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We show that the entropy per quantum vortex per layer in superconductors in external magnetic fields is bounded by the universal value kBln 2, which explains puzzling results of recent experiments on the Nernst effect. The observed plateau of the Nernst signal as a function of the magnetic field is correspondingly attributed to a manifestation of the integer quantum Nernst effect.

Electric-magnetic duality or S-duality, extending the symmetry of Maxwell&rsquo, s equations by including the symmetry between Noether electric charges and topological magnetic monopoles, is one of the most fundamental concepts of modern physics. In two-dimensional systems harboring Cooper pairs, S-duality manifests in the emergence of superinsulation, a state dual to superconductivity, which exhibits an infinite resistance at finite temperatures. The mechanism behind this infinite resistance is the linear charge confinement by a magnetic monopole plasma. This plasma constricts electric field lines connecting the charge&ndash, anti-charge pairs into electric strings, in analogy to quarks within hadrons. However, the origin of the monopole plasma remains an open question. Here, we consider a two-dimensional Josephson junction array (JJA) and reveal that the magnetic monopole plasma arises as quantum instantons, thus establishing the underlying mechanism of superinsulation as two-dimensional quantum tunneling events. We calculate the string tension and the dimension of an electric pion determining the minimal size of a system capable of hosting superinsulation. Our findings pave the way for study of fundamental S-duality in desktop experiments on JJA and superconducting films.

Despite more than three decades of tireless efforts, the nature of high-temperature superconductivity (HTS) remains a mystery. A recently proposed long-distance effective field theory, accounting for all the universal features of HTS and the equally mysterious pseudogap phase, related them to the coexistence of a charge condensate with a condensate of dyons, particles carrying both magnetic and electric charges. Central to this picture are magnetic monopoles emerging in the proximity of the topological quantum superconductor-insulator transition (SIT) that dominates the HTS phase diagram. However, the mechanism responsible for spatially localized electron pairing, characteristic of HTS, remains a puzzle. Here we show that real-space, localized electron pairing is mediated by magnetic monopoles and occurs at temperatures well above the superconducting transition temperature $T_{\mathrm c}$. Localized electron pairing promotes the formation of superconducting granules connected by Josephson links. Global superconductivity sets in when these granules form an infinite cluster at $T_{\mathrm c}$ which is estimated to fall in the range from hundred to thousand Kelvins. Our findings pave the way to tailoring materials with elevated superconducting transition temperatures.

We provide a microscopic-level derivation of earlier results showing that in the critical vicinity of the superconductor-to-insulator transition (SIT), disorder and localization become negligible and the structure of the emergent phases is determined by topological effects arising from the competition between two quantum orders, superconductivity and superinsulation. We find that around the critical point the ground state is a composite incompressible quantum fluid of Cooper pairs and vortices coexisting with an intertwined Wigner crystal comprising the excesses of both types of excitations with respect to integer filling.

Despite decades-long efforts, magnetic monopoles were never found as elementary particles. Monopoles and associated currents were directly measured in experiments and identified as topological quasiparticle excitations in emergent condensed matter systems. These monopoles and the related electric-magnetic symmetry were restricted to classical electrodynamics, with monopoles behaving as classical particles. Here we show that the electric-magnetic symmetry is most fundamental and extends to full quantum behavior. We demonstrate that at low temperatures magnetic monopoles can form a quantum Bose condensate dual to the charge Cooper pair condensate in superconductors. The monopole Bose condensate manifests as a superinsulating state with infinite resistance, dual to superconductivity. Monopole supercurrents result in the electric analog of the Meissner effect and lead to linear confinement of Cooper pairs by Polyakov electric strings in analogy to quarks in hadrons., Comment: 6 pages, 2 figures

