Showing papers in "Journal of Physics A in 2016"

The role of quantum information in thermodynamics—a topical review

Abstract: This topical review article gives an overview of the interplay between quantum information theory and thermodynamics of quantum systems. We focus on several trending topics including the foundations of statistical mechanics, resource theories, entanglement in thermodynamic settings, fluctuation theorems and thermal machines. This is not a comprehensive review of the diverse field of quantum thermodynamics; rather, it is a convenient entry point for the thermo-curious information theorist. Furthermore this review should facilitate the unification and understanding of different interdisciplinary approaches emerging in research groups around the world.

Measures and applications of quantum correlations

Abstract: Quantum information theory is built upon the realisation that quantum resources like coherence and entanglement can be exploited for novel or enhanced ways of transmitting and manipulating information, such as quantum cryptography, teleportation, and quantum computing. We now know that there is potentially much more than entanglement behind the power of quantum information processing. There exist more general forms of non-classical correlations, stemming from fundamental principles such as the necessary disturbance induced by a local measurement, or the persistence of quantum coherence in all possible local bases. These signatures can be identified and are resilient in almost all quantum states, and have been linked to the enhanced performance of certain quantum protocols over classical ones in noisy conditions. Their presence represents, among other things, one of the most essential manifestations of quantumness in cooperative systems, from the subatomic to the macroscopic domain. In this work we give an overview of the current quest for a proper understanding and characterisation of the frontier between classical and quantum correlations (QCs) in composite states. We focus on various approaches to define and quantify general QCs, based on different yet interlinked physical perspectives, and comment on the operational significance of the ensuing measures for quantum technology tasks such as information encoding, distribution, discrimination and metrology. We then provide a broader outlook of a few applications in which quantumness beyond entanglement looks fit to play a key role.

Recent developments in bimetric theory

Abstract: This review is dedicated to recent progress in the eld of classical, in- teracting, massive spin-2 theories, with a focus on ghost-free bimetric theory. We will outline its history and its development as a nontrivial extension and generalisation of nonlinear massive gravity. We present a detailed discussion of the consistency proofs of both theories, before we review Einstein solutions to the bimetric equations of motion in vacuum as well as the resulting mass spectrum. We introduce couplings to matter and then discuss the general relativity and massive gravity limits of bimetric theory, which correspond to decoupling the massive or the massless spin-2 eld from the mat- ter sector, respectively. More general classical solutions are reviewed and the present status of bimetric cosmology is summarised. An interesting corner in the bimetric parameter space which could potentially give rise to a nonlinear theory for partially massless spin-2 elds is also discussed. Relations to higher-curvature theories of gravity are explained and nally we give an overview of possible extensions of the theory and review its formulation in terms of vielbeins.

Diffusion under time-dependent resetting

Abstract: We study a Brownian particle diffusing under a time-modulated stochastic resetting mechanism to a fixed position. The rate of resetting r(t) is a function of the time t since the last reset event. We derive a sufficient condition on r(t) for a steady-state probability distribution of the position of the particle to exist. We derive the form of the steady-state distributions under some particular choices of r(t) and also consider the late time relaxation behavior of the probability distribution. We consider first passage time properties for the Brownian particle to reach the origin and derive a formula for the mean first passage time (MFPT). Finally, we study optimal properties of the MFPT and show that a threshold function is at least locally optimal for the problem of minimizing the MFPT.

On the superconformal index of Argyres–Douglas theories

Abstract: We conjecture a closed-form expression for the Schur limit of the superconformal index of two infinite series of Argyres-Douglas (AD) superconformal field theories (SCFTs): the (A1,A2n−3) and the (A1,D2n) theories. While these SCFTs can be realized at special points on the Coulomb branch of certain N = 2 gauge theories, their superconformal R symmetries are emergent, and hence their indices cannot be evaluated by localization. Instead, we construct the (A1,A2n−3) and (A1,D2n) indices by using a relation to two-dimensional qdeformed Yang-Mills theory and data from the class S construction. Our results generalize the indices derived from the torus partition functions of the two-dimensional chiral algebras associated with the (A1,A3) and (A1,D4) SCFTs. As checks of our conjectures, we study the consistency of our results with an S-duality recently discussed by us in collaboration with Giacomelli and Papageorgakis, we reproduce known Higgs branch relations, we check consistency with a series of renormalization group flows, and we verify that the small S 1 limits of our indices reproduce expected Cardy-like behavior. We will discuss the S 1

