TY - JOUR
AB - We construct a complete set of local integrals of motion that characterize the many-body localized (MBL) phase. Our approach relies on the assumption that local perturbations act locally on the eigenstates in the MBL phase, which is supported by numerical simulations of the random-field XXZ spin chain. We describe the structure of the eigenstates in the MBL phase and discuss the implications of local conservation laws for its nonequilibrium quantum dynamics. We argue that the many-body localization can be used to protect coherence in the system by suppressing relaxation between eigenstates with different local integrals of motion.
AU - Maksym Serbyn
AU - Papić, Zlatko
AU - Abanin, Dmitry A
ID - 973
IS - 12
JF - Physical Review Letters
TI - Local conservation laws and the structure of the many body localized states
VL - 111
ER -
TY - JOUR
AB - We propose a possible realization of the overscreened Kondo impurity problem by a magnetic s=1/2 impurity embedded in a two-dimensional S=1 U(1) spin liquid with a Fermi surface. This problem contains an interesting interplay between non-Fermi-liquid behavior induced by a U(1) gauge field coupled to fermions and a non-Fermi-liquid fixed point in the overscreened Kondo problem. Using a large-N expansion together with an expansion in the dynamical exponent of the gauge field, we find that the coupling to the gauge field leads to weak but observable changes in the physical properties of the system at the overscreened Kondo fixed point. We discuss the extrapolation of this result to a physical case and argue that the realization of overscreened Kondo physics could lead to observations of effects due to gauge fields.
AU - Serbyn, Maksym
AU - Senthil, Todadri
AU - Lee, Patrick
ID - 974
IS - 2
JF - Physical Review B - Condensed Matter and Materials Physics
TI - Overscreened Kondo fixed point in S=1 spin liquid
VL - 88
ER -
TY - JOUR
AB - Recent numerical work by Bardarson, Pollmann, and Moore revealed a slow, logarithmic in time, growth of the entanglement entropy for initial product states in a putative many-body localized phase. We show that this surprising phenomenon results from the dephasing due to exponentially small interaction-induced corrections to the eigenenergies of different states. For weak interactions, we find that the entanglement entropy grows as ξln (Vt/), where V is the interaction strength, and ξ is the single-particle localization length. The saturated value of the entanglement entropy at long times is determined by the participation ratios of the initial state over the eigenstates of the subsystem. Our work shows that the logarithmic entanglement growth is a universal phenomenon characteristic of the many-body localized phase in any number of spatial dimensions, and reveals a broad hierarchy of dephasing time scales present in such a phase.
AU - Maksym Serbyn
AU - Papić, Zlatko
AU - Abanin, Dmitry A
ID - 975
IS - 26
JF - Physical Review Letters
TI - Universal slow growth of entanglement in interacting strongly disordered systems
VL - 110
ER -
TY - JOUR
AB - Motivated by a search for experimental probes to access the physics of fractionalized excitations called spinons in spin liquids, we study the interaction of spinons with lattice vibrations. We consider the case of algebraic spin liquid, when spinons have fermionic statistics and a Dirac-like dispersion. We establish the general procedure for deriving spinon-phonon interactions, which is based on symmetry considerations. The procedure is illustrated for four different algebraic spin liquids: π-flux and staggered-flux phases on a square lattice, π-flux phase on a kagome lattice, and zero-flux phase on a honeycomb lattice. Although the low-energy description is similar for all these phases, different underlying symmetry groups lead to a distinct form of spinon-phonon interaction Hamiltonian. The explicit form of the spinon-phonon interaction is used to estimate the attenuation of ultrasound in an algebraic spin liquid. The prospects of the sound attenuation as a probe of spinons are discussed.
AU - Maksym Serbyn
AU - Lee, Patrick
ID - 976
IS - 17
JF - Physical Review B - Condensed Matter and Materials Physics
TI - Spinon-phonon interaction in algebraic spin liquids
VL - 87
ER -
TY - CONF
AB - We study two-player zero-sum games over infinite-state graphs equipped with ωB and finitary conditions. Our first contribution is about the strategy complexity, i.e the memory required for winning strategies: we prove that over general infinite-state graphs, memoryless strategies are sufficient for finitary Büchi, and finite-memory suffices for finitary parity games. We then study pushdown games with boundedness conditions, with two contributions. First we prove a collapse result for pushdown games with ωB-conditions, implying the decidability of solving these games. Second we consider pushdown games with finitary parity along with stack boundedness conditions, and show that solving these games is EXPTIME-complete.
