Constraints and Hamiltonian in light-front quantized field theory
International Nuclear Information System (INIS)
Srivastava, P.P.
1993-01-01
Self-consistent hamiltonian formulation of scalar theory on the null plane is constructed and quantized following the Dirac procedure. The theory contains also constraint equations which would give, if solved, to a nonlocal Hamiltonian. In contrast to the equal-time formulation we obtain a different description of the spontaneous symmetry breaking in the continuum and the symmetry generators are found to annihilate the light-front vacuum. Two examples are given where the procedure cannot be applied self-consistently. The corresponding theories are known to be ill-defined from the equal-time quantization. (author)
Transverse Lattice Approach to Light-Front Hamiltonian QCD
Dalley, S
1999-01-01
We describe a non-perturbative procedure for solving from first principles the light-front Hamiltonian problem of SU(N) pure gauge theory in D spacetime dimensions (D>2), based on enforcing Lorentz covariance of observables. A transverse lattice regulator and colour-dielectric link fields are employed, together with an associated effective potential. We argue that the light-front vacuum is necessarily trivial for large enough lattice spacing, and clarify why this leads to an Eguchi-Kawai dimensional reduction of observables to 1+1-dimensions in the infinite N limit. The procedure is then tested by explicit calculations for 2+1-dimensional SU(infinity) gauge theory, within a first approximation to the lattice effective potential. We identify a scaling trajectory which produces Lorentz covariant behaviour for the lightest glueballs. The predicted masses, in units of the measured string tension, are in agreement with recent results from conventional Euclidean lattice simulations. In addition, we obtain the poten...
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?
Hamiltonian Light-Front Field Theory: Recent Progress and Tantalizing Prospects
International Nuclear Information System (INIS)
Vary, J. P.
2012-01-01
Fundamental theories, such as quantum electrodynamics and quantum chromodynamics promise great predictive power addressing phenomena over vast scales from the microscopic to cosmic scales. However, new non-perturbative tools are required for physics to span from one scale to the next. I outline recent theoretical and computational progress to build these bridges and provide illustrative results for Hamiltonian Light Front Field Theory. One key area is our development of basis function approaches that cast the theory as a Hamiltonian matrix problem while preserving a maximal set of symmetries. Regulating the theory with an external field that can be removed to obtain the continuum limit offers additional possibilities as seen in an application to the anomalous magnetic moment of the electron. Recent progress capitalizes on algorithm and computer developments for setting up and solving very large sparse matrix eigenvalue problems. Matrices with dimensions of 20 billion basis states are now solved on leadership-class computers for their low-lying eigenstates and eigenfunctions. (author)
Paston, S A; Prokhvatilov, E V
2002-01-01
The Hamiltonian, reproducing the results of the two-dimensional quantum electrodynamics in the Lorentz coordinates, is constructed on the light front. The procedure of bosonization and analysis of the boson perturbation theory in all the orders by the fermions mass are applied for this purpose. Besides the common terms, originating by the naive quantization on the light front, the obtained Hamiltonian contains an additional counterterm. It is proportional to the linear combination of the fermion zero modes (multiplied by a certain factor compensating the charge and fermion number). The coefficient before this counterterm has no ultraviolet divergence, depends on the value of the fermion condensate in the theta-vacuum and by the small fermion mass is linear by it
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.
International Nuclear Information System (INIS)
Kulshreshtha, U.
1998-01-01
A chiral Schwinger model with the Faddeevian regularization a la Mitra is studied in the light-front frame. The front-form theory is found to be gauge-non-invariant. The Hamiltonian formulation of this gauge-non-invariant theory is first investigated and then the Stueckelberg term for this theory is constructed. Finally, the Hamiltonian and BRST formulations of the resulting gauge-invariant theory, obtained by the inclusion of the Stueckelberg term in the action of the above gauge-non-invariant theory, are investigated with some specific gauge choices. (orig.)
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.
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.
International Nuclear Information System (INIS)
Brodsky, Stanley J.; de Teramond, Guy F.
2011-01-01
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 ζ 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 β-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 Quantization of Gauge Theories
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.
2003-03-25
Light-front wavefunctions provide a frame-independent representation of hadrons in terms of their physical quark and gluon degrees of freedom. The light-front Hamiltonian formalism provides new nonperturbative methods for obtaining the QCD spectrum and eigensolutions, including resolvant methods, variational techniques, and discretized light-front quantization. A new method for quantizing gauge theories in light-cone gauge using Dirac brackets to implement constraints is presented. In the case of the electroweak theory, this method of light-front quantization leads to a unitary and renormalizable theory of massive gauge particles, automatically incorporating the Lorentz and 't Hooft conditions as well as the Goldstone boson equivalence theorem. Spontaneous symmetry breaking is represented by the appearance of zero modes of the Higgs field leaving the light-front vacuum equal to the perturbative vacuum. I also discuss an ''event amplitude generator'' for automatically computing renormalized amplitudes in perturbation theory. The importance of final-state interactions for the interpretation of diffraction, shadowing, and single-spin asymmetries in inclusive reactions such as deep inelastic lepton-hadron scattering is emphasized.
Light-Front Quantization of Gauge Theories
Energy Technology Data Exchange (ETDEWEB)
Brodskey, Stanley
2002-12-01
Light-front wavefunctions provide a frame-independent representation of hadrons in terms of their physical quark and gluon degrees of freedom. The light-front Hamiltonian formalism provides new nonperturbative methods for obtaining the QCD spectrum and eigensolutions, including resolvant methods, variational techniques, and discretized light-front quantization. A new method for quantizing gauge theories in light-cone gauge using Dirac brackets to implement constraints is presented. In the case of the electroweak theory, this method of light-front quantization leads to a unitary and renormalizable theory of massive gauge particles, automatically incorporating the Lorentz and 't Hooft conditions as well as the Goldstone boson equivalence theorem. Spontaneous symmetry breaking is represented by the appearance of zero modes of the Higgs field leaving the light-front vacuum equal to the perturbative vacuum. I also discuss an ''event amplitude generator'' for automatically computing renormalized amplitudes in perturbation theory. The importance of final-state interactions for the interpretation of diffraction, shadowing, and single-spin asymmetries in inclusive reactions such as deep inelastic lepton-hadron scattering is emphasized.
Light-front quantization of the sine-Gordon model
International Nuclear Information System (INIS)
Burkardt, M.
1993-01-01
It is shown how to modify the canonical light-front quantization of the (1+1)-dimensional sine-Gordon model such that the zero-mode problem of light-front quantization is avoided. The canonical sine-Gordon Lagrangian is replaced by an effective Lagrangian which does not lead to divergences as k + =(k 0 +k 1 )/ √2 →0. After canonically quantizing the effective Lagrangian, one obtains the effective light-front Hamiltonian which agrees with the naive light-front (LF) Hamiltonian, up to one additional renormalization. The spectrum of the effective LF Hamiltonian is determined using discrete light-cone quantization and agrees with results from equal-time quantization
QCD Phenomenology and Light-Front Wavefunctions
International Nuclear Information System (INIS)
Brodsky, Stanley J.
2001-01-01
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.
New results in light-front phenomenology
International Nuclear Information System (INIS)
Brodsky, S.J.
2005-01-01
The light-front quantization of gauge theories in light-cone gauge provides a frame-independent wavefunction representation of relativistic bound states, simple forms for current matrix elements, explicit unitarity, and a trivial vacuum. In this talk I review the theoretical methods and constraints which can be used to determine these central elements of QCD phenomenology. The freedom to choose the light-like quantization four-vector provides an explicitly covariant formulation of light-front quantization and can be used to determine the analytic structure of light-front wave functions and define a kinematical definition of angular momentum. The AdS/CFT correspondence of large N c supergravity theory in higher-dimensional anti-de Sitter space with supersymmetric QCD in four-dimensional space-time has interesting implications for hadron phenomenology in the conformal limit, including an all-orders demonstration of counting rules for exclusive processes. String/gauge duality also predicts the QCD power-law behavior of light-front Fock-state hadronic wavefunctions with arbitrary orbital angular momentum at high momentum transfer. The form of these near-conformal wavefunctions can be used as an initial ansatz for a variational treatment of the light-front QCD Hamiltonian. The light-front Fock-state wavefunctions encode the bound state properties of hadrons in terms of their quark and gluon degrees of freedom at the amplitude level. The nonperturbative Fock-state wavefunctions contain intrinsic gluons, and sea quarks at any scale Q with asymmetries such as s(x) ≠ s-bar(x), u-bar(x) ≠ d-bar(x). Intrinsic charm and bottom quarks appear at large x in the light-front wavefunctions since this minimizes the invariant mass and off-shellness of the higher Fock state. In the case of nuclei, the Fock state expansion contains 'hidden color' states which cannot be classified in terms of of nucleonic degrees of freedom. I also briefly review recent analyses which show that some
Light-front dynamics of Chern-Simons systems
International Nuclear Information System (INIS)
Srivastava, P.P.
1994-10-01
The Chern-Simons theory coupled to complex scalars is quantized on the light-front in the local light-cone gauge by constructing the self-consistent Hamiltonian theory. It is shown that no inconsistency arises on using two local gauge-fixing conditions in the Dirac procedure. The light-front Hamiltonian turns out to be simple and the framework may be useful to construct renormalized field theory of particles with fractional statistics (anyons). The theory is shown to be relativistic and the extra term in the transformation of the matter field under space rotations, interpreted in previous works as anomaly, is argued to be gauge artefact. (author). 20 refs
Light-front quantization of field theory
Energy Technology Data Exchange (ETDEWEB)
Srivastava, Prem P. [Universidade do Estado, Rio de Janeiro, RJ (Brazil). Inst. de Fisica]|[Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)
1996-07-01
Some basic topics in Light-Front (LF) quantized field theory are reviewed. Poincare algebra and the LF spin operator are discussed. The local scalar field theory of the conventional framework is shown to correspond to a non-local Hamiltonian theory on the LF in view of the constraint equations on the phase space, which relate the bosonic condensates to the non-zero modes. This new ingredient is useful to describe the spontaneous symmetry breaking on the LF. The instability of the symmetric phase in two dimensional scalar theory when the coupling constant grows is shown in the LF theory renormalized to one loop order. Chern-Simons gauge theory, regarded to describe excitations with fractional statistics, is quantized in the light-cone gauge and a simple LF Hamiltonian obtained which may allow us to construct renormalized theory of anyons. (author). 20 refs.
Light-front quantization of field theory
International Nuclear Information System (INIS)
Srivastava, Prem P.
1996-07-01
Some basic topics in Light-Front (LF) quantized field theory are reviewed. Poincare algebra and the LF spin operator are discussed. The local scalar field theory of the conventional framework is shown to correspond to a non-local Hamiltonian theory on the LF in view of the constraint equations on the phase space, which relate the bosonic condensates to the non-zero modes. This new ingredient is useful to describe the spontaneous symmetry breaking on the LF. The instability of the symmetric phase in two dimensional scalar theory when the coupling constant grows is shown in the LF theory renormalized to one loop order. Chern-Simons gauge theory, regarded to describe excitations with fractional statistics, is quantized in the light-cone gauge and a simple LF Hamiltonian obtained which may allow us to construct renormalized theory of anyons. (author). 20 refs
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 field theory: an advanced primer
International Nuclear Information System (INIS)
Martinovic, L.
2007-01-01
We present an elementary introduction to quantum field theory formulated in terms of Dirac's light front variables. In addition to general principles and methods, a few more specific topics and approaches based on the author's work will be discussed. Most of the discussion deals with massive two-dimensional models formulated in a finite spatial volume starting with a detailed comparison between quantization of massive free fields in the usual field theory and the light front (LF) quantization. We discuss basic properties such as relativistic invariance and causality. After the LF treatment of the soluble Federbush model, a LF approach to spontaneous symmetry breaking is explained and a simple gauge theory - the massive Schwinger model in various gauges is studied. A LF version of bosonization and the massive Thirring model are also discussed. A special chapter is devoted to the method of discretized light cone quantization and its application to calculations of the properties of quantum solitons. The problem of LF zero modes is illustrated with the example of the two/dimensional Yukawa model. Hamiltonian perturbation theory in the LF formulation is derived and applied to a few simple processes to demonstrate its advantages. As a byproduct, it is shown that the LF theory cannot be obtained as a 'light-like' limit of the usual field theory quantized on a initial space-like surface. A simple LF formulation of the Higgs mechanism is then given Since our intention was to provide a treatment of the light front quantization accessible to postgradual students, an effort was made to discuss most of the topics pedagogically and number of technical details and derivations are contained in the appendices (Author)
Light-front QCD. II. Two-component theory
International Nuclear Information System (INIS)
Zhang, W.; Harindranath, A.
1993-01-01
The light-front gauge A a + =0 is known to be a convenient gauge in practical QCD calculations for short-distance behavior, but there are persistent concerns about its use because of its ''singular'' nature. The study of nonperturbative field theory quantizing on a light-front plane for hadronic bound states requires one to gain a priori systematic control of such gauge singularities. In the second paper of this series we study the two-component old-fashioned perturbation theory and various severe infrared divergences occurring in old-fashioned light-front Hamiltonian calculations for QCD. We also analyze the ultraviolet divergences associated with a large transverse momentum and examine three currently used regulators: an explicit transverse cutoff, transverse dimensional regularization, and a global cutoff. We discuss possible difficulties caused by the light-front gauge singularity in the applications of light-front QCD to both old-fashioned perturbative calculations for short-distance physics and upcoming nonperturbative investigations for hadronic bound states
Light front quantum chromodynamics: Towards phenomenology
Indian Academy of Sciences (India)
Light front dynamics; quantum chromodynamics; deep inelastic scattering. PACS Nos 11.10. ... What makes light front dynamics appealing from high energy phenomenology point of view? .... given in terms of Poincarй generators by. MВ = W P ...
Semileptonic Bc decays in the light-front quark model
International Nuclear Information System (INIS)
Choi, Ho-Meoyng; Ji, Chueng-Ryong
2010-01-01
We investigate the exclusive semileptonic B c →(D,η c ,B,B s )lν l , η b →B c lν l (l=e,μ,τ) decays using the light-front quark model constrained by the variational principle for the QCD motivated effective Hamiltonian. The form factors f + (q 2 ) and f - (q 2 ) are obtained from the analytic continuation method in the q + =0 frame. While the form factor f + (q 2 ) is free from the zero mode, the form factor f - (q 2 ) is not free from the zero mode in the q + =0 frame. Using our effective method to relate the non-wave function vertex to the light-front valence wave function, we incorporate the zero-mode contribution as a convolution of zero-mode operator with the initial and final state wave functions.
Membrane dynamics in the intrinsic light-front coordinates
International Nuclear Information System (INIS)
Aragone, C.; Restuccia, A.; Torrealba, R.
1991-01-01
The authors study the dynamics of the membrane, using internal light-front (LF) coordinates. The set of constraints, although equivalent to the standard one, is different. The intrinsic LF gauge is defined. Four additional, alternative gauge-fixing conditions are analyzed. Two of them polynomialize the system, while the other two are convenient for studying the initial-value problem. In particular, one of them is also extrinsically (i.e., in the ambient space) light-front. In this gauge, the system is shown to be consistently reduced to attain a canonical form in terms of pure transverse variables. Two constraints on these variables still hold, clearly showing the presence, as they must, of D - 3 degrees of freedom. Finally, the initial-value problem in this intrinsic-extrinsic. LF gauge is solved. Although the paper is based on the first-order action, the LF-Hamiltonian approach is discussed too
QCD Phenomenology and Light-Front Wave Functions
International Nuclear Information System (INIS)
Brodsky, St.J.
2001-01-01
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 wave functions. 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 wave functions 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 wave functions. (author)
Nuclear Physics on the Light Front
Miller, Gerald A.
1999-01-01
High energy scattering experiments involving nuclei are typically analyzed in terms of light front variables. The desire to provide realistic, relativistic wave functions expressed in terms of these variables led me to try to use light front dynamics to compute nuclear wave functions. The progress is summarized here.
Brodsky, Stanley J.
2018-05-01
Light-front holography, together with superconformal algebra, have provided new insights into the physics of color confinement and the spectroscopy and dynamics of hadrons. As shown by de Alfaro, Fubini and Furlan, 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. If one applies the procedure of de Alfaro et al. to the frame-independent light-front Hamiltonian, it leads uniquely to a confining q \\bar{q} potential κ ^4 ζ ^2, where ζ ^2 is the light-front radial variable related in momentum space to the q \\bar{q} invariant mass. The same result, including spin terms, is obtained using light-front holography—the duality between the front form and AdS_5, the space of isometries of the conformal group—if one modifies the action of AdS_5 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 lead to a a unified Regge spectroscopy of meson, baryon, and tetraquarks, including supersymmetric relations between their masses and their wavefunctions. One also predicts hadronic light-front wavefunctions and observables such as structure functions, transverse momentum distributions, and the distribution amplitudes. 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 result is an effective coupling α _s(Q^2) defined at all momenta. The matching of the high and low momentum transfer regimes determines a scale Q_0 which sets the interface between perturbative and nonperturbative hadron dynamics. I also discuss a number of applications of light-front phenomenology.
Quantum electrodynamics in the light-front Weyl gauge
International Nuclear Information System (INIS)
Przeszowski, J.; Naus, H.W.; Kalloniatis, A.C.
1996-01-01
We examine (3+1)-dimensional QED quantized in the open-quote open-quote front form close-quote close-quote with finite open-quote open-quote volume close-quote close-quote regularization, namely, in discretized light-cone quantization. Instead of the light-cone or Coulomb gauges, we impose the light-front Weyl gauge A - =0. The Dirac method is used to arrive at the quantum commutation relations for the independent variables. We apply open-quote open-quote quantum-mechanical gauge fixing close-quote close-quote to implement Gauss close-quote law, and derive the physical Hamiltonian in terms of unconstrained variables. As in the instant form, this Hamiltonian is invariant under global residual gauge transformations, namely, displacements. On the light cone the symmetry manifests itself quite differently. copyright 1996 The American Physical Society
Statistical Physics and Light-Front Quantization
Energy Technology Data Exchange (ETDEWEB)
Raufeisen, J
2004-08-12
Light-front quantization has important advantages for describing relativistic statistical systems, particularly systems for which boost invariance is essential, such as the fireball created in a heavy ion collisions. In this paper the authors develop light-front field theory at finite temperature and density with special attention to quantum chromodynamics. They construct the most general form of the statistical operator allowed by the Poincare algebra and show that there are no zero-mode related problems when describing phase transitions. They then demonstrate a direct connection between densities in light-front thermal field theory and the parton distributions measured in hard scattering experiments. The approach thus generalizes the concept of a parton distribution to finite temperature. In light-front quantization, the gauge-invariant Green's functions of a quark in a medium can be defined in terms of just 2-component spinors and have a much simpler spinor structure than the equal-time fermion propagator. From the Green's function, the authors introduce the new concept of a light-front density matrix, whose matrix elements are related to forward and to off-diagonal parton distributions. Furthermore, they explain how thermodynamic quantities can be calculated in discretized light-cone quantization, which is applicable at high chemical potential and is not plagued by the fermion-doubling problems.
Light-front nuclear shell-model
International Nuclear Information System (INIS)
Johnson, M.B.
1990-01-01
I examine the effects of nuclear structure on high-energy, high-momentum transfer processes, specifically the EMC effect. For pedagogical reasons, a fictitious but simple two-body system consisting of two equal-mass particles interacting in a harmonic oscillator potential has been chosen. For this toy nucleus, I utilize a widely-used link between instant-form and light-front dynamics, formulating nuclear structure and deep-inelastic scattering consistently in the laboratory system. Binding effects are compared within conventional instant-form and light-front dynamical frameworks, with appreciable differences being found in the two cases. 20 refs
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
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 non-perturbative regime of QCD and its transition to the perturbative domain. This novel framework allows hadronic...... projected on the free Fock basis provides the complete set of valence and non-valence light-front Fock state wavefunctions Psi(n)/H(x(i), k(perpendicular to i), lambda(i)) which describe the hadron's momentum and spin distributions needed to compute the direct measures of hadron structure at the quark...
Vector mesons on the light front
International Nuclear Information System (INIS)
Naito, K.; Maedan, S.; Itakura, K.
2004-01-01
We apply the light-front quantization to the Nambu-Jona-Lasinio model with the vector interaction, and compute vector meson's mass and light-cone wavefunction in the large N limit. Following the same procedure as in the previous analyses for scalar and pseudo-scalar mesons, we derive the bound-state equations of a qq-bar system in the vector channel. We include the lowest order effects of the vector interaction. The resulting transverse and longitudinal components of the bound-state equation look different from each other. But eventually after imposing an appropriate cutoff, one finds these two are identical, giving the same mass and the same (spin-independent) light-cone wavefunction. Mass of the vector meson decreases as one increases the strength of the vector interaction
Light-like noncommutativity, light-front quantization and new light on UV/IR mixing
International Nuclear Information System (INIS)
Sheikh-Jabbari, M.M.; Tureanu, A.
2011-01-01
We revisit the problem of quantizing field theories on noncommutative Moyal space-time with light-like noncommutativity. To tackle the issues arising from noncommuting and hence nonlocal time, we argue that for this case light-front quantization procedure should be employed. In this appropriate quantization scheme we perform the non-planar loop analysis for the light-like noncommutative field theories. One of the important and peculiar features of light-front quantization is that the UV cutoff of the light-cone Hamiltonian manifests itself as an IR cutoff for the light-cone momentum, p + . Due to this feature, the naive results of covariant quantization for the light-like case allude to the absence of the UV/IR mixing in the light-front quantization. However, by a careful analysis of non-planar loop integrals we show that this is not the case and the UV/IR mixing persists. In addition, we argue in favour of the perturbative unitarity of light-like noncommutative field theories in the light-front quantization scheme.
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.
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.
Light-Front Dynamics in Hadron Physics
International Nuclear Information System (INIS)
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 Minkowski space as well as its distinct feature of accounting for the vacuum fluctuations in quantum field theories. In the last few years, however, it has been emphasized that treacherous points such as LF singularities and zero-modes should be taken into account for successful LFD applications to hadron phenomenology. In this paper, we discuss a typical example of the contemporary relativistic hadron physics in which the fundamental issues should be taken into account for the successful application of LFD. In particular, we focus on the kinematic issue of GPDs in deeply virtual Compton scattering (DVCS). Although this fundamental issue has been glossed over in the literature, it must be taken care of for the correct analysis of DVCS data. (author)
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.
Light-front field theory in the description of hadrons
Ji, Chueng-Ryong
2017-03-01
We discuss the use of light-front field theory in the descriptions of hadrons. In particular, we clarify the confusion in the prevailing notion of the equivalence between the infinite momentum frame and the light-front dynamics and the advantage of the light-front dynamics in hadron physics. As an application, we present our recent work on the flavor asymmetry in the proton sea and identify the presence of the delta-function contributions associated with end-point singularities arising from the chiral effective theory calculation. The results pave the way for phenomenological applications of pion cloud models that are manifestly consistent with the chiral symmetry properties of QCD.
Gluon cascades and amplitudes in light-front perturbation theory
International Nuclear Information System (INIS)
Cruz-Santiago, C.A.; Staśto, A.M.
2013-01-01
We construct the gluon wave functions, fragmentation functions and scattering amplitudes within the light-front perturbation theory. Recursion relations on the light-front are constructed for the wave functions and fragmentation functions, which in the latter case are the light-front analogs of the Berends–Giele recursion relations. Using general relations between wave functions and scattering amplitudes it is demonstrated how to obtain the maximally-helicity violating amplitudes, and explicit verification of the results is based on simple examples.
Poincare invariant algebra from instant to light-front quantization
International Nuclear Information System (INIS)
Ji, Chueng-Ryong; Mitchell, Chad
2001-01-01
We present the Poincare algebra interpolating between instant and light-front time quantizations. The angular momentum operators satisfying SU(2) algebra are constructed in an arbitrary interpolation angle and shown to be identical to the ordinary angular momentum and Leutwyler-Stern angular momentum in the instant and light-front quantization limits, respectively. The exchange of the dynamical role between the transverse angular mometum and the boost operators is manifest in our newly constructed algebra
International Nuclear Information System (INIS)
Srivastava, Prem P.
1994-01-01
The Dirac procedure is used to construct the Hamiltonian formulation of the scalar field theory on the light-front. The theory is quantized and the mechanism of the spontaneous symmetry breaking in the front form and the instant form dynamics are compared. The phase transition in (φ 4 )2 theory is also discussed and found to be of the second order. (author). 36 refs
Zero modes in discretized light-front quantization
International Nuclear Information System (INIS)
Martinovic, E.
1997-01-01
The current understanding of the role of bosonic zero modes in field-theoretical models quantized at the equal light-front time is reviewed. After a brief discussion of the main features of the light-front field theories - in particular the simplicity of the physical vacuum - the light-front canonical formalism for the quantum electrodynamics and the Yukawa model is sketched. The zero mode of Maskawa and Yamawaki is reviewed. Reasons for the appearance of the constrained and/or dynamical zero modes are explained along with the subtleties of the gauge fixing in presence of boundary conditions. Perturbative treatment of the corresponding constraint equations in the Yukawa model and quantum electrodynamics (3+1) is outlined. The next topic is the manifestation of the symmetry breaking in the light-front field theory. A pattern of multiple solutions to the zero-mode constraint equations replacing physical picture of multiple vacua of the conventionally quantized field theories is illustrated on an example of 2-dimensional theory. The importance of a (regularized) constrained zero mode of the pion field for the consistency of the Nambu-Goldstone phase of the discretized light-front linear a/model is demonstrated. Finally, a non-trivial physical vacuum based on the dynamical zero mode is constructed for the two-dimensional light-front quantum electrodynamics. (authors)
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.
Light-front field theory in the description of hadrons
Directory of Open Access Journals (Sweden)
Ji Chueng-Ryong
2017-01-01
Full Text Available We discuss the use of light-front field theory in the descriptions of hadrons. In particular, we clarify the confusion in the prevailing notion of the equivalence between the infinite momentum frame and the light-front dynamics and the advantage of the light-front dynamics in hadron physics. As an application, we present our recent work on the flavor asymmetry in the proton sea and identify the presence of the delta-function contributions associated with end-point singularities arising from the chiral effective theory calculation. The results pave the way for phenomenological applications of pion cloud models that are manifestly consistent with the chiral symmetry properties of QCD.
Light-front view of the axial anomaly
International Nuclear Information System (INIS)
Ji, C.; Rey, S.
1996-01-01
Motivated by an apparent puzzle of the light-front vacua incompatible with the axial anomaly, we have considered the two-dimensional massless Schwinger model for an arbitrary interpolating angle of Hornbostel close-quote s interpolating quantization surface. By examining spectral deformation of the Dirac sea under an external electric field semiclassically, we have found that the axial anomaly is quantization angle independent. This indicates an intricate nontrivial vacuum structure present even in the light-front limit. copyright 1996 The American Physical Society
Rotational covariance and light-front current matrix elements
International Nuclear Information System (INIS)
Keister, B.D.
1994-01-01
Light-front current matrix elements for elastic scattering from hadrons with spin 1 or greater must satisfy a nontrivial constraint associated with the requirement of rotational covariance for the current operator. Using a model ρ meson as a prototype for hadronic quark models, this constraint and its implications are studied at both low and high momentum transfers. In the kinematic region appropriate for asymptotic QCD, helicity rules, together with the rotational covariance condition, yield an additional relation between the light-front current matrix elements
Vacuum Polarization Tensor for QED in the Light Front Gauge
International Nuclear Information System (INIS)
Suzuki, A.T.; Soriano, L.A.; Bolzan, J.D.; Sales, J.H.O.
2012-01-01
The use of light front coordinates in quantum field theories (QFT) always brought some problems and controversies. In this work we explore some aspects of its formalism with respect to the employment of dimensional regularization in the computation of the photon's self-energy at the one-loop level and how the fermion propagator has an important role in the outcoming results. (author)
Nucleon parton distributions in a light-front quark model
International Nuclear Information System (INIS)
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, 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_v(x) and δq_v(x). Our results are very relevant for the current and future program of the COMPASS experiment at SPS (CERN). (orig.)
Taylor-Lagrange regularization scheme and light-front dynamics
International Nuclear Information System (INIS)
Grange, P.; Mathiot, J.-F.; Mutet, B.; Werner, E.
2010-01-01
The recently proposed renormalization scheme based on the definition of field operators as operator valued distributions acting on specific test functions is shown to be very convenient in explicit calculations of physical observables within the framework of light-front dynamics. We first recall the main properties of this procedure based on identities relating the test functions to their Taylor remainder of any order expressed in terms of Lagrange's formulae, hence the name given to this scheme. We thus show how it naturally applies to the calculation of state vectors of physical systems in the covariant formulation of light-front dynamics. As an example, we consider the case of the Yukawa model in the simple two-body Fock state truncation.
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.)
Application of a Light-Front Coupled Cluster Method
International Nuclear Information System (INIS)
Chabysheva, S.S.; Hiller, J.R.
2012-01-01
As a test of the new light-front coupled-cluster method in a gauge theory, we apply it to the nonperturbative construction of the dressed-electron state in QED, for an arbitrary covariant gauge, and compute the electron's anomalous magnetic moment. The construction illustrates the spectator and Fock-sector independence of vertex and self-energy contributions and indicates resolution of the difficulties with uncanceled divergences that plague methods based on Fock-space truncation. (author)
Feynman versus Bakamjian-Thomas in light-front dynamics
International Nuclear Information System (INIS)
Araujo, W.R.B. de; Beyer, M.; Weber, H.J.; Frederico, T.
1999-01-01
We compare the Bakamjian-Thomas (BT) formulation of relativistic few-body systems with light-front field theories that maintain closer contact with Feynman diagrams. We find that Feynman diagrams distinguish Melosh rotations and other kinematical quantities belonging to various composite subsystem frames that correspond to different loop integrals. The BT formalism knows only the rest frame of the whole composite system, where everything is evaluated. (author)
Light-front wave function of composite system with spin
International Nuclear Information System (INIS)
Karmanov, V.A.
1979-01-01
The method to construct the relativistic wave function with spin on the light front is developed. The spin structure of the deuteron wave function in relativistic range is found. The calculation methods are illustrated by the calculation of elastic pd-scattering cross section. The consideration carried out is equivalent to the solution of the problem of taking into account the spins and angular momenta in the parton wave functions in the infinite momentum frame
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.
Higgs mechanism in light-front quantized field theory
Energy Technology Data Exchange (ETDEWEB)
Srivastava, P P
1993-12-31
The spontaneous symmetry breaking of continuous symmetry in light-front quantized scalar field theory is studied following the standard Dirac procedure for constrained dynamical systems. A non-local constraint is found to follow. The values of the constant backgrounds fields (zero modes) at the tree level, as a consequence, are shown to given by minimizing the light-front energy. The zero modes are shown to commute with the non-zero ones and the isovector built from them is seen to characterize a (non-perturbative) vacuum state and the corresponding physical sector. The infinite degeneracy of the vacuum is described by the continuum of the allowed orientations of this background isovector in the isospin space. The symmetry generators in the quantized field theory annihilate the vacuum is contrast to the case of equal-time quantization. Not all of them are conserved and the conserved ones determine the surviving symmetry of the quantum theory Lagrangian. The criteria for determining the background isovector and the counting of the number of Goldstone bosons goes as in the equal-time case. A demonstration in favour of the absence of Goldstone bosons in two dimensions is also found. Finally, is extended to an understanding of the Higgs mechanism in light-front frame. (author). 13 refs.
Higgs mechanism in light-front quantized field theory
International Nuclear Information System (INIS)
Srivastava, P.P.
1992-01-01
The spontaneous symmetry breaking of continuous symmetry in light-front quantized scalar field theory is studied following the standard Dirac procedure for constrained dynamical systems. A non-local constraint is found to follow. The values of the constant backgrounds fields (zero modes) at the tree level, as a consequence, are shown to given by minimizing the light-front energy. The zero modes are shown to commute with the non-zero ones and the isovector built from them is seen to characterize a (non-perturbative) vacuum state and the corresponding physical sector. The infinite degeneracy of the vacuum is described by the continuum of the allowed orientations of this background isovector in the isospin space. The symmetry generators in the quantized field theory annihilate the vacuum is contrast to the case of equal-time quantization. Not all of them are conserved and the conserved ones determine the surviving symmetry of the quantum theory Lagrangian. The criteria for determining the background isovector and the counting of the number of Goldstone bosons goes as in the equal-time case. A demonstration in favour of the absence of Goldstone bosons in two dimensions is also found. Finally, is extended to an understanding of the Higgs mechanism in light-front frame. (author). 13 refs
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.
Electromagnetic form factors in the light-front dynamics
International Nuclear Information System (INIS)
Karmanov, V.A.; Smirnov, A.V.
1992-01-01
It is shown that the electromagnetic vertex of a nucleus (and of any bound system), expressed through the wave function in the light-front dynamics at relativistic values of momentum transfer, contains a contribution of nonphysical form factors which increases the total number of invariant form factors (for the deuteron from 3 up to 11). This fact explains an ambiguity in the form factors calculated previously. The physical and nonphysical form factors are covariantly separated. Explicit expressions for physical form factors of systems with spin 0, 1/2 and 1 through the vertex functions are obtained. (orig.)
Semileptonic and radiative decays of the Bc meson in the light-front quark model
International Nuclear Information System (INIS)
Choi, Ho-Meoyng; Ji, Chueng-Ryong
2009-01-01
We investigate the exclusive semileptonic B c →(D,η c ,B,B s )lν l , η b →B c lν l (l=e,μ,τ) decays using the light-front quark model constrained by the variational principle for the QCD-motivated effective Hamiltonian. The form factors f + (q 2 ) and f - (q 2 ) are obtained from the analytic continuation method in the q + =0 frame. While the form factor f + (q 2 ) is free from the zero mode, the form factor f - (q 2 ) is not free from the zero mode in the q + =0 frame. We quantify the zero-mode contributions to f - (q 2 ) for various semileptonic B c decays. Using our effective method to relate the non-wave-function vertex to the light-front valence wave function, we incorporate the zero-mode contribution as a convolution of the zero-mode operator with the initial and final state wave functions. Our results are then compared to the available experimental data and the results from other theoretical approaches. Since the prediction on the magnetic dipole B c *→B c +γ decay turns out to be very sensitive to the mass difference between B c * and B c mesons, the decay width Γ(B c *→B c γ) may help in determining the mass of B c * experimentally. Furthermore, we compare the results from the harmonic oscillator potential and the linear potential and identify the decay processes that are sensitive to the choice of confining potential. From the future experimental data on these sensitive processes, one may obtain more realistic information on the potential between the quark and antiquark in the heavy meson system.
Spontaneous symmetry breaking of (1+1)-dimensional φ4 theory in light-front field theory. II
International Nuclear Information System (INIS)
Pinsky, S.S.; van de Sande, B.
1994-01-01
We discuss spontaneous symmetry breaking of (1+1)-dimensional φ 4 theory in light-front field theory using a Tamm-Dancoff truncation. We show that, even though light-front field theory has a simple vacuum state which is an eigenstate of the full Hamiltonian, the field can develop a nonzero vacuum expectation value. This occurs because the zero mode of the field must satisfy an operator-valued constraint equation. In the context of (1+1)-dimensional φ 4 theory we present solutions to the constraint equation using a Tamm-Dancoff truncation to a finite number of particles and modes. We study the behavior of the zero mode as a function of coupling and Fock space truncation. The zero mode introduces new interactions into the Hamiltonian which breaks the Z 2 symmetry of the theory when the coupling is stronger than the critical coupling. We investigate the energy spectrum in the symmetric and broken phases, show that the theory does not break down in the vicinity of the critical coupling, and discuss the connection to perturbation theory. Finally, we study the spectrum of the field φ and show that, in the broken phase, the field is localized away from φ=0 as one would expect from equal-time calculations. We explicitly show that tunneling occurs
Renormalization of Hamiltonians
International Nuclear Information System (INIS)
Glazek, S.D.; Wilson, K.G.
1993-01-01
This paper presents a new renormalization procedure for Hamiltonians such as those of light-front field theory. The bare Hamiltonian with an arbitrarily large, but finite cutoff, is transformed by a specially chosen similarity transformation. The similarity transformation has two desirable features. First, the transformed Hamiltonian is band diagonal: in particular, all matrix elements vanish which would otherwise have caused transitions with big energy jumps, such as from a state of bounded energy to a state with an energy of the order of the cutoff. At the same time, neither the similarity transformation nor the transformed Hamiltonian, computed in perturbation theory, contain vanishing or near-vanishing energy denominators. Instead, energy differences in denominators can be replaced by energy sums for purposes of order of magnitude estimates needed to determine cutoff dependences. These two properties make it possible to determine relatively easily the list of counterterms needed to obtain finite low energy results (such as for eigenvalues). A simple model Hamiltonian is discussed to illustrate the method
International Nuclear Information System (INIS)
Brodsky, S
2008-01-01
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 ζ 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
Decay constants and radiative decays of heavy mesons in light-front quark model
International Nuclear Information System (INIS)
Choi, Ho-Meoyng
2007-01-01
We investigate the magnetic dipole decays V→Pγ of various heavy-flavored mesons such as (D,D*,D s ,D s *,η c ,J/ψ) and (B,B*,B s ,B s *,η b ,Υ) using the light-front quark model constrained by the variational principle for the QCD-motivated effective Hamiltonian. The momentum dependent form factors F VP (q 2 ) for V→Pγ* decays are obtained in the q + =0 frame and then analytically continued to the timelike region by changing q perpendicular to iq perpendicular in the form factors. The coupling constant g VPγ for real photon case is then obtained in the limit as q 2 →0, i.e. g VPγ =F VP (q 2 =0). The weak decay constants of heavy pseudoscalar and vector mesons are also calculated. Our numerical results for the decay constants and radiative decay widths for the heavy-flavored mesons are overall in good agreement with the available experimental data as well as other theoretical model calculations
Selected Topics in Light Front Field Theory and Applications to the High Energy Phenomena
Kundu, Rajen
1999-10-01
In this thesis, we have presented some of the aspects of light-front (LF) field theory through their successful application in the Deep Inelastic Scattering (DIS). We have developed a LFQCD Hamiltonian description of the DIS structure functions starting from Bjorken-Johnson-Low limit of virtual forward Compton scattering amplitude and using LF current commutators. We worked in the LF gauge A^+=0 and used the old-fashioned LFQCD perturbation theory in our calculations. The importance of our work are summarized below. Our approach shares the intution of parton model and addresses directly the structure functions, which are experimental objects, instead of its moments as in OPE method. Moreover, it can potentially incorporate the non-perturbative contents of the structure functions as we have demonstrated by introducing a new factorization scheme. In the context of nucleonic helicity structure, the well known gauge fixed LF helicity operator is shown to provide consistent physical information and helps us defining new relevant structure functions. The anomalous dimensions relevant for the Q^2-evolution of such structure functions are calculated. Our study is important in establishing the equivalance of LF field theory and the usual equal-time one through perturbative calculations of the dressed parton structure functions reproducing the well known results. Also the importance of Gallilean boost symmetry in understanding the correctness of any higher order calculation using (x^+)-ordered LFQCD perturbation theory are emphasized.
