Existence of Monetary Steady States in a Matching Model: Indivisible Money

Existence of a monetary steady state is established for a random matching model with divisible goods, indivisible money, and take-it-or-leave-it offers by consumers. There is no restriction on individual money holdings. The background environment is that in papers by Shi and by Trejos and Wright. The monetary steady state shown to exist has nice properties: the value function, defined on money holdings, is increasing and strictly concave, and the measure over money holdings has full support.

Effective dynamics of strongly dissipative Rydberg gases

We investigate the evolution of interacting Rydberg gases in the limit of strong noise and dissipation. Starting from a description in terms of a Markovian quantum master equation we derive effective equations of motion that govern the dynamics on a "coarse-grained" timescale where fast dissipative degrees of freedom have been adiabatically eliminated. Specifically, we consider two scenarios which are of relevance for current theoretical and experimental studies --- Rydberg atoms in a two-level (spin) approximation subject to strong dephasing noise as well as Rydberg atoms under so-called electromagnetically induced transparency (EIT) conditions and fast radiative decay. In the former case we find that the effective dynamics is described by classical rate equations up to second order in an appropriate perturbative expansion. This drastically reduces the computational complexity of numerical simulations in comparison to the full quantum master equation. When accounting for the fourth order correction in this expansion, however, we find that the resulting equation breaks the preservation of positivity and thus cannot be interpreted as a proper classical master rate equation. In the EIT system we find that the expansion up to second order retains information not only on the "classical" observables, but also on some quantum coherences. Nevertheless, this perturbative treatment still achieves a non-trivial reduction of complexity with respect to the original problem

Light-cone-like spreading of correlations in a quantum many-body system

How fast can correlations spread in a quantum many-body system? Based on the seminal work by Lieb and Robinson, it has recently been shown that several interacting many-body systems exhibit an effective light cone that bounds the propagation speed of correlations. The existence of such a "speed of light" has profound implications for condensed matter physics and quantum information, but has never been observed experimentally. Here we report on the time-resolved detection of propagating correlations in an interacting quantum many-body system. By quenching a one-dimensional quantum gas in an optical lattice, we reveal how quasiparticle pairs transport correlations with a finite velocity across the system, resulting in an effective light cone for the quantum dynamics. Our results open important perspectives for understanding relaxation of closed quantum systems far from equilibrium as well as for engineering efficient quantum channels necessary for fast quantum computations.Comment: 7 pages, 5 figures, 2 table

Simulation of the many-body dynamical quantum Hall effect in an optical lattice

We propose an experimental scheme to simulate the many-body dynamical quantum Hall effect with ultra-cold bosonic atoms in a one-dimensional optical lattice. We first show that the required model Hamiltonian of a spin-1/2 Heisenberg chain with an effective magnetic field and tunable parameters can be realized in this system. For dynamical response to ramping the external fields, the quantized plateaus emerge in the Berry curvature of the interacting atomic spin chain as a function of the effective spin-exchange interaction. The quantization of this response in the parameter space with the interaction-induced topological transition characterizes the many-body dynamical quantum Hall effect. Furthermore, we demonstrate that this phenomenon can be observed in practical cold-atom experiments with numerical simulations.Comment: 8 pages, 3 figures; accepted in Quantum Information Processin

Enhancement of Rydberg-mediated single-photon nonlinearities by electrically tuned Förster resonances

