M. Noga

Multi-Hamiltonian structure of Lotka-Volterra and quantum Volterra models

Abstract We consider evolution equations of the Lotka-Volterra type, and elucidate especially their formulation as canonical Hamiltonian systems. The general conditions under which these equations admit several conserved quantities (multi-Hamiltonians) are analysed. A special case, which is related to the Liouville model on a lattice, is considered in detail, both as a classical and as a quantum system.

First-order Lagrangians and the Hamiltonian formalism

Abstract We consider the problem of constructing a general unconstrained Hamiltonian formalism for a system with a finite number of degrees of freedom, starting from a general first-order Lagrangian. This construction, which uses only elements of linear algebra and the theory of partial differential equations, is given in a rather explicit form. An application of the formalism to the quantization of two-dimensional real self-dual fields is given.

Third-order phase transition and superconductivity in thin films

We have found a new mean field solution in the BCS theory of superconductivity. This unconventional solution indicates the existence of superconducting phase transitions of third order in thin films, or in bulk matter with a layered structure. The critical temperature increases with decreasing thickness of the layer, and does not exhibit the isotope effect. The electronic specific heat is a continuous function of temperature with a discontinuity in its derivative.

LOCAL NON-ABELIAN GAUGE SYMMETRY OF THE HUBBARD MODEL*)

It is shown that the field operators of an electron system on a lattice can be decomposed into direct products of two kinds of operators acting in two separate Hilbert spaces. The Hilbert space of electron states thus becomes a direct product of two Hilbert spaces. By this fact a certain class of electron systems exhibits a formal separation of charge and spin degrees of freedom into two kinds of elementary excitations. A typical example of such a system is given by the Hubbard model. The separation of charge and spin resulting from the new representation of the field operators can be considered as a rigorous realization and generalization of an idea expressed by Anderson concerning the separation of spin and charge degrees of freedom in strongly correlated electron systems. The new representation of electron field operators implies the existence of a localU(2) gauge symmetry in the theory. The theory of superconductivity based on the Hubbard model is then represented by a non-abelian gauge field theory.

New kinds of superconductivity and superfluidity

Abstract Formation of self-organized macroscopic and periodic structures in a physical system of interacting fermions are derived from first principles. The system of structureless and chargeless fermions with magnetic moments can have four different phases. Two of these phases exhibit the totally unique phenomena typical for superconductivity and superfluidity as well as various kinds of structural singularities such as disgyrations in the superfluid 3He.

Laser annealing and theory of photostimulated structures

It is shown that a circularly polarized laser light passing through a disordered system represented by a thin film of an amorphous semiconductor gives rise to a self-organization of new ordered states. Laser annealing of implanted semiconductors, emergence of charge density waves, light-induced transmittance oscillations and optical stopping effect are explained on a unified ground within the framework of quantum field theory.

The self-consistent determination of the πNN and πNN∗ vertex functions

Abstract The self-consistent method of Zachariasen and Zemach is used to calculate the πNN and π NN ∗ vertex functions. The calculated thresholds of the spectral representation of these vertex functions agree with those found by Karplus, Sommerfield and Wichmann.

Superconductivity in crystals with covalent bonds

Novel types of ground states associated with properties of heavy fermion systems are derived for crystals with covalent bonds generated by short-range exchange forces between valence electrons of atoms localized at lattice sites. It is shown that the short-range exchange forces can give rise to a narrow energy band in which electrons can exhibit an enormous effective mass. The same exchange forces provide the microscopic mechanism for spin-singlet pairing of electrons into Cooper pairs which are responsible for superconductivity in these systems. This superconductivity exhibits several different anisotropic superconducting states. The effective mass, Fermi energy, specific heat, Pauli susceptibility, critical temperatures and critical magnetic field of heavy fermion systems are calculated and compared with experimental data.

Theory of the unconventional superconductivity in magnetic materials

Recent experimental observations of superconductivity in the presence of strong paramagnetism of lanthanide and actinide materials are theoretically analysed. The formation of superconducting electron pairs in the system of localized and delocalized electrons interacting through the Heisenberg exchange interaction is derived. Theoretical results show that the superconducting transition in the magnetic materials is due to the spin-triplet pairing of the electrons and exhibits the electronic analogy of the superfluid transition in3He.

Spontaneously self-organized structures by magnetic interactions

For heavy-fermion superconductivity a new alternate mechanism of magnetic origin and of antiferromagnetic nature has been found. By using nonperturbative methods it is explicitly shown that a system of itinerant electrons interacting through Heisenbergs exchange interaction can undergo a phase transition from the paramagnetic state either to superconducting or to magnetically ordered state depending on whether the coupling constant is negative or positive.