies via Regge models, in condensed matter physics in the context of the XXZ-spin chain, in interacting boson models in nuclear physics, in integrable quantum field theories as Toda field theories with complex coupling constants, and also very recently in a field theoretical scenario in the quantization procedure of strings on an AdS5 x S5 background. Concrete experimental realizations of these types of systems in the form of optical lattices have been proposed in 2007. In the area of mathematical physics similar non-systematic results appeared sporadically over the years. However, intensive and more systematic investigation of these types of non- Hermitian Hamiltonians with real eigenvalue spectra only began about ten years ago, when the surprising discovery was made that a large class of one-particle systems perturbed by a simple non-Hermitian potential term possesses a real energy spectrum. Since then regular international workshops devoted to this theme have taken place. This special issue is centred around the 6th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics held in July 2007 at City University London. All the contributions contain significant new results or alternatively provide a survey of the state of the art of the subject or a critical assessment of the present understanding of the topic and a discussion of open problems. Original contributions from non-participants were also invited. Meanwhile many interesting results have been obtained and consensus has been reached on various central conceptual issues in the
DEFF Research Database (Denmark)
Flensberg, Karsten; Svensmark, Henrik
1993-01-01
The dynamics and the stability of a forced damped nonlinear oscillator driven at twice its resonance frequency is studied. At the transition from a dissipative system to a Hamiltonian system, simple scalings relations are found by the use of the Floquet theory of the linearized problem. The Floqu...... exponents and the period-doubling bifurcation point are determined analytically in the limit of small damping. The theory is compared to numerical calculations on a Duffing oscillator and excellent agreement is found....
Full-field drift Hamiltonian particle orbits in axisymmetric tokamak geometry
Cooper, W.A.; Cooper, G.A.; Graves, J P; Isaev, M. Yu
2011-01-01
A Hamiltonian/Lagrangian theory to describe guiding center orbit drift motion that is canonical in Boozer magnetic coordinates is developed to include full electrostatic and electromagnetic perturbed fields in axisymmetric tokamak geometry. Furthermore, the radial component of the equilibrium magnetic field in the covariant representation is retained and the background equilibrium state extends to anisotropic plasma pressure conditions. A gauge transformation on the perturbed vector potentia...
Full-field drift Hamiltonian particle orbits in 3D geometry
Cooper, W.A.; Graves, J P; Brunner, S. (Prof. Dr.); Isaev, M. Yu
2011-01-01
A Hamiltonian/Lagrangian theory to describe guiding centre orbit drift motion which is canonical in the Boozer coordinate frame has been extended to include full electromagnetic perturbed fields in anisotropic pressure 3D equilibria with nested magnetic flux surfaces. A redefinition of the guiding centre velocity to eliminate the motion due to finite equilibrium radial magnetic fields and the choice of a gauge condition that sets the radial component of the electromagnetic vector potential to...
A 2+1-Dimensional Non-Isothermal Magnetogasdynamic System. Hamiltonian-Ermakov Integrable Reduction
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Hongli An
2012-08-01
Full Text Available A 2+1-dimensional anisentropic magnetogasdynamic system with a polytropic gas law is shown to admit an integrable elliptic vortex reduction when γ=2 to a nonlinear dynamical subsystem with underlying integrable Hamiltonian-Ermakov structure. Exact solutions of the magnetogasdynamic system are thereby obtained which describe a rotating elliptic plasma cylinder. The semi-axes of the elliptical cross-section, remarkably, satisfy a Ermakov-Ray-Reid system.
A Port-Hamiltonian Approach to Optimal Frequency Regulation in Power Grids
Stegink, Tjerk; De Persis, Claudio; van der Schaft, Arjan
2015-01-01
This paper studies the problem of frequency regulation in power grids, while maximizing the social welfare. Two price-based controllers are proposed; the first one an internal-model-based controller and the second one based on a continuous gradient method for optimization. Both controllers can be implemented in a fully distributed fashion, with freedom in choosing a controller communication network. As a result, two real-time dynamic pricing models described by port- Hamiltonian systems are o...