An invitation to quantum incompatibility

Abstract: In the context of a physical theory, two devices, A and B, described by the theory are called incompatible if the theory does not allow the existence of a third device C that would have both A and B as its components. Incompatibility is a fascinating aspect of physical theories, especially in the case of quantum theory. The concept of incompatibility gives a common ground for several famous impossibility statements within quantum theory, such as “no-cloning” and “no information without disturbance”; these can be all seen as statements about incompatibility of certain devices. The purpose of this paper is to give a concise overview of some of the central aspects of incompatibility.

Semi-classical and quantum Rabi models: in celebration of 80 years

Abstract: This is an introduction to the special issue collection of articles on Semi-classical and quantum Rabi models to be published in J. Phys. A: Mathematical and Theoretical to mark the 80th anniversary of the Rabi model.

Higher spin interactions in four-dimensions: Vasiliev versus Fronsdal

Abstract: We consider four-dimensional Higher-Spin Theory at the first nontrivial order corresponding to the cubic action. All Higher-Spin interaction vertices are explicitly obtained from Vasiliev’s equations. In particular, we obtain the vertices that are not determined solely by the Higher-Spin algebra structure constants. The dictionary between the Fronsdal fields and Higher-Spin connections is found and the corrections to the Fronsdal equations are derived. These corrections turn out to involve derivatives of arbitrary order. We observe that the vertices not determined by the Higher-Spin algebra produce naked infinities, when decomposed into the minimal derivative vertices and improvements. Therefore, standard methods can only be used to check a rather limited number of correlation functions within the HS AdS/CFT duality. A possible resolution of the puzzle is discussed. 1 ar X iv :1 50 8. 04 13 9v 1 [ he pth ] 1 7 A ug 2 01 5

Homogeneous Yang–Baxter deformations as non-abelian duals of the AdS 5 σ-model

Abstract: We propose that the Yang-Baxter deformation of the symmetric space sigma-model parameterized by an r-matrix solving the homogeneous (classical) Yang-Baxter equation is equivalent to the non-abelian dual of the undeformed model with respect to a subgroup determined by the structure of the r-matrix. We explicitly demonstrate this on numerous examples in the case of the AdS_5 sigma-model. The same should also be true for the full AdS_5 x S^5 supercoset model, providing an explanation for and generalizing several recent observations relating homogeneous Yang-Baxter deformations based on non-abelian r-matrices to the undeformed AdS_5 x S^5 model by a combination of T-dualities and non-linear coordinate redefinitions. This also includes the special case of deformations based on abelian r-matrices, which correspond to TsT transformations: they are equivalent to non-abelian duals of the original model with respect to a central extension of abelian subalgebras.

The simplest model of jamming

Abstract: We study a well known neural network model—the perceptron—as a simple statistical physics model of jamming of hard objects. We exhibit two regimes: (1) a convex optimization regime where jamming is hypostatic and non-critical; (2) a non-convex optimization regime where jamming is isostatic and critical. We characterize the critical jamming phase through exponents describing the distribution laws of forces and gaps. Surprisingly we find that these exponents coincide with the corresponding ones recently computed in high dimensional hard spheres. In addition, modifying the perceptron to a random linear programming problem, we show that isostaticity is not a sufficient condition for singular force and gap distributions. For that, fragmentation of the space of solutions (replica symmetry breaking) appears to be a crucial ingredient. We hypothesize universality for a large class of non-convex constrained satisfaction problems with continuous variables.

