International Journal of Modern Physics B

Neutron scattering experiments on a ³He layer on graphite show an unexpected behavior of the collective mode. After having been broadened by Landau damping at intermediate wave vectors, the phonon-roton mode resharpens at large wave vectors and even emerges from the particle-hole continuum at low energies. The measured spectra cannot be explained by a random phase approximation with any static interaction. We show here that the data are well described if dynamic two-pair fluctuations are accounted for. We predict similar effects for electron layers.

In a number of strongly-interacting Fermi systems, the existence of a quantum critical point (QCP) is signaled by a divergent density of states and effective mass at zero temperature. Competing scenarios and corresponding mechanisms for the QCP are contrasted and analyzed. The conventional scenario invokes critical fluctuations of a collective mode in the close vicinity of a second-order phase transition and attributes divergence of the effective mass to a coincident vanishing of the quasiparticle pole strength. It is argued that this collective scenario is disfavored by certain experimental observations as well as theoretical inconsistencies, including violation of conservation laws applicable in the strongly interacting medium. An alternative topological scenario for the QCP is developed self-consistently within the general framework of Landau quasiparticle theory. In this scenario, the topology of the Fermi surface is transfigured when the quasiparticle group velocity vanishes at the QCP, yet the quasiparticle picture remains meaningful and no symmetry is broken. The topological scenario is found to explain the non-Fermi-liquid behavior observed experimentally in Yb-based heavy-fermion systems close to the QCP. This study suggests that integration of the topological scenario with the theory of second-order, symmetry-breaking quantum phase transitions will furnish a proper foundation for theoretical understanding of the extended QCP region.

We investigate the wetting behavior of helium on nanostructured alkali metal surfaces, at temperatures below and slightly above the bulk superfluidity threshold. Starting from a determination of the phase diagram of helium on semiinfinite planar Cs up to 3 K, performed within finite–range, temperature–dependent density functional theory, we examine the modifications of the isotherms introduced by an infinite array of nanocavities. We compare the hysterectic loops of helium on nonwettable Cs surfaces and on wettable Na substrates in the same temperature range.

This paper reports progress on the simulation of metallic clusters embedded in a quantum fluid matrix such as ⁴He. In previous work we have reported progress developing a real-space density functional method. The core of the method is a diffusion algorithm that extracts the low-lying eigenfunctions of the Kohn-Sham Hamiltonian by propagating the wave functions (which are represented on a real-space grid) in imaginary time. Due to the diffusion character of the kinetic energy operator in imaginary time, algorithms developed so far are at most fourth order in the time-step. The first part of this paper discusses further progress, in particular we show that for a grid based algorithm, imaginary time propagation of any even order can be devised on the basis of multi-product splitting. The new propagation method is particularly suited for modern parallel computing environments. The second part of this paper addresses a yet unsolved problem, namely a consistent description of the interaction between helium atoms and a metallic cluster that can bridge the whole range from a single atom to a metal. Using a combination of DFT calculations to determine the response of the valence electrons, and phenomenological acounts of Pauli repulsion and short-ranged correlations that are poorly described in DFT, we show how such an interaction can be derived.

We present several new classes of metamaterials and/or locally resonant sonic crystal that are comprised of complex resonators. The proposed systems consist of multiple resonating inclusion that correspond to different excitation frequencies. This causes the formation of multiple overlapped resonance band gaps. We demonstrate theoretically and experimentally that the individual band gaps achieved, span a far greater range (≈ 2kHz) than previously reported cases. The position and width of the band gap is independent of the crystal's lattice constant and forms in the low frequency regime significantly below the conventional Bragg band gap. The broad envelope of individual resonance band gaps is attractive for sound proofing applications and furthermore the devices can be tailored to attenuate lower or higher frequency ranges, i.e., from seismic to ultrasonic.

