Search results for "Hamiltonian"
showing 10 items of 662 documents
(2+1)-dimensional Einstein-Kepler problem in the centre-of-mass frame
1999
We formulate and analyze the Hamiltonian dynamics of a pair of massive spinless point particles in (2+1)-dimensional Einstein gravity by anchoring the system to a conical infinity, isometric to the infinity generated by a single massive but possibly spinning particle. The reduced phase space \Gamma_{red} has dimension four and topology R^3 x S^1. \Gamma_{red} is analogous to the phase space of a Newtonian two-body system in the centre-of-mass frame, and we find on \Gamma_{red} a canonical chart that makes this analogue explicit and reduces to the Newtonian chart in the appropriate limit. Prospects for quantization are commented on.
Self‐consistent intermediate Hamiltonians : A coupled cluster type formulation of the singles and doubles configuration interaction matrix dressing
1995
This paper presents a new self‐consistent dressing of a singles and doubles configuration interaction matrix which insures size‐consistency, separability into closed‐shell subsystems if localized molecular orbitals (MOs) are used, and which includes all fourth order corrections. This method yields, among several schemes, a reformulation of the coupled cluster method, including fully the cluster operators of single and double excitations, and partially those of the triples (Bartlett’s algorithm named CCSDT‐1a). Further improvement can be easily included by adding exclusion principle violating corrections. Since it leads to a matrix diagonalization, the method behaves correctly in case of nea…
Classical thermodynamics of the Heisenberg chain in a field by generalized Bethe ansatz method
1990
Abstract Using the classical action-angle variables for the continuous model, we study the thermodynamics of the classical Heisenberg chain in an applied field by a generalized Bethe ansatz approach. The crucial point consists in the derivation of a phase-shifted density of states for the excitations of the model, obtained by imposing periodic boundary conditions. In the thermodynamic limit, the free energy can be expressed in terms of the solution of a non-linear integral equation, showing the universal dependece of the variable x=(JH) 1 2 /T .
Stationary problems for equation of the KdV type and dynamical r-matrices
1995
We study a quite general family of dynamical $r$-matrices for an auxiliary loop algebra ${\cal L}({su(2)})$ related to restricted flows for equations of the KdV type. This underlying $r$-matrix structure allows to reconstruct Lax representations and to find variables of separation for a wide set of the integrable natural Hamiltonian systems. As an example, we discuss the Henon-Heiles system and a quartic system of two degrees of freedom in detail.
Hamiltonian lattice QCD at finite density: equation of state in the strong coupling limit
2001
The equation of state of Hamiltonian lattice QCD at finite density is examined in the strong coupling limit by constructing a solution to the equation of motion corresponding to an effective Hamiltonian describing the ground state of the many body system. This solution exactly diagonalizes the Hamiltonian to second order in field operators for all densities and is used to evaluate the vacuum energy density from which we obtain the equation of state. We find that up to and beyond the chiral symmetry restoration density the pressure of the quark Fermi sea can be negative indicating its mechanical instability. Our result is in qualitative agreement with continuum models and should be verifiabl…
Nonequilibrium dressing in a cavity with a movable reflecting mirror
2017
We consider a movable mirror coupled to a one-dimensional massless scalar field in a cavity. Both the field and the mirror's mechanical degrees of freedom are described quantum-mechanically, and they can interact each other via the radiation pressure operator. We investigate the dynamical evolution of mirror and field starting from a nonequilibrium initial state, and their local interaction which brings the system to a stationary configuration for long times. This allows us to study the time-dependent dressing process of the movable mirror interacting with the field, and its dynamics leading to a local equilibrium dressed configuration. Also, in order to explore the effect of the radiation …
Abelian charges in a nonabelian Yang-Mills theory from the stratification of the space of gauge potentials
1992
Abstract The Abelian charges in a non-Abelian Yang-Mills-Dirac theory arising from the reduction of the structure group are studied. They are defined by the concept of the stabilizer gauge transformations. Their properties are investigated. The relationship between the whole class of stabilizers and the stratification of the space of gauge potentials is given. The effect of the spontaneous symmetry breaking mechanism on these charges is discussed.
Phase space coordinates and the Hamiltonian constraint of Regge calculus.
1994
We suggest that the phase space of Regge calculus is spanned by the areas and the deficit angles corresponding to the two-simplexes on the spacelike hypersurface of simplicial spacetime. Our proposal is based on a slight modification of the Ashtekar formulation of canonical gravity. In terms of these phase space coordinates we write an equation which we suggest to be a simplicial version of the Hamiltonian constraint of canonical gravity.
The Higgs Mechanism and Spontaneous Symmetry Breaking
2002
As is well known all gauge bosons of a pure Yang-Mills theory are necessarily massless. This is so because any ad-hoc mass term such as $$ m_i^2 A_\mu ^{(i)} A^{(i)\mu } or \sum\limits_{ik} {M_{ik} } A_\mu ^{(i)} A^{(k)\mu } $$ is incompatible with local gauge invariance. It is saidthat W. Pauli hadd evelopednonab elian gauge theory for himself (or knew about it from the work of H. Weyl and O. Klein) before the work of C.N. Yang and R. Mills (1954) but dismissedit because he hadrealizedthat the gauge particles wouldall be massless. As there was only one massless spin-1 particle known at the time (the photon) nonabelian gauge theory was to be rejectedon physical grounds. The few facts that w…
X(5) critical-point symmetries in 138Gd
2011
International audience; The lifetimes of low-lying transitions in 138Gd have been measured using the recoil-distance Doppler-shift technique. The resultant reduced transition probabilities have been compared to X(5) critical-point calculations to assess the potential 'phase-transitional' behaviour of 138Gd. The X(5) symmetry describes the first order 'phase transition' between sphericity, U(5) and an axially deformed nuclear shape, SU(3). Although a high degree of correspondence is observed between the experimental and theoretical excitation energies, the large uncertainties of the experimental B(E2) values cannot preclude contributions from either vibrational or rotational modes of excitat…