Conformal QED$_d$, $F$-Theorem and the $\epsilon$ Expansion

Abstract: We calculate the free energies F for U(1) gauge theories on the d dimensional sphere of radius R. For the theory with free Maxwell action we find the exact result as a function of d, it contains the term $\frac{d-4}{2}\mathrm{log}R$ consistent with the lack of conformal invariance in dimensions other than 4. When the U(1) gauge theory is coupled to a sufficient number N ( )f( ) of massless four-component fermions, it acquires an interacting conformal phase, which in $d\lt 4$ describes the long distance behavior of the model. The conformal phase can be studied using large N ( )f( ) methods. Generalizing the d = 3 calculation in arXiv:1112.5342, we compute its sphere free energy as a function of d, ignoring the terms of order $1/{N}_{f}$ and higher. For finite N ( )f( ), following arXiv:1409.1937 and arXiv:1507.01960, we develop the $4-\epsilon $ expansion for the sphere free energy of conformal QED( )d( ). Its extrapolation to d = 3 shows very good agreement with the large N ( )f( ) approximation for ${N}_{f}\gt 3$. For N ( )f( ) at or below some critical value ${N}_{{\rm{crit}}}$, the ${SU}(2{N}_{f})$ symmetric conformal phase of QED(3) is expected to disappear or become unstable. By using the F-theorem and comparing the sphere free energies in the conformal and broken symmetry phases, we show that ${N}_{{\rm{crit}}}\leqslant 4$. As another application of our results, we calculate the one loop beta function in conformal QED(6), where the gauge field has a four-derivative kinetic term. We show that this theory coupled to N ( )f( ) massless fermions is asymptotically free.

Relations between elliptic multiple zeta values and a special derivation algebra

Abstract: We investigate relations between elliptic multiple zeta values and describe a method to derive the number of indecomposable elements of given weight and length. Our method is based on representing elliptic multiple zeta values as iterated integrals over Eisenstein series and exploiting the connection with a special derivation algebra. Its commutator relations give rise to constraints on the iterated integrals over Eisenstein series relevant for elliptic multiple zeta values and thereby allow to count the indecomposable representatives. Conversely, the above connection suggests apparently new relations in the derivation algebra. Under https://tools.aei.mpg.de/emzv we provide relations for elliptic multiple zeta values over a wide range of weights and lengths. ar X iv :1 50 7. 02 25 4v 1 [ he pth ] 8 J ul 2 01 5

Conformal Manifolds in Four Dimensions and Chiral Algebras

Abstract: M. B.’s work is partially supported by the Royal Society under the grant “New Constraints and Phenomena in Quantum Field Theory” and by the U.S. Department of Energy under grant DE-SC0009924. T. N. is partially supported by the Yukawa Memorial Foundation.

Cascading failure analysis and restoration strategy in an interdependent network

Abstract: In modern society, many infrastructures are interdependent owing to functional and logical relations among components in different systems. These networked infrastructures can be modeled as interdependent networks. In the real world, different networks carry different traffic loads whose values are dynamic and stem from the load redistribution in the same network and disturbance from the interdependent network. Interdependency makes interdependent networks so fragile that even a slight initial disturbance may lead to a cascading failure of the entire systems. In this paper, interdependencies among networks are modeled and a failure cascade process is studied considering their effects on failure propagation. Meanwhile, an in-process restoration strategy after the initial failure is investigated. The restoration effects depend strongly on the trigger timing, restoration probability and priority of the restoration actions along with the additional disturbances. Our findings highlight the necessity to decrease the large-scale cascading failure by structuring and managing an interdependent network reasonably.

An integrability primer for the gauge-gravity correspondence: an introduction

Abstract: We introduce a series of articles reviewing various aspects of integrable models relevant to the AdS/CFT correspondence. Topics covered in these reviews are: classical integrability, Yangian symmetry, factorized scattering, the Bethe ansatz, the thermodynamic Bethe ansatz, and integrable structures in (conformal) quantum field theory. In the present article we highlight how these concepts have found application in AdS/CFT, and provide a brief overview of the material contained in this series.