A glassy phase in disordered two dimensional (2D) electron systems may exist at low temperatures for electron densities lying intermediate between the Fermi liquid and Wigner crystal limits. The glassy phase is generated by the combined effects of disorder and the strong electron-electron correlations arising from the repulsive Coulomb interactions. Our approach here is motivated by the observation that at low electron densities the electron pair correlation function, as numerically determined for a non-disordered 2D system from Monte Carlo simulations, is very similar to the pair correlation function for a 2D classical system of hard discs. This suggests that theoretical approaches to 2D classical systems of hard discs may be of use in studying the disordered, low density electron problem. We use this picture to study its dynamics on the electron-liquid side of a glass transition. At long times the major relaxation process in the electron-liquid will be a rearrangement of increasingly large groups of the discs, rather than the movement of the discs separately. Such systems have been studied numerically and they display all the characteristics of glassy behaviour. There is a slowing down of the dynamics and a limiting value of the retarded spatial correlations. Motivated by the success of mode-coupling theories for hard spheres and discs in reproducing experimental results in classical fluids, we use the Mori formalism within a mode-coupling theory to obtain semi-quantitative insight into the role of electron correlations as they affect the time response of the weakly disordered 2D electron system at low densities.

The dynamical response of one dimensional chains containing 55 till 309 atoms is investigated using a restricted molecular dynamics simulation scheme. The total momentum correlation function of an electron cloud shows resonances that are related to different collective excitation modes of the nano plasma. Spatially resolved cross correlation functions are calculated to deduce the spatial structure and strength of these resonance modes. The dependence of the corresponding resonance frequencies on temperature, density and chain size is investigated. The width of the resonances is analyzed in terms of a mode dependent collision frequency.

Correlated Density Matrix (CDM) theory permits formal analyses of microscopic properties of strongly correlated quantum fluids and liquids at nonzero temperatures. Equilibrium properties, thermodynamic potentials, correlation and structure functions can be studied formally as well as numerically within the CDM algorithm. Here we provide the essential building blocks for studying the radial distribution function and the single-particle momentum distribution of the ingredients of the quantum systems. We focus on the statistical properties of correlated fluids and introduce the concept of renormalized bosons and fermions. These entities carry the main statistical features of the correlated systems such as liquid ⁴He through their specific dependence on temperature, particle number density, and wavenumber encapsulated in their effective masses. The formalism is developed for systems of bosons and of fermions. Numerical calculations for fluid ⁴He in the normal phase demonstrate the power of the renormalization concept. The formalism is further extended to analyze the Bose-Einstein condensed phases and gives a microscopic understanding of Tisza's two-fluid model for the normal and superfluid density components.

Nuclei in dense matter are influenced by the medium. In the cluster mean-field approximation, an effective Schrodinger equation for the A-nucleon cluster is obtained accounting for the effects of the surrounding medium, such as self-energy and Pauli blocking. Similar to the single-baryon states (free protons and neutrons), the light elements (A ≤ 4) are treated as quasiparticles. Fit formulae are given for the quasiparticle shifts as function of temperature, density, asymmetry, and momentum. Composition, quantum condensates and thermodynamic functions are considered. The relevance for nuclear structure, heavy ion collisions and supernova astrophysics is shown.

We study the spin-1/2 and spin-1 Heisenberg antiferromagnets (HAFs) on an infinite, anisotropic, two-dimensional triangular lattice, using the coupled cluster method. With respect to an underlying square-lattice geometry the model contains antiferromagnetic (J₁ > 0) bonds between nearest neighbours and competing bonds between next-nearest-neighbours across only one of the diagonals of each square plaquette, the same diagonal in each square. In a topologically equivalent triangular-lattice geometry the model has two sorts of nearest-neighbour bonds, with bonds along parallel chains and with J₁ bonds providing an interchain coupling. The model thus interpolates between an isotropic HAF on the square lattice at one extreme (κ = 0) and a set of decoupled chains at the other (κ → ∞), with the isotropic HAF on the triangular lattice in between at κ = 1. For the spin-1/2 model, we find a weakly first-order (or possibly second-order) quantum phase transition from a Néel-ordered state to a helical state at a first critical point at κ_c1 = 0.80 ± 0.01, and a second critical point at κ_c2 = 1.8 ± 0.4 where a first-order transition occurs between the helical state and a collinear stripe-ordered state. For the corresponding spin-1 model we find an analogous transition of the second-order type at κ_c1 = 0.62 ± 0.01 between states with Néel and helical ordering, but we find no evidence of a further transition in this case to a stripe-ordered phase.