We demonstrate experimentally that Stark-tuned Förster resonances can be used to substantially increase the interaction between individual photons mediated by Rydberg interaction inside an optical medium. This technique is employed to boost the gain of a Rydberg-mediated single-photon transistor and to enhance the non-destructive detection of single Rydberg atoms. Furthermore, our all-optical detection scheme enables high-resolution spectroscopy of two-state Förster resonances, revealing the fine structure splitting of high-n Rydberg states and the non-degeneracy of Rydberg Zeeman substates in finite fields. We show that the ∣50S1/2,48S1/2⟩↔∣49P1/2,48P1/2⟩ pair state resonance in 87Rb enables simultaneously a transistor gain G>100 and all-optical detection fidelity of single Rydberg atoms F>0.8. We demonstrate for the first time the coherent operation of the Rydberg transistor with G>2 by reading out the gate photon after scattering source photons. Comparison of the observed readout efficiency to a theoretical model for the projection of the stored spin wave yields excellent agreement and thus successfully identifies the main decoherence mechanism of the Rydberg transistor

Protocol analysis modulo combination of theories: A case study in Maude-NPA

There is a growing interest in formal methods and tools to analyze cryptographic protocols modulo algebraic properties of their underlying cryptographic functions. It is well-known that an intruder who uses algebraic equivalences of such functions can mount attacks that would be impossible if the cryptographic functions did not satisfy such equivalences. In practice, however, protocols use a collection of well-known functions, whose algebraic properties can naturally be grouped together as a union of theories E 1... ¿ n. Reasoning symbolically modulo the algebraic properties E 1... ¿ n requires performing (E 1... ¿ n)-unification. However, even if a unification algorithm for each individual E i is available, this requires combining the existing algorithms by methods that are highly non-deterministic and have high computational cost. In this work we present an alternative method to obtain unification algorithms for combined theories based on variant narrowing. Although variant narrowing is less efficient at the level of a single theory E i, it does not use any costly combination method. Furthermore, it does not require that each E i has a dedicated unification algorithm in a tool implementation. We illustrate the use of this method in the Maude-NPA tool by means of a well-known protocol requiring the combination of three distinct equational theories. © 2011 Springer-Verlag.R. Sasse and J. Meseguer have been partially supported by NSF Grants CNS0716638, CNS-0831064 and CNS-0904749. S. Escobar has been partially supported by the EU (FEDER) and the Spanish MEC/MICINN under grant TIN 2007-68093- C02-02. C. Meadows has been partially supported by NSF Grant CNS-0904749National Science Foundation, EEUUSasse, R.; Escobar Román, S.; Meadows, C.; Meseguer, J. (2011). Protocol analysis modulo combination of theories: A case study in Maude-NPA. En Security and Trust Management. Springer Verlag (Germany). 6710:163-178. doi:10.1007/978-3-642-22444-7_11S1631786710Abadi, M., Cortier, V.: Deciding knowledge in security protocols under equational theories. Theoretical Computer Science 367(1-2), 2–32 (2006)Armando, A., Basin, D.A., Boichut, Y., Chevalier, Y., Compagna, L., Cuéllar, J., Drielsma, P.H., Héam, P.-C., Kouchnarenko, O., Mantovani, J., Mödersheim, S., von Oheimb, D., Rusinowitch, M., Santiago, J., Turuani, M., Viganò, L., Vigneron, L.: The avispa tool for the automated validation of internet security protocols and applications. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 281–285. Springer, Heidelberg (2005)Baader, F., Schulz, K.U.: Unification in the union of disjoint equational theories: Combining decision procedures. In: Kapur, D. (ed.) CADE 1992. LNCS, vol. 607, pp. 50–65. Springer, Heidelberg (1992)Basin, D.A., Mödersheim, S., Viganò, L.: An on-the-fly model-checker for security protocol analysis. 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Comput. 206(2-4), 352–377 (2008)Chevalier, Y., Rusinowitch, M.: Symbolic protocol analysis in the union of disjoint intruder theories: Combining decision procedures. Theor. Comput. Sci. 411(10), 1261–1282 (2010)Ciobâcă, Ş., Delaune, S., Kremer, S.: Computing knowledge in security protocols under convergent equational theories. In: Schmidt, R.A. (ed.) CADE-22. LNCS, vol. 5663, pp. 355–370. Springer, Heidelberg (2009)Comon-Lundh, H., Delaune, S.: The finite variant property: How to get rid of some algebraic properties. In: Giesl, J. (ed.) RTA 2005. LNCS, vol. 3467, pp. 294–307. Springer, Heidelberg (2005)Cortier, V., Delaitre, J., Delaune, S.: Safely composing security protocols. In: Arvind, V., Prasad, S. (eds.) FSTTCS 2007. LNCS, vol. 4855, pp. 352–363. Springer, Heidelberg (2007)Cremers, C.J.F.: The scyther tool: Verification, falsification, and analysis of security protocols. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 414–418. Springer, Heidelberg (2008)Escobar, S., Meadows, C., Meseguer, J.: A rewriting-based inference system for the NRL protocol analyzer and its meta-logical properties. Theoretical Computer Science 367(1-2), 162–202 (2006)Escobar, S., Meadows, C., Meseguer, J.: Maude-NPA: Cryptographic protocol analysis modulo equational properties. In: Aldini, A., Barthe, G., Gorrieri, R. (eds.) FOSAD 2007/2008/2009 Tutorial Lectures. LNCS, vol. 5705, pp. 1–50. Springer, Heidelberg (2009)Escobar, S., Meseguer, J., Sasse, R.: Effectively checking or disproving the finite variant property. Technical Report UIUCDCS-R-2008-2960, Department of Computer Science - University of Illinois at Urbana-Champaign (April 2008)Escobar, S., Meseguer, J., Sasse, R.: Effectively checking the finite variant property. In: Voronkov, A. (ed.) RTA 2008. LNCS, vol. 5117, pp. 79–93. Springer, Heidelberg (2008)Escobar, S., Meseguer, J., Sasse, R.: Variant narrowing and equational unification. Electr. Notes Theor. Comput. 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A Proof Theoretic Analysis of Intruder Theories