Geometry of the generalized Bloch sphere for qutrits

Abstract: The geometry of the generalized Bloch sphere Ω3, the state space of a qutrit, is studied. Closed form expressions for Ω3, its boundary ∂Ω3, and the set of extremals are obtained by use of an elementary observation. These expressions and analytic methods are used to classify the 28 two-sections and the 56 three-sections of Ω3 into unitary equivalence classes, completing the works of earlier authors. It is shown, in particular, that there are families of two-sections and of three-sections which are equivalent geometrically but not unitarily, a feature that does not appear to have been appreciated earlier. A family of three-sections of obese-tetrahedral shape whose symmetry corresponds to the 24-element tetrahedral point group T d is examined in detail. This symmetry is traced to the natural reduction of the adjoint representation of SU(3), the symmetry underlying Ω3, into direct sum of the two-dimensional and the two (inequivalent) three-dimensional irreducible representations of T d .

Lectures on Yangian Symmetry

Abstract: In these introductory lectures we discuss the topic of Yangian symmetry from various perspectives. Forming the classical counterpart of the Yangian and an extension of ordinary Noether symmetries, first the concept of nonlocal charges in classical, two-dimensional field theory is reviewed. We then define the Yangian algebra following Drinfel’d's original motivation to construct solutions to the quantum Yang–Baxter equation. Different realizations of the Yangian and its mathematical role as a Hopf algebra and quantum group are discussed. We demonstrate how the Yangian algebra is implemented in quantum, two-dimensional field theories and how its generators are renormalized. Implications of Yangian symmetry on the two-dimensional scattering matrix are investigated. We furthermore consider the important case of discrete Yangian symmetry realized on integrable spin chains. Finally we give a brief introduction to Yangian symmetry in planar, four-dimensional super Yang–Mills theory and indicate its impact on the dilatation operator and tree-level scattering amplitudes. These lectures are illustrated by several examples, in particular the two-dimensional chiral Gross–Neveu model, the Heisenberg spin chain and ${ \mathcal N }=4$ superconformal Yang–Mills theory in four dimensions.

Argyres–Douglas theories, S 1 reductions, and topological symmetries

Abstract: In a recent paper, we proposed closed-form expressions for the superconformal indices of the (A1,A2n 3) and (A1,D2n) Argyres-Douglas (AD) superconformal field theories (SCFTs) in the Schur limit. Following up on our results, we turn our attention to the small S 1 regime of these indices. As expected on general grounds, our study reproduces the S 3 partition functions of the resulting dimensionally reduced theories. However, we show that in all cases—with the exception of the reduction of the (A1,D4) SCFT—certain imaginary partners of real mass terms are turned on in the corresponding mirror theories. We interpret these deformations as R symmetry mixing with the topological symmetries of the direct S 1 reductions. Moreover, we argue that these shifts occur in any of our theories whose fourdimensional N = 2 superconformal U(1)R symmetry does not obey an SU(2) quantization condition. We then use our R symmetry map to find the four-dimensional ancestors of certain three-dimensional operators. Somewhat surprisingly, this picture turns out to imply that the scaling dimensions of many of the chiral operators of the four-dimensional theory are encoded in accidental symmetries of the three-dimensional theory. We also comment on the implications of our work on the space of general N = 2 SCFTs.

Bulk-edge correspondence of one-dimensional quantum walks

Abstract: We outline a theory of symmetry protected topological phases of one-dimensional quantum walks. We assume spectral gaps around the symmetry-distinguished points +1 and −1, in which only discrete eigenvalues are allowed. The phase classification by integer or binary indices extends the classification known for translation invariant systems in terms of their band structure. However, our theory requires no translation invariance whatsoever, and the indices we define in this general setting are invariant under arbitrary symmetric local perturbations, even those that cannot be continuously contracted to the identity. More precisely we define two indices for every walk, characterizing the behavior far to the right and far to the left, respectively. Their sum is a lower bound on the number of eigenstates at +1 and −1. For a translation invariant system the indices add up to zero, so one of them already characterizes the phase. By joining two bulk phases with different indices we get a walk in which the right and left indices no longer cancel, so the theory predicts bound states at +1 or −1. This is a rigorous statement of bulk-edge correspondence. The results also apply to the Hamiltonian case with a single gap at zero.

