5,425 research outputs found

    On probabilistic analog automata

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    We consider probabilistic automata on a general state space and study their computational power. The model is based on the concept of language recognition by probabilistic automata due to Rabin and models of analog computation in a noisy environment suggested by Maass and Orponen, and Maass and Sontag. Our main result is a generalization of Rabin's reduction theorem that implies that under very mild conditions, the computational power of the automaton is limited to regular languages

    General Relation between Entanglement and Fluctuations in One Dimension

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    In one dimension very general results from conformal field theory and exact calculations for certain quantum spin systems have established universal scaling properties of the entanglement entropy between two parts of a critical system. Using both analytical and numerical methods, we show that if particle number or spin is conserved, fluctuations in a subsystem obey identical scaling as a function of subsystem size, suggesting that fluctuations are a useful quantity for determining the scaling of entanglement, especially in higher dimensions. We investigate the effects of boundaries and subleading corrections for critical spin and bosonic chains.Comment: 4 pages, 2 figures. Minor changes, references added

    Chaotic quantum ratchets and filters with cold atoms in optical lattices: properties of Floquet states

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    Recently, cesium atoms in optical lattices subjected to cycles of unequally-spaced pulses have been found to show interesting behavior: they represent the first experimental demonstration of a Hamiltonian ratchet mechanism, and they show strong variability of the Dynamical Localization lengths as a function of initial momentum. The behavior differs qualitatively from corresponding atomic systems pulsed with equal periods, which are a textbook implementation of a well-studied quantum chaos paradigm, the quantum delta-kicked particle (delta-QKP). We investigate here the properties of the corresponding eigenstates (Floquet states) in the parameter regime of the new experiments and compare them with those of the eigenstates of the delta-QKP at similar kicking strengths. We show that, with the properties of the Floquet states, we can shed light on the form of the observed ratchet current as well as variations in the Dynamical Localization length.Comment: 9 pages, 9 figure

    Design of small CRPA arrays with circular microstrip loops for electromagnetically coupled feed

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    This paper proposes a design of small controlled reception pattern antenna (CRPA) arrays using circular microstrip loops with frequencyinsensitive characteristics. The proposed array consists of seven identical upper and lower circular loops that are electromagnetically coupled, which results in a frequency-insensitive behavior. To demonstrate the feasibility of the proposed feeding mechanism, the proposed array is fabricated, and its antenna characteristics are measured in a full-anechoic chamber. The operating principle of the proposed feeding mechanism is then interpreted using an equivalent circuit model, and the effectiveness of the circular loop shape is demonstrated by calculating near electromagnetic fields in proximity to the radiator. The results confirm that the proposed feeding mechanism is suitable to have frequency- insensitive behavior and induces strong electric and magnetic field strengths for higher radiation gain in extremely small antenna arrays

    Time-reversal symmetry breaking in circuit-QED based photon lattices

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    Breaking time-reversal symmetry is a prerequisite for accessing certain interesting many-body states such as fractional quantum Hall states. For polaritons, charge neutrality prevents magnetic fields from providing a direct symmetry breaking mechanism and similar to the situation in ultracold atomic gases, an effective magnetic field has to be synthesized. We show that in the circuit QED architecture, this can be achieved by inserting simple superconducting circuits into the resonator junctions. In the presence of such coupling elements, constant parallel magnetic and electric fields suffice to break time-reversal symmetry. We support these theoretical predictions with numerical simulations for realistic sample parameters, specify general conditions under which time-reversal is broken, and discuss the application to chiral Fock state transfer, an on-chip circulator, and tunable band structure for the Kagome lattice.Comment: minor revisions, version published in PRA; 19 pages, 13 figures, 2 table

    Entanglement from Charge Statistics: Exact Relations for Many-Body Systems

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    We present exact formulas for the entanglement and R\'{e}nyi entropies generated at a quantum point contact (QPC) in terms of the statistics of charge fluctuations, which we illustrate with examples from both equilibrium and non-equilibrium transport. The formulas are also applicable to groundstate entanglement in systems described by non-interacting fermions in any dimension, which in one dimension includes the critical spin-1/2 XX and Ising models where conformal field theory predictions for the entanglement and R\'{e}nyi entropies are reproduced from the full counting statistics. These results may play a crucial role in the experimental detection of many-body entanglement in mesoscopic structures and cold atoms in optical lattices

    Scaling of entanglement entropy across Lifshitz transitions

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    We investigate the scaling of the bipartite entanglement entropy across Lifshitz quantum phase transitions, where the topology of the Fermi surface changes without any changes in symmetry. We present both numerical and analytical results which show that Lifshitz transitions are characterized by a well-defined set of critical exponents for the entanglement entropy near the phase transition. In one dimension, we show that the entanglement entropy exhibits a length scale that diverges as the system approaches a Lifshitz critical point. In two dimensions, the leading and sub-leading coefficients of the scaling of entanglement entropy show distinct power-law singularities at critical points. The effect of weak interactions is investigated using the density matrix renormalization group algorithm.Comment: 11 pages, 11 figures; v2) references adde
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