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  • 1.
    Aurell, Erik
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST). Aalto Univ ;Chinese Acad Sci.
    Global Estimates of Errors in Quantum Computation by the Feynman-Vernon Formalism2018In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 171, no 5, p. 745-767Article in journal (Refereed)
    Abstract [en]

    The operation of a quantum computer is considered as a general quantum operation on a mixed state on many qubits followed by a measurement. The general quantum operation is further represented as a Feynman-Vernon double path integral over the histories of the qubits and of an environment, and afterward tracing out the environment. The qubit histories are taken to be paths on the two-sphere as in Klauder's coherent-state path integral of spin, and the environment is assumed to consist of harmonic oscillators initially in thermal equilibrium, and linearly coupled to to qubit operators . The environment can then be integrated out to give a Feynman-Vernon influence action coupling the forward and backward histories of the qubits. This representation allows to derive in a simple way estimates that the total error of operation of a quantum computer without error correction scales linearly with the number of qubits and the time of operation. It also allows to discuss Kitaev's toric code interacting with an environment in the same manner.

  • 2.
    Aurell, Erik
    et al.
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Gawȩdzki, K.
    Mejía-Monasterio, C.
    Mohayaee, R.
    Muratore-Ginanneschi, P.
    Refined Second Law of Thermodynamics for Fast Random Processes2012In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 147, no 3, p. 487-505Article in journal (Refereed)
    Abstract [en]

    We establish a refined version of the Second Law of Thermodynamics for Langevin stochastic processes describing mesoscopic systems driven by conservative or non-conservative forces and interacting with thermal noise. The refinement is based on the Monge-Kantorovich optimal mass transport and becomes relevant for processes far from quasi-stationary regime. General discussion is illustrated by numerical analysis of the optimal memory erasure protocol for a model for micron-size particle manipulated by optical tweezers.

  • 3. Balinsky, A.
    et al.
    Laptev, Ari
    KTH, Superseded Departments, Mathematics.
    Sobolev, A. V.
    Generalized Hardy inequality for the magnetic Dirichlet forms2004In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 116, no 4-Jan, p. 507-521Article in journal (Refereed)
    Abstract [en]

    We obtain lower bounds for the magnetic Dirichlet form in dimensions d greater than or equal to 2. For d = 2 the results generalize a well known lower bound by the magnetic field strength: we replace the actual magnetic field B by an non-vanishing effective field which decays outside the support of B as dist( x, supp B)(-2). In the case d greater than or equal to 3 we establish that the magnetic form is bounded from below by the magnetic field strength, if one assumes that the field does not vanish and its direction is slowly varying.

  • 4. Bermolen, Paola
    et al.
    Jonckheere, Matthieu
    Sanders, Jaron
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Scaling Limits and Generic Bounds for Exploration Processes2017In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 169, no 5, p. 989-1018Article in journal (Refereed)
    Abstract [en]

    We consider exploration algorithms of the random sequential adsorption type both for homogeneous random graphs and random geometric graphs based on spatial Poisson processes. At each step, a vertex of the graph becomes active and its neighboring nodes become blocked. Given an initial number of vertices N growing to infinity, we study statistical properties of the proportion of explored (active or blocked) nodes in time using scaling limits. We obtain exact limits for homogeneous graphs and prove an explicit central limit theorem for the final proportion of active nodes, known as the jamming constant, through a diffusion approximation for the exploration process which can be described as a unidimensional process. We then focus on bounding the trajectories of such exploration processes on random geometric graphs, i.e., random sequential adsorption. As opposed to exploration processes on homogeneous random graphs, these do not allow for such a dimensional reduction. Instead we derive a fundamental relationship between the number of explored nodes and the discovered volume in the spatial process, and we obtain generic bounds for the fluid limit and jamming constant: bounds that are independent of the dimension of space and the detailed shape of the volume associated to the discovered node. Lastly, using coupling techinques, we give trajectorial interpretations of the generic bounds.

