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arXiv1995

Effect of superconducting correlation on the localization of quasiparticles in low dimensions

Localization lengths of superconducting quasiparticles $λ_s$ are evaluated and compared with the corresponding normal state values $λ_n$ in one and two dimensional lattices. The effect of superconducting correlation on the localization of quasiparticles is generally stronger in an off-site pairing state than in an on-site pairing state. The modification of superconducting correlation to $λ$ is strongly correlated with the density of states (DOS) of superconducting quasiparticles. $λ_s$ drops within the energy gap but is largely enhanced around energies where DOS peaks appear. For a gapless pairing state in 1D or a d-wave pairing state in 2D, $λ_s/ λ_n$ at the Fermi energy $E_F$ is of order 1 and determined purely by the value of gap parameter not by the random potential. For the d-wave pairing state, the localization effect is largely weakened compared with the corresponding normal state and quasiparticles with energies close to $E_F$ are more strongly localized than other low energy quasiparticles.

cond-mat↗

arXiv1995

Vortices in Schwinger-Boson Mean-Field Theory of Two-Dimensional Quantum Antiferromagnets

In this paper we study the properties of vortices in two dimensional quantum antiferromagnets with spin magnitude S on a square lattice within the framework of Schwinger-boson mean field theory. Based on a continuum description, we show that vortices are stable topological excitations in the disordered state of quantum antiferromagnets. Furthermore, we argue that vortices can be divided into two kinds: the first kind always carries zero angular momentum and are bosons, whereas the second kind carries angular momentum S under favourable conditions and are fermions if S is half-integer. A plausible consequence of our results relating to RVB theories of High-Tc superconductors is pointed out.

cond-mat↗

arXiv1995

Spin-ordering and magnon collective modes for two-dimensional electron lattices in strong magnetic fields

We study the spin-ordering and the magnon collective modes of the two-dimensional Wigner crystal state at strong magnetic fields. Our work is based on the Hartree-Fock approximation for the ground state and the time-dependent Hartree-Fock approximation for the collective modes. We find that the ground state is ferromagnetic, i.e that all spins are aligned at T=0 even when the electronic g-factor is negligibly small. The magnon calculations show that the spin-stiffness is much smaller in the crystal state than in fluid states which occur at nearby Landau level filling factors.

cond-mat↗

arXiv1996

Critical Behaviour of the Two Dimensional Step Model

We use finite--size scaling of Lee--Yang partition function zeroes to study the critical behaviour of the two dimensional step or sgn $O(2)$ model. We present evidence that, like the closely related $XY$--model, this has a phase transition from a disordered high temperature phase to a low temperature massless phase where the model remains critical. The critical parameters (including logarithmic corrections) are compatible with those of the $XY$--model indicating that both models belong to the same universality class.

hep-lat↗

arXiv1995

Strong-coupling expansions for the pure and disordered bose Hubbard model

A strong-coupling expansion for the phase boundary of the (incompressible) Mott insulator is presented for the bose Hubbard model. Both the pure case and the disordered case are examined. Extrapolations of the series expansions provide results that are as accurate as the Monte Carlo simulations and agree with the exact solutions. The shape difference between Kosterlitz-Thouless critical behavior in one-dimension and power-law singularities in higher dimensions arises naturally in this strong-coupling expansion. Bounded disorder distributions produce a ``first-order'' kink to the Mott phase boundary in the thermodynamic limit because of the presence of Lifshitz's rare regions.

cond-mat↗

arXiv1995

2-Dimensional Electron Gas in a Linearly Varying Magnetic Field. ``Quantisation'' of the Electron and Current Density

We have developed new methods to calculate dispersion curves (analytically in the simpler cases) from which we are able to derive the spatial distribution of electron and current densities. We investigate the case where the magnetic field varies linearly with position and the results provide useful insights into the properties of this and other field distributions. We consider spin as well as a confining electrostatic potential. We show that the electron and the current density exhibit a very rich structure related to the quantisation of the energy. Moreover there is a direct contribution to the current density due to the spin which could be of interest in relation to spin polarised current.

