The HeisenbergXXZ Hamiltonian with Dzyaloshinsky-Moriya interactions

The quantum Heisenberg chain with Dzyaloshinsky-Moriya interactions is solved by relating it to theXXZ Hamiltonian with a certain type of boundary conditions. Several properties of the ground state are derived which agree with the intuition derived from related soluble classical models. Implications to the model of known results from the theory of conformal invariance, as well as generalizations to higher spin, are briefly discussed.     

Hamiltonian BRST interactions in Abelian theories

Consistent couplings between an Abelian gauge field and three types of matter fields are investigated by means of the Hamiltonian BRST deformation theory based on cohomological techniques. In this manner, scalar electrodynamics, the Stuckelberg theory for Abelian zero- and one-forms, respectively, spinor electrodynamics, are inferred. Received: 6 December 2000 / Published online: 23 February 2001     

Nonabelian interactions from Hamiltonian BRST cohomology

Consistent Hamiltonian couplings between a set of vector fields and a system of matter fields are derived by means of BRST cohomological techniques. Received: 20 June 2001 / Published online: 17 August 2001     

Hamiltonian for Reggeon interactions in QCD

It is shown, that the interaction of the reggeized gluons in the leading logarithmic approximation of the multicolour QCD has a number of remarkable properties including the duality symmetry. The duality relation for the Odderon wave function takes a form of the one-dimensional Schrödinger equation. It gives a possibility to express the Odderon Hamiltonian as a function of its integrals of motion.     

Separable interactions in classical relativistic Hamiltonian mechanics

We show the existence of separable interactions in classical relativistic Hamiltonian mechanics of particles interacting at a distance. The framework which is used is that of manifestly covariant systems with constraints.Laboratoire associé au CNRS.     

Relativistic addition of interactions in constraint Hamiltonian mechanics

The problem of constructing separable N-particle interactions for given two-body forces in the constraint Hamiltonian approach to relativistic classical mechanics is tackled in two different ways. A formal expression for the N-particle constraints is given in terms of a classical wave operator. An (independent) iterative scheme for these constraints is carried out. Explicit formulas for the three-particle interactions are written down, accurate up to second order in the two-body coupling constants and symmetric with respect to particle permutations.     

Integrable Hamiltonian systems and interactions through quadratic constraints

O _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.     

Parity-violating nuclear interactions and models of the weak Hamiltonian

The derivation of the parity-violating internucleon one-meson-exchange potentials is presented, stressing their connection with models of the weak interactions. Relevant problems concerning second class currents, gauge invariance, off-mass-shell effects, symmetry breaking and multimeson exchanges are discussed. An extensive bibliography of existing literature is also presented.     

A Hamiltonian model of dissipative wave-particle interactions and the negative-mass effect

The effect of radiation friction is included in the Hamiltonian treatment of wave-particle interactions with autoresonant phase-locking, yielding a generalized canonical approach to the problem of dissipative dynamics near a nonlinear resonance. As an example, the negative-mass effect exhibited by a charged particle in a pump wave and a static magnetic field is studied in the presence of the friction force due to cyclotron radiation. Particles with negative parallel masses m_∥ are shown to transfer their kinetic energy to the pump wave, thus amplifying it. Counterintuitively, such particles also undergo stable dynamics, decreasing their transverse energy monotonically due to cyclotron cooling, whereas some of those with positive m_∥ undergo cyclotron heating instead, extracting energy from the pump wave.     

Relativistic action-at-a-distance interactions: Lagrangian and Hamiltonian to terms of second order

Relativistic systems of particles interacting pairwise at a distance (interactions not mediated by fields) in flat spacetime are studied. It is assumed that the interactions propagate at the speed of light in vacuum and that all masses are scalars under Poincaré transformations. The action functional of the theory depends on multiple times (the proper times of the particles). In the static limit, the theory has three components: a linearly rising potential, a Coulomb-like interaction and a dynamical component to the Poincaré invariant mass. In this Letter we obtain explicitly, to terms of second order, the Lagrangian and the Hamiltonian with all the dynamical variables depending on a single time. Approximate solutions of the relativistic two-body problem are presented.     