Fermions in light front transverse lattice quantum chromodynamics
Indian Academy of Sciences (India)
Ur(x-aˆr)]}. (3). After eliminating the constraint fields we arrive at the transverse lattice Hamiltonian. P. =P. 1 +P. 2 ,. (4) where P. 1 arises from the elimination of ψ (hence sensitive to how fermions are put on the transverse lattice) and P. 2 contains Wilson plaquette term and the terms arising from the elimination of A . Explicitly.
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.
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...
Light-front realization of chiral symmetry breaking
International Nuclear Information System (INIS)
Itakura, Kazunori; Maedan, Shinji
2001-01-01
We discuss a description of chiral symmetry breaking in the light-front (LF) formalism. Based on careful analyses of several modes, we give clear answers to the following three fundamental questions: (i) What is the difference between the LF chiral transformation and the ordinary chiral transformation? (ii) How does a gap equation for the chiral condensate emerge? (iii) What is the consequence of the coexistence of a nonzero chiral condensate and the trivial Fock vacuum? The answer to Question (i) is given through a classical analysis of each model. Question (ii) is answered based on our recognition of the importance of characteristic constraints, such as the zero-mode and fermionic constraints. Question (iii) is intimately related to another important problem, reconciliation of the nonzero chiral condensate ≠ 0 and the invariance of the vacuum under the LF chiral transformation Q 5 LF | 0> = 0. This and Question (iii) are understood in terms of the modified chiral transformation laws of the dependent variables. The characteristic ways in which the chiral symmetry breaking is realized are that the chiral charge Q 5 LF is no longer conserved and that the transformation of the scalar and pseudoscalar fields is modified. We also discuss other outcomes, such as the light-cone wave function of the pseudoscalar meson in the Nambu-Jona-Lasinio model. (author)
Vector anomaly and practicality of light-front dynamics
International Nuclear Information System (INIS)
Chueng-Ryong Ji; Bakker, B.L.G.
2005-01-01
Light-front dynamics (LFD) is like sweeping dirt to a corner to make the rest of the space clean. This feature allows many practical applications of LFD to the phenomenology of particle physics. To strengthen the practicality of LFD, however, it is necessary to check where the dirt is piled and to find ways to handle the associate complications. In this presentation, we discuss an explicit example of a non-vanishing zero-mode contribution to physical amplitudes which has been regarded as one of the typical complications in LFD. In particular, we analyze the vector anomaly occurring in the calculation of the CP-even form factors of the elementary W ± gauge bosons and find that the zero-mode contribution to the helicity zero-to-zero amplitude for the W ± gauge bosons is crucial for the correct LFD calculations. Further, we confirm that the anomaly-free condition found in the analysis of the axial anomaly can also get rid of the vector anomaly in LFD as well as in the manifestly covariant calculations. Our findings in this work may provide a bottom-up fitness test not only to the LFD calculations but also to the theory itself, whether it is the standard model or any extension of the standard model. (author)
Light-front Ward-Takahashi identity for two-fermion systems
International Nuclear Information System (INIS)
Marinho, J. A. O.; Frederico, T.; Pace, E.; Salme, G.; Sauer, P. U.
2008-01-01
We propose a three-dimensional electromagnetic current operator within light-front dynamics that satisfies a light-front Ward-Takahashi identity for two-fermion systems. The light-front current operator is obtained by a quasipotential reduction of the four-dimensional current operator and acts on the light-front valence component of bound or scattering states. A relation between the light-front valence wave function and the four-dimensional Bethe-Salpeter amplitude both for bound or scattering states is also derived, such that the matrix elements of the four-dimensional current operator can be fully recovered from the corresponding light-front ones. The light-front current operator can be perturbatively calculated through a quasipotential expansion, and the divergence of the proposed current satisfies a Ward-Takahashi identity at any given order of the expansion. In the quasipotential expansion the instantaneous terms of the fermion propagator are accounted for by the effective interaction and two-body currents. We exemplify our theoretical construction in the Yukawa model in the ladder approximation, investigating in detail the current operator at the lowest nontrivial order of the quasipotential expansion of the Bethe-Salpeter equation. The explicit realization of the light-front form of the Ward-Takahashi identity is verified. We also show the relevance of instantaneous terms and of the pair contribution to the two-body current and the Ward-Takahashi identity
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
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)-dimensional physical space-time, thus providing a compelling physical interpretation of the Ad...
Projecting the Bethe-Salpeter Equation onto the Light-Front and Back: A Short Review
International Nuclear Information System (INIS)
Frederico, T.; Salme, G.
2011-01-01
The technique of projecting the four-dimensional two-body Bethe-Salpeter equation onto the three-dimensional Light-Front hypersurface, combined with the quasi-potential approach, is briefly illustrated, by placing a particular emphasis on the relation between the projection method and the effective dynamics of the valence component of the Light-Front wave function. Some details on how to construct the Fock expansion of both (a) the Light-Front effective interaction and (b) the electromagnetic current operator, satisfying the proper Ward-Takahashi identity, will be presented, addressing the relevance of the Fock content in the operators living onto the Light-Front hypersurface. Finally, the generalization of the formalism to the three-particle case will be outlined. (author)
Photon polarization tensor in the light front field theory at zero and finite temperatures
International Nuclear Information System (INIS)
Silva, Charles da Rocha; Perez, Silvana; Strauss, Stefan
2012-01-01
Full text: In recent years, light front quantized field theories have been successfully generalized to finite temperature. The light front frame was introduced by Dirac , and the quantization of field theories on the null-plane has found applications in many branches of physics. In order to obtain the thermal contribution, we consider the hard thermal loop approximation. This technique was developed by Braaten and Pisarski for the thermal quantum field theory at equal times and is particularly useful to extract the leading thermal contributions to the amplitudes in perturbative quantum field theories. In this work, we consider the light front quantum electrodynamics in (3+1) dimensions and evaluate the photon polarization tensor at one loop for both zero and finite temperatures. In the first case, we apply the dimensional regularization method to extract the finite contribution and find the transverse structure for the amplitude in terms of the light front coordinates. The result agrees with one-loop covariant calculation. For the thermal corrections, we generalize the hard thermal loop approximation to the light front and calculate the dominant temperature contribution to the polarization tensor, consistent with the Ward identity. In both zero as well as finite temperature calculations, we use the oblique light front coordinates. (author)
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.
Gravitational form factors and angular momentum densities in light-front quark-diquark model
Energy Technology Data Exchange (ETDEWEB)
Kumar, Narinder [Indian Institute of Technology Kanpur, Department of Physics, Kanpur (India); Mondal, Chandan [Chinese Academy of Sciences, Institute of Modern Physics, Lanzhou (China); Sharma, Neetika [I K Gujral Punjab Technical University, Department of Physical Sciences, Jalandhar, Punjab (India); Panjab University, Department of Physics, Chandigarh (India)
2017-12-15
We investigate the gravitational form factors (GFFs) and the longitudinal momentum densities (p{sup +} densities) for proton in a light-front quark-diquark model. The light-front wave functions are constructed from the soft-wall AdS/QCD prediction. The contributions from both the scalar and the axial vector diquarks are considered here. The results are compared with the consequences of a parametrization of nucleon generalized parton distributions (GPDs) in the light of recent MRST measurements of parton distribution functions (PDFs) and a soft-wall AdS/QCD model. The spatial distribution of angular momentum for up and down quarks inside the nucleon has been presented. At the density level, we illustrate different definitions of angular momentum explicitly for an up and down quark in the light-front quark-diquark model inspired by AdS/QCD. (orig.)
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
Isovector meson-exchange currents in the light-front dynamics
International Nuclear Information System (INIS)
Desplanques, B.; Karmanov, V.A.; Mathiot, J.F.
1994-09-01
In the light-front dynamics, there is no pair term that plays the role of the dominant isovector pion exchange current. This current gives rise to the large and experimentally observed contribution to the deuteron electrodisintegration cross-section near threshold for pseudo-scalar πNN coupling. It is analytically shown that in leading 1/m order the amplitude in the light-front dynamics coincides, however, with the one given by the pair term. At high Q 2 , it consists of two equal parts. One comes from extra components of the deuteron and final state relativistic wave functions. The other results from the contact NNπγ interaction which appears in the light-front dynamics. This provides a transparent link between relativistic and non-relativistic approaches. (author). 16 refs., 4 figs
Relation between equal-time and light-front wave functions
International Nuclear Information System (INIS)
Miller, Gerald A.; Tiburzi, Brian C.
2010-01-01
The relation between equal-time and light-front wave functions is studied using models for which the four-dimensional solution of the Bethe-Salpeter wave function can be obtained. The popular prescription of defining the longitudinal momentum fraction using the instant-form free kinetic energy and third component of momentum is found to be incorrect except in the nonrelativistic limit. One may obtain light-front wave functions from rest-frame, instant-form wave functions by boosting the latter wave functions to the infinite momentum frame. Despite this difficulty, we prove a relation between certain integrals of the equal-time and light-front wave functions.
{theta}-vacua in the light-front quantized Schwinger model
Energy Technology Data Exchange (ETDEWEB)
Srivastava, Prem P. [Universidade do Estado, Rio de Janeiro, RJ (Brazil). Inst. de Fisica]|[Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)
1996-09-01
The light-front quantization of the bosonized Schwinger model is discussed in the continuum formulation. The proposal, successfully used earlier for describing the spontaneous symmetry breaking on the light-front, of separating first the scalar field into the dynamical condensate and the fluctuation fields before employing the standard Dirac method works here as well. Some topics on the front form theory are summarized in the Appendices and attention is drawn to the fact that the theory quantized, at x{sup +} seems already to carry information on equal x{sup -} commutators as well. (author). 21 refs.
θ-vacua in the light-front quantized Schwinger model
International Nuclear Information System (INIS)
Srivastava, Prem P.
1996-09-01
The light-front quantization of the bosonized Schwinger model is discussed in the continuum formulation. The proposal, successfully used earlier for describing the spontaneous symmetry breaking on the light-front, of separating first the scalar field into the dynamical condensate and the fluctuation fields before employing the standard Dirac method works here as well. Some topics on the front form theory are summarized in the Appendices and attention is drawn to the fact that the theory quantized, at x + seems already to carry information on equal x - commutators as well. (author). 21 refs
Hadron spectroscopy and dynamics from light-front holography and conformal symmetry
Directory of Open Access Journals (Sweden)
de Téramond Guy F.
2014-06-01
Full Text Available To a first semiclassical approximation one can reduce the multi-parton light-front problem in QCD to an effective one-dimensional quantum field theory, which encodes the fundamental conformal symmetry of the classical QCD Lagrangian. This procedure leads to a relativistic light-front wave equation for arbitrary spin which incorporates essential spectroscopic and non-perturbative dynamical features of hadron physics. The mass scale for confinement and higher dimensional holographic mapping to AdS space are also emergent properties of this framework.
Hard Thermal Loop approximation in the Light Front Quantum Field Theory
International Nuclear Information System (INIS)
Silva, Charles da Rocha; Perez, Silvana
2011-01-01
Full text: In this paper we generalize the Hard Thermal Loop approximation (HTL) for the Thermal Light Front Quantum Field Theory. This technique was developed by Braaten e Pisarski [PRL. 63 (1989) 1129, Nucl. Phys. B337 (1990) 569], for the Thermal Quantum Field Theory at equal time and is particularly useful to solve problems of convergence of the amplitudes within Quantum Chromodynamics, caused by the inherently nonperturbative behavior. The HTL approximation satisfies simple Ward identities, is ultraviolet finite and gauge independent. Here we use the light front generalized coordinates (GLFC) proposed by one of us (V. S. Alves, Ashok Das, e Silvana Perez [PRD. 66, (2002) 125008]) and analyze the one loop amplitudes for the λφ3 theory and the Quantum Electrodynamics in (3+1) dimensions at finite temperature in the HTL approximation. For the scalar theory, we evaluate the two-point function, recovering the usual dispersion relations. We also analyze the rotational invariance of the model. We then consider the Quantum Electrodynamics in (3+1) dimensions and calculate the polarization tensor and the vertex function at finite temperature in the HTL approximation. In future, our interest will be to apply the Generalized Light Front formalism to understand the confinement mechanism which occurs in the Quantum Chromodynamics. There is an expectation that the Light Front Quantum Field Theory formalism is more appropriate to study this problems. (author)
Hard Thermal Loop approximation in the Light Front Quantum Field Theory
Energy Technology Data Exchange (ETDEWEB)
Silva, Charles da Rocha [Instituto Federal de Educacao, Ciencia e Tecnologia do Para (IFPA), Belem, PA (Brazil); Universidade Federal do Para (UFPA), Belem, PA (Brazil); Perez, Silvana [Universidade Federal do Para (UFPA), Belem, PA (Brazil)
2011-07-01
Full text: In this paper we generalize the Hard Thermal Loop approximation (HTL) for the Thermal Light Front Quantum Field Theory. This technique was developed by Braaten e Pisarski [PRL. 63 (1989) 1129, Nucl. Phys. B337 (1990) 569], for the Thermal Quantum Field Theory at equal time and is particularly useful to solve problems of convergence of the amplitudes within Quantum Chromodynamics, caused by the inherently nonperturbative behavior. The HTL approximation satisfies simple Ward identities, is ultraviolet finite and gauge independent. Here we use the light front generalized coordinates (GLFC) proposed by one of us (V. S. Alves, Ashok Das, e Silvana Perez [PRD. 66, (2002) 125008]) and analyze the one loop amplitudes for the {lambda}{phi}3 theory and the Quantum Electrodynamics in (3+1) dimensions at finite temperature in the HTL approximation. For the scalar theory, we evaluate the two-point function, recovering the usual dispersion relations. We also analyze the rotational invariance of the model. We then consider the Quantum Electrodynamics in (3+1) dimensions and calculate the polarization tensor and the vertex function at finite temperature in the HTL approximation. In future, our interest will be to apply the Generalized Light Front formalism to understand the confinement mechanism which occurs in the Quantum Chromodynamics. There is an expectation that the Light Front Quantum Field Theory formalism is more appropriate to study this problems. (author)
Nucleon-generalized parton distributions in the light-front quark model
Indian Academy of Sciences (India)
2016-01-12
Jan 12, 2016 ... 1. Introduction. Generalized parton distributions (GPDs) are the important set of parameters that give us ... The AdS/CFT is the correspondence between the string theory on a higher-dimensional anti-de Sitter ... matching the soft-wall model of AdS/QCD and light-front QCD for EFFs of hadrons with arbitrary ...
Spacelike and timelike form factors for ω→πγ* and K*→Kγ* in the light-front quark model
International Nuclear Information System (INIS)
Choi, Ho-Meoyng
2008-01-01
We investigate space- and timelike form factors for ω→πγ* and K*→Kγ* decays using the light-front quark model constrained by the variational principle for the QCD-motivated effective Hamiltonian. The momentum dependent spacelike form factors are obtained in the q + =0 frame and then analytically continued to the timelike region. Our prediction for the timelike form factor F ωπ (q 2 ) is in good agreement with the experimental data. We also find that the spacelike form factor F K* ± K ± (Q 2 ) for charged kaons encounters a zero because of the negative interference between the two currents to the quark and the antiquark.
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.
Light-front zero-mode contribution to the Ward Identity
International Nuclear Information System (INIS)
Sales, J.H.O.; Suzuki, A.T.
2010-01-01
In a covariant gauge we implicitly assume that the Green's function propagates information from one point of the space-time to another, so that the Green's function is responsible for the dynamics of the relativistic particle. In the light front form one would naively expect that this feature would be preserved. In this manner, the fermionic field propagator can be split into a propagating piece and a non-propagating ('contact') term. Since the latter ('contact') one does not propagate information, and therefore, supposedly can be discarded with no harm to the field dynamics we wanted to know what would be the impact of dropping it off. To do that, we investigated its role in the Ward identity in the light front. Here we use the terminology Ward identity to identify the limiting case of photon's zero momentum transfer in the vertex from the more general Ward-Takahashi identity with nonzero momentum transfer.
Leading Twist TMDs in a Light-Front Quark-Diquark Model for Proton
Maji, Tanmay; Chakrabarti, Dipankar
2018-05-01
We present p_{\\perp } variation (fixed x) of the leading-twist T-even transverse momentum dependent parton distributions (TMDs) of a proton in a light-front quark-diquark model at μ ^2=2.4 and 20 GeV^2. The quark densities for unpolarized and transversely polarized proton are also presented. We observe a Soffer bound for TMDs in this model.
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.
Relativistic two-and three-particle scattering equations using instant and light-front dynamics
International Nuclear Information System (INIS)
Adhikari, S.K.; Tomio, L.; Frederico, T.
1992-01-01
Starting from the Bethe-Salpeter equation for two particles in the ladder approximation and integrating over the time component of momentum we derive three dimensional scattering integral equations satisfying constraints of unitarity and relativity, both employing the light-front and instant-form variables. The equations we arrive at are those first derived by Weinberg and by Blankenbecler and Sugar, and are shown to be related by a transformation of variables. Hence we show how to perform and relate identical dynamical calculation using these two equations. We extends this procedure to the case of three particles interacting via two-particle separable potentials. Using light-front and instant form variables we suggest a couple of three dimensional three-particle scattering equations satisfying constraints of two and three-particle unitarity and relativity. The three-particle light-front equation is shown to be approximately related by a transformation of variables to one of the instant-form three-particle equations. (author)
The vacuum structure of light-front φ41+1-theory
International Nuclear Information System (INIS)
Heinzl, T.; Stern, C.; Werner, E.; Zellermann, B.
1996-01-01
We discuss the vacuum structure of φ 4 -theory in 1+1 dimensions quantised on the light-front x + =0. To this end, one has to solve a non-linear, operator-valued constraint equation. It expresses that mode of the field operator having longitudinal light-front momentum equal to zero, as a function of all the other modes in the theory. We analyse whether this zero mode can lead to a non-vanishing vacuum expectation value of the field φ and thus to spontaneous symmetry breaking. In perturbation theory, we get no symmetry breaking. If we solve the constraint, however, non-perturbatively, within a mean-field type Fock ansatz, the situation changes: while the vacuum state itself remains trivial, we find a non-vanishing vacuum expectation value above a critical coupling. Exactly the same result is obtained within a light-front Tamm-Dancoff approximation, if the renormalisation is done in the correct way. (orig.). With 1 fig
A covariant formulation of the relativistic Hamiltonian theory on the light cone (fields with spin)
International Nuclear Information System (INIS)
Atakishiev, N.M.; Mir-Kasimov, R.M.; Nagiyev, Sh.M.
1978-01-01
A Hamiltonian formulation of quantum field theory on the light cone, developed earlier, is extended to the case of particles with spin. The singularities accompanying each field theory in light-front variables are removed by the introduction of an infinite number of counterterms of a new type, which can be included into the interaction Hamiltonian. A three-dimensional diagram technique is formulated, which is applied to calculate the fermion self-energy in the lowest order of perturbation theory
Meeds, E.; Leenders, R.; Welling, M.; Meila, M.; Heskes, T.
2015-01-01
Approximate Bayesian computation (ABC) is a powerful and elegant framework for performing inference in simulation-based models. However, due to the difficulty in scaling likelihood estimates, ABC remains useful for relatively lowdimensional problems. We introduce Hamiltonian ABC (HABC), a set of
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.
Universality of Generalized Parton Distributions in Light-Front Holographic QCD
de Téramond, Guy F.; Liu, Tianbo; Sufian, Raza Sabbir; Dosch, Hans Günter; Brodsky, Stanley J.; Deur, Alexandre; Hlfhs Collaboration
2018-05-01
The structure of generalized parton distributions is determined from light-front holographic QCD up to a universal reparametrization function w (x ) which incorporates Regge behavior at small x and inclusive counting rules at x →1 . A simple ansatz for w (x ) that fulfills these physics constraints with a single-parameter results in precise descriptions of both the nucleon and the pion quark distribution functions in comparison with global fits. The analytic structure of the amplitudes leads to a connection with the Veneziano model and hence to a nontrivial connection with Regge theory and the hadron spectrum.
Ab initio Hamiltonian approach to light nuclei and quantum field theory
International Nuclear Information System (INIS)
Vary, James P.
2009-01-01
A basis-function approach that has proven successful for solving the nonrelativistic strongly interacting nuclear many-body problem and appears promising for solving relativistic field theory in a light-front Hamiltonian framework is presented. Both conventional nuclear manybody theory and light-front field theory face common issues within the Hamiltonian approach - i.e. how to; (1) define the Hamiltonian; (2) renormalize to a finite space; (3) solve for non-perturbative observables, preserving as many symmetries as possible; and (4) take the continuum limit. Each of these challenges requires a substantial undertaking but appears solvable. Advances in computational physics, both algorithms and parallel computers, have proven essential to the recent progress. I will present results that illustrate the recent advances and indicate the path forward to ever more realistic applications
In-Medium K^+ Electromagnetic Form Factor with a Symmetric Vertex in a Light Front Approach
Yabusaki, George H. S.; de Melo, J. P. B. C.; de Paula, Wayne; Tsushima, K.; Frederico, T.
2018-05-01
Using the light-front K^ +-Meson wave function based on a Bethe-Salpeter amplitude model for the Quark-Antiquark bound state, we study the Electromagnetic Form Factor (EMFF) of the K^ +-Meson in nuclear medium within the framework of light-front field theory. The K^ +-Meson model we adopt is well constrained by previous and recent studies to explain its properties in vacuum. The in-medium K^ +-Meson EMFF is evaluated for the plus-component of the electromagnetic current, J^+, in the Breit frame. In order to consistently incorporate the constituent up and antistrange Quarks of the K^ +-Meson immersed in symmetric nuclear matter, we use the Quark-Meson coupling model, which has been widely applied to various hadronic and nuclear phenomena in a nuclear medium with success. We predict the in-medium modification of the K^ +-Meson EMFF in symmetric nuclear matter. It is found that, after a fine tuning of the regulator mass, i.e. m_R = 0.600 GeV, the model is suitable to fit the available experimental data in vacuum within the theoretical uncertainties, and based on this we predict the in-medium modification of the K^ +-Meson EMFF.
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
International Nuclear Information System (INIS)
Peggs, S.; Talman, R.
1987-01-01
As proton accelerators get larger, and include more magnets, the conventional tracking programs which simulate them run slower. The purpose of this paper is to describe a method, still under development, in which element-by-element tracking around one turn is replaced by a single man, which can be processed far faster. It is assumed for this method that a conventional program exists which can perform faithful tracking in the lattice under study for some hundreds of turns, with all lattice parameters held constant. An empirical map is then generated by comparison with the tracking program. A procedure has been outlined for determining an empirical Hamiltonian, which can represent motion through many nonlinear kicks, by taking data from a conventional tracking program. Though derived by an approximate method this Hamiltonian is analytic in form and can be subjected to further analysis of varying degrees of mathematical rigor. Even though the empirical procedure has only been described in one transverse dimension, there is good reason to hope that it can be extended to include two transverse dimensions, so that it can become a more practical tool in realistic cases
Form factors of ηc in light-front quark model
International Nuclear Information System (INIS)
Geng, Chao-Qiang; Lih, Chong-Chung
2013-01-01
We study the form factors of the η c meson in the light-front quark model. We explicitly show that the transition form factor of η c → γ * γ as a function of the momentum transfer is consistent with the experimental data by the BaBar collaboration, while the decay constant of η c is found to be f η c = 230.5 +52.2 -61.0 and 303.6 +115.2 -116.4 MeV for η c ∝ c anti c by using two η c → γγ decay widths of 5.3 ± 0.5 and 7.2 ± 2.1 keV, given by Particle Data Group and Lattice QCD calculation, respectively. (orig.)
Form factors of {eta}{sub c} in light-front quark model
Energy Technology Data Exchange (ETDEWEB)
Geng, Chao-Qiang [Chongqing University of Posts and Telecommunications, College of Mathematics and Physics, Chongqing (China); National Center for Theoretical Sciences, Physics Division, Hsinchu (China); National Tsing Hua University, Department of Physics, Hsinchu (China); Lih, Chong-Chung [Shu-Zen College of Medicine and Management, Department of Optometry, Kaohsiung Hsien (China); National Center for Theoretical Sciences, Physics Division, Hsinchu (China); National Tsing Hua University, Department of Physics, Hsinchu (China)
2013-08-15
We study the form factors of the {eta}{sub c} meson in the light-front quark model. We explicitly show that the transition form factor of {eta}{sub c} {yields} {gamma}{sup *}{gamma} as a function of the momentum transfer is consistent with the experimental data by the BaBar collaboration, while the decay constant of {eta}{sub c} is found to be f{sub {eta}{sub c}} = 230.5{sup +52.2}{sub -61.0} and 303.6{sup +115.2}{sub -116.4} MeV for {eta}{sub c} {proportional_to} c anti c by using two {eta}{sub c} {yields} {gamma}{gamma} decay widths of 5.3 {+-} 0.5 and 7.2 {+-} 2.1 keV, given by Particle Data Group and Lattice QCD calculation, respectively. (orig.)
Semileptonic decays of B and D mesons in the light-front formalism
International Nuclear Information System (INIS)
Jaus, W.
1990-01-01
The light-front formalism is used to present a relativistic calculation of form factors for semileptonic D and B decays in the constituent quark model. The quark-antiquark wave functions of the mesons can be obtained, in principle, from an analysis of the meson spectrum, but are approximated in this work by harmonic-oscillator wave functions. The predictions of the model are consistent with the experimental data for B decays. The Kobayashi-Maskawa (KM) matrix element |V cs | is determined by a comparison of the experimental and theoretical rates for D 0 →K - e + ν, and is consistent with a unitary KM matrix for three families. The predictions for D→K * transitions are in conflict with the data
Some heavy vector and tensor meson decay constants in light-front quark model
Energy Technology Data Exchange (ETDEWEB)
Geng, Chao-Qiang [Chongqing Jiaotong University, College of Materials Science and Engineering, Chongqing (China); National Tsing Hua University, Department of Physics, Hsinchu (China); National Center for Theoretical Sciences, Physics Division, Hsinchu (China); Lih, Chong-Chung [National Center for Theoretical Sciences, Physics Division, Hsinchu (China); Shu-Zen College of Medicine and Management, Department of Optometry, Kaohsiung Hsien (China); Xia, Chuanhui [Chongqing Jiaotong University, College of Materials Science and Engineering, Chongqing (China)
2016-06-15
We study the decay constants (f{sub M}) of the heavy vector (D{sup *}, D{sub s}{sup *}, B{sup *}, B{sub s}{sup *}, B{sub c}{sup *}) and tensor (D{sub 2}{sup *}, D{sub s2}{sup *}, B{sub 2}{sup *}, B{sub s2}{sup *}) mesons in the light-front quarkmodel.With the known pseudoscalar meson decay constants of f{sub D}, f{sub Ds}, f{sub B}, f{sub Bs}, and f{sub Bc} as the input parameters to determine the light-front meson wave functions, we obtain f{sub D{sup *},D{sub s{sup *}B{sup *}B{sub s{sup *},B{sub c{sup *}}}}} = (252.0{sub -11.6}{sup +13.8}, 318.3{sub -12.6}{sup +15.3}, 201.9{sub -41.4}{sup +43.2}, 244.2 ± 7.0, 473.4 ± 18.2) and (264.9{sub -9.5}{sup +10.2}, 330.9{sub -9.0}{sup +9.9}, 220.2{sub -46.2}{sup +49.1}, 265.7 ± 8.0, 487.6 ± 19.2) MeV with Gaussian and power-law wave functions, respectively, while we have f{sub D{sub 2{sup *},D{sub s{sub 2{sup *}B{sub 2{sup *}B{sub s{sub 2{sup *}}}}}}}} = (143.6{sub -21.8}{sup +24.9}, 209.5{sub -24.2}{sup +29.1}, 80.9{sub -27.7}{sup +33.8}, 109.7{sub -15.0}{sup +15.7}) MeV with only Gaussian wave functions. (orig.)
Non-Perturbative QCD Coupling and Beta Function from Light Front Holography
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.; /SLAC /Southern Denmark U., CP3-Origins; de Teramond, Guy F.; /Costa Rica U.; Deur, Alexandre; /Jefferson Lab
2010-05-26
The light-front holographic mapping of classical gravity in AdS space, modified by a positive-sign dilaton background, leads to a non-perturbative effective coupling {alpha}{sub s}{sup AdS} (Q{sup 2}). It agrees with hadron physics data extracted from different observables, such as the effective charge defined by the Bjorken sum rule, as well as with the predictions of models with built-in confinement and lattice simulations. It also displays a transition from perturbative to nonperturbative conformal regimes at a momentum scale {approx} 1 GeV. The resulting {beta}-function appears to capture the essential characteristics of the full {beta}-function of QCD, thus giving further support to the application of the gauge/gravity duality to the confining dynamics of strongly coupled QCD. Commensurate scale relations relate observables to each other without scheme or scale ambiguity. In this paper we extrapolate these relations to the nonperturbative domain, thus extending the range of predictions based on {alpha}{sub s}{sup AdS} (Q{sup 2}).
Non-Perturbative QCD Coupling and Beta Function from Light Front Holography
International Nuclear Information System (INIS)
Brodsky, Stanley J.
2010-01-01
The light-front holographic mapping of classical gravity in AdS space, modified by a positive-sign dilaton background, leads to a non-perturbative effective coupling α s AdS (Q 2 ). It agrees with hadron physics data extracted from different observables, such as the effective charge defined by the Bjorken sum rule, as well as with the predictions of models with built-in confinement and lattice simulations. It also displays a transition from perturbative to nonperturbative conformal regimes at a momentum scale ∼ 1 GeV. The resulting β-function appears to capture the essential characteristics of the full β-function of QCD, thus giving further support to the application of the gauge/gravity duality to the confining dynamics of strongly coupled QCD. Commensurate scale relations relate observables to each other without scheme or scale ambiguity. In this paper we extrapolate these relations to the nonperturbative domain, thus extending the range of predictions based on α s AdS (Q 2 ).
Symmetries for Light-Front Quantization of Yukawa Model with Renormalization
Żochowski, Jan; Przeszowski, Jerzy A.
2017-12-01
In this work we discuss the Yukawa model with the extra term of self-interacting scalar field in D=1+3 dimensions. We present the method of derivation the light-front commutators and anti-commutators from the Heisenberg equations induced by the kinematical generating operator of the translation P+. Mentioned Heisenberg equations are the starting point for obtaining this algebra of the (anti-) commutators. Some discrepancies between existing and proposed method of quantization are revealed. The Lorentz and the CPT symmetry, together with some features of the quantum theory were applied to obtain the two-point Wightman function for the free fermions. Moreover, these Wightman functions were computed especially without referring to the Fock expansion. The Gaussian effective potential for the Yukawa model was found in the terms of the Wightman functions. It was regularized by the space-like point-splitting method. The coupling constants within the model were redefined. The optimum mass parameters remained regularization independent. Finally, the Gaussian effective potential was renormalized.
Scaling for deuteron structure functions in a relativistic light-front model
International Nuclear Information System (INIS)
Polyzou, W.N.; Gloeckle, W.
1996-01-01
Scaling limits of the structure functions [B.D. Keister, Phys. Rev. C 37, 1765 (1988)], W 1 and W 2 , are studied in a relativistic model of the two-nucleon system. The relativistic model is defined by a unitary representation, U(Λ,a), of the Poincaracute e group which acts on the Hilbert space of two spinless nucleons. The representation is in Dirac close-quote s [P.A.M. Dirac, Rev. Mod. Phys. 21, 392 (1949)] light-front formulation of relativistic quantum mechanics and is designed to give the experimental deuteron mass and n-p scattering length. A model hadronic current operator that is conserved and covariant with respect to this representation is used to define the structure tensor. This work is the first step in a relativistic extension of the results of Hueber, Gloeckle, and Boemelburg. The nonrelativistic limit of the model is shown to be consistent with the nonrelativistic model of Hueber, Gloeckle, and Boemelburg. [D. Hueber et al. Phys. Rev. C 42, 2342 (1990)]. The relativistic and nonrelativistic scaling limits, for both Bjorken and y scaling are compared. The interpretation of y scaling in the relativistic model is studied critically. The standard interpretation of y scaling requires a soft wave function which is not realized in this model. The scaling limits in both the relativistic and nonrelativistic case are related to probability distributions associated with the target deuteron. copyright 1996 The American Physical Society
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.
Nucleon momentum distribution in deuteron and other nuclei within the light-front dynamics method
International Nuclear Information System (INIS)
Antonov, A.N.; Gaidarov, M.K.; Ivanov, M.V.; Kadrev, D.N.; Krumova, G.Z.; Hodgson, P.E.; Geramb, H.V. von
2002-01-01
The relativistic light-front dynamics (LFD) method has been shown to give a correct description of the most recent data for the deuteron monopole and quadrupole charge form factors obtained at the Jefferson Laboratory for elastic electron-deuteron scattering for six values of the squared momentum transfer between 0.66 and 1.7 (GeV/c) 2 . The good agreement with the data is in contrast with the results of the existing nonrelativistic approaches. In this work we first make a complementary test of the LFD applying it to calculate another important characteristic, the nucleon momentum distribution n(q) of the deuteron, using six invariant functions f i (i=1,...,6) instead of two (S and D waves) in the nonrelativistic case. The comparison with the y-scaling data shows the decisive role of the function f 5 which at q≥500 MeV/c exceeds all other f functions (as well as the S and D waves) for the correct description of n(q) of the deuteron in the high-momentum region. Comparison with other calculations using S and D waves corresponding to various nucleon-nucleon potentials is made. Second, using clear indications that the high-momentum components of n(q) in heavier nuclei are related to those in the deuteron, we develop an approach within the natural orbital representation to calculate n(q) in (A,Z) nuclei on the basis of the deuteron momentum distribution. As examples, n(q) in 4 He, 12 C, and 56 Fe are calculated and good agreement with the y-scaling data is obtained
Spontaneous symmetry breaking of (1+1)-dimensional φ4 theory in light-front field theory
International Nuclear Information System (INIS)
Bender, C.M.; Pinsky, S.; van de Sande, B.
1993-01-01
We study spontaneous symmetry breaking in (1+1)-dimensional φ 4 theory using the light-front formulation of field theory. Since the physical vacuum is always the same as the perturbative vacuum in light-front field theory the fields must develop a vacuum expectation value through the zero-mode components of the field. We solve the nonlinear operator equation for the zero mode in the one-mode approximation. We find that spontaneous symmetry breaking occurs at λ critical =4π(3+ √3 )μ 2 , which is consistent with the value λ critical =54.27μ 2 obtained in the equal-time theory. We calculate the vacuum expectation value as a function of the coupling constant in the broken phase both numerically and analytically using the δ expansion. We find two equivalent broken phases. Finally we show that the energy levels of the system have the expected behavior for the broken phase
Counterterms in Gravity in the Light-Front Formulation and a D=2 Conformal-like Symmetry in Gravity
Bengtsson, Anders K. H.; Brink, Lars; Kim, Sung-Soo
2012-01-01
In this paper we discuss gravity in the light-front formulation (light-cone gauge) and show how possible counterterms arise. We find that Poincare invariance is not enough to find the three-point counterterms uniquely. Higher-spin fields can intrude and mimic three-point higher derivative gravity terms. To select the correct term we have to use the remaining reparametrization invariance that exists after the gauge choice. We finally sketch how the corresponding programme for N=8 Supergravity ...
International Nuclear Information System (INIS)
Srivastava, P.P.
1993-01-01
The field theory quantized on the light-front is compared with the conventional equal-time quantized theory. The arguments based on the micro causality principle would imply that the light-front field theory may become nonlocal with respect to the longitudinal coordinate even though the corresponding equal-time formulation is local. This is found to be the case for the scalar theory. The conventional instant form theory is sometimes required to be constrained by invoking external physical considerations; the analogous conditions seem to be already built in the theory on the light-front. In spite of the different mechanisms of the spontaneous symmetry breaking in the two forms of dynamics they result in the same physical content. The phase transition in (φ 4 ) 2 theory is also discussed. The symmetric vacuum state for vanishingly small couplings is found to turn into an unstable symmetric one when the coupling is increased and may result in a phase transition of the second order in contrast to the first order transition concluded from the usual variational methods. (author)
A model of mesons based on χSB in the light-front frame
International Nuclear Information System (INIS)
Susskind, L.; Burkardt, M.
1994-01-01
Spontaneous breaking of chiral symmetry is discussed in the light-cone framework. The essential ingredient is an infinite number of constituents near zero light-cone momentum. These high (light-cone) energy degrees of freedom freeze out and leave behind some explicit symmetry breaking in the low (light-cone) energy effective Hamiltonian. Connections with Regge theory and soft pion theorems are discussed. Taking the order parameter to be the 4-th component of a chiral 4-vector, the effect of the spontaneous symmetry breaking on meson masses and decay width is calculated and compared with experimental data
Light-front quark model analysis of the exclusive rare Bc→D(s)(l+l-,νlνl) decays
International Nuclear Information System (INIS)
Choi, Ho-Meoyng
2010-01-01
We investigate the exclusive rare B c →D (s) ν l ν l and B→D (s) l + l - (l=e, μ, τ) decays within the standard model and the light-front quark model constrained by the variational principle for the QCD-motivated effective Hamiltonian. The form factors f ± (q 2 ) and f T (q 2 ) are obtained from the analytic continuation method in the q + =0 frame. While the form factors f + (q 2 ) and f T (q 2 ) are free from the zero mode, the form factor f - (q 2 ) is not free from the zero mode in the q + =0 frame. We discuss the covariance (i.e. frame independence) of our model calculation and quantify the zero-mode contributions to f - (q 2 ) for B c →D (s) decays. The branching ratios and the longitudinal lepton polarization asymmetries are calculated with and without the long-distance contributions. Our numerical results for the nonresonant branching ratios for and B c →D(D s )l + l - are in the order of 10 -8 (10 -7 ) and 10 -9 (10 -8 ), respectively. The averaged values of the lepton polarization asymmetries obtained from the linear (harmonic oscillator) potential parameters are found to be -0.99 (-0.99) for B c →Dμ + μ - and -0.16 (-0.15) for B c →Dτ + τ - , and -0.98 (-0.98) for B c →D s μ + μ - and -0.14 (-0.12) for B c →D s τ + τ - , respectively.
