Electrical resistivity for thes-fmodel within the alloy analogy approximation (CPA)

The spin disorder resistivity for thes-f Hamiltonian with an additional Coulomb interaction between conduction electrons is calculated. The many body Hamiltonian is replaced by a four component alloy-Hamiltonian with temperatureT- and band-fillingn-dependent concentrations of the constituents. A self-consistent CPA-theory for conductivity and spin disorder resistivity is applied and numerically evaluated for different temperatures and parameters of the model Hamiltonian. Analytical formulae for the spin disorder resistivity are derived for two limiting cases. These results exhibit a strong dependence on the band-fillingn and the structure of the Bloch density of states near the chemical potential . A comparison with other theories and experimental data is presented.     

The ADM Hamiltonian at the postlinear approximation

The ADM Hamiltonian for a many-particle system is calculated up to the postlinear approximation, i.e., to the approximation that both the equations of motion for the particles and the equations of motion for the gravitational field in case of no-incoming radiation correctly result up to the postlinear approximation. The relation of this Hamiltonian to the ADM Hamiltonian obtained by a post-Newtonian approximation scheme which was applied up to the first radiation-reaction and radiation levels is discussed. From here the standard formulas for the mechanical angular momentum and energy losses as well as the radiated energy and angular momentum are deduced. Background logarithmic and logarithmic radiative terms are shown to be not present at our approximation if the condition of no-incoming radiation is fulfilled.     

Collective pairing Hamiltonian in the GCM approximation

Using the generator coordinate method and the gaussian overlap approximation we derived the collective Schrödinger-type equation starting from a microscopic single-particle plus pairing hamiltonian for one kind of particle. The BCS wave function was used as the generator function. The pairing energy-gap parameter Δ and the gauge transformation angle ø were taken as the generator coordinates. Numerical results have been obtained for the full and the mean-field pairing hamiltonians and compared with the cranking estimates. A significant role played by the zero-point energy correction in the collective pairing potential is found. The ground-state energy dependence on the pairing strength agrees very well with the exact solution of the Richardson model for a set of equidistant doubly-degenerate single-particle levels.     

Optimal symplectic approximation of Hamiltonian flows

Long term simulations of Hamiltonian dynamical systems benefit from enforcing the symplectic symmetry. One of the several available methods to perform this symplectification is provided by the recently developed theory of extended generating functions. The theory offers an infinite supply of generator types that can be used for symplectification. Using Hofer's metric, a condition for optimal symplectification is given. In the weakly nonlinear case, the condition provides a generator type that, based on the limited information available on the system, in general gives optimal results.     

Simple approximation scheme for the Anderson impurity Hamiltonian

A simple approximation scheme is presented for solving the Anderson impurity model within the Noncrossing Approximation (NCA). It is shown that with it the computations reduce to an extent that the scheme can be readily applied to interpret different experiments. The theory is applied to calculate the temperature dependence of the quadrupole moment and of the static and dynamic magnetic susceptibility. The effects of the crystalline electric field (CEF) are thereby incorporated. A comparison of the static susceptibility with exact Bethe ansatz results is given, when the effect of the CEF is neglected. Comparisons with the numerically exact solutions of the NCA are made where they are available. The application of the present theory to YbCu₂Si₂ is discussed.     

Effective Hamiltonian of the Jaynes–Cummings model beyond rotating-wave approximation

The Jaynes–Cummings model with or without rotating-wave approximation plays a major role to study the interaction between atom and light. We investigate the Jaynes–Cummings model beyond the rotating-wave approximation. Treating the counter-rotating terms as periodic drivings, we solve the model in the extended Floquet space. It is found that the full energy spectrum folded in the quasi-energy bands can be described by an effective Hamiltonian derived in the highfrequency regime. In contrast to the Z_2 symmetry of the original model, the effective Hamiltonian bears an enlarged U(1)symmetry with a unique photon-dependent atom-light detuning and coupling strength. We further analyze the energy spectrum, eigenstate fidelity and mean photon number of the resultant polaritons, which are shown to be in accordance with the numerical simulations in the extended Floquet space up to an ultra-strong coupling regime and are not altered significantly for a finite atom-light detuning. Our results suggest that the effective model provides a good starting point to investigate the rich physics brought by counter-rotating terms in the frame of Floquet theory.     

Effective Hamiltonian for scalar theories in the Gaussian approximation

We use a Gaussian wave functional for the ground state to reorder the Hamiltonian into a free part with a variationally determined mass and the rest. Once spontaneous symmetry breaking is taken into account, the residual Hamiltonian can, in principle, be treated perturbatively. In this scheme we analyze the O(1) and O(2) scalar models. For the O(2)-theory we first explicitly calculate the massless Goldstone excitation and then show that the one-loop corrections of the effective Hamiltonian do not generate a mass.     

On the chiral hubbard model and the chiral Kondo lattice model

The integrability of the one-dimensional chiral Hubbard model is discussed in the limit of strong interaction,U=. The system is shown to be integrable in the sense of the existence of an infinite number of constants of motion. The system is related to a chiral Kondo lattice model at strong interactionJ=+.     

Coulomb correlations in nickel within the alloy analogy of the Hubbard model

Coulomb correlations in transition metals are treated self-consistently within the alloy analogy of the Hubbard model, taking into account the full degeneracy of the d-band. Numerical calculations are performed in the case of nickel: the calculated optical excitations spectrum exhibits two satellites corresponding to d⁹ and d⁸ configurations. Finally, we comment on the core level spectra.     

