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Adiabatic theorem for bipartite quantum systems in weak coupling limit

We study the adiabatic approximation of the dynamics of a bipartite quantum system with respect to one of the components, when the coupling between its two components is perturbative. We show that the density matrix of the considered component is described by adiabatic transport formulae exhibiting operator-valued geometric and dynamical phases. The present results can be used to study the quantum control of the dynamics of qubits and of open quantum systems where the two components are the system and its environment. We treat two examples, the control of an atomic qubit interacting with another one and the control of a spin in the middle of a Heisenberg spin chain

Screening variability and change of soil moisture under wide-ranging climate conditions : Snow dynamics effects

Acknowledgments This work has been supported by the Stockholm University strategic environmental research program Ekoklim and The Swedish Research Council Formas (project 2012-790).Peer reviewedPublisher PD

Coulombic Quantum Liquids in Spin-1/2 Pyrochlores

We develop a non-perturbative "gauge Mean Field Theory" (gMFT) method to study a general effective spin-1/2 model for magnetism in rare earth pyrochlores. gMFT is based on a novel exact slave-particle formulation, and matches both the perturbative regime near the classical spin ice limit and the semiclassical approximation far from it. We show that the full phase diagram contains two exotic phases: a quantum spin liquid and a coulombic ferromagnet, both of which support deconfined spinon excitations and emergent quantum electrodynamics. Phenomenological properties of these phases are discussed.Comment: 4+ pages, 6+ pages of Supplementary Material, 4 figures, 1 tabl

Analyses of the transmission of the disorder from a disturbed environment to a spin chain

We study spin chains submitted to disturbed kick trains described by classical dynamical processes. The spin chains are described by Heisenberg and Ising models. We consider decoherence, entanglement and relaxation processes induced by the kick irregularity in the multipartite system (the spin chain). We show that the different couplings transmit the disorder along the chain differently and also to each spin density matrix with different efficiencies. In order to analyze and to interpret the observed effects we use a semi-classical analysis across the Husimi distribution. It consists to consider the classical spin orientation movements. A possibility of conserving the order into the spin chain is finally analyzed.Comment: arXiv admin note: substantial text overlap with arXiv:1402.241

Quantum chimera states

We study a theoretical model of closed quasi-hermitian chain of spins which exhibits quantum analogues of chimera states, i.e. long life classical states for which a part of an oscillator chain presents an ordered dynamics whereas another part presents a disordered chaotic dynamics. For the quantum analogue, the chimera behavior deals with the entanglement between the spins of the chain. We discuss the entanglement properties, quantum chaos, quantum disorder and semi-classical similarity of our quantum chimera system. The quantum chimera concept is novel and induces new perspectives concerning the entanglement of multipartite systems

Spin Liquid Regimes at Nonzero Temperature in Quantum Spin Ice

Quantum spin liquids are highly entangled ground states of quantum systems with emergent gauge structure, fractionalized spinon excitations, and other unusual properties. While these features clearly distinguish quantum spin liquids from conventional, mean-field-like states at zero temperature (T), their status at T>0 is less clear. Strictly speaking, it is known that most quantum spin liquids lose their identity at non-zero temperature, being in that case adiabatically transformable into a trivial paramagnet. This is the case for the U(1) quantum spin liquid states recently proposed to occur in the quantum spin ice pyrochlores. Here we propose, however, that in practical terms, the latter quantum spin liquids can be regarded as distinct phases from the high temperature paramagnet. Through a combination of gauge mean field theory calculations and physical reasoning, we argue that these systems sustain both quantum spin liquid and thermal spin liquid phases, dominated by quantum fluctuations and entropy, respectively. These phases are separated by a first order "thermal confinement" transition, such that for temperatures below the transition, spinons and emergent photons are coherently propagating excitations, and above it the dynamics is classical. Even for parameters for which the ground state is magnetically ordered and not a quantum spin liquid, this strong first order transition occurs, pre-empting conventional Landau-type criticality. We argue that this picture explains the anomalously low temperature phase transition observed in the quantum spin ice material Yb2Ti2O7.Comment: 15 pages (including 7 pages of appendices), 3 figures, 1 tabl

Chebyshev's bias for products of irreducible polynomials

For any $k\geq 1$, this paper studies the number of polynomials having $k$ irreducible factors (counted with or without multiplicities) in $\mathbf{F}_q[t]$ among different arithmetic progressions. We obtain asymptotic formulas for the difference of counting functions uniformly for $k$ in a certain range. In the generic case, the bias dissipates as the degree of the modulus or $k$ gets large, but there are cases when the bias is extreme. In contrast to the case of products of $k$ prime numbers, we show the existence of complete biases in the function field setting, that is the difference function may have constant sign. Several examples illustrate this new phenomenon.Comment: The exposition has been improved, we now present the case of the number of irreducible factors both counting and not counting multiplicities. We also add some results on the possible values of the bia