Approximate programmable quantum processors

A quantum processor is a programmable quantum circuit in which both the data and the program, which specifies the operation that is carried out on the data, are quantum states. We study the situation in which we want to use such a processor to approximate a set of unitary operators to a specified level of precision. We measure how well an operation is performed by the process fidelity between the desired operation and the operation produced by the processor. We show how to find the program for a given processor that produces the best approximation of a particular unitary operation. We also place bounds on the dimension of the program space that is necessary to approximate a set of unitary operators to a specified level of precision.Comment: 8 page

Dielectric Breakdown of a Mott Insulator

We study the nonequilibrium steady state of a Mott insulator coupled to a thermostat and driven by a constant electric field, starting from weak fields, until the dielectric breakdown, and beyond. We find that the conventional Zener picture does not describe the steady-state physics. In particular, the current at weak field is found to be controlled by the dissipation. Moreover, in connection with the electric-field-driven dimensional crossover, we find that the dielectric breakdown occurs when the field strength is on the order of the Mott gap of the corresponding lower-dimensional system. We also report a resonance and the meltdown of the quasiparticle peak when the field strength is half of this Mott gap.Comment: 5 pages, 5 figures. v2: references adde

Theory of dissipationless Nernst effects

We develop a theory of transverse thermoelectric (Peltier) conductivity, \alpha_{xy}, in finite magnetic field -- this particular conductivity is often the most important contribution to the Nernst thermopower. We demonstrate that \alpha_{xy} of a free electron gas can be expressed purely and exactly as the entropy per carrier irrespective of temperature (which agrees with seminal Hall bar result of Girvin and Jonson). In two dimensions we prove the universality of this result in the presence of disorder which allows explicit demonstration of a number features of interest to experiments on graphene and other two-dimensional materials. We also exploit this relationship in the low field regime and to analyze the rich singularity structure in \alpha_{xy}(B, T) in three dimensions; we discuss its possible experimental implications.Comment: 4.5 pages, 2 figure

Green-Function-Based Monte Carlo Method for Classical Fields Coupled to Fermions

Microscopic models of classical degrees of freedom coupled to non-interacting fermions occur in many different contexts. Prominent examples from solid state physics are descriptions of colossal magnetoresistance manganites and diluted magnetic semiconductors, or auxiliary field methods for correlated electron systems. Monte Carlo simulations are vital for an understanding of such systems, but notorious for requiring the solution of the fermion problem with each change in the classical field configuration. We present an efficient, truncation-free O(N) method on the basis of Chebyshev expanded local Green functions, which allows us to simulate systems of unprecedented size N.Comment: 4 pages, 3 figure

Thermoelectric properties of AgGaTe2_2 and related chalcopyrite structure materials

We present an analysis of the potential thermoelectric performance of p-type AgGaTe$_{2}$, which has already shown a $ZT$ of 0.8 with partial optimization, and observe that the same band structure features, such as a mixture of light and heavy bands and isotropic transport, that lead to this good performance are present in certain other ternary chalcopyrite structure semiconductors. We find that optimal performance of AgGaTe$_2$ will be found for hole concentrations between 4 $\times 10^{19}$ and 2 $\times 10^{20}$cm$^{-3}$ at 900 K, and 2 $\times 10^{19}$ and 10$^{20}$ cm$^{-3}$ at 700 K, and that certain other chalcopyrite semiconductors might show good thermoelectric performance at similar doping ranges and temperatures if not for higher lattice thermal conductivity

Negative effective mass transition and anomalous transport in power-law hopping bands

We study the stability of spinless Fermions with power law hopping $H_{ij} \propto |i - j|^{-\alpha}$. It is shown that at precisely $\alpha_c =2$, the dispersive inflection point coalesces with the band minimum and the charge carriers exhibit a transition into negative effective mass regime, $m_\alpha^* < 0$ characterized by retarded transport in the presence of an electric field. Moreover, bands with $\alpha < 2$ must be accompanied by counter-carriers with $m_\alpha^* > 0$, having a positive band curvature, thus stabilizing the system in order to maintain equilibrium conditions and a proper electrical response. We further examine the semi-classical transport and response properties, finding an infrared divergent conductivity for 1/r hopping($\alpha =1$). The analysis is generalized to regular lattices in dimensions $d$ = 1, 2, and 3.Comment: 6 pages. 2 figure