Entropic Dynamics: from Entropy and Information Geometry to Hamiltonians and Quantum Mechanics
Caticha, Ariel; Bartolomeo, Daniel; Reginatto, Marcel
2014-01-01
Entropic Dynamics is a framework in which quantum theory is derived as an application of entropic methods of inference. There is no underlying action principle. Instead, the dynamics is driven by entropy subject to the appropriate constraints. In this paper we show how a Hamiltonian dynamics arises as a type of non-dissipative entropic dynamics. We also show that the particular form of the "quantum potential" that leads to the Schroedinger equation follows naturally from information geometry.
Directory of Open Access Journals (Sweden)
Sixing Tao
2013-01-01
Full Text Available Nonlinear integrable couplings of super Broer-Kaup-Kupershmidt hierarchy based upon an enlarged matrix Lie super algebra were constructed. Then its super Hamiltonian structures were established by using super trace identity, and the conserved functionals were proved to be in involution in pairs under the defined Poisson bracket. As its reduction, nonlinear integrable couplings of the classical integrable hierarchy were obtained.
Lattice Hamiltonian approach to the massless Schwinger model. Precise extraction of the mass gap
Energy Technology Data Exchange (ETDEWEB)
Cichy, Krzysztof [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Poznan Univ. (Poland). Faculty of Physics; Kujawa-Cichy, Agnieszka [Poznan Univ. (Poland). Faculty of Physics; Szyniszewski, Marcin [Poznan Univ. (Poland). Faculty of Physics; Manchester Univ. (United Kingdom). NOWNano DTC
2012-12-15
We present results of applying the Hamiltonian approach to the massless Schwinger model. A finite basis is constructed using the strong coupling expansion to a very high order. Using exact diagonalization, the continuum limit can be reliably approached. This allows to reproduce the analytical results for the ground state energy, as well as the vector and scalar mass gaps to an outstanding precision better than 10{sup -6} %.
Existence for stationary mean-field games with congestion and quadratic Hamiltonians
Gomes, Diogo A.
2015-09-03
Here, we investigate the existence of solutions to a stationary mean-field game model introduced by J.-M. Lasry and P.-L. Lions. This model features a quadratic Hamiltonian and congestion effects. The fundamental difficulty of potential singular behavior is caused by congestion. Thanks to a new class of a priori bounds, combined with the continuation method, we prove the existence of smooth solutions in arbitrary dimensions. © 2015 Springer Basel
Projection formalism for constrained dynamical systems: from Newtonian to Hamiltonian mechanics.
Kneller, Gerald R
2007-10-28
The Hamiltonian of a holonomically constrained dynamical many-particle system in Cartesian coordinates has been recently derived for applications in statistical mechanics [G. R. Kneller, J. Chem. Phys. 125, 114107 (2006)]. Using the same projector formalism, we show here the equivalence of the corresponding equations of motion with those obtained from a Newtonian and a Lagrangian description. In the case of Newtonian mechanics, the general case of nonholonomic constraints is considered, too.
Lusanna, Luca
1995-01-01
A review is given of the presymplectic approach to relativistic physical systems and of the determination of their Dirac's observables. After relativistic mechanics and Nambu string, the Dirac's observables of Yang-Mills theory with fermions are given for the case of massless vector bosons (like in QED). A Dirac-Yukawa-like intrinsic ultraviolet cut-off is identified from the study of the covariantization of Hamiltonian classical field theory in the Dirac-Tomonaga-Schwinger sens. The implicat...
The Hamiltonian Structure-Preserving Control and Some Applications to Nonlinear Astrodynamics
Ming Xu; Yan Wei; Shengli Liu
2013-01-01
A systematic research on the structure-preserving controller is investigated in this paper, including its applications to the second-order, first-order, time-periodic, or degenerated astrodynamics, respectively. The general form of the controller is deduced for the typical Hamiltonian system in full feedback and position-only feedback modes, which is successful in changing the hyperbolic equilibrium to an elliptic one. With the poles assigned at any different positions on imaginary axis, the ...
Dubček, Tena; Lelas, Karlo; Jukić, Dario; Pezer, Robert; Soljačić, Marin; Buljan, Hrvoje
2015-12-01
We propose the realization of a grating assisted tunneling scheme for tunable synthetic magnetic fields in optically induced one- and two-dimensional dielectric photonic lattices. As a signature of the synthetic magnetic fields, we demonstrate conical diffraction patterns in particular realization of these lattices, which possess Dirac points in k-space. We compare the light propagation in these realistic (continuous) systems with the evolution in discrete models representing the Harper-Hofstadter Hamiltonian, and obtain excellent agreement.