We consider a formal discretisation of Euclidean quantum gravity defined by a statistical model of random $3$-regular graphs and making using of the Ollivier curvature, a coarse analogue of the Ricci curvature. Numerical analysis shows that the Hausdorff and spectral dimensions of the model approach $1$ in the joint classical-thermodynamic limit and we argue that the scaling limit of the model is the circle of radius $r$, $S^1_r$. Given mild kinematic constraints, these claims can be proven with full mathematical rigour: speaking precisely, it may be shown that for $3$-regular graphs of girth at least $4$, any sequence of action minimising configurations converges in the sense of Gromov-Hausdorff to $S^1_r$. We also present strong evidence for the existence of a second-order phase transition through an analysis of finite size effects. This -- essentially solvable -- toy model of emergent one-dimensional geometry is meant as a controllable paradigm for the nonperturbative definition of random flat surfaces., Comment: Minor revisions

The key to unraveling the nature of high-temperature superconductivity (HTS) lies in resolving the enigma of the pseudogap state. The pseudogap state in the underdoped region is a distinct thermodynamic phase characterized by nematicity, temperature-quadratic resistive behavior, and magnetoelectric effects. Till present, a general description of the observed universal features of the pseudogap phase and their connection with HTS was lacking. The proposed work constructs a unifying effective field theory capturing all universal characteristics of HTS materials and explaining the observed phase diagram. The pseudogap state is established to be a phase where a charged magnetic monopole condensate confines Cooper pairs to form an oblique version of a superinsulator. The HTS phase diagram is dominated by a tricritical point (TCP) at which the first order transition between a fundamental Cooper pair condensate and a charged magnetic monopole condensate merges with the continuous superconductor-normal metal and superconductor-pseudogap state phase transitions. The universality of the HTS phase diagram reflects a unique topological mechanism of competition between the magnetic monopole condensate, inherent to antiferromagnetic-order-induced Mott insulators and the Cooper pair condensate. The obtained results establish the topological nature of the HTS and provide a platform for devising materials with the enhanced superconducting transition temperature.

Superinsulators (SI) are a new topological state of matter, predicted by our collaboration and experimentally observed in the critical vicinity of the superconductor-insulator transition (SIT). SI are dual to superconductors and realise electric-magnetic (S)-duality. The effective field theory that describes this topological phase of matter is governed by a compact Chern-Simons in (2+1) dimensions and a compact BF term in (3+1) dimensions. While in a superconductor the condensate of Cooper pairs generates the Meissner effect, which constricts the magnetic field lines penetrating a type II superconductor into Abrikosov vortices, in superinsulators Cooper pairs are linearly bound by electric fields squeezed into strings (dual Meissner effect) by a monopole condensate. Magnetic monopoles, while elusive as elementary particles, exist in certain materials in the form of emergent quasiparticle excitations. We demonstrate that at low temperatures magnetic monopoles can form a quantum Bose condensate (plasma in (2+1) dimensions) dual to the charge condensate in superconductors. The monopole Bose condensate manifests as a superinsulating state with infinite resistance, dual to superconductivity. The monopole supercurrents result in the electric analogue of the Meissner effect and lead to linear confinement of the Cooper pairs by Polyakov electric strings in analogy to quarks in hadrons. Superinsulators realise thus one of the mechanism proposed to explain confinement in QCD. Moreover, the string mechanism of confinement implies asymptotic freedom at the IR fixed point. We predict thus for superinsulators a metallic-like low temperature behaviour when samples are smaller than the string scale. This has been experimentally confirmed. We predict that an oblique version of SI is realised as the pseudogap state of high-TC superconductors.

We present a Euclidean quantum gravity model in which random graphs dynamically self-assemble into discrete manifold structures. Concretely, we consider a statistical model driven by a discretisation of the Euclidean Einstein-Hilbert action; contrary to previous approaches based on simplicial complexes and Regge calculus our discretisation is based on the Ollivier curvature, a coarse analogue of the manifold Ricci curvature defined for generic graphs. The Ollivier curvature is generally difficult to evaluate due to its definition in terms of optimal transport theory, but we present a new exact expression for the Ollivier curvature in a wide class of relevant graphs purely in terms of the numbers of short cycles at an edge. This result should be of independent intrinsic interest to network theorists. Action minimising configurations prove to be cubic complexes up to defects; there are indications that such defects are dynamically suppressed in the macroscopic limit. Closer examination of a defect free model shows that certain classical configurations have a geometric interpretation and discretely approximate vacuum solutions to the Euclidean Einstein-Hilbert action. Working in a configuration space where the geometric configurations are stable vacua of the theory, we obtain direct numerical evidence for the existence of a continuous phase transition; this makes the model a UV completion of Euclidean Einstein gravity. Notably, this phase transition implies an area-law for the entropy of emerging geometric space. Certain vacua of the theory can be interpreted as baby universes; we find that these configurations appear as stable vacua in a mean field approximation of our model, but are excluded dynamically whenever the action is exact indicating the dynamical stability of geometric space. The model is intended as a setting for subsequent studies of emergent time mechanisms., Comment: 26 pages, 9 figures, 2 appendices

