Landau diamagnetism revisited

In the ballistic limit, the Landauer conductance steps of a mesoscopic quantum wire have been explained by coherent and dissipationless transmission of individual electrons across a one-dimensional barrier. This leaves untouched the central issue of conduction: a quantum wire, albeit ballistic, has finite resistance and so must dissipate energy. Exactly HOW does the quantum wire shed its excess electrical energy? We show that the answer is provided, uniquely, by many-body qua...

The non-Markovian dynamics of a charged particle linearly coupled to a neutral bosonic heat bath is investigated in an external uniform magnetic field. The analytical expressions for the time-dependent and asymptotic friction and diffusion coefficients, cyclotron frequencies, variances of the coordinate and momentum, and orbital magnetic moments are derived. The role of magnetic field in the dissipation and diffusion processes is illustrated by several examples in the low- an...

We investigate the relation between broken time-reversal symmetry and localization of the electronic states, in the explicitly tractable case of the Landau model. We first review, for the reader's convenience, the symmetries of the Landau Hamiltonian and the relation of the latter with the Segal-Bargmann representation of Quantum Mechanics. We then study the localization properties of the Landau eigenstates by applying an abstract version of the Balian-Low Theorem to the oper...

Low-temperature, electronic transport in Landau levels N>1 of a two-dimensional electron system is strongly anisotropic. At half-filling of either spin level of each such Landau level the magnetoresistance either collapses to form a deep minimum or is peaked in a sharp maximum, depending on the in-plane current direction. Such anisotropies are absent in the N=0 and N=1 Landau level, which are dominated by the states of the fractional quantum Hall effect. The transport anisotr...

Summary of Quantum Magnetism Conference, Institute for Theoretical Physics, University of California, Santa Barbara, California, August 16-20, 1999.

Motivated by questions about the open-system dynamics of topological quantum matter, we investigated the quantum Brownian motion of an electron in a homogeneous magnetic field. When the Fermi length $l_F=\hbar/(v_Fm_{\text{eff}})$ becomes much longer than the magnetic length $l_B=(\hbar c/eB)^{1/2}$, then the spatial coordinates $X,Y$ of the electron cease to commute, $[X,Y]=il_B^2$. As a consequence, localization of the electron becomes limited by Heisenberg uncertainty, and...

The nonequilibrium steady states of quantum materials have many challenges. Here, we highlight issues with the relaxation time approximation (RTA) for the DC conductivity in insulating systems. The RTA to the quantum master equation (QME) is frequently employed as a simple method, yet this phenomenological approach is exposed as a fatal approximation, displaying metallic DC conductivity in insulating systems within the linear response regime. We find that the unexpected metal...

Following on from our previous work [Phys. Rev. Lett. 98, 166801 (2007)] we examine the finite temperature magnetothermoelectric response in the vicinity of a quantum critical point (QCP). We begin with general scaling considerations relevant to an arbitrary QCP, either with or without Lorentz invariance, and in arbitrary dimension. In view of the broad connections to high temperature superconductivity, and cold atomic gases, we focus on the quantum critical fluctuations of t...

The linear response of two-dimensional electron gas in a perpendicular magnetic field in the presence of a spatially dependent classically smooth electrostatic potential is studied theoretically, by application of the Kubo formula for nonlocal conductivity tensor. In the classical transport regime, a general expression for the conductivity tensor through the correlation functions of the homogeneous electron gas is derived. The quantum transport regime, when Landau quantizatio...

Electromagnetism is a \textit{relativistic} theory and one must exercise care in coupling this theory with \textit{nonrelativistic} classical mechanics and with \textit{nonrelativistic} classical statistical mechanics. Indeed historically, both the blackbody radiation spectrum and diamagnetism within classical theory have been misunderstood because of two crucial failures: 1)the neglect of classical electromagnetic zero-point radiation, and 2) the use of erroneous combination...