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arXiv1997

Frequency shift and mode coupling in the nonlinear dynamics of a Bose condensed gas

We investigate the behavior of large amplitude oscillations of a trapped Bose-condensed gas of alkali atoms at zero temperature, by solving the equations of hydrodynamics for collective modes. Due to the atom-atom interaction, the equations of motion are nonlinear and give rise to significant frequency shift and mode coupling. We provide analytic expressions for the frequency shift, pointing out the crucial role played by the anisotropy of the confining potential. For special values of the anisotropy parameter the mode coupling is particularly strong and the frequency shift becomes large, revealing a peculiar behavior of the Bose-condensed gas. Consequences on the theory of collapse and revival of collective excitations are also discussed.

cond-mat↗

arXiv1997

Semiclassical wave functions and energy levels of Bose-condensed gases in spherically symmetric traps

The WKB-approximation for the Bogoliubov-equations of the quasi-particle excitations in Bose-gases with condensate is worked out in the case of spherically symmetric trap potentials on the basis of the resulting quantization rule. The excitation spectrum is calculated numerically and also analytically in certain limiting cases. It is found that the energy levels of a Bohr-Sommerfeld type quantization may be considerably shifted when the classical turning point gets close to the surface of the condensate.

cond-mat↗

arXiv1997

Two-Fluid Hydrodynamics for a Trapped Weakly-Interacting Bose Gas

We derive the coupled equations of motion for the condensate (superfluid) and non-condensate (normal fluid) degrees of freedom in a trapped Bose gas at finite temperatures. Our results are based on the Hartree-Fock-Popov approximation for the time-dependent condensate wavefunction and an assumption of local equilibrium for the non-condensate atoms. In the case of a uniform weakly-interacting gas, our formalism gives a microscopic derivation of the well-known two-fluid equations of Landau. The collective modes in a parabolically trapped Bose gas include the analogue of the out-of-phase second sound mode in uniform systems.

cond-mat↗

arXiv1997

Collective excitations of Bose-Einstein condensed gases at finite temperatures

We have applied the Popov version of the Hartree-Fock-Bogoliubov (HFB) approximation to calculate the finite-temperature excitation spectrum of a Bose-Einstein condensate (BEC) of $^{87}$Rb atoms. For lower values of the temperature, we find excellent agreement with recently-published experimental data for the JILA TOP trap. In contrast to recent comparison of the results of HFB--Popov theory with experimental condensate fractions and specific heats, there is disagreement of the theoretical and recent experimental results near the BEC phase transition temperature.

cond-mat↗

arXiv1998

Homodyne Measurements on a Bose-Einstein Condensate

We investigate a non-destructive measurement technique to monitor Josephson-like oscillations between two spatially separated neutral atom Bose-Einstein condensates. One condensate is placed in an optical cavity, which is strongly driven by a coherent optical field. The cavity output field is monitored using a homodyne detection scheme. The cavity field is well detuned from an atomic resonance, and experiences a dispersive phase shift proportional to the number of atoms in the cavity. The detected current is modulated by the coherent tunneling oscillations of the condensate. Even when there is an equal number of atoms in each well initially, a phase is established by the measurement process and Josephson-like oscillations develop due to measurement back-action noise alone.

cond-mat↗

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

Antiferromagnetic Excitations and Van Hove Singularities in YBa$_2$Cu$_3$O$_{6+x}$

We show that in quasi-two-dimensional $d$-wave superconductors Van Hove singularities close to the Fermi surface lead to novel magnetic quasi-particle excitations. We calculate the temperature and doping dependence of dynamical magnetic susceptibility for YBCO and show that the proposed excitations are in agreement with inelastic neutron scattering experiments. In addition, the values of the gap parameter and in-plane antiferromagnetic coupling are much smaller than usually believed.

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

Corrections to scaling in 2--dimensional polymer statistics

Writing $ = AN^{2ν}(1+BN^{-Δ_1}+CN^{-1}+ ...)$ for the mean square end--to--end length $ $ of a self--avoiding polymer chain of $N$ links, we have calculated $Δ_1$ for the two--dimensional {\em continuum} case from a new {\em finite} perturbation method based on the ground state of Edwards self consistent solution which predicts the (exact) $ν=3/4$ exponent. This calculation yields $Δ_1=1/2$. A finite size scaling analysis of data generated for the continuum using a biased sampling Monte Carlo algorithm supports this value, as does a re--analysis of exact data for two--dimensional lattices.

cond-mat↗

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

Phase Diagram of the 1D Anderson Lattice

We map out the phase diagram of the one--dimensional Anderson lattice by studying the ground state magnetization as a function of band--filling using the density matrix renormalization group technique. For strong coupling, we find that the quarter--filled system has an S=0 ground state with strong antiferromagnetic correlations. As additional electrons are put in, we find first a ferromagnetic phase, as reported by Möller and Wölfle, and then a phase in which the ground state has total spin $S=0$. Within this $S=0$ phase, we find RKKY oscillations in the spin--spin correlation functions.

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

A mixed ultrasoft/normconserved pseudopotential scheme

A variant of the Vanderbilt ultrasoft pseudopotential scheme, where the normconservation is released for only one or a few angular channels, is presented. Within this scheme some difficulties of the truly ultrasoft pseudopotentials are overcome without sacrificing the pseudopotential softness. i) Ghost states are easily avoided without including semicore shells. ii) The ultrasoft pseudo-charge-augmentation functions can be made more soft. iii) The number of nonlocal operators is reduced. The scheme will be most useful for transition metals, and the feasibility and accuracy of the scheme is demonstrated for the 4d transition metal rhodium.

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↗