It has been believed that the superinsulating state which is the low-temperature charge Berezinskii-Kosterlitz- Thouless (BKT) phase can exist only in two dimensions. We develop a general gauge description of the su- perinsulating state and the related deconfinement transition of Cooper pairs and predict the existence of the superinsulating state in three dimensions (3d). We find that 3d superinsulators exhibit Vogel-Fulcher-Tammann (VFT) critical behavior at the phase transition. This is the 3d string analogue of the Berezinski-Kosterlitz- Thouless (BKT) criticality for logarithmically and linearly interacting point particles in 2d. Our results show that singular exponential scaling behaviors of the BKT type are generic for phase transitions associated with the condensation of topological excitations., Comment: 5 pages, no figures

I propose a quantum gravity model in which geometric space emerges from random bits in a quantum phase transition driven by the combinatorial Ollivier-Ricci curvature and corresponding to the condensation of short cycles in random graphs. This quantum critical point defines quantum gravity non-perturbatively. In the ordered geometric phase at large distances the action reduces to the standard Einstein-Hilbert term., Revised version to appear in JHEP

By establishing a relation between information erasure and continuous phase transitions we generalise the Landauer bound to analog computing systems. The entropy production per degree of freedom during erasure of an analog variable (reset to standard value) is given by the logarithm of the configurational volume measured in units of its minimal quantum. As a consequence every computation has to be carried on with a finite number of bits and infinite precision is forbidden by the fundamental laws of physics, since it would require an infinite amount of energy., 5 pages, no figures, to appear in Phys. Rev. E

Recently I proposed a simple dynamical network model for discrete space-time which self-organizes as a graph with Hausdorff dimension d_H=4. The model has a geometric quantum phase transition with disorder parameter (d_H-d_s) where d_s is the spectral dimension of the dynamical graph. Self-organization in this network model is based on a competition between a ferromagnetic Ising model for vertices and an antiferromagnetic Ising model for edges. In this paper I solve a toy version of this model defined on a bipartite graph in the mean field approximation. I show that the geometric phase transition corresponds exactly to the antiferromagnetic transition for edges, the dimensional disorder parameter of the former being mapped to the staggered magnetization order parameter of the latter. The model has a critical point with long-range correlations between edges, where a continuum random geometry can be defined, exactly as in Kazakov's famed 2D random lattice Ising model but now in any number of dimensions., Comment: To appear in Physical Review E

I review and expand the model of quantum associative memory that I have recently proposed. In this model binary patterns of n bits are stored in the quantum superposition of the appropriate subset of the computational basis of n qbits. Information can be retrieved by performing an input-dependent rotation of the memory quantum state within this subset and measuring the resulting state. The amplitudes of this rotated memory state are peaked on those stored patterns which are closest in Hamming distance to the input, resulting in a high probability of measuring a memory pattern very similar to it. The accuracy of pattern recall can be tuned by adjusting a parameter playing the role of an effective temperature. This model solves the well-known capacity shortage problem of classical associative memories, providing a large improvement in capacity. PACS: 03.67.-a

Spin-charge separation, a crucial ingredient in 2D models of strongly correlated systems, in mostly considered in condensed matter applications. In this paper we present a relativistic field-theoretic model in which charged particles of spin 1/2 emerge by soldering spinless charges and magnetic vortices in a confinement quantum phase transition modelled as a tensor Higgs mechanism. The model involves two gauge fields, a vector one and a two-form gauge field interacting by the topological BF term. When this tensor gauge symmetry is spontaneously broken charges are soldered to the ends of magnetic vortices and thus confined by a linear potential. If the vector potential has a topological $\theta $-term with value $\theta = \pi$, the constituents of this "meson" acquire spin 1/2 in this transition., Comment: 5 pages, no figures. arXiv admin note: substantial text overlap with arXiv:1112.3281