  • 5.
    Björnberg, Jakob Erik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Critical Value of the Quantum Ising Model on Star-Like Graphs2009In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 135, no 3, p. 571-583Article in journal (Refereed)
    Abstract [en]

    We present a rigorous determination of the critical value of the ground-state quantum Ising model in a transverse field, on a class of planar graphs which we call star-like. These include the junction of several copies of a"currency sign at a single point. Our approach is to use the graphical, or fk-, representation of the model, and the probabilistic and geometric tools associated with it.

  • 6.
    Bo, Stefano
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden.
    Celani, A.
    Detecting Concentration Changes with Cooperative Receptors2015In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 162, no 5, p. 1365-1382Article in journal (Refereed)
    Abstract [en]

    Cells constantly need to monitor the state of the environment to detect changes and timely respond. The detection of concentration changes of a ligand by a set of receptors can be cast as a problem of hypothesis testing, and the cell viewed as a Neyman–Pearson detector. Within this framework, we investigate the role of receptor cooperativity in improving the cell’s ability to detect changes. We find that cooperativity decreases the probability of missing an occurred change. This becomes especially beneficial when difficult detections have to be made. Concerning the influence of cooperativity on how fast a desired detection power is achieved, we find in general that there is an optimal value at finite levels of cooperation, even though easy discrimination tasks can be performed more rapidly by noncooperative receptors.

  • 7.
    Chhita, Sunil
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    The Height Fluctuations of an Off-Critical Dimer Model on the Square Grid2012In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 148, no 1, p. 67-88Article in journal (Refereed)
    Abstract [en]

    The dimer model on a planar bipartite graph can be viewed as a random surface measure. We study these fluctuations for a dimer model on the square grid with two different classes of weights and provide a condition for their equivalence. In the thermodynamic limit and scaling window, these height fluctuations are shown to be non-Gaussian.

  • 8.
    de Woul, Jonas
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Gauge Invariance, Correlated Fermions, and Photon Mass in 2+1 Dimensions2014In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 154, no 3, p. 877-894Article in journal (Refereed)
    Abstract [en]

    We present a 2+1 dimensional quantum gauge theory with correlated fermions that is exactly solvable by bosonization. This model describes a system of Luttinger liquids propagating on two sets of equidistant lines forming a grid embedded in two dimensional continuum space; this system has two dimensional character due to density-density interactions and due to a coupling to dynamical photons propagating in the continuous embedding space. We argue that this model gives an effective description of partially gapped fermions on a square lattice that have density-density interactions and are coupled to photons. Our results include the following: after non-trivial renormalizations of the coupling parameters, the model remains well-defined in the quantum field theory limit as the grid of lines becomes a continuum; the photons in this model are massive due to gauge-invariant normal-ordering, similarly as in the Schwinger model; the exact excitation spectrum of the model has two gapped and one gapless mode.

  • 9.
    de Woul, Jonas
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Partially Gapped Fermions in 2D2010In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 139, no 6, p. 1033-1065Article in journal (Refereed)
    Abstract [en]

    We compute mean field phase diagrams of two closely related interacting fermion models in two spatial dimensions (2D). The first is the so-called 2D t-t'-V model describing spinless fermions on a square lattice with local hopping and density-density interactions. The second is the so-called 2D Luttinger model that provides an effective description of the 2D t-t'-V model and in which parts of the fermion degrees of freedom are treated exactly by bosonization. In mean field theory, both models have a charge-density-wave (CDW) instability making them gapped at half-filling. The 2D t-t'-V model has a significant parameter regime away from half-filling where neither the CDW nor the normal state are thermodynamically stable. We show that the 2D Luttinger model allows to obtain more detailed information about this mixed region. In particular, we find in the 2D Luttinger model a partially gapped phase that, as we argue, can be described by an exactly solvable model.