cond-mat↗

arXiv1995

Elementary excitations in the $Δ$-chain

We clarify elementary excitations in the $Δ$-chain. They are found to be `kink'-`antikink' type domain wall excitations to the dimer singlet ground state. The characters of a kink and an antikink are quite different in this system: a kink has no excitation energy and is localized, while an antikink has a finite excitation energy and propagates. The excitation energy of a kink-antikink pair consists of a finite energy gap and a kinetic energy due to the free motion of the antikink. Variational wave functions for an antikink are studied to clarify its propagating states. All the numerical results are explained consistently based on this picture. At finite temperatures, thermally excited antikinks are moving in regions bounded by localized kinks. The origin of the low-temperature peak in the specific heat reported previously is explained and the peak position in the thermodynamic limit is estimated.

cond-mat↗

arXiv1996

Dirac Fermions with Disorder in Two Dimensions: Exact Result

Dirac fermions on a two-dimensional lattice with disorder are considered. The Dirac mass, which controls the gap between the two bands of the fermions, is subject to random fluctuations. Another type of disorder is discussed presented by a random vector potential. It is shown that the imaginary part of the one-particle Green's function can be written as the imaginary part of another Green's function which has only poles on the lower half-plane. Therefore, it is possible to perform a Cauchy integration for a Lorentzian distribution in analogy with the Lloyd model. The results are compared with calculations performed in the continuum limit based on renormalization group and bosonization methods.

cond-mat↗

arXiv1995

Theory of the c-Axis Penetration Depth in the Cuprates

Recent measurements of the London penetration depth tensor in the cuprates find a weak temperature dependence along the c-direction which is seemingly inconsistent with evidence for d-wave pairing deduced from in-plane measurements. We demonstrate in this paper that these disparate results are not in contradiction, but can be explained within a theory based on incoherent quasiparticle hopping between the CuO2 layers. By relating the calculated temperature dependence of the penetration depth λ_c(T) to the c-axis resistivity, we show how the measured ratio λ_c^2(0) / λ_c^2(T) can provide insight into the behavior of c-axis transport below Tc and the related issue of ``confinement.''

cond-mat↗

arXiv1995

Spectral Correlation and Response functions in Quantum Dots

We derive a general relation between correlators of density of states fluctuations and density response functions. It applies equally to quantum chaotic systems of pure symmetry (unitary, orthogonal, and symplectic) as well as to the crossover region between the universality classes. This relation is much more robust than Wigner-Dyson statistics; its validity extends to disordered metals with finite conductance and even to the Anderson insulators with large localization length.

cond-mat↗

arXiv1995

An exchange-correlation energy for a two-dimensional electron gas in a magnetic field

We present the results of a variational Monte Carlo calculation of the exchange-correlation energy for a spin-polarized two-dimensional electron gas in a perpendicular magnetic field. These energies are a necessary input to the recently developed current-density functional theory. Landau-level mixing is included in a variational manner, which gives the energy at finite density at finite field, in contrast to previous approaches. Results are presented for the exchange-correlation energy and excited-state gap at $ν=$ 1/7, 1/5, 1/3, 1, and 2. We parameterize the results as a function of $r_s$ and $ν$ in a form convenient for current-density functional calculations.

cond-mat↗

arXiv1996

The Magnus force in superfluids and superconductors

The forces on the vortex, transverse to its velocity, are considered. In addition to the superfluid Magnus force from the condensate (superfluid component), there are transverse forces from thermal quasiparticles and external fields violating the translational invariance. The forces between quasiparticles and the vortex originate from interference of quasiparticles with trajectories on the left and on the right from the vortex like similar forces for electrons interacting with the thin magnetic-flux tube (the Aharonov-Bohm effect). These forces are derived in the Born approximation for phonons from the equations of superfluid hydrodynamics, and for BCS quasiparticles from the Bogolyubov-de Gennes equations. The effect of external fields violating translational invariance is analyzed for vortices in the two-dimensional Josephson junction array. The symmetry analysis of the classical equations for the array shows that the total transverse force on the vortex vanishes. Therefore the Hall effect which is linear in the transverse force is absent also. This means that the Magnus force from the superfluid component exactly cancels with the transverse force from the external fields. The results of other approaches are also brought together for discussion.