We propose a new string model by adding a higher-order gradient term to the rigid string, so that the stiffness can be positive or negative without loosing stability. In the large-D approximation, the model has three phases, one of which with a new type of generalized "antiferromagnetic" orientational correlations. We find an infrared-stable fixed point describing world-sheets with vanishing tension and Hausdorff dimension D_H=2. Crumpling is prevented by the new term which suppresses configurations with rapidly changing extrinsic curvature., Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper also at http://www.physik.fu-berlin.de/~kleinert/kleiner_re276

We present a new Higgsless model of superconductivity, inspired from anyon superconductivity but P- and T-invariant and generalizable to any dimension. While the original anyon superconductivity mechanism was based on incompressible quantum Hall fluids as average field states, our mechanism involves topological insulators as average field states. In D space dimensions it involves a (D-1)-form fictitious pseudovector gauge field which originates from the condensation of topological defects in compact low-energy effective BF theories. In the average field approximation, the corresponding uniform emergent charge creates a gap for the (D-2)-dimensional branes via the Magnus force, the dual of the Lorentz force. One particular combination of intrinsic and emergent charge fluctuations that leaves the total charge distribution invariant constitutes an isolated gapless mode leading to superfluidity. The remaining massive modes organise themselves into a D-dimensional charged, massive vector. There is no massive Higgs scalar as there is no local order parameter. When electromagnetism is switched on, the photon acquires mass by the topological BF mechanism. Although the charge of the gapless mode (2) and the topological order (4) are the same as those of the standard Higgs model, the two models of superconductivity are clearly different since the origins of the gap, reflected in the high-energy sectors are totally different. In 2D this type of superconductivity is explicitly realized as global superconductivity in Josephson junction arrays. In 3D this model predicts a possible phase transition from topological insulators to Higgsless superconductors., Comment: 12 pages, no figures

We briefly review these low-energy effective theories for the quantum Hall effect, with emphasis and language familiar to field theorists. Two models have been proposed for describing the most stable Hall plateaus (the Jain series): the multi-component Abelian theories and the minimal W1+∞ models. They both lead to a-priori classifications of quantum Hall universality classes. Some experiments already confirmed the basic predictions common to both effective theories, while other experiments will soon pin down their detailed properties and differences. Based on the study of partition functions, we show that the Abelian theories are rational conformal field theories while the minimal W1+∞ models are not.

We show that the zero-temperature physics of planar Josephson junction arrays in the self-dual approximation is governed by an Abelian gauge theory with periodic mixed Chern-Simons term describing the charge-vortex coupling. The periodicity requires the existence of (Euclidean) topological excitations which determine the quantum phase structure of the model. The electric-magnetic duality leads to a quantum phase transition between a superconductor and a superinsulator at the self-dual point. We also discuss in this framework the recently proposed quantum Hall phases for charges and vortices in presence of external offset charges and magnetic fluxes: we show how the periodicity of the charge-vortex coupling can lead to transitions to anyon superconductivity phases. We finally generalize our results to three dimensions, where the relevant gauge theory is the so-called BF system, with an antisymmetric Kalb-Ramond gauge field., 39 pages, harvmac, two figures available on request

Data are paramount to modern targeted drug design. Precious revelations obtained by applying data mining and computational chemistry on large molecular databases, innovative at one time, are now everyday procedures for therapy identification. However, there is an even larger source of valuable information available that can potentially be tapped for discoveries: repositories constituted by research documents. While numerical methods for the analysis of structured data like those in genomics and proteomics databases are well developed and standard toolboxes are easily available, knowledge discovery from unstructured data in text documents is still considered the “Holy Grail” of text mining and no stable methodology has yet emerged from the scant few known attempts. Here we review a recent pilot experiment to discover novel biomarkers and phenotypes for diabetes and obesity by self-organized text mining of about 120,000 PubMed abstracts, public clinical trial summaries, and internal Merck research documents by the InfoCodex semantic engine. Retrieval of known entities missed by other traditional approaches could be demonstrated and the InfoCodex semantic engine was shown to discover new diabetes and obesity biomarkers and phenotypes, although noticeable noise (uninteresting or obvious terms) was generated. The reported text mining approach to biomarker discovery shows much promise and has the potential to be developed into a new avenue for pharmaceutical research, especially to shorten time-to-market of novel drugs, or speed up early recognition of dead ends and adverse reactions.