We show that, by recourse to thermodynamics's third law, quantum phase transitions in a system of fermions can be detected, in the sense that thereby one automatically finds the values of the external parameter (here coupling strengths of the pertinent Hamiltonian) at which these transitions occur. We illustrate our considerations with reference to an exactly solvable model of Plastino and Moszkowski [Il Nuovo Cimento 47, 470 (1978)].

The dynamical description of a semi quantum nonlinear systems whose classical limit is not chaotic is still an open question. These systems are characterized by mixing a classical system with a quantum-mechanical one. As some of them lead to an irregular dynamics, the name "semi quantum chaos" arises. In this contribution we study two different Hamiltonians through the Maximum Entropy Principle Approach (MEP). Taking advantage of the MEP formalism, it can be clearly established that the Hamiltonians belonging to the SU(2) Lie algebra have common properties and a common treatment can be developed for them. These Hamiltonians resemble a quantum spin system coupled to a classical cavity. In the present contribution, we show that all of them share the generalized uncertainty principle as an invariant of the motion and other invariants as well. Two different classical potentials V(q) have been studied. Their specific heat are evaluated in terms of the extensive (mean values) and the intensive (Lagrange multipliers) variables. The main result of the present contribution is to show that the specific heat of these systems can be fixed independently of the temperature by setting only the initial conditions on the extensive or intensive variables, as well as the value of the quantum-classical coupling parameter. It could be possible to infer that this result can be extended to generalized forms for the V(q) classical potential.

Fluids confined within narrow channels exhibit a variety of phases and phase transitions associated with their reduced dimensionality. In this review paper, we illustrate the crossover from quasi-one dimensional to higher effective dimensionality behavior of fluids adsorbed within different carbon nanotubes geometries. In the single nanotube geometry, no phase transitions can occur at finite temperature. Instead, we identify a crossover from a quasi-one dimensional to a two dimensional behavior of the adsorbate. In bundles of nanotubes, phase transitions at finite temperature arise from the transverse coupling of interactions between channels.

Absorption spectra of small molecular aggregates (oligomers) are considered. The dipole-dipole interaction between the monomers leads to shifts of the oligomer spectra with respect to the monomer absorption. The line-shapes of monomer as well as oligomer absorption depend strongly on the coupling to vibrational modes. Using a recently developed approach [Roden et al., PRL 103, 058301] we investigate the length dependence of spectra of one-dimensional aggregates for various values of the interaction strength between the monomers. It is demonstrated, that the present approach is well suited to describe the occurrence of the J- and H-bands.

Many of the most intriguing quantum effects are observed or could be measured in transport experiments through nanoscopic systems such as quantum dots, wires and rings formed by large molecules or arrays of quantum dots. In particular, the separation of charge and spin degrees of freedom and interference effects have important consequences in the conductivity through these systems.

Charge-spin separation was predicted theoretically in one-dimensional strongly interacting systems (Luttinger liquids) and, although observed indirectly in several materials formed by chains of correlated electrons, it still lacks direct observation. We present results on transport properties through Aharonov-Bohm rings (pierced by a magnetic flux) with one or more channels represented by paradigmatic strongly-correlated models. For a wide range of parameters we observe characteristic dips in the conductance as a function of magnetic flux which are a signature of spin and charge separation.

