On the equivalence between stochastic baker's maps and two-dimensional spin systems

We show that there is a class of stochastic baker's transformations that is equivalent to the class of equilibrium solutions of two-dimensional spin systems with finite interaction. The construction is such that the equilibrium distribution of the spin lattice is identical to the invariant measure in the corresponding baker's transformation. We also find that the entropy of the spin system is up to a constant equal to the rate of entropy production in the corresponding stochastic baker's transformation. We illustrate the equivalence by deriving two stochastic baker's maps representing the Ising model at a temperature above and below the critical temperature, respectively. We calculate the invariant measure of the stochastic baker's transformation numerically. The equivalence is demonstrated by finding that the free energy in the baker system is in agreement with analytic results of the two-dimensional Ising model.Comment: 4 pages, 4 figure

Performance of the coupled cluster singles and doubles method on two-dimensional quantum dots

An implementation of the coupled-cluster single- and double excitations (CCSD) method on two-dimensional quantum dots is presented. Advantages and limitations are studied through comparison with other high accuracy approaches for two to eight confined electrons. The possibility to effectively use a very large basis set is found to be an important advantage compared to full configuration interaction implementations. For the two to eight electron ground states, with a confinement strength close to what is used in experiments, the error in the energy introduced by truncating triple excitations and beyond is shown to be on the same level or less than the differences in energy given by two different Quantum Monte Carlo methods. Convergence of the iterative solution of the coupled cluster equations is, for some cases, found for surprisingly weak confinement strengths even when starting from a non-interacting basis. The limit where the missing triple and higher excitations become relevant is investigated through comparison with full Configuration Interaction results.Comment: 11 pages, 1 figure, 5 table

Effects of screened Coulomb impurities on autoionizing two-electron resonances in spherical quantum dots

In a recent paper (Phys. Rev. B {\bf 78}, 075316 (2008)), Sajeev and Moiseyev demonstrated that the bound-to-resonant transitions and lifetimes of autoionizing states in spherical quantum dots can be controlled by varying the confinment strength. In the present paper, we report that such control can in some cases be compromised by the presence of Coulomb impurities. It is demonstrated that a screened Coulomb impurity placed in the vicinity of the dot center can lead to bound-to-resonant transitions and to avoided crossings-like behavior when the screening of the impurity charge is varied. It is argued that these properties also can have impact on electron transport through quantum dot arrays

Coupled-cluster calculations of properties of Boron atom as a monovalent system

We present relativistic coupled-cluster (CC) calculations of energies, magnetic-dipole hyperfine constants, and electric-dipole transition amplitudes for low-lying states of atomic boron. The trivalent boron atom is computationally treated as a monovalent system. We explore performance of the CC method at various approximations. Our most complete treatment involves singles, doubles and the leading valence triples. The calculations are done using several approximations in the coupled-cluster (CC) method. The results are within 0.2-0.4% of the energy benchmarks. The hyperfine constants are reproduced with 1-2% accuracy

"Dressing" lines and vertices in calculations of matrix elements with the coupled-cluster method and determination of Cs atomic properties

We consider evaluation of matrix elements with the coupled-cluster method. Such calculations formally involve infinite number of terms and we devise a method of partial summation (dressing) of the resulting series. Our formalism is built upon an expansion of the product $C^\dagger C$ of cluster amplitudes $C$ into a sum of $n$-body insertions. We consider two types of insertions: particle/hole line insertion and two-particle/two-hole random-phase-approximation-like insertion. We demonstrate how to ``dress'' these insertions and formulate iterative equations. We illustrate the dressing equations in the case when the cluster operator is truncated at single and double excitations. Using univalent systems as an example, we upgrade coupled-cluster diagrams for matrix elements with the dressed insertions and highlight a relation to pertinent fourth-order diagrams. We illustrate our formalism with relativistic calculations of hyperfine constant $A(6s)$ and $6s_{1/2}-6p_{1/2}$ electric-dipole transition amplitude for Cs atom. Finally, we augment the truncated coupled-cluster calculations with otherwise omitted fourth-order diagrams. The resulting analysis for Cs is complete through the fourth-order of many-body perturbation theory and reveals an important role of triple and disconnected quadruple excitations.Comment: 16 pages, 7 figures; submitted to Phys. Rev.

Effect of dopant atoms on local superexchange in cuprate superconductors: a perturbative treatment

Recent scanning tunneling spectroscopy experiments have provided evidence that dopant impurities in high- Tc superconductors can strongly modify the electronic structure of the CuO2 planes nearby, and possibly influence the pairing. To investigate this connection, we calculate the local magnetic superexchange J between Cu ions in the presence of dopants within the framework of the three-band Hubbard model, up to fifth-order in perturbation theory. We demonstrate that the sign of the change in J depends on the relative dopant-induced spatial variation of the atomic levels in the CuO2 plane, contrary to results obtained within the one-band Hubbard model. We discuss some realistic cases and their relevance for theories of the pairing mechanism in the cupratesComment: 5 pages, 4 figures, revised versio

Geometry of effective Hamiltonians

We give a complete geometrical description of the effective Hamiltonians common in nuclear shell model calculations. By recasting the theory in a manifestly geometric form, we reinterpret and clarify several points. Some of these results are hitherto unknown or unpublished. In particular, commuting observables and symmetries are discussed in detail. Simple and explicit proofs are given, and numerical algorithms are proposed, that improve and stabilize common methods used today.Comment: 1 figur

Partitioning technique for a discrete quantum system

We develop the partitioning technique for quantum discrete systems. The graph consists of several subgraphs: a central graph and several branch graphs, with each branch graph being rooted by an individual node on the central one. We show that the effective Hamiltonian on the central graph can be constructed by adding additional potentials on the branch-root nodes, which generates the same result as does the the original Hamiltonian on the entire graph. Exactly solvable models are presented to demonstrate the main points of this paper.Comment: 7 pages, 2 figure

Properties from relativistic coupled-cluster without truncation: hyperfine constants of 25Mg+^{25}{\rm Mg}^+, 43Ca+^{43}{\rm Ca}^+ , 87Sr+^{87}{\rm Sr}^+ and 137Ba+^{137}{\rm Ba}^+

We demonstrate an iterative scheme for coupled-cluster properties calculations without truncating the dressed properties operator. For validation, magnetic dipole hyperfine constants of alkaline Earth ions are calculated with relativistic coupled-cluster and role of electron correlation examined. Then, a detailed analysis of the higher order terms is carried out. Based on the results, we arrive at an optimal form of the dressed operator. Which we recommend for properties calculations with relativistic coupled-cluster theory.Comment: 13 pages, 4 figures, 5 table

Fock space relativistic coupled-Cluster calculations of Two-Valence Atoms

We have developed an all particle Fock-space relativistic coupled-cluster method for two-valence atomic systems. We then describe a scheme to employ the coupled-cluster wave function to calculate atomic properties. Based on these developments we calculate the excitation energies, magnetic hyperfine constants and electric dipole matrix elements of Sr, Ba and Yb. Further more, we calculate the electric quadrupole HFS constants and the electric dipole matrix elements of Sr$^+$, Ba$^+$ and Yb$^+$. For these we use the one-valence coupled-cluster wave functions obtained as an intermediate in the two-valence calculations. We also calculate the magnetic dipole hyperfine constants of Yb$^+$.Comment: 23 pages, 12 figures, 10 tables typos are corrected and some minor modifications in some of the section