We propose a vortex gauge field theory in which the curl of a Dirac fermion current density plays the role of the pseudovector charge density. In this field-theoretic model, vortex interactions are mediated by a single scalar gauge boson in its antisymmetric tensor formulation. We show that these long range vortex interactions induce a gauge invariant photon mass in the one-loop effective action. The fermion loop generates a coupling between photons and the vortex gauge boson, which acquires thus charge. This coupling represents also an induced, gauge invariant, topological mass for the photons, leading to the Meissner effect. The one-loop effective equations of motion for the charged vortex gauge boson are the London equations. We propose thus vortex gauge interactions as an alternative, topological mechanism for superconductivity in which no spontaneous symmetry breaking is involved., Comment: 4 pages, no figures, fews typos corrected

We investigate the non-perturbative structure of two planar $Z_p \times Z_p$ lattice gauge models and discuss their relevance to two-dimensional condensed matter systems and Josephson junction arrays. Both models involve two compact U(1) gauge fields with Chern-Simons interactions, which break the symmetry down to $Z_p \times Z_p$. By identifying the relevant topological excitations (instantons) and their interactions we determine the phase structure of the models. Our results match observed quantum phase transitions in Josephson junction arrays and suggest also the possibility of {\it oblique confining ground states} corresponding to quantum Hall regimes for either charges or vortices., Comment: 32 pages, harvmac

In this paper, we pursue our analysis of the W-infinity symmetry of the low-energy edge excitations of incompressible quantum Hall fluids. These excitations are described by (1+1)-dimensional effective field theories, which are built by representations of the W-infinity algebra. Generic W-infinity theories predict many more fluids than the few, stable ones found in experiments. Here we identify a particular class of W-infinity theories, the minimal models, which are made of degenerate representations only - a familiar construction in conformal field theory. The W-infinity minimal models exist for specific values of the fractional conductivity, which nicely fit the experimental data and match the results of the Jain hierarchy of quantum Hall fluids. We thus obtain a new hierarchical construction, which is based uniquely on the concept of quantum incompressible fluid and is independent of Jain's approach and hypotheses. Furthermore, a surprising non-Abelian structure is found in the W-infinity minimal models: they possess neutral quark-like excitations with SU(m) quantum numbers and non-Abelian fractional statistics. The physical electron is made of anyon and quark excitations. We discuss some properties of these neutral excitations which could be seen in experiments and numerical simulations.

Biometric traits are increasingly viewed as the ultimate proof of identity. Unfortunately, biometrics also raises many privacy concerns. In order to overcome these, template protection technologies have been developed in which privacy protection is embedded at the technological level. Standard template protection schemes, however either require secret key management or are vulnerable to brute force and cross-matching attacks and they are unsuitable for identification purposes. Here I review a new key-binding mechanism that I have recently proposed and explain why it is expected to be robust against brute force and cross-matching attacks and how it can be used for identification. The security principle underlying this new template protection scheme is the complexity of the energy landscape of spin glasses. The idea is to exploit the mixed ferromagnetic and spin glass phase of the Hopfield neural network to encode the key as a local minimum configuration of the energy functional, "lost" amidst the exponentially growing number of valleys and minima representing the spin glass. The correct fingerprint will be able to retrieve the key by dynamical evolution to the nearest attractor. Other fingerprints will be driven far away from the key.