Convergence of the Light-Front Coupled-Cluster Method in Scalar Yukawa Theory
Usselman, Austin
We use Fock-state expansions and the Light-Front Coupled-Cluster (LFCC) method to study mass eigenvalue problems in quantum field theory. Specifically, we study convergence of the method in scalar Yukawa theory. In this theory, a single charged particle is surrounded by a cloud of neutral particles. The charged particle can create or annihilate neutral particles, causing the n-particle state to depend on the n + 1 and n - 1-particle state. Fock state expansion leads to an infinite set of coupled equations where truncation is required. The wave functions for the particle states are expanded in a basis of symmetric polynomials and a generalized eigenvalue problem is solved for the mass eigenvalue. The mass eigenvalue problem is solved for multiple values for the coupling strength while the number of particle states and polynomial basis order are increased. Convergence of the mass eigenvalue solutions is then obtained. Three mass ratios between the charged particle and neutral particles were studied. This includes a massive charged particle, equal masses and massive neutral particles. Relative probability between states can also be explored for more detailed understanding of the process of convergence with respect to the number of Fock sectors. The reliance on higher order particle states depended on how large the mass of the charge particle was. The higher the mass of the charged particle, the more the system depended on higher order particle states. The LFCC method solves this same mass eigenvalue problem using an exponential operator. This exponential operator can then be truncated instead to form a finite system of equations that can be solved using a built in system solver provided in most computational environments, such as MatLab and Mathematica. First approximation in the LFCC method allows for only one particle to be created by the new operator and proved to be not powerful enough to match the Fock state expansion. The second order approximation allowed one
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.
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.
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.
Renormalization of Hamiltonian QCD
International Nuclear Information System (INIS)
Andrasi, A.; Taylor, John C.
2009-01-01
We study to one-loop order the renormalization of QCD in the Coulomb gauge using the Hamiltonian formalism. Divergences occur which might require counter-terms outside the Hamiltonian formalism, but they can be cancelled by a redefinition of the Yang-Mills electric field.
Magnetic field line Hamiltonian
International Nuclear Information System (INIS)
Boozer, A.H.
1984-03-01
The magnetic field line Hamiltonian and the associated canonical form for the magnetic field are important concepts both for understanding toroidal plasma physics and for practical calculations. A number of important properties of the canonical or Hamiltonian representation are derived and their importance is explained
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 ...
Magnetic field line Hamiltonian
International Nuclear Information System (INIS)
Boozer, A.H.
1985-02-01
The basic properties of the Hamiltonian representation of magnetic fields in canonical form are reviewed. The theory of canonical magnetic perturbation theory is then developed and applied to the time evolution of a magnetic field embedded in a toroidal plasma. Finally, the extension of the energy principle to tearing modes, utilizing the magnetic field line Hamiltonian, is outlined
Diagonalization of Hamiltonian; Diagonalization of Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Garrido, L M; Pascual, P
1960-07-01
We present a general method to diagonalized the Hamiltonian of particles of arbitrary spin. In particular we study the cases of spin 0,1/2, 1 and see that for spin 1/2 our transformation agrees with Foldy's and obtain the expression for different observables for particles of spin C and 1 in the new representation. (Author) 7 refs.
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.)
Theory of collective Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Zhang Qingying
1982-02-01
Starting from the cranking model, we derive the nuclear collective Hamiltonian. We expand the total energy of the collective motion of the ground state of even--even nuclei in powers of the deformation parameter ..beta... In the first approximation, we only take the lowest-order non-vanished terms in the expansion. The collective Hamiltonian thus obtained rather differs from the A. Bohr's Hamiltonian obtained by the irrotational incompressible liquid drop model. If we neglect the coupling term between ..beta..-and ..gamma..-vibration, our Hamiltonian then has the same form as that of A. Bohr. But there is a difference between these collective parameters. Our collective parameters are determined by the state of motion of the nucleous in the nuclei. They are the microscopic expressions. On the contrary, A. Bohr's collective parameters are only the simple functions of the microscopic physical quantities (such as nuclear radius and surface tension, etc.), and independent of the state of motion of the nucleons in the nuclei. Furthermore, there exist the coupling term between ..beta..-and ..gamma..-vibration and the higher-order terms in our expansion. They can be treated as the perturbations. There are no such terms in A. Bohr's Hamiltonian. These perturbation terms will influence the rotational, vibrational spectra and the ..gamma..-transition process, etc.
Bound-state problem in the light-front Tamm-Dancoff approximation: Numerical study in 1+1 dimensions
International Nuclear Information System (INIS)
Harindranath, A.; Perry, R.J.; Shigemitsu, J.
1992-01-01
Numerical solutions to the two-fermion bound-state problem in the (1+1)-dimensional Yukawa model are presented within the lowest-order light-front Tamm-Dancoff approximation (i.e., keeping only two-fermion and two-fermion--one-boson sectors). Our motivation is twofold. First, we want to understand the dynamics of the model from the very-weak-coupling domain, where the system is governed by nonrelativistic dynamics, to moderate and strong-coupling domains where retardation and self-energy effects become important. Second, we want to develop techniques for solving coupled Tamm-Dancoff integral equations, in particular, methods that can be generalized to higher-order Tamm-Dancoff approximations. To achieve the first goal we first simplify the problem considerably (from a numerical point of view) by the explicit elimination of the higher Fock-space sector. The resulting integral equation, whose kernel depends upon the invariant mass of the state, is solved for the coupling constant, for a given set of the invariant mass and fermion and boson mass parameters. To achieve the second goal we solve the coupled set of equations using both basis functions and direct-discretization techniques. Results from these more general techniques are compared with the explicit-elimination method
Time dependent drift Hamiltonian
International Nuclear Information System (INIS)
Boozer, A.H.
1982-04-01
The motion of individual charged particles in a given magnetic and an electric fields is discussed. An idea of a guiding center distribution function f is introduced. The guiding center distribution function is connected to the asymptotic Hamiltonian through the drift kinetic equation. The general non-stochastic magnetic field can be written in a contravariant and a covariant forms. The drift Hamiltonian is proposed, and the canonical gyroradius is presented. The proposed drift Hamiltonian agrees with Alfven's drift velocity to lowest non-vanishing order in the gyroradius. The relation between the exact, time dependent equations of motion and the guiding center equation is clarified by a Lagrangian analysis. The deduced Lagrangian represents the drift motion. (Kato, T.)
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...
Effective magnetic Hamiltonians
Czech Academy of Sciences Publication Activity Database
Drchal, Václav; Kudrnovský, Josef; Turek, I.
2013-01-01
Roč. 26, č. 5 (2013), s. 1997-2000 ISSN 1557-1939 R&D Projects: GA ČR GA202/09/0775 Institutional support: RVO:68378271 Keywords : effective magnetic Hamiltonian * ab initio * magnetic structure Subject RIV: BE - Theoretical Physics Impact factor: 0.930, year: 2013
Dissipative systems and Bateman's Hamiltonian
International Nuclear Information System (INIS)
Pedrosa, I.A.; Baseia, B.
1983-01-01
It is shown, by using canonical transformations, that one can construct Bateman's Hamiltonian from a Hamiltonian for a conservative system and obtain a clear physical interpretation which explains the ambiguities emerging from its application to describe dissipative systems. (Author) [pt
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...
Noncanonical Hamiltonian mechanics
International Nuclear Information System (INIS)
Litteljohn, R.G.
1986-01-01
Noncanonical variables in Hamiltonian mechanics were first used by Lagrange in 1808. In spite of this, most work in Hamiltonian mechanics has been carried out in canonical variables, up to this day. One reason for this is that noncanonical coordinates are seldom needed for mechanical problems based on Lagrangians of the form L = T - V, where T is the kinetic energy and V is the potential energy. Of course, such Lagrangians arise naturally in celestial mechanics, and as a result they form the paradigms of nineteenth-century mechanics and have become enshrined in all the mechanics textbooks. Certain features of modern problems, however, lead to the use of noncanonical coordinates. Among these are issues of gauge invariance and singular Lagrange a Poisson structures. In addition, certain problems, like the flow of magnetic-field lines in physical space, are naturally formulated in terms of noncanonical coordinates. None of these features is present in the nineteenth-century paradigms of mechanics, but they do arise in problems involving particle motion in the presence of magnetic fields. For example, the motion of a particle in an electromagnetic wave is an important one in plasma physics, but the usual Hamiltonian formulation is gauge dependent. For this problem, noncanonical approaches based on Lagrangians in phase space lead to powerful computational techniques which are gauge invariant. In the limit of strong magnetic fields, particle motion becomes 'guiding-center motion'. Guiding-center motion is also best understood in terms of noncanonical coordinates. Finally the flow of magnetic-field lines through physical space is a Hamiltonian system which is best understood with noncanonical coordinates. No doubt many more systems will arise in the future for which these noncanonical techniques can be applied. (author)
Instability in Hamiltonian systems
Directory of Open Access Journals (Sweden)
A. Pumarino
2005-11-01
Besides proving the existence of Arnold diffusion for a new family of three degrees of freedom Hamiltonian systems, another goal of this book is not only to show how Arnold-like results can be extended to substantially larger sets of parameters, but also how to obtain effective estimates on the splitting of separatrices size when the frequency of the perturbation belongs to open real sets.
Discrete variational Hamiltonian mechanics
International Nuclear Information System (INIS)
Lall, S; West, M
2006-01-01
The main contribution of this paper is to present a canonical choice of a Hamiltonian theory corresponding to the theory of discrete Lagrangian mechanics. We make use of Lagrange duality and follow a path parallel to that used for construction of the Pontryagin principle in optimal control theory. We use duality results regarding sensitivity and separability to show the relationship between generating functions and symplectic integrators. We also discuss connections to optimal control theory and numerical algorithms
Approximate symmetries of Hamiltonians
Chubb, Christopher T.; Flammia, Steven T.
2017-08-01
We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest.
International Nuclear Information System (INIS)
Prokhorov, L.V.
1982-01-01
Problems related to consideration of operator nonpermutability in Hamiltonian path integral (HPI) are considered in the review. Integrals are investigated using trajectories in configuration space (nonrelativistic quantum mechanics). Problems related to trajectory integrals in HPI phase space are discussed: the problem of operator nonpermutability consideration (extra terms problem) and corresponding equivalence rules; ambiguity of HPI usual recording; transition to curvilinear coordinates. Problem of quantization of dynamical systems with couplings has been studied. As in the case of canonical transformations, quantization of the systems with couplings of the first kind requires the consideration of extra terms
International Nuclear Information System (INIS)
Mankiewicz, L.; Sawicki, M.
1989-01-01
Within a relativistically correct yet analytically solvable model of light-front quantum mechanics we construct the electromagnetic form factor of the two-body bound state and we study the validity of the static approximation to the full form factor. Upon comparison of full form factors calculated for different values of binding energy we observe an unexpected effect that for very strongly bound states further increase in binding leads to an increase in the size of the bound system. A similar effect is found for another quantum-mechanical model of relativistic dynamics
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley [SLAC National Accelerator Lab., Menlo Park, CA (United States)
2017-01-01
In this paper we show that the intrinsic heavy-quark QCD mechanism for the hadroproduction of heavy hadrons at large $x_F$ can resolve the apparent conflict between measurements of double-charm baryons by the SELEX fixed-target experiment and the LHCb experiment at the LHC collider. We show that both experiments are compatible, and that both results can be correct. The observed spectroscopy of double-charm hadrons is in agreement with the predictions of supersymmetric light front holographic QCD.
Robust online Hamiltonian learning
International Nuclear Information System (INIS)
Granade, Christopher E; Ferrie, Christopher; Wiebe, Nathan; Cory, D G
2012-01-01
In this work we combine two distinct machine learning methodologies, sequential Monte Carlo and Bayesian experimental design, and apply them to the problem of inferring the dynamical parameters of a quantum system. We design the algorithm with practicality in mind by including parameters that control trade-offs between the requirements on computational and experimental resources. The algorithm can be implemented online (during experimental data collection), avoiding the need for storage and post-processing. Most importantly, our algorithm is capable of learning Hamiltonian parameters even when the parameters change from experiment-to-experiment, and also when additional noise processes are present and unknown. The algorithm also numerically estimates the Cramer–Rao lower bound, certifying its own performance. (paper)
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.
Alternative Hamiltonian representation for gravity
Energy Technology Data Exchange (ETDEWEB)
Rosas-RodrIguez, R [Instituto de Fisica, Universidad Autonoma de Puebla, Apdo. Postal J-48, 72570, Puebla, Pue. (Mexico)
2007-11-15
By using a Hamiltonian formalism for fields wider than the canonical one, we write the Einstein vacuum field equations in terms of alternative variables. This variables emerge from the Ashtekar's formalism for gravity.
Alternative Hamiltonian representation for gravity
International Nuclear Information System (INIS)
Rosas-RodrIguez, R
2007-01-01
By using a Hamiltonian formalism for fields wider than the canonical one, we write the Einstein vacuum field equations in terms of alternative variables. This variables emerge from the Ashtekar's formalism for gravity
Scattering theory for Stark Hamiltonians
International Nuclear Information System (INIS)
Jensen, Arne
1994-01-01
An introduction to the spectral and scattering theory for Schroedinger operators is given. An abstract short range scattering theory is developed. It is applied to perturbations of the Laplacian. Particular attention is paid to the study of Stark Hamiltonians. The main result is an explanation of the discrepancy between the classical and the quantum scattering theory for one-dimensional Stark Hamiltonians. (author). 47 refs
Hamiltonian description of the ideal fluid
International Nuclear Information System (INIS)
Morrison, P.J.
1994-01-01
Fluid mechanics is examined from a Hamiltonian perspective. The Hamiltonian point of view provides a unifying framework; by understanding the Hamiltonian perspective, one knows in advance (within bounds) what answers to expect and what kinds of procedures can be performed. The material is organized into five lectures, on the following topics: rudiments of few-degree-of-freedom Hamiltonian systems illustrated by passive advection in two-dimensional fluids; functional differentiation, two action principles of mechanics, and the action principle and canonical Hamiltonian description of the ideal fluid; noncanonical Hamiltonian dynamics with examples; tutorial on Lie groups and algebras, reduction-realization, and Clebsch variables; and stability and Hamiltonian systems
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.
Variational identities and Hamiltonian structures
International Nuclear Information System (INIS)
Ma Wenxiu
2010-01-01
This report is concerned with Hamiltonian structures of classical and super soliton hierarchies. In the classical case, basic tools are variational identities associated with continuous and discrete matrix spectral problems, targeted to soliton equations derived from zero curvature equations over general Lie algebras, both semisimple and non-semisimple. In the super case, a supertrace identity is presented for constructing Hamiltonian structures of super soliton equations associated with Lie superalgebras. We illustrate the general theories by the KdV hierarchy, the Volterra lattice hierarchy, the super AKNS hierarchy, and two hierarchies of dark KdV equations and dark Volterra lattices. The resulting Hamiltonian structures show the commutativity of each hierarchy discussed and thus the existence of infinitely many commuting symmetries and conservation laws.
Dynamical decoupling of unbounded Hamiltonians
Arenz, Christian; Burgarth, Daniel; Facchi, Paolo; Hillier, Robin
2018-03-01
We investigate the possibility to suppress interactions between a finite dimensional system and an infinite dimensional environment through a fast sequence of unitary kicks on the finite dimensional system. This method, called dynamical decoupling, is known to work for bounded interactions, but physical environments such as bosonic heat baths are usually modeled with unbounded interactions; hence, here, we initiate a systematic study of dynamical decoupling for unbounded operators. We develop a sufficient decoupling criterion for arbitrary Hamiltonians and a necessary decoupling criterion for semibounded Hamiltonians. We give examples for unbounded Hamiltonians where decoupling works and the limiting evolution as well as the convergence speed can be explicitly computed. We show that decoupling does not always work for unbounded interactions and we provide both physically and mathematically motivated examples.
Invariant metrics for Hamiltonian systems
International Nuclear Information System (INIS)
Rangarajan, G.; Dragt, A.J.; Neri, F.
1991-05-01
In this paper, invariant metrics are constructed for Hamiltonian systems. These metrics give rise to norms on the space of homeogeneous polynomials of phase-space variables. For an accelerator lattice described by a Hamiltonian, these norms characterize the nonlinear content of the lattice. Therefore, the performance of the lattice can be improved by minimizing the norm as a function of parameters describing the beam-line elements in the lattice. A four-fold increase in the dynamic aperture of a model FODO cell is obtained using this procedure. 7 refs
Derivation of Hamiltonians for accelerators
Energy Technology Data Exchange (ETDEWEB)
Symon, K.R.
1997-09-12
In this report various forms of the Hamiltonian for particle motion in an accelerator will be derived. Except where noted, the treatment will apply generally to linear and circular accelerators, storage rings, and beamlines. The generic term accelerator will be used to refer to any of these devices. The author will use the usual accelerator coordinate system, which will be introduced first, along with a list of handy formulas. He then starts from the general Hamiltonian for a particle in an electromagnetic field, using the accelerator coordinate system, with time t as independent variable. He switches to a form more convenient for most purposes using the distance s along the reference orbit as independent variable. In section 2, formulas will be derived for the vector potentials that describe the various lattice components. In sections 3, 4, and 5, special forms of the Hamiltonian will be derived for transverse horizontal and vertical motion, for longitudinal motion, and for synchrobetatron coupling of horizontal and longitudinal motions. Hamiltonians will be expanded to fourth order in the variables.
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 ...
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 formulation of the supermembrane
International Nuclear Information System (INIS)
Bergshoeff, E.; Sezgin, E.; Tanii, Y.
1987-06-01
The Hamiltonian formulation of the supermembrane theory in eleven dimensions is given. The covariant split of the first and second class constraints is exhibited, and their Dirac brackets are computed. Gauge conditions are imposed in such a way that the reparametrizations of the membrane with divergence free 2-vectors are unfixed. (author). 10 refs
Relativistic non-Hamiltonian mechanics
International Nuclear Information System (INIS)
Tarasov, Vasily E.
2010-01-01
Relativistic particle subjected to a general four-force is considered as a nonholonomic system. The nonholonomic constraint in four-dimensional space-time represents the relativistic invariance by the equation for four-velocity u μ u μ + c 2 = 0, where c is the speed of light in vacuum. In the general case, four-forces are non-potential, and the relativistic particle is a non-Hamiltonian system in four-dimensional pseudo-Euclidean space-time. We consider non-Hamiltonian and dissipative systems in relativistic mechanics. Covariant forms of the principle of stationary action and the Hamilton's principle for relativistic mechanics of non-Hamiltonian systems are discussed. The equivalence of these principles is considered for relativistic particles subjected to potential and non-potential forces. We note that the equations of motion which follow from the Hamilton's principle are not equivalent to the equations which follow from the variational principle of stationary action. The Hamilton's principle and the principle of stationary action are not compatible in the case of systems with nonholonomic constraint and the potential forces. The principle of stationary action for relativistic particle subjected to non-potential forces can be used if the Helmholtz conditions are satisfied. The Hamilton's principle and the principle of stationary action are equivalent only for a special class of relativistic non-Hamiltonian systems.
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
Geometric Hamiltonian structures and perturbation theory
International Nuclear Information System (INIS)
Omohundro, S.
1984-08-01
We have been engaged in a program of investigating the Hamiltonian structure of the various perturbation theories used in practice. We describe the geometry of a Hamiltonian structure for non-singular perturbation theory applied to Hamiltonian systems on symplectic manifolds and the connection with singular perturbation techniques based on the method of averaging
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
Constructing Dense Graphs with Unique Hamiltonian Cycles
Lynch, Mark A. M.
2012-01-01
It is not difficult to construct dense graphs containing Hamiltonian cycles, but it is difficult to generate dense graphs that are guaranteed to contain a unique Hamiltonian cycle. This article presents an algorithm for generating arbitrarily large simple graphs containing "unique" Hamiltonian cycles. These graphs can be turned into dense graphs…
The Hamiltonian of QED. Zero mode
International Nuclear Information System (INIS)
Zastavenko, L.G.
1990-01-01
We start with the standard QED Lagrangian. New derivation of the spinor QED Hamiltonian is given. We have taken into account the zero mode. Our derivation is faultless from the point of view of gauge invariance. It gives important corrections to the standard QED Hamiltonian. Our derivation of the Hamiltonian can be generalized to the case of QCD. 5 refs
Hamiltonian PDEs and Frobenius manifolds
International Nuclear Information System (INIS)
Dubrovin, Boris A
2008-01-01
In the first part of this paper the theory of Frobenius manifolds is applied to the problem of classification of Hamiltonian systems of partial differential equations depending on a small parameter. Also developed is a deformation theory of integrable hierarchies including the subclass of integrable hierarchies of topological type. Many well-known examples of integrable hierarchies, such as the Korteweg-de Vries, non-linear Schroedinger, Toda, Boussinesq equations, and so on, belong to this subclass that also contains new integrable hierarchies. Some of these new integrable hierarchies may be important for applications. Properties of the solutions to these equations are studied in the second part. Consideration is given to the comparative study of the local properties of perturbed and unperturbed solutions near a point of gradient catastrophe. A Universality Conjecture is formulated describing the various types of critical behaviour of solutions to perturbed Hamiltonian systems near the point of gradient catastrophe of the unperturbed solution.
Hamiltonian PDEs and Frobenius manifolds
Energy Technology Data Exchange (ETDEWEB)
Dubrovin, Boris A [Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)
2008-12-31
In the first part of this paper the theory of Frobenius manifolds is applied to the problem of classification of Hamiltonian systems of partial differential equations depending on a small parameter. Also developed is a deformation theory of integrable hierarchies including the subclass of integrable hierarchies of topological type. Many well-known examples of integrable hierarchies, such as the Korteweg-de Vries, non-linear Schroedinger, Toda, Boussinesq equations, and so on, belong to this subclass that also contains new integrable hierarchies. Some of these new integrable hierarchies may be important for applications. Properties of the solutions to these equations are studied in the second part. Consideration is given to the comparative study of the local properties of perturbed and unperturbed solutions near a point of gradient catastrophe. A Universality Conjecture is formulated describing the various types of critical behaviour of solutions to perturbed Hamiltonian systems near the point of gradient catastrophe of the unperturbed solution.
Weak KAM for commuting Hamiltonians
International Nuclear Information System (INIS)
Zavidovique, M
2010-01-01
For two commuting Tonelli Hamiltonians, we recover the commutation of the Lax–Oleinik semi-groups, a result of Barles and Tourin (2001 Indiana Univ. Math. J. 50 1523–44), using a direct geometrical method (Stoke's theorem). We also obtain a 'generalization' of a theorem of Maderna (2002 Bull. Soc. Math. France 130 493–506). More precisely, we prove that if the phase space is the cotangent of a compact manifold then the weak KAM solutions (or viscosity solutions of the critical stationary Hamilton–Jacobi equation) for G and for H are the same. As a corollary we obtain the equality of the Aubry sets and of the Peierls barrier. This is also related to works of Sorrentino (2009 On the Integrability of Tonelli Hamiltonians Preprint) and Bernard (2007 Duke Math. J. 136 401–20)
Hamiltonian dynamics of extended objects
Capovilla, R.; Guven, J.; Rojas, E.
2004-12-01
We consider relativistic extended objects described by a reparametrization-invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the dynamics of such higher derivative models which is motivated by the ADM formulation of general relativity. The canonical momenta are identified by looking at boundary behaviour under small deformations of the action; the relationship between the momentum conjugate to the embedding functions and the conserved momentum density is established. The canonical Hamiltonian is constructed explicitly; the constraints on the phase space, both primary and secondary, are identified and the role they play in the theory is described. The multipliers implementing the primary constraints are identified in terms of the ADM lapse and shift variables and Hamilton's equations are shown to be consistent with the Euler Lagrange equations.
A Hamiltonian approach to Thermodynamics
Energy Technology Data Exchange (ETDEWEB)
Baldiotti, M.C., E-mail: baldiotti@uel.br [Departamento de Física, Universidade Estadual de Londrina, 86051-990, Londrina-PR (Brazil); Fresneda, R., E-mail: rodrigo.fresneda@ufabc.edu.br [Universidade Federal do ABC, Av. dos Estados 5001, 09210-580, Santo André-SP (Brazil); Molina, C., E-mail: cmolina@usp.br [Escola de Artes, Ciências e Humanidades, Universidade de São Paulo, Av. Arlindo Bettio 1000, CEP 03828-000, São Paulo-SP (Brazil)
2016-10-15
In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic Mechanics. Our proposal is constructed on top of a usual symplectic manifold, where phase space is even dimensional and one has well-defined Poisson brackets. The main idea is the introduction of an extended phase space where thermodynamic equations of state are realized as constraints. We are then able to apply the canonical transformation toolkit to thermodynamic problems. Throughout this development, Dirac’s theory of constrained systems is extensively used. To illustrate the formalism, we consider paradigmatic examples, namely, the ideal, van der Waals and Clausius gases. - Highlights: • A strictly Hamiltonian approach to Thermodynamics is proposed. • Dirac’s theory of constrained systems is extensively used. • Thermodynamic equations of state are realized as constraints. • Thermodynamic potentials are related by canonical transformations.
Hamiltonian description of bubble dynamics
International Nuclear Information System (INIS)
Maksimov, A. O.
2008-01-01
The dynamics of a nonspherical bubble in a liquid is described within the Hamiltonian formalism. Primary attention is focused on the introduction of the canonical variables into the computational algorithm. The expansion of the Dirichlet-Neumann operator in powers of the displacement of a bubble wall from an equilibrium position is obtained in the explicit form. The first three terms (more specifically, the second-, third-, and fourth-order terms) in the expansion of the Hamiltonian in powers of the canonical variables are determined. These terms describe the spectrum and interaction of three essentially different modes, i.e., monopole oscillations (pulsations), dipole oscillations (translational motions), and surface oscillations. The cubic nonlinearity is analyzed for the problem associated with the generation of Faraday ripples on the wall of a bubble in an acoustic field. The possibility of decay processes occurring in the course of interaction of surface oscillations for the first fifteen (experimentally observed) modes is investigated.
Hamiltonian dynamics of extended objects
International Nuclear Information System (INIS)
Capovilla, R; Guven, J; Rojas, E
2004-01-01
We consider relativistic extended objects described by a reparametrization-invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the dynamics of such higher derivative models which is motivated by the ADM formulation of general relativity. The canonical momenta are identified by looking at boundary behaviour under small deformations of the action; the relationship between the momentum conjugate to the embedding functions and the conserved momentum density is established. The canonical Hamiltonian is constructed explicitly; the constraints on the phase space, both primary and secondary, are identified and the role they play in the theory is described. The multipliers implementing the primary constraints are identified in terms of the ADM lapse and shift variables and Hamilton's equations are shown to be consistent with the Euler-Lagrange equations
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.
A Hamiltonian approach to Thermodynamics
International Nuclear Information System (INIS)
Baldiotti, M.C.; Fresneda, R.; Molina, C.
2016-01-01
In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic Mechanics. Our proposal is constructed on top of a usual symplectic manifold, where phase space is even dimensional and one has well-defined Poisson brackets. The main idea is the introduction of an extended phase space where thermodynamic equations of state are realized as constraints. We are then able to apply the canonical transformation toolkit to thermodynamic problems. Throughout this development, Dirac’s theory of constrained systems is extensively used. To illustrate the formalism, we consider paradigmatic examples, namely, the ideal, van der Waals and Clausius gases. - Highlights: • A strictly Hamiltonian approach to Thermodynamics is proposed. • Dirac’s theory of constrained systems is extensively used. • Thermodynamic equations of state are realized as constraints. • Thermodynamic potentials are related by canonical transformations.
On the domain of the Nelson Hamiltonian
Griesemer, M.; Wünsch, A.
2018-04-01
The Nelson Hamiltonian is unitarily equivalent to a Hamiltonian defined through a closed, semibounded quadratic form, the unitary transformation being explicitly known and due to Gross. In this paper, we study the mapping properties of the Gross-transform in order to characterize the regularity properties of vectors in the form domain of the Nelson Hamiltonian. Since the operator domain is a subset of the form domain, our results apply to vectors in the domain of the Hamiltonian as well. This work is a continuation of our previous work on the Fröhlich Hamiltonian.
Hamiltonian systems in accelerator physics
International Nuclear Information System (INIS)
Laslett, L.J.
1985-06-01
General features of the design of annular particle accelerators or storage rings are outlined and the Hamiltonian character of individual-ion motion is indicated. Examples of phase plots are presented, for the motion in one spatial degree of freedom, of an ion subject to a periodic nonlinear focusing force. A canonical transformation describing coupled nonlinear motion also is given, and alternative types of graphical display are suggested for the investigation of long-term stability in such cases. 7 figs
Contact symmetries and Hamiltonian thermodynamics
International Nuclear Information System (INIS)
Bravetti, A.; Lopez-Monsalvo, C.S.; Nettel, F.
2015-01-01
It has been shown that contact geometry is the proper framework underlying classical thermodynamics and that thermodynamic fluctuations are captured by an additional metric structure related to Fisher’s Information Matrix. In this work we analyse several unaddressed aspects about the application of contact and metric geometry to thermodynamics. We consider here the Thermodynamic Phase Space and start by investigating the role of gauge transformations and Legendre symmetries for metric contact manifolds and their significance in thermodynamics. Then we present a novel mathematical characterization of first order phase transitions as equilibrium processes on the Thermodynamic Phase Space for which the Legendre symmetry is broken. Moreover, we use contact Hamiltonian dynamics to represent thermodynamic processes in a way that resembles the classical Hamiltonian formulation of conservative mechanics and we show that the relevant Hamiltonian coincides with the irreversible entropy production along thermodynamic processes. Therefore, we use such property to give a geometric definition of thermodynamically admissible fluctuations according to the Second Law of thermodynamics. Finally, we show that the length of a curve describing a thermodynamic process measures its entropy production
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 dynamics of preferential attachment
International Nuclear Information System (INIS)
Zuev, Konstantin; Papadopoulos, Fragkiskos; Krioukov, Dmitri
2016-01-01
Prediction and control of network dynamics are grand-challenge problems in network science. The lack of understanding of fundamental laws driving the dynamics of networks is among the reasons why many practical problems of great significance remain unsolved for decades. Here we study the dynamics of networks evolving according to preferential attachment (PA), known to approximate well the large-scale growth dynamics of a variety of real networks. We show that this dynamics is Hamiltonian, thus casting the study of complex networks dynamics to the powerful canonical formalism, in which the time evolution of a dynamical system is described by Hamilton’s equations. We derive the explicit form of the Hamiltonian that governs network growth in PA. This Hamiltonian turns out to be nearly identical to graph energy in the configuration model, which shows that the ensemble of random graphs generated by PA is nearly identical to the ensemble of random graphs with scale-free degree distributions. In other words, PA generates nothing but random graphs with power-law degree distribution. The extension of the developed canonical formalism for network analysis to richer geometric network models with non-degenerate groups of symmetries may eventually lead to a system of equations describing network dynamics at small scales. (paper)
de Araújo, W. R. B.; de Melo, J. P. B. C.; Tsushima, K.
2018-02-01
We study the nucleon electromagnetic (EM) form factors in symmetric nuclear matter as well as in vacuum within a light-front approach using the in-medium inputs calculated by the quark-meson coupling model. The same in-medium quark properties are used as those used for the study of in-medium pion properties. The zero of the proton EM form factor ratio in vacuum, the electric to magnetic form factor ratio μpGEp (Q2) /GMp (Q2) (Q2 = -q2 > 0 with q being the four-momentum transfer), is determined including the latest experimental data by implementing a hard constituent quark component in the nucleon wave function. A reasonable fit is achieved for the ratio μpGEp (Q2) /GMp (Q2) in vacuum, and we predict that the Q02 value to cross the zero of the ratio to be about 15 GeV2. In addition the double ratio data of the proton EM form factors in 4He and H nuclei, [GEp4He (Q2) /G4HeMp (Q2) ] / [GEp1H (Q2) /GMp1H (Q2) ], extracted by the polarized (e → ,e‧ p →) scattering experiment on 4He at JLab, are well described. We also predict that the Q02 value satisfying μpGEp (Q02) /GMp (Q0 2) = 0 in symmetric nuclear matter, shifts to a smaller value as increasing nuclear matter density, which reflects the facts that the faster falloff of GEp (Q2) as increasing Q2 and the increase of the proton mean-square charge radius. Furthermore, we calculate the neutron EM form factor double ratio in symmetric nuclear matter for 0.1 neutron double ratio is enhanced relative to that in vacuum, while for the proton it is quenched, and agrees with an existing theoretical prediction.
Hamiltonian Chaos and Fractional Dynamics
International Nuclear Information System (INIS)
Combescure, M
2005-01-01
This book provides an introduction and discussion of the main issues in the current understanding of classical Hamiltonian chaos, and of its fractional space-time structure. It also develops the most complex and open problems in this context, and provides a set of possible applications of these notions to some fundamental questions of dynamics: complexity and entropy of systems, foundation of classical statistical physics on the basis of chaos theory, and so on. Starting with an introduction of the basic principles of the Hamiltonian theory of chaos, the book covers many topics that can be found elsewhere in the literature, but which are collected here for the readers' convenience. In the last three parts, the author develops topics which are not typically included in the standard textbooks; among them are: - the failure of the traditional description of chaotic dynamics in terms of diffusion equations; - he fractional kinematics, its foundation and renormalization group analysis; - 'pseudo-chaos', i.e. kinetics of systems with weak mixing and zero Lyapunov exponents; - directional complexity and entropy. The purpose of this book is to provide researchers and students in physics, mathematics and engineering with an overview of many aspects of chaos and fractality in Hamiltonian dynamical systems. In my opinion it achieves this aim, at least provided researchers and students (mainly those involved in mathematical physics) can complement this reading with comprehensive material from more specialized sources which are provided as references and 'further reading'. Each section contains introductory pedagogical material, often illustrated by figures coming from several numerical simulations which give the feeling of what's going on, and thus is very useful to the reader who is not very familiar with the topics presented. Some problems are included at the end of most sections to help the reader to go deeper into the subject. My one regret is that the book does not
Coherent states for quadratic Hamiltonians
International Nuclear Information System (INIS)
Contreras-Astorga, Alonso; Fernandez C, David J; Velazquez, Mercedes
2011-01-01
The coherent states for a set of quadratic Hamiltonians in the trap regime are constructed. A matrix technique which allows us to directly identify the creation and annihilation operators will be presented. Then, the coherent states as simultaneous eigenstates of the annihilation operators will be derived, and will be compared with those attained through the displacement operator method. The corresponding wavefunction will be found, and a general procedure for obtaining several mean values involving the canonical operators in these states will be described. The results will be illustrated through the asymmetric Penning trap.
Perturbation theory of effective Hamiltonians
International Nuclear Information System (INIS)
Brandow, B.H.
1975-01-01
This paper constitutes a review of the many papers which have used perturbation theory to derive ''effective'' or ''model'' Hamiltonians. It begins with a brief review of nondegenerate and non-many-body perturbation theory, and then considers the degenerate but non-many-body problem in some detail. It turns out that the degenerate perturbation problem is not uniquely defined, but there are some practical criteria for choosing among the various possibilities. Finally, the literature dealing with the linked-cluster aspects of open-shell many-body systems is reviewed. (U.S.)
Integrable and nonintegrable Hamiltonian systems
International Nuclear Information System (INIS)
Percival, I.
1986-01-01
Traditionally Hamiltonian systems with a finite number of degrees of freedom have been divided into those with few degrees of freedom which were supposed to exhibit some kind of regular ordered motions and those with large numbers of degrees of freedom for which the methods of statistical mechanics should be used. The last few decades have seen a complete change of view. The change of view affects almost all the practical applications, particularly in mathematical physics, which has been dominated for many decades by linear mathematics, coming from quantum theory. The authors consider how this change of view affects some specific applications of dynamics and also the relation between dynamical theory and applications
Perspective: Quantum Hamiltonians for optical interactions
Andrews, David L.; Jones, Garth A.; Salam, A.; Woolley, R. Guy
2018-01-01
The multipolar Hamiltonian of quantum electrodynamics is extensively employed in chemical and optical physics to treat rigorously the interaction of electromagnetic fields with matter. It is also widely used to evaluate intermolecular interactions. The multipolar version of the Hamiltonian is commonly obtained by carrying out a unitary transformation of the Coulomb gauge Hamiltonian that goes by the name of Power-Zienau-Woolley (PZW). Not only does the formulation provide excellent agreement with experiment, and versatility in its predictive ability, but also superior physical insight. Recently, the foundations and validity of the PZW Hamiltonian have been questioned, raising a concern over issues of gauge transformation and invariance, and whether observable quantities obtained from unitarily equivalent Hamiltonians are identical. Here, an in-depth analysis of theoretical foundations clarifies the issues and enables misconceptions to be identified. Claims of non-physicality are refuted: the PZW transformation and ensuing Hamiltonian are shown to rest on solid physical principles and secure theoretical ground.
Generalized oscillator representations for Calogero Hamiltonians
International Nuclear Information System (INIS)
Tyutin, I V; Voronov, B L
2013-01-01
This paper is a natural continuation of the previous paper (Gitman et al 2011 J. Phys. A: Math. Theor. 44 425204), where oscillator representations for nonnegative Calogero Hamiltonians with coupling constant α ⩾ − 1/4 were constructed. In this paper, we present generalized oscillator representations for all Calogero Hamiltonians with α ⩾ − 1/4. These representations are generally highly nonunique, but there exists an optimum representation for each Hamiltonian. (comment)
Hamiltonian formulation of reduced magnetohydrodynamics
International Nuclear Information System (INIS)
Morrison, P.J.; Hazeltine, R.D.
