arXiv subjects

Anthony J. Leggett

Publications and source records attributed to Anthony J. Leggett.

22 records · Page 2Linked to original sources

arXiv1998

Free Energy of an Inhomogeneous Superconductor: a Wave Function Approach

A new method for calculating the free energy of an inhomogeneous superconductor is presented. This method is based on the quasiclassical limit (or Andreev approximation) of the Bogoliubov-de Gennes (or wave function) formulation of the theory of weakly coupled superconductors. The method is applicable to any pure bulk superconductor described by a pair potential with arbitrary spatial dependence, in the presence of supercurrents and external magnetic field. We find that both the local density of states and the free energy density of an inhomogeneous superconductor can be expressed in terms of the diagonal resolvent of the corresponding Andreev Hamiltonian, resolvent which obeys the so-called Gelfand-Dikii equation. Also, the connection between the well known Eilenberger equation for the quasiclassical Green's function and the less known Gelfand-Dikii equation for the diagonal resolvent of the Andreev Hamiltonian is established. These results are used to construct a general algorithm for calculating the (gauge invariant) gradient expansion of the free energy density of an inhomogeneous superconductor at arbitrary temperatures.

cond-mat.supr-con↗

arXiv1998

Macroscopic Quantum Tunneling of a Bose-Einstein Condensate with Attractive Interaction

A Bose-Einstein condensate with attractive interaction can be metastable if it is spatially confined and if the number of condensate bosons $N_0$ is below a certain critical value $N_{\rm c}$. By applying a variational method and the instanton techinique to the Gross-Pitaevskii energy functional, we find analytically the frequency of the collective excitation and the rate of macroscopic quantum tunneling (MQT). We show that near the critical point the tunneling exponent vanishes according to $(1-N_0/N_c)^\frac{5}{4}$ and that MQT can be a dominant decay mechanism of the condensate for $N_0$ very close to $N_{\rm c}$.

cond-mat↗

arXiv1997

Josephson effect between trapped Bose-Einstein condensates

We study the Josephson effect between atomic Bose-Einstein condensates. By drawing on an electrostatic analogy, we derive a semiclassical functional expression for the three-dimensional Josephson coupling energy in terms of the condensate density. Estimates of the capacitive energy and of the Josephson plasma frequency are also given. The effect of dissipation due to the incoherent exchange of normal atoms is analysed. We conclude that coherent Josephson dynamics may already be observable in current experimental systems.

cond-mat↗

arXiv1997

Nonlocal Effects on the Magnetic Penetration Depth in d-wave Superconductors

We show that, under certain conditions, the low temperature behavior of the magnetic penetration depth $λ(T)$ of a pure d-wave superconductor is determined by nonlocal electrodynamics and, contrary to the general belief, the deviation $Δλ(T) = λ(T)-λ(0)$ is proportional to T^2 and not T. We predict that the $Δλ(T)\propto T^2$ dependence, due to nonlocality, should be observable experimentally in nominally clean high-T_c superconductors below a crossover temperature $T^* = (ξ_o/λ_o)Δ_o \sim 1 K$. Possible complications due to impurities, surface quality and crystal axes orientation are discussed.

cond-mat.supr-con↗