Conformal field theories do not only classify 2D classical critical behavior but they also govern a certain class of 2D quantum critical behavior. In this latter case it is the ground state wave functional of the quantum theory that is conformally invariant, rather than the classical action. We show that the superconducting-insulating (SI) quantum phase transition in 2D Josephson junction arrays (JJAs) is a (doubled) $c=1$ Gaussian conformal quantum critical point. The quantum action describing this system is a doubled Maxwell-Chern-Simons model in the strong coupling limit. We also argue that the SI quantum transitions in frustrated JJAs realize the other possible universality classes of conformal quantum critical behavior, corresponding to the unitary minimal models at central charge $c=1-6/m(m+1)$., Comment: 4 pages, no figures

Topological matter is characterized by the presence of a topological BF term in its long-distance effective action. Topological defects due to the compactness of the U(1) gauge fields induce quantum phase transitions between topological insulators, topological superconductors, and topological confinement. In conventional superconductivity, because of spontaneous symmetry breaking, the photon acquires a mass due to the Anderson-Higgs mechanism. In this paper we derive the corresponding effective actions for the electromagnetic field in topological superconductors and topological confinement phases. In topological superconductors magnetic flux is confined and the photon acquires a topological mass through the BF mechanism: no symmetry breaking is involved, the ground state has topological order, and the transition is induced by quantum fluctuations. In topological confinement, instead, electric charge is linearly confined and the photon becomes a massive antisymmetric tensor via the St\"uckelberg mechanism. Oblique confinement phases arise when the string condensate carries both magnetic and electric flux (dyonic strings). Such phases are characterized by a vortex quantum Hall effect potentially relevant for the dissipationless transport of information stored on vortices.

Free planar electrons in a uniform magnetic field are shown to possess the symmetry of area-preserving diffeomorphisms ($W$-infinity algebra). Intuitively, this is a consequence of gauge invariance, which forces dynamics to depend only on the flux. The infinity of generators of this symmetry act within each Landau level, which is infinite-dimensional in the thermodynamical limit. The incompressible ground states corresponding to completely filled Landau levels (integer quantum Hall effect) are shown to be infinitely symmetric, since they are annihilated by an infinite subset of generators. This geometrical characterization of incompressibility also holds for fractional fillings of the lowest level (simplest fractional Hall effect) in the presence of Haldane's effective two-body interactions. Although these modify the symmetry algebra, the corresponding incompressible ground states proposed by Laughlin are again symmetric with respect to the modified infinite algebra., Comment: 28 pages

The Laughlin states for $N$ interacting electrons at the plateaus of the fractional Hall effect are studied in the thermodynamic limit of large $N$. It is shown that this limit leads to the semiclassical regime for these states, thereby relating their stability to their semiclassical nature. The equivalent problem of two-dimensional plasmas is solved analytically, to leading order for $N\to\infty$, by the saddle point approximation - a two-dimensional extension of the method used in random matrix models of quantum gravity and gauge theories. To leading order, the Laughlin states describe classical droplets of fluids with uniform density and sharp boundaries, as expected from the Laughlin ``plasma analogy''. In this limit, the dynamical $W_\infty$-symmetry of the quantum Hall states expresses the kinematics of the area-preserving deformations of incompressible liquid droplets., 13 pages (+1 figure, available upon request), CERN-TH 6810/93

We show that different classes of topological order can be distinguished by the dynamical symmetry algebra of edge excitations. Fundamental topological order is realized when this algebra is the largest possible, the algebra of quantum area-preserving diffeomorphisms, called $W_{1+\infty}$. We argue that this order is realized in the Jain hierarchy of fractional quantum Hall states and show that it is more robust than the standard Abelian Chern-Simons order since it has a lower entanglement entropy due to the non-Abelian character of the quasi-particle anyon excitations. These behave as SU($m$) quarks, where $m$ is the number of components in the hierarchy. We propose the topological entanglement entropy as the experimental measure to detect the existence of these quantum Hall quarks. Non-Abelian anyons in the $\nu = 2/5$ fractional quantum Hall states could be the primary candidates to realize qbits for topological quantum computation., Comment: 5 pages, no figures, a few typos corrected, a reference added

We show that electrically and magnetically frustrated Josephson junction arrays (JJAs) realize topological order with a non-trivial ground state degeneracy on manifolds with non-trivial topology. The low-energy theory has the same gauge dynamics of the unfrustrated JJAs but for different, "fractional" degrees of freedom, a principle reminescent of Jain's composite electrons in the fractional quantum Hall effect., Comment: 5 pages; to appear in EPL

