Soliton equations and coherent states

The τ-functions, which represent the totality of solutions for hierarchies of equations in soliton theory, are identified with the coherent states of the infinite dimensional Lie algebra gl(∞). The associated quantum system can be realized by an infinite set of harmonically interacting fermionic modes. The soliton dynamical evolution is thus mapped into a quantum hamiltonian evolution, and the latter back into a classical hamiltonian flow corresponding to a succession of infinitesimal contact Bäcklund transformations.     

Ideal incompressible hydrodynamics in terms of the vortex momentum density

Equations satisfied by the vortex momentum density are derived and are transformed into hamiltonian form. New lagrangian invariants are found with the help of these equations. The case in which the flow is representable by the known Clebsch potentials is analysed.     

Time-dependent variational principle on the group SO(2r): Generalizations of time-dependent Hartree-Fock

The family of all Hartree-Fock-Bogoliubov (HFB) states for a given set of r isosopin-spin orbitals form a set of coherent states. The set of antisymmetrized geminal power (AGP) states for a given set of r isospin-spin orbitals form a set of charge-projected coherent states, with the number of particles n as the “charge” and the HFB coherent state as the generating function. Both these coherent states are associated with the group SO(2r). The approximate time evolution of the system generated by restricting the quantum mechanical evolution to the family of HFB and AGP coherent states is described as a classical dynamics with the energy of the coherent state as hamiltonian function. The phase space is isomorphic to the coset space SO(2r)/U(r). The random phase approximation based on HFB and AGP states is derived by considering the harmonic approximation to the hamiltonian function. This work generalizes the group theoretical approaches to Hartree-Fock, and time-dependent Hartree-Fock theory by the use of non-number-conserving (HFB) and correlated (AGP) states.     

Pressure induced transitions in calcium: a tight-binding approach

A tight-binding (TB) hamiltonian for calcium is built with a high precision parametrization technique based on density functional calculations of the energy bands and the total energy at various lattice volumes. The new set of TB parameters is appropriate to study phenomena under pressures as high as 20 GPa. Specifically, both the metal to nonmetal transition at 4 GPa and the structural transition fcc to bcc at 19 GPa are well reproduced. These transitions and several static properties are in excellent agreement with experiments. Phonon frequencies, plasmon energy, melting temperature and the coefficient of thermal expansion were calculated with a molecular dynamics scheme of this TB hamiltonian.     

Stochastic model of nuclear levelwidth

We investigate here the origin of nuclear levelwidth as an effect of the coupling of particle mode and the surface vibration mode of the nucleus. This interaction is taken to be stochastic in nature, characterized by a single correlation timet ₀, the random nature of the interaction originating from the partition of the total hamiltonian into those of the two modes. The Redfield equation of motion for the density matrix for the particle mode is solved. The solution of the Redfield equation shows that the occupation number in any particle state decays with a time constant depending on the correlation timet ₀ and the quantum-mechanical matrix elements of the interaction hamiltonian. The inverse of this decay time will give the width of this level. Numerical calculations have been done for ₈₂ ²⁰⁷ Pb₁₂₅.     

Nuclear hyperfine interactions in non-linear semi-rigid molecules

From the expression for the hamiltonian in molecular coordinates we obtained previously, the computation of an effective hamiltonian for a nondegenerate electronic state is performed to second order in degenerate perturbation theory. We thus obtain explicitly all dominant parameters for the spin-vibration and spin-rotation interactions; in addition, the parameters associated with the interactions between the magnetic moment induced by the molecular motion and an external magnetic field are computed. The vibrational dependence of these parameters is studied and the hamiltonian is written in a form adapted to the computation of an effective hamiltonian for an arbitrary vibrational state.     

A hamiltonian approach to the roper resonance

The breathing modes along with the spin-isospin zero modes of the ω-stabilized skyrmion are quantized using Dirac's method. The result is a hamiltonian for the nucleon, the δ-isobar and the Roper with explicit meson couplings. The linear pion coupling is used to evaluate the decay width of the Roper into πN.     

Non-abelian Cheshire cat bag models in 1+1 dimensions

Non-abelian Cheshire cat models are investigated in their lagrangian and hamiltonian formulations. The lagrangian bag boundary conditions are used to derive the form of non-abelian soliton operators, through which fermions are represented in bosonic language. These soliton operators are then used to construct the boundary interaction in the hamiltonian picture, wherein the bosonic sector is formulated by means of a current algebra involving anomalous commutators. The hamiltonian and the momentum operator are shown to commute, thus implying that the Cheshire cat criterion — the independence of the energy spectrum on the bag wall position — is fulfilled by the system.     