We consider the problem of intruder deduction in security protocol analysis: that is, deciding whether a given message M can be deduced from a set of messages Gamma under the theory of blind signatures and arbitrary convergent equational theories modulo associativity and commutativity (AC) of certain binary operators. The traditional formulations of intruder deduction are usually given in natural-deduction-like systems and proving decidability requires significant effort in showing that the rules are "local" in some sense. By using the well-known translation between natural deduction and sequent calculus, we recast the intruder deduction problem as proof search in sequent calculus, in which locality is immediate. Using standard proof theoretic methods, such as permutability of rules and cut elimination, we show that the intruder deduction problem can be reduced, in polynomial time, to the elementary deduction problem, which amounts to solving certain equations in the underlying individual equational theories. We show that this result extends to combinations of disjoint AC-convergent theories whereby the decidability of intruder deduction under the combined theory reduces to the decidability of elementary deduction in each constituent theory. To further demonstrate the utility of the sequent-based approach, we show that, for Dolev-Yao intruders, our sequent-based techniques can be used to solve the more difficult problem of solving deducibility constraints, where the sequents to be deduced may contain gaps (or variables) representing possible messages the intruder may produce.Comment: Extended version of RTA 2009 pape

Magnetic crystals and helical liquids in alkaline-earth fermionic gases

The joint action of a synthetic gauge potential and of atomic contact repulsion in a one-dimensional alkaline-earth(-like) fermionic gas with nuclear spin I leads to the existence of a hierarchy of fractional insulating and conducting states with intriguing properties. We unveil the existence and the features of those phases by means of both analytical bosonization techniques and numerical methods based on the density-matrix renormalization group algorithm. In particular, we show that the gapless phases can support helical modes, whereas the gapped states, which appear under certain conditions, are characterised both by density and magnetic order. Several distinct features emerge solely for spin I larger than 1/2, thus making their study with cold-atoms unique. We will finally argue that these states are related to the properties of an unconventional fractional quantum Hall effect in the thin-torus limit. The properties of this hierarchy of states can be experimentally studied in state-of-the-art cold-atom laboratories