Spin-vibrational interactions in geminate radical pairs: Effective spin Hamiltonian including anharmonicity

An equation for the effective spin Hamiltonian including the interaction of radical pair spins with vibrations in both linear and higher approximations was obtained. Even in the linear approximation, the Hamiltonian was found to be non-Heisenberg. The influence of a sound field on the probability of geminate radical pair recombination is considered in the Appendix. The results obtained can be of use for solving certain nanochemistry problems.     

Relativistic Hamiltonian dynamics. II. Momentum-dependent interactions, confinement and quantization

The previously developed covariant classical relativistic N-particle dynamics is extended to momentum-dependent interactions and generalized to a gauge-independent constraint reduction. This reduction is made via center-of-momentum variables as well as via the more conventional individual particle variables. A canonical quantization is then carried out. The two-body problem is discussed in detail for the case of momentum-dependent interactions. It is demonstrated that such interactions can give rise to dynamical confinement both classically and quantum mechanically. The prototype interaction −β²(ξ · π)² has a harmonic oscillator type spectrum and shows a linear dependence of the binding energy on the angular momentum for small particle rest masses (m₁, m₂ β).     

Properties of a pseudo-Hermitian Hamiltonian for harmonic oscillator decorated with Dirac delta interactions

We have investigated bound state solutions of the Schrodinger equation for one-dimensional harmonic oscillator potential together with even number of Dirac delta functions. These point interactions are located at symmetric points x = x _i and x = −x _i (i = 1, 2,..., N) and they have complex conjugate strengths and , respectively. We present explicit forms of eigenfunctions and an algebraic eigenvalue equation and numerical solutions for this -symmetric Hamiltonian. Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22, 2005.     

Does a Heisenberg Hamiltonian describe magnetic interactions in a MnSi film properly?

We report theoretical studies of magnetic excitations in an ultra-thin MnSi film on Si(0 0 1) substrate. Both transversal and longitudinal fluctuations of the magnetic moments are discussed. We show that the values of the Heisenberg exchange parameters depend on the assumed distance of the short range magnetic order and on the values of the atomic moments. The limitations of the mapping of the system on a Heisenberg model are studied.     

Real Hamiltonian forms of Hamiltonian systems

We introduce the notion of a real form of a Hamiltonian dynamical system in analogy with the notion of real forms for simple Lie algebras. This is done by restricting the complexified initial dynamical system to the fixed point set of a given involution. The resulting subspace is isomorphic (but not symplectomorphic) to the initial phase space. Thus to each real Hamiltonian system we are able to associate another nonequivalent (real) ones. A crucial role in this construction is played by the assumed analyticity and the invariance of the Hamiltonian under the involution. We show that if the initial system is Liouville integrable, then its complexification and its real forms will be integrable again and this provides a method of finding new integrable systems starting from known ones. We demonstrate our construction by finding real forms of dynamics for the Toda chain and a family of Calogero-Moser models. For these models we also show that the involution of the complexified phase space induces a Cartan-like involution of their Lax representations.Received: 8 October 2003, Published online: 8 June 2004PACS: 02.30.Ik Integrable systems - 45.20.Jj Lagrangian and Hamiltonian mechanics     

Regular dynamics of canonical post-Newtonian Hamiltonian for spinning compact binaries with next-to-leading order spin-orbit interactions

This paper shows that a conservative canonical post-Newtonian Hamiltonian formulation of spinning compact binaries with a pure orbital part up to third post-Newtonian order and spin-orbit contributions at the next-to-leading post-Newtonian order is explicitly integrable and regular because there are 5 independent exact isolating integrals in the 10-dimensional phase space. With the help of symplectic integrators and the fast Lyapunov indicators of two nearby trajectories, numerical investigations also support the absence of chaos.