Interference effects could also be controlled in certain molecules and interesting properties could be observed. We analyze transport properties of conjugated molecules, benzene in particular, and find that the conductance depends on the lead configuration. In molecules with translational symmetry, the conductance can be controlled by breaking or restoring this symmetry, e.g. by the application of a local external potential.

These results open the possibility of observing these peculiar physical properties in anisotropic ladder systems and in real nanoscopic and molecular devices.

The intrinsic metastable crystal structure of the cuprates results in local dynamical lattice instabilities, strongly coupled to the density fluctuations of the charge carriers. They acquire in this way simultaneously both, delocalized and localized features. It is responsible for a partial fractioning of the Fermi surface, i.e., the Fermi surface gets hidden in a region around the anti-nodal points, because of the opening of a pseudogap in the normal state, arising from a partial charge localization. The high energy localized single-particle features are a result of a segregation of the homogeneous crystal structure into checker-board local nano-size structures, which breaks the local translational and rotational symmetry. The pairing in such a system is dynamical rather than static, whereby charge carriers get momentarily trapped into pairs in a deformable dynamically fluctuating ligand environment. We conclude that the intrinsically heterogeneous structure of the cuprates must play an important role in this type of superconductivity.

We develop a new condensed matter theory of the formation of thermodynamically stable vortex structures in quantum nanowires. We write down the Gibbs free energy functional for the systems and we minimise the free energy to obtain the optimal position of vortices for different applied fields and temperatures. We also study the nucleation of vortices in, and their escape from, the nanostructural superconductors.

Experimental realizations of a two-qubit quantum logic gate based on cold atom collisions have been elusive mainly due to the decoherence effects introduced during the quantum gate operation, which cause transitions out of the two-qubit space and lead to a decreased gate operation fidelity. This type of decoherence effects, due to the non closeness of the interacting two-qubit system, are characteristic of the electromagnetic interaction, since the electromagnetic vacuum acts as a reservoir whose eigenmodes might become active during the gate operation. To describe the cold-atom collision we consider the quantum non-Hermitian dipole-dipole interaction instead of the less realistic s-scattering approach widely used in the literature. By adding an ancillary qubit, we take advantage of the spatial modulation of the non-Hermitian part of the interaction potential to obtain a "resonant" condition that should be satisfied to achieve lossless operation of a specific two-qubit quantum phase-gate. We demonstrate that careful engineering of the collision is required to obtain a specific truth table and to suppress the effects inherent in the openness of the system arising from the electromagnetic interaction.

We adapt the classical Ornstein-Zernike equation for the direct correlation function of classical theory of liquids in order to obtain a model for the exchange-correlation hole based on the electronic direct correlation function. Because we explicitly account for the identical-particle nature of electrons, our result recovers the normalization of the exchange-correlation hole. In addition, the modified direct correlation function is shorted-ranged compared to the classical formula. Functionals based on hole models require six-dimensional integration of a singular integrand to evaluate the exchange-correlation energy, and we present several strategies for efficiently evaluating the exchange-correlation integral in a numerically stable way.

The study of bimetallic catalysts has scientific and technologic importance because of special catalytic activity towards several reactions. RhCu is an interesting bimetallic system due to combination of the very different catalytic activities of Rh and Cu. The catalytic activity of this bimetallic does not result from simple interpolation of the constituents. In fact, at low Cu content, the catalytic activity of RhCu is superior to that of Rh but when the Cu content is higher the activity decays. This is a curious trend which theoretical works had attempted to explain. This paper reports an overview of the most recent research works about this bimetallic system with emphasis in its especial characteristics.

We consider the problem of constructing kinetic energy functionals in density functional theory. We first discuss the functional generated through the application of local-scaling transformations to the exact analytic wavefunctions for the Hookean model of ⁴He (a finite mass three-particle system), and contrast this result with a previous one for ^∞He (infinite mass system). It is shown that an exact non-Born-Oppenheimer treatment not only leads to mass-correction terms in the kinetic energy, but to a basically different functional expression. In addition, we report and comment on some recently advanced approximate kinetic energy functionals generated in the context of the constraint-based approach to orbital-free molecular dynamics. The positivity and non-singularity of a new family of kinetic energy functionals specifically designed for orbital-free molecular dynamics is discussed. Finally, we present some conclusions.