Associative pattern retrieval, one of the hallmarks of intelligence, cannot only be realized by the traditional attractor dynamics of the Hopfield model but also by a reversible, unitary evolution of quantum bits (qubits). We will show that qubit networks with long-range interactions governed by the Hebb rule can be used as quantum associative memories. Starting from a uniform superposition, the unitary evolution generated by these interactions drives the network through a quantum phase transition at a critical computation time, after which ferromagnetic order guarantees that a measurement retrieves the stored patterns. The memory capacity of these qubit networks depends on the computation time: the maximum capacity is reached at a memory density α = p/n = 1, after which a phase transition to a quantum spin glass state implies total amnesia. At these loading factors, however the retrieval quality is poor; admitting only a few percent of errors requires lower memory loading factors, comparable with the classical Hopfield model.

We quantize gauge field theories in odd dimensional space-time with actions including both a Chern-Simons term and a Yang-Mills term. Such theories will be referred to as CSYM theories. We show that there are deep connections between these theories and chiral anomalies and current algebra in even dimensional space-time. The classical canonical structure of the CSYM theories is intimately related to the algebraic properties of the consistent and covariant chiral anomalies. The quantization of the CSYM theories involves a one-cocycle which is the Wess-Zumino functional and, depending on the dimension of space-time and the gauge group, the consistent realization of gauge invariance at the quantum level imposes a quantization condition on the Chern-Simons coupling parameter. The associated cocycle behavior of physical states may be understood in terms of an Abelian functional curvature on the space of all spatial gauge fields. By considering the CSYM theories on a space-time with a spatial boundary we show that the algebra of Gauss law generators acquires a boundary-valued anomaly which is cohomologous to the Faddeev-Shatashvili proposal for the anomaly in the equal-time commutator of Gauss law operators in the theory of massless chiral fermions interacting with a gauge field in even dimensional space-time.

We review our recent work on the algebraic characterization of quantum Hall fluids. Specifically, we explain how the incompressible quantum fluid ground states can be classified by effective edge field theories with the W 1+∞ dynamical symmetry of “quantum area-preserving diffeomorphisms”. Using the representation theory of W 1+∞ , we show how all fluids with filling factors v = m /( pm + 1) and v = m /( pm − 1) with m and p positive integers, p even, correspond exactly to the W 1+∞ minimal models.

We propose a mechanism of superconductivity in which the order of the ground state does not arise from the usual Landau mechanism of spontaneous symmetry breaking but is rather of topological origin. The low-energy effective theory is formulated in terms of emerging gauge fields rather than a local order parameter and the ground state is degenerate on topologically non-trivial manifolds. The simplest example of this mechanism of superconductivty is concretely realized as global superconductivty in Josephson junction arrays., Comment: 4 pages, no figures

Typical address-oriented computer memories cannot recognize incomplete or noisy information. Associative (content-addressable) memories solve this problem but suffer from severe capacity shortages. I propose a model of a quantum memory that solves both problems. The storage capacity is exponential in the number of qbits and thus optimal. The retrieval mechanism for incomplete or noisy inputs is probabilistic, with postselection of the measurement result. The output is determined by a probability distribution on the memory which is peaked around the stored patterns closest in Hamming distance to the input., Comment: Revised version to appear in Phys. Rev. Lett

We review our recent work on the algebraic characterization of quantum Hall fluids. Specifically, we explain how the incompressible quantum fluid ground states can be classified by effective edge field theories with the W 1+∞ dynamical symmetry of “quantum area-preserving diffeomorphisms.” Using the representation theory of W 1+∞ we show how all fluids with filling factors m/(pm + 1) and v = m/(pm - 1) with m and p positive integers and p even, correspond exactly to the W 1+∞ minimal models.