Adiabatic approximation for the evolution generated by an A-uniformly pseudo-Hermitian Hamiltonian
Wang, Wenhua; Cao, Huaixin; Chen, Zhengli
2017-09-01
We discuss an adiabatic approximation for the evolution generated by an A-uniformly pseudo-Hermitian Hamiltonian H(t). Such a Hamiltonian is a time-dependent operator H(t) similar to a time-dependent Hermitian Hamiltonian G(t) under a time-independent invertible operator A. Using the relation between the solutions of the evolution equations H(t) and G(t), we prove that H(t) and H† (t) have the same real eigenvalues and the corresponding eigenvectors form two biorthogonal Riesz bases for the state space. For the adiabatic approximate solution in case of the minimum eigenvalue and the ground state of the operator H(t), we prove that this solution coincides with the system state at every instant if and only if the ground eigenvector is time-independent. We also find two upper bounds for the adiabatic approximation error in terms of the norm distance and in terms of the generalized fidelity. We illustrate the obtained results with several examples.
Olsen, Seth
2012-01-01
We propose a single effective Hamiltonian to describe the low-energy electronic structure of a series of symmetric cationic diarylmethanes, which are all bridge-substituted derivatives of Michler's Hydrol Blue. Three-state diabatic Hamiltonians for the dyes are calculated using four-electron three-orbital state-averaged complete active space self-consistent field and multi-state multi-reference perturbation theory models. The approach takes advantage of an isolobal analogy that can be established between the orbitals spanning the active spaces of the different substituted dyes. The solutions of the chemical problem are expressed in a diabatic Hilbert space that is analogous to classical resonance models. The effective Hamiltonians for all dyes can be fit to a single functional form that depends on the mixing angle between a bridge-charged diabatic state and a superposition representing the canonical resonance. We find that the structure of the bridge-charged state changes in a regular fashion across the serie...
A Hamiltonian driven quantum-like model for overdistribution in episodic memory recollection.
Broekaert, Jan B.; Busemeyer, Jerome R.
2017-06-01
While people famously forget genuine memories over time, they also tend to mistakenly over-recall equivalent memories concerning a given event. The memory phenomenon is known by the name of episodic overdistribution and occurs both in memories of disjunctions and partitions of mutually exclusive events and has been tested, modeled and documented in the literature. The total classical probability of recalling exclusive sub-events most often exceeds the probability of recalling the composed event, i.e. a subadditive total. We present a Hamiltonian driven propagation for the Quantum Episodic Memory model developed by Brainerd (et al., 2015) for the episodic memory overdistribution in the experimental immediate item false memory paradigm (Brainerd and Reyna, 2008, 2010, 2015). Following the Hamiltonian method of Busemeyer and Bruza (2012) our model adds time-evolution of the perceived memory state through the stages of the experimental process based on psychologically interpretable parameters - γ_c for recollection capability of cues, κ_p for bias or description-dependence by probes and β for the average gist component in the memory state at start. With seven parameters the Hamiltonian model shows good accuracy of predictions both in the EOD-disjunction and in the EOD-subadditivity paradigm. We noticed either an outspoken preponderance of the gist over verbatim trace, or the opposite, in the initial memory state when β is real. Only for complex β a mix of both traces is present in the initial state for the EOD-subadditivity paradigm.
DFT/MRCI Hamiltonian for odd and even numbers of electrons
Heil, Adrian; Marian, Christel M.
2017-11-01
DFT/MRCI is a well-established method of Grimme and Waletzke [J. Chem. Phys. 111, 5645 (1999)] combining density functional theory and multireference configuration interaction. It was later redesigned by Lyskov, Kleinschmidt, and Marian [J. Chem. Phys. 144, 034104 (2016)] to provide a better treatment of bi-chromophores while treating all other systems as well as Grimme's version did by computing individual energy shifts for each state function of a configuration. But all previous operators lack the ability to compute states with an odd number of electrons (doublet and quartet states). Here we present a general Hamiltonian based on Lyskov's redesign which calculates excited singlet, doublet, triplet, and quartet states of systems that have up to one open shell in the parent determinant. The multiplicity-independent correction parameters provide an extra correction for the open shell in the parent determinant. The Hamiltonian in combination with two parameter sets for different selection thresholds has been tested and compared to experimental vertical excitation and ionization energies yielding similar statistics for all multiplicities with a root mean square deviation smaller than 0.2 eV while maintaining the good computational performance of the Hamiltonians of Grimme and Lyskov.
