arXiv subjects

J. H. Schenker

Publications and source records attributed to J. H. Schenker.

3 recordsLinked to original sources

arXiv2006

Hamiltonian treatment of time dispersive and dissipative media within the linear response theory

We develop a Hamiltonian theory for a time dispersive and dissipative (TDD) inhomogeneous medium, as described by a linear response equation respecting causality and power dissipation. The canonical Hamiltonian constructed here exactly reproduces the original dissipative evolution after integrating out auxiliary fields. In particular, for a dielectric medium we obtain a simple formula for the Hamiltonian and closed form expressions for the energy density and energy flux involving the auxiliary fields. The developed approach also allows to treat a long standing problem of scattering from a lossy non-spherical obstacle and, more generally, wave propagation in TDD media.

physics.class-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↗

arXiv2000

Constructive Fractional-Moment Criteria for Localization in Random Operators

We present a family of finite-volume criteria which cover the regime of exponential decay for the fractional moments of Green functions of operators with random potentials. Such decay is a technically convenient characterization of localization for it is known to imply spectral localization, absence of level repulsion, dynamical localization and a related condition which plays a significant role in the quantization of the Hall conductance in two-dimensional Fermi gases. The constructive criteria also preclude fast power-law decay of the Green functions at mobility edges.

math-ph↗