Energy spectrum of the Hamiltonian of the Jaynes-Cummings model without rotating-wave approximation

The energy spectrum of the Hamiltonian of the Jaynes-Cummings model without a rotating-wave approximation is studied. The trajectories of eigenvalues as functions of the dimensionless coupling constant are constructed. It is shown that the spectrum approaches the equidistant spectrum, i.e., the oscillator spectrum, as the coupling constant increases. As a result, each energy level becomes doubly degenerate.     

Relativistic closed-form Hamiltonian for many-body gravitating systems in the post-Minkowskian approximation

The Hamiltonian for a system of relativistic bodies interacting by their gravitational field is found in the post-Minkowskian approximation, including all terms linear in the gravitational constant. It is given in a surprisingly simple closed form as a function of canonical variables describing the bodies only. The field is eliminated by solving inhomogeneous wave equations, applying transverse-traceless projections, and using the Routh functional. By including all special relativistic effects our Hamiltonian extends the results described in classical textbooks of theoretical physics. As an application, the scattering of relativistic objects is considered.     

Optical conductivity of the half-filled hubbard chain

We combine well-controlled analytical and numerical methods to determine the optical conductivity of the one-dimensional Mott-Hubbard insulator at zero temperature. A dynamical density-matrix renormalization group method provides the entire absorption spectrum for all but very small coupling strengths. In this limit we calculate the conductivity analytically using exact field-theoretical methods. Above the Lieb-Wu gap the conductivity exhibits a characteristic square-root increase. For small to moderate interactions, a sharp maximum occurs just above the gap. For larger interactions, another weak feature becomes visible around the middle of the absorption band.     

Exact solution of the simplified hubbard model

We present the exact solution of the simplified Hubbard model in which only one kind of electrons can hop and this quantum mechanical hopping of electrons is assumed to be unconstrained. It is shown that the model still behaves nontrivially, although it no longer depends on the lattice structure and the dimensionality of the system. For this case we find: (i) a gap in the ground state energy always exists at the half-filled band point (n=1), (ii) a preferred magnetic state atn=1 and largeU is a total spin singlet, (iii)U-dependence of the ground state energy has qualitatively the same form as one of the conventional Hubbard model with the (t ²/U)-behavior at largeU. A phase diagram of the model is discussed.     

On the spectrum of the Heisenberg Hamiltonian

The quantum, antiferromagnetic, spin-1/2 Heisenberg Hamiltonian on thed-dimensional cubic lattice ^d is considered for any dimensiond. First the anisotropic case is considered for small transversal coupling and a convergent expansion is given for a family of eigenprojections which is complete in all finite-volume truncations. Then the general case is considered, for which an upper bound to the ground-state energy is given which is optimal for strong enough anisotropy. This bound is expressed through a functional involving the statistical expectation value at finite temperature of a certain correlation function of an Ising model defined on the lattice ^d itself.     

On the Convexity of the KdV Hamiltonian

Motivated by perturbation theory, we prove that the nonlinear part \({H^{*}}\) of the KdV Hamiltonian \({H^{kdv}}\), when expressed in action variables \({I = (I_{n})_{n \geqslant 1}}\), extends to a real analytic function on the positive quadrant \({\ell^{2}_{+}(\mathbb{N})}\) of \({\ell^{2}(\mathbb{N})}\) and is strictly concave near \({0}\). As a consequence, the differential of \({H^{*}}\) defines a local diffeomorphism near 0 of \({\ell_{\mathbb{C}}^{2}(\mathbb{N})}\). Furthermore, we prove that the Fourier-Lebesgue spaces \({\mathcal{F}\mathcal{L}^{s,p}}\) with \({-1/2 \leqslant s \leqslant 0}\) and \({2 \leqslant p < \infty}\), admit global KdV-Birkhoff coordinates. In particular, it means that \({\ell^{2}_+(\mathbb{N})}\) is the space of action variables of the underlying phase space \({\mathcal{F}\mathcal{L}^{-1/2,4}}\) and that the KdV equation is globally in time \({C^{0}}\)-well-posed on \({\mathcal{F}\mathcal{L}^{-1/2,4}}\).     

d-wave superconductivity in the hubbard model

The superconducting instabilities of the doped repulsive 2D Hubbard model are studied in the intermediate to strong coupling regime with the help of the dynamical cluster approximation. To solve the effective cluster problem we employ an extended noncrossing approximation, which allows for a transition to the broken symmetry state. At sufficiently low temperatures we find stable d-wave solutions with off-diagonal long-range order. The maximal T(c) approximately 150 K occurs for a doping delta approximately 20% and the doping dependence of the transition temperatures agrees well with the generic high- T(c) phase diagram.     

One-dimensional approximation of the effective rotational Hamiltonian of the ground state of the water molecule

A method is presented for summation of the divergent perturbation-theory series used in molecular spectroscopy, by means of a one-dimensional approximation. Application of the proposed method enables one to fit the energy levels of the ground state of the water molecule (Mol. Phys. 32, 499–521 (1976)) to a maximum difference between the observed and the calculated levels of less than 8 cm^?1 for levels with the maximum rotational quantum numbers K = 20 and J = 20 in a model with 24 parameters and terms up to J⁸.