  • 10.
    Del Ferraro, Gino
    et al.
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Wang, Chuang
    Zhou, Hai-Jun
    Aurell, Erik
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. Aalto University, Finland.
    On one-step replica symmetry breaking in the Edwards-Anderson spin glass model2016In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, article id 073305Article in journal (Refereed)
    Abstract [en]

    We consider a one-step replica symmetry breaking description of the Edwards–Anderson spin glass model in 2D. The ingredients of this description are a Kikuchi approximation to the free energy and a second-level statistical model built on the extremal points of the Kikuchi approximation, which are also fixed points of a generalized belief propagation (GBP) scheme. We show that a generalized free energy can be constructed where these extremal points are exponentially weighted by their Kikuchi free energy and a Parisi parameter y, and that the Kikuchi approximation of this generalized free energy leads to second-level, one-step replica symmetry breaking (1RSB), GBP equations. We then proceed analogously to the Bethe approximation case for tree-like graphs, where it has been shown that 1RSB belief propagation equations admit a survey propagation solution. We discuss when and how the one-step-replica symmetry breaking GBP equations that we obtain also allow a simpler class of solutions which can be interpreted as a class of generalized survey propagation equations for the single instance graph case.

  • 11. Friedland, S.
    et al.
    Krop, E.
    Lundow, Per Håkan
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Condensed Matter Theory.
    Markstrom, K.
    On the Validations of the Asymptotic Matching Conjectures2008In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 133, no 3, p. 513-533Article in journal (Refereed)
    Abstract [en]

    In this paper we review the asymptotic matching conjectures for r-regular bipartite graphs, and their connections in estimating the monomer-dimer entropies in d-dimensional integer lattice and Bethe lattices. We prove new rigorous upper and lower bounds for the monomer-dimer entropies, which support these conjectures. We describe a general construction of infinite families of r-regular tori graphs and give algorithms for computing the monomer-dimer entropy of density p, for any p is an element of[0,1], for these graphs. Finally we use tori graphs to test the asymptotic matching conjectures for certain infinite r-regular bipartite graphs.

  • 12. Haggkvist, R.
    et al.
    Lundow, Per Håkan
    KTH, Superseded Departments, Physics.
    The Ising partition function for 2D grids with periodic boundary: Computation and analysis2002In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 108, no 04-mar, p. 429-457Article in journal (Refereed)
    Abstract [en]

    The Ising partition function for a graph counts the number of bipartitions of the vertices with given sizes, with a given size of the induced edge cut. Expressed as a 2-variable generating function it is easily translatable into the corresponding partition function studied in statistical physics. In the current paper a comparatively efficient transfer matrix method is described for computing the generating function for the nxn grid with periodic boundary. We have applied the method to up to the 15 x 15 grid, in total 225 vertices. We examine the phase transition that takes place when the edge cut reaches a certain critical size. From the physical partition function we extract quantities such as magnetisation and susceptibility and study their asymptotic behaviour at the critical temperature.

  • 13.
    Haimi, Antti
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Hedenmalm, Håkan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    The Polyanalytic Ginibre Ensembles2013In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 153, no 1, p. 10-47Article in journal (Refereed)
    Abstract [en]

    For integers n,q=1,2,3,aEuro broken vertical bar aEuro parts per thousand, let Pol (n,q) denote the -linear space of polynomials in z and , of degree a parts per thousand currency signn-1 in z and of degree a parts per thousand currency signq-1 in . We supply Pol (n,q) with the inner product structure of the resulting Hilbert space is denoted by Pol (m,n,q) . Here, it is assumed that m is a positive real. We let K (m,n,q) denote the reproducing kernel of Pol (m,n,q) , and study the associated determinantal process, in the limit as m,n ->+a while n=m+O(1); the number q, the degree of polyanalyticity, is kept fixed. We call these processes polyanalytic Ginibre ensembles, because they generalize the Ginibre ensemble-the eigenvalue process of random (normal) matrices with Gaussian weight. There is a physical interpretation in terms of a system of free fermions in a uniform magnetic field so that a fixed number of the first Landau levels have been filled. We consider local blow-ups of the polyanalytic Ginibre ensembles around points in the spectral droplet, which is here the closed unit disk . We obtain asymptotics for the blow-up process, using a blow-up to characteristic distance m (-1/2); the typical distance is the same both for interior and for boundary points of . This amounts to obtaining the asymptotical behavior of the generating kernel K (m,n,q) . Following (Ameur et al. in Commun. Pure Appl. Math. 63(12):1533-1584, 2010), the asymptotics of the K (m,n,q) are rather conveniently expressed in terms of the Berezin measure (and density) For interior points |z|< 1, we obtain that in the weak-star sense, where delta (z) denotes the unit point mass at z. Moreover, if we blow up to the scale of m (-1/2) around z, we get convergence to a measure which is Gaussian for q=1, but exhibits more complicated Fresnel zone behavior for q > 1. In contrast, for exterior points |z|> 1, we have instead that , where is the harmonic measure at z with respect to the exterior disk . For boundary points, |z|=1, the Berezin measure converges to the unit point mass at z, as with interior points, but the blow-up to the scale m (-1/2) exhibits quite different behavior at boundary points compared with interior points. We also obtain the asymptotic boundary behavior of the 1-point function at the coarser local scale q (1/2) m (-1/2).