Carbon-based materials, due to their low cost and weight, have long been considered as suitable physisorption substrates for the reversible storage of hydrogen. Nanoporous carbons can be engineered to achieve exceptional storage capacities: gravimetric excess adsorption of 0.073 ± 0.003 kgH₂/kg carbon, gravimetric storage capacity of 0.106 ± 0.005 kgH₂/kg carbon, and volumetric storage capacity of 0.040 ± 0.002 kgH₂/liter carbon, at 80 K and 50 bar. The nanopores generage high storage capacity by having a very high surface are, by generating a high H₂-wall interaction potential, and by allowing multi-layer adsorption of H₂ (at cryogenic temperatures). In this paper we show how the experimental adsorption isotherms can be understood from basic theoretical considerations and computational simulations of the adsorption in a bimodal distribution of narrow and wide pore spaces. We also analyze the possibility of multi-layer adsorption, and the effects of hypothetical larger adsorption energies. Finally, we present the results of coupled ab initio calculations and Monte Carlo simulations showing that partial substitution of carbon atoms in nanoporous matrix with boron results in significant increases of the adsorption energy and storage capacity.

Unification of the BCS and the Bose-Einstein condensation (BEC) theories is surveyed in detail via a generalized BEC (GBEC) finite-temperature statistical formalism. Its major difference with BCS theory is that it can be diagonalized exactly. Under specified conditions it yields the precise BCS gap equation for all temperatures as well as the precise BCS zero-temperature condensation energy for all couplings, thereby suggesting that a BCS condensate is a BE condensate in a ternary mixture of kinematically independent unpaired electrons coexisting with equally proportioned weakly-bound two-electron and two-hole Cooper pairs. Without abandoning the electron-phonon mechanism in moderately weak coupling it suffices, in principle, to reproduce the unusually high values of T_c (in units of the Fermi temperature T_F) of 0.01-0.05 empirically reported in the so-called "exotic" superconductors of the Uemura plot, including cuprates, in contrast to the low values of T_c/T_F ≤ 10^-3 roughly reproduced by BCS theory for conventional (mostly elemental) superconductors. Replacing the characteristic phonon-exchange Debye temperature by a characteristic magnon-exchange one more than twice in size can lead to a simple interaction model associated with spin-fluctuation-mediated pairing.

Kohn anomaly occurs in metals as a weak but discernible kink in the phonon spectrum around 2k_F arising out of screened Coulombic interaction. Over the years this has been observed in a number of normal metallic systems. As a major surprise however, the recent neutron spin-echo experiments on elemental (conventional) superconductors Pb and Nb reveal a very important and striking relation that Kohn (anomaly) energy equals twice the energy of the superconducting gap. In this paper we explore the microscopic origin of this novel phenomenon and discuss its implication to the standard model BCS Theory.

We first study the spectrum of the excitonic polaritons in semiconductors in the presence of a condensed phase. With the help of the Hubbard-Stratonovich transformation we propose an exact mapping of the extended Hubbard model onto an excitonic-polariton model describing the light propagation in semiconductors. This approach allows us to derive exact formulas for spin-spin and charge-charge correlation functions for spin-triplet superconductivity.

We investigate the temperature dependence of thermal expansion of the ferromagnetic triplet superconductors and their thermal expansion coefficients below the superconducting transition temperature of a majority spin conduction band. The free energy of the ferromagnetic superconductors derived by Linder et al. is used. The superconducting gaps in the A2 phase of ³He and with a node in UGe₂ are considered. By applying Takahashi's method to the free energy, i.e. by taking into account the volume dependence of the free energy explicitly, the temperature dependence of the thermal expansion and the thermal expansion coefficients is studied below the superconducting transition temperature of the majority spin conduction band. We find that we have anomalies of the thermal expansion in the vicinity of the superconducting transition temperatures and that we have divergence of the thermal expansion coefficients are divergent at the superconducting transition temperatures. The Grüneisen's relation between the temperature dependence of the thermal expansion coefficients and the temperature dependence of the specific heat at low temperatures is satisfied.