Dynamics of the Gribov horizon: A one-mode treatment

Properties of the Gribov horizon in Coulomb-gauge nonabelian Yang-Mills theory are studied in an approximation which retains global color symmetry but truncates the spin-space degrees of freedom of the transverse gauge field to a single mode. The facilities an explicit evaluation of the contribution of the Faddeev-Popov zeroes to the effective quantum potential, which is accomplished with a sturmian expansion in the zero modes of the inverse ghost propagator. In particular, the singularities of the one-mode hamiltonian at the horizon are isolated and analyzed for their effect on the spectrum. Quantizing on the compact manifold S³ and utilizing the hyperspherical techniques developed by Cutkosky, the formalism is applied to pure gluonic systems of long-wave-length modes. It is found that in the limit a cutoff on integration over ghost momenta is removed to infinity, the hamiltonian reduces to a trivial (quadratic) theory with a mass gap which is a simple multiplicative modification of the free-field result.     

A laser-like model of vibrational condensation

A trilinear hamiltonian describing the interaction of three vibrational modes is proposed as a possible simplified version able to describe a nonequilibrium vibrational condensation of the Fröhlich type.     

On the interpretation of fermionic zero-modes

We examine the effect of fermionic zero modes on tunneling amplitudes within some simple quantum mechanical models. It is shown that the fermionic zero modes do not cause a total suppression of the tunneling, although it may be reduced. With a θ term present, due to a non-trivial topology, it is shown that the θ dependence is not eliminated by the zero modes. Instead the non-trivial topology introduces a “twist” in the fermionic coordinates which breaks a symmetry of the hamiltonian.     

A string-like equation for a U(N) gauge theory

A change of variables is made in the hamiltonian of a U(N) gauge theory so that the independent variables are the path dependent phase factors. The resulting hamiltonian is similar in form to that of the Nambu-Gato string     

Multifragmentation calculated with relativistic forces

A saturating hamiltonian is presented in a relativistically covariant formalism. The interaction is described by scalar and vector mesons, with coupling strengths adjusted to nuclear matter. No explicit density dependence is assumed and the momentum dependence results from the relativistic expansion. The hamiltonian is applied in a QMD calculation to determine the fragment distribution in O+Br collisions at different energies (50–200 Me V/u) to test the applicability of the model at low energies. The results are compared with experiment and with previous non-relativistic calculations.     

Effective hamiltonians

Non-linear equations, generalizing those determining Bloch's transformation to an effective hamiltonian, are set up in a very simple way. It is shown how they immediately determine the results of Van Vleck, Bloch and Soliverez. Treating the Foldy-Wouthuysen transformation as a special case of the Van Vleck transformation, sixth-order expressions are obtained by means of the non-linear equations. The transformations of Soliverez, Roussy and Kvasnicka are shown to be strictly identical—because they all have a simple property which is proven to be unique for that of Soliverez. Kvasnicka relates his transformation to that of Primas'. We shall see that it is also very closely related to that of Van Vleck's. A certain non-hermitian effective hamiltonian also given by Roussy is proven to be identical to that of Bloch's. Primas' level shift transformation gives an effective hamiltonian for each level in zeroth order. This effective hamiltonian is seen to be identical to that of Soliverez's up to and including third order—and to all orders if one makes a simple change in ‘normalization’. Computer treatment of finite matrices is discussed. The sixth-order Van Vleck hamiltonian recently given by Jørgensen and Pedersen in terms of commutators is derived in a more simple way.     

Boundary conditions on current carrying states and the implications for observations of bloch oscillations

The problem of the precise form (together with the associated boundary conditions) of a one-dimensional hamiltonian describing a particle of variable mass is addressed. It is shown that although hermiticity may be a necessary condition, it is not sufficient to specify uniquely the hamiltonian. In particular one form of the latter that is widely employed in the literature is shown to lead to a violation of the Heisenberg Uncertainty Principle. However imposition of the additional demand that any singular terms arising from the kinetic energy can be transformed away does lead to a unique specification of the hamiltonian. Finally the implications of the latter with regard to the standard probability interpretation of the wavefunction and for the observation of Bloch oscillations in quantum well structures is described.     

A canonical formulation of dissipative mechanics using complex-valued hamiltonians

We show that a large class of dissipative systems can be brought to a canonical form by introducing complex co-ordinates in phase space and a complex-valued hamiltonian. A naive canonical quantization of these systems lead to non-hermitean hamiltonian operators. The excited states are unstable and decay to the ground state. We also compute the tunneling amplitude across a potential barrier by solving the dissipative version of the Schrödinger equation. We then generalize the formalism to cases where the configuration space is a curved Riemannian manifold.     

A general dispersion relation for spin-phonon excitations in paramagnets

The advantage of using standard basis operators in evaluating the semi-invariants occurring in the diagrammatic theory of spin-phonon modes is discussed. The dispersion relation of the coupled-mode excitations is derived for paramagnetic ions of arbitrary spin having a general static spin hamiltonian.     

An approximate theory for bunched solitons on finite Josephson tunnel junctions

An approximate hamiltonian theory is used to predict critical bias currents for the transition from bunched to symmetric soliton modes on Josephson junctions of finite length, recently observed experimentally and numerically.     

Relativistic fluid dynamics as a Hamiltonian system

The equations of ideal relativistic fluid dynamics in the laboratory frame form a noncanonical hamiltonian system with the same Poisson bracket as for nonrelativistic fluids, but with dynamical variables and hamiltonian obtained via a regular deformation of their nonrelativistic counterparts.