1983-07-01
Reduced magnetohydrodynamics (RMHD) has become a principal tool for understanding nonlinear processes, including disruptions, in tokamak plasmas. Although analytical studies of RMHD turbulence have been useful, the model's impressive ability to simulate tokamak fluid behavior has been revealed primarily by numerical solution. The present work describes a new analytical approach, not restricted to turbulent regimes, based on Hamiltonian field theory. It is shown that the nonlinear (ideal) RMHD system, in both its high-beta and low-beta versions, can be expressed in Hanmiltonian form. Thus a Poisson bracket, [ , ], is constructed such that each RMHD field quantitity, xi/sub i/, evolves according to xi/sub i/ = [xi/sub i/,H], where H is the total field energy. The new formulation makes RMHD accessible to the methodology of Hamiltonian mechanics; it has lead, in particular, to the recognition of new RMHD invariants and even exact, nonlinear RMHD solutions. A canonical version of the Poisson bracket, which requires the introduction of additional fields, leads to a nonlinear variational principle for time-dependent RMHD
General technique to produce isochronous Hamiltonians
International Nuclear Information System (INIS)
Calogero, F; Leyvraz, F
2007-01-01
We introduce a new technique-characterized by an arbitrary positive constant Ω, with which we associate the period T = 2π/Ω-to 'Ω-modify' a Hamiltonian so that the new Hamiltonian thereby obtained is entirely isochronous, namely it yields motions all of which (except possibly for a lower dimensional set of singular motions) are periodic with the same fixed period T in all their degrees of freedom. This technique transforms real autonomous Hamiltonians into Ω-modified Hamiltonians which are also real and autonomous, and it is widely applicable, for instance, to the most general many-body problem characterized by Newtonian equations of motion ('acceleration equal force') provided it is translation invariant. The Ω-modified Hamiltonians are of course not translation invariant, but for Ω = 0 they reduce (up to marginal changes) to the unmodified Hamiltonians they were obtained from. Hence, when this technique is applied to translation-invariant Hamiltonians yielding, in their center-of-mass systems, chaotic motions with a natural time scale much smaller than T, the corresponding Ω-modified Hamiltonians shall display a chaotic behavior for quite some time before the isochronous character of the motions takes over. We moreover show that the quantized versions of these Ω-modified Hamiltonians feature equispaced spectra
Collective Hamiltonians for dipole giant resonances
International Nuclear Information System (INIS)
Weiss, L.I.
1991-07-01
The collective hamiltonian for the Giant Dipole resonance (GDR), in the Goldhaber-Teller-Model, is analytically constructed using the semiclassical and generator coordinates method. Initially a conveniently parametrized set of many body wave functions and a microscopic hamiltonian, the Skyrme hamiltonian - are used. These collective Hamiltonians are applied to the investigation of the GDR, in He 4 , O 16 and Ca 40 nuclei. Also the energies and spectra of the GDR are obtained in these nuclei. The two sets of results are compared, and the zero point energy effects analysed. (author)
Canonical transformations and hamiltonian path integrals
International Nuclear Information System (INIS)
Prokhorov, L.V.
1982-01-01
Behaviour of the Hamiltonian path integrals under canonical transformations produced by a generator, is investigated. An exact form is determined for the kernel of the unitary operator realizing the corresponding quantum transformation. Equivalence rules are found (the Hamiltonian formalism, one-dimensional case) enabling one to exclude non-standard terms from the action. It is shown that the Hamiltonian path integral changes its form under cononical transformations: in the transformed expression besides the classical Hamiltonian function there appear some non-classical terms
Noncanonical Hamiltonian methods in plasma dynamics
International Nuclear Information System (INIS)
Kaufman, A.N.
1981-11-01
A Hamiltonian approach to plasma dynamics has numerous advantages over equivalent formulations which ignore the underlying Hamiltonian structure. In addition to achieving a deeper understanding of processes, Hamiltonian methods yield concise expressions (such as the Kubo form for linear susceptibility), greatly shorten the length of calculations, expose relationships (such as between the ponderomotive Hamiltonian and the linear susceptibility), determine invariants in terms of symmetry operations, and cover situations of great generality. In addition, they yield the Poincare invariants, in particular Liouville volume and adiabatic actions
Identity of the SU(3) model phenomenological hamiltonian and the hamiltonian of nonaxial rotator
International Nuclear Information System (INIS)
Filippov, G.F.; Avramenko, V.I.; Sokolov, A.M.
1984-01-01
Interpretation of nonspheric atomic nuclei spectra on the basis of phenomenological hamiltonians of SU(3) model showed satisfactory agreement of simulation calculations with experimental data. Meanwhile physical sense of phenomenological hamiltonians was not yet discussed. It is shown that phenomenological hamiltonians of SU(3) model are reduced to hamiltonian of nonaxial rotator but with additional items of the third and fourth powers angular momentum operator of rotator
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
Hamiltonian analysis of Plebanski theory
International Nuclear Information System (INIS)
Buffenoir, E; Henneaux, M; Noui, K; Roche, Ph
2004-01-01
We study the Hamiltonian formulation of Plebanski theory in both the Euclidean and Lorentzian cases. A careful analysis of the constraints shows that the system is non-regular, i.e., the rank of the Dirac matrix is non-constant on the non-reduced phase space. We identify the gravitational and topological sectors which are regular subspaces of the non-reduced phase space. The theory can be restricted to the regular subspace which contains the gravitational sector. We explicitly identify first- and second-class constraints in this case. We compute the determinant of the Dirac matrix and the natural measure for the path integral of the Plebanski theory (restricted to the gravitational sector). This measure is the analogue of the Leutwyler-Fradkin-Vilkovisky measure of quantum gravity
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 Direct Method of Hamiltonian Structure
International Nuclear Information System (INIS)
Li Qi; Chen Dengyuan; Su Shuhua
2011-01-01
A direct method of constructing the Hamiltonian structure of the soliton hierarchy with self-consistent sources is proposed through computing the functional derivative under some constraints. The Hamiltonian functional is related with the conservation densities of the corresponding hierarchy. Three examples and their two reductions are given. (general)
Port Hamiltonian modeling of Power Networks
van Schaik, F.; van der Schaft, Abraham; Scherpen, Jacquelien M.A.; Zonetti, Daniele; Ortega, R
2012-01-01
In this talk a full nonlinear model for the power network in port–Hamiltonian framework is derived to study its stability properties. For this we use the modularity approach i.e., we first derive the models of individual components in power network as port-Hamiltonian systems and then we combine all
Hamiltonian representation of divergence-free fields
International Nuclear Information System (INIS)
Boozer, A.H.
1984-11-01
Globally divergence-free fields, such as the magnetic field and the vorticity, can be described by a two degree of freedom Hamiltonian. The Hamiltonian function provides a complete topological description of the field lines. The formulation also separates the dissipative and inertial time scale evolution of the magnetic and the vorticity fields
Hamiltonian structure of linearly extended Virasoro algebra
International Nuclear Information System (INIS)
Arakelyan, T.A.; Savvidi, G.K.
1991-01-01
The Hamiltonian structure of linearly extended Virasoro algebra which admits free bosonic field representation is described. An example of a non-trivial extension is found. The hierarchy of integrable non-linear equations corresponding to this Hamiltonian structure is constructed. This hierarchy admits the Lax representation by matrix Lax operator of second order
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...
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
On Distributed Port-Hamiltonian Process Systems
Lopezlena, Ricardo; Scherpen, Jacquelien M.A.
2004-01-01
In this paper we use the term distributed port-Hamiltonian Process Systems (DPHPS) to refer to the result of merging the theory of distributed Port-Hamiltonian systems (DPHS) with the theory of process systems (PS). Such concept is useful for combining the systematic interconnection of PHS with the
Relativistic magnetohydrodynamics as a Hamiltonian system
International Nuclear Information System (INIS)
Holm, D.D.; Kupershmidt, A.
1985-01-01
The equations of ideal relativistic magnetohydrodynamics in the laboratory frame form a noncanonical Hamiltonian system with the same Poisson bracket as for the nonrelativistic system, but with dynamical variables and Hamiltonian obtained via a regular deformation of their nonrelativistic counterparts [fr
Hamiltonian Cycles on Random Eulerian Triangulations
DEFF Research Database (Denmark)
Guitter, E.; Kristjansen, C.; Nielsen, Jakob Langgaard
1998-01-01
. Considering the case n -> 0, this implies that the system of random Eulerian triangulations equipped with Hamiltonian cycles describes a c=-1 matter field coupled to 2D quantum gravity as opposed to the system of usual random triangulations equipped with Hamiltonian cycles which has c=-2. Hence, in this case...
Almost periodic Hamiltonians: an algebraic approach
International Nuclear Information System (INIS)
Bellissard, J.
1981-07-01
We develop, by analogy with the study of periodic potential, an algebraic theory for almost periodic hamiltonians, leading to a generalized Bloch theorem. This gives rise to results concerning the spectral measures of these operators in terms of those of the corresponding Bloch hamiltonians
Nested Sampling with Constrained Hamiltonian Monte Carlo
Betancourt, M. J.
2010-01-01
Nested sampling is a powerful approach to Bayesian inference ultimately limited by the computationally demanding task of sampling from a heavily constrained probability distribution. An effective algorithm in its own right, Hamiltonian Monte Carlo is readily adapted to efficiently sample from any smooth, constrained distribution. Utilizing this constrained Hamiltonian Monte Carlo, I introduce a general implementation of the nested sampling algorithm.
Indirect quantum tomography of quadratic Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Burgarth, Daniel [Institute for Mathematical Sciences, Imperial College London, London SW7 2PG (United Kingdom); Maruyama, Koji; Nori, Franco, E-mail: daniel@burgarth.de, E-mail: kmaruyama@riken.jp [Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198 (Japan)
2011-01-15
A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few resources. We found that almost all the properties of the Hamiltonian are determined by its surface and that these properties can be measured even if the system can only be initialized to a mixed state. Therefore, our method can be applied to various physical models, with important examples including coupled nano-mechanical oscillators, hopping fermions in optical lattices and transverse Ising chains.
Single-particle dynamics - Hamiltonian formulation
International Nuclear Information System (INIS)
Montague, B.W.
1977-01-01
In this paper the Hamiltonian formalism is applied to the linear theory of accelerator dynamics. The reasons for the introduction of this method rather than the more straightforward use of second order differential equations of motion are briefly discussed. An outline of Lagrangian and Hamiltonian formalism is given, some properties of the Hamiltonian are discussed and canonical transformations are illustrated. The methods are demonstrated using elementary examples such as the simple pendulum and the procedures adopted to handle specific problems in accelerator theory are indicated. (B.D.)
Incomplete Dirac reduction of constrained Hamiltonian systems
Energy Technology Data Exchange (ETDEWEB)
Chandre, C., E-mail: chandre@cpt.univ-mrs.fr
2015-10-15
First-class constraints constitute a potential obstacle to the computation of a Poisson bracket in Dirac’s theory of constrained Hamiltonian systems. Using the pseudoinverse instead of the inverse of the matrix defined by the Poisson brackets between the constraints, we show that a Dirac–Poisson bracket can be constructed, even if it corresponds to an incomplete reduction of the original Hamiltonian system. The uniqueness of Dirac brackets is discussed. The relevance of this procedure for infinite dimensional Hamiltonian systems is exemplified.
Quantum entangling power of adiabatically connected Hamiltonians
International Nuclear Information System (INIS)
Hamma, Alioscia; Zanardi, Paolo
2004-01-01
The space of quantum Hamiltonians has a natural partition in classes of operators that can be adiabatically deformed into each other. We consider parametric families of Hamiltonians acting on a bipartite quantum state space. When the different Hamiltonians in the family fall in the same adiabatic class, one can manipulate entanglement by moving through energy eigenstates corresponding to different values of the control parameters. We introduce an associated notion of adiabatic entangling power. This novel measure is analyzed for general dxd quantum systems, and specific two-qubit examples are studied
Quantum Hamiltonian Physics with Supercomputers
International Nuclear Information System (INIS)
Vary, James P.
2014-01-01
The vision of solving the nuclear many-body problem in a Hamiltonian framework with fundamental interactions tied to QCD via Chiral Perturbation Theory is gaining support. The goals are to preserve the predictive power of the underlying theory, to test fundamental symmetries with the nucleus as laboratory and to develop new understandings of the full range of complex quantum phenomena. Advances in theoretical frameworks (renormalization and many-body methods) as well as in computational resources (new algorithms and leadership-class parallel computers) signal a new generation of theory and simulations that will yield profound insights into the origins of nuclear shell structure, collective phenomena and complex reaction dynamics. Fundamental discovery opportunities also exist in such areas as physics beyond the Standard Model of Elementary Particles, the transition between hadronic and quark–gluon dominated dynamics in nuclei and signals that characterize dark matter. I will review some recent achievements and present ambitious consensus plans along with their challenges for a coming decade of research that will build new links between theory, simulations and experiment. Opportunities for graduate students to embark upon careers in the fast developing field of supercomputer simulations is also discussed
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.
Jacobi fields of completely integrable Hamiltonian systems
International Nuclear Information System (INIS)
Giachetta, G.; Mangiarotti, L.; Sardanashvily, G.
2003-01-01
We show that Jacobi fields of a completely integrable Hamiltonian system of m degrees of freedom make up an extended completely integrable system of 2m degrees of freedom, where m additional first integrals characterize a relative motion
Quantum Hamiltonian reduction in superspace formalism
International Nuclear Information System (INIS)
Madsen, J.O.; Ragoucy, E.
1994-02-01
Recently the quantum Hamiltonian reduction was done in the case of general sl(2) embeddings into Lie algebras and superalgebras. The results are extended to the quantum Hamiltonian reduction of N=1 affine Lie superalgebras in the superspace formalism. It is shown that if we choose a gauge for the supersymmetry, and consider only certain equivalence classes of fields, then our quantum Hamiltonian reduction reduces to quantum Hamiltonian reduction of non-supersymmetric Lie superalgebras. The super energy-momentum tensor is constructed explicitly as well as all generators of spin 1 (and 1/2); thus all generators in the superconformal, quasi-superconformal and Z 2 *Z 2 superconformal algebras are constructed. (authors). 21 refs
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.
Spectral properties of almost-periodic Hamiltonians
International Nuclear Information System (INIS)
Lima, R.
1983-12-01
We give a description of some spectral properties of almost-periodic hamiltonians. We put the stress on some particular points of the proofs of the existence of absolutely continuous or pure point spectrum [fr
Air parcels and air particles: Hamiltonian dynamics
Bokhove, Onno; Lynch, Peter
We present a simple Hamiltonian formulation of the Euler equations for fluid flow in the Lagrangian framework. In contrast to the conventional formulation, which involves coupled partial differential equations, our "innovative'' mathematical formulation involves only ordinary differential equations
Discrete Hamiltonian evolution and quantum gravity
International Nuclear Information System (INIS)
Husain, Viqar; Winkler, Oliver
2004-01-01
We study constrained Hamiltonian systems by utilizing general forms of time discretization. We show that for explicit discretizations, the requirement of preserving the canonical Poisson bracket under discrete evolution imposes strong conditions on both allowable discretizations and Hamiltonians. These conditions permit time discretizations for a limited class of Hamiltonians, which does not include homogeneous cosmological models. We also present two general classes of implicit discretizations which preserve Poisson brackets for any Hamiltonian. Both types of discretizations generically do not preserve first class constraint algebras. Using this observation, we show that time discretization provides a complicated time gauge fixing for quantum gravity models, which may be compared with the alternative procedure of gauge fixing before discretization
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.
Variable Delay in port-Hamiltonian Telemanipulation
Secchi, C; Stramigioli, Stefano; Fantuzzi, C.
2006-01-01
In several applications involving bilateral telemanipulation, master and slave act at different power scales. In this paper a strategy for passively dealing with variable communication delay in scaled port-Hamiltonian based telemanipulation over packet switched networks is proposed.
On local Hamiltonians and dissipative systems
Energy Technology Data Exchange (ETDEWEB)
Castagnino, M. [CONICET-Institutos de Fisica Rosario y de Astronomia y Fisica del Espacio Casilla de Correos 67, Sucursal 28, 1428, Buenos Aires (Argentina); Gadella, M. [Facultad de Ciencias Exactas, Ingenieria y Agrimensura UNR, Rosario (Argentina) and Departamento de Fisica Teorica, Facultad de Ciencias c. Real de Burgos, s.n., 47011 Valladolid (Spain)]. E-mail: manuelgadella@yahoo.com.ar; Lara, L.P. [Facultad de Ciencias Exactas, Ingenieria y Agrimensura UNR, Rosario (Argentina)
2006-11-15
We study a type of one-dimensional dynamical systems on the corresponding two-dimensional phase space. By using arguments related to the existence of integrating factors for Pfaff equations, we show that some one-dimensional non-Hamiltonian systems like dissipative systems, admit a Hamiltonian description by sectors on the phase plane. This picture is not uniquely defined and is coordinate dependent. A simple example is exhaustively discussed. The method, is not always applicable to systems with higher dimensions.
Generalized Hubbard Hamiltonian: renormalization group approach
International Nuclear Information System (INIS)
Cannas, S.A.; Tamarit, F.A.; Tsallis, C.
1991-01-01
We study a generalized Hubbard Hamiltonian which is closed within the framework of a Quantum Real Space Renormalization Group, which replaces the d-dimensional hypercubic lattice by a diamond-like lattice. The phase diagram of the generalized Hubbard Hamiltonian is analyzed for the half-filled band case in d = 2 and d = 3. Some evidence for superconductivity is presented. (author). 44 refs., 12 figs., 2 tabs
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.
Effective Hamiltonian for travelling discrete breathers
MacKay, Robert S.; Sepulchre, Jacques-Alexandre
2002-05-01
Hamiltonian chains of oscillators in general probably do not sustain exact travelling discrete breathers. However solutions which look like moving discrete breathers for some time are not difficult to observe in numerics. In this paper we propose an abstract framework for the description of approximate travelling discrete breathers in Hamiltonian chains of oscillators. The method is based on the construction of an effective Hamiltonian enabling one to describe the dynamics of the translation degree of freedom of moving breathers. Error estimate on the approximate dynamics is also studied. The concept of the Peierls-Nabarro barrier can be made clear in this framework. We illustrate the method with two simple examples, namely the Salerno model which interpolates between the Ablowitz-Ladik lattice and the discrete nonlinear Schrödinger system, and the Fermi-Pasta-Ulam chain.
Noncanonical Hamiltonian methods in plasma dynamics
International Nuclear Information System (INIS)
Kaufman, A.N.
1982-01-01
A Hamiltonian approach to plasma dynamics is described. The Poisson bracket of two observables g 1 and g 2 is given by using an antisymmetric tensor J, and must satisfy the Jacobi condition. The J can be obtained by elementary tensor analysis. The evolution in time of an observable g is given in terms of the Poisson bracket and a Hamiltonian H(Z). The guiding-center description of particle motion was presented by Littlejohn. The ponderomotive drift and force, the wave-induced oscillation-center velocity, and the gyrofrequency shift are obtained. The Lie transform yields the wave-induced increment to the gyromomentum. In the coulomb model for a Vlasov system, the dynamical variable is the Vlasov distribution f(z). The Hamiltonian functional and the Poisson bracket are obtained. The coupling of f(z) to the Maxwell field appears in the Poisson bracket. The evolution equation yields the Vlasov-Maxwell system. (Kato, T.)
Hamiltonian boundary term and quasilocal energy flux
International Nuclear Information System (INIS)
Chen, C.-M.; Nester, James M.; Tung, R.-S.
2005-01-01
The Hamiltonian for a gravitating region includes a boundary term which determines not only the quasilocal values but also, via the boundary variation principle, the boundary conditions. Using our covariant Hamiltonian formalism, we found four particular quasilocal energy-momentum boundary term expressions; each corresponds to a physically distinct and geometrically clear boundary condition. Here, from a consideration of the asymptotics, we show how a fundamental Hamiltonian identity naturally leads to the associated quasilocal energy flux expressions. For electromagnetism one of the four is distinguished: the only one which is gauge invariant; it gives the familiar energy density and Poynting flux. For Einstein's general relativity two different boundary condition choices correspond to quasilocal expressions which asymptotically give the ADM energy, the Trautman-Bondi energy and, moreover, an associated energy flux (both outgoing and incoming). Again there is a distinguished expression: the one which is covariant
Bäcklund transformations and Hamiltonian flows
International Nuclear Information System (INIS)
Zullo, Federico
2013-01-01
In this work we show that, under certain conditions, parametric Bäcklund transformations for a finite dimensional integrable system can be interpreted as solutions to the equations of motion defined by an associated non-autonomous Hamiltonian. The two systems share the same constants of motion. This observation leads to the identification of the Hamiltonian interpolating the iteration of the discrete map defined by the transformations, which indeed in numerical applications can be considered a linear combination of the integrals appearing in the spectral curve of the Lax matrix. An example with the periodic Toda lattice is given. (paper)
Hamiltonian dynamics for complex food webs
Kozlov, Vladimir; Vakulenko, Sergey; Wennergren, Uno
2016-03-01
We investigate stability and dynamics of large ecological networks by introducing classical methods of dynamical system theory from physics, including Hamiltonian and averaging methods. Our analysis exploits the topological structure of the network, namely the existence of strongly connected nodes (hubs) in the networks. We reveal new relations between topology, interaction structure, and network dynamics. We describe mechanisms of catastrophic phenomena leading to sharp changes of dynamics and hence completely altering the ecosystem. We also show how these phenomena depend on the structure of interaction between species. We can conclude that a Hamiltonian structure of biological interactions leads to stability and large biodiversity.
Convergence to equilibrium under a random Hamiltonian
Brandão, Fernando G. S. L.; Ćwikliński, Piotr; Horodecki, Michał; Horodecki, Paweł; Korbicz, Jarosław K.; Mozrzymas, Marek
2012-09-01
We analyze equilibration times of subsystems of a larger system under a random total Hamiltonian, in which the basis of the Hamiltonian is drawn from the Haar measure. We obtain that the time of equilibration is of the order of the inverse of the arithmetic average of the Bohr frequencies. To compute the average over a random basis, we compute the inverse of a matrix of overlaps of operators which permute four systems. We first obtain results on such a matrix for a representation of an arbitrary finite group and then apply it to the particular representation of the permutation group under consideration.
Ostrogradski Hamiltonian approach for geodetic brane gravity
International Nuclear Information System (INIS)
Cordero, Ruben; Molgado, Alberto; Rojas, Efrain
2010-01-01
We present an alternative Hamiltonian description of a branelike universe immersed in a flat background spacetime. This model is named geodetic brane gravity. We set up the Regge-Teitelboim model to describe our Universe where such field theory is originally thought as a second order derivative theory. We refer to an Ostrogradski Hamiltonian formalism to prepare the system to its quantization. This approach comprize the manage of both first- and second-class constraints and the counting of degrees of freedom follows accordingly.
Adaptive control of port-Hamiltonian systems
Dirksz, D.A.; Scherpen, J.M.A.; Edelmayer, András
2010-01-01
In this paper an adaptive control scheme is presented for general port-Hamiltonian systems. Adaptive control is used to compensate for control errors that are caused by unknown or uncertain parameter values of a system. The adaptive control is also combined with canonical transformation theory for
Iterated Hamiltonian type systems and applications
Tiba, Dan
2018-04-01
We discuss, in arbitrary dimension, certain Hamiltonian type systems and prove existence, uniqueness and regularity properties, under the independence condition. We also investigate the critical case, define a class of generalized solutions and prove existence and basic properties. Relevant examples and counterexamples are also indicated. The applications concern representations of implicitly defined manifolds and their perturbations, motivated by differential systems involving unknown geometries.
Symmetry and resonance in Hamiltonian systems
Tuwankotta, J.M.; Verhulst, F.
2000-01-01
In this paper we study resonances in two degrees of freedom, autonomous, hamiltonian systems. Due to the presence of a symmetry condition on one of the degrees of freedom, we show that some of the resonances vanish as lower order resonances. After giving a sharp estimate of the resonance domain, we
Symmetry and resonance in Hamiltonian systems
Tuwankotta, J.M.; Verhulst, F.
1999-01-01
In this paper we study resonances in two degrees of freedom, autonomous, hamiltonian systems. Due to the presence of a symmetry condition on one of the degrees of freedom, we show that some of the resonances vanish as lower order resonances. After determining the size of the resonance domain, we
Hamiltonian evolutions of twisted polygons in RPn
International Nuclear Information System (INIS)
Beffa, Gloria Marì; Wang, Jing Ping
2013-01-01
In this paper we find a discrete moving frame and their associated invariants along projective polygons in RP n , and we use them to describe invariant evolutions of projective N-gons. We then apply a reduction process to obtain a natural Hamiltonian structure on the space of projective invariants for polygons, establishing a close relationship between the projective N-gon invariant evolutions and the Hamiltonian evolutions on the invariants of the flow. We prove that any Hamiltonian evolution is induced on invariants by an invariant evolution of N-gons—what we call a projective realization—and both evolutions are connected explicitly in a very simple way. Finally, we provide a completely integrable evolution (the Boussinesq lattice related to the lattice W 3 -algebra), its projective realization in RP 2 and its Hamiltonian pencil. We generalize both structures to n-dimensions and we prove that they are Poisson, defining explicitly the n-dimensional generalization of the planar evolution (a discretization of the W n -algebra). We prove that the generalization is completely integrable, and we also give its projective realization, which turns out to be very simple. (paper)
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...
The hamiltonian structures of the KP hierarchy
International Nuclear Information System (INIS)
Das, A.; Panda, S.; Huang Wenjui
1991-01-01
We obtain the two hamiltonian structures of the KP hierarchy following the method of Drinfeld and Sokolov. We point out how the second structure of Drinfeld and Sokolov needs to be modified in the present case. We briefly comment on the connection between these structures and the W 1+∞ algebra. (orig.)
Hamiltonian structure for rescaled integrable Lorenz systems
International Nuclear Information System (INIS)
Haas, F.; Goedert, J.
1993-01-01
It is shown that three among the known invariants for the Lorenz system recast the original equations into a Hamiltonian form. This is made possible by an appropriate time-dependent rescaling and the use of a generalized formalism with non-trivial structure functions. (author)
Singularities of Poisson structures and Hamiltonian bifurcations
Meer, van der J.C.
2010-01-01
Consider a Poisson structure on C8(R3,R) with bracket {, } and suppose that C is a Casimir function. Then {f, g} =<¿C, (¿g x ¿f) > is a possible Poisson structure. This confirms earlier observations concerning the Poisson structure for Hamiltonian systems that are reduced to a one degree of freedom
Transparency in port-Hamiltonian based telemanipulation
Secchi, C; Stramigioli, Stefano; Fantuzzi, C.
2005-01-01
After stability, transparency is the major issue in the design of a telemanipulation system. In this paper we exploit a behavioral approach in order to provide an index for the evaluation of transparency in port-Hamiltonian based teleoperators. Furthermore we provide a transparency analysis of
Transparency in Port-Hamiltonian-Based Telemanipulation
Secchi, Cristian; Stramigioli, Stefano; Fantuzzi, Cesare
After stability, transparency is the major issue in the design of a telemanipulation system. In this paper, we exploit the behavioral approach in order to provide an index for the evaluation of transparency in port-Hamiltonian-based teleoperators. Furthermore, we provide a transparency analysis of
Equivalence of Lagrangian and Hamiltonian BRST quantizations
International Nuclear Information System (INIS)
Grigoryan, G.V.; Grigoryan, R.P.; Tyutin, I.V.
1992-01-01
Two approaches to the quantization of gauge theories using BRST symmetry are widely used nowadays: the Lagrangian quantization, developed in (BV-quantization) and Hamiltonian quantization, formulated in (BFV-quantization). For all known examples of field theory (Yang-Mills theory, gravitation etc.) both schemes give equivalent results. However the equivalence of these approaches in general wasn't proved. The main obstacle in comparing of these formulations consists in the fact, that in Hamiltonian approach the number of ghost fields is equal to the number of all first-class constraints, while in the Lagrangian approach the number of ghosts is equal to the number of independent gauge symmetries, which is equal to the number of primary first-class constraints only. This paper is devoted to the proof of the equivalence of Lagrangian and Hamiltonian quantizations for the systems with first-class constraints only. This is achieved by a choice of special gauge in the Hamiltonian approach. It's shown, that after integration over redundant variables on the functional integral we come to effective action which is constructed according to rules for construction of the effective action in Lagrangian quantization scheme
Hamiltonian formulation of anomaly free chiral bosons
International Nuclear Information System (INIS)
Abdalla, E.; Abdalla, M.C.B.; Devecchi, F.P.; Zadra, A.
1988-01-01
Starting out of an anomaly free Lagrangian formulation for chiral scalars, which a Wess-Zumino Term (to cancel the anomaly), we formulate the corresponding hamiltonian problem. Ther we use the (quantum) Siegel invariance to choose a particular, which turns out coincide with the obtained by Floreanini and Jackiw. (author) [pt
Hamiltonian structure of gravitational field theory
International Nuclear Information System (INIS)
Rayski, J.
1992-01-01
Hamiltonian generalizations of Einstein's theory of gravitation introducing a laminar structure of spacetime are discussed. The concepts of general relativity and of quasi-inertial coordinate systems are extended beyond their traditional scope. Not only the metric, but also the coordinate system, if quantized, undergoes quantum fluctuations
Port-Hamiltonian Systems on Open Graphs
Schaft, A.J. van der; Maschke, B.M.
2010-01-01
In this talk we discuss how to define in an intrinsic manner port-Hamiltonian dynamics on open graphs. Open graphs are graphs where some of the vertices are boundary vertices (terminals), which allow interconnection with other systems. We show that a directed graph carries two natural Dirac
Gauge theories of infinite dimensional Hamiltonian superalgebras
International Nuclear Information System (INIS)
Sezgin, E.
1989-05-01
Symplectic diffeomorphisms of a class of supermanifolds and the associated infinite dimensional Hamiltonian superalgebras, H(2M,N) are discussed. Applications to strings, membranes and higher spin field theories are considered: The embedding of the Ramond superconformal algebra in H(2,1) is obtained. The Chern-Simons gauge theory of symplectic super-diffeomorphisms is constructed. (author). 29 refs
The Hamiltonian structures of the KP hierarchy
International Nuclear Information System (INIS)
Das, A.; Panda, S.; Huang Wenjui
1991-08-01
We obtain the two Hamiltonian structures of the KP hierarchy following the method of Drinfeld and Sokolov. We point out how the second structure of Drinfeld and Sokolov needs to be modified in the present case. We briefly comment on the connection between these structures and the W 1+∞ algebra. (author). 18 refs
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.
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...
Hamiltonian constraint in polymer parametrized field theory
International Nuclear Information System (INIS)
Laddha, Alok; Varadarajan, Madhavan
2011-01-01
Recently, a generally covariant reformulation of two-dimensional flat spacetime free scalar field theory known as parametrized field theory was quantized using loop quantum gravity (LQG) type ''polymer'' representations. Physical states were constructed, without intermediate regularization structures, by averaging over the group of gauge transformations generated by the constraints, the constraint algebra being a Lie algebra. We consider classically equivalent combinations of these constraints corresponding to a diffeomorphism and a Hamiltonian constraint, which, as in gravity, define a Dirac algebra. Our treatment of the quantum constraints parallels that of LQG and obtains the following results, expected to be of use in the construction of the quantum dynamics of LQG: (i) the (triangulated) Hamiltonian constraint acts only on vertices, its construction involves some of the same ambiguities as in LQG and its action on diffeomorphism invariant states admits a continuum limit, (ii) if the regulating holonomies are in representations tailored to the edge labels of the state, all previously obtained physical states lie in the kernel of the Hamiltonian constraint, (iii) the commutator of two (density weight 1) Hamiltonian constraints as well as the operator correspondent of their classical Poisson bracket converge to zero in the continuum limit defined by diffeomorphism invariant states, and vanish on the Lewandowski-Marolf habitat, (iv) the rescaled density 2 Hamiltonian constraints and their commutator are ill-defined on the Lewandowski-Marolf habitat despite the well-definedness of the operator correspondent of their classical Poisson bracket there, (v) there is a new habitat which supports a nontrivial representation of the Poisson-Lie algebra of density 2 constraints.
The group of Hamiltonian automorphisms of a star product
La Fuente-Gravy, Laurent
2015-01-01
We deform the group of Hamiltonian diffeomorphisms into the group of Hamiltonian automorphisms of a formal star product on a symplectic manifold. We study the geometry of that group and deform the Flux morphism in the framework of deformation quantization.
QCD string with quarks. 2. Light cone Hamiltonian
International Nuclear Information System (INIS)
Dubin, A.Yu.; Kaidalov, A.B.; Simonov, Yu.A.
1994-01-01
The light-cone Hamiltonian is derived from the general gauge - and Lorentz - invariant expression for the qq-bar Green function. The resulting Hamiltonian contains in a non-additive way contributions from quark and string degrees of freedom
Hamiltonian analysis of transverse dynamics in axisymmetric rf photoinjectors
International Nuclear Information System (INIS)
Wang, C.-x.
2006-01-01
A general Hamiltonian that governs the beam dynamics in an rf photoinjector is derived from first principles. With proper choice of coordinates, the resulting Hamiltonian has a simple and familiar form, while taking into account the rapid acceleration, rf focusing, magnetic focusing, and space-charge forces. From the linear Hamiltonian, beam-envelope evolution is readily obtained, which better illuminates the theory of emittance compensation. Preliminary results on the third-order nonlinear Hamiltonian will be given as well.
On integrable Hamiltonians for higher spin XXZ chain
International Nuclear Information System (INIS)
Bytsko, Andrei G.
2003-01-01
Integrable Hamiltonians for higher spin periodic XXZ chains are constructed in terms of the spin generators; explicit examples for spins up to (3/2) are given. Relations between Hamiltonians for some U q (sl 2 )-symmetric and U(1)-symmetric universal r-matrices are studied; their properties are investigated. A certain modification of the higher spin periodic chain Hamiltonian is shown to be an integrable U q (sl 2 )-symmetric Hamiltonian for an open chain
Numerical determination of the magnetic field line Hamiltonian
International Nuclear Information System (INIS)
Kuo-Petravic, G.; Boozer, A.H.
1986-03-01
The structure of a magnetic field is determined by a one-degree of freedom, time-dependent Hamiltonian. This Hamiltonian is evaluated for a given field in a perturbed action-angle form. The location and the size of magnetic islands in the given field are determined from Hamiltonian perturbation theory and from an ordinary Poincare plot of the field line trajectories
Effective Hamiltonians in quantum physics: resonances and geometric phase
International Nuclear Information System (INIS)
Rau, A R P; Uskov, D
2006-01-01
Effective Hamiltonians are often used in quantum physics, both in time-dependent and time-independent contexts. Analogies are drawn between the two usages, the discussion framed particularly for the geometric phase of a time-dependent Hamiltonian and for resonances as stationary states of a time-independent Hamiltonian
Coherent states of systems with quadratic Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Bagrov, V.G., E-mail: bagrov@phys.tsu.ru [Department of Physics, Tomsk State University, Tomsk (Russian Federation); Gitman, D.M., E-mail: gitman@if.usp.br [Tomsk State University, Tomsk (Russian Federation); Pereira, A.S., E-mail: albertoufcg@hotmail.com [Universidade de Sao Paulo (USP), Sao Paulo, SP (Brazil). Instituto de Fisica
2015-06-15
Different families of generalized coherent states (CS) for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. In principle, all known CS of systems with quadratic Hamiltonian are members of these families. Some of the constructed generalized CS are close enough to the well-known due to Schroedinger and Glauber CS of a harmonic oscillator; we call them simply CS. However, even among these CS, there exist different families of complete sets of CS. These families differ by values of standard deviations at the initial time instant. According to the values of these initial standard deviations, one can identify some of the families with semiclassical CS. We discuss properties of the constructed CS, in particular, completeness relations, minimization of uncertainty relations and so on. As a unknown application of the general construction, we consider different CS of an oscillator with a time dependent frequency. (author)
Coherent states of systems with quadratic Hamiltonians
International Nuclear Information System (INIS)
Bagrov, V.G.; Gitman, D.M.; Pereira, A.S.
2015-01-01
Different families of generalized coherent states (CS) for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. In principle, all known CS of systems with quadratic Hamiltonian are members of these families. Some of the constructed generalized CS are close enough to the well-known due to Schroedinger and Glauber CS of a harmonic oscillator; we call them simply CS. However, even among these CS, there exist different families of complete sets of CS. These families differ by values of standard deviations at the initial time instant. According to the values of these initial standard deviations, one can identify some of the families with semiclassical CS. We discuss properties of the constructed CS, in particular, completeness relations, minimization of uncertainty relations and so on. As a unknown application of the general construction, we consider different CS of an oscillator with a time dependent frequency. (author)
Effective Hamiltonian for high Tc Cu oxides
International Nuclear Information System (INIS)
Fukuyama, H.; Matsukawa, H.
1989-01-01
Effective Hamiltonian has been derived for CuO 2 layers in the presence of extra holes doped mainly into O-sites by taking both on-site and intersite Coulomb interaction into account. A special case with a single hole has been examined in detail. It is found that there exist various types of bound states, singlet and triplet with different spatial symmetry, below the hole bank continuum. The spatial extent of the Zhang-Rice singlet state, which is most stabilized, and the effective transfer integral between these singlet states are seen to be very sensitive to the relative magnitude of the direct and the indirect transfer integrals between O-sites. Effective Hamiltonian for the case of electron doping has also been derived
Partial quantization of Lagrangian-Hamiltonian systems
International Nuclear Information System (INIS)
Amaral, C.M. do; Soares Filho, P.C.