AU - Chatterjee, Krishnendu
AU - Fijalkow, Nathanaël
ID - 1374
T2 - 22nd EACSL Annual Conference on Computer Science Logic
TI - Infinite-state games with finitary conditions
VL - 23
ER -
TY - CONF
AB - It is often difficult to correctly implement a Boolean controller for a complex system, especially when concurrency is involved. Yet, it may be easy to formally specify a controller. For instance, for a pipelined processor it suffices to state that the visible behavior of the pipelined system should be identical to a non-pipelined reference system (Burch-Dill paradigm). We present a novel procedure to efficiently synthesize multiple Boolean control signals from a specification given as a quantified first-order formula (with a specific quantifier structure). Our approach uses uninterpreted functions to abstract details of the design. We construct an unsatisfiable SMT formula from the given specification. Then, from just one proof of unsatisfiability, we use a variant of Craig interpolation to compute multiple coordinated interpolants that implement the Boolean control signals. Our method avoids iterative learning and back-substitution of the control functions. We applied our approach to synthesize a controller for a simple two-stage pipelined processor, and present first experimental results.
AU - Hofferek, Georg
AU - Gupta, Ashutosh
AU - Könighofer, Bettina
AU - Jiang, Jie
AU - Bloem, Roderick
ID - 1385
T2 - 2013 Formal Methods in Computer-Aided Design
TI - Synthesizing multiple boolean functions using interpolation on a single proof
ER -
TY - CONF
AB - Choices made by nondeterministic word automata depend on both the past (the prefix of the word read so far) and the future (the suffix yet to be read). In several applications, most notably synthesis, the future is diverse or unknown, leading to algorithms that are based on deterministic automata. Hoping to retain some of the advantages of nondeterministic automata, researchers have studied restricted classes of nondeterministic automata. Three such classes are nondeterministic automata that are good for trees (GFT; i.e., ones that can be expanded to tree automata accepting the derived tree languages, thus whose choices should satisfy diverse futures), good for games (GFG; i.e., ones whose choices depend only on the past), and determinizable by pruning (DBP; i.e., ones that embody equivalent deterministic automata). The theoretical properties and relative merits of the different classes are still open, having vagueness on whether they really differ from deterministic automata. In particular, while DBP ⊆ GFG ⊆ GFT, it is not known whether every GFT automaton is GFG and whether every GFG automaton is DBP. Also open is the possible succinctness of GFG and GFT automata compared to deterministic automata. We study these problems for ω-regular automata with all common acceptance conditions. We show that GFT=GFG⊃DBP, and describe a determinization construction for GFG automata.
AU - Boker, Udi
AU - Kuperberg, Denis
AU - Kupferman, Orna
AU - Skrzypczak, Michał
ID - 1387
IS - PART 2
TI - Nondeterminism in the presence of a diverse or unknown future
VL - 7966
ER -
TY - JOUR
AB - We give a cohomological interpretation of both the Kac polynomial and the refined Donaldson-Thomas-invariants of quivers. This interpretation yields a proof of a conjecture of Kac from 1982 and gives a new perspective on recent work of Kontsevich-Soibelman. Thisis achieved by computing, via an arithmetic Fourier transform, the dimensions of the isotypical components of the cohomology of associated Nakajima quiver varieties under the action of a Weyl group. The generating function of the corresponding Poincare polynomials is an extension of Hua's formula for Kac polynomials of quivers involving Hall-Littlewood symmetric functions. The resulting formulae contain a wide range of information on the geometry of the quiver varieties.
AU - Tamas Hausel
AU - Letellier, Emmanuel
AU - Rodríguez Villegas, Fernando
ID - 1442
IS - 3
JF - Annals of Mathematics
TI - Positivity for Kac polynomials and DT-invariants of quivers
VL - 177
ER -
TY - CHAP
AB - Here we survey several results and conjectures on the cohomology of the total space of the Hitchin system: the moduli space of semi-stable rank n and degree d Higgs bundles on a complex algebraic curve C. The picture emerging is a dynamic mixture of ideas originating in theoretical physics such as gauge theory and mirror symmetry, Weil conjectures in arithmetic algebraic geometry, representation theory of finite groups of Lie type and Langlands duality in number theory.
AU - Tamas Hausel
ID - 1443
T2 - Handbook of Moduli: Volume II
TI - Global topology of the Hitchin system
VL - 25
ER -
TY - JOUR
AB - We show that a natural isomorphism between the rational cohomology groups of the two zero-dimensional Hilbert schemes of n-points of two surfaces, the affine plane minus the axes and the cotangent bundle of an elliptic curve, exchanges the weight filtration on the first set of cohomology groups with the perverse Leray filtration associated with a natural fibration on the second set of cohomology groups. We discuss some associated hard Lefschetz phenomena.
