Preparation information and optimal decompositions for mixed quantum states

Consider a joint quantum state of a system and its environment. A measurement on the environment induces a decomposition of the system state. Using algorithmic information theory, we define the preparation information of a pure or mixed state in a given decomposition. We then define an optimal decomposition as a decomposition for which the average preparation information is minimal. The average preparation information for an optimal decomposition characterizes the system-environment correlations. We discuss properties and applications of the concepts introduced above and give several examples.Comment: 13 pages, latex, 2 postscript figure

Quasiperiodic functions theory and the superlattice potentials for a two-dimensional electron gas

We consider Novikov problem of the classification of level curves of quasiperiodic functions on the plane and its connection with the conductivity of two-dimensional electron gas in the presence of both orthogonal magnetic field and the superlattice potentials of special type. We show that the modulation techniques used in the recent papers on the 2D heterostructures permit to obtain the general quasiperiodic potentials for 2D electron gas and consider the asymptotic limit of conductivity when $\tau \to \infty$. Using the theory of quasiperiodic functions we introduce here the topological characteristics of such potentials observable in the conductivity. The corresponding characteristics are the direct analog of the "topological numbers" introduced previously in the conductivity of normal metals.Comment: Revtex, 16 pages, 12 figure

Analytical approximation for single-impurity Anderson model

We have applied the recently developed dual fermion technique to the spectral properties of single-band Anderson impurity problem (SIAM). In our approach a series expansion is constructed in vertices of the corresponding atomic Hamiltonian problem. This expansion contains a small parameter in two limiting cases: in the weak coupling case ($U/t \to 0$), due to the smallness of the irreducible vertices, and near the atomic limit ($U/t \to \infty$), when bare propagators are small. Reasonable results are obtained also for the most interesting case of strong correlations ($U \approx t$). The atomic problem of the Anderson impurity model has a degenerate ground state, so the application of the perturbation theory is not straightforward. We construct a special approach dealing with symmetry-broken ground state of the renormalized atomic problem. Formulae for the first-order dual diagram correction are obtained analytically in the real-time domain. Most of the Kondo-physics is reproduced: logarithmic contributions to the self energy arise, Kondo-like peak at the Fermi level appears, and the Friedel sum rule is fulfilled. Our approach describes also renormalization of atomic resonances due to hybridization with a conduction band. A generalization of the proposed scheme to a multi-orbital case can be important for the realistic description of correlated solids.Comment: 6 pages, 5 figure

Towards a gauge invariant volume-weighted probability measure for eternal inflation

An improved volume-weighted probability measure for eternal inflation is proposed. For the models studied in this paper it leads to simple and intuitively expected gauge-invariant results.Comment: 16 pages, 3 figs, few misprints corrected, comments adde

QCD partition function in the external field in the covariant gauge

The QCD partition function in the external stationary gluomagnetic field is computed in the third order in external field invariants in arbitrary dimension and arbitrary covariant gauge. The contributions proportional to third order invariants in gluon field strength are shown to be dependent on covariant quantum gauge fixing parameter \alph

Electron waves in chemically substituted graphene

We present exact analytical and numerical results for the electronic spectra and the Friedel oscillations around a substitutional impurity atom in a graphene lattice. A chemical dopant in graphene introduces changes in the on-site potential as well as in the hopping amplitude. We employ a T-matrix formalism and find that disorder in the hopping introduces additional interference terms around the impurity that can be understood in terms of bound, semi-bound, and unbound processes for the Dirac electrons. These interference effects can be detected by scanning tunneling microscopy.Comment: 4 pages, 7 figure

Quasi-degenerate self-trapping in one-dimensional charge transfer exciton

The self-trapping by the nondiagonal particle-phonon interaction between two quasi-degenerate energy levels of excitonic system, is studied. We propose this is realized in charge transfer exciton, where the directions of the polarization give the quasi-degeneracy. It is shown that this mechanism, unlike the conventional diagonal one, allows a coexistence and resonance of the free and self-trapped states even in one-dimensional systems and a quantitative theory for the optical properties (light absorption and time-resolved luminescence) of the resonating states is presented. This theory gives a consistent resolution for the long-standing puzzles in quasi-one-dimensional compound A-PMDA.Comment: accepted to Phys. Rev. Letter

Ground State Properties of Anderson Impurity in a Gapless Host

Using the Bethe ansatz method, we study the ground state properties of a $U\to\infty$ Anderson impurity in a ``gapless'' host, where a density of band states vanishes at the Fermi level $\epsilon_F$ as $|\epsilon-\epsilon_F|$. As in metals, the impurity spin is proven to be screened at arbitrary parameters of the system. However, the impurity occupancy as a function of the bare impurity energy is shown to acquire novel qualitative features which demonstrate a nonuniversal behavior of the system. The latter explains why the Kondo screening is absent (or exists only at quite a large electron-impurity coupling) in earlier studies based on scaling arguments.Comment: 5 pages, no figure, RevTe

Magnetism and superconductivity in underscreened Kondo chains

We present a one dimensional model of electrons coupled to localized moments of spin $S\ge 1$ in which magnetism and superconductivity interplay in a nontrivial manner. This model has a non-Fermi liquid ground state of the chiral spin liquid type. A non-conventional odd-frequency pairing is shown to be the dominant instability of the system, together with antiferromagnetism of the local moments. We argue that this model captures the physics of the Kondo-Heisenberg spin S=1 chain, in the limit of strong Kondo coupling. Finally, we discuss briefly the effect of interchain coupling.Comment: no figures, 4 two column pages, Revte

The second-order electron self-energy in hydrogen-like ions

A calculation of the simplest part of the second-order electron self-energy (loop after loop irreducible contribution) for hydrogen-like ions with nuclear charge numbers $3 \leq Z \leq 92$ is presented. This serves as a test for the more complicated second-order self-energy parts (loop inside loop and crossed loop contributions) for heavy one-electron ions. Our results are in strong disagreement with recent calculations of Mallampalli and Sapirstein for low $Z$ values but are compatible with the two known terms of the analytical $Z\alpha$-expansion.Comment: 13 LaTex pages, 2 figure