  • 14. Häggkvist, R.
    et al.
    Rosengren, Anders
    KTH, Superseded Departments, Physics.
    Andrén, D.
    Kundrotas, Petras
    KTH, Superseded Departments, Physics.
    Lundow, Per Håkan
    KTH, Superseded Departments, Physics.
    Markström, K.
    A Monte Carlo sampling scheme for the Ising model2004In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 114, no 02-jan, p. 455-480Article in journal (Refereed)
    Abstract [en]

    In this paper we describe a Monte Carlo sampling scheme for the Ising model and similar discrete-state models. The scheme does not involve any particular method of state generation but rather focuses on a new way of measuring and using the Monte Carlo data. We show how to reconstruct the entropy S of the model, from which, e.g., the free energy can be obtained. Furthermore we discuss how this scheme allows us to more or less completely remove the effects of critical fluctuations near the critical temperature and likewise how it reduces critical slowing down. This makes it possible to use simple state generation methods like the Metropolis algorithm also for large lattices.

  • 15.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    A 2D Luttinger Model2010In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 141, no 1, p. 17-52Article in journal (Refereed)
    Abstract [en]

    A detailed derivation of a two dimensional (2D) low energy effective model for spinless fermions on a square lattice with local interactions is given. This derivation utilizes a particular continuum limit that is justified by physical arguments. It is shown that the effective model thus obtained can be treated by exact bosonization methods. It is also discussed how this effective model can be used to obtain physical information about the corresponding lattice fermion system.

  • 16.
    Langmann, Edwin
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Lindblad, Göran
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Fermi's Golden Rule and Exponential Decay as a RG Fixed Point2009In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 134, no 4, p. 749-768Article in journal (Refereed)
    Abstract [en]

    We discuss the decay of unstable states into a quasicontinuum using Hamiltonian models. We show that exponential decay and the golden rule are exact in a suitable scaling limit, and that there is an associated renormalization group (RG) with these properties as a fixed point. The method is inspired by a limit theorem for infinitely divisible distributions in probability theory, where there is a RG with a Cauchy distribution, i.e. a Lorentz line shape, as a fixed point. Our method of solving for the spectrum is well known; it does not involve a perturbation expansion in the interaction, and needs no assumption of a weak interaction. Using random matrices for the interaction we show that the ensemble fluctuations vanish in the scaling limit. For non-random models we can use uniformity assumptions on the density of states and the interaction matrix elements to estimate the deviations from the decay rate defined by the golden rule.