AU - De Cataldo, Mark A
AU - Tamas Hausel
AU - Migliorini, Luca
ID - 1470
JF - Journal of Singularities
TI - Exchange between perverse and weight filtration for the Hilbert schemes of points of two surfaces
VL - 7
ER -
TY - JOUR
AB - Cells in a developing embryo have no direct way of "measuring" their physical position. Through a variety of processes, however, the expression levels of multiple genes come to be correlated with position, and these expression levels thus form a code for "positional information." We show how to measure this information, in bits, using the gap genes in the Drosophila embryo as an example. Individual genes carry nearly two bits of information, twice as much as expected if the expression patterns consisted only of on/off domains separated by sharp boundaries. Taken together, four gap genes carry enough information to define a cell's location with an error bar of ~1% along the anterior-posterior axis of the embryo. This precision is nearly enough for each cell to have a unique identity, which is the maximum information the system can use, and is nearly constant along the length of the embryo. We argue that this constancy is a signature of optimality in the transmission of information from primary morphogen inputs to the output of the gap gene network.
AU - Dubuis, Julien
AU - Tkacik, Gasper
AU - Wieschaus, Eric
AU - Gregor, Thomas
AU - Bialek, William
ID - 3261
IS - 41
JF - PNAS
TI - Positional information, in bits
VL - 110
ER -
TY - JOUR
AB - Copper-based selenides are attracting increasing interest due to their outstanding optoelectronic and thermoelectric properties. Herein a novel colloidal synthetic route to prepare Cu2SnSe3 nanocrystals with controlled size, shape and composition is presented. The high yield of the developed procedure allowed its up-scaling to the production of grams of colloidal Cu2SnSe3 nanocrystals. These nanocrystals were used as building blocks for the production of Cu2SnSe3 bulk nanostructured materials by spark plasma sintering. The thermoelectric properties of the prepared nanocrystalline Cu2SnSe3 pellets were characterized in the temperature range from 300 to 720 K. The obtained results show the bottom-up production of nanocrystalline materials from solution-processed nanocrystals to be a potentially advantageous alternative to conventional methods of production of efficient thermoelectric materials.
AU - Ibanez, Maria
AU - Cadavid, Doris
AU - Anselmi-Tamburini, Umberto
AU - Zamani, Reza R
AU - Gorsse, Stéphane
AU - Li, Wenhua
AU - López, Antonio M
AU - Morante, Joan R
AU - Arbiol, Jordi
AU - Cabot, Andreu
ID - 344
IS - 4
JF - Journal of Materials Chemistry A
TI - Colloidal synthesis and thermoelectric properties of Cu 2SnSe3 nanocrystals
VL - 1
ER -
TY - CONF
AB - Leakage resilient cryptography attempts to incorporate side-channel leakage into the black-box security model and designs cryptographic schemes that are provably secure within it. Informally, a scheme is leakage-resilient if it remains secure even if an adversary learns a bounded amount of arbitrary information about the schemes internal state. Unfortunately, most leakage resilient schemes are unnecessarily complicated in order to achieve strong provable security guarantees. As advocated by Yu et al. [CCS’10], this mostly is an artefact of the security proof and in practice much simpler construction may already suffice to protect against realistic side-channel attacks. In this paper, we show that indeed for simpler constructions leakage-resilience can be obtained when we aim for relaxed security notions where the leakage-functions and/or the inputs to the primitive are chosen non-adaptively. For example, we show that a three round Feistel network instantiated with a leakage resilient PRF yields a leakage resilient PRP if the inputs are chosen non-adaptively (This complements the result of Dodis and Pietrzak [CRYPTO’10] who show that if a adaptive queries are allowed, a superlogarithmic number of rounds is necessary.) We also show that a minor variation of the classical GGM construction gives a leakage resilient PRF if both, the leakage-function and the inputs, are chosen non-adaptively.
AU - Faust, Sebastian
AU - Pietrzak, Krzysztof Z
AU - Schipper, Joachim
ID - 2048
T2 - Conference proceedings CHES 2012
TI - Practical leakage-resilient symmetric cryptography
VL - 7428
ER -
TY - CONF
AB - We propose a new authentication protocol that is provably secure based on a ring variant of the learning parity with noise (LPN) problem. The protocol follows the design principle of the LPN-based protocol from Eurocrypt’11 (Kiltz et al.), and like it, is a two round protocol secure against active attacks. Moreover, our protocol has small communication complexity and a very small footprint which makes it applicable in scenarios that involve low-cost, resource-constrained devices.
Performance-wise, our protocol is more efficient than previous LPN-based schemes, such as the many variants of the Hopper-Blum (HB) protocol and the aforementioned protocol from Eurocrypt’11. Our implementation results show that it is even comparable to the standard challenge-and-response protocols based on the AES block-cipher. Our basic protocol is roughly 20 times slower than AES, but with the advantage of having 10 times smaller code size. Furthermore, if a few hundred bytes of non-volatile memory are available to allow the storage of some off-line pre-computations, then the online phase of our protocols is only twice as slow as AES.
