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J. E. Avron

Publications and source records attributed to J. E. Avron.

At least 37 records · Page 2Linked to original sources
arXiv2007

Swimming, Pumping and Gliding at low Reynolds numbers

Simple, linear equations relate microscopic swimmers to the corresponding gliders and pumps. They have the following set of consequences: The swimming velocity of free swimmers can be inferred from the force on the tethered swimmer and vice versa; A tethered swimmer dissipates more energy than a free swimmer; It is possible to swim with arbitrarily high efficiency, but it is impossible to pump with arbitrarily high efficiency and finally that pumping is geometric. We also solve several optimization problems associated with swimming and pumping: The problem of optimal anchoring for a certain class of swimmers that includes the Purcell swimmer and the three linked spheres and the optimal geometries of helices considered as swimmers and pumps.

physics.flu-dyn↗
arXiv2006

Swimming in curved space or The Baron and the cat

We study the swimming of non-relativistic deformable bodies in (empty) static curved spaces. We focus on the case where the ambient geometry allows for rigid body motions. In this case the swimming equations turn out to be geometric. For a small swimmer, the swimming distance in one stroke is determined by the Riemann curvature times certain moments of the swimmer.

math-ph↗
arXiv2005

Topological swimming in a quantum sea

We propose a quantum theory of swimming for swimmers that are small relative to the coherence length of the medium. The quantum swimming equation is derived from known results on quantum pumps. For a one-dimensional Fermi gas at zero temperature we find that swimming is topological: The distance covered in one swimming stroke is quantized in half integer multiples of the Fermi wave length. Moreover, one can swim without dissipation.

cond-mat.mes-hall↗
arXiv2005

Pushmepullyou: An efficient micro-swimmer

The swimming of a pair of spherical bladders that change their volumes and mutual distance is efficient at low Reynolds numbers and is superior to other models of artificial swimmers. The change of shape resembles the wriggling motion known as {\it metaboly} of certain protozoa.

math-ph↗
arXiv2004

Optimal Swimming at low Reynolds numbers

Efficient swimming at low Reynolds numbers is a major concern of microbots. To compare the efficiencies of different swimmers we introduce the notion of ``swimming drag coefficient'' which allows for the ranking of swimmers. We find the optimal swimmer within a certain class of two dimensional swimmers using conformal mappings techniques.

math-ph↗
arXiv2004

Semiclassical analysis and the magnetization of the Hofstadter model

The magnetization and the de Haas-van Alphen oscillations of Bloch electrons are calculated near commensurate magnetic fluxes. Two phases that appear in the quantization of mixed systems--the Berry's phase and a phase first discovered by Wilkinson--play a key role in the theory.

cond-mat.stat-mech↗
arXiv2003

Optimal rotations of deformable bodies and orbits in magnetic fields

Deformations can induce rotation with zero angular momentum where dissipation is a natural ``cost function''. This gives rise to an optimization problem of finding the most effective rotation with zero angular momentum. For certain plastic and viscous media in two dimensions the optimal path is the orbit of a charged particle on a surface of constant negative curvature with magnetic field whose total flux is half a quantum unit.

physics.class-ph↗
arXiv2003

Transport and Dissipation in Quantum Pumps

This paper is about adiabatic transport in quantum pumps. The notion of ``energy shift'', a self-adjoint operator dual to the Wigner time delay, plays a role in our approach: It determines the current, the dissipation, the noise and the entropy currents in quantum pumps. We discuss the geometric and topological content of adiabatic transport and show that the mechanism of Thouless and Niu for quantized transport via Chern numbers cannot be realized in quantum pumps where Chern numbers necessarily vanish.

math-ph↗
arXiv2003

Magnetic Fingerprints of Fractal Spectra and Duality of Hofstadter Models

We study the de-Haas van Alphen oscillations in the magnetization of the Hofstadter model. Near a split band the magnetization is a rapidly oscillating function of the Fermi energy with lip shaped envelopes. For generic magnetic fields this structure appears on all scales and provides a thermodynamic fingerprint of the fractal properties of the model. The analysis applies equally well to the two dual interpretations of the Hofstadter model and the nature of the duality transformation is elucidated.

cond-mat.stat-mech↗
arXiv2003

Topological quantum numbers in the Hall effect

Topological quantum numbers account for the precise quantization that occurs in the integer Hall effect. In this theory, Kubo's formula for the conductance acquires a topological interpretation in terms of Chern numbers and their non-commutative analog, the Fredholm Indices.

math-ph↗
arXiv2003

Adiabatic charge pumping in open quantum systems

We introduce a mathematical setup for charge transport in quantum pump connected to a number of external leads. It is proved that under rather general assumption on the Hamiltonian describing the system, in the adiabatic limit, the current through the pump is given by a formula of Buttiker, Pretre, and Thomas, relating it to the frozen S-matrix and its time derivative.

math-ph↗
arXiv2002

Time-Energy coherent states and adiabatic scattering

Coherent states in the time-energy plane provide a natural basis to study adiabatic scattering. We relate the (diagonal) matrix elements of the scattering matrix in this basis with the frozen on-shell scattering data. We describe an exactly solvable model, and show that the error in the frozen data cannot be estimated by the Wigner time delay alone. We introduce the notion of energy shift, a conjugate of Wigner time delay, and show that for incoming state $ρ(H_0)$ the energy shift determines the outgoing state.

math-ph↗
arXiv2001

Butterflies and topological quantum numbers

The Hofstadter model illustrates the notion of topological quantum numbers and how they account for the quantization of the Hall conductance. It gives rise to colorful fractal diagrams of butterflies where the colors represent the topological quantum numbers.

math-ph↗
arXiv2001

Optimal Quantum Pumps

We study adiabatic quantum pumps on time scales that are short relative to the cycle of the pump. In this regime the pump is characterized by the matrix of energy shift which we introduce as the dual to Wigner's time delay. The energy shift determines the charge transport, the dissipation, the noise and the entropy production. We prove a general lower bound on dissipation in a quantum channel and define optimal pumps as those that saturate the bound. We give a geometric characterization of optimal pumps and show that they are noiseless and transport integral charge in a cycle. Finally we discuss an example of an optimal pump related to the Hall effect.

math-ph↗
arXiv2000

The Born Oppenheimer wave function near level crossing

The standard Born Oppenheimer theory does not give an accurate description of the wave function near points of level crossing. We give such a description near an isotropic conic crossing, for energies close to the crossing energy. This leads to the study of two coupled second order ordinary differential equations whose solution is described in terms of the generalized hypergeometric functions of the kind 0F3(;a,b,c;z). We find that, at low angular momenta, the mixing due to crossing is surprisingly large, scaling like μ^(1/6), where μis the electron to nuclear mass ratio.

quant-ph↗
arXiv2000

Geometry, Statistics and Asymptotics of Quantum Pumps

We give a pedestrian interpretation of a formula of Buttiker et. al. (BPT) relating the adiabatically pumped current to the S matrix and its (time) derivatives. We relate the charge in BPT to Berry's phase and the corresponding Brouwer pumping formula to curvature. As applications we derive explicit formulas for the joint probability density of pumping and conductance when the S matrix is uniformly distributed; and derive a new formula that describes hard pumping when the S matrix is periodic in the driving parameters.

cond-mat.mes-hall↗