1979-05-01
A classical variational principle is constructed in the Weiss form, for dynamical systems with support spaces of the configuration-phase kind. This extended principle rules the dynamics of classical systems, partially Hamiltonian, in interaction with Lagrangean parameterized subsidiary dynamics. The variational family of equations obtained, consists of an equation of the Hamilton-Jacobi type, coupled to a family of differential equations of the Euler-Lagrange form. The basic dynamical function appearing in the equations is a function of the Routh kind. By means of an ansatz induced by the variationally obtained family, a generalized set of equation, is proposed constituted by a wave equation of Schroedinger type, coupled to a family of equations formaly analog to those Euler-Lagrange equations. A basic operator of Routh type appears in our generalized set of equations. This operator describes the interaction between a quantized Hamiltonian dynamics, with a parameterized classical Lagrangean dynamics in semi-classical closed models. (author) [pt
Quadratic hamiltonians and relativistic quantum mechanics
International Nuclear Information System (INIS)
Razumov, A.V.; Solov'ev, V.O.; Taranov, A.Yu.
1981-01-01
For the case of a charged scalar field described by a quadratic hamiltonian the equivalent relativistic quantum mechanics is constructed in one-particle sector. Complete investigation of a charged relativistic particle motion in the Coulomb field is carried out. Subcritical as well as supercritical cases are considered. In the course of investigation of the charged scalar particle in the Coulomb field the diagonalization of the quadratic hamiltonian describing the charged scalar quantized field interaction with the external Coulomb field has taken place. Mathematically this problem is bound to the construction of self-conjugated expansions of the symmetric operator. The construction of such expansion is necessary at any small external field magnitude [ru
Hamiltonian mechanics and divergence-free fields
International Nuclear Information System (INIS)
Boozer, A.H.
1986-08-01
The field lines, or integral curves, of a divergence-free field in three dimensions are shown to be topologically equivalent to the trajectories of a Hamiltonian with two degrees of freedom. The consideration of fields that depend on a parameter allow the construction of a canonical perturbation theory which is valid even if the perturbation is large. If the parametric dependence of the magnetic, or the vorticity field is interpreted as time dependence, evolution equations are obtained which give Kelvin's theorem or the flux conservation theorem for ideal fluids and plasmas. The Hamiltonian methods prove especially useful for study of fields in which the field lines must be known throughout a volume of space
Quantum mechanical Hamiltonian models of discrete processes
International Nuclear Information System (INIS)
Benioff, P.
1981-01-01
Here the results of other work on quantum mechanical Hamiltonian models of Turing machines are extended to include any discrete process T on a countably infinite set A. The models are constructed here by use of scattering phase shifts from successive scatterers to turn on successive step interactions. Also a locality requirement is imposed. The construction is done by first associating with each process T a model quantum system M with associated Hilbert space H/sub M/ and step operator U/sub T/. Since U/sub T/ is not unitary in general, M, H/sub M/, and U/sub T/ are extended into a (continuous time) Hamiltonian model on a larger space which satisfies the locality requirement. The construction is compared with the minimal unitary dilation of U/sub T/. It is seen that the model constructed here is larger than the minimal one. However, the minimal one does not satisfy the locality requirement
Boundary Hamiltonian Theory for Gapped Topological Orders
Hu, Yuting; Wan, Yidun; Wu, Yong-Shi
2017-06-01
We report our systematic construction of the lattice Hamiltonian model of topological orders on open surfaces, with explicit boundary terms. We do this mainly for the Levin-Wen string-net model. The full Hamiltonian in our approach yields a topologically protected, gapped energy spectrum, with the corresponding wave functions robust under topology-preserving transformations of the lattice of the system. We explicitly present the wavefunctions of the ground states and boundary elementary excitations. The creation and hopping operators of boundary quasi-particles are constructed. It is found that given a bulk topological order, the gapped boundary conditions are classified by Frobenius algebras in its input data. Emergent topological properties of the ground states and boundary excitations are characterized by (bi-) modules over Frobenius algebras.
Hamiltonian reduction of Kac-Moody algebras
International Nuclear Information System (INIS)
Kimura, Kazuhiro
1991-01-01
Feigin-Fucks construction provides us methods to treat rational conformal theories in terms of free fields. This formulation enables us to describe partition functions and correlation functions in the Fock space of free fields. There are several attempt extending to supersymmetric theories. In this report authors present an explicit calculation of the Hamiltonian reduction based on the free field realization. In spite of the results being well-known, the relations can be clearly understood in the language of bosons. Authors perform the hamiltonian reduction by imposing a constraint with appropriate gauge transformations which preserve the constraint. This approaches enables us to gives the geometric interpretation of super Virasoro algebras and relations of the super gravity. In addition, author discuss the properties of quantum groups by using the explicit form of the group element. It is also interesting to extend to super Kac-Moody algebras. (M.N.)
Phase transitions in the Hubbard Hamiltonian
International Nuclear Information System (INIS)
Chaves, C.M.; Lederer, P.; Gomes, A.A.
1977-05-01
Phase transition in the isotropic non-degenerate Hubbard Hamiltonian within the renormalization group techniques is studied, using the epsilon = 4 - d expansion to first order in epsilon. The functional obtained from the Hubbard Hamiltonian displays full rotation symmetry and describes two coupled fields: a vector spin field, with n components and a non-soft scalar charge field. This coupling is pure imaginary, which has interesting consequences on the critical properties of this coupled field system. The effect of simple constraints imposed on the charge field is considered. The relevance of the coupling between the fields in producing Fisher renormalization of the critical exponents is discussed. The possible singularities introduced in the charge-charge correlation function by the coupling are also discussed
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.
A diagrammatic construction of formal E-independent model hamiltonian
International Nuclear Information System (INIS)
Kvasnicka, V.
1977-01-01
A diagrammatic construction of formal E-independent model interaction (i.e., without second-quantization formalism) is suggested. The construction starts from the quasi-degenerate Brillouin-Wigner perturbation theory, in the framework of which an E-dependent model Hamiltonian is simply constructed. Applying the ''E-removing'' procedure to this E-dependent model Hamiltonian, the E-independent formal model Hamiltonian either Hermitian or non-Hermitian can diagrammatically be easily derived. For the formal E-independent model Hamiltonian the separability theorem is proved, which can be profitably used for a rather ''formalistic ''construction of a many-body E-independent model Hamiltonian
Boson mapping and the microscopic collective nuclear Hamiltonian
International Nuclear Information System (INIS)
Dobes, J.; Ivanova, S.P.; Dzholos, R.V.; Pedrosa, R.
1990-01-01
Starting with the mapping of the quadrupole collective states in the fermion space onto the boson space, the fermion nuclear problem is transformed into the boson one. The boson images of the bifermion operators and of the fermion Hamiltonian are found. Recurrence relations are used to obtain approximately the norm matrix which appears in the boson-fermion mapping. The resulting boson Hamiltonian contains terms which go beyond the ordinary SU(6) symmetry Hamiltonian of the interacting boson model. Calculations, however, suggest that on the phenomenological level the differences between the mapped Hamiltonian and the SU(6) Hamiltonian are not too important. 18 refs.; 2 figs
Recursive tridiagonalization of infinite dimensional Hamiltonians
International Nuclear Information System (INIS)
Haydock, R.; Oregon Univ., Eugene, OR
1989-01-01
Infinite dimensional, computable, sparse Hamiltonians can be numerically tridiagonalized to finite precision using a three term recursion. Only the finite number of components whose relative magnitude is greater than the desired precision are stored at any stage in the computation. Thus the particular components stored change as the calculation progresses. This technique avoids errors due to truncation of the orbital set, and makes terminators unnecessary in the recursion method. (orig.)
Hamiltonian theory of guiding-center motion
International Nuclear Information System (INIS)
Littlejohn, R.G.
1980-05-01
A Hamiltonian treatment of the guiding center problem is given which employs noncanonical coordinates in phase space. Separation of the unperturbed system from the perturbation is achieved by using a coordinate transformation suggested by a theorem of Darboux. As a model to illustrate the method, motion in the magnetic field B=B(x,y)z is studied. Lie transforms are used to carry out the perturbation expansion
Hamiltonian kinetic theory of plasma ponderomotive processes
International Nuclear Information System (INIS)
McDonald, S.W.; Kaufman, A.N.
1982-01-01
The nonlinear nonresonant interaction of plasma waves and particles is formulated in Hamiltonian kinetic theory which treats the wave-action and particle distributions on an equal footing, thereby displaying reciprocity relations. In the quasistatic limit, a nonlinear wave-kinetic equation is obtained. The generality of the formalism allows for applications to arbitrary geometry, with the nonlinear effects expressed in terms of the linear susceptibility
Symplectic Geometric Algorithms for Hamiltonian Systems
Feng, Kang
2010-01-01
"Symplectic Geometry Algorithms for Hamiltonian Systems" will be useful not only for numerical analysts, but also for those in theoretical physics, computational chemistry, celestial mechanics, etc. The book generalizes and develops the generating function and Hamilton-Jacobi equation theory from the perspective of the symplectic geometry and symplectic algebra. It will be a useful resource for engineers and scientists in the fields of quantum theory, astrophysics, atomic and molecular dynamics, climate prediction, oil exploration, etc. Therefore a systematic research and development
Dynamical invariants for variable quadratic Hamiltonians
International Nuclear Information System (INIS)
Suslov, Sergei K
2010-01-01
We consider linear and quadratic integrals of motion for general variable quadratic Hamiltonians. Fundamental relations between the eigenvalue problem for linear dynamical invariants and solutions of the corresponding Cauchy initial value problem for the time-dependent Schroedinger equation are emphasized. An eigenfunction expansion of the solution of the initial value problem is also found. A nonlinear superposition principle for generalized Ermakov systems is established as a result of decomposition of the general quadratic invariant in terms of the linear ones.
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.
Quantization of non-Hamiltonian physical systems
International Nuclear Information System (INIS)
Bolivar, A.O.
1998-09-01
We propose a general method of quantization of non-Hamiltonian physical systems. Applying it, for example, to a dissipative system coupled to a thermal reservoir described by the Fokker-Planck equation, we are able to obtain the Caldeira-Leggett master equation, the non-linear Schroedinger-Langevin equation and Caldirola-Kanai equation (with an additional term), as particular cases. (author)
Hamiltonian kinetic theory of plasma ponderomotive processes
International Nuclear Information System (INIS)
McDonald, S.W.; Kaufman, A.N.
1981-12-01
The nonlinear nonresonant interaction of plasma waves and particles is formulated in a Hamiltonian kinetic theory which treats the wave-action and particle distributions on an equal footing, thereby displaying reciprocity relations. In the quasistatic limit, a nonlinear wave-kinetic equation is obtained. The generality of the formalism allows for applications to arbitrary geometry, with the nonlinear effects expressed in terms of the linear susceptibility
Symplectic topology of integrable Hamiltonian systems
International Nuclear Information System (INIS)
Nguyen Tien Zung.
1993-08-01
We study the topology of integrable Hamiltonian systems, giving the main attention to the affine structure of their orbit spaces. In particular, we develop some aspects of Fomenko's theory about topological classification of integrable non-degenerate systems, and consider some relations between such systems and ''pure'' contact and symplectic geometry. We give a notion of integrable surgery and use it to obtain some interesting symplectic structures. (author). Refs, 10 figs
Hamiltonian description and quantization of dissipative systems
Enz, Charles P.
1994-09-01
Dissipative systems are described by a Hamiltonian, combined with a “dynamical matrix” which generalizes the simplectic form of the equations of motion. Criteria for dissipation are given and the examples of a particle with friction and of the Lotka-Volterra model are presented. Quantization is first introduced by translating generalized Poisson brackets into commutators and anticommutators. Then a generalized Schrödinger equation expressed by a dynamical matrix is constructed and discussed.
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.
Hamiltonian description of the ideal fluid
International Nuclear Information System (INIS)
Morrison, P.J.
1998-01-01
The Hamiltonian viewpoint of fluid mechanical systems with few and infinite number of degrees of freedom is described. Rudimentary concepts of finite-degree-of-freedom Hamiltonian dynamics are reviewed, in the context of the passive advection of a scalar or tracer field by a fluid. The notions of integrability, invariant-tori, chaos, overlap criteria, and invariant-tori breakup are described in this context. Preparatory to the introduction of field theories, systems with an infinite number of degrees of freedom, elements of functional calculus and action principles of mechanics are reviewed. The action principle for the ideal compressible fluid is described in terms of Lagrangian or material variables. Hamiltonian systems in terms of noncanonical variables are presented, including several examples of Eulerian or inviscid fluid dynamics. Lie group theory sufficient for the treatment of reduction is reviewed. The reduction from Lagrangian to Eulerian variables is treated along with Clebsch variable decompositions. Stability in the canonical and noncanonical Hamiltonian contexts is described. Sufficient conditions for stability, such as Rayleigh-like criteria, are seen to be only sufficient in the general case because of the existence of negative-energy modes, which are possessed by interesting fluid equilibria. Linearly stable equilibria with negative energy modes are argued to be unstable when nonlinearity or dissipation is added. The energy-Casimir method is discussed and a variant of it that depends upon the notion of dynamical accessibility is described. The energy content of a perturbation about a general fluid equilibrium is calculated using three methods. copyright 1998 The American Physical Society
Large-scale stochasticity in Hamiltonian systems
International Nuclear Information System (INIS)
Escande, D.F.
1982-01-01
Large scale stochasticity (L.S.S.) in Hamiltonian systems is defined on the paradigm Hamiltonian H(v,x,t) =v 2 /2-M cos x-P cos k(x-t) which describes the motion of one particle in two electrostatic waves. A renormalization transformation Tsub(r) is described which acts as a microscope that focusses on a given KAM (Kolmogorov-Arnold-Moser) torus in phase space. Though approximate, Tsub(r) yields the threshold of L.S.S. in H with an error of 5-10%. The universal behaviour of KAM tori is predicted: for instance the scale invariance of KAM tori and the critical exponent of the Lyapunov exponent of Cantori. The Fourier expansion of KAM tori is computed and several conjectures by L. Kadanoff and S. Shenker are proved. Chirikov's standard mapping for stochastic layers is derived in a simpler way and the width of the layers is computed. A simpler renormalization scheme for these layers is defined. A Mathieu equation for describing the stability of a discrete family of cycles is derived. When combined with Tsub(r), it allows to prove the link between KAM tori and nearby cycles, conjectured by J. Greene and, in particular, to compute the mean residue of a torus. The fractal diagrams defined by G. Schmidt are computed. A sketch of a methodology for computing the L.S.S. threshold in any two-degree-of-freedom Hamiltonian system is given. (Auth.)
NLO renormalization in the Hamiltonian truncation
Elias-Miró, Joan; Rychkov, Slava; Vitale, Lorenzo G.
2017-09-01
Hamiltonian truncation (also known as "truncated spectrum approach") is a numerical technique for solving strongly coupled quantum field theories, in which the full Hilbert space is truncated to a finite-dimensional low-energy subspace. The accuracy of the method is limited only by the available computational resources. The renormalization program improves the accuracy by carefully integrating out the high-energy states, instead of truncating them away. In this paper, we develop the most accurate ever variant of Hamiltonian Truncation, which implements renormalization at the cubic order in the interaction strength. The novel idea is to interpret the renormalization procedure as a result of integrating out exactly a certain class of high-energy "tail states." We demonstrate the power of the method with high-accuracy computations in the strongly coupled two-dimensional quartic scalar theory and benchmark it against other existing approaches. Our work will also be useful for the future goal of extending Hamiltonian truncation to higher spacetime dimensions.
Redesign of the DFT/MRCI Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Lyskov, Igor; Kleinschmidt, Martin; Marian, Christel M., E-mail: Christel.Marian@hhu.de [Institute of Theoretical and Computational Chemistry, Heinrich-Heine-University Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf (Germany)
2016-01-21
The combined density functional theory and multireference configuration interaction (DFT/MRCI) method of Grimme and Waletzke [J. Chem. Phys. 111, 5645 (1999)] is a well-established semi-empirical quantum chemical method for efficiently computing excited-state properties of organic molecules. As it turns out, the method fails to treat bi-chromophores owing to the strong dependence of the parameters on the excitation class. In this work, we present an alternative form of correcting the matrix elements of a MRCI Hamiltonian which is built from a Kohn-Sham set of orbitals. It is based on the idea of constructing individual energy shifts for each of the state functions of a configuration. The new parameterization is spin-invariant and incorporates less empirism compared to the original formulation. By utilizing damping techniques together with an algorithm of selecting important configurations for treating static electron correlation, the high computational efficiency has been preserved. The robustness of the original and redesigned Hamiltonians has been tested on experimentally known vertical excitation energies of organic molecules yielding similar statistics for the two parameterizations. Besides that, our new formulation is free from artificially low-lying doubly excited states, producing qualitatively correct and consistent results for excimers. The way of modifying matrix elements of the MRCI Hamiltonian presented here shall be considered as default choice when investigating photophysical processes of bi-chromophoric systems such as singlet fission or triplet-triplet upconversion.
Energy Technology Data Exchange (ETDEWEB)
Shi, Yu-Ji; Zhao, Zhen-Xing [Shanghai Jiao-Tong University, INPAC, Shanghai Key Laboratory for Particle Physics and Cosmology, Department of Physics and Astronomy, Shanghai (China); Wang, Wei [Shanghai Jiao-Tong University, INPAC, Shanghai Key Laboratory for Particle Physics and Cosmology, Department of Physics and Astronomy, Shanghai (China); Chinese Academy of Sciences, State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Beijing (China)
2016-10-15
We suggest to study the B{sub s} and its excitations B{sub sJ} in the B{sub c} decays. We calculate the B{sub c} → B{sub sJ} and B{sub c} → B{sub J} form factors within the covariant light-front quark model, where the B{sub sJ} and B{sub J} denote an s-wave or p-wave anti bs and anti bd meson, respectively. The form factors at q{sup 2} = 0 are directly computed while their q{sup 2}-distributions are obtained by extrapolation. The derived form factors are then used to study semileptonic B{sub c} → (B{sub sJ}, B{sub J}) anti lν decays, and nonleptonic B{sub c} → B{sub 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{sup +}e{sup -} 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. (orig.)
Relativistic deuteron wave function on light front
International Nuclear Information System (INIS)
Karmanov, V.A.
1980-01-01
In the framework of the one boson exchange model the approximate analytical expression for the deuteron wave function (WF) at relativistic relative momenta is obtained. WF depends on extra variable having the form of a unit vector and is determined by six functions instead of two ones (S-and D-waves) in the nonrelativistic case. At moderate momenta the WF is matched with WF in the Reid model. It is emphasized the importance of indication of the qualitative observed phenomena associated with change of parametrization and spin structure of relativistic deuteron WF
Quantum Hamiltonian reduction and conformal field theories
International Nuclear Information System (INIS)
Bershadsky, M.
1991-01-01
It is proved that irreducible representation of the Virasoro algebra can be extracted from an irreducible representation space of the SL (2, R) current algebra by putting a constraint on the latter using the BRST formalism. Thus there is a SL(2, R) symmetry in the Virasoro algebra which is gauged and hidden. This construction of the Virasoro algebra is the quantum analog of the Hamiltonian reduction. The author then naturally leads to consider an SL(2, R) Wess-Zumino-Witten model. This system is related to the quantum field theory of the coadjoint orbit of the Virasoro group. Based on this result he presents the canonical derivation of the SL(2, R) current algebra in Polyakov's theory of two dimensional gravity; it is manifestation of the SL(2, R) symmetry in the conformal field theory hidden by the quantum Hamiltonian reduction. He discusses the quantum Hamiltonian reduction of the SL(n, R) current algebra for the general type of constraints labeled by index 1 ≤ l ≤ (n - 1) and claim that it leads to the new extended conformal algebras W n l . For l = 1 he recovers the well known W n algebra introduced by A. Zamolodchikov. For SL(3, R) Wess-Zumino-Witten model there are two different possibilities of constraining it. The first possibility gives the W 3 algebra, while the second leads to the new chiral algebra W 3 2 generated by the stress-energy tensor, two bosonic supercurrents with spins 3/2 and the U(1) current. He conjectures a Kac formula that describes the highly reducible representation for this algebra. He also makes some speculations concerning the structure of W gravity
Integrable Time-Dependent Quantum Hamiltonians
Sinitsyn, Nikolai A.; Yuzbashyan, Emil A.; Chernyak, Vladimir Y.; Patra, Aniket; Sun, Chen
2018-05-01
We formulate a set of conditions under which the nonstationary Schrödinger equation with a time-dependent Hamiltonian is exactly solvable analytically. The main requirement is the existence of a non-Abelian gauge field with zero curvature in the space of system parameters. Known solvable multistate Landau-Zener models satisfy these conditions. Our method provides a strategy to incorporate time dependence into various quantum integrable models while maintaining their integrability. We also validate some prior conjectures, including the solution of the driven generalized Tavis-Cummings model.
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...
Resonant driving of a nonlinear Hamiltonian system
International Nuclear Information System (INIS)
Palmisano, Carlo; Gervino, Gianpiero; Balma, Massimo; Devona, Dorina; Wimberger, Sandro
2013-01-01
As a proof of principle, we show how a classical nonlinear Hamiltonian system can be driven resonantly over reasonably long times by appropriately shaped pulses. To keep the parameter space reasonably small, we limit ourselves to a driving force which consists of periodic pulses additionally modulated by a sinusoidal function. The main observables are the average increase of kinetic energy and of the action variable (of the non-driven system) with time. Applications of our scheme aim for driving high frequencies of a nonlinear system with a fixed modulation signal.
Nonabelian N=2 superstrings: Hamiltonian structure
International Nuclear Information System (INIS)
Isaev, A.P.; Ivanov, E.A.
1991-04-01
We examine the Hamiltonian structure of nonabelian N=2 superstring models which are the supergroup manifold extensions of N=2 Green-Schwarz superstring. We find the Kac-Moody and Virasoro type superalgebras of the relevant constraints and present elements of the corresponding quantum theory. A comparison with the type IIA Green-Schwarz superstring moving in a general curved 10-d supergravity background is also given. We find that nonabelian superstrings (for d=10) present a particular case of this general system corresponding to a special choice of the background. (author). 22 refs
Effective Hamiltonians for phosphorene and silicene
DEFF Research Database (Denmark)
Voon, L. C. Lew Yan; Lopez-Bezanilla, A.; Wang, J.
2015-01-01
We derived the effective Hamiltonians for silicene and phosphorene with strain, electric field andmagnetic field using the method of invariants. Our paper extends the work of Geissler et al 2013 (NewJ. Phys. 15 085030) on silicene, and Li and Appelbaum 2014 (Phys. Rev. B 90, 115439) on phosphorene.......For phosphorene, it is shown that the bands near the Brillouin zone center only have terms ineven powers of the wave vector. We predict that the energies change quadratically in the presence of aperpendicular external electric field but linearly in a perpendicular magnetic field, as opposed to thosefor silicene...
Hamiltonian Description of Convective-cell Generation
International Nuclear Information System (INIS)
Krommes, J.A.; Kolesnikov, R.A.
2004-01-01
The nonlinear statistical growth rate eq for convective cells driven by drift-wave (DW) interactions is studied with the aid of a covariant Hamiltonian formalism for the gyrofluid nonlinearities. A statistical energy theorem is proven that relates eq to a second functional tensor derivative of the DW energy. This generalizes to a wide class of systems of coupled partial differential equations a previous result for scalar dynamics. Applications to (i) electrostatic ion-temperature-gradient-driven modes at small ion temperature, and (ii) weakly electromagnetic collisional DW's are noted
Eigenfunctions of quadratic hamiltonians in Wigner representation
International Nuclear Information System (INIS)
Akhundova, Eh.A.; Dodonov, V.V.; Man'ko, V.I.
1984-01-01
Exact solutions of the Schroedinger equation in Wigner representation are obtained for an arbitrary non-stationary N-dimensional quadratic Hamiltonian. It is shown that the complete system of the solutions can always be chosen in the form of the products of Laguerre polynomials, the arguments of which are the quadratic integrals of motion of the corresponding classical problem. The generating function is found for the transition probabilities between Fock states which represent a many-dimensional generatization of a well-known Husimi formula for the oscillator of variable frequency. As an example, the motion of a charged particle in an uniform alternate electromagnetic field is considered in detail
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
A new perturbative treatment of pentadiagonal Hamiltonians
International Nuclear Information System (INIS)
Znojil, M.
1987-01-01
A new formulation of the Rayleich - Schroedinger perturbation theory is proposed. It is inspired by a recurent construction of propagators, and its main idea lies in a replacement of the auxiliary matrix elements (generalized continued fractions) by their non-numerical approximants. In a test of convergence (the anharmonic oscillator), the asymptotic fixed-point approximation scheme is used. The results indicate a good applicability of this fixed-point version of our formalism to systems with a band-matrix structure of the Hamiltonian
Effective hamiltonian within the microscopic unitary nuclear model
International Nuclear Information System (INIS)
Avramenko, V.I.; Blokhin, A.L.
1989-01-01
Within the microscopic version of the unitary collective model with the horizontal mixing the effective Hamiltonian for 18 O and 18 Ne nuclei is constructed. The algebraic structure of the Hamiltonian is compared to the familiar phenomenological ones with the SU(3)-mixing terms which describe the coupled rotational and vibrational spectra. The Hamiltonian, including central nuclear and Coulomb interaction, is diagonalized on the basis of three SU(3) irreducible representations with two orbital symmetries. 32 refs.; 2 figs.; 4 tabs
A Hamiltonian functional for the linearized Einstein vacuum field equations
International Nuclear Information System (INIS)
Rosas-RodrIguez, R
2005-01-01
By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a conserved functional as Hamiltonian; this Hamiltonian is not the analog of the energy of the field. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained. The generator of spatial translations associated with such bracket is also obtained
Introduction to thermodynamics of spin models in the Hamiltonian limit
Energy Technology Data Exchange (ETDEWEB)
Berche, Bertrand [Groupe M, Laboratoire de Physique des Materiaux, UMR CNRS No 7556, Universite Henri Poincare, Nancy 1, BP 239, F-54506 Vandoeuvre les Nancy, (France); Lopez, Alexander [Instituto Venezolano de Investigaciones CientIficas, Centro de Fisica, Carr. Panamericana, km 11, Altos de Pipe, Aptdo 21827, 1020-A Caracas, (Venezuela)
2006-01-01
A didactic description of the thermodynamic properties of classical spin systems is given in terms of their quantum counterpart in the Hamiltonian limit. Emphasis is on the construction of the relevant Hamiltonian and the calculation of thermal averages is explicitly done in the case of small systems described, in Hamiltonian field theory, by small matrices. The targeted students are those of a graduate statistical physics course.
Hamiltonian structure of the Lotka-Volterra equations
Nutku, Y.
1990-03-01
The Lotka-Volterra equations governing predator-prey relations are shown to admit Hamiltonian structure with respect to a generalized Poisson bracket. These equations provide an example of a system for which the naive criterion for the existence of Hamiltonian structure fails. We show further that there is a three-component generalization of the Lotka-Volterra equations which is a bi-Hamiltonian system.
Hamiltonian structures of some non-linear evolution equations
International Nuclear Information System (INIS)
Tu, G.Z.
1983-06-01
The Hamiltonian structure of the O(2,1) non-linear sigma model, generalized AKNS equations, are discussed. By reducing the O(2,1) non-linear sigma model to its Hamiltonian form some new conservation laws are derived. A new hierarchy of non-linear evolution equations is proposed and shown to be generalized Hamiltonian equations with an infinite number of conservation laws. (author)
Geometry and Hamiltonian mechanics on discrete spaces
International Nuclear Information System (INIS)
Talasila, V; Clemente-Gallardo, J; Schaft, A J van der
2004-01-01
Numerical simulation is often crucial for analysing the behaviour of many complex systems which do not admit analytic solutions. To this end, one either converts a 'smooth' model into a discrete (in space and time) model, or models systems directly at a discrete level. The goal of this paper is to provide a discrete analogue of differential geometry, and to define on these discrete models a formal discrete Hamiltonian structure-in doing so we try to bring together various fundamental concepts from numerical analysis, differential geometry, algebraic geometry, simplicial homology and classical Hamiltonian mechanics. For example, the concept of a twisted derivation is borrowed from algebraic geometry for developing a discrete calculus. The theory is applied to a nonlinear pendulum and we compare the dynamics obtained through a discrete modelling approach with the dynamics obtained via the usual discretization procedures. Also an example of an energy-conserving algorithm on a simple harmonic oscillator is presented, and its effect on the Poisson structure is discussed
Thermalization Time Bounds for Pauli Stabilizer Hamiltonians
Temme, Kristan
2017-03-01
We prove a general lower bound to the spectral gap of the Davies generator for Hamiltonians that can be written as the sum of commuting Pauli operators. These Hamiltonians, defined on the Hilbert space of N-qubits, serve as one of the most frequently considered candidates for a self-correcting quantum memory. A spectral gap bound on the Davies generator establishes an upper limit on the life time of such a quantum memory and can be used to estimate the time until the system relaxes to thermal equilibrium when brought into contact with a thermal heat bath. The bound can be shown to behave as {λ ≥ O(N^{-1} exp(-2β overline{ɛ}))}, where {overline{ɛ}} is a generalization of the well known energy barrier for logical operators. Particularly in the low temperature regime we expect this bound to provide the correct asymptotic scaling of the gap with the system size up to a factor of N -1. Furthermore, we discuss conditions and provide scenarios where this factor can be removed and a constant lower bound can be proven.
Normal form for mirror machine Hamiltonians
International Nuclear Information System (INIS)
Dragt, A.J.; Finn, J.M.
1979-01-01
A systematic algorithm is developed for performing canonical transformations on Hamiltonians which govern particle motion in magnetic mirror machines. These transformations are performed in such a way that the new Hamiltonian has a particularly simple normal form. From this form it is possible to compute analytic expressions for gyro and bounce frequencies. In addition, it is possible to obtain arbitrarily high order terms in the adiabatic magnetic moment expansion. The algorithm makes use of Lie series, is an extension of Birkhoff's normal form method, and has been explicitly implemented by a digital computer programmed to perform the required algebraic manipulations. Application is made to particle motion in a magnetic dipole field and to a simple mirror system. Bounce frequencies and locations of periodic orbits are obtained and compared with numerical computations. Both mirror systems are shown to be insoluble, i.e., trajectories are not confined to analytic hypersurfaces, there is no analytic third integral of motion, and the adiabatic magnetic moment expansion is divergent. It is expected also that the normal form procedure will prove useful in the study of island structure and separatrices associated with periodic orbits, and should facilitate studies of breakdown of adiabaticity and the onset of ''stochastic'' behavior
Nonextensive formalism and continuous Hamiltonian systems
International Nuclear Information System (INIS)
Boon, Jean Pierre; Lutsko, James F.
2011-01-01
A recurring question in nonequilibrium statistical mechanics is what deviation from standard statistical mechanics gives rise to non-Boltzmann behavior and to nonlinear response, which amounts to identifying the emergence of 'statistics from dynamics' in systems out of equilibrium. Among several possible analytical developments which have been proposed, the idea of nonextensive statistics introduced by Tsallis about 20 years ago was to develop a statistical mechanical theory for systems out of equilibrium where the Boltzmann distribution no longer holds, and to generalize the Boltzmann entropy by a more general function S q while maintaining the formalism of thermodynamics. From a phenomenological viewpoint, nonextensive statistics appeared to be of interest because maximization of the generalized entropy S q yields the q-exponential distribution which has been successfully used to describe distributions observed in a large class of phenomena, in particular power law distributions for q>1. Here we re-examine the validity of the nonextensive formalism for continuous Hamiltonian systems. In particular we consider the q-ideal gas, a model system of quasi-particles where the effect of the interactions are included in the particle properties. On the basis of exact results for the q-ideal gas, we find that the theory is restricted to the range q<1, which raises the question of its formal validity range for continuous Hamiltonian systems.
Hamiltonian Anomalies from Extended Field Theories
Monnier, Samuel
2015-09-01
We develop a proposal by Freed to see anomalous field theories as relative field theories, namely field theories taking value in a field theory in one dimension higher, the anomaly field theory. We show that when the anomaly field theory is extended down to codimension 2, familiar facts about Hamiltonian anomalies can be naturally recovered, such as the fact that the anomalous symmetry group admits only a projective representation on the Hilbert space, or that the latter is really an abelian bundle gerbe over the moduli space. We include in the discussion the case of non-invertible anomaly field theories, which is relevant to six-dimensional (2, 0) superconformal theories. In this case, we show that the Hamiltonian anomaly is characterized by a degree 2 non-abelian group cohomology class, associated to the non-abelian gerbe playing the role of the state space of the anomalous theory. We construct Dai-Freed theories, governing the anomalies of chiral fermionic theories, and Wess-Zumino theories, governing the anomalies of Wess-Zumino terms and self-dual field theories, as extended field theories down to codimension 2.
Effective Hamiltonians for phosphorene and silicene
International Nuclear Information System (INIS)
Lew Yan Voon, L C; Lopez-Bezanilla, A; Wang, J; Zhang, Y; Willatzen, M
2015-01-01
We derived the effective Hamiltonians for silicene and phosphorene with strain, electric field and magnetic field using the method of invariants. Our paper extends the work of Geissler et al 2013 (New J. Phys. 15 085030) on silicene, and Li and Appelbaum 2014 (Phys. Rev. B 90, 115439) on phosphorene. Our Hamiltonians are compared to an equivalent one for graphene. For silicene, the expression for band warping is obtained analytically and found to be of different order than for graphene. We prove that a uniaxial strain does not open a gap, resolving contradictory numerical results in the literature. For phosphorene, it is shown that the bands near the Brillouin zone center only have terms in even powers of the wave vector. We predict that the energies change quadratically in the presence of a perpendicular external electric field but linearly in a perpendicular magnetic field, as opposed to those for silicene which vary linearly in both cases. Preliminary ab initio calculations for the intrinsic band structures have been carried out in order to evaluate some of the k⋅p parameters. (paper)
Phase space eigenfunctions of multidimensional quadratic Hamiltonians
International Nuclear Information System (INIS)
Dodonov, V.V.; Man'ko, V.I.
1986-01-01
We obtain the explicit expressions for phace space eigenfunctions (PSE),i.e. Weyl's symbols of dyadic operators like vertical stroken> ,vertical strokem>, being the solution of the Schroedinger equation with the Hamiltonian which is a quite arbitrary multidimensional quadratic form of the operators of Cartesian coordinates and conjugated to them momenta with time-dependent coefficients. It is shown that for an arbitrary quadratic Hamiltonian one can always construct the set of completely factorized PSE which are products of N factors, each factor being dependent only on two arguments for nnot=m and on a single argument for n=m. These arguments are nothing but constants of motion of the correspondent classical system. PSE are expressed in terms of the associated Laguerre polynomials in the case of a discrete spectrum and in terms of the Airy functions in the continuous spectrum case. Three examples are considered: a harmonic oscillator with a time-dependent frequency, a charged particle in a nonstationary uniform magnetic field, and a particle in a time-dependent uniform potential field. (orig.)
Diffeomorphism invariance in the Hamiltonian formulation of General Relativity
International Nuclear Information System (INIS)
Kiriushcheva, N.; Kuzmin, S.V.; Racknor, C.; Valluri, S.R.
2008-01-01
It is shown that when the Einstein-Hilbert Lagrangian is considered without any non-covariant modifications or change of variables, its Hamiltonian formulation leads to results consistent with principles of General Relativity. The first-class constraints of such a Hamiltonian formulation, with the metric tensor taken as a canonical variable, allow one to derive the generator of gauge transformations, which directly leads to diffeomorphism invariance. The given Hamiltonian formulation preserves general covariance of the transformations derivable from it. This characteristic should be used as the crucial consistency requirement that must be met by any Hamiltonian formulation of General Relativity
Matchings Extend to Hamiltonian Cycles in 5-Cube
Directory of Open Access Journals (Sweden)
Wang Fan
2018-02-01
Full Text Available Ruskey and Savage asked the following question: Does every matching in a hypercube Qn for n ≥ 2 extend to a Hamiltonian cycle of Qn? Fink confirmed that every perfect matching can be extended to a Hamiltonian cycle of Qn, thus solved Kreweras’ conjecture. Also, Fink pointed out that every matching can be extended to a Hamiltonian cycle of Qn for n ∈ {2, 3, 4}. In this paper, we prove that every matching in Q5 can be extended to a Hamiltonian cycle of Q5.
Squeezed states from a quantum deformed oscillator Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Ramírez, R. [IFLP, CONICET–Department of Mathematics, University of La Plata c.c. 67 1900, La Plata (Argentina); Reboiro, M., E-mail: marta.reboiro@gmail.com [IFLP, CONICET–Department of Physics, University of La Plata c.c. 67 1900, La Plata (Argentina)
2016-03-11
The spectrum and the time evolution of a system, which is modeled by a non-hermitian quantum deformed oscillator Hamiltonian, is analyzed. The proposed Hamiltonian is constructed from a non-standard realization of the algebra of Heisenberg. We show that, for certain values of the coupling constants and for a range of values of the deformation parameter, the deformed Hamiltonian is a pseudo-hermitic Hamiltonian. We explore the conditions under which the Hamiltonian is similar to a Swanson Hamiltonian. Also, we show that the lowest eigenstate of the system is a squeezed state. We study the time evolution of the system, for different initial states, by computing the corresponding Wigner functions. - Highlights: • A generalization of the squeezed harmonic oscillator is constructed from a non-standard realization of the Heisenberg algebra. • It is proved that, for certain values of the parameters of the model, the Hamiltonian is a pseudo-hermitian Hamiltonian. • It is shown that the lowest eigenstate of the Hamiltonian is a squeezed state. • The squeezing behavior of the associated Gazeau–Klauder state, as a function of time, is discussed.
Spectral and resonance properties of the Smilansky Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Exner, Pavel [Department of Theoretical Physics, Nuclear Physics Institute, Czech Academy of Sciences, 25068 Řež near Prague (Czech Republic); Doppler Institute for Mathematical Physics and Applied Mathematics, Czech Technical University, Břehová 7, 11519 Prague (Czech Republic); Lotoreichik, Vladimir [Department of Theoretical Physics, Nuclear Physics Institute, Czech Academy of Sciences, 25068 Řež near Prague (Czech Republic); Tater, Miloš, E-mail: tater@ujf.cas.cz [Department of Theoretical Physics, Nuclear Physics Institute, Czech Academy of Sciences, 25068 Řež near Prague (Czech Republic)
2017-02-26
We analyze the Hamiltonian proposed by Smilansky to describe irreversible dynamics in quantum graphs and studied further by Solomyak and others. We derive a weak-coupling asymptotics of the ground state and add new insights by finding the discrete spectrum numerically in the subcritical case. Furthermore, we show that the model then has a rich resonance structure. - Highlights: • We derive conditions on bound states and on resonances of the Smilansky Hamiltonian. • Using these conditions we find numerically discrete spectrum and resonances of this Hamiltonian. • Our numerical tests confirm known properties of the Hamiltonian and allow us to conjecture new ones.
