Large deviations in quantum lattice systems: one-phase region

We give large deviation upper bounds, and discuss lower bounds, for the Gibbs-KMS state of a system of quantum spins or an interacting Fermi gas on the lattice. We cover general interactions and general observables, both in the high temperature regime and in dimension one.Comment: 30 pages, LaTeX 2

Foreclosing Competition through Access Charges and Price Discrimination

This article analyzes competition between two asymmetric networks, an incumbent and a new entrant. Networks compete in non-linear tariffs and may charge different prices for on-net and off-net calls. Departing from cost-based access pricing allows the incumbent to foreclose the market in a profitable way. If the incumbent benefits from customer inertia, then it has an incentive to insist in the highest possible access markup even if access charges are reciprocal and even in the absence of actual switching costs. If instead the entrant benefits from customer activism, then foreclosure is profitable only when switching costs are large enough.Access Pricing, Entry Deterrence, Interconnection, Network Competition, Two-way Access

Quantum lattice models at intermediate temperatures

We analyze the free energy and construct the Gibbs-KMS states for a class of quantum lattice systems, at low temperatures and when the interactions are almost diagonal in a suitable basis. We study systems with continuous symmetry, but our results are valid for discrete symmetry breaking only. Such phase transitions occur at intermediate temperatures where the continuous symmetry is not broken, while at very low temperature continuous symmetry breaking may occur.Comment: 25 pages, 6 figure

Foreclosing competition through access charges and price discrimination

This article analyzes competition between two asymmetric networks, an incumbent and a new entrant. Networks compete in non-linear tariffs and may charge different prices for on-net and off-net calls. Departing from cost-based access pricing allows the incumbent to foreclose the market in a profitable way. If the incumbent benefits from customer inertia, then it has an incentive to insist on the highest possible access markup even if access charges are reciprocal and even in the absence of actual switching costs. If instead the entrant benefits from customer activism, then foreclosure is profitable only when switching costs are large enough.Networks; benefits; costs; customer;

Quantum limited measurements of atomic scattering properties

We propose a method to perform precision measurements of the interaction parameters in systems of N ultra-cold spin 1/2 atoms. The spectroscopy is realized by first creating a coherent spin superposition of the two relevant internal states of each atom and then letting the atoms evolve under a squeezing Hamiltonian. The non-linear nature of the Hamiltonian decreases the fundamental limit imposed by the Heisenberg uncertainty principle to N^(-2), a factor of N smaller than the fundamental limit achievable with non-interacting atoms. We study the effect of decoherence and show that even with decoherence, entangled states can outperform the signal to noise limit of non-entangled states. We present two possible experimental implementations of the method using Bose-Einstein spinor condensates and fermionic atoms loaded in optical lattices and discuss their advantages and disadvantages.Comment: 7 pages, 5 figures. References adde

Simulating generic spin-boson models with matrix product states

The global coupling of few-level quantum systems ("spins") to a discrete set of bosonic modes is a key ingredient for many applications in quantum science, including large-scale entanglement generation, quantum simulation of the dynamics of long-range interacting spin models, and hybrid platforms for force and spin sensing. We present a general numerical framework for treating the out-of-equilibrium dynamics of such models based on matrix product states. Our approach applies for generic spin-boson systems: it treats any spatial and operator dependence of the two-body spin-boson coupling and places no restrictions on relative energy scales. We show that the full counting statistics of collective spin measurements and infidelity of quantum simulation due to spin-boson entanglement, both of which are difficult to obtain by other techniques, are readily calculable in our approach. We benchmark our method using a recently developed exact solution for a particular spin-boson coupling relevant to trapped ion quantum simulators. Finally, we show how decoherence can be incorporated within our framework using the method of quantum trajectories, and study the dynamics of an open-system spin-boson model with spatially non-uniform spin-boson coupling relevant for trapped atomic ion crystals in the presence of molecular ion impurities.Comment: 13 pages+refs. 13 figure