Interactions Of Arbitrary Strength Research Articles

Gutzwiller approximation for indistinguishable interacting Brownian particles on a lattice.

Nonequilibrium Brownian systems can be described using a creation and annihilation operator formalism for classical indistinguishable particles. This formalism has recently been used to derive a many-body master equationfor Brownian particles on a lattice with interactions of arbitrary strength and range. One advantage of this formalism is the possibility of using solution methods for analogous many-body quantum systems. In this paper, we adapt the Gutzwiller approximation for the quantum Bose-Hubbard model to the many-body master equationfor interacting Brownian particles in a lattice in the large-particle limit. Using the adapted Gutzwiller approximation, we numerically explore the complex behavior of nonequilibrium steady-state drift and number fluctuations throughout the full range of interaction strengths and densities for on-site and nearest-neighbor interactions.

Binary lattice-gases of particles with soft exclusion: exact phase diagrams for tree-like lattices

We study equilibrium properties of binary lattice-gases comprising A and B particles, which undergo continuous exchanges with their respective reservoirs, maintained at chemical potentials μ A = μ B = μ. The particles interact via on-site hard-core exclusion and also between the nearest-neighbours: there are a soft repulsion between AB pairs and also interactions of arbitrary strength J, positive or negative, for AA and BB pairs. For tree-like Bethe and Husimi lattices we determine the full phase diagram of such a ternary mixture of particles and voids. We show that for J being above a lattice-dependent threshold value, the critical behaviour is similar: the system undergoes a transition at μ = μ c from a phase with equal mean densities of species into a phase with a spontaneously broken symmetry, in which the mean densities are no longer equal. Depending on the value of J, this transition can be either continuous or of the first order. For sufficiently large negative J, the behaviour on the two lattices becomes markedly different: on the Bethe lattice there exist two separate phases with different kinds of structural order, which are absent on the Husimi lattice, due to stronger frustration effects.

Perturbation theory for arbitrary coupling strength?

We present a new formulation of perturbation theory for quantum systems, designated here as: “mean field perturbation theory” (MFPT), which is free from power-series-expansion in any physical parameter, including the coupling strength. Its application is thereby extended to deal with interactions of arbitrary strength and to compute system-properties having non-analytic dependence on the coupling, thus overcoming the primary limitations of the “standard formulation of perturbation theory” (SFPT). MFPT is defined by developing perturbation about a chosen input Hamiltonian, which is exactly solvable but which acquires the nonlinearity and the analytic structure (in the coupling strength) of the original interaction through a self-consistent, feedback mechanism. We demonstrate Borel-summability of MFPT for the case of the quartic- and sextic-anharmonic oscillators and the quartic double-well oscillator (QDWO) by obtaining uniformly accurate results for the ground state of the above systems for arbitrary physical values of the coupling strength. The results obtained for the QDWO may be of particular significance since “renormalon”-free, unambiguous results are achieved for its spectrum in contrast to the well-known failure of SFPT in this case.

Magnetic and electric phase transitions in the Hubbard model

Within the Hubbard model, two boson Green’s functions that describe the propagation of collective excitations of the electronic system—magnons (states with a single electron spin flip) and doublons (states with two electrons at one site of the crystal lattice)—are calculated for a Coulomb interaction of arbitrary strength and for an arbitrary electron concentration by applying a decoupling procedure to the double-time X-operator Green’s functions. It is found that the magnon and doublon Green’s functions are similar in structure and there is a close analogy between them. Instability of the paramagnetic phase with respect to spin ordering is investigated using the magnon Green’s function, and instability of the metallic phase to charge ordering is analyzed with the help of the doublon Green’s function. Criteria for the paramagnet-ferromagnet and metal-insulator phase transitions are found.

Crossover between BCS and preformed-boson theories with increasing interactions

The author reviews recent work on Fermi systems with attractive interactions of arbitrary strength. First, he describes the results of a functional integral formulation to study the crossover from cooperative Cooper pairing to independent bound state formation and condensation. The inadequacy of a saddle point approximation with increasing coupling is pointed out, and the importance of temporal (quantum) fluctuations for normal state properties at intermediate and strong coupling is emphasized. Next, results from a quantum Monte Carlo simulation of the 2D attractive Hubbard model are described. The intermediate coupling normal state is found to deviate markedly from a canonical Fermi liquid: {open_quotes}spin-gap{close_quotes} behavior, with 1/T{sub 1}T {approximately} {chi}(T), is found in a degenerate Fermi system.

Theoretical Investigation of the Hopping Conductivity in Disordered Systems in a Large Frequency Range

AbstractThe frequency dependence of the hopping conductivity in disordered systems is investigated taking electron‐phonon interaction of arbitrary strength into account. The underlying theoretical concept is based on the density matrix formalism. The hopping conductivity is shown to be essentially governed by two parameters with a dimension of a time τ, the average time between two consecutive hops from site to site and δt, the average time of restoring the equilibrium on a site after a hop. The dimensionless parameter ωτ, governs the relative contribution of the diffusive and the Ohmic currents to the total current. The quantity ω δt is responsible for presence or absence of memory in hopping processes.