A Hamiltonian approach to model and analyse networks of ...
Indian Academy of Sciences (India)
2015-09-24
Sep 24, 2015 ... Gyroscopes; energy harvesters; synchronization; Hamiltonian mechanics. ... ideas and methods from nonlinear dynamics system theory, in particular, ... deploy highly sensitive, lowpower, magnetic and electric field sensors.
Geometric solitons of Hamiltonian flows on manifolds
Energy Technology Data Exchange (ETDEWEB)
Song, Chong, E-mail: songchong@xmu.edu.cn [School of Mathematical Sciences, Xiamen University, Xiamen 361005 (China); Sun, Xiaowei, E-mail: sunxw@cufe.edu.cn [School of Applied Mathematics, Central University of Finance and Economics, Beijing 100081 (China); Wang, Youde, E-mail: wyd@math.ac.cn [Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190 (China)
2013-12-15
It is well-known that the LIE (Locally Induction Equation) admit soliton-type solutions and same soliton solutions arise from different and apparently irrelevant physical models. By comparing the solitons of LIE and Killing magnetic geodesics, we observe that these solitons are essentially decided by two families of isometries of the domain and the target space, respectively. With this insight, we propose the new concept of geometric solitons of Hamiltonian flows on manifolds, such as geometric Schrödinger flows and KdV flows for maps. Moreover, we give several examples of geometric solitons of the Schrödinger flow and geometric KdV flow, including magnetic curves as geometric Schrödinger solitons and explicit geometric KdV solitons on surfaces of revolution.
Hamiltonian indices and rational spectral densities
Byrnes, C. I.; Duncan, T. E.
1980-01-01
Several (global) topological properties of various spaces of linear systems, particularly symmetric, lossless, and Hamiltonian systems, and multivariable spectral densities of fixed McMillan degree are announced. The study is motivated by a result asserting that on a connected but not simply connected manifold, it is not possible to find a vector field having a sink as its only critical point. In the scalar case, this is illustrated by showing that only on the space of McMillan degree = /Cauchy index/ = n, scalar transfer functions can one define a globally convergent vector field. This result holds both in discrete-time and for the nonautonomous case. With these motivations in mind, theorems of Bochner and Fogarty are used in showing that spaces of transfer functions defined by symmetry conditions are, in fact, smooth algebraic manifolds.
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.
A Hamiltonian five-field gyrofluid model
Energy Technology Data Exchange (ETDEWEB)
Keramidas Charidakos, I.; Waelbroeck, F. L.; Morrison, P. J. [Institute for Fusion Studies and Department of Physics, The University of Texas at Austin, Austin, TX 78712 (United States)
2015-11-15
A Lie-Poisson bracket is presented for a five-field gyrofluid model, thereby showing the model to be Hamiltonian. The model includes the effects of magnetic field curvature and describes the evolution of the electron and ion gyro-center densities, the parallel component of the ion and electron velocities, and the ion temperature. The quasineutrality property and Ampère's law determine, respectively, the electrostatic potential and magnetic flux. The Casimir invariants are presented, and shown to be associated with five Lagrangian invariants advected by distinct velocity fields. A linear, local study of the model is conducted both with and without Landau and diamagnetic resonant damping terms. Stability criteria and dispersion relations for the electrostatic and the electromagnetic cases are derived and compared with their analogs for fluid and kinetic models.
Hamiltonian circuited simulations in reactor physics
International Nuclear Information System (INIS)
Rio Hirowati Shariffudin
2002-01-01
In the assessment of suitability of reactor designs and in the investigations into reactor safety, the steady state of a nuclear reactor has to be studied carefully. The analysis can be done through mockup designs but this approach costs a lot of money and consumes a lot of time. A less expensive approach is via simulations where the reactor and its neutron interactions are modelled mathematically. Finite difference discretization of the diffusion operator has been used to approximate the steady state multigroup neutron diffusion equations. The steps include the outer scheme which estimates the resulting right hand side of the matrix equation, the group scheme which calculates the upscatter problem and the inner scheme which solves for the flux for a particular group. The Hamiltonian circuited simulations for the inner iterations of the said neutron diffusion equation enable the effective use of parallel computing, especially where the solutions of multigroup neutron diffusion equations involving two or more space dimensions are required. (Author)
Hamiltonian inclusive fitness: a fitter fitness concept.
Costa, James T
2013-01-01
In 1963-1964 W. D. Hamilton introduced the concept of inclusive fitness, the only significant elaboration of Darwinian fitness since the nineteenth century. I discuss the origin of the modern fitness concept, providing context for Hamilton's discovery of inclusive fitness in relation to the puzzle of altruism. While fitness conceptually originates with Darwin, the term itself stems from Spencer and crystallized quantitatively in the early twentieth century. Hamiltonian inclusive fitness, with Price's reformulation, provided the solution to Darwin's 'special difficulty'-the evolution of caste polymorphism and sterility in social insects. Hamilton further explored the roles of inclusive fitness and reciprocation to tackle Darwin's other difficulty, the evolution of human altruism. The heuristically powerful inclusive fitness concept ramified over the past 50 years: the number and diversity of 'offspring ideas' that it has engendered render it a fitter fitness concept, one that Darwin would have appreciated.
Renormalized semiclassical quantization for rescalable Hamiltonians
International Nuclear Information System (INIS)
Takahashi, Satoshi; Takatsuka, Kazuo
2004-01-01
A renormalized semiclassical quantization method for rescalable Hamiltonians is proposed. A classical Hamilton system having a potential function that consists of homogeneous polynomials like the Coulombic potential can have a scale invariance in its extended phase space (phase space plus time). Consequently, infinitely many copies of a single trajectory constitute a one-parameter family that is characterized in terms of a scaling factor. This scaling invariance in classical dynamics is lost in quantum mechanics due to the presence of the Planck constant. It is shown that in a system whose classical motions have a self-similarity in the above sense, classical trajectories adopted in the semiclassical scheme interact with infinitely many copies of their own that are reproduced by the relevant scaling procedure, thereby undergoing quantum interference among themselves to produce a quantized spectrum
Effective hamiltonian calculations using incomplete model spaces
International Nuclear Information System (INIS)
Koch, S.; Mukherjee, D.
1987-01-01
It appears that the danger of encountering ''intruder states'' is substantially reduced if an effective hamiltonian formalism is developed for incomplete model spaces (IMS). In a Fock-space approach, the proof a ''connected diagram theorem'' is fairly straightforward with exponential-type of ansatze for the wave-operator W, provided the normalization chosen for W is separable. Operationally, one just needs a suitable categorization of the Fock-space operators into ''diagonal'' and ''non-diagonal'' parts that is generalization of the corresponding procedure for the complete model space. The formalism is applied to prototypical 2-electron systems. The calculations have been performed on the Cyber 205 super-computer. The authors paid special attention to an efficient vectorization for the construction and solution of the resulting coupled non-linear equations
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.
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.
Hamiltonian formulation for the Martin-Taylor model
International Nuclear Information System (INIS)
Vasconcelos, D.B.; Viana, R.L.
1993-01-01
Locally stochastic layer and its optimization are studied. In order to accomplish this task, it is employed a Hamiltonian formulation of magnetic field line flow with a subsequent application of Escande-Doveil renormalization method which have been extensively used to obtain accurate estimates of stochasticity thresholds in systems exhibiting Hamiltonian chaos. (author)
Formulation of Hamiltonian mechanics with even and odd Poisson brackets
International Nuclear Information System (INIS)
Khudaverdyan, O.M.; Nersesyan, A.P.
1987-01-01
A possibility is studied as to constrict the odd Poisson bracket and odd Hamiltonian by the given dynamics in phase superspace - the even Poisson bracket and even Hamiltonian so the transition to the new structure does not change the equations of motion. 9 refs
Effective Hamiltonian within the microscopic unitary nuclear model
International Nuclear Information System (INIS)
Filippov, G.F.; Blokhin, A.L.
1989-01-01
A technique of projecting the microscopic nuclear Hamiltonian on the SU(3)-group enveloping algebra is developed. The approach proposed is based on the effective Hamiltonian restored from the matrix elements between the coherent states of the SU(3) irreducible representations. The technique is displayed for almost magic nuclei within the mixed representation basis, and for arbitrary nuclei within the single representation. 40 refs
Classical and quantum mechanics of complex Hamiltonian systems ...
Indian Academy of Sciences (India)
Vol. 73, No. 2. — journal of. August 2009 physics pp. 287–297. Classical and quantum mechanics of complex. Hamiltonian systems: An extended complex phase space ... 1Department of Physics, Ramjas College (University Enclave), University of Delhi,. Delhi 110 ... 1.1 Motivation behind the study of complex Hamiltonians.
Local Hamiltonians for maximally multipartite-entangled states
Facchi, P.; Florio, G.; Pascazio, S.; Pepe, F.
2010-10-01
We study the conditions for obtaining maximally multipartite-entangled states (MMESs) as nondegenerate eigenstates of Hamiltonians that involve only short-range interactions. We investigate small-size systems (with a number of qubits ranging from 3 to 5) and show some example Hamiltonians with MMESs as eigenstates.
Local Hamiltonians for maximally multipartite-entangled states
International Nuclear Information System (INIS)
Facchi, P.; Florio, G.; Pascazio, S.; Pepe, F.
2010-01-01
We study the conditions for obtaining maximally multipartite-entangled states (MMESs) as nondegenerate eigenstates of Hamiltonians that involve only short-range interactions. We investigate small-size systems (with a number of qubits ranging from 3 to 5) and show some example Hamiltonians with MMESs as eigenstates.
Modelling chaotic Hamiltonian systems as a Markov Chain ...
African Journals Online (AJOL)
The behaviour of chaotic Hamiltonian system has been characterised qualitatively in recent times by its appearance on the Poincaré section and quantitatively by the Lyapunov exponent. Studying the dynamics of the two chaotic Hamiltonian systems: the Henon-Heiles system and non-linearly coupled oscillators as their ...
On the physical applications of hyper-Hamiltonian dynamics
International Nuclear Information System (INIS)
Gaeta, Giuseppe; Rodriguez, Miguel A
2008-01-01
An extension of Hamiltonian dynamics, defined on hyper-Kahler manifolds ('hyper-Hamiltonian dynamics') and sharing many of the attractive features of standard Hamiltonian dynamics, was introduced in previous work. In this paper, we discuss applications of the theory to physically interesting cases, dealing with the dynamics of particles with spin 1/2 in a magnetic field, i.e. the Pauli and the Dirac equations. While the free Pauli equation corresponds to a hyper-Hamiltonian flow, it turns out that the hyper-Hamiltonian description of the Dirac equation, and of the full Pauli one, is in terms of two commuting hyper-Hamiltonian flows. In this framework one can use a factorization principle discussed here (which is a special case of a general phenomenon studied by Walcher) and provide an explicit description of the resulting flow. On the other hand, by applying the familiar Foldy-Wouthuysen and Cini-Tousheck transformations (and the one recently introduced by Mulligan) which separate-in suitable limits-the Dirac equation into two equations, each of these turn out to be described by a single hyper-Hamiltonian flow. Thus the hyper-Hamiltonian construction is able to describe the fundamental dynamics for particles with spin
The Group of Hamiltonian Automorphisms of a Star Product
International Nuclear Information System (INIS)
La Fuente-Gravy, Laurent
2016-01-01
We deform the group of Hamiltonian diffeomorphisms into a group of Hamiltonian automorphisms, Ham(M,∗), of a formal star product ∗ on a symplectic manifold (M,ω). We study the geometry of that group and deform the Flux morphism in the framework of deformation quantization.
Hamiltonian reduction of SU(2) Yang-Mills field theory
International Nuclear Information System (INIS)
Khvedelidze, A.M.; Pavel, H.-P.
1998-01-01
The unconstrained system equivalent to SU (2) Yang-Mills field theory is obtained in the framework of the generalized Hamiltonian formalism using the method of Hamiltonian reduction. The reduced system is expressed in terms of fields with 'nonrelativistic' spin-0 and spin-2
An effective Hamiltonian approach to quantum random walk
Indian Academy of Sciences (India)
2017-02-09
Feb 9, 2017 ... Abstract. In this article we present an effective Hamiltonian approach for discrete time quantum random walk. A form of the Hamiltonian for one-dimensional quantum walk has been prescribed, utilizing the fact that Hamil- tonians are generators of time translations. Then an attempt has been made to ...
Model reduction of port-Hamiltonian systems as structured systems
Polyuga, R.V.; Schaft, van der A.J.
2010-01-01
The goal of this work is to demonstrate that a specific projection-based model reduction method, which provides an H2 error bound, turns out to be applicable to port-Hamiltonian systems, preserving the port-Hamiltonian structure for the reduced order model, and, as a consequence, passivity.
Port Hamiltonian Formulation of Infinite Dimensional Systems I. Modeling
Macchelli, Alessandro; Schaft, Arjan J. van der; Melchiorri, Claudio
2004-01-01
In this paper, some new results concerning the modeling of distributed parameter systems in port Hamiltonian form are presented. The classical finite dimensional port Hamiltonian formulation of a dynamical system is generalized in order to cope with the distributed parameter and multi-variable case.
Port-Hamiltonian approaches to motion generation for mechanical systems
Sakai, Satoru; Stramigioli, Stefano
This paper gives new motion generation methods for mechanical port-Hamiltonian systems. First, we propose a generation method based on an asymptotic stabilization method without damping assignment. This asymptotic stabilization method preserves the Hamiltonian structure in the closed-loop system
Structure preserving port-Hamiltonian model reduction of electrical circuits
Polyuga, R.; Schaft, van der A.J.; Benner, P.; Hinze, M.; Maten, ter E.J.W.
2011-01-01
This paper discusses model reduction of electrical circuits based on a port-Hamiltonian representation. It is shown that by the use of the Kalman decomposition an uncontrollable and/or unobservable port-Hamiltonian system is reduced to a controllable/observable system that inherits the
Residual gauge invariance of Hamiltonian lattice gauge theories
International Nuclear Information System (INIS)
Ryang, S.; Saito, T.; Shigemoto, K.
1984-01-01
The time-independent residual gauge invariance of Hamiltonian lattice gauge theories is considered. Eigenvalues and eigenfunctions of the unperturbed Hamiltonian are found in terms of Gegengauer's polynomials. Physical states which satisfy the subsidiary condition corresponding to Gauss' law are constructed systematically. (orig.)
A generalized AKNS hierarchy and its bi-Hamiltonian structures
International Nuclear Information System (INIS)
Xia Tiecheng; You Fucai; Chen Dengyuan
2005-01-01
First we construct a new isospectral problem with 8 potentials in the present paper. And then a new Lax pair is presented. By making use of Tu scheme, a class of new soliton hierarchy of equations is derived, which is integrable in the sense of Liouville and possesses bi-Hamiltonian structures. After making some reductions, the well-known AKNS hierarchy and other hierarchies of evolution equations are obtained. Finally, in order to illustrate that soliton hierarchy obtained in the paper possesses bi-Hamiltonian structures exactly, we prove that the linear combination of two-Hamiltonian operators admitted are also a Hamiltonian operator constantly. We point out that two Hamiltonian operators obtained of the system are directly derived from a recurrence relations, not from a recurrence operator
Local modular Hamiltonians from the quantum null energy condition
Koeller, Jason; Leichenauer, Stefan; Levine, Adam; Shahbazi-Moghaddam, Arvin
2018-03-01
The vacuum modular Hamiltonian K of the Rindler wedge in any relativistic quantum field theory is given by the boost generator. Here we investigate the modular Hamiltonian for more general half-spaces which are bounded by an arbitrary smooth cut of a null plane. We derive a formula for the second derivative of the modular Hamiltonian with respect to the coordinates of the cut which schematically reads K''=Tv v . This formula can be integrated twice to obtain a simple expression for the modular Hamiltonian. The result naturally generalizes the standard expression for the Rindler modular Hamiltonian to this larger class of regions. Our primary assumptions are the quantum null energy condition—an inequality between the second derivative of the von Neumann entropy of a region and the stress tensor—and its saturation in the vacuum for these regions. We discuss the validity of these assumptions in free theories and holographic theories to all orders in 1 /N .
Periodic solutions of asymptotically linear Hamiltonian systems without twist conditions
Energy Technology Data Exchange (ETDEWEB)
Cheng Rong [Coll. of Mathematics and Physics, Nanjing Univ. of Information Science and Tech., Nanjing (China); Dept. of Mathematics, Southeast Univ., Nanjing (China); Zhang Dongfeng [Dept. of Mathematics, Southeast Univ., Nanjing (China)
2010-05-15
In dynamical system theory, especially in many fields of applications from mechanics, Hamiltonian systems play an important role, since many related equations in mechanics can be written in an Hamiltonian form. In this paper, we study the existence of periodic solutions for a class of Hamiltonian systems. By applying the Galerkin approximation method together with a result of critical point theory, we establish the existence of periodic solutions of asymptotically linear Hamiltonian systems without twist conditions. Twist conditions play crucial roles in the study of periodic solutions for asymptotically linear Hamiltonian systems. The lack of twist conditions brings some difficulty to the study. To the authors' knowledge, very little is known about the case, where twist conditions do not hold. (orig.)
Sdg interacting boson hamiltonian in the seniority scheme
Energy Technology Data Exchange (ETDEWEB)
Yoshinaga, N.
1989-03-06
The sdg interacting boson hamiltonian is derived in the seniority scheme. We use the method of Otsuka, Arima and Iachello in order to derive the boson hamiltonian from the fermion hamiltonian. To examine how good is the boson approximation in the zeroth-order, we carry out the exact shell model calculations in a single j-shell. It is found that almost all low-lying levels are reproduced quite well by diagonalizing the sdg interacting boson hamiltonian in the vibrational case. In the deformed case the introduction of g-bosons improves the reproduction of the spectra and of the binding energies which are obtained by diagnoalizing the exact shell model hamiltonian. In particular the sdg interacting boson model reproduces well-developed rotational bands.
sdg Interacting boson hamiltonian in the seniority scheme
Yoshinaga, N.
1989-03-01
The sdg interacting boson hamiltonian is derived in the seniority scheme. We use the method of Otsuka, Arima and Iachello in order to derive the boson hamiltonian from the fermion hamiltonian. To examine how good is the boson approximation in the zeroth-order, we carry out the exact shell model calculations in a single j-shell. It is found that almost all low-lying levels are reproduced quite well by diagonalizing the sdg interacting boson hamiltonian in the vibrational case. In the deformed case the introduction of g-bosons improves the reproduction of the spectra and of the binding energies which are obtained by diagonalizing the exact shell model hamiltonian. In particular the sdg interacting boson model reproduces well-developed rotational bands.
Frustration-free Hamiltonians supporting Majorana zero edge modes
International Nuclear Information System (INIS)
Jevtic, Sania; Barnett, Ryan
2017-01-01
A one-dimensional fermionic system, such as a superconducting wire, may host Majorana zero-energy edge modes (MZMs) at its edges when it is in the topological phase. MZMs provide a path to realising fault-tolerant quantum computation, and so are the focus of intense experimental and theoretical studies. However, given a Hamiltonian, determining whether MZMs exist is a daunting task as it relies on knowing the spectral properties of the Hamiltonian in the thermodynamic limit. The Kitaev chain is a paradigmatic non-interacting model that supports MZMs and the Hamiltonian can be fully diagonalised. However, for interacting models, the situation is far more complex. Here we consider a different classification of models, namely, ones with frustration-free Hamiltonians. Within this class of models, interacting and non-interacting systems are treated on an equal footing, and we identify exactly which Hamiltonians can realise MZMs. (paper)
Frustration-free Hamiltonians supporting Majorana zero edge modes
Jevtic, Sania; Barnett, Ryan
2017-10-01
A one-dimensional fermionic system, such as a superconducting wire, may host Majorana zero-energy edge modes (MZMs) at its edges when it is in the topological phase. MZMs provide a path to realising fault-tolerant quantum computation, and so are the focus of intense experimental and theoretical studies. However, given a Hamiltonian, determining whether MZMs exist is a daunting task as it relies on knowing the spectral properties of the Hamiltonian in the thermodynamic limit. The Kitaev chain is a paradigmatic non-interacting model that supports MZMs and the Hamiltonian can be fully diagonalised. However, for interacting models, the situation is far more complex. Here we consider a different classification of models, namely, ones with frustration-free Hamiltonians. Within this class of models, interacting and non-interacting systems are treated on an equal footing, and we identify exactly which Hamiltonians can realise MZMs.
Model Hamiltonian Calculations of the Nonlinear Polarizabilities of Conjugated Molecules.
Risser, Steven Michael
This dissertation advances the theoretical knowledge of the nonlinear polarizabilities of conjugated molecules. The unifying feature of these molecules is an extended delocalized pi electron structure. The pi electrons dominate the electronic properties of the molecules, allowing prediction of molecular properties based on the treatment of just the pi electrons. Two separate pi electron Hamiltonians are used in the research. The principal Hamiltonian used is the non-interacting single-particle Huckel Hamiltonian, which replaces the Coulomb interaction among the pi electrons with a mean field interaction. The simplification allows for exact solution of the Hamiltonian for large molecules. The second Hamiltonian used for this research is the interacting multi-particle Pariser-Parr-Pople (PPP) Hamiltonian, which retains explicit Coulomb interactions. This limits exact solutions to molecules containing at most eight electrons. The molecular properties being investigated are the linear polarizability, and the second and third order hyperpolarizabilities. The hyperpolarizabilities determine the nonlinear optical response of materials. These molecular parameters are determined by two independent approaches. The results from the Huckel Hamiltonian are obtained through first, second and third order perturbation theory. The results from the PPP Hamiltonian are obtained by including the applied field directly in the Hamiltonian and determining the ground state energy at a series of field strengths. By fitting the energy to a polynomial in field strength, the polarizability and hyperpolarizabilities are determined. The Huckel Hamiltonian is used to calculate the third order hyperpolarizability of polyenes. These calculations were the first to show the average hyperpolarizability of the polyenes to be positive, and also to show the saturation of the hyperpolarizability. Comparison of these Huckel results to those from the PPP Hamiltonian shows the lack of explicit Coulomb
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.
Greenberger-Horne-Zeilinger States and Few-Body Hamiltonians
Facchi, Paolo; Florio, Giuseppe; Pascazio, Saverio; Pepe, Francesco V.
2011-12-01
The generation of Greenberger-Horne-Zeilinger (GHZ) states is a crucial problem in quantum information. We derive general conditions for obtaining GHZ states as eigenstates of a Hamiltonian. We find that a necessary condition for an n-qubit GHZ state to be a nondegenerate eigenstate of a Hamiltonian is the presence of m-qubit couplings with m≥[(n+1)/2]. Moreover, we introduce a Hamiltonian with a GHZ eigenstate and derive sufficient conditions for the removal of the degeneracy.
Homotopical Dynamics IV: Hopf invariants and hamiltonian flows
Cornea, Octavian
2001-01-01
In a non-compact context the first natural step in the search for periodic orbits of a hamiltonian flow is to detect bounded ones. In this paper we show that, in a non-compact setting, certain algebraic topological constraints imposed to a gradient flow of the hamiltonian function $f$ imply the existence of bounded orbits for the hamiltonian flow of $f$. Once the existence of bounded orbits is established, under favorable circumstances, application of the $C^{1}$-closing lemma leads to period...
New Hamiltonian constraint operator for loop quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Yang, Jinsong, E-mail: yangksong@gmail.com [Department of Physics, Guizhou university, Guiyang 550025 (China); Institute of Physics, Academia Sinica, Taiwan (China); Ma, Yongge, E-mail: mayg@bnu.edu.cn [Department of Physics, Beijing Normal University, Beijing 100875 (China)
2015-12-17
A new symmetric Hamiltonian constraint operator is proposed for loop quantum gravity, which is well defined in the Hilbert space of diffeomorphism invariant states up to non-planar vertices with valence higher than three. It inherits the advantage of the original regularization method to create new vertices to the spin networks. The quantum algebra of this Hamiltonian is anomaly-free on shell, and there is less ambiguity in its construction in comparison with the original method. The regularization procedure for this Hamiltonian constraint operator can also be applied to the symmetric model of loop quantum cosmology, which leads to a new quantum dynamics of the cosmological model.
Remarks on Hamiltonian structures in G2-geometry
International Nuclear Information System (INIS)
Cho, Hyunjoo; Salur, Sema; Todd, A. J.
2013-01-01
In this article, we treat G 2 -geometry as a special case of multisymplectic geometry and make a number of remarks regarding Hamiltonian multivector fields and Hamiltonian differential forms on manifolds with an integrable G 2 -structure; in particular, we discuss existence and make a number of identifications of the spaces of Hamiltonian structures associated to the two multisymplectic structures associated to an integrable G 2 -structure. Along the way, we prove some results in multisymplectic geometry that are generalizations of results from symplectic geometry
Hamiltonian reduction and supersymmetric mechanics with Dirac monopole
International Nuclear Information System (INIS)
Bellucci, Stefano; Nersessian, Armen; Yeranyan, Armen
2006-01-01
We apply the technique of Hamiltonian reduction for the construction of three-dimensional N=4 supersymmetric mechanics specified by the presence of a Dirac monopole. For this purpose we take the conventional N=4 supersymmetric mechanics on the four-dimensional conformally-flat spaces and perform its Hamiltonian reduction to three-dimensional system. We formulate the final system in the canonical coordinates, and present, in these terms, the explicit expressions of the Hamiltonian and supercharges. We show that, besides a magnetic monopole field, the resulting system is specified by the presence of a spin-orbit coupling term. A comparision with previous work is also carried out
The Hamiltonian structure of general relativistic perfect fluids
International Nuclear Information System (INIS)
Bao, D.; Houston Univ., TX; Marsden, J.; Walton, R.
1985-01-01
We show that the evolution equations for a perfect fluid coupled to general relativity in a general lapse and shift, are Hamiltonian relative to a certain Poisson structure. For the fluid variables, a Lie-Poisson structure associated to the dual of a semi-direct product Lie algebra is used, while the bracket for the gravitational variables has the usual canonical symplectic structure. The evolution is governed by a Hamiltonian which is equivalent to that obtained from a canonical analysis. The relationship of our Hamiltonian structure with other approaches in the literature, such as Clebsch potentials, Lagrangian to Eulerian transformations, and its use in clarifying linearization stability, are discussed. (orig.)
Linear Port-Hamiltonian Systems on Infinite-dimensional Spaces
Jacob, Birgit
2012-01-01
This book provides a self-contained introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems. The textbook starts with elementary known results, then progresses smoothly to advanced topics in current research. Many physical systems can be formulated using a Hamiltonian framework, leading to models described by ordinary or partial differential equations. For the purpose of control and for the interconnection of two or more Hamiltonian systems it is essential to take into account this interaction with the environment. This book is the fir
Toric codes and quantum doubles from two-body Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Brell, Courtney G; Bartlett, Stephen D; Doherty, Andrew C [Centre for Engineered Quantum Systems, School of Physics, University of Sydney, Sydney (Australia); Flammia, Steven T, E-mail: cbrell@physics.usyd.edu.au [Perimeter Institute for Theoretical Physics, Waterloo (Canada)
2011-05-15
We present here a procedure to obtain the Hamiltonians of the toric code and Kitaev quantum double models as the low-energy limits of entirely two-body Hamiltonians. Our construction makes use of a new type of perturbation gadget based on error-detecting subsystem codes. The procedure is motivated by a projected entangled pair states (PEPS) description of the target models, and reproduces the target models' behavior using only couplings that are natural in terms of the original Hamiltonians. This allows our construction to capture the symmetries of the target models.
Greenberger-Horne-Zeilinger states and few-body Hamiltonians.
Facchi, Paolo; Florio, Giuseppe; Pascazio, Saverio; Pepe, Francesco V
2011-12-23
The generation of Greenberger-Horne-Zeilinger (GHZ) states is a crucial problem in quantum information. We derive general conditions for obtaining GHZ states as eigenstates of a Hamiltonian. We find that a necessary condition for an n-qubit GHZ state to be a nondegenerate eigenstate of a Hamiltonian is the presence of m-qubit couplings with m≥[(n+1)/2]. Moreover, we introduce a Hamiltonian with a GHZ eigenstate and derive sufficient conditions for the removal of the degeneracy.
Quantum bootstrapping via compressed quantum Hamiltonian learning
International Nuclear Information System (INIS)
Wiebe, Nathan; Granade, Christopher; Cory, D G
2015-01-01
A major problem facing the development of quantum computers or large scale quantum simulators is that general methods for characterizing and controlling are intractable. We provide a new approach to this problem that uses small quantum simulators to efficiently characterize and learn control models for larger devices. Our protocol achieves this by using Bayesian inference in concert with Lieb–Robinson bounds and interactive quantum learning methods to achieve compressed simulations for characterization. We also show that the Lieb–Robinson velocity is epistemic for our protocol, meaning that information propagates at a rate that depends on the uncertainty in the system Hamiltonian. We illustrate the efficiency of our bootstrapping protocol by showing numerically that an 8 qubit Ising model simulator can be used to calibrate and control a 50 qubit Ising simulator while using only about 750 kilobits of experimental data. Finally, we provide upper bounds for the Fisher information that show that the number of experiments needed to characterize a system rapidly diverges as the duration of the experiments used in the characterization shrinks, which motivates the use of methods such as ours that do not require short evolution times. (fast track communication)
Relativistic and separable classical hamiltonian particle dynamics
International Nuclear Information System (INIS)
Sazdjian, H.
1981-01-01
We show within the Hamiltonian formalism the existence of classical relativistic mechanics of N scalar particles interacting at a distance which satisfies the requirements of Poincare invariance, separability, world-line invariance and Einstein causality. The line of approach which is adopted here uses the methods of the theory of systems with constraints applied to manifestly covariant systems of particles. The study is limited to the case of scalar interactions remaining weak in the whole phase space and vanishing at large space-like separation distances of the particles. Poincare invariance requires the inclusion of many-body, up to N-body, potentials. Separability requires the use of individual or two-body variables and the construction of the total interaction from basic two-body interactions. Position variables of the particles are constructed in terms of the canonical variables of the theory according to the world-line invariance condition and the subsidiary conditions of the non-relativistic limit and separability. Positivity constraints on the interaction masses squared of the particles ensure that the velocities of the latter remain always smaller than the velocity of light
g Algebra and two-dimensional quasiexactly solvable Hamiltonian ...
Indian Academy of Sciences (India)
Keywords. g2 algebra; quasiexactly solvable Hamiltonian; hidden algebra; Poschl–Teller potential. ... space of the polynomials, restricting to a linear transformation on this space, the associ- .... The operators L6 and L7 are the positive root.
Integrable Hamiltonian systems and interactions through quadratic constraints
International Nuclear Information System (INIS)
Pohlmeyer, K.
1975-08-01
Osub(n)-invariant classical relativistic field theories in one time and one space dimension with interactions that are entirely due to quadratic constraints are shown to be closely related to integrable Hamiltonian systems. (orig.) [de
Towards practical characterization of quantum systems with quantum Hamiltonian learning
Santagati, R.; Wang, J.; Paesani, S.; Knauer, S.; Gentile, A. A.; Wiebe, N.; Petruzzella, M.; O'Brien, J. L.; Rarity, J. G.; Laing, A.; Thompson, M. G.
2017-01-01
Here we show the first experimental implementation of quantum Hamiltonian Learning, where a silicon-on-insulator quantum photonic simulator is used to learn the dynamics of an electron-spin in an NV center in diamond.
On the quantization of sectorially Hamiltonian dissipative systems
Energy Technology Data Exchange (ETDEWEB)
Castagnino, M. [Instituto de Fisica de Rosario, 2000 Rosario (Argentina); Instituto de Astronomia y Fisica del Espacio, Casilla de Correos 67, Sucursal 28, 1428 Buenos Aires (Argentina); Gadella, M. [Instituto de Fisica de Rosario, 2000 Rosario (Argentina); Departamento de Fisica Teorica, Atomica y Optica, Facultad de Ciencias, Universidad de Valladolid, 47005 Valladolid (Spain)], E-mail: manuelgadella@yahoo.com.ar; Lara, L.P. [Instituto de Fisica de Rosario, 2000 Rosario (Argentina); Facultad Regional Rosario, UTN, 2000 Rosario (Argentina)
2009-10-15
We present a theoretical discussion showing that, although some dissipative systems may have a sectorial Hamiltonian description, this description does not allow for canonical quantization. However, a quantum Liouville counterpart of these systems is possible, although it is not unique.
On the quantization of sectorially Hamiltonian dissipative systems
International Nuclear Information System (INIS)
Castagnino, M.; Gadella, M.; Lara, L.P.
2009-01-01
We present a theoretical discussion showing that, although some dissipative systems may have a sectorial Hamiltonian description, this description does not allow for canonical quantization. However, a quantum Liouville counterpart of these systems is possible, although it is not unique.
Hamiltonian formalisms and symmetries of the Pais–Uhlenbeck oscillator
Directory of Open Access Journals (Sweden)
Krzysztof Andrzejewski
2014-12-01
Full Text Available The study of the symmetry of Pais–Uhlenbeck oscillator initiated in Andrzejewski et al. (2014 [24] is continued with special emphasis put on the Hamiltonian formalism. The symmetry generators within the original Pais and Uhlenbeck Hamiltonian approach as well as the canonical transformation to the Ostrogradski Hamiltonian framework are derived. The resulting algebra of generators appears to be the central extension of the one obtained on the Lagrangian level; in particular, in the case of odd frequencies one obtains the centrally extended l-conformal Newton–Hooke algebra. In this important case the canonical transformation to an alternative Hamiltonian formalism (related to the free higher derivatives theory is constructed. It is shown that all generators can be expressed in terms of the ones for the free theory and the result agrees with that obtained by the orbit method.
Experimental Hamiltonian identification for controlled two-level systems
International Nuclear Information System (INIS)
Schirmer, S.G.; Kolli, A.; Oi, D.K.L.
2004-01-01
We present a strategy to empirically determine the internal and control Hamiltonians for an unknown two-level system (black box) subject to various (piecewise constant) control fields when direct readout by measurement is limited to a single, fixed observable
A local inverse spectral theorem for Hamiltonian systems
International Nuclear Information System (INIS)
Langer, Matthias; Woracek, Harald
2011-01-01
We consider (2 × 2)-Hamiltonian systems of the form y'(x) = zJH(x)y(x), x in [s − , s + ). If a system of this form is in the limit point case, an analytic function is associated with it, namely its Titchmarsh–Weyl coefficient q H . The (global) uniqueness theorem due to de Branges says that the Hamiltonian H is (up to reparameterization) uniquely determined by the function q H . In this paper we give a local uniqueness theorem; if the Titchmarsh–Weyl coefficients q H 1 and q H 2 corresponding to two Hamiltonian systems are exponentially close, then the Hamiltonians H 1 and H 2 coincide (up to reparameterization) up to a certain point of their domain, which depends on the quantitative degree of exponential closeness of the Titchmarsh–Weyl coefficients
Hamiltonian Approach to 2+1 Dimensional Gravity
Cantini, L.; Menotti, P.; Seminara, D.
2002-12-01
It is shown that the reduced particle dynamics of 2+1 dimensional gravity in the maximally slicing gauge has hamiltonian form. We give the exact diffeomorphism which transforms the spinning cone metric in the Deser, Jackiw, 't Hooft gauge to the maximally slicing gauge. It is explicitly shown that the boundary term in the action, written in hamiltonian form gives the hamiltonian for the reduced particle dynamics. The quantum mechanical translation of the two particle hamiltonian gives rise to the logarithm of the Laplace-Beltrami operator on a cone whose angular deficit is given by the total energy of the system irrespective of the masses of the particles thus proving at the quantum level a conjecture by 't Hooft on the two particle dynamics.
Diffusion Monte Carlo approach versus adiabatic computation for local Hamiltonians
Bringewatt, Jacob; Dorland, William; Jordan, Stephen P.; Mink, Alan
2018-02-01
Most research regarding quantum adiabatic optimization has focused on stoquastic Hamiltonians, whose ground states can be expressed with only real non-negative amplitudes and thus for whom destructive interference is not manifest. This raises the question of whether classical Monte Carlo algorithms can efficiently simulate quantum adiabatic optimization with stoquastic Hamiltonians. Recent results have given counterexamples in which path-integral and diffusion Monte Carlo fail to do so. However, most adiabatic optimization algorithms, such as for solving MAX-k -SAT problems, use k -local Hamiltonians, whereas our previous counterexample for diffusion Monte Carlo involved n -body interactions. Here we present a 6-local counterexample which demonstrates that even for these local Hamiltonians there are cases where diffusion Monte Carlo cannot efficiently simulate quantum adiabatic optimization. Furthermore, we perform empirical testing of diffusion Monte Carlo on a standard well-studied class of permutation-symmetric tunneling problems and similarly find large advantages for quantum optimization over diffusion Monte Carlo.
Time and a physical Hamiltonian for quantum gravity.
Husain, Viqar; Pawłowski, Tomasz
2012-04-06
We present a nonperturbative quantization of general relativity coupled to dust and other matter fields. The dust provides a natural time variable, leading to a physical Hamiltonian with spatial diffeomorphism symmetry. The surprising feature is that the Hamiltonian is not a square root. This property, together with the kinematical structure of loop quantum gravity, provides a complete theory of quantum gravity, and puts applications to cosmology, quantum gravitational collapse, and Hawking radiation within technical reach. © 2012 American Physical Society
A hierarchy of Liouville integrable discrete Hamiltonian equations
Energy Technology Data Exchange (ETDEWEB)
Xu Xixiang [College of Science, Shandong University of Science and Technology, Qingdao 266510 (China)], E-mail: xixiang_xu@yahoo.com.cn
2008-05-12
Based on a discrete four-by-four matrix spectral problem, a hierarchy of Lax integrable lattice equations with two potentials is derived. Two Hamiltonian forms are constructed for each lattice equation in the resulting hierarchy by means of the discrete variational identity. A strong symmetry operator of the resulting hierarchy is given. Finally, it is shown that the resulting lattice equations are all Liouville integrable discrete Hamiltonian systems.