We show that the recently proposed confining string theory describes smooth surfaces with long-range correlations for the normal components of tangent vectors. These long-range correlations arise as a consequence of a "frustrated antiferromagnetic" interaction whose two main features are non-locality and a negative stiffness., Comment: 10 pages, harvmac, no figures. submitted to Phys. Lett. B

We consider several aspects of `confining strings', recently proposed to describe the confining phase of gauge field theories. We perform the exact duality transformation that leads to the confining string action and show that it reduces to the Polyakov action in the semiclassical approximation. In 4D we introduce a `$\theta$-term' and compute the low-energy effective action for the confining string in a derivative expansion. We find that the coefficient of the extrinsic curvature (stiffness) is negative, confirming previous proposals. In the absence of a $\theta$-term, the effective string action is only a cut-off theory for finite values of the coupling e, whereas for generic values of $\theta$, the action can be renormalized and to leading order we obtain the Nambu-Goto action plus a topological `spin' term that could stabilize the system., Comment: 11 pages, harvmac

We study the different phases of field theories of compact antisymmetric tensors of rank $h-1$ in arbitrary space-time dimensions $D=d+1$. Starting in a `Coulomb' phase, topological defects of dimension $d-h-1$ ($(d-h-1)$-branes) may condense leading to a generalized `confinement' phase. If the dual theory is also compact the model may also have a third, generalized `Higgs' phase, driven by the condensation of the dual $(h-2)$-branes. Developing on the work of Julia and Toulouse for ordered solid-state media, we obtain the low energy effective action for these phases. Each phase has two dual descriptions in terms of antisymmetric tensors of different ranks, which are massless for the Coulomb phase but massive for the Higgs and confinement phases. We illustrate our prescription in detail for compact QED in 4D. Compact QED and $O(2)$ models in 3D, as well as a periodic scalar field in 2D (strings on a circle), are also discussed. In this last case we show how $T$-duality is maintained if one considers both worldsheet instantons and their duals. We also unify various approaches to the problem of the axion mass in 4D string models. Finally we discuss possible implications of our results for non-perturbative issues in string theory., Comment: 35 pages, harvmac (section 4 (4D QED) rewritten,extra minor corrections and one reference added)

A speech and textual analysis device and method for forming a search and/or classification catalog. The device is based on a linguistic database and includes a taxonomy table containing variable taxon nodes. The speech and textual analysis device includes a weighting module, a weighting parameter being additionally assigned to each stored taxon node to register recurrence frequency of terms in the linguistic and/or textual data that is to be classified and/or sorted. The speech and/or textual analysis device includes an integration module for determining a predefinable number of agglomerates based on the weighting parameters of the taxon nodes in the taxonomy table and at least one neuronal network module for classifying and/or sorting the speech and/or textual data based on the agglomerates in the taxonomy table.

We investigate non-perturbative features of a planar Chern-Simons gauge theory modeling the long distance physics of quantum Hall systems, including a finite gap M for excitations. By formulating the model on a lattice, we identify the relevant topological configurations and their interactions. For M bigger than a critical value, the model exhibits an oblique confinement phase, which we identify with Lauglin's incompressible quantum fluid. For M smaller than the critical value, we obtain a phase transition to a Coulomb phase or a confinement phase, depending on the value of the electromagnetic coupling., Comment: 8 pages, harvmac, DFUPG 91/94 and MPI-PhT/94-92

We show how two-dimensional incompressible quantum fluids and their excitations can be viewed as ${\mathit{W}}_{1+\mathrm{\ensuremath{\infty}}}$ edge conformal field theories, thereby providing an algebraic characterization of incompressibility. The Kac-Radul representation theory of the ${\mathit{W}}_{1+\mathrm{\ensuremath{\infty}}}$ algebra leads then to a purely algebraic complete classification of hierarchical quantum Hall states, which encompasses all measured fractions. Spin-polarized electrons in single-layer devices can only have Abelian anyon excitations.

We construct a lattice model of compact (2+1)-dimensional Maxwell-Chern- Simons theory, starting from its formulation in terms of gauge invariant quantities proposed by Deser and Jackiw. We thereby identify the topological excitations and their interactions. These consist of monopolo- antimonopole pairs bounded by strings carrying both magnetic flux and electric charge. The electric charge renders the Dirac strings observable and endows them with a finite energy per unit length, which results in a linearly confining string tension. Additionally, the strings interact via an imaginary, topological term measuring the (self-) linking number of closed strings., Comment: harvmac, CERN-TH. 6906/93, DFUPG 80/93