A quantum-statistical binary gas mixture model consisting of positive-energy resonant bosonic Cooper electron pairs in chemical and thermal equilibrium with single unpaired electrons yields, via two-time retarded Green functions, an analytic expression for a dimensionless coupling λ- and temperature T-dependent generalized energy gap E_g(λ, T) in the single-electron spectrum. The new gap gives a reasonable description of overdoped Bi₂Sr₂CuO_6+δ (Bi2201).

This paper constitutes a short review of the main experimental investigations into the subject as they were known on November 2009. The paper is also intended to be useful as an introduction to the physics of superconductivity under the presence of domain walls. First, the author briefly discusses general aspects of Superconductor/Ferromagnet (S/F) proximity effects as these can be important depending of the ferromagnet thickness. Then the so called domain wall superconductivity (DWS) and stray field effects (SFE) are clarified. The experimental evidence on each of these effects is qualitatively discussed. The difficulties on DWS experiments are outlined. The article concludes with a discussion of some outstanding issues and desirable future work.

In this article, we show that the Bardeen-Cooper-Schrieffer (BCS) formalism applied to a Hubbard model is capable to predict the s-, p- and d-wave superconductivity within a single theoretical scheme. This study is performed on a square lattice described by a generalized Hubbard Hamiltonian, in which correlated-hopping interactions are included in addition to the repulsive Coulombic one. Within the BCS formalism using a variable chemical potential, the superconducting ground states are determined by two coupled integral equations, whose integrand functions have main contributions around the Fermi surface. We observe the existence of a maximum critical temperature for s-, p- and d-wave superconducting channels that occur at the medium, low and high electron densities, respectively. Furthermore, the p- and d-wave superconducting specific heats show a power-law temperature dependence, instead of the exponential one for the s channel. Finally, the smallness of the anisotropic single-energy-excitation-gap minima is essential for the specific heat behavior, and this fact allows to understand the experimental data obtained from Sr₂RuO₄ and La_2-xSr_xCuO₄ superconductors.

The physical theory for the ergodic hypothesis is premised on the idea that the hypothesis is measurable by scattering experiment. Therewith it proves the hypothesis by measurable properties of the response function. Birkhoff's theorem proves the ergodic hypothesis by abstract properties of phase space, the measure and transitivity. In this work we apply the two independent approaches to a particular many-body model (spin-1/2 XY model) to see whether they arrive at the same conclusions on the ergodicity question. The two approaches are compared to gain insight into their goals.

The electron-electron potential in the one-photon exchange approximation with the omission of the spin-spin interaction, leads to the classical Coulomb interaction, but the inclusion of the latter results in the Møller interaction. Bethe and Fermi showed that the latter interaction leads to the Breit potential, if a few of the terms in the expansion of the retardation effect are considered. In this article, it is shown that the higher order terms omitted in the Bethe-Fermi treatment reduces to terms of the same order in Dirac's alpha-matrices considered by Bethe and Fermi. This raises questions whether the Breit interaction is the appropriate first order correction to the Coulomb potential in the non-relativistic limit. It is pointed out that the nature of the interaction between two bound (1s) electron derived by Brown using the Schwinger formalism of the quantum electrodynamics but proposed empirically in 1929 by Gaunt could be a better correction to the Coulomb potential for bound electrons in atoms. The calculated energies using these matrix elements plus the vacuum polarization energies are in reasonable agreement with the data. For comparison, calculated energies using the Breit interaction plus vacuum polarization energies are also presented.