We provide fast algorithms for simulating many body Fermi systems on a universal quantum computer. Both first and second quantized descriptions are considered, and the relative computational complexities are determined in each case. In order to accommodate fermions using a first quantized Hamiltonian, an efficient quantum algorithm for antisymmetrization is given. Finally, a simulation of the H...

We study semi-classical limits of eigenfunctions of a quantized linear hyperbolic automorphism of the torus (“cat map”). For some values of Planck’s constant, the spectrum of the quantized map has large degeneracies. Our first goal in this paper is to show that these degeneracies are coupled to the existence of quantum symmetries. There is a commutative group of unitary operators on the state-s...

The dynamics of vortices in a superfluid film at the absolute zero of temperature is studied. The quantum-mechanical, i.e., “first-quantized” description is compared to a recently proposed quantum-field-theoretic, i.e., “second-quantized” description. The theory, consisting of the nonrelativistic effective action of phonons linearly coupled to a Chern-Simons term, is used to calculate the one-l...

A subtle relation between quantum Hall physics and the phenomenon of pairing is unveiled. By use of second quantization, we establish a connection between (i) a broad class of rotationally symmetric two-body interactions within the lowest Landau level and (ii) integrable hyperbolic Richardson-Gaudin-type Hamiltonians that arise in (px + ipy) superconductivity. Specifically, we show that general...

in this paper, we study the plasmonic thermal conductance of ordered stacks of metallic nanorings in a host material. using second quantized formalism of the random phase approximation, we first determine the dispersion relations of surface plasmon waves on the stacks of nanorings. then, using landauer-buttiker formalism, we determine the coefficient of plasmonic thermal conductance and heat cu...

A survey is given of applications of the “string-inspired” worldline formalism to the computation of amplitudes and effective actions in QED. INTRODUCTION: QED IN FIRST QUANTIZATION The “worldline” or “string-inspired” formalism is an alternative to the usual second-quantized formalism in quantum field theory based on relativistic particle path integrals. Although it was invented by Feynman [1,...