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A. Elgart

Publications and source records attributed to A. Elgart.

11 recordsLinked to original sources
arXiv2016

Large Block Properties of the Entanglement Entropy of Disordered Fermions

We consider a macroscopic disordered system of free $d$-dimensional lattice fermions whose one-body Hamiltonian is a Schrödinger operator $H$ with ergodic potential. We assume that the Fermi energy lies in the exponentially localized part of the spectrum of $H$. We prove that if $S_Λ$ is the entanglement entropy of a lattice cube $Λ$ of side length $L$ of the system, then for any $d \ge 1$ the expectation $\mathbf{ E}\{L^{-(d-1)}S_Λ\}$ has a finite limit as $L \to \infty$ and we identify the limit. Next, we prove that for $d=1$ the entanglement entropy admits a well defined asymptotic form for all typical realizations (with probability 1) as $ L \to \infty$. According to numerical results of [33] the limit is not selfaveraging even for an i.i.d. potential. On the other hand, we show that for $d \ge 2$ and an i.i.d. random potential the variance of $L^{-(d-1)}S_Λ$ decays polynomially as $L \to \infty$, i.e., the entanglement entropy is selfaveraging.

quant-ph↗
arXiv2005

Equality of the bulk and edge Hall conductances in a mobility gap

We consider the edge and bulk conductances for 2D quantum Hall systems in which the Fermi energy falls in a band where bulk states are localized. We show that the resulting quantities are equal, when appropriately defined. An appropriate definition of the edge conductance may be obtained through a suitable time averaging procedure or by including a contribution from states in the localized band. In a further result on the Harper Hamiltonian, we show that this contribution is essential. In an appendix we establish quantized plateaus for the conductance of systems which need not be translation ergodic.

math-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

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

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

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↗
arXiv1999

Smooth adiabatic evolutions with leaky power tails

Adiabatic evolutions with a gap condition have, under a range of circumstances, exponentially small tails that describe the leaking out of the spectral subspace. Adiabatic evolutions without a gap condition do not seem to have this feature in general. This is a known fact for eigenvalue crossing. We show that this is also the case for eigenvalues at the threshold of the continuous spectrum by considering the Friedrichs model.

quant-ph↗
arXiv1999

Adiabatic Theorem without a Gap Condition

We prove the adiabatic theorem for quantum evolution without the traditional gap condition. All that this adiabatic theorem needs is a (piecewise) twice differentiable finite dimensional spectral projection. The result implies that the adiabatic theorem holds for the ground state of atoms in quantized radiation field. The general result we prove gives no information on the rate at which the adiabatic limit is approached. With additional spectral information one can also estimate this rate.

math-ph↗
arXiv1998

An Adiabatic Theorem without a Gap Condition: Two level system coupled to quantized radiation field

We prove an adiabatic theorem for the ground state of the Dicke model in a slowly rotating magnetic field and show that for weak electron-photon coupling, the adiabatic time scale is close to the time scale of the corresponding two level system--without the quantized radiation field. There is a correction to this time scale which is the Lamb shift of the model. The photon field affect the rate of approach to the adiabatic limit through a logarithmic correction originating from an infrared singularity characteristic of QED.

math.FA↗