On the topological entropy of an optical Hamiltonian flow
Niche, Cesar J.
2000-01-01
In this article we prove two formulas for the topological entropy of an F-optical Hamiltonian flow induced by a C^{\\infty} Hamiltonian, where F is a Lagrangian distribution. In these formulas, we calculate the topological entropy as the exponential growth rate of the average of the determinant of the differential of the flow, restricted to the Lagrangian distribution or to a proper modification.
SOLVING THE HAMILTONIAN CYCLE PROBLEM USING SYMBOLIC DETERMINANTS
Ejov, V.; Filar, J. A.; Lucas, S. K.; Nelson, J. L.
2006-01-01
In this note we show how the Hamiltonian Cycle problem can be reduced to solving a system of polynomial equations related to the adjacency matrix of a graph. This system of equations can be solved using the method of Gröbner bases, but we also show how a symbolic determinant related to the adjacency matrix can be used to directly decide whether a graph has a Hamiltonian cycle.
Noncanonical Hamiltonian density formulation of hydrodynamics and ideal MHD
International Nuclear Information System (INIS)
Morrison, P.J.; Greene, J.M.
1980-04-01
A new Hamiltonian density formulation of a perfect fluid with or without a magnetic field is presented. Contrary to previous work the dynamical variables are the physical variables, rho, v, B, and s, which form a noncanonical set. A Poisson bracket which satisfies the Jacobi identity is defined. This formulation is transformed to a Hamiltonian system where the dynamical variables are the spatial Fourier coefficients of the fluid variables
Families of superintegrable Hamiltonians constructed from exceptional polynomials
International Nuclear Information System (INIS)
Post, Sarah; Tsujimoto, Satoshi; Vinet, Luc
2012-01-01
We introduce a family of exactly-solvable two-dimensional Hamiltonians whose wave functions are given in terms of Laguerre and exceptional Jacobi polynomials. The Hamiltonians contain purely quantum terms which vanish in the classical limit leaving only a previously known family of superintegrable systems. Additional, higher-order integrals of motion are constructed from ladder operators for the considered orthogonal polynomials proving the quantum system to be superintegrable. (paper)
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)
Orbits and variational principles for conservative Hamiltonian systems
International Nuclear Information System (INIS)
Torres del Castillo, G.F.
1989-01-01
It is shown that for any Hamiltonian system whose Hamiltonian is time-independent the equations that determine the orbits followed by the system, without making reference to time, have the form of Hamilton's equations in a phase space of dimension two units smaller than that of the original phase space. By considering the cases of classical mechanics and of geometrical optics, it is shown that this result amounts, respectively, to Maupertuis' least action principle and to Fermat's principle. (Author)
Oscillator representations for self-adjoint Calogero Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Gitman, D M [Institute of Physics, University of Sao Paulo (Brazil); Tyutin, I V; Voronov, B L, E-mail: gitman@dfn.if.usp.br, E-mail: tyutin@lpi.ru, E-mail: voronov@lpi.ru [Lebedev Physical Institute, Moscow (Russian Federation)
2011-10-21
In Gitman et al (2010 J. Phys. A: Math. Theor. 43 145205), we presented a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential V(x) = {alpha}x{sup -2}. We described all possible self-adjoint (s.a.) operators (s.a. Hamiltonians) associated with the differential operation H=-d{sub x}{sup 2}+{alpha}x{sup -2} for the Calogero Hamiltonian. Here, we discuss a new aspect of the problem, the so-called oscillator representations for the Calogero Hamiltonians. As is known, operators of the form N-hat = a-hat{sup +} a-hat and A-hat = a-hat a-hat{sup +} are called operators of oscillator type. Oscillator-type operators possess a number of useful properties in the case when the elementary operators a-hat are closed. It turns out that some s.a. Calogero Hamiltonians allow oscillator-type representations. We describe such Hamiltonians and find the corresponding mutually adjoint elementary operators a-hat and a-hat{sup +}. An oscillator-type representation for a given Hamiltonian is generally not unique. (paper)
Oscillator representations for self-adjoint Calogero Hamiltonians
International Nuclear Information System (INIS)
Gitman, D M; Tyutin, I V; Voronov, B L
2011-01-01
In Gitman et al (2010 J. Phys. A: Math. Theor. 43 145205), we presented a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential V(x) = αx -2 . We described all possible self-adjoint (s.a.) operators (s.a. Hamiltonians) associated with the differential operation H=-d x 2 +αx -2 for the Calogero Hamiltonian. Here, we discuss a new aspect of the problem, the so-called oscillator representations for the Calogero Hamiltonians. As is known, operators of the form N-hat = a-hat + a-hat and A-hat = a-hat a-hat + are called operators of oscillator type. Oscillator-type operators possess a number of useful properties in the case when the elementary operators a-hat are closed. It turns out that some s.a. Calogero Hamiltonians allow oscillator-type representations. We describe such Hamiltonians and find the corresponding mutually adjoint elementary operators a-hat and a-hat + . An oscillator-type representation for a given Hamiltonian is generally not unique. (paper)
Hamiltonian quantum simulation with bounded-strength controls
International Nuclear Information System (INIS)
Bookatz, Adam D; Wocjan, Pawel; Viola, Lorenza
2014-01-01
We propose dynamical control schemes for Hamiltonian simulation in many-body quantum systems that avoid instantaneous control operations and rely solely on realistic bounded-strength control Hamiltonians. Each simulation protocol consists of periodic repetitions of a basic control block, constructed as a modification of an ‘Eulerian decoupling cycle,’ that would otherwise implement a trivial (zero) target Hamiltonian. For an open quantum system coupled to an uncontrollable environment, our approach may be employed to engineer an effective evolution that simulates a target Hamiltonian on the system while suppressing unwanted decoherence to the leading order, thereby allowing for dynamically corrected simulation. We present illustrative applications to both closed- and open-system simulation settings, with emphasis on simulation of non-local (two-body) Hamiltonians using only local (one-body) controls. In particular, we provide simulation schemes applicable to Heisenberg-coupled spin chains exposed to general linear decoherence, and show how to simulate Kitaev's honeycomb lattice Hamiltonian starting from Ising-coupled qubits, as potentially relevant to the dynamical generation of a topologically protected quantum memory. Additional implications for quantum information processing are discussed. (papers)
Naz, Rehana
2018-01-01
Pontrygin-type maximum principle is extended for the present value Hamiltonian systems and current value Hamiltonian systems of nonlinear difference equations for uniform time step $h$. A new method termed as a discrete time current value Hamiltonian method is established for the construction of first integrals for current value Hamiltonian systems of ordinary difference equations arising in Economic growth theory.
Hamiltonian derivation of a gyrofluid model for collisionless magnetic reconnection
International Nuclear Information System (INIS)
Tassi, E
2014-01-01
We consider a simple electromagnetic gyrokinetic model for collisionless plasmas and show that it possesses a Hamiltonian structure. Subsequently, from this model we derive a two-moment gyrofluid model by means of a procedure which guarantees that the resulting gyrofluid model is also Hamiltonian. The first step in the derivation consists of imposing a generic fluid closure in the Poisson bracket of the gyrokinetic model, after expressing such bracket in terms of the gyrofluid moments. The constraint of the Jacobi identity, which every Poisson bracket has to satisfy, selects then what closures can lead to a Hamiltonian gyrofluid system. For the case at hand, it turns out that the only closures (not involving integro/differential operators or an explicit dependence on the spatial coordinates) that lead to a valid Poisson bracket are those for which the second order parallel moment, independently for each species, is proportional to the zero order moment. In particular, if one chooses an isothermal closure based on the equilibrium temperatures and derives accordingly the Hamiltonian of the system from the Hamiltonian of the parent gyrokinetic model, one recovers a known Hamiltonian gyrofluid model for collisionless reconnection. The proposed procedure, in addition to yield a gyrofluid model which automatically conserves the total energy, provides also, through the resulting Poisson bracket, a way to derive further conservation laws of the gyrofluid model, associated with the so called Casimir invariants. We show that a relation exists between Casimir invariants of the gyrofluid model and those of the gyrokinetic parent model. The application of such Hamiltonian derivation procedure to this two-moment gyrofluid model is a first step toward its application to more realistic, higher-order fluid or gyrofluid models for tokamaks. It also extends to the electromagnetic gyrokinetic case, recent applications of the same procedure to Vlasov and drift- kinetic systems
An extended discrete gradient formula for oscillatory Hamiltonian systems
International Nuclear Information System (INIS)
Liu Kai; Shi Wei; Wu Xinyuan
2013-01-01
In this paper, incorporating the idea of the discrete gradient method into the extended Runge–Kutta–Nyström integrator, we derive and analyze an extended discrete gradient formula for the oscillatory Hamiltonian system with the Hamiltonian H(p,q)= 1/2 p T p+ 1/2 q T Mq+U(q), where q:R→R d represents generalized positions, p:R→R d represents generalized momenta and M is an element of R dxd is a symmetric and positive semi-definite matrix. The solution of this system is a nonlinear oscillator. Basically, many nonlinear oscillatory mechanical systems with a partitioned Hamiltonian function lend themselves to this approach. The extended discrete gradient formula presented in this paper exactly preserves the energy H(p, q). We derive some properties of the new formula. The convergence is analyzed for the implicit schemes based on the discrete gradient formula, and it turns out that the convergence of the implicit schemes based on the extended discrete gradient formula is independent of ‖M‖, which is a significant property for the oscillatory Hamiltonian system. Thus, it transpires that a larger step size can be chosen for the new energy-preserving schemes than that for the traditional discrete gradient methods when applied to the oscillatory Hamiltonian system. Illustrative examples show the competence and efficiency of the new schemes in comparison with the traditional discrete gradient methods in the scientific literature. (paper)
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)
Non-stoquastic Hamiltonians in quantum annealing via geometric phases
Vinci, Walter; Lidar, Daniel A.
2017-09-01
We argue that a complete description of quantum annealing implemented with continuous variables must take into account the non-adiabatic Aharonov-Anandan geometric phase that arises when the system Hamiltonian changes during the anneal. We show that this geometric effect leads to the appearance of non-stoquasticity in the effective quantum Ising Hamiltonians that are typically used to describe quantum annealing with flux qubits. We explicitly demonstrate the effect of this geometric non-stoquasticity when quantum annealing is performed with a system of one and two coupled flux qubits. The realization of non-stoquastic Hamiltonians has important implications from a computational complexity perspective, since it is believed that in many cases quantum annealing with stoquastic Hamiltonians can be efficiently simulated via classical algorithms such as Quantum Monte Carlo. It is well known that the direct implementation of non-stoquastic Hamiltonians with flux qubits is particularly challenging. Our results suggest an alternative path for the implementation of non-stoquasticity via geometric phases that can be exploited for computational purposes.
Effective Hamiltonian for protected edge states in graphene
International Nuclear Information System (INIS)
Winkler, R.; Deshpande, H.
2017-01-01
Edge states in topological insulators (TIs) disperse symmetrically about one of the time-reversal invariant momenta Λ in the Brillouin zone (BZ) with protected degeneracies at Λ. Commonly TIs are distinguished from trivial insulators by the values of one or multiple topological invariants that require an analysis of the bulk band structure across the BZ. We propose an effective two-band Hamiltonian for the electronic states in graphene based on a Taylor expansion of the tight-binding Hamiltonian about the time-reversal invariant M point at the edge of the BZ. This Hamiltonian provides a faithful description of the protected edge states for both zigzag and armchair ribbons, though the concept of a BZ is not part of such an effective model. In conclusion, we show that the edge states are determined by a band inversion in both reciprocal and real space, which allows one to select Λ for the edge states without affecting the bulk spectrum.
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.
Hamiltonian formalism of two-dimensional Vlasov kinetic equation.
Pavlov, Maxim V
2014-12-08
In this paper, the two-dimensional Benney system describing long wave propagation of a finite depth fluid motion and the multi-dimensional Russo-Smereka kinetic equation describing a bubbly flow are considered. The Hamiltonian approach established by J. Gibbons for the one-dimensional Vlasov kinetic equation is extended to a multi-dimensional case. A local Hamiltonian structure associated with the hydrodynamic lattice of moments derived by D. J. Benney is constructed. A relationship between this hydrodynamic lattice of moments and the two-dimensional Vlasov kinetic equation is found. In the two-dimensional case, a Hamiltonian hydrodynamic lattice for the Russo-Smereka kinetic model is constructed. Simple hydrodynamic reductions are presented.
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.
Riemannian geometry of Hamiltonian chaos: hints for a general theory.
Cerruti-Sola, Monica; Ciraolo, Guido; Franzosi, Roberto; Pettini, Marco
2008-10-01
We aim at assessing the validity limits of some simplifying hypotheses that, within a Riemmannian geometric framework, have provided an explanation of the origin of Hamiltonian chaos and have made it possible to develop a method of analytically computing the largest Lyapunov exponent of Hamiltonian systems with many degrees of freedom. Therefore, a numerical hypotheses testing has been performed for the Fermi-Pasta-Ulam beta model and for a chain of coupled rotators. These models, for which analytic computations of the largest Lyapunov exponents have been carried out in the mentioned Riemannian geometric framework, appear as paradigmatic examples to unveil the reason why the main hypothesis of quasi-isotropy of the mechanical manifolds sometimes breaks down. The breakdown is expected whenever the topology of the mechanical manifolds is nontrivial. This is an important step forward in view of developing a geometric theory of Hamiltonian chaos of general validity.
Intertwined Hamiltonians in two-dimensional curved spaces
International Nuclear Information System (INIS)
Aghababaei Samani, Keivan; Zarei, Mina
2005-01-01
The problem of intertwined Hamiltonians in two-dimensional curved spaces is investigated. Explicit results are obtained for Euclidean plane, Minkowski plane, Poincare half plane (AdS 2 ), de Sitter plane (dS 2 ), sphere, and torus. It is shown that the intertwining operator is related to the Killing vector fields and the isometry group of corresponding space. It is shown that the intertwined potentials are closely connected to the integral curves of the Killing vector fields. Two problems are considered as applications of the formalism presented in the paper. The first one is the problem of Hamiltonians with equispaced energy levels and the second one is the problem of Hamiltonians whose spectrum is like the spectrum of a free particle
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...
Lie transforms and their use in Hamiltonian perturbation theory
International Nuclear Information System (INIS)
Cary, J.R.
1978-06-01
A review is presented of the theory of Lie transforms as applied to Hamiltonian systems. We begin by presenting some general background on the Hamiltonian formalism and by introducing the operator notation for canonical transformations. We then derive the general theory of Lie transforms. We derive the formula for the new Hamiltonian when one uses a Lie transform to effect a canonical transformation, and we use Lie transforms to prove a very general version of Noether's theorem, or the symmetry-equals-invariant theorem. Next we use the general Lie transform theory to derive Deprit's perturbation theory. We illustrate this perturbation theory by application to two well-known problems in classical mechanics. Finally we present a chapter on conventions. There are many ways to develop Lie transforms. The last chapter explains the reasons for the choices made here
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.
Blocking Radial Diffusion in a Double-Waved Hamiltonian Model
International Nuclear Information System (INIS)
Martins, Caroline G L; De Carvalho, R Egydio; Marcus, F A; Caldas, I L
2011-01-01
A non-twist Hamiltonian system perturbed by two waves with particular wave numbers can present Robust Tori, barriers created by the vanishing of the perturbing Hamiltonian at some defined positions. When Robust Tori exist, any trajectory in phase space passing close to them is blocked by emergent invariant curves that prevent the chaotic transport. We analyze the breaking up of the RT as well the transport dependence on the wave numbers and on the wave amplitudes. Moreover, we report the chaotic web formation in the phase space and how this pattern influences the transport.
Some sufficient conditions for Hamiltonian property in terms of ...
Indian Academy of Sciences (India)
[1, D], or Wf (G) ≥ f (1). 2 n2 + [f(2) − 3. 2 f(1)]n − 2[f(2) − f(1)] for a monotonically decreasing function f(x) on x ∈ [1, D], then G is Hamiltonian, unless G ∼= K∗ n or K2∨3K1. Proof. Assume that G is not a Hamiltonian graph with degree sequence (d1,d2,...,dn), where d1 ≤ d2 ≤ ··· ≤ dn and n ≥ 3. By Lemma 1, there is a ...
Painlevé IV Hamiltonian systems and coherent states
International Nuclear Information System (INIS)
Bermudez, D; Contreras-Astorga, A; Fernández C, D J
2015-01-01
Schrödinger Hamiltonians with third-order differential ladder operators are linked to the Painlevé IV equation. Some of these appear from applying SUSY QM to the harmonic oscillator. Departing from them, we will build coherent states as eigenstates of the annihilation operator, then as displaced versions of the extremal states, both involving the third-order ladder operators, and finally as displaced extremal states using linearized ladder operators. To each Hamiltonian corresponds two families of coherent states for fixed ladder operators: one in the infinite dimension subspace associated with the oscillator spectrum and another in the finite dimension one generated by the eigenstates created by SUSY QM. (paper)
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.
Topological color codes and two-body quantum lattice Hamiltonians
Kargarian, M.; Bombin, H.; Martin-Delgado, M. A.
2010-02-01
Topological color codes are among the stabilizer codes with remarkable properties from the quantum information perspective. In this paper, we construct a lattice, the so-called ruby lattice, with coordination number 4 governed by a two-body Hamiltonian. In a particular regime of coupling constants, in a strong coupling limit, degenerate perturbation theory implies that the low-energy spectrum of the model can be described by a many-body effective Hamiltonian, which encodes the color code as its ground state subspace. Ground state subspace corresponds to a vortex-free sector. The gauge symmetry Z2×Z2 of the color code could already be realized by identifying three distinct plaquette operators on the ruby lattice. All plaquette operators commute with each other and with the Hamiltonian being integrals of motion. Plaquettes are extended to closed strings or string-net structures. Non-contractible closed strings winding the space commute with Hamiltonian but not always with each other. This gives rise to exact topological degeneracy of the model. A connection to 2-colexes can be established via the coloring of the strings. We discuss it at the non-perturbative level. The particular structure of the two-body Hamiltonian provides a fruitful interpretation in terms of mapping onto bosons coupled to effective spins. We show that high-energy excitations of the model have fermionic statistics. They form three families of high-energy excitations each of one color. Furthermore, we show that they belong to a particular family of topological charges. The emergence of invisible charges is related to the string-net structure of the model. The emerging fermions are coupled to nontrivial gauge fields. We show that for particular 2-colexes, the fermions can see the background fluxes in the ground state. Also, we use the Jordan-Wigner transformation in order to test the integrability of the model via introducing Majorana fermions. The four-valent structure of the lattice prevents the
Necessary conditions for super-integrability of Hamiltonian systems
Energy Technology Data Exchange (ETDEWEB)
Maciejewski, Andrzej J. [Institute of Astronomy, University of Zielona Gora, Podgorna 50, PL-65-246 Zielona Gora (Poland)], E-mail: maciejka@astro.ia.uz.zgora.pl; Przybylska, Maria [Torun Centre for Astronomy, N. Copernicus University, Gagarina 11, PL-87-100 Torun (Poland)], E-mail: maria.przybylska@astri.uni.torun.pl; Yoshida, Haruo [National Astronomical Observatory, 2-21-1 Osawa, Mitaka, 181-8588 Tokyo (Japan)], E-mail: h.yoshida@nao.ac.jp
2008-08-18
We formulate a general theorem which gives a necessary condition for the maximal super-integrability of a Hamiltonian system. This condition is expressed in terms of properties of the differential Galois group of the variational equations along a particular solution of the considered system. An application of this general theorem to natural Hamiltonian systems of n degrees of freedom with a homogeneous potential gives easily computable and effective necessary conditions for the super-integrability. To illustrate an application of the formulated theorems, we investigate: three known families of integrable potentials, and the three body problem on a line.
A progressive diagonalization scheme for the Rabi Hamiltonian
International Nuclear Information System (INIS)
Pan, Feng; Guan, Xin; Wang, Yin; Draayer, J P
2010-01-01
A diagonalization scheme for the Rabi Hamiltonian, which describes a qubit interacting with a single-mode radiation field via a dipole interaction, is proposed. It is shown that the Rabi Hamiltonian can be solved almost exactly using a progressive scheme that involves a finite set of one variable polynomial equations. The scheme is especially efficient for the lower part of the spectrum. Some low-lying energy levels of the model with several sets of parameters are calculated and compared to those provided by the recently proposed generalized rotating-wave approximation and a full matrix diagonalization.
A Class of Quasi-exact Solutions of Rabi Hamiltonian
International Nuclear Information System (INIS)
Pan Feng; Yao Youkun; Xie Mingxia; Han Wenjuan; Draayer, J.P.
2007-01-01
A class of quasi-exact solutions of the Rabi Hamiltonian, which describes a two-level atom interacting with a single-mode radiation field via a dipole interaction without the rotating-wave approximation, are obtained by using a wavefunction ansatz. Exact solutions for part of the spectrum are obtained when the atom-field coupling strength and the field frequency satisfy certain relations. As an example, the lowest exact energy level and the corresponding atom-field entanglement at the quasi-exactly solvable point are calculated and compared to results from the Jaynes-Cummings and counter-rotating cases of the Rabi Hamiltonian.
Phase transition in the non-degenerate Hubbard Hamiltonian
International Nuclear Information System (INIS)
Chaves, C.M.; Lederer, P.; Gomes, A.A.
1976-01-01
Phase transition in the isotropic non-degenerate Hubbard Hamiltonian within the renormalization group techniques, using the epsilon = 4 - d expansion to first order in epsilon, is studied. The functional obtained from the Hubbard Hamiltonian displays full rotation symmetry and describes two coupled fields: a vector spin field, with n components and a non-soft scalar charge field. The possibility of tricritical behavior then emerges. The effects of simple constraints imposed on the charge field is considered. The relevance of the coupling between the fields in producing Fisher renormalization of the critical exponents is discussed. The possible singularities introduced in the charge-charge correlation function by the coupling are also discussed
Additional integrals of the motion of classical Hamiltonian wave systems
International Nuclear Information System (INIS)
Shul'man, E.I.
1989-01-01
It is shown that a classical Hamiltonian wave system that possesses at least one additional integral of the motion with quadratic principal part has an infinite number of such integrals in the cases of both nondegenerate and degenerate dispersion laws. Conditions under which in a space of dimension d ≥ 2 a system with nondegenerate dispersion law is completely integratable and its Hamiltonian can be reduced to normal form are found. In the case of a degenerate dispersion law integrals are not sufficient for complete integrability
Floquet-Green function formalism for harmonically driven Hamiltonians
International Nuclear Information System (INIS)
Martinez, D F
2003-01-01
A method is proposed for the calculation of the Floquet-Green function of a general Hamiltonian with harmonic time dependence. We use matrix continued fractions to derive an expression for the 'dynamical effective potential' that can be used to calculate the Floquet-Green function of the system. We demonstrate the formalism for the simple case of a space-periodic (in the tight-binding approximation) Hamiltonian with a defect whose on-site energy changes harmonically with time. We study the local density of states for this system and the behaviour of the localized states as a function of the different parameters that characterize the system
Divide and conquer approach to quantum Hamiltonian simulation
Hadfield, Stuart; Papageorgiou, Anargyros
2018-04-01
We show a divide and conquer approach for simulating quantum mechanical systems on quantum computers. We can obtain fast simulation algorithms using Hamiltonian structure. Considering a sum of Hamiltonians we split them into groups, simulate each group separately, and combine the partial results. Simulation is customized to take advantage of the properties of each group, and hence yield refined bounds to the overall simulation cost. We illustrate our results using the electronic structure problem of quantum chemistry, where we obtain significantly improved cost estimates under very mild assumptions.
Hamiltonian formulation of QCD in the Schwinger gauge
International Nuclear Information System (INIS)
Schutte, D.
1989-01-01
The structure of the Hamiltonian related to a regularized non-Abelian gauge field theory is discussed in the light of different choices for gauge-invariant wave functionals (loop space, Coulomb, axial, Schwinger gauge). Arguments are given for the suggestion that the Schwinger gauge offers a specially suited framework for the computation of bound-state (hadron) properties. The most important reasons are the manifest rotation invariance, the lack of a Gribov horizon (giving standard many-body techniques a better chance), and the fact that a regularization analogous to the lattice regularization is easily implementable. Some details of the Schwinger-gauge Hamiltonian theory are discussed
Scattering theory of infrared divergent Pauli-Fierz Hamiltonians
Derezinski, J
2003-01-01
We consider in this paper the scattering theory of infrared divergent massless Pauli-Fierz Hamiltonians. We show that the CCR representations obtained from the asymptotic field contain so-called {\\em coherent sectors} describing an infinite number of asymptotically free bosons. We formulate some conjectures leading to mathematically well defined notion of {\\em inclusive and non-inclusive scattering cross-sections} for Pauli-Fierz Hamiltonians. Finally we give a general description of the scattering theory of QFT models in the presence of coherent sectors for the asymptotic CCR representations.
The detectability lemma and its applications to quantum Hamiltonian complexity
International Nuclear Information System (INIS)
Aharonov, Dorit; Arad, Itai; Vazirani, Umesh; Landau, Zeph
2011-01-01
Quantum Hamiltonian complexity, an emerging area at the intersection of condensed matter physics and quantum complexity theory, studies the properties of local Hamiltonians and their ground states. In this paper we focus on a seemingly specialized technical tool, the detectability lemma (DL), introduced in the context of the quantum PCP challenge (Aharonov et al 2009 arXiv:0811.3412), which is a major open question in quantum Hamiltonian complexity. We show that a reformulated version of the lemma is a versatile tool that can be used in place of the celebrated Lieb-Robinson (LR) bound to prove several important results in quantum Hamiltonian complexity. The resulting proofs are much simpler, more combinatorial and provide a plausible path toward tackling some fundamental open questions in Hamiltonian complexity. We provide an alternative simpler proof of the DL that removes a key restriction in the original statement (Aharonov et al 2009 arXiv:0811.3412), making it more suitable for the broader context of quantum Hamiltonian complexity. Specifically, we first use the DL to provide a one-page proof of Hastings' result that the correlations in the ground states of gapped Hamiltonians decay exponentially with distance (Hastings 2004 Phys. Rev. B 69 104431). We then apply the DL to derive a simpler and more intuitive proof of Hastings' seminal one-dimensional (1D) area law (Hastings 2007 J. Stat. Mech. (2007) P8024) (both these proofs are restricted to frustration-free systems). Proving the area law for two and higher dimensions is one of the most important open questions in the field of Hamiltonian complexity, and the combinatorial nature of the DL-based proof holds out hope for a possible generalization. Indeed, soon after the first publication of the methods presented here, they were applied to derive exponential improvements to Hastings' result (Arad et al 2011, Aharonov et al 2011) in the case of frustration-free 1D systems. Finally, we also provide a more general
The intrinsic stochasticity of near-integrable Hamiltonian systems
Energy Technology Data Exchange (ETDEWEB)
Krlin, L [Ceskoslovenska Akademie Ved, Prague (Czechoslovakia). Ustav Fyziky Plazmatu
1989-09-01
Under certain conditions, the dynamics of near-integrable Hamiltonian systems appears to be stochastic. This stochasticity (intrinsic stochasticity, or deterministic chaos) is closely related to the Kolmogorov-Arnold-Moser (KAM) theorem of the stability of near-integrable multiperiodic Hamiltonian systems. The effect of the intrinsic stochasticity attracts still growing attention both in theory and in various applications in contemporary physics. The paper discusses the relation of the intrinsic stochasticity to the modern ergodic theory and to the KAM theorem, and describes some numerical experiments on related astrophysical and high-temperature plasma problems. Some open questions are mentioned in conclusion. (author).
Hamiltonian models for the Madelung fluid and generalized Langevin equations
International Nuclear Information System (INIS)
Nonnenmacher, T.F.
1985-01-01
We present a Hamiltonian formulation of some type of an 'electromagnetic' Madelung fluid leading to a fluid mechanics interpretation of the Aharonov-Bohm effect and to a subsidary condition to be required in order to make the correspondence between Schroedinger's quantum mechanics and Madelung's fluid mechanics unique. Then we discuss some problems related with the Brownian oscillator. Our aim is to start out with a Hamiltonian for the composite system with surrounding heat bath) and to finally arrive at a stochastic differential equation with completely determined statistical properties. (orig./HSI)
Continuum-time Hamiltonian for the Baxter's model
International Nuclear Information System (INIS)
Libero, V.L.
1983-01-01
The associated Hamiltonian for the symmetric eight-vertex model is obtained by taking the time-continuous limit in an equivalent Ashkin-Teller model. The result is a Heisenberg Hamiltonian with coefficients J sub(x), J sub(y) and J sub(z) identical to those found by Sutherland for choices of the parameters a, b, c and d that bring the model close to the transition. The change in the operators is accomplished explicitly, the relation between the crossover operator for the Ashkin-Teller model and the energy operator for the eight-vertex model being obtained in a transparent form. (Author) [pt
Quantum-circuit model of Hamiltonian search algorithms
International Nuclear Information System (INIS)
Roland, Jeremie; Cerf, Nicolas J.
2003-01-01
We analyze three different quantum search algorithms, namely, the traditional circuit-based Grover's algorithm, its continuous-time analog by Hamiltonian evolution, and the quantum search by local adiabatic evolution. We show that these algorithms are closely related in the sense that they all perform a rotation, at a constant angular velocity, from a uniform superposition of all states to the solution state. This makes it possible to implement the two Hamiltonian-evolution algorithms on a conventional quantum circuit, while keeping the quadratic speedup of Grover's original algorithm. It also clarifies the link between the adiabatic search algorithm and Grover's algorithm
Useful forms of the Hamiltonian for ion-optical systems
International Nuclear Information System (INIS)
Davies, W.G.
1991-04-01
The symbiosis of differential algebra and the Lie-algebraic formulation of optics provides a set of very powerful tools for analyzing and understanding the orbit dynamics of complex accelerators up to very high orders. In order to use these tools effectively it is usually necessary to express the Hamiltonian in the appropriate coordinate system. In this report, the relativistic Hamiltonian is derived in curvilinear (the fundamental coordinate system for ion-optics), Cartesian and polar coordinates, in forms suitable for solving problems in ion optics and accelerator physics both with and without the help of differential algebra
Naz, Rehana; Naeem, Imran
2018-03-01
The non-standard Hamiltonian system, also referred to as a partial Hamiltonian system in the literature, of the form {\\dot q^i} = {partial H}/{partial {p_i}},\\dot p^i = - {partial H}/{partial {q_i}} + {Γ ^i}(t,{q^i},{p_i}) appears widely in economics, physics, mechanics, and other fields. The non-standard (partial) Hamiltonian systems arise from physical Hamiltonian structures as well as from artificial Hamiltonian structures. We introduce the term `artificial Hamiltonian' for the Hamiltonian of a model having no physical structure. We provide here explicitly the notion of an artificial Hamiltonian for dynamical systems of ordinary differential equations (ODEs). Also, we show that every system of second-order ODEs can be expressed as a non-standard (partial) Hamiltonian system of first-order ODEs by introducing an artificial Hamiltonian. This notion of an artificial Hamiltonian gives a new way to solve dynamical systems of first-order ODEs and systems of second-order ODEs that can be expressed as a non-standard (partial) Hamiltonian system by using the known techniques applicable to the non-standard Hamiltonian systems. We employ the proposed notion to solve dynamical systems of first-order ODEs arising in epidemics.
Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations
DEFF Research Database (Denmark)
Nam, Phan Thanh; Napiorkowski, Marcin; Solovej, Jan Philip
2016-01-01
We provide general conditions for which bosonic quadratic Hamiltonians on Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover the case when quantum systems have infinite degrees of freedom and the associated one-body kinetic and paring operators are unbounded. Our...
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…
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 ...
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 ...
Periodic Hamiltonian hierarchies and non-uniqueness of ...
Indian Academy of Sciences (India)
2016-12-02
Dec 2, 2016 ... Ca. 1. Introduction. Through the past few decades, research in supersym- ... The subject of periodic Hamiltonians has been exam- ined for a long time ... The plan of this paper is as follows: In §2, a brief resume of SUSYQM is ...
Nuclear properties with realistic Hamiltonians through spectral distribution theory
International Nuclear Information System (INIS)
Vary, J.P.; Belehrad, R.; Dalton, B.J.
1979-01-01
Motivated by the need of non-perturbative methods for utilizing realistic nuclear Hamiltonians H, the authors use spectral distribution theory, based on calculated moments of H, to obtain specific bulk and valence properties of finite nuclei. The primary emphasis here is to present results for the binding energies of nuclei obtained with and without an assumed core. (Auth.)
Existence and multiplicity results for homoclinic orbits of Hamiltonian systems
Directory of Open Access Journals (Sweden)
Chao-Nien Chen
1997-03-01
Full Text Available Homoclinic orbits play an important role in the study of qualitative behavior of dynamical systems. Such kinds of orbits have been studied since the time of Poincare. In this paper, we discuss how to use variational methods to study the existence of homoclinic orbits of Hamiltonian systems.
Multi-component bi-Hamiltonian Dirac integrable equations
Energy Technology Data Exchange (ETDEWEB)
Ma Wenxiu [Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700 (United States)], E-mail: mawx@math.usf.edu
2009-01-15
A specific matrix iso-spectral problem of arbitrary order is introduced and an associated hierarchy of multi-component Dirac integrable equations is constructed within the framework of zero curvature equations. The bi-Hamiltonian structure of the obtained Dirac hierarchy is presented be means of the variational trace identity. Two examples in the cases of lower order are computed.
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].
Hamiltonian Noether theorem for gauge systems and two time physics
International Nuclear Information System (INIS)
Villanueva, V M; Nieto, J A; Ruiz, L; Silvas, J
2005-01-01
The Noether theorem for Hamiltonian constrained systems is revisited. In particular, our review presents a novel method to show that the gauge transformations are generated by the conserved quantities associated with the first class constraints. We apply our results to the relativistic point particle, to the Friedberg et al model and, with special emphasis, to two time physics
Conventional hamiltonian for first-order differential systems
International Nuclear Information System (INIS)
Farias, J.R.
1984-01-01
Lagrangian systems corresponding to a given set of 2n first-order ordinary differential equations are singular ones. In despite this, it is shown that these systems can be put into a Hamiltonian form in the usual manner. (Author) [pt
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 ...
Propagator of a time-dependent unbound quadratic Hamiltonian system
International Nuclear Information System (INIS)
Yeon, K.H.; Kim, H.J.; Um, C.I.; George, T.F.; Pandey, L.N.
1996-01-01
The propagator for a time-dependent unbound quadratic Hamiltonian system is explicitly evaluated using the path integral method. Two time-invariant quantities of the system are found where these invariants determine whether or not the system is bound. Several examples are considered to illustrate that the propagator obtained for the unbound systems is correct
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
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.
Spectra of PT -symmetric Hamiltonians on tobogganic contours
Indian Academy of Sciences (India)
The term PT -symmetric quantum mechanics, although defined to be of a much broader use, was coined in tight connection with C. Bender's analysis of one- ... on the other hand, the other members of the family were strange Hamiltonians with imaginary potentials which do not appear physical at all. The aim of the.
On the minimization of Hamiltonians over pure Gaussian states
DEFF Research Database (Denmark)
Derezinski, Jan; Napiorkowski, Marcin; Solovej, Jan Philip
2013-01-01
that this procedure eliminates from the Hamiltonian terms of degree 1 and 2 that do not preserve the particle number, and leaves only terms that can be interpreted as quasiparticles excitations. We propose to call this fact Beliaev's Theorem, since to our knowledge it was mentioned for the first time in a paper...
Hamiltonian formulation of QED in the superaxial gauge
International Nuclear Information System (INIS)
Girotti, H.O.; Rothe, H.J.
A Hamiltonian formulation of QED in a fully fixed axial gauge is presented. The equal-time commutators for all field variables are computed and are shown to lead to the correct equations of motion. The constraints and gauge conditions hold as strong operator relations. (Author) [pt
Fractional Hamiltonian analysis of higher order derivatives systems
International Nuclear Information System (INIS)
Baleanu, Dumitru; Muslih, Sami I.; Tas, Kenan
2006-01-01
The fractional Hamiltonian analysis of 1+1 dimensional field theory is investigated and the fractional Ostrogradski's formulation is obtained. The fractional path integral of both simple harmonic oscillator with an acceleration-squares part and a damped oscillator are analyzed. The classical results are obtained when fractional derivatives are replaced with the integer order derivatives
The generalized Mayer theorem in the approximating hamiltonian method
International Nuclear Information System (INIS)
Bakulev, A.P.; Bogoliubov, N.N. Jr.; Kurbatov, A.M.
1982-07-01
With the help of the generalized Mayer theorem we obtain the improved inequality for free energies of model and approximating systems, where only ''connected parts'' over the approximating hamiltonian are taken into account. For the concrete system we discuss the problem of convergency of appropriate series of ''connected parts''. (author)
On Interconnections of Infinite-dimensional Port-Hamiltonian Systems
Pasumarthy, Ramkrishna; Schaft, Arjan J. van der
2004-01-01
Network modeling of complex physical systems leads to a class of nonlinear systems called port-Hamiltonian systems, which are defined with respect to a Dirac structure (a geometric structure which formalizes the power-conserving interconnection structure of the system). A power conserving
On interconnections of infinite-dimensional port-Hamiltonian systems
Ramkrishna Pasumarthy, R.P.; van der Schaft, Arjan
2004-01-01
Network modeling of complex physical systems leads to a class of nonlinear systems called port-Hamiltonian systems, which are defined with respect to a Dirac structure (a geometric structure which formalizes the power-conserving interconnection structure of the system). A power conserving
Hamiltonian model analysis of ππ scattering and production
International Nuclear Information System (INIS)
Obu, Mitsuaki
2000-01-01
A simple Hamiltonian model for ππ scattering and production is presented which incorporates resonant and background interactions. Analysis of isoscalar S wave ππ phase shift indicates that the background interaction plays only a minor role and the σ may be a dynamical resonance which is not originated from a corresponding bare state. (author)
Energy preserving integration of bi-Hamiltonian partial differential equations
Karasozen, B.; Simsek, G.