Dominant role of impurity scattering over crystalline anisotropy for magnetotransport properties in the quasi-1D Hollandite Ba1.2Rh8O16

Angular magnetotransport measurements have been performed to tackle the origin of the magnetoresistance in the quasi-1D Hollandite Ba1.2Rh8O16. Three samples of different impurities amount were measured. We observe that the low temperature resistivity upturn is not due to a charge density wave transition, and a dominant role of impurities scattering for low temperature transport properties is instead demonstrated. The components of magnetoresistance were separated by using the Kohler plot and the angular dependency of the resistance under magnetic field. It shows the major contribution of an isotropic, likely spin driven, negative magnetoresistance. Galvanomagnetic characteristics are then consistent with a Kondo effect and appear to be essentially 3D at low temperature.Comment: accepted for publication in PR

Theory of cooling by flow through narrow pores

We consider the possibility of adding a stage to a dilution refrigerator to provide additional cooling by ``filtering out'' hot atoms. Three methods are considered: 1) Effusion, where holes having diameters larger than a mean-free path allow atoms to pass through easily; 2) Particle waveguide-like motion using very narrow channels that greatly restrict the quantum states of the atoms in a channel. 3) Wall-limited diffusion through channels, in which the wall scattering is disordered so that local density equilibrium is established in a channel. We assume that channel dimension are smaller than the mean-free path for atom-atom interactions. The particle waveguide and the wall-limited diffusion methods using channels on order of the de Broglie wavelength give cooling. Recent advances in nano-filters give this method some hope of being practical.Comment: 10 pages, 3 figures. Corrected typos and made some minor wording change

Concurrence vs. purity: Influence of local channels on Bell states of two qubits

We analyze how a maximally entangled state of two-qubits (e.g., the singlet $\psi_s$) is affected by action of local channels described by completely positive maps \cE . We analyze the concurrence and the purity of states \varrho_\cE=\cE\otimes\cI[\psi_s].Using the concurrence-{\it vs}-purity phase diagram we characterize local channels \cE by their action on the singlet state $\psi_s$. We specify a region of the concurrence-{\it vs.}-purity diagram that is achievable from the singlet state via the action of unital channels. We show that even most general (including non-unital) local channels acting just on a single qubit of the original singlet state cannot generate the maximally entangled mixed states (MEMS). We study in detail various time evolutions of the original singlet state induced by local Markovian semigroups. We show that the decoherence process is represented in the concurrence-{\it vs.}-purity diagram by a line that forms the lower bound of the achievable region for unital maps. On the other hand, the depolarization process is represented by a line that forms the upper bound of the region of maps induced by unital maps.Comment: 9 pages, 6 figure

Dynamics of the Formation of Bright Solitary Waves of Bose-Einstein Condensates in Optical Lattices

We present a detailed description of the formation of bright solitary waves in optical lattices. To this end, we have considered a ring lattice geometry with large radius. In this case, the ring shape does not have a relevant effect in the local dynamics of the condensate, while offering a realistic set up to implement experiments with conditions usually not available with linear lattices (in particular, to study collisions). Our numerical results suggest that the condensate radiation is the relevant dissipative process in the relaxation towards a self-trapped solution. We show that the source of dissipation can be attributed to the presence of higher order dispersion terms in the effective mass approach. In addition, we demonstrate that the stability of the solitary solutions is linked with particular values of the width of the wavepacket in the reciprocal space. Our study suggests that these critical widths for stability depend on the geometry of the energy band, but are independent of the condensate parameters (momentum, atom number, etc.). Finally, the non-solitonic nature of the solitary waves is evidenced showing their instability under collisions.Comment: 7 pages, 7 figures, to appear in PR