Passive simulation of the nonlinear port-Hamiltonian modeling of a Rhodes Piano
Falaize, Antoine; Hélie, Thomas
2017-03-01
This paper deals with the time-domain simulation of an electro-mechanical piano: the Fender Rhodes. A simplified description of this multi-physical system is considered. It is composed of a hammer (nonlinear mechanical component), a cantilever beam (linear damped vibrating component) and a pickup (nonlinear magneto-electronic transducer). The approach is to propose a power-balanced formulation of the complete system, from which a guaranteed-passive simulation is derived to generate physically-based realistic sound synthesis. Theses issues are addressed in four steps. First, a class of Port-Hamiltonian Systems is introduced: these input-to-output systems fulfill a power balance that can be decomposed into conservative, dissipative and source parts. Second, physical models are proposed for each component and are recast in the port-Hamiltonian formulation. In particular, a finite-dimensional model of the cantilever beam is derived, based on a standard modal decomposition applied to the Euler-Bernoulli model. Third, these systems are interconnected, providing a nonlinear finite-dimensional Port-Hamiltonian System of the piano. Fourth, a passive-guaranteed numerical method is proposed. This method is built to preserve the power balance in the discrete-time domain, and more precisely, its decomposition structured into conservative, dissipative and source parts. Finally, simulations are performed for a set of physical parameters, based on empirical but realistic values. They provide a variety of audio signals which are perceptively relevant and qualitatively similar to some signals measured on a real instrument.
Nodal-line entanglement entropy: Generalized Widom formula from entanglement Hamiltonians
Pretko, Michael
2017-06-01
A system of fermions forming a Fermi surface exhibits a large degree of quantum entanglement, even in the absence of interactions. In particular, the usual case of a codimension one Fermi surface leads to a logarithmic violation of the area law for entanglement entropy as dictated by the Widom formula. We here generalize this formula to the case of arbitrary codimension, which is of particular interest for nodal lines in three dimensions. We first re-derive the standard Widom formula by calculating an entanglement Hamiltonian for Fermi-surface systems, obtained by repurposing a trick commonly applied to relativistic theories. The entanglement Hamiltonian will take a local form in terms of a low-energy patch theory for the Fermi surface, although it is nonlocal with respect to the microscopic fermions. This entanglement Hamiltonian can then be used to derive the entanglement entropy, yielding a result in agreement with the Widom formula. The method is then generalized to arbitrary codimension. For nodal lines, the area law is obeyed, and the magnitude of the coefficient for a particular partition is nonuniversal. However, the coefficient has a universal dependence on the shape and orientation of the nodal line relative to the partitioning surface. By comparing the relative magnitude of the area law for different partitioning cuts, entanglement entropy can be used as a tool for diagnosing the presence and shape of a nodal line in a ground-state wave function.
Quaternionic soliton equations from Hamiltonian curve flows in HP{sup n}
Energy Technology Data Exchange (ETDEWEB)
Anco, Stephen C; Asadi, Esmaeel [Department of Mathematics, Brock University, St Catharines, ON (Canada)], E-mail: sanco@brocku.ca, E-mail: easadi@brocku.ca
2009-12-04
A bi-Hamiltonian hierarchy of quaternion soliton equations is derived from geometric non-stretching flows of curves in the quaternionic projective space HP{sup n}. The derivation adapts the method and results in recent work by one of us on the Hamiltonian structure of non-stretching curve flows in Riemannian symmetric spaces M = G/H by viewing HP{sup n} as a symmetric space in terms of compact real symplectic groups and quaternion unitary groups. As main results, scalar-vector (multi-component) versions of the sine-Gordon (SG) equation and the modified Korteweg-de Vries (mKdV) equation are obtained along with their bi-Hamiltonian integrability structure consisting of a shared hierarchy of quaternionic symmetries and conservation laws generated by a hereditary recursion operator. The corresponding geometric curve flows in HP{sup n} are shown to be described by a non-stretching wave map and a mKdV analog of a non-stretching Schroedinger map.
