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International Journal of Modern Physics B

QUANTUM REFLECTION, EVAPORATION, AND TRANSPORT CURRENTS AT 4 He SURFACES

V. Apaja, E. Krotscheck, Axel Rimnac, Robert E. Zillich

Published Dec 15, 2006• 1 citation
Publisher

Abstract

In this work, we study transport currents in excited states. This requires the calculation of particle currents [Formula: see text] to second order in the excitation amplitudes. For that purpose, we take a well-tested microscopic theory of inhomogeneous quantum liquids and extend it to find the mass currents created when atoms scatter off a surface or when excitations evaporate atoms. This is the first theoretical study of transport phenomena in a quantum liquid based on a quantitative microscopic theory.

DOI
10.1142/s0217979206036089

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In this work, we study transport currents in excited states. This requires the calculation of particle currents [Formula: see text] to second order in the excitation amplitudes. For that purpose, we take a well-tested microscopic theory of inhomogeneous quantum liquids and extend it to find the mass currents created when atoms scatter off a surface or when excitations evaporate atoms. This is the first theoretical study of transport phenomena in a quantum liquid based on a quantitative microscopic theory.
Until now, most of what has been said about excitations in quantum liquids has concerned the dynamic structure function, which is observable by means of neutron scattering. The dynamic structure function can be calculated using standard linear response theory. However, at this level one needs only transition densities 〈0|ρ̂|n〉 or transition currents 〈0|ĵ|n〉, which are oscillatory in time and hence do not describe mass transport. In this work we go a step further and study transport currents in excited states, 〈n|ĵ|n〉, which requires the calculation of 〈n|ĵ|n〉 to second order. For that purpose, we take a well‐tested microscopic theory of inhomogeneous quantum liquids and extend it to find the currents formed when helium atoms scatter off a helium slab or when excitations evaporate atoms (a setup experimented by A. F. G. Wyatt’s group in Exeter). Current conservation was already a major theoretical problem encountered by R. Feynman and led him to introduce backflow corrections. We show that perfect current conservation is expected only for exact solutions of the time‐dependent many‐body Schrödinger equation. This is the first extensive theoretical study of transport phenomena in a quantum liquid based on an accurate microscopic theory.
We develop a first-principles, microscopic theory of impurity atom scattering from inhomogeneous quantum liquids such as adsorbed films, slabs, or clusters of 4He.{}^{4}\mathrm{He}.4He. The theory is built upon a quantitative, microscopic description of the ground state of both the host liquid as well as the impurity atom. Dynamic effects are treated by allowing all ground-state correlation functions to be time dependent. Our description includes both the elastic and inelastic coupling of impurity motion to the excitations of the host liquid. As a specific example, we study the scattering of 3He{}^{3}\mathrm{He}3He atoms from adsorbed 4He{}^{4}\mathrm{He}4He films. We examine the dependence of ``quantum reflection'' on the substrate, and the consequences of impurity bound states, resonances, and background excitations for scattering properties. A thorough analysis of the theoretical approach and the physical circumstances point towards the essential role played by inelastic processes which determine almost exclusively the reflection probabilities. The coupling to impurity resonances within the film leads to a visible dependence of the reflection coefficient on the direction of the impinging particle.
This chapter concludes the study of superfluidity in Bose liquids with a brief summary of the strengths, and of the inadequacies, of the theory. A clear understanding of the static and the long wavelength dynamic properties of an equilibrium Bose liquid, including a microscopic basis for the two-fluid model. Variational calculations of the excitation spectrum of liquid He II, which are in good quantitative agreement with experiment. A satisfactory phenomenological treatment of the interactions between elementary excitations which give rise to various irreversible phenomena. A microscopic theory of the ground state and elementary excitation spectrum of liquid He II; in fact, even the theory of the simple dilute Bose gas has not yet been extended to treat the system at finite temperatures, and under non-equilibrium situations. A clear understanding of a number of "vortex" properties, including the critical current for superfluid flow in thin capillaries.
We give a method of describing thermodynamical transport phenomena, based on a quantum scattering theoretical approach. We consider a quantum system of particles connected to thermodynamical reservoirs by leads. The effects of the reservoirs are imposed as an asymptotic condition at the end of the leads. We derive an expression for a current of a conserved quantity, which is independent of the details of the Hamiltonian operator. The Landauer formula and its generalizations are derived from this method.
Landau (1958) gave a rigorous microscopic derivation of his phenomenological Fermi -liquid theory starting from the first principles Hamiltonian of strongly interacting Fermions. The derivation is based on an asymptotic expansion in small parameters such as q/kF, bc.>/EF, kT/EF, where q and c.> represent the wave numbers and frequencies of real excitations of the system. Landau showed that the dynamics of these low-lying excitations (quasiparticles and collective modes) is governed by classical transport equations with all quantum many-body effects absorbed into effective interaction parameters. Landau's approach has been generalized to superfluid Fermi liquids and superconductors by Leggett (1965) and, going beyond linear response, by Eliashberg (1971). Their ideas merged into a recent review on the quasiclassical approach to superfluid 3 He by Serene and Rainer (1983). I will use the notation of this review throughout this paper. Landau's transport theory together with its offsprings will be called 'quasiclassical theory in the following. In this context it is important to mention that Eilenberger (1968) and Larkin and Ovchinnikov (1968) have shown that the complete theory of superconductors can be formulated as a quasiclassical transport theory. Surprisingly, this theory permits calculating microscopic properties, e.g. the quasiparticle excitation spectrum, which are predominantly governed by quantum effects.
We give a brief introduction to Luttinger liquids and to the phenomena of electronic transport or conductance in quantum wires. We explain why the subject of transport in Luttinger liquids is relevant and fascinating and review some important results on tunneling through barriers in a one-dimensional quantum wire and the phenomena of persistent currents in mesoscopic rings. We give a brief description of our own work on transport through doubly-crossed Luttinger liquids and transport in the Schulz–Shastry exactly solvable Luttinger-like model. With a view to making this article accessible to researchers in diverse fields such as nuclear physics, particle physics, formal field theory and condensed matter physics, we begin by first giving a brief introduction. In Sec. 1, we explain the words such as "Luttinger liquid" and "transport" in the title. We also motivate the study of this subject by showing that field is very important at the current time from the applications point of view and describe why it is theoretically fascinating. We then give a quick review of some of the important results in the field in Sec. 2, before we go on to describe some work that we have recently done and are doing in this field in Sec. 3. Finally, in Sec. 4, we conclude by re-emphasizing the importance of this area and drawing attention towards future possibilities.