2013-01-01
The energy preserving average vector field (AVF) integrator is applied to evolutionary partial differential equations (PDEs) in bi-Hamiltonian form with nonconstant Poisson structures. Numerical results for the Korteweg de Vries (KdV) equation and for the Ito type coupled KdV equation confirm the
On resonances and bound states of Smilansky Hamiltonian
Czech Academy of Sciences Publication Activity Database
Exner, Pavel; Lotoreichik, Vladimir; Tater, Miloš
2016-01-01
Roč. 7, č. 5 (2016), s. 789-802 ISSN 2220-8054 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : Smilansky Hamiltonian * resonances * resonance free region * weak coupling asymptotics * Riemann surface * bound states Subject RIV: BE - Theoretical Physics
Statistical properties of the nuclear shell-model Hamiltonian
International Nuclear Information System (INIS)
Dias, H.; Hussein, M.S.; Oliveira, N.A. de
1986-01-01
The statistical properties of realistic nuclear shell-model Hamiltonian are investigated in sd-shell nuclei. The probability distribution of the basic-vector amplitude is calculated and compared with the Porter-Thomas distribution. Relevance of the results to the calculation of the giant resonance mixing parameter is pointed out. (Author) [pt
The Lagrangians and Hamiltonians of damped coupled vibrations
International Nuclear Information System (INIS)
Ding Guangtao; Gan Huilan; Zheng Xianfeng; Cui Zhifeng
2012-01-01
In this paper, the analytical mechanization of two kinds of damped coupled vibrations is studied. First, by use of coordinate transformations the equations of motion are transformed into the self-ad- joint form. Secondly, the Lagrangians are obtained according to Engels method. Finally the Lagrangians and Hamiltonians of the original equations are deduced by using the inverse transformation. (authors)
Maxwell-Vlasov equations as a continuous Hamiltonian system
International Nuclear Information System (INIS)
Morrison, P.J.
1980-09-01
The well-known Maxwell-Vlasov equations that describe a collisionless plasma are cast into Hamiltonian form. The dynamical variables are the physical although noncanonical variables E, B and f. We present a Poisson bracket which acts on these variables and the energy functional to produce the equations of motion
New bi-Hamiltonian systems on the plane
Tsiganov, A. V.
2017-06-01
We discuss several new bi-Hamiltonian integrable systems on the plane with integrals of motion of third, fourth, and sixth orders in momenta. The corresponding variables of separation, separated relations, compatible Poisson brackets, and recursion operators are also presented in the framework of the Jacobi method.
A Hamiltonian structure for the linearized Einstein vacuum field equations
International Nuclear Information System (INIS)
Torres del Castillo, G.F.
1991-01-01
By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained (Author)
Hamiltonian Cycles on a Random Three-coordinate Lattice
DEFF Research Database (Denmark)
Eynard, B.; Guitter, E.; Kristjansen, C.
1998-01-01
Consider a random three-coordinate lattice of spherical topology having 2v vertices and being densely covered by a single closed, self-avoiding walk, i.e. being equipped with a Hamiltonian cycle. We determine the number of such objects as a function of v. Furthermore we express the partition...
Hamiltonian theory of vacuum helical torus lines of magnetic force
International Nuclear Information System (INIS)
Gnudi, Giovanni; Hatori, Tadatsugu
1994-01-01
For making plasma into equilibrium state, the lines of magnetic force must have magnetic surfaces. However in a helical system, space is divided into the region having magnetic surface structure and the region that does not have it. Accordingly, it is an important basic research for the plasma confinement in a helical system to examine where is the boundary of both regions and how is the large area structure of the lines of magnetic force in the boundary region. The lines of magnetic force can be treated as a Hamilton mechanics system, and it has been proved that the Hamiltonian for the lines of magnetic force can be expressed by a set of canonical variables and the function of time. In this research, the Hamiltonian that describes the lines of magnetic force of helical system torus coordination in vacuum was successfully determined concretely. Next, the development of new linear symplectic integration method was carried out. The important supports for the theory of determining Hamiltonian are Lie transformation and paraxial expansion. The procedure is explained. In Appendix, Lie transformation, Hamiltonian for the lines of magnetic force, magnetic potential, Taylor expansion of the potential, cylindrical limit approximation, helical toroidal potential and integrable model are described. (K.I.)
Error Estimates for the Approximation of the Effective Hamiltonian
International Nuclear Information System (INIS)
Camilli, Fabio; Capuzzo Dolcetta, Italo; Gomes, Diogo A.
2008-01-01
We study approximation schemes for the cell problem arising in homogenization of Hamilton-Jacobi equations. We prove several error estimates concerning the rate of convergence of the approximation scheme to the effective Hamiltonian, both in the optimal control setting and as well as in the calculus of variations setting
On squaring the primary constraints in a generalized Hamiltonian dynamics
International Nuclear Information System (INIS)
Nesterenko, V.V.
1993-01-01
Consideration of the model of the relativistic particle with curvature and torsion in the three-dimensional space-time shows that the squaring of the primary constraints entails a wrong result. The complete set of the Hamiltonian constraints arising here corresponds to another model with an action similar but not identical with the initial action. 16 refs
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
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
Relating Lagrangian and Hamiltonian Formalisms of LC Circuits
Clemente-Gallardo, Jesús; Scherpen, Jacquelien M.A.
2003-01-01
The Lagrangian formalism earlier defined for (switching) electrical circuits, is adapted to the Lagrangian formalism defined on Lie algebroids. This allows us to define regular Lagrangians and consequently, well-defined Hamiltonian descriptions of arbitrary LC networks. The relation with other
Quantum finance Hamiltonian for coupon bond European and barrier options.
Baaquie, Belal E
2008-03-01
Coupon bond European and barrier options are financial derivatives that can be analyzed in the Hamiltonian formulation of quantum finance. Forward interest rates are modeled as a two-dimensional quantum field theory and its Hamiltonian and state space is defined. European and barrier options are realized as transition amplitudes of the time integrated Hamiltonian operator. The double barrier option for a financial instrument is "knocked out" (terminated with zero value) if the price of the underlying instrument exceeds or falls below preset limits; the barrier option is realized by imposing boundary conditions on the eigenfunctions of the forward interest rates' Hamiltonian. The price of the European coupon bond option and the zero coupon bond barrier option are calculated. It is shown that, is general, the constraint function for a coupon bond barrier option can -- to a good approximation -- be linearized. A calculation using an overcomplete set of eigenfunctions yields an approximate price for the coupon bond barrier option, which is given in the form of an integral of a factor that results from the barrier condition times another factor that arises from the payoff function.
Hamiltonian thermodynamics of charged three-dimensional dilatonic black holes
International Nuclear Information System (INIS)
Dias, Goncalo A. S.; Lemos, Jose P. S.
2008-01-01
The action for a class of three-dimensional dilaton-gravity theories, with an electromagnetic Maxwell field and a cosmological constant, can be recast in a Brans-Dicke-Maxwell type action, with its free ω parameter. For a negative cosmological constant, these theories have static, electrically charged, and spherically symmetric black hole solutions. Those theories with well formulated asymptotics are studied through a Hamiltonian formalism, and their thermodynamical properties are found out. The theories studied are general relativity (ω→±∞), a dimensionally reduced cylindrical four-dimensional general relativity theory (ω=0), and a theory representing a class of theories (ω=-3), all with a Maxwell term. The Hamiltonian formalism is set up in three dimensions through foliations on the right region of the Carter-Penrose diagram, with the bifurcation 1-sphere as the left boundary, and anti-de Sitter infinity as the right boundary. The metric functions on the foliated hypersurfaces and the radial component of the vector potential one-form are the canonical coordinates. The Hamiltonian action is written, the Hamiltonian being a sum of constraints. One finds a new action which yields an unconstrained theory with two pairs of canonical coordinates (M,P M ;Q,P Q ), where M is the mass parameter, which for ω M is the conjugate momenta of M, Q is the charge parameter, and P Q is its conjugate momentum. The resulting Hamiltonian is a sum of boundary terms only. A quantization of the theory is performed. The Schroedinger evolution operator is constructed, the trace is taken, and the partition function of the grand canonical ensemble is obtained, where the chemical potential is the scalar electric field φ. Like the uncharged cases studied previously, the charged black hole entropies differ, in general, from the usual quarter of the horizon area due to the dilaton.
Hamiltonian reductions in plasma physics about intrinsic gyrokinetic
International Nuclear Information System (INIS)
Guillebon de Resnes, L. de
2013-01-01
Gyrokinetic is a key model for plasma micro-turbulence, commonly used for fusion plasmas or small-scale astrophysical turbulence, for instance. The model still suffers from several issues, which could imply to reconsider the equations. This thesis dissertation clarifies three of them. First, one of the coordinates caused questions, both from a physical and from a mathematical point of view; a suitable constrained coordinate is introduced, which removes the issues from the theory and explains the intrinsic structures underlying the questions. Second, the perturbative coordinate transformation for gyrokinetic was computed only at lowest orders; explicit induction relations are obtained to go arbitrary order in the expansion. Third, the introduction of the coupling between the plasma and the electromagnetic field was not completely satisfactory; using the Hamiltonian structure of the dynamics, it is implemented in a more appropriate way, with strong consequences on the gyrokinetic equations, especially about their Hamiltonian structure. In order to address these three main points, several other results are obtained, for instance about the origin of the guiding-center adiabatic invariant, about a very efficient minimal guiding center transformation, or about an intermediate Hamiltonian model between Vlasov-Maxwell and gyrokinetic, where the characteristics include both the slow guiding-center dynamics and the fast gyro-angle dynamics. In addition, various reduction methods are used, introduced or developed, e.g. a Lie-transform of the equations of motion, a lifting method to transfer particle reductions to the corresponding Hamiltonian field dynamics, or a truncation method related both to Dirac's theory of constraints and to a projection onto a Lie-subalgebra. Besides gyrokinetic, this is useful to clarify other Hamiltonian reductions in plasma physics, for instance for incompressible or electrostatic dynamics, for magnetohydrodynamics, or for fluid closures including
Hamiltonian formalism for perfect fluids in general relativity
International Nuclear Information System (INIS)
Demaret, J.; Moncrief, V.
1980-01-01
Schutz's Hamiltonian theory of a relativistic perfect fluid, based on the velocity-potential version of classical perfect fluid hydrodynamics as formulated by Seliger and Whitham, is used to derive, in the framework of the Arnowitt, Deser, and Misner (ADM) method, a general partially reduced Hamiltonian for relativistic systems filled with a perfect fluid. The time coordinate is chosen, as in Lund's treatment of collapsing balls of dust, as minus the only velocity potential different from zero in the case of an irrotational and isentropic fluid. A ''semi-Dirac'' method can be applied to quantize astrophysical and cosmological models in the framework of this partially reduced formalism. If one chooses Taub's adapted comoving coordinate system, it is possible to derive a fully reduced ADM Hamiltonian, which is equal to minus the total baryon number of the fluid, generalizing a result previously obtained by Moncrief in the more particular framework of Taub's variational principle, valid for self-gravitating barotropic relativistic perfect fluids. An unconstrained Hamiltonian density is then explicitly derived for a fluid obeying the equation of state p=(gamma-1)rho (1 < or = γ < or = 2), which can adequately describe the phases of very high density attained in a catastrophic collapse or during the early stages of the Universe. This Hamiltonian density, shown to be equivalent to Moncrief's in the particular case of an isentropic fluid, can be simplified for fluid-filled class-A diagonal Bianchi-type cosmological models and appears as a suitable starting point for the study of the canonical quantization of these models
Hamiltonian structure of the integrable coupling of the Jaulent-Miodek hierarchy
International Nuclear Information System (INIS)
Zhang, Yufeng; Fan, Engui
2006-01-01
A scheme for deducing Hamiltonian structures of the higher-dimensional hierarchies of evolution equations is presented which is devoting to obtaining the Hamiltonian structures of integrable coupling of the Jaulent-Miodek hierarchy
Integrable quadratic classical Hamiltonians on so(4) and so(3, 1)
International Nuclear Information System (INIS)
Sokolov, Vladimir V; Wolf, Thomas
2006-01-01
We investigate a special class of quadratic Hamiltonians on so(4) and so(3, 1) and describe Hamiltonians that have additional polynomial integrals. One of the main results is a new integrable case with an integral of sixth degree
Homoclinic Orbits for a Class of Nonperiodic Hamiltonian Systems with Some Twisted Conditions
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Qi Wang
2013-01-01
Full Text Available By the Maslov index theory, we will study the existence and multiplicity of homoclinic orbits for a class of asymptotically linear nonperiodic Hamiltonian systems with some twisted conditions on the Hamiltonian functions.
Exact smooth classification of Hamiltonian vector fields on symplectic 2-manifolds
International Nuclear Information System (INIS)
Krouglikov, B.S.
1994-10-01
Complete exact classification of Hamiltonian systems with one degree of freedom and Morse Hamiltonian is carried out. As it is a main part of trajectory classification of integrable Hamiltonian systems with two degrees of freedom, the corresponding generalization is considered. The dual problem of classification of symplectic form together with Morse foliation is carried out as well. (author). 10 refs, 16 figs
Determination of Hamiltonian matrix for IBM4 and compare it is self value with shells model
International Nuclear Information System (INIS)
Slyman, S.; Hadad, S.; Souman, H.
2004-01-01
The Hamiltonian is determined using the procedure OAI and the mapping of (IBM4) states into the shell model, which is based on the seniority classification scheme. A boson sub-matrix of the shell model Hamiltonian for the (sd) 4 configuration is constructed, and is proved to produce the same eigenvalues as the shell model Hamiltonian for the corresponding fermion states. (authors)
Generalized internal long wave equations: construction, hamiltonian structure and conservation laws
International Nuclear Information System (INIS)
Lebedev, D.R.
1982-01-01
Some aspects of the theory of the internal long-wave equations (ILW) are considered. A general class of the ILW type equations is constructed by means of the Zakharov-Shabat ''dressing'' method. Hamiltonian structure and infinite numbers of conservation laws are introduced. The considered equations are shown to be Hamiltonian in the so-called second Hamiltonian structu
The hamiltonian index of a graph and its branch-bonds
Xiong, Liming; Broersma, Haitze J.; Li, Xueliang; Li, Xueliang; Li, MingChu
2004-01-01
Let G be an undirected and loopless finite graph that is not a path. The smallest integer m such that the iterated line graph Lm(G) is hamiltonian is called the hamiltonian index of G, denoted by h(G). A reduction method to determine the hamiltonian index of a graph G with h(G) ≤ 2 is given here. We
Lith, van B.S.; Thije Boonkkamp, ten J.H.M.; IJzerman, W.L.; Tukker, T.W.
2015-01-01
We compute numerical solutions of Liouville's equation with a discontinuous Hamiltonian. We assume that the underlying Hamiltonian system has a well-defined behaviour even when the Hamiltonian is discontinuous. In the case of geometrical optics such a discontinuity yields the familiar Snell's law or
van Lith, B.S.; ten Thije Boonkkamp, J.H.M.; IJzerman, W.L.; Tukker, T.W.
A novel scheme is developed that computes numerical solutions of Liouville’s equation with a discontinuous Hamiltonian. It is assumed that the underlying Hamiltonian system has well-defined behaviour even when the Hamiltonian is discontinuous. In the case of geometrical optics such a discontinuity
New Hamiltonian structure of the fractional C-KdV soliton equation hierarchy
International Nuclear Information System (INIS)
Yu Fajun; Zhang Hongqing
2008-01-01
A generalized Hamiltonian structure of the fractional soliton equation hierarchy is presented by using of differential forms and exterior derivatives of fractional orders. Example of the fractional Hamiltonian system of the C-KdV soliton equation hierarchy is constructed, which is a new Hamiltonian structure
Solving a Hamiltonian Path Problem with a bacterial computer
Baumgardner, Jordan; Acker, Karen; Adefuye, Oyinade; Crowley, Samuel Thomas; DeLoache, Will; Dickson, James O; Heard, Lane; Martens, Andrew T; Morton, Nickolaus; Ritter, Michelle; Shoecraft, Amber; Treece, Jessica; Unzicker, Matthew; Valencia, Amanda; Waters, Mike; Campbell, A Malcolm; Heyer, Laurie J; Poet, Jeffrey L; Eckdahl, Todd T
2009-01-01
Background The Hamiltonian Path Problem asks whether there is a route in a directed graph from a beginning node to an ending node, visiting each node exactly once. The Hamiltonian Path Problem is NP complete, achieving surprising computational complexity with modest increases in size. This challenge has inspired researchers to broaden the definition of a computer. DNA computers have been developed that solve NP complete problems. Bacterial computers can be programmed by constructing genetic circuits to execute an algorithm that is responsive to the environment and whose result can be observed. Each bacterium can examine a solution to a mathematical problem and billions of them can explore billions of possible solutions. Bacterial computers can be automated, made responsive to selection, and reproduce themselves so that more processing capacity is applied to problems over time. Results We programmed bacteria with a genetic circuit that enables them to evaluate all possible paths in a directed graph in order to find a Hamiltonian path. We encoded a three node directed graph as DNA segments that were autonomously shuffled randomly inside bacteria by a Hin/hixC recombination system we previously adapted from Salmonella typhimurium for use in Escherichia coli. We represented nodes in the graph as linked halves of two different genes encoding red or green fluorescent proteins. Bacterial populations displayed phenotypes that reflected random ordering of edges in the graph. Individual bacterial clones that found a Hamiltonian path reported their success by fluorescing both red and green, resulting in yellow colonies. We used DNA sequencing to verify that the yellow phenotype resulted from genotypes that represented Hamiltonian path solutions, demonstrating that our bacterial computer functioned as expected. Conclusion We successfully designed, constructed, and tested a bacterial computer capable of finding a Hamiltonian path in a three node directed graph. This proof
Solving a Hamiltonian Path Problem with a bacterial computer
Directory of Open Access Journals (Sweden)
Treece Jessica
2009-07-01
Full Text Available Abstract Background The Hamiltonian Path Problem asks whether there is a route in a directed graph from a beginning node to an ending node, visiting each node exactly once. The Hamiltonian Path Problem is NP complete, achieving surprising computational complexity with modest increases in size. This challenge has inspired researchers to broaden the definition of a computer. DNA computers have been developed that solve NP complete problems. Bacterial computers can be programmed by constructing genetic circuits to execute an algorithm that is responsive to the environment and whose result can be observed. Each bacterium can examine a solution to a mathematical problem and billions of them can explore billions of possible solutions. Bacterial computers can be automated, made responsive to selection, and reproduce themselves so that more processing capacity is applied to problems over time. Results We programmed bacteria with a genetic circuit that enables them to evaluate all possible paths in a directed graph in order to find a Hamiltonian path. We encoded a three node directed graph as DNA segments that were autonomously shuffled randomly inside bacteria by a Hin/hixC recombination system we previously adapted from Salmonella typhimurium for use in Escherichia coli. We represented nodes in the graph as linked halves of two different genes encoding red or green fluorescent proteins. Bacterial populations displayed phenotypes that reflected random ordering of edges in the graph. Individual bacterial clones that found a Hamiltonian path reported their success by fluorescing both red and green, resulting in yellow colonies. We used DNA sequencing to verify that the yellow phenotype resulted from genotypes that represented Hamiltonian path solutions, demonstrating that our bacterial computer functioned as expected. Conclusion We successfully designed, constructed, and tested a bacterial computer capable of finding a Hamiltonian path in a three node
Newton algorithm for Hamiltonian characterization in quantum control
International Nuclear Information System (INIS)
Ndong, M; Sugny, D; Salomon, J
2014-01-01
We propose a Newton algorithm to characterize the Hamiltonian of a quantum system interacting with a given laser field. The algorithm is based on the assumption that the evolution operator of the system is perfectly known at a fixed time. The computational scheme uses the Crank–Nicholson approximation to explicitly determine the derivatives of the propagator with respect to the Hamiltonians of the system. In order to globalize this algorithm, we use a continuation method that improves its convergence properties. This technique is applied to a two-level quantum system and to a molecular one with a double-well potential. The numerical tests show that accurate estimates of the unknown parameters are obtained in some cases. We discuss the numerical limits of the algorithm in terms of the basin of convergence and the non-uniqueness of the solution. (paper)
A phenomenological Hamiltonian for the Lotka-Volterra problem
International Nuclear Information System (INIS)
Georgian, T.; Findley, G.L.
1996-01-01
We have presented a Hamiltonian theory of phenomenological chemical kinetics. In the present paper, we extend this treatment to the Lotka-Volterra model of sustained oscillations. Our approach begins with the usual definition of an intrinsic reaction coordinate space (x 1 ,x 2 ) for the Lotka-Volterra problem, which leads to the rate equations x 1 =ax 1 -bx 1 x 2 , x 2 =-cx 2 +bx 1 x 2 , with a,b and c being real constants. We thereafter present a Hamiltonian function H(x,y)[y 1 = x 1 and y 2 = x 2 ] and an associated holonomic constraint, which give rise to the above rates as half of Hamilton's equations. We provide trajectories by numerical integration (4th order Runge-Kutta) and show that H(x,y) is a constant of the motion. Finally, issues involved in developing an analytic solution to this problem are discussed
Hamiltonian Dynamics of Doubly-Foliable Space-Times
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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.
Adiabatic Hamiltonian deformation, linear response theory, and nonequilibrium molecular dynamics
International Nuclear Information System (INIS)
Hoover, W.G.
1980-01-01
Although Hamiltonians of various kinds have previously been used to derive Green-Kubo relations for the transport coefficients, the particular choice described is uniquely related to thermodynamics. This nonequilibrium Hamiltonian formulation of fluid flow provides pedagogically simple routes to nonequilibrium fluxes and distribution functions, to theoretical understanding of long-time effects, and to new numerical methods for simulating systems far from equilibrium. The same methods are now being applied to solid-phase problems. At the relatively high frequencies used in the viscous fluid calculations described, solids typically behave elastically. Lower frequencies lead to the formation of dislocations and other defects, making it possible to study plastic flow. A property of the nonequilibrium equations of motion which might be profitably explored is their effective irreversibility. Because only a few particles are necessary to generate irreversible behavior, simulations using adiabatic deformations of the kind described here could perhaps elucidate the instability in the equations of motion responsible for irreversibility
Extended hamiltonian formalism and Lorentz-violating lagrangians
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Don Colladay
2017-09-01
Full Text Available 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.
Quasi-superconformal algebras in two dimensions and hamiltonian reduction
International Nuclear Information System (INIS)
Romans, L.J.
1991-01-01
In the standard quantum hamiltonian reduction, constraining the SL(3, R) WZNW model leads to a model of Zamolodchikov's W 3 -symmetry. In recent work, Polyakov and Bershadsky have considered an alternative reduction which leads to a new algebra, W 3 2 , a nonlinear extension of the Virasoro algebra by a spin-1 current and two bosonic spin-3/2 currents. Motivated by this result, we display two new infinite series of nonlinear extended conformal algebras, containing 2N bosonic spin-3/2 currents and spin-1 Kac-Moody currents for either U(N) or Sp(2 N); the W 3 2 algebra appears as the N = 1 member of the U(N) series. We discuss the relationship between these algebras and the Knizhnik-Bershadsky superconformal algebras, and provide realisations in terms of free fields coupled to Kac-Moody currents. We propose a specific procedure for obtaining the algebras for general N through hamiltonian reduction. (orig.)
Optimal control methods for rapidly time-varying Hamiltonians
International Nuclear Information System (INIS)
Motzoi, F.; Merkel, S. T.; Wilhelm, F. K.; Gambetta, J. M.
2011-01-01
In this article, we develop a numerical method to find optimal control pulses that accounts for the separation of timescales between the variation of the input control fields and the applied Hamiltonian. In traditional numerical optimization methods, these timescales are treated as being the same. While this approximation has had much success, in applications where the input controls are filtered substantially or mixed with a fast carrier, the resulting optimized pulses have little relation to the applied physical fields. Our technique remains numerically efficient in that the dimension of our search space is only dependent on the variation of the input control fields, while our simulation of the quantum evolution is accurate on the timescale of the fast variation in the applied Hamiltonian.
Focal points and principal solutions of linear Hamiltonian systems revisited
Šepitka, Peter; Šimon Hilscher, Roman
2018-05-01
In this paper we present a novel view on the principal (and antiprincipal) solutions of linear Hamiltonian systems, as well as on the focal points of their conjoined bases. We present a new and unified theory of principal (and antiprincipal) solutions at a finite point and at infinity, and apply it to obtain new representation of the multiplicities of right and left proper focal points of conjoined bases. We show that these multiplicities can be characterized by the abnormality of the system in a neighborhood of the given point and by the rank of the associated T-matrix from the theory of principal (and antiprincipal) solutions. We also derive some additional important results concerning the representation of T-matrices and associated normalized conjoined bases. The results in this paper are new even for completely controllable linear Hamiltonian systems. We also discuss other potential applications of our main results, in particular in the singular Sturmian theory.
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.
arXiv Lightcone Effective Hamiltonians and RG Flows
Fitzpatrick, A. Liam; Katz, Emanuel; Vitale, Lorenzo G.; Walters, Matthew T.
We present a prescription for an effective lightcone (LC) Hamiltonian that includes the effects of zero modes, focusing on the case of Conformal Field Theories (CFTs) deformed by relevant operators. We show how the prescription resolves a number of issues with LC quantization, including i) the apparent non-renormalization of the vacuum, ii) discrepancies in critical values of bare parameters in equal-time vs LC quantization, and iii) an inconsistency at large N in CFTs with simple AdS duals. We describe how LC quantization can drastically simplify Hamiltonian truncation methods applied to some large N CFTs, and discuss how the prescription identifies theories where these simplifications occur. We demonstrate and check our prescription in a number of examples.
Generalized massive gravity in arbitrary dimensions and its Hamiltonian formulation
International Nuclear Information System (INIS)
Huang, Qing-Guo; Zhang, Ke-Chao; Zhou, Shuang-Yong
2013-01-01
We extend the four-dimensional de Rham-Gabadadze-Tolley (dRGT) massive gravity model to a general scalar massive-tensor theory in arbitrary dimensions, coupling a dRGT massive graviton to multiple scalars and allowing for generic kinetic and mass matrix mixing between the massive graviton and the scalars, and derive its Hamiltonian formulation and associated constraint system. When passing to the Hamiltonian formulation, two different sectors arise: a general sector and a special sector. Although obtained via different ways, there are two second class constraints in either of the two sectors, eliminating the BD ghost. However, for the special sector, there are still ghost instabilities except for the case of two dimensions. In particular, for the special sector with one scalar, there is a ''second BD ghost''
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
Tsallis thermostatistics for finite systems: a Hamiltonian approach
Adib, Artur B.; Moreira, Andrã© A.; Andrade, José S., Jr.; Almeida, Murilo P.
2003-05-01
The derivation of the Tsallis generalized canonical distribution from the traditional approach of the Gibbs microcanonical ensemble is revisited (Phys. Lett. A 193 (1994) 140). We show that finite systems whose Hamiltonians obey a generalized homogeneity relation rigorously follow the nonextensive thermostatistics of Tsallis. In the thermodynamical limit, however, our results indicate that the Boltzmann-Gibbs statistics is always recovered, regardless of the type of potential among interacting particles. This approach provides, moreover, a one-to-one correspondence between the generalized entropy and the Hamiltonian structure of a wide class of systems, revealing a possible origin for the intrinsic nonlinear features present in the Tsallis formalism that lead naturally to power-law behavior. Finally, we confirm these exact results through extensive numerical simulations of the Fermi-Pasta-Ulam chain of anharmonic oscillators.
Entangled trajectories Hamiltonian dynamics for treating quantum nuclear effects
Smith, Brendan; Akimov, Alexey V.
2018-04-01
A simple and robust methodology, dubbed Entangled Trajectories Hamiltonian Dynamics (ETHD), is developed to capture quantum nuclear effects such as tunneling and zero-point energy through the coupling of multiple classical trajectories. The approach reformulates the classically mapped second-order Quantized Hamiltonian Dynamics (QHD-2) in terms of coupled classical trajectories. The method partially enforces the uncertainty principle and facilitates tunneling. The applicability of the method is demonstrated by studying the dynamics in symmetric double well and cubic metastable state potentials. The methodology is validated using exact quantum simulations and is compared to QHD-2. We illustrate its relationship to the rigorous Bohmian quantum potential approach, from which ETHD can be derived. Our simulations show a remarkable agreement of the ETHD calculation with the quantum results, suggesting that ETHD may be a simple and inexpensive way of including quantum nuclear effects in molecular dynamics simulations.
RG-Whitham dynamics and complex Hamiltonian systems
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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...
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...
Optimal protocols for Hamiltonian and Schrödinger dynamics
International Nuclear Information System (INIS)
Schmiedl, Tim; Dieterich, Eckhard; Dieterich, Peter-Simon; Seifert, Udo
2009-01-01
For systems in an externally controllable time dependent potential, the optimal protocol minimizes the mean work spent in a finite time transition between given initial and final values of a control parameter. For an initially thermalized ensemble, we consider both Hamiltonian evolution for classical systems and Schrödinger evolution for quantum systems. In both cases, we show that for harmonic potentials, the optimal work is given by the adiabatic work even in the limit of short transition times. This result is counter-intuitive because the adiabatic work is substantially smaller than the work for an instantaneous jump. We also perform numerical calculations for the optimal protocol for Hamiltonian dynamics in an anharmonic quartic potential. For a two-level spin system, we give examples where the adiabatic work can be reached in either a finite or an arbitrarily short transition time depending on the allowed parameter space
Error bounds for molecular Hamiltonians inverted from experimental data
International Nuclear Information System (INIS)
Geremia, J.M.; Rabitz, Herschel
2003-01-01
Inverting experimental data provides a powerful technique for obtaining information about molecular Hamiltonians. However, rigorously quantifying how laboratory error propagates through the inversion algorithm has always presented a challenge. In this paper, we develop an inversion algorithm that realistically treats experimental error. It propagates the distribution of observed laboratory measurements into a family of Hamiltonians that are statistically consistent with the distribution of the data. This algorithm is built upon the formalism of map-facilitated inversion to alleviate computational expense and permit the use of powerful nonlinear optimization algorithms. Its capabilities are demonstrated by identifying inversion families for the X 1 Σ g + and a 3 Σ u + states of Na 2 that are consistent with the laboratory data
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 infinite-order two-component relativistic Hamiltonian by a simple one-step transformation.
Ilias, Miroslav; Saue, Trond
2007-02-14
The authors report the implementation of a simple one-step method for obtaining an infinite-order two-component (IOTC) relativistic Hamiltonian using matrix algebra. They apply the IOTC Hamiltonian to calculations of excitation and ionization energies as well as electric and magnetic properties of the radon atom. The results are compared to corresponding calculations using identical basis sets and based on the four-component Dirac-Coulomb Hamiltonian as well as Douglas-Kroll-Hess and zeroth-order regular approximation Hamiltonians, all implemented in the DIRAC program package, thus allowing a comprehensive comparison of relativistic Hamiltonians within the finite basis approximation.
Quantum control mechanism analysis through field based Hamiltonian encoding
International Nuclear Information System (INIS)
Mitra, Abhra; Rabitz, Herschel
2006-01-01
Optimal control of quantum dynamics in the laboratory is proving to be increasingly successful. The control fields can be complex, and the mechanisms by which they operate have often remained obscure. Hamiltonian encoding (HE) has been proposed as a method for understanding mechanisms in quantum dynamics. In this context mechanism is defined in terms of the dominant quantum pathways leading to the final state of the controlled system. HE operates by encoding a special modulation into the Hamiltonian and decoding its signature in the dynamics to determine the dominant pathway amplitudes. Earlier work encoded the modulation directly into the Hamiltonian operators. This present work introduces the alternative scheme of field based HE, where the modulation is encoded into the control field and not directly into the Hamiltonian operators. This distinct form of modulation yields a new perspective on mechanism and is computationally faster than the earlier approach. Field based encoding is also an important step towards a laboratory based algorithm for HE as it is the only form of encoding that may be experimentally executed. HE is also extended to cover systems with noise and uncertainty and finally, a hierarchical algorithm is introduced to reveal mechanism in a stepwise fashion of ever increasing detail as desired. This new hierarchical algorithm is an improvement over earlier approaches to HE where the entire mechanism was determined in one stroke. The improvement comes from the use of less complex modulation schemes, which leads to fewer evaluations of Schroedinger's equation. A number of simulations are presented on simple systems to illustrate the new field based encoding technique for mechanism assessment
Investigations on the local structure and the spin-Hamiltonian ...
Indian Academy of Sciences (India)
2016-07-13
Jul 13, 2016 ... (2016) 87: 22 c Indian Academy of Sciences. DOI 10.1007/s12043-016-1234-6. Investigations on the local structure and the spin-Hamiltonian parameters for the tetragonal Cu. 2+ centre in ZnGeF6·6H2O crystal. LI CHAO-YING. ∗. , HUANG YING and ZHENG XUE MEI. School of Physics and Electronic ...
Solutions to higher hamiltonians in the Toda hierarchies
International Nuclear Information System (INIS)
Ferreira, L.A.; Londe, R.M.
1988-01-01
We present a method for constructing the general solution to higher hamiltonians of the Toda hierarchies of integrable models associated to a simple Lie group G. The method depends on some special properties of the representations of the Lie algebra of G and it constitutes a generalization of the method used to construct the solutions of the Toda Molecula models. The SL(3) and SL(4) cases are discussed in detail. (author) [pt
Origin of constraints in relativistic classical Hamiltonian dynamics
International Nuclear Information System (INIS)
Mallik, S.; Hugentobler, E.
1979-01-01
We investigate the null-plane or the front form of relativistic classical Hamiltonian dynamics as proposed by Dirac and developed by Leutwyler and Stern. For systems of two spinless particles we show that the algebra of Poincare generators is equivalent to describing dynamics in terms of two covariant constraint equations, the Poisson bracket of the two constraints being weakly zero. The latter condition is solved for certain simple forms of constraints
Relativistic Many-Body Hamiltonian Approach to Mesons
Llanes-Estrada, Felipe J.; Cotanch, Stephen R.
2001-01-01
We represent QCD at the hadronic scale by means of an effective Hamiltonian, $H$, formulated in the Coulomb gauge. As in the Nambu-Jona-Lasinio model, chiral symmetry is explicity broken, however our approach is renormalizable and also includes confinement through a linear potential with slope specified by lattice gauge theory. This interaction generates an infrared integrable singularity and we detail the computationally intensive procedure necessary for numerical solution. We focus upon app...
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.
Locally Hamiltonian systems with symmetry and a generalized Noether's theorem
International Nuclear Information System (INIS)
Carinena, J.F.; Ibort, L.A.
1985-01-01
An analysis of global aspects of the theory of symmetry groups G of locally Hamiltonian dynamical systems is carried out for particular cases either of the symmetry group, or the differentiable manifold M supporting the symplectic structure, or the action of G on M. In every case it is obtained a generalization of Noether's theorem. It has been looked at the classical Noether's theorem for Lagrangian systems from a modern perspective
Fermion Bag Approach to Lattice Hamiltonian Field Theories
Huffman, Emilie
2018-03-01
Using a model in the Gross-Neveu Ising universality class, we show how the fermion bag idea can be applied to develop algorithms to Hamiltonian lattice field theories. We argue that fermion world lines suggest an alternative method to the traditional techniques for calculating ratios of determinants in a stable manner. We show the power behind these ideas by extracting the physics of the model on large lattices.
Analytic solutions of QCD motivated Hamiltonians at low energy
International Nuclear Information System (INIS)
Yepez, T.; Amor, A.; Hess, P.O.; Szczepaniak, A.; Civitarese, O.
2011-01-01
A model Hamiltonian, motivated by QCD, is investigated in order to study only the quark sector, then only the gluon sector and finally both together. Restricting to the pure quark sector and setting the mass of the quarks to zero, we find analytic solutions, involving two to three orbitals. Allowing the mass of the quarks to be different to zero, we find semi-analytic solutions involving an arbitrary number of orbitals. Afterwards, we indicate on how to incorporate gluons. (author)
Fundamental length in quantum theories with PT-symmetric Hamiltonians
Czech Academy of Sciences Publication Activity Database
Znojil, Miloslav
2009-01-01
Roč. 80, č. 4 (2009), 045022/1-045022/20 ISSN 1550-7998 R&D Projects: GA MŠk LC06002; GA ČR GA202/07/1307 Institutional research plan: CEZ:AV0Z10480505 Keywords : non-Hermitian Hamiltonians * anharmonic-oscillators * noncommutative space Subject RIV: BE - Theoretical Physics Impact factor: 4.922, year: 2009
Goldstone's theorem and Hamiltonian of multi-Galileon modified gravity
International Nuclear Information System (INIS)
Zhou Shuangyong
2011-01-01
The Galileon model was recently proposed to locally describe a class of modified gravity theories, including the braneworld Dvali-Gabadadze-Porrati model. We discuss spontaneous symmetry breaking of the self-accelerating branch in a multi-Galileon theory with internal global symmetries. We show that a modified version of Goldstone's theorem is applicable to the symmetry breaking pattern and discuss its implications. We also derive the Hamiltonian of a general multi-Galileon theory and discuss its implications.
Towards a nonperturbative calculation of weak Hamiltonian Wilson coefficients
Bruno, Mattia; Lehner, Christoph; Soni, Amarjit; Rbc; Ukqcd Collaborations
2018-04-01
We propose a method to compute the Wilson coefficients of the weak effective Hamiltonian to all orders in the strong coupling constant using Lattice QCD simulations. We perform our calculations adopting an unphysically light weak boson mass of around 2 GeV. We demonstrate that systematic errors for the Wilson coefficients C1 and C2 , related to the current-current four-quark operators, can be controlled and present a path towards precise determinations in subsequent works.
Analytic calculations of masses in Hamiltonian lattice theories
International Nuclear Information System (INIS)
Horn, D.
1985-01-01
The t-expansion of the vacuum energy function is discussed and several relations involving the connected matrix elements of powers of the hamiltonian are established. On the basis of these relations we show that the masses of the lowest lying O ++ states can be expressed as ratios of derivatives of the energy function. Other sectors of Hilbert space are discussed and a recent result for the SU(2) glueball mass, derived by using such relations as described here, is briefly reviewed. (author)