Hamiltonian and Lagrangian dynamics of charged particles including the effects of radiation damping
Qin, Hong; Burby, Joshua; Davidson, Ronald; Fisch, Nathaniel; Chung, Moses
2015-11-01
The effects of radiation damping (radiation reaction) on accelerating charged particles in modern high-intensity accelerators and high-intensity laser beams have becoming increasingly important. Especially for electron accelerators and storage rings, radiation damping is an effective mechanism and technique to achieve high beam luminosity. We develop Hamiltonian and Lagrangian descriptions of the classical dynamics of a charged particle including the effects of radiation damping in the general electromagnetic focusing channels encountered in accelerators. The direct connection between the classical Hamiltonian and Lagrangian theories and the more fundamental QED description of the synchrotron radiation process is also addressed. In addition to their theoretical importance, the classical Hamiltonian and Lagrangian theories of the radiation damping also enable us to numerically integrate the dynamics using advanced structure-preserving geometric algorithms. These theoretical developments can also be applied to runaway electrons and positrons generated during the disruption or startup of tokamak discharges. This research was supported by the U.S. Department of Energy (DE-AC02-09CH11466).
Electrostatics of proteins in dielectric solvent continua. II. Hamiltonian reaction field dynamics.
Bauer, Sebastian; Tavan, Paul; Mathias, Gerald
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.
A Hamiltonian Driven Quantum-Like Model for Overdistribution in Episodic Memory Recollection
Directory of Open Access Journals (Sweden)
Jan B. Broekaert
2017-06-01
Full Text Available While people famously forget genuine memories over time, they also tend to mistakenly over-recall equivalent memories concerning a given event. The memory phenomenon is known by the name of episodic overdistribution and occurs both in memories of disjunctions and partitions of mutually exclusive events and has been tested, modeled and documented in the literature. The total classical probability of recalling exclusive sub-events most often exceeds the probability of recalling the composed event, i.e., a subadditive total. We present a Hamiltonian driven propagation for the Quantum Episodic Memory model developed by Brainerd et al. [1] for the episodic memory overdistribution in the experimental immediate item false memory paradigm [1–3]. Following the Hamiltonian method of Busemeyer and Bruza [4] our model adds time-evolution of the perceived memory state through the stages of the experimental process based on psychologically interpretable parameters—γc for recollection capability of cues, κp for bias or description-dependence by probes and β for the average gist component in the memory state at start. With seven parameters the Hamiltonian model shows good accuracy of predictions both in the EOD-disjunction and in the EOD-subadditivity paradigm. We noticed either an outspoken preponderance of the gist over verbatim trace, or the opposite, in the initial memory state when β is real. Only for complex β a mix of both traces is present in the initial state for the EOD-subadditivity paradigm.
Self-duality of the compactified Ruijsenaars-Schneider system from quasi-Hamiltonian reduction
Energy Technology Data Exchange (ETDEWEB)
Feher, L., E-mail: lfeher@rmki.kfki.hu [Department of Theoretical Physics, WIGNER RCP, RMKI, H-1525 Budapest, P.O.B. 49 (Hungary); Department of Theoretical Physics, University of Szeged, Tisza Lajos krt 84-86, H-6720 Szeged (Hungary); Klimcik, C., E-mail: klimcik@univmed.fr [Institut de mathematiques de Luminy, 163, Avenue de Luminy, F-13288 Marseille (France)
2012-07-21
The Delzant theorem of symplectic topology is used to derive the completely integrable compactified Ruijsenaars-Schneider III{sub b} system from a quasi-Hamiltonian reduction of the internally fused double SU(n) Multiplication-Sign SU(n). In particular, the reduced spectral functions depending respectively on the first and second SU(n) factor of the double engender two toric moment maps on the III{sub b} phase space CP(n-1) that play the roles of action-variables and particle-positions. A suitable central extension of the SL(2,Z) mapping class group of the torus with one boundary component is shown to act on the quasi-Hamiltonian double by automorphisms and, upon reduction, the standard generator S of the mapping class group is proved to descend to the Ruijsenaars self-duality symplectomorphism that exchanges the toric moment maps. We give also two new presentations of this duality map: one as the composition of two Delzant symplectomorphisms and the other as the composition of three Dehn twist symplectomorphisms realized by Goldman twist flows. Through the well-known relation between quasi-Hamiltonian manifolds and moduli spaces, our results rigorously establish the validity of the interpretation [going back to Gorsky and Nekrasov] of the III{sub b} system in terms of flat SU(n) connections on the one-holed torus.