Generalized type IIB supergravity equations and non-Abelian classical r-matrices

Abstract: We study Yang–Baxter deformations of the AdS₅ superstring with non-Abelian classical r-matrices which satisfy the homogeneous classical Yang–Baxter equation. By performing a supercoset construction, we can get deformed AdS₅ x S⁵ backgrounds. While this is a new area of research, the current understanding is that Abelian classical r-matrices give rise to solutions of type IIB supergravity, while non-Abelian classical r-matrices lead to solutions of the generalized supergravity equations. We examine here some examples of non-Abelian classical r-matrices and derive the associated backgrounds explicitly. All of the resulting backgrounds satisfy the generalized equations. For some of them, we derive 'T-dualized' backgrounds by adding a linear coordinate dependence to the dilaton and show that these satisfy the usual type IIB supergravity equations. Remarkably, some of the 'T-dualized' backgrounds are locally identical to undeformed AdS₅ x S⁵ after an appropriate coordinate transformation, but this seems not to be generally the case.

Topological defects on the lattice: I. The Ising model

Abstract: In this paper and its sequel, we construct topologically invariant defects in two-dimensional classical lattice models and quantum spin chains. We show how defect lines commute with the transfer matrix/Hamiltonian when they obey the defect commutation relations, cousins of the Yang–Baxter equation. These relations and their solutions can be extended to allow defect lines to branch and fuse, again with properties depending only on topology. In this part I, we focus on the simplest example, the Ising model. We define lattice spin-flip and duality defects and their branching, and prove they are topological. One useful consequence is a simple implementation of Kramers–Wannier duality on the torus and higher genus surfaces by using the fusion of duality defects. We use these topological defects to do simple calculations that yield exact properties of the conformal field theory describing the continuum limit. For example, the shift in momentum quantization with duality-twisted boundary conditions yields the conformal spin 1/16 of the chiral spin field. Even more strikingly, we derive the modular transformation matrices explicitly and exactly.

On critical exponents without Feynman diagrams

Abstract: In order to achieve a better analytic handle on the modern conformal bootstrap program, we re-examine and extend the pioneering 1974 work of Polyakov's, which was based on consistency between the operator product expansion and unitarity. As in the bootstrap approach, this method does not depend on evaluating Feynman diagrams. We show how this approach can be used to compute the anomalous dimensions of certain operators in the O(n) model at the Wilson-Fisher fixed point in 4 - epsilon dimensions up to O(epsilon(2)).

Strong zero modes and eigenstate phase transitions in the XYZ/interacting Majorana chain

Abstract: I explicitly construct a strong zero mode in the XYZ chain or, equivalently, Majorana wires coupled via a four-fermion interaction. The strong zero mode is an operator that pairs states in different symmetry sectors, resulting in identical spectra up to exponentially small finite-size corrections. Such pairing occurs in the Ising/Majorana fermion chain and possibly in strongly disordered many-body localized phases. The proof here shows that the strong zero mode occurs in a clean interacting system, and that it possesses some remarkable structure—despite being a rather elaborate operator, it squares to the identity. Eigenstate phase transitions separate regions with different strong zero modes.

Two-photon Rabi model: analytic solutions and spectral collapse

Abstract: The two-photon quantum Rabi model is analyzed using the -symmetry and -algebra. We derive the G-function whose zeros give the exact eigenvalues of the Hamiltonian. The singularity structure of the G-function allows to draw conclusions about the distribution of these eigenvalues along the real axis and we derive the spectral collapse phenomenon at critical coupling , found numerically before. The spectrum at consists of a discrete and a continuous part: the ground state is always separated from the continuum by a finite excitation gap, ruling out a quantum phase transition in the usual sense. For large qubit splitting, also other low lying states split off from the continuum. However, perturbation theory predicts the vanishing of the gap to all orders, demonstrating its non-perturbative nature. We corroborate this result with a variational calculation for the ground state.