AU - Heyse, Stefan
AU - Kiltz, Eike
AU - Lyubashevsky, Vadim
AU - Paar, Christof
AU - Pietrzak, Krzysztof Z
ID - 2049
T2 - Conference proceedings FSE 2012
TI - Lapin: An efficient authentication protocol based on ring-LPN
VL - 7549
ER -
TY - JOUR
AB - We consider a class of stochastic PDEs of Burgers type in spatial dimension 1, driven by space–time white noise. Even though it is well known that these equations are well posed, it turns out that if one performs a spatial discretization of the nonlinearity in the “wrong” way, then the sequence of approximate equations does converge to a limit, but this limit exhibits an additional correction term. This correction term is proportional to the local quadratic cross-variation (in space) of the gradient of the conserved quantity with the solution itself. This can be understood as a consequence of the fact that for any fixed time, the law of the solution is locally equivalent to Wiener measure, where space plays the role of time. In this sense, the correction term is similar to the usual Itô–Stratonovich correction term that arises when one considers different temporal discretizations of stochastic ODEs.
AU - Hairer, Martin M
AU - Jan Maas
ID - 2125
IS - 4
JF - Annals of Probability
TI - A spatial version of the Itô-Stratonovich correction
VL - 40
ER -
TY - JOUR
AB - We study a new notion of Ricci curvature that applies to Markov chains on discrete spaces. This notion relies on geodesic convexity of the entropy and is analogous to the one introduced by Lott, Sturm, and Villani for geodesic measure spaces. In order to apply to the discrete setting, the role of the Wasserstein metric is taken over by a different metric, having the property that continuous time Markov chains are gradient flows of the entropy. Using this notion of Ricci curvature we prove discrete analogues of fundamental results by Bakry–Émery and Otto–Villani. Further, we show that Ricci curvature bounds are preserved under tensorisation. As a special case we obtain the sharp Ricci curvature lower bound for the discrete hypercube.
AU - Erbar, Matthias
AU - Jan Maas
ID - 2127
IS - 3
JF - Archive for Rational Mechanics and Analysis
TI - Ricci curvature of finite Markov chains via convexity of the entropy
VL - 206
ER -
TY - JOUR
AB - We introduce a technique for handling Whitney decompositions in Gaussian harmonic analysis and apply it to the study of Gaussian analogues of the classical tent spaces T 1,q of Coifman–Meyer–Stein.
AU - Jan Maas
AU - van Neerven, Jan M
AU - Portal, Pierre
ID - 2128
IS - 2
JF - Arkiv för Matematik
TI - Whitney coverings and the tent spaces T 1,q (γ) for the Gaussian measure
VL - 50
ER -
TY - JOUR
AU - Mikhail Lemeshko
AU - Krems, Roman V
AU - Weimer, Hendrik A
ID - 2151
IS - 4
JF - Physical Review Letters
TI - Erratum: Nonadiabatic preparation of spin crystals with ultracold polar molecules
VL - 109
ER -
TY - JOUR
AB - We study the growth dynamics of ordered structures of strongly interacting polar molecules in optical lattices. Using a dipole blockade of microwave excitations, we map the system onto an interacting spin-1/2 model possessing ground states with crystalline order, and describe a way to prepare these states by nonadiabatically driving the transitions between molecular rotational levels. The proposed technique bypasses the need to cross a phase transition and allows for the creation of ordered domains of considerably larger size compared to approaches relying on adiabatic preparation.
AU - Mikhail Lemeshko
AU - Krems, Roman V
AU - Weimer, Hendrik
ID - 2201
IS - 3
JF - Physical Review Letters
TI - Nonadiabatic preparation of spin crystals with ultracold polar molecules
VL - 109
ER -
TY - JOUR
AB - We propose a method for sensitive parallel detection of low-frequency electromagnetic fields based on the fine structure interactions in paramagnetic polar molecules. Compared to the recently implemented scheme employing ultracold 87Rb atoms by Böhi, the technique based on molecules offers a 100-fold higher sensitivity, the possibility to measure both the electric and magnetic field components, and a probe of a wide range of frequencies from the dc limit to the THz regime.
AU - Alyabyshev, Sergey V
AU - Mikhail Lemeshko
AU - Krems, Roman V
ID - 2202
IS - 1
JF - Physical Review A - Atomic, Molecular, and Optical Physics
TI - Sensitive imaging of electromagnetic fields with paramagnetic polar molecules
VL - 86
ER -