cond-mat↗

arXiv1999

On the Structure of the Bose-Einstein Condensate Ground State

We construct a macroscopic wave function that describes the Bose-Einstein condensate and weakly excited states, using the su(1,1) structure of the mean-field hamiltonian, and compare this state with the experimental values of second and third order correlation functions.

cond-mat↗

arXiv2003

Quasi-classical Approach to Bose Condensation in a Finite Potential Well

We treat the problem of self-consistently interacting bosons in the presence of a finite (but macroscopic) potential well within a quasi-classical approximation for the normal component and the order parameter. We solve the equilibrium problem and show, that actually condensation occurs in two steps. One already at low densities with Bose condensation only in the well and another one corresponding to the usual condensation in bulk. The peak and width of the distribution of trapped particles in the well display a distinct signature of the local condensation. A possible connection to recent experiments with excitons is discussed.

cond-mat↗

arXiv1994

The Phases and Triviality of Scalar Quantum Electrodynamics

The phase diagram and critical behavior of scalar quantum electrodynamics are investigated using lattice gauge theory techniques. The lattice action fixes the length of the scalar (``Higgs'') field and treats the gauge field as non-compact. The phase diagram is two dimensional. No fine tuning or extrapolations are needed to study the theory's critical behovior. Two lines of second order phase transitions are discovered and the scaling laws for each are studied by finite size scaling methods on lattices ranging from $6^4$ through $24^4$. One line corresponds to monopole percolation and the other to a transition between a ``Higgs'' and a ``Coulomb'' phase, labelled by divergent specific heats. The lines of transitions cross in the interior of the phase diagram and appear to be unrelated. The monopole percolation transition has critical indices which are compatible with ordinary four dimensional percolation uneffected by interactions. Finite size scaling and histogram methods reveal that the specific heats on the ``Higgs-Coulomb'' transition line are well-fit by the hypothesis that scalar quantum electrodynamics is logarithmically trivial. The logarithms are measured in both finite size scaling of the specific heat peaks as a function of volume as well as in the coupling constant dependence of the specific heats measured on fixed but large lattices. The theory is seen to be qualitatively similar to $λϕ^{4}$. The standard CRAY random number generator RANF proved to be inadequate

hep-lat↗

arXiv1995

Polymer-Chain Adsorption Transition at a Cylindrical Boundary

In a recent letter, a simple method was proposed to generate solvable models that predict the critical properties of statistical systems in hyperspherical geometries. To that end, it was shown how to reduce a random walk in $D$ dimensions to an anisotropic one-dimensional random walk on concentric hyperspheres. Here, I construct such a random walk to model the adsorption-desorption transition of polymer chains growing near an attractive cylindrical boundary such as that of a cell membrane. I find that the fraction of adsorbed monomers on the boundary vanishes exponentially when the adsorption energy decreases towards its critical value. When the adsorption energy rises beyond a certain value above the critical point whose scale is set by the radius of the cell, the adsorption fraction exhibits a crossover to a linear increase characteristic to polymers growing near planar boundaries.

hep-lat↗

arXiv1995

Kinetics of A+B--->0 with Driven Diffusive Motion

We study the kinetics of two-species annihilation, A+B--->0, when all particles undergo strictly biased motion in the same direction and with an excluded volume repulsion between same species particles. It was recently shown that the density in this system decays as t^{-1/3}, compared to t^{-1/4} density decay in A+B--->0 with isotropic diffusion and either with or without the hard-core repulsion. We suggest a relatively simple explanation for this t^{-1/3} decay based on the Burgers equation. Related properties associated with the asymptotic distribution of reactants can also be accounted for within this Burgers equation description.

cond-mat↗

arXiv1995

Correlations in Ising chains with non-integrable interactions

Two-spin correlations generated by interactions which decay with distance r as r^{-1-sigma} with -1 \infty, but they contain a singular structure for r/L -> 0 which can be observed by introducing magnified correlations, LC(r,L)-\sum_r C(r,L). The magnified correlations are shown to have a scaling form F(r/L) and the singular structure of F(x) for x->0 is found to be the same at all temperatures including the critical point. These conclusions are supported by the results of Monte Carlo simulations for systems with sigma =-0.50 and -0.25 both at the critical temperature T=Tc and at T=2Tc.

cond-mat↗