  • 17.
    Langmann, Edwin
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory. Univ Claude Bernard, Univ Lyon, ENS Lyon, CNRS,Lab Phys, F-69342 Lyon, France..
    Moosavi, Per
    KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Finite-Time Universality in Nonequilibrium CFT2018In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 172, no 2, p. 353-378Article in journal (Refereed)
    Abstract [en]

    Recently, remarkably simple exact results were presented about the dynamics of heat transport in the local Luttinger model for nonequilibrium initial states defined by position-dependent temperature profiles. We present mathematical details on how these results were obtained. We also give an alternative derivation using only algebraic relations involving the energy-momentum tensor which hold true in any unitary conformal field theory (CFT). This establishes a simple universal correspondence between initial temperature profiles and the resulting heat-wave propagation in CFT. We extend these results to larger classes of nonequilibrium states. It is proposed that such universal CFT relations provide benchmarks to identify nonuniversal properties of nonequilibrium dynamics in other models.

  • 18.
    Langmann, Edwin
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Wallin, Mats
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.
    Mean field magnetic phase diagrams for the two dimensional t-t '-U Hubbard model2007In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 127, no 4, p. 825-840Article in journal (Refereed)
    Abstract [en]

    We study the ground state phase diagram of the two dimensional t - t' - U Hubbard model concentrating on the competition between antiferro-, ferro-, and paramagnetism. It is known that unrestricted Hartree-Fock- and quantum Monte Carlo calculations for this model predict inhomogeneous states in large regions of the parameter space. Standard mean field theory, i.e., Hartree-Fock theory restricted to homogeneous states, fails to produce such inhomogeneous phases. We show that a generalization of the mean field method to the grand canonical ensemble circumvents this problem and predicts inhomogeneous states, represented by mixtures of homogeneous states, in large regions of the parameter space. We present phase diagrams which differ considerably from previous mean field results but are consistent with, and extend, results obtained with more sophisticated methods.

  • 19.
    Lundholm, Douglas
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Rougerie, Nicolas
    CNRS & LPMMC Grenoble.
    The Average Field Approximation for Almost Bosonic Extended Anyons2015In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 161, p. 1236-1267Article in journal (Refereed)
    Abstract [en]

    Anyons are 2D or 1D quantum particles with intermediate statistics, interpolating between bosons and fermions. We study the ground state of a large number N of 2D anyons, in a scaling limit where the statistics parameter α is proportional to N−1 when N→∞. This means that the statistics is seen as a “perturbation from the bosonic end”. We model this situation in the magnetic gauge picture by bosons interacting through long-range magnetic potentials. We assume that these effective statistical gauge potentials are generated by magnetic charges carried by each particle, smeared over discs of radius R (extended anyons). Our method allows to take R→0 not too fast at the same time as N→∞. In this limit we rigorously justify the so-called “average field approximation”: the particles behave like independent, identically distributed bosons interacting via a self-consistent magnetic field.

  • 20. Toppaladoddi, Srikanth
    et al.
    Wettlaufer, J. S.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Statistical Mechanics and the Climatology of the Arctic Sea Ice Thickness Distribution2017In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 167, no 3-4, p. 683-702Article in journal (Refereed)
    Abstract [en]

    We study the seasonal changes in the thickness distribution of Arctic sea ice, g(h), under climate forcing. Our analytical and numerical approach is based on a Fokker-Planck equation for g(h) (Toppaladoddi and Wettlaufer in Phys Rev Lett 115(14): 148501, 2015), in which the thermodynamic growth rates are determined using observed climatology. In particular, the Fokker-Planck equation is coupled to the observationally consistent thermodynamic model of Eisenman and Wettlaufer (Proc Natl Acad Sci USA 106: 28-32, 2009). We find that due to the combined effects of thermodynamics and mechanics, g(h) spreads during winter and contracts during summer. This behavior is in agreement with recent satellite observations from CryoSat-2 (Kwok and Cunningham in Philos Trans R Soc A 373(2045): 20140157, 2015). Because g(h) is a probability density function, we quantify all of the key moments (e. g., mean thickness, fraction of thin/thick ice, mean albedo, relaxation time scales) as greenhouse-gas radiative forcing, Delta F-0, increases. The mean ice thickness decays exponentially with Delta F-0, but much slower than do solely thermodynamic models. This exhibits the crucial role that ice mechanics plays in maintaining the ice cover, by redistributing thin ice to thick ice-far more rapidly than can thermal growth alone.

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