Universal scaling of the logarithmic negativity in massive quantum field theory

Abstract: We consider the logarithmic negativity, a measure of bipartite entanglement, in a general unitary 1 + 1-dimensional massive quantum field theory, not necessarily integrable. We compute the negativity between a finite region of length r and an adjacent semi-infinite region, and that between two semi-infinite regions separated by a distance r. We show that the former saturates to a finite value, and that the latter tends to zero, as r -> ∞. We show that in both cases, the leading corrections are exponential decays in r (described by modified Bessel functions) that are solely controlled by the mass spectrum of the model, independently of its scattering matrix. This implies that, like the entanglement entropy (EE), the logarithmic negativity displays a very high level of universality, allowing one to extract information about the mass spectrum. Further, a study of sub-leading terms shows that, unlike the EE, a large-r analysis of the negativity allows for the detection of bound states.

Chain reconfiguration in active noise

Abstract: In a typical single molecule experiment, the dynamics of an unfolded protein is studied by determining the reconfiguration time using long-range Forster resonance energy transfer, where the reconfiguration time is the characteristic decay time of the position correlation between two residues of the protein. In this paper we theoretically calculate the reconfiguration time for a single flexible polymer in the presence of active noise. The study suggests that though the mean square displacement grows faster, the chain reconfiguration is always slower in the presence of long-lived active noise with exponential temporal correlation. Similar behavior is observed for a worm-like semi-flexible chain and a Zimm chain. However it is primarily the characteristic correlation time of the active noise and not the strength that controls the increase in the reconfiguration time. In brief, such active noise makes the polymer move faster but the correlation loss between the monomers becomes slow.

Quantization conditions and functional equations in ABJ(M) theories

Abstract: The partition function of ABJ(M) theories on the three-sphere can be regarded as the canonical partition function of an ideal Fermi gas with a non-trivial Hamiltonian. We propose an exact expression for the spectral determinant of this Hamiltonian, which generalizes recent results obtained in the maximally supersymmetric case. As a consequence, we nd an exact WKB quantization condition determining the spectrum which is in agreement with numerical results. In addition, we investigate the factorization properties and functional equations for our conjectured spectral determinants. These functional equations relate the spectral determinants of ABJ theories with consecutive ranks of gauge groups but the same Chern-Simons coupling.

Statistical and dynamical properties of covariant lyapunov vectors in a coupled atmosphere-ocean model—multiscale effects, geometric degeneracy, and error dynamics

Abstract: We study a simplified coupled atmosphere-ocean model using the formalism of covariant Lyapunov vectors (CLVs), which link physically-based directions of perturbations to growth/decay rates. The model is obtained via a severe truncation of quasi-geostrophic equations for the two fluids, and includes a simple yet physically meaningful representation of their dynamical/thermodynamical coupling. The model has 36 degrees of freedom, and the parameters are chosen so that a chaotic behaviour is observed. There are two positive Lyapunov exponents (LEs), sixteen negative LEs, and eighteen near-zero LEs. The presence of many near-zero LEs results from the vast time-scale separation between the characteristic time scales of the two fluids, and leads to nontrivial error growth properties in the tangent space spanned by the corresponding CLVs, which are geometrically very degenerate. Such CLVs correspond to two different classes of ocean/atmosphere coupled modes. The tangent space spanned by the CLVs corresponding to the positive and negative LEs has, instead, a non-pathological behaviour, and one can construct robust large deviations laws for the finite time LEs, thus providing a universal model for assessing predictability on long to ultra-long scales along such directions. Interestingly, the tangent space of the unstable manifold has substantial projection on both atmospheric and oceanic components. The results show the difficulties in using hyperbolicity as a conceptual framework for multiscale chaotic dynamical systems, whereas the framework of partial hyperbolicity seems better suited, possibly indicating an alternative definition for the chaotic hypothesis. They also suggest the need for an accurate analysis of error dynamics on different time scales and domains and for a careful set-up of assimilation schemes when looking at coupled atmosphere-ocean models.

Hexagonal Wilson loops in planar ${ \mathcal N }=4$ SYM theory at finite coupling

Abstract: We report on the complete OPE series for the 6-gluon MHV and NMHV amplitudes in planar SYM theory. Namely, we provide a finite coupling prediction for all the terms in the expansion of these amplitudes around the collinear limit. These